A system of linear equations with more equations than unknowns is called overdetermined system. This system always be consistent. Because it may result in contradictions or inconsistencies.
An overdetermined system of linear equations cannot always be consistent, due to contradictions or inconsistencies. Since there are more equations than unknowns, there are likely to be restrictions and dependencies among the equations, and not all of them may be satisfied simultaneously.
However, in certain cases, an overdetermined system can still be consistent if the equations are compatible and do not contradict each other. In such cases, the system may have a unique solution or a set of solutions that satisfy all of the equations.
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Find the volume of the cylinder rounded to the nearest tenth.
Diameter is 12
Height is 4
I'm sorry for no providing a picture it wont allow me to screenshot!
Answer:
452.39
Step-by-step explanation:
Used volume formula
Answer:
V = 452.4
Step-by-step explanation:
V = πr²h
(3.14)(6)²(4) = 452.38934211
Considering the results from part a it follows that the volume of a cylinder can be found in the same way as the volume of a rectangular prism. Use your results in what you know about volume to explain how to find the volume of a cylinder with a base radius of r units and a height of h units.
The explaination of the volume of the cylinder calculation is below
To find the volume of a cylinder with a base radius of r units and a height of h units, you can use the formula:
V = πr²h
Where V is the volume of the cylinder, π is a mathematical constant approximately equal to 3.14, r is the radius of the cylinder's base, and h is the height of the cylinder.
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Write the general equation for the circle that passes through the points (1, 1), (1, 3), and (9, 2).
You must include the appropriate sign (+ or -) in your answer. Do not use spaces in your answer.
8 x 2 + 8 y 2
x
y
= 0
Answer: The general equation for a circle with center (h, k) and radius r is:
(x - h)^2 + (y - k)^2 = r^2
To find the equation of the circle that passes through the points (1, 1), (1, 3), and (9, 2), we can use the fact that the perpendicular bisectors of any two chords of a circle intersect at the center of the circle.
The midpoint and slope of the chord connecting (1, 1) and (1, 3) are:
Midpoint: ((1+1)/2, (1+3)/2) = (1, 2)
Slope: undefined (since x values are the same)
The perpendicular bisector of this chord passes through the midpoint (1, 2) and has a slope of 0. Therefore, its equation is:
y - 2 = 0
Simplifying this equation gives:
y = 2
Similarly, the midpoint and slope of the chord connecting (1, 1) and (9, 2) are:
Midpoint: ((1+9)/2, (1+2)/2) = (5, 1.5)
Slope: (2 - 1)/(9 - 1) = 1/8
The perpendicular bisector of this chord passes through the midpoint (5, 1.5) and has a slope of -8 (the negative reciprocal of the slope of the chord). Therefore, its equation is:
y - 1.5 = -8(x - 5)
Simplifying this equation gives:
y = -8x + 41.5
The intersection of the two perpendicular bisectors (y = 2 and y = -8x + 41.5) is the center of the circle. Solving for x gives:
2 = -8x + 41.5
8x = 39.5
x = 4.9375
Substituting x = 4.9375 into either equation for the perpendicular bisectors gives:
y = 2
Therefore, the center of the circle is (4.9375, 2) and the radius is the distance from the center to any of the three given points. For example, the distance from (4.9375, 2) to (1, 1) is:
r = sqrt((4.9375 - 1)^2 + (2 - 1)^2) = sqrt(24.9219) = 4.992
So the equation of the circle is:
(x - 4.9375)^2 + (y - 2)^2 = (4.992)^2
Expanding and simplifying this equation gives:
x^2 - 9.875x + 24.526 + y^2 - 4y + 0.076 = 24.916
Rearranging terms gives:
x^2 + y^2 - 9.875x - 4y - 0.34 = 0
So the general equation for the circle is:
x^2 + y^2 - 9.875x - 4y - 0.34 = 0
Step-by-step explanation:
Give most precise classification for the figure below:
Answer:
parallelogram
Step-by-step explanation:
opposite angles and sides are congruent
Quick for 100 points and 5 stars please help!!
