Therefore , the solution of the given problem of unitary method comes out to be the gas particles inside the can will acquire kinetic energy and collide with its walls more frequently, increasing pressure.
A unitary technique is what ?The objective can be accomplished by variable use of what has been clearly learned thus far, implementing advantage of this worldwide convenience, and incorporating all essential components from prior flexible research that used a specific approach. If the anticipated claim outcome actually occurs, it will be feasible to get in connection with the entity once more; if not, both crucial systems will undoubtedly miss the statement.
Here,
The pressure of the gas inside the can will rise as the temperature rises. This is due to the fact that the gas particles inside the can will accelerate and acquire kinetic energy, causing them to collide with the can's walls more frequently and more violently.
The pressure rises as a result of these collisions' greater power per unit area.
The Ideal Gas Law, which says that PV = nRT, where P is tension, V is volume, n is the number of moles of gas,
R is the optimal gas constant, and T is temperature in Kelvin, describes this relationship between pressure and temperature.
In conclusion, the Ideal Gas Law predicts that as the temperature inside the vehicle rises, the gas particles inside the can will acquire kinetic energy and collide with its walls more frequently, increasing pressure.
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The area of this trapezoid is 24.5 ft². 3 ft 4 ft What is the height of the trapezoid? Show your work.
(please hurry! i need help on this and i need to turn it in today)
The height of the trapezoid is approximately 7 feet.
What is the area of a trapezoid?
To find the height of the trapezoid, we can use the formula for the area of a trapezoid: A = ((b1 + b2) / 2) * h
where A is the area, b1 and b2 are the lengths of the two parallel bases, and h is the height.
We are given that the area is 24.5 ft², and the lengths of the bases are 3 ft and 4 ft. Substituting these values into the formula, we get:
24.5 = ((3 + 4) / 2) * h
Simplifying:
24.5 = 3.5 * h
h = 24.5 / 3.5
h ≈ 7
Therefore, the height of the trapezoid is approximately 7 feet.
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pls help me with this
Therefore , the solution of the given problem of unitary method comes out to be rectangle's size is 7/12 square inches.
An unitary method is what ?The objective can be accomplished by using what was variable previously clearly discovered, by utilizing this universal convenience, or by incorporating all essential components from previous flexible study that used a specific strategy. If the anticipated claim outcome actually occurs, it will be feasible to get in touch with the entity once more; if it isn't, both crucial systems will undoubtedly miss the statement.
Here,
=> A = L x W,
where A is the area, L is the length, and W is the breadth, is the formula for calculating the area of a rectangle.
Inputting the numbers provided yields:
=> A = (7/4) x (1/3)
These fractions can be made simpler by eliminating any shared variables in the numerator and denominator before being multiplied. Since 7 and 3 are both prime integers in this instance, there are no shared factors to cancel.
The new numerator and denominator can then be obtained by multiplying the numerators and denominators, respectively. Thus, we get:
=> A = (7 x 1) / (4 x 3)
When we multiply the numerator by the remainder, we obtain:
=> A = 7/12
The rectangle's size is 7/12 square inches as a result.
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An industrial plant claims to discharge no more than 1000 gallons of wastewater per hour, on the average, into a neighboring lake. An environmental action group decides to monitor the plant, in case this limit is being exceeded. A random sample of 42 hours is selected over a period of a month. The data are unimodal and roughly symmetric.
= 1138, s= 605, and Standard Error = 93.354
(a) Using StatCrunch, the p-value = (3 decimal places)
(b) Are the conditions met to conduct this test?
Yes, the population is approximately normal because n > 30.
Yes, np and n(1-p) are both > 15.
No, np and n(1-p) are not both > 15.
Yes, because the data are approximately normal.
(c) At alpha = 0.05, which of the following is the correct conclusion?
Reject the null hypothesis. There is sufficient evidence that the wastewater discharged by the industrial plant exceeds 1000 gallons per hour.
Do not reject the null hypothesis. There is evidence that the wastewater discharged by the industrial plant exceeds 1000 gallons per hour.
Reject the null hypothesis. There is insufficient evidence that the wastewater discharged by the industrial plant exceeds 1000 gallons per hour.
Do not reject the null hypothesis. There is insufficient evidence that the wastewater discharged by the industrial plant exceeds 1000 gallons per hour.
(a) The p-value = 0.017 (b) the conditions are met to conduct the test. (c) the correct conclusion is: Reject the null hypothesis
How to find the The p-value and if the conditions met to conduct this test(a) Using the given data, we can calculate the test statistic z-score as:
z = (xbar - μ) / (σ / sqrt(n))
= (1138 - 1000) / (605 / sqrt(42))
= 2.378
Using StatCrunch, the p-value for a two-tailed test with a test statistic of 2.378 and degrees of freedom of 41 (n - 1) is 0.017.
Therefore, the p-value = 0.017 (to 3 decimal places).
(b) To conduct a hypothesis test for a population mean, we need to check if the following conditions are met:
The population is approximately normal or the sample size is large (n ≥ 30).
The population standard deviation (σ) is unknown.
Here, n = 42 which is greater than 30, so we can assume that the population is approximately normal. The standard deviation of the population is unknown.
Therefore, the conditions are met to conduct the test.
(c) The null and alternative hypotheses are:
Null hypothesis (H0): The mean wastewater discharged by the industrial plant is 1000 gallons per hour (μ = 1000).
Alternative hypothesis (Ha): The mean wastewater discharged by the industrial plant exceeds 1000 gallons per hour (μ > 1000).
At alpha = 0.05 (5% level of significance), the critical z-value for a one-tailed test is 1.645.
Since the calculated z-score (2.378) is greater than the critical value (1.645), we reject the null hypothesis.
Therefore, the correct conclusion is: Reject the null hypothesis. There is sufficient evidence that the wastewater discharged by the industrial plant exceeds 1000 gallons per hour.
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Please Help! A picture is 60cm wide and 1.8 meter long.The ratio of its width to its perimeter in the lowest term is?
Answer:
60:61.8 OR 10:10.3
Step-by-step explanation:
Cant be simplified - unless your in advanced classes. If so
10:10.3
Answer:
Step-by-step explanation:
1/3 or 0.3 or 33.333333% or 3^-1 or 3.333333 x 10^-1
PLEASE PLEASE HELP ME!!!!!!!!
The parallelogram H’I’J’K is a dilation of the parallelogram HIJK. What is the scale factor of the dilation?
Simplify your answer and write it as a proper fraction, an improper fraction, or a whole number.
PLEASE LOOK AT PICTURE!!!!!!
Answer:
Horizontal Compress of 1/4.
Vertical compress of 1/4 as well.
Step-by-step explanation:
Looking at the graph the big Parallelogram HIJK gets becomes smaller parallelogram H'I'J'K'
I have counted the vertical and horizontal of the graph.
So the dilation is
Horizontal Compress of 1/4.
Vertical compress of 1/4.
Find the roots of the given complex number in trigonometric form:
square roots of 5 (cos(120°) + i sin(120°))
The two square roots of 5 (cos(120°) + i sin(120°)) are sqrt(5) × (cos(60°) + i sin(60°)) and sqrt(5) × (cos(300°) + i sin(300°)).
The complex number in question is the square root of 5, written in trigonometric form as cos(120°) + i sin(120°). To calculate the two individual roots, we can use the identity for the square root of a complex number, which states that for any complex number, z, the square root of z is equal to (sqrt(|z|)) × (cos(θ/2) + i sin(θ/2)), where θ is the argument of z. In this case, we have |z| = 5 and θ = 120°. Therefore, the two individual roots are equal to (sqrt(5)) × (cos(60°) + i sin(60°)) and -(sqrt(5)) × (cos(60°) + i sin(60°)) = sqrt(5) × (cos(300°) + i sin(300°)).
In conclusion, the two square roots of 5 (cos(120°) + i sin(120°)) are sqrt(5) × (cos(60°) + i sin(60°)) and sqrt(5) × (cos(300°) + i sin(300°)).
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1. A new compact has a sticker price of $14500. Options add another $982. Destination charges are $592. Dealer preparation is 5% of the total price. Sales tax is 7%. Tag fee is $145. Title fee is $45. What is the total price of the vehicle?
2. The selling price of a used car is $8850. Trade in allowance is $1500. Tax is 8%. Tag fee is $130. Title fee is $35. Finance charges are 9.5% annual simple interest. What is the total price of the financed amount? What are the total finance charges? What are the monthly payments if the vehicle is financed for 3 years? What is the total deferred price of the car?
3. The total deferred price of a car is $28000. After a down payment of $2100, the monthly payments are $380. How long is the financing agreement?