For a certain video game, the number of points awarded to the player is proportional to the amount of time the game is played. For every 1 minute of play, the game awards one half point, and for every 7 minutes of play, the game awards three and one half points.
Part A: Find the constant of proportionality. Show every step of your work. (4 points)
Part B: Write an equation that represents the relationship. Show every step of your work. (2 points)
Part C: Describe how you would graph the relationship. Use complete sentences. (4 points)
Part D: How many points are awarded for 18 minutes of play? (2 points)
Step-by-step explanation:
Please find the attached pics for answers.
he food marketing institute shows that of households spend more than per week on groceries. assume the population proportion is and a simple random sample of households will be selected from the population. use the z-table. a. show the sampling distribution of , the sample proportion of households spending more than per week on groceries. 0.17 (to decimals) 0.0133 (to decimals) b. what is the probability that the sample proportion will be within of the population proportion (to decimals)? c. answer part (b) for a sample of households (to decimals). 0.0094
a. the sampling distribution is [tex]\sqrt{[(0.17 \times (1-0.17)) / n]}[/tex]
b. The probability that the sample proportion is within 0.03 of the population proportion is 0.4101.
c. The probability that the sample proportion is within 0.03 of the population proportion for a sample of 200 households is 0.7738.
a. The sampling distribution of the sample proportion, [tex]\bar p[/tex], can be approximated by a normal distribution with mean equal to the population proportion, p, and standard deviation equal to the square root of [tex][(p \times (1-p)) / n][/tex],
where n is the sample size.
Given that p = 0.17 and assuming a large enough sample size, we can use the formula to calculate the standard deviation of the sampling distribution:
Standard deviation = [tex]\sqrt{[(0.17 \times (1-0.17)) / n]}[/tex]
b. To find the probability that the sample proportion will be within a certain range of the population proportion, we need to calculate the z-score for the lower and upper bounds of that range and then find the area under the normal curve between those z-scores.
Let's say we want to find the probability that the sample proportion is within 0.03 of the population proportion. This means we want to find
P([tex]\bar p[/tex]- p ≤ 0.03) = P(([tex]\bar p[/tex]-- p) / [tex]\sqrt{[(p \times (1-p)) / n]}[/tex] ≤ 0.03 / [tex]\sqrt{[(p \times (1-p)) / n][/tex]
We can use the standard normal distribution and z-scores to find this probability:
[tex]z_1[/tex] = (0.03 / [tex]\sqrt{(0.17 \times (1-0.17)/n}[/tex])
[tex]z_2[/tex] = (-0.03 / [tex]\sqrt{(0.17 \times (1-0.17))/n}[/tex])
We can find the probability that the z-score is between [tex]z_1[/tex] and [tex]z_2[/tex]:
P([tex]z_1[/tex]≤ Z ≤ [tex]z_2[/tex]) = P(-0.541 ≤ Z ≤ 0.541) = 0.4101
c. To answer part (c), we need to specify the sample size. Let's say we are taking a sample of 200 households.
Using the formula for standard deviation of the sampling distribution from part (a), we get:
Standard deviation = [tex]\sqrt{(0.17 \times(1-0.17)) / 200}[/tex] = 0.034
Now we can repeat the same steps as in part (b) with this standard deviation:
[tex]z_1[/tex] = (0.03 / 0.034)
[tex]z_2[/tex] = (-0.03 / 0.034)
P([tex]z_1[/tex]≤ Z ≤ [tex]z_2[/tex]) = P(-0.882 ≤ Z ≤ 0.882) = 0.7738
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the product of twice a number and four
The product of twice a number and four is 8 times the number.
What is product of a number?The product means a number that you get by multiplying two or more other numbers together.
Equation:The product of twice a number and four can be represented algebraically as:
4(2x)
where x is the number we are referring to.
Simplifying the expression, we get:
4(2x) = 8x
Therefore, the product of twice a number and four is 8 times the number.