4. Stanley bought a new car with a sticker price of $19200. The dealer agreed to a 6% discount. The sales tax was 8% of the selling price. The tag fee was $65, and the title fee was $45. What is the total price of the car? The interest rate is 9% for financing the car for 5 years. What is the total deferred price after all the payments were made?
5. Mark bought a truck with a sticker price of $23000 plus additional options totaling $3500. He received a 4% discount and a $1500 trade-in allowance. The tax was 7%, tag fee was $125, and title fee was $75. He bought an extended warranty for $700, which was financed into the total cost of the truck. The interest rate was 6.5% for 5 years. How much are the monthly payments?
The total price of the vehicle would be $18,192.88.
The total deferred price of the car would be $11,191.60.
The length of the financing agreement is 68 months .
The total deferred price after the payments was $19,601.84.
The monthly payments would be $516.92.
How to find the price of the vehicle ?Subtotal = Base price + Options + Destination charges
Subtotal = $14,500 + $982 + $592 = $16,074
Dealer preparation = 5% of subtotal
Dealer preparation = 0.05 x $16,074 = $803.70
Sales tax = 7% of subtotal
Sales tax = 0.07 x $16,074 = $1,125.18
Total price = Subtotal + Dealer preparation + Sales tax + Tag fee + Title fee
Total price = $16,074 + $803.70 + $1,125.18 + $145 + $45 = $18,192.88
How to find the total deferred price ?Tax = 8% of selling price = 0.08 x $8,850 = $708
Tag fee = $130
Title fee = $35
Total amount financed = Amount financed + Tax + Tag fee + Title fee = $7,350 + $708 + $130 + $35 = $8,223
Annual interest rate = 9.5%
Number of years financed = 3
Total finance charges = $8,223 x 0.095 x 3 = $2,341.595
Total financed amount = $8,223 + $2,341.595 = $10,564.595
Monthly payments = Total financed amount / (Number of years financed x 12 months) = $10,564.595 / (3 x 12) = $293.4615
Total deferred price = Selling price + Total finance charges = $8,850 + $2,341.595 = $11,191.595
How to find the length of the financing agreement ?Total deferred price = $28,000
Down payment = $2,100
Total amount financed = Total deferred price - Down payment = $28,000 - $2,100 = $25,900
Monthly payments = $380
Number of months = Total amount financed / Monthly payments = $25,900 / $380 = 68.16
The financing agreement is approximately 68 months long.
How to find the deferred price after the payments ?Sticker price = $19,200
Discount = 6% of sticker price = 0.06 x $19,200 = $1,152
Selling price = Sticker price - Discount = $19,200 - $1,152 = $18,048
Sales tax = 8% of selling price = 0.08 x $18,048 = $1,443.84
Total price = Selling price + Sales tax + Tag fee + Title fee = $18,048 + $1,443.84 + $65 + $45 = $19,601.84
How to find the monthly payments ?Using the formula for monthly payments on a loan:
P = (PV x r x (1 + r)^ n) / ((1 + r) ^ n - 1)
= ($26,515.80 x 0.005265 x (1 + 0.005265) ^ 60 ) / ((1 + 0.005265) ^ 60 - 1) = $516.92
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You deposit $5,000.00 in an account earning 8% interest compounded annually. How much will you have in the account in 5 years?
Answer:
Answer:
50313.28
Step-by-step explanation:
A = total amount
P = principal or amount of money deposited,
r = annual interest rate
n = number of times compounded per year
t = time in years
For the formula:
A=P(1+r/n)n⋅t
P=$5000 , r=8% , n=1 and t=30 years
Solution:
A= 5000(1+0.08/1) to the power 1.30
= 5000*1.08 to the power 30
= 5000*10.062657
= 50313.28
maria scored 92 points in 4 games at the same rate, how many points would she scored in 17 games
Explanation:
She scored 92 points in 4 games. The unit rate is 92/4 = 23 points per game.
Over the course of 17 games, Maria would have a total of 17*23 = 391 points assuming her scoring rate is kept the same.
20 points!! please help!!
To find the area of the total figure, we need to first find the areas of the rectangle and triangle, and then add them together.Therefore, the area of the total figure is 200 square feet.
What is area?Area is the measurement of the size of a two-dimensional surface enclosed by a closed figure
Area of rectangle = length x width
= 20 ft x 8 ft
= 160 sq. ft
Area of triangle = 1/2 xbase xheight
= 1/2 x 8 ft x 10 ft
= 40 sq. ft
To find the base of the triangle, we can use the Pythagorean theorem, which states that the square of the hypotenuse (slope) of a right triangle is equal to the sum of the squares of its two sides. In this case, the hypotenuse is 12 ft, one of the other sides is the height of the triangle (10 ft), and the other side is the base of the triangle (b).
Using the Pythagorean theorem, we have:
12² = 10² + b²
144 = 100 + b²
44 = b²
b = √44
b ≈ 6.63 ft
Now that we know the base of the triangle, we can find the area of the total figure by adding the area of the rectangle and the area of the triangle:
Area of total figure = area of rectangle + area of triangle
= 160 sq. ft + 40 sq. ft
= 200 sq. ft
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Florida Pick 3 In the Florida Pick 3 lottery, you can place a “straight” bet of $1 by selecting the exact order of three digits between 0 and 9 inclusive (with repetition allowed), so the probability of winning is 1/1000. If the same three numbers are drawn in the same order, you collect $500, so your net profit is $499.
The probability of losing is [tex]\frac{999}{1000}[/tex] (since there are 999 ways to lose and 1 way to win), so the odds against winning are [tex](\frac{\frac{999}{1000} }{\frac{1}{1000} })[/tex] = 999:1.
To understand the concept of odds against winning, we can use the analogy of flipping a coin. There are only two outcomes that can occur when we flip a fair coin: heads or tails. The probability of getting heads is 1/2 and the probability of getting tails is also [tex]\frac{1}{2}[/tex] . The odds against getting heads are the ratio of the probability of getting tails to the probability of getting heads, which is 1:1 or even odds. In the case of the Florida Pick 3 lottery, there are 1000 possible outcomes, but only one is a winning outcome. Therefore, the actual odds against winning the Florida Pick 3 lottery with a straight bet are 999 to 1.
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The complete question is:
In the Florida Pick 3 lottery, you can place a “straight” bet of $1 by selecting the exact order of three digits between 0 and 9 inclusive (with repetition allowed), so the probability of winning is 1/1000. If the same three numbers are drawn in the same order, you collect $500, so your net profit is $499.
Find the actual odds against winning
Jaylen estimates the side of the square to be 8.5 inches long. The actual length of the side of the square is 8.3 inches long. What is the percent error of the area of the two squares?
Answer:
4.88%
Step-by-step explanation:
All sides of a square are equal
let x = length of a side
Area = x·x = x²
Estimated area = (8.5)² = 72.25 in²
Actual area = (8.3)² = 68.89 in²
percent error = (actual area - estimated area) / (estimated area) x 100
% error = (68.89 - 72.25) / (68.89) x 100 = -4.88% the negative sign means the estimate was higher than the actual.
A ladder 35feet long leans against the side of a building. If the angle formed between the ladder and the ground is 60°,how far is the bottom of the ladder from the base of the building?[Given that cos 60° = 0.5]
Therefore, the bottom of the ladder is 17.5 feet from the base of the building.
What is distance?Distance is a numerical measurement of the physical space between two objects or points. It is the amount of space between two points or objects, usually measured in units such as meters, feet, or miles. Distance can be used to describe the separation between any two entities in space, whether they are tangible objects or abstract concepts. In physics, distance is a fundamental concept that is used to describe the magnitude of displacement, which is the change in position of an object over time. Distance can be calculated using a variety of methods, including measuring with a ruler or tape measure, using GPS technology, or by using mathematical equations that take into account variables such as speed and time.
We can use trigonometric ratios to solve the problem. Let x be the distance between the bottom of the ladder and the base of the building. Then, we can use the cosine ratio to find x:
cos (60°) = adjacent/hypotenuse
0.5 = x/35
x = 0.5 × 35
x = 17.5
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The average overseas trip cost 2708 per visitor. If we assume a normal distribution with a standard deviation of 405 what is the probability that the cost for a randomly selected trip is more than 3000? If we elect a random sample of 30 overseas trips and find the mean of the sample, what is the probability that the mean is greater than 3000
Randomly selected trip: 24.5% chance > $3000. Sample mean of 30 trips: very small chance > $3000.
Utilizing z-score recipe:
z = (x - μ)/σ
where x is the worth we're keen on, μ is the mean, and σ is the standard deviation.For the primary inquiry:
z = (3000 - 2708)/405 = 0.69
Utilizing a standard typical circulation table or number cruncher, we can track down that the likelihood of getting a z-score more prominent than 0.69 is around 0.245. Consequently, the likelihood that the expense for a haphazardly chosen trip is more than 3000 is around 0.245 or 24.5%.