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15. Melissa put $900 in her savings account. She spent $25 on gas every week and x dollars on clothes every week. Write TWO expression to show how much money Melissa would have after 10 weeks. Expression 1: Expression 2:
The two expressions to show how much money Melissa would have after 10 weeks are:
1. 900 - 250 - 10x
2. 900 - (10 × 25 + 10x)
Expression 1: To calculate how much money Melissa would have after 10 weeks, first find the total amount she spends
on gas in 10 weeks by multiplying the weekly gas cost by the number of weeks:
25 10 = 250.
Next, find the total amount she spends on clothes in 10 weeks by multiplying the weekly clothes cost (x) by the number of weeks:
x × 10 = 10x.
Now, subtract both of these expenses from her initial savings to find the remaining balance:
900 - 250 - 10x.
Expression 2: You can also find the total expenses in 10 weeks by adding the gas and clothes costs together:
25 + x.
Then, multiply this combined weekly cost by 10 to find the total cost in 10 weeks:
10(25 + x) = 10 × 25 + 10x.
Finally, subtract the total cost from her initial savings:
900 - (10 × 25 + 10x).
So, the two expressions to show how much money Melissa would have after 10 weeks are:
1. 900 - 250 - 10x
2. 900 - (10 × 25 + 10x)
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How many lines can be formed in a cube please help tomorrow na ang deadline nito
In a cube, a total of 12 lines can be formed.
It has 8 vertices and 12 edges. In geometry, a line is a straight geometric figure that extends indefinitely in both directions. The lines in a cube are the straight lines that connect two vertices or edges of the cube. When two points are connected with a line, it creates an edge. In a cube, there are 12 edges. Each edge is shared by two faces, and the edges are the line segments that make up the sides of the cube.
Thus, the number of lines that can be formed in a cube is 12. When two or more lines meet at a point, it is called a vertex. A cube has eight vertices or corners. When a line is drawn between any two vertices of a cube, it is called a diagonal. In a cube, there are 12 diagonals. A diagonal is a straight line segment that connects two non-adjacent vertices of a polygon. So, the number of lines that can be formed in a cube is 12, which includes the 12 edges.
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Suppose you purchased a house for $250,000, and three years later it is valued at $280,00. How much equity do you have in the house?
Show your work
According to the given data the equity in the house is $30,000.
What is meant by equity?Equity is the difference between the current market value of the property and the outstanding mortgage balance on the property.
According to the given information:If you purchased the house for $250,000 and it is now valued at $280,000, your equity in the house can be calculated as follows:
Equity = Current market value - Outstanding mortgage balance
Assuming you took out a mortgage for the full purchase price of the house and haven't made any extra payments, your outstanding mortgage balance would be the same as the original mortgage amount, which is $250,000. Therefore, your equity in the house would be:
Equity = $280,000 - $250,000
Equity = $30,000
So, your equity in the house is $30,000.
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What is the sign of
−
9
⋅
(
0
−
3
)
−9⋅(
−3
0
)minus, 9, dot, left parenthesis, start fraction, 0, divided by, minus, 3, end fraction, right parenthesis?
The expression is undefined, so the sign cannot be determined.
How to determine sign for the given problem?
The following given expression can be more simplified as follows:
-9 * (0 - 3) - (9 * (-3/0))
= -9 * (-3) - 9 * undefined [Note: Division by zero is undefined]
= 27 - undefined
As anything subtracted from undefined remains undefined, the overall result is undefined.
Therefore, the sign of the expression cannot be determined.
Undefined values represent the absence of a meaningful result or outcome. In this case, the expression involves division by zero, which is undefined. As a result, any operation involving an undefined value will also be undefined, including subtraction. Thus, the overall result is undefined.
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Answer:
ITS ZEROOOO
Step-by-step explanation:
i guesses and ended up getting it right.
A spherical boulder is 24 ft in diameter and weighs almost 6 tons. Find the volume. Use 3.14 for .