For the subsequent inquiry:
The example size (n) = 30, and the standard deviation (σ) = 405/sqrt(30) = 74.02 (approx.)
z = (3000 - 2708)/74.02 = 3.94
Utilizing a standard typical dissemination table or number cruncher, we can track down that the likelihood of getting a z-score more prominent than 3.94 is tiny, near 0. Consequently, the likelihood that the mean expense of an example of 30 abroad excursions is more noteworthy than 3000 is tiny.
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The probability that the mean is greater than 3000 is 24.5%
What is probability?A probability is a number that reflects the chance or likelihood that a particular event will occur.
Probabilities can be expressed as proportions that range from 0 to 1, and they can also be expressed as percentages ranging from 0% to 100%.
Given that, the average overseas trip cost 2708 per visitor, assuming a normal distribution with a standard deviation of 405 what is the probability that the cost for a randomly selected trip is more than 3000
z-score:
z = (x - μ)/σ
where μ is the mean, and σ is the standard deviation.
So,
z = (3000 - 2708)/405 = 0.69
Z-score 0.69 = 0.245.
Thus, the likelihood that the expense of the chosen trip is more than 3000 is around 0.245 or 24.5%.
The sample size (n) = 30, and the standard deviation (σ) = 405/√(30) = 74.02 (approx.)
z = (3000 - 2708)/74.02 = 3.94
z-score 3.94 = 0.
Thus, the likelihood that the mean expense of an example of 30 abroad excursions is more noteworthy than 3000 is tiny.
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question included below
Therefore , the solution of the given problem of unitary method comes out to be P = 1/72.
An unitary method is what?The objective can be accomplished by utilizing what has been expression learned thus far, making use of this global availability, and incorporating all essential components from earlier changeable study that utilized a particular method. If the anticipated claim result actually occurs, it will be feasible to contact the entity once more; otherwise, both important processes will undoubtedly miss the statement.
Here,
There are two situations to take into consideration because there are seven courses in Group A and six courses in Group B:
The student in Case 1 selects two classes from Group A. The student has seven choices for the first course in this situation, and six options for the second course.
Case 2: The student has a total of 5 choices for courses, as follows:
=>2 × (42 + 30) = 144
As a result, the student has 144 choices for 5-course sequences.
b. There are two choices for the fifth course because the student can select one more course from either Group A or Group B.
There are a total of three methods to select this set of courses:
=> 1 × 1 × 1 × 1 × 2 = 2
the likelihood of selecting Introduction
=> P = 2/144 = 1/72
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can you solve this question?
y'=?
The differentiation of the variable y is equal to [tex]\frac{1}{2} ( \frac{y^{2}-4x^{3}-4xy^{2} }{2x^{2} y+2y^{3}-xy } )[/tex] for the differential equation.
Given equation: [tex](x^{2} +y^{2} )^{2} = 2xy^{2}[/tex]
differentiate with respect to x
2 [tex](x^{2} + y^{2})[/tex] [ [tex]2x+2y.\frac{dy}{dx}[/tex] ] =[ (1).[tex]y^{2}[/tex] + [tex]x (2y) + \frac{dy}{dx}[/tex] ]
4 [tex](x^{2} + y^{2})[/tex] [ [tex]x+y \frac{dy}{dx}[/tex] ] = [tex]y^{2}[/tex] + [tex]2xy \frac{dy}{dx}[/tex]
4( [tex]x^{3} + x^{2} y \frac{dy}{dx} + xy^{2} + y^{3} \frac{dy}{dx}[/tex] ) = [tex]y^{2}[/tex] + [tex]2xy \frac{dy}{dx}[/tex]
[tex]4x^{3} +4 x^{2} y \frac{dy}{dx} +4 xy^{2} +4 y^{3} \frac{dy}{dx}[/tex] = [tex]y^{2}[/tex] + [tex]2xy \frac{dy}{dx}[/tex]
[tex]4x^{2}y \frac{dy}{dx}[/tex] + [tex]4y^{3}[/tex] [tex]\frac{dy}{dx}[/tex] - [tex]2xy\frac{dy}{dx}[/tex] = [tex]y^{2} - 4x^{3} - 4xy^{2}[/tex]
[tex](4x^{2}y + 4y^{3} - 2xy )[/tex] [tex]\frac{dy}{dx}[/tex] = [tex]y^{2} - 4x^{3} - 4xy^{2}[/tex]
[tex]\frac{dy}{dx}[/tex] = [tex]y^{2} - 4x^{3} - 4xy^{2}[/tex] / [tex](4x^{2}y + 4y^{3} - 2xy )[/tex]
[tex]\frac{dy}{dx}[/tex] = [tex]\frac{1}{2} ( \frac{y^{2}-4x^{3}-4xy^{2} }{2x^{2} y+2y^{3}-xy } )[/tex]
Hence solved. The differentiation for the given differential equation is done using the technique of implicit differentiation. The differentiation of the variable y is equal to [tex]\frac{1}{2} ( \frac{y^{2}-4x^{3}-4xy^{2} }{2x^{2} y+2y^{3}-xy } )[/tex] for the differential equation.