The volume of the boulder is approximately ft.
(Round to the nearest whole number as needed.)
27
The radius of the spherical boulder is half the diameter, so:
radius = 24 ft / 2 = 12 ft
The formula for the volume of a sphere is:
V = (4/3)πr³
Substituting the given values, we get:
V = (4/3) x 3.14 x (12 ft)³
V = 7238.08 cubic feet
Rounding to the nearest whole number, we get:
V ≈ 7238 cubic feet
Jay is planting a maximum of 60 bulbs of lilies and tulips in her garden. She wants to plant
at least twice as many tulips (x) as lilies (y). Tulip bulbs cost 1.60 each and lily bulbs cost
$1.25 each. How many bulbs of each should Jay purchase to minimize her costs? (Solution
should contain object function, constraints, and graph).
The minimum cost occurs when Jay plants 30 tulip bulbs and 15 lily bulbs, and the minimum cost is $67.50.
Let x be the number of tulip bulbs that Jay plants, and let y be the number of lily bulbs that Jay plants.
Since Jay wants to plant at least twice as many tulips as lilies, we have the constraint:
x ≥ 2y
Also, the total number of bulbs that Jay plants cannot exceed 60, so we have the constraint:
x + y ≤ 60
We want to minimize the total cost of the bulbs that Jay purchases, which is given by the object function:
C = 1.6x + 1.25y
To solve this problem, we can use linear programming. First, we graph the two constraints on a coordinate plane:
The shaded region represents the feasible region, which is the region that satisfies both constraints. The vertices of the feasible region are (0, 0), (40, 20), (60, 0), and (30, 15).
Next, we evaluate the object function at each vertex to find the minimum value. We have:
C(0, 0) = 0
C(40, 20) = 1.6(40) + 1.25(20) = 92
C(60, 0) = 1.6(60) + 1.25(0) = 96
C(30, 15) = 1.6(30) + 1.25(15) = 67.5
Therefore, the minimum cost occurs when Jay plants 30 tulip bulbs and 15 lily bulbs, and the minimum cost is $67.50.
Graphically, we can see that the optimal solution occurs at the intersection of the two constraints, which is the point (30, 15). This is where the slope of the object function is equal to the slope of the feasible region, which indicates that the object function is optimized at this point.
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Find the values of the missing sides of the right triangle
The values of the missing sides a and c are 3√6/2 and 3√2 respectively using the trigonometric ratio of tan 45° for the right triangle.
What is trigonometric ratios?The trigonometric ratios is concerned with the relationship of an angle of a right-angled triangle to ratios of two side lengths.
The basic trigonometric ratios includes;
sine, cosine and tangent.
using the trigonometric ratio of tan 60°
{recall that cos 45° and sin 45° are equal to √2/2}
cos 45° = 3/c {adjacent/hypotenuse}
c = 3 × 2/√2 {cross multiplication}
c = 3√2
sin 45° = a/3√2 {opposite/hypotenuse}
a = 3√2 × √3/2
a = 3√6/2
Therefore, the values of the missing sides a and c are 3√6/2 and 3√2 respectively using the trigonometric ratio of tan 45° for the right triangle.
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A human body contains about 1.6 x 10^11 red blood cells per pound of body weight. About
how many red blood cells are in the body of a 125-pound person, expressed in scientific
notation?
Answer ASAP AND Show work pls
Thank you
Using multiplication we know that there are 2,00,00,00,00,00,000 red blood cells in the body of a 125-pound person.
What is multiplication?One of the four fundamental arithmetic operations, along with addition, subtraction, and division, is multiplication.
A product is the output of a multiplication operation.
When you take a single number and multiply it by several, you are multiplying.
We multiplied the number five by four times.
Due to this, multiplication is occasionally referred to as "times."
So, we have:
= 1.6 * 10¹¹
Solve as follows:
= 1.6 * 10¹¹
= (1.6 * 10¹¹) * 125
= (1.6 * 100000000000) * 125
= 1,60,00,00,00,000 * 125
= 2,00,00,00,00,00,000
Therefore, using multiplication we know that there are 2,00,00,00,00,00,000 red blood cells in the body of a 125-pound person.
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Is the volume of the sphere 2/3 the volume of cylinder now ?
Volume of the sphere is equal to two-third of the volume of a cylinder.
Describe Volume of sphere?Volume is a mathematical concept that refers to the amount of space occupied by a three-dimensional object. It is expressed in cubic units, such as cubic meters or cubic centimeters, and can be calculated using a specific formula for each type of geometric shape.
A sphere is a perfectly round, three-dimensional object that looks like a ball. It has no edges or vertices and is symmetric around its center point. The formula for calculating the volume of a sphere is V = 4/3 πr³, where V is the volume, π is a mathematical constant approximately equal to 3.14, and r is the radius of the sphere.
True.
Assume that both the sphere's and cylinder's radius is r.
Considering that the base's diameter equals the cylinder's height
⇒h = 2r
Sphere radius = cylinder radius = r
Assuming the conditions are met, the sphere's volume:
= [tex]\frac{2}{3}[/tex] × Volume of cylinder
= [tex]\frac{4}{3}[/tex]πr³= [tex]\frac{2}{3}[/tex] × πr² × 2r
=[tex]\frac{4}{3}[/tex]πr³= [tex]\frac{4}{3}[/tex]πr³
Hence, volume of the sphere is equal to two-third of the volume of a cylinder.
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The complete question is:
The volume of a sphere is equal to two-third of the volume of a cylinder whose height and diameter are equal to the diameter of the sphere.
Which answer choice below is closest to the length of segment DE?
Answer:
15.71
Step-by-step explanation:
Triangle ABC and triangle ADE are similar triangles so we can find the length of DE using similarity ratio.
[tex] \frac{14}{22} = \frac{10}{de} [/tex]
Cross multiply fractions14×DE = 220
Divide both sides by 14DE = 15.71 approximately.
a botanist wants to create an srs of size 10 from 60 plants that are arranged in an array of 10 rows of 6 plants each. she numbers the plants in each row from one to six. for each of the 10 rows, she rolls a six-sided number cube and selects the plant corresponding to the number rolled. which statements are true? check all that apply. the sample is a random sample. the sample is an srs. the sample is not a random sample. there are restrictions placed on the sample. each plant has an equal chance of being selected
The statements: the sample is random, the sample is an srs, and restrictions are placed on the sample, each plant has an equal chance of being selected are true.
Each tree has an equal chance of being selected.
This sample is a simple random sample (SRS) because each tree has an equal chance of being selected and the selection of each tree is independent of the others.
Restrictions are imposed on the sample because the botanist selects only one plant from each row, based on a specific criterion (roll a cube).
Hence the following statements are true by probability
The sample is random.
The template is an SRS.
Restrictions are imposed on the sample.
Each tree has an equal chance of being selected.
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Find the probability of exactly three successes in eight trials of a binomial experiment in which the probability of success is 45%.
The probability of exactly three successes in eight trials is approximately 26.61%
To find the probability of exactly three successes in eight trials of a binomial experiment with a success probability of 45%, use the binomial probability formula:
P(x) = C(n, x) * [tex]p^x[/tex] * [tex](1-p)^{(n-x)}[/tex]
where n is the number of trials, x is the number of successes, p is the probability of success, and C(n, x) is the combination function representing the number of ways to choose x successes from n trials.
In this case, n = 8, x = 3, and p = 0.45.
Calculate the probability:
P(3) = C(8, 3) * [tex]0.45^3[/tex] * [tex](1-0.45)^{(8-3)}[/tex]
P(3) = 56 * 0.091125 * 0.1721865
P(3) ≈ 0.2661
So, the probability of exactly three successes in eight trials is approximately 26.61%.