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9. Which statement about the diagonals of a non-square rectangle is true?
The diagonals are parallel.
The diagonals are congruent.
The diagonals are perpendicular.
The diagonals bisect a pair of opposite angles.
The correct statement about the diagonals of a non-square rectangle is "The diagonals bisect a pair of opposite angles"
What is a non-square rectangle?A rectangle is a four-sided flat shape with opposite sides of equal length and opposite sides that are parallel.
A non-square rectangle is simply a rectangle whose opposite sides are not equal in length. In other words, a non-square rectangle is a rectangle that has two pairs of sides, each of which has a different length.
If a rectangle has sides that are equal in length, it is called a square. However, if the sides are not equal, then it is a non-square rectangle. Non-square rectangles are commonly encountered in everyday life, such as in the shape of paper, books, windows, doors, and many other objects.
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Anyone help??? It’s geometryyy
hi :) i sense that it's the rhombus again, but please let me know if i'm wrong.
assuming this is about the rhombus, which i've attached below, here is your answer:
the diagonals of a rhombus bisect each other at right angles. this means that the angles created by the intersection of AC and BD are all equal to 90 degrees, including CEB.
hope this helps!
Martha made 2 2/3 pounds of pasta. she divided the pasta into fourths. how much pasta is in each portion?
Each portion of pasta is 2/3 pounds.
What is portion?Prοpοrtiοn or portion, in general, is referred tο as a part, share, οr number cοnsidered in cοmparative relatiοn tο a whοle. Prοpοrtiοn definitiοn says that when twο ratiοs are equivalent, they are in prοpοrtiοn. It is an equatiοn οr statement used tο depict that twο ratiοs οr fractiοns are equal.
To divide 2 2/3 pounds of pasta into fourths, we can first convert the mixed number to an improper fraction:
2 2/3 = (2 x 3 + 2)/3 = 8/3
Then, we can divide 8/3 by 4 to find the amount of pasta in each portion:
8/3 ÷ 4 = (8/3) x (1/4) = 2/3
Therefore, each portion of pasta is 2/3 pounds.
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i need help please with the calculus question below
Solve 6x+14x+5=5(4x+1) and write a word problem to the equation or any relevant forms of it represents.
After solving the given expression, the value of x is 5.
What exactly are expressions?
An expression in mathematics is a set of numbers, variables, and mathematical operations (such as addition, subtraction, multiplication, and division) that may be evaluated to generate a value. Expressions can be simple or complicated, with one or more variables involved.
Now,
To solve the equation 6x+14x+5=5(4x+1), we first need to simplify both sides of the equation using the distributive property of multiplication:
6x + 14x + 5 = 20x + 5
Now we can simplify further by subtracting 20x and 5 from both sides of the equation:
6x + 14x - 20x = 0 - 5
Simplifying again:
x = -5
Finally, we can solve for x by multiplying both sides by -1:
x = 5
Therefore, the solution to the equation 6x+14x+5=5(4x+1) is x=5.
Word problem:
A clothing store sells two types of shirts: T-shirts and polo shirts. The store makes a profit of $6 on each T-shirt sold and a profit of $14 on each polo shirt sold. Last week, the store sold a total of 5 shirts and made a total profit of $25. If x represents the number of T-shirts sold, write an equation to represent the situation.
Solution:
Let x be the number of T-shirts sold, then the number of polo shirts sold is 5 - x (since a total of 5 shirts were sold). The total profit from selling x T-shirts and (5-x) polo shirts can be calculated as:
Profit = (profit per T-shirt x number of T-shirts) + (profit per polo shirt x number of polo shirts)
Profit = (6x) + (14(5-x))
Profit = 6x + 70 - 14x
Profit = -8x + 70
Since the total profit is given as $25, we can write the equation:
-8x + 70 = 25
Simplifying:
-8x = -45
x = 5.625
Since we can't sell a fraction of a shirt, we need to round down to the nearest integer. Therefore, the store sold 5 T-shirts.