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help please! need by 10:45
Answer: 1.5 feet (rounded to the nearest tenth) or 1.4644
Complete the inequality so that it represents the whole-number values that side a could be to create a triangle.
The possible whole-number values of 'a' that satisfy the triangle inequality are 2, 3, 4, 5, and 6.
What is triangle?A triangle is a three-sided polygon with three vertices. The triangle's internal angle, which is 180 degrees, is constructed.
To create a triangle with sides a, b, and c, the sum of the lengths of any two sides must be greater than the length of the third side. This can be represented by the triangle inequality:
a + b > c
a + 6 > 7 (substituting the given values for b and c)
a > 1
b + c > a
6 + 7 > a
13 > a
a + c > b
a + 7 > 6
a > -1
Since the length of a cannot be negative, the inequality can be simplified to:
a > 1
Therefore, to create a triangle with side lengths of 7, 6, and some whole number value for a, a must be greater than 1. The possible whole-number values of 'a' that satisfy the triangle inequality are 2, 3, 4, 5, and 6.
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Pls 50 point for each person will mark brainiest for the best answer
Please show me the three common methods for solving quadratic equations
factoring, using the square roots, completing the square and the quadratic formula.
thanks
Answer:
The three most common methods for solving quadratic equations are factoring, completing the square, and the quadratic formula.
Here's a quadratic equation you can solve by factoring:
x^2 - 4x + 3 = 0
(x - 1)(x - 3) =0
x = 1, 3
Verify the identity so that the left side looks like the right side.
[tex]\frac{1-cos(x)}{sin(x)}=\frac{sin(x)}{1+cos(x)}[/tex]
By trigonometry Taking a look at the equation's left side 1-COSX/SINX is = (SINX/SINX) - (COSX/SINX) = (SINX - COSX)/SINX.
What are a few uses for trigonometry?Several fields, including architecture, physics, astronomy, surveying, oceanography, navigation, electronics, and many more, use trigonometry. These are a few instances:
- In physics, trigonometry is used to calculate forces and analyze waves. - In astronomy, trigonometry is used to calculate distances between stars and planets. - In surveying, trigonometry is used to calculate distances and heights of objects. - In oceanography, trigonometry is used to calculate the heights of waves and tides in oceans.
We must make one side of the equation appear to be the other side in order to prove that 1-COSX/SINX=SINX/1+COSX.
Taking a look at the equation's left side first:
1-COSX/SINX is = (SINX/SINX) - (COSX/SINX) = (SINX - COSX)/SINX.
Let's now adjust the equation's right side:
SINX/1+COSX = (SINX/1+COSX) * (1-COSX/1-COSX)
= (SINX - SINXCOSX)/(1-COSXSINX)
= (SINX - COSXSINX)/(1-COSXSINX)
= (SINX - COSX)/((1-SINXCOSX)/( (1-SINXCOSX)
As the identities on both sides are equal to (SINX - COSX)/SINX, we can conclude that they are correct.
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Work out the equation of the line which has a gradient of 3 and passes through the point (-1,3).
this poll was shown in july 2018. it shows a moe (margin of error) of 3%, or 0.03. it shows poll results of issues that millennials care about most: jobs/economy 25%, immigration 17%, healthcare 16%, education 16%, environment 12%. what is the upper limit of the confidence interval for the proportion of millennials that care about immigration? write your answer as a proportion (decimal) and not as a percent. do not round.
The upper limit of the confidence interval for the proportion of millennials that care about immigration is 0.20.
In order to find the upper limit of the confidence interval for the proportion of millennials that care about immigration,
we first need to calculate the confidence interval using the margin of error (MOE) and sample proportion.
The formula to find the confidence interval is given by:
Confidence Interval = Sample Proportion ± Margin of Error (MOE)
Where Sample Proportion = Poll Result / 100
Let's first find the Sample Proportion of millennials that care about immigration.
Sample Proportion = Poll Result / 100= 17 / 100= 0.17
Now let's calculate the confidence interval using the MOE.