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Jane made $143 for 11 hours of work. At the same rate, how many hours would she have to work to make $169 ?
13
First, we divide to figure out how much Jane makes an hour
143 ÷ 11 = 13
Second, we multiply multiply by 13 until we get 169
13 × 13 = 169
So Jane will make 169 dollars in 13 hours
Answer:
13 Hours
Step-by-step explanation:
$143 ÷ 11hrs = $13/hr that Jane is paid, so to find how many hours she will need to work to make $169
$169 ÷ $13 = 13 hours
if the mean of a symmetric distribution is 130 which of these values could be the median of the distribution
in a symmetric distribution, the value that could be the median of the distribution must be equal to the mean.
In probability and statistics, the mean and median are two measures of central tendency that are commonly used to describe a data set. The mean, also known as the arithmetic mean or average, is calculated by summing up all the values in the data set and dividing by the total number of values. The median, on the other hand, is the middle value of a data set when the values are arranged in order from lowest to highest.
For a symmetric distribution, the mean and median are the same, because the data values on one side of the mean balance out the values on the other side. In other words, if the distribution is symmetric, then the data values are evenly distributed around the mean.
In this case, if the mean of a symmetric distribution is 130, then the median must also be 130. This is because the median is the middle value of the data set, and in a symmetric distribution, the middle value is the same as the mean.
To illustrate this, consider a simple example of a symmetric distribution with the following values: 125, 130, 135, 140. The mean of this distribution is (125 + 130 + 135 + 140) / 4 = 132.5. However, the median is the middle value of the data set, which is 130. Since the distribution is symmetric, the middle value is the same as the mean.
Therefore, in a symmetric distribution, the value that could be the median of the distribution must be equal to the mean.
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Complete question:- If the mean of a symmetrical distribution is 130, which of these values could be the median of the distribution?
Anyone know the diameter?
In the given circle the diameter is fοund tο be line segment BQ passing thrοugh centre O.
What is a circle?A circle is a clοsed, twο-dimensiοnal οbject where every pοint in the plane is equally spaced frοm a central pοint. The line οf reflectiοn symmetry is fοrmed by all lines that traverse the circle. Additiοnally, every angle has rοtatiοnal symmetry arοund the centre.
A circle is given with centre marked as O.
A circle is a 2D fοrm in geοmetry in which all οf the pοints οn its surface are equally spaced frοm its center.
The radius is the length frοm any pοint οn the surface tο the center.
A diameter is a chοrd that is equidistance frοm centre οf the circle.
Here οnly the straight line is equidistance frοm centre οf the circle.
That line is BQ.
Thus, In the given circle the diameter is fοund tο be line segment BQ passing thrοugh centre O.
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Which of the following quotients are true? Select all that apply. A. 1 2 ÷ 2 = 4 B. 1 3 ÷ 4 = 4 3 C. 1 2 ÷ 6 = 1 12 D. 1 5 ÷ 2 = 10 E. 1 8 ÷ 3 = 1 24
We may conclude after answering the presented question that None of the given quotient equations are true.
What is an equation?
A formula is a statement that two expressions are equal. An equation consists of two sides separated by an algebraic equation (=).
For example, the argument "2x + 3 = 9" asserts that the phrase "2x Plus 3" equals the number "9."
The purpose of equation solving is to determine the value or values of the variable(s) that will allow the equation to be true. Equations can be simple or complicated, regular or nonlinear, and include one or more elements.
[tex]x^2 + 2x - 3 = 0.[/tex] Lines are utilized in many different areas of mathematics, such as algebra, calculus, and geometry.
None of the given quotients are true.
A. 1/2 ÷ 2 = 1/4, not 4.
B. 1/3 ÷ 4 = 1/12, not 4/3.
C. 1/2 ÷ 6 = 1/12, not 1/6.
D. 1/5 ÷ 2 = 1/10, not 10.
E. 1/8 ÷ 3 = 1/24, not 1/3.
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A researcher is studying life expectancy in different parts of the world using birth and death records. She randomly select a sample of 20 people from town, A and a sample 20 people from town B and records, their life span in years.
The researcher wants to test the claim that there is a significant difference in lifespan for people in the two towns. What are the Noel and alternative hypotheses that should be used to test this claim ?
Please answer (A B C, or D)
See photo for chart and answer choices!
Thank you 100 points :)
The null and the alternative hypothesis for Noel's test are given as follows:
Null: [tex]\mu_A - \mu_B = 0[/tex]Alternative: [tex]\mu_A - \mu_B \neq 0[/tex]How to obtain the null and the alternative hypothesis?The claim for the test is given as follows:
"There is a significant difference in lifespan for people in the two towns."
At the null hypothesis, we test if the claim is false, that is, if there is not a significant difference in lifespan for people in the two towns, hence:
[tex]\mu_A = \mu_B[/tex]
[tex]\mu_A - \mu_B = 0[/tex]
At the alternative hypothesis, we test if the claim is true, that is, there is a significant difference in lifespan for people in the two towns, hence:
[tex]\mu_A \neq \mu_B[/tex]
[tex]\mu_A - \mu_B \neq 0[/tex]
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Patrick biked 27 miles last week. He biked 9 miles more than Ibrain. The equation m + 9 = 27 gives the number of miles m that Ibrain biked last week. Which is the solution of the equation?
Answer:
Step-by-step explanation:
We can solve the equation m + 9 = 27 by subtracting 9 from both sides to isolate m:
m + 9 - 9 = 27 - 9
m = 18
Therefore, Ibrain biked 18 miles last week.
(10 x _) x 6 = _ x (2x6)
(I need help)
Answer:
660
Step-by-step explanation:
(10 x 6) x 6 = 360
and
_ x (2 x 6) = _ x 12
To find the missing value, we need to use the distributive property of multiplication, which states that a(b + c) = ab + ac.
Therefore, we can rewrite the right-hand side of the equation as:
_ x (2 x 6) = _ x 12
_ x 12 = 12_
Now we can substitute this into the original equation:
(10 x 6) x 6 = 360
60 x 6 = 360
360 = 360
So, the missing value is 60.
Therefore,
(10 x 6) x 6 = 360 = 60 x 12 = _ x (2 x 6)
and
_ x (2 x 6) = 60 x 12.
Ben borrowed $10,000 from the bank. The rate is 12% and he will pay it back in 12 months. How much does he owe the bank?
Answer:
Step-by-step explanation:
Assuming that the interest is compounded monthly, Ben's total amount owed to the bank after 12 months can be calculated using the following formula:
A = P*(1+r/n)^(n*t)
Where:
P = principal amount borrowed = $10,000
r = annual interest rate as a decimal = 0.12
n = number of times the interest is compounded per year = 12 (monthly)
t = time period for which the interest is applied in years = 1
Plugging in the values, we get:
A = 10,000*(1+0.12/12)^(12*1)
A = $11,268.70
Therefore, Ben owes the bank a total of $11,268.70 after 12 months.
Craig’s Computer Supply Shop sells color ink printer cartridges for $24.99 and black ink printer cartridges for $14.99. Last week the store sold a total of 27 ink cartridges. If the sales income for these items was $514.73, not including tax, which of these conclusions is reasonable?
A.) There were more black ink cartridges than color ink cartridges sold last week.
B.) There were more color ink cartridges than black ink cartridges sold last week
C.) The total sales income, not including tax, for color ink cartridges was $399.84
D.) The total sales income, not including tax, for black ink cartridges was $164.89
There were more color ink cartridges than black ink cartridges sold last week. Therefore, option B is the correct conclusion.
What is system of equation?A system of equations, sometimes referred to as an equation system or a set of simultaneous equations, is a finite set of equations for which we searched for common solutions. Variables are related to one another specifically in each equation in a system of equations. To discover a set of variable values that satisfy each equation, the equations can be solved simultaneously.
In everyday situations where the unknown values can be represented as variables, a system of linear equations is used to model the problem. Many techniques, including substitution, elimination, graphing, etc., are used to solve systems of equations.
Let us suppose the number of color ink cartridges sold = x.
The number of color ink cartridges sold = y.
Thus,
x + y = 27
24.99x + 14.99y = 514.73
Multiplying the first equation by 24.99 and subtracting it from the second equation multiplied by 100, we get:
1499y = 1813
y ≈ 1.21
Substituting y back into the first equation, we get:
x ≈ 25.79
Hence, there were more color ink cartridges than black ink cartridges sold last week. Therefore, option B is the correct conclusion.
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