Confidence Interval = Sample Proportion ± Margin of Error (MOE)
Upper Limit of Confidence Interval = Sample Proportion + MOE= 0.17 + 0.03= 0.20
Therefore, the upper limit of the confidence interval for the proportion of millennials that care about immigration is
0.20.
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What is the equation of the circle? *
(0,0)
O(x+1)^2+(y+1)^2=49
O(x-1)^2+(y-1)^2=49
O(x)^2+(y)^2=49
O(x+1)^2+(y+1)^2=7
1 point
Answer:
(C) (x)^2 + (y)^2 = 49.
Step-by-step explanation:
The equation of a circle with center (h, k) and radius r is given by:
(x - h)^2 + (y - k)^2 = r^2
In this case, the center of the circle is (0, 0), so h = 0 and k = 0. The radius of the circle is not given, but we can see that the equation must have a radius of 7 because the only terms involving x and y are squared and have coefficients of 1, which means they represent the distance from the center squared.
Therefore, the equation of the circle is:
(x - 0)^2 + (y - 0)^2 = 7^2
Simplifying, we get:
x^2 + y^2 = 49
So the correct answer is (C) (x)^2 + (y)^2 = 49.
A spring has a natural length of 30.0 cm. If a 20.0-N force is required to keep it stretched to a length of 42.0 cm, how much work W is required to stretch it from 30.0 cm to 36.0 cm? (Round your answer to three decimal places.) W = ______ J
The amount of work required to stretch the spring from 30.0 cm to 36.0 cm is 1.411 joules, which can be rounded to three decimal places.
According to Hooke's Law, the amount of work required to stretch or compress a spring by a certain amount is given by the formula:
W = (1/2) k (x2 - x1)²
where W is the work done (in joules), k is the spring constant (in newtons per meter), x1 is the initial displacement (in meters), and x2 is the final displacement (in meters).
In this case, the spring has a natural length of 30.0 cm, which is equivalent to 0.3 meters. To find the spring constant, we can use the fact that a 20.0-N force is required to keep it stretched to a length of 42.0 cm, which is equivalent to 0.42 meters.
Using Hooke's Law, we have
F = k (x2 - x1)20.0 N
= k (0.42 - 0.3) m
=> k = 80.0 N/m
Now we can use Hooke's Law again to find the amount of work required to stretch the spring from 30.0 cm to 36.0 cm, which is equivalent to 0.36 meters.
Using Hooke's Law, we have:
F = k (x2 - x1)W
= (1/2) k (x2 - x1)²W
= (1/2) (80.0 N/m) (0.36 - 0.3) m²W
= 1.411 J
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the size of bass caught in strawberry lake is normally distributed with a mean of 12 inches and a standard deviation of 5 inches. suppose you catch 6 fish. what is the probability the average size of the fish you caught is more than 14 inches? g
The probability that the average size of the fish you caught is more than 14 inches is 0.1635 or 0.164
The size of bass caught in Strawberry Lake is normally distributed with a mean of 12 inches and a standard deviation of 5 inches.
If you catch 6 fish, the probability that the average size of the fish you caught is more than 14 inches is 0.202.
Here,
we need to find the probability that the average size of the fish you caught is more than 14 inches.
Let us denote the size of the bass caught in Strawberry Lake by X.
Then, X ~ N(μ = 12, σ = 5) represents the normal distribution of the size of bass caught in Strawberry Lake.
Let Y be the sample mean of 6 bass caught in the Strawberry Lake.
Then,
We know that Y ~ N(μ = 12, σ = 5/√6) represents the sampling distribution of the sample mean,
where σ = 5/√6
= 2.0412 (approx).
We are given that we have caught 6 fish.
Therefore, the sample size n = 6.
Then,
The probability that the average size of the fish you caught is more than 14 inches can be obtained as follows:
P(Y > 14) = P((Y - μ)/σ > (14 - μ)/σ)
= P(Z > (14 - 12)/2.0412)
= P(Z > 0.977)
= 1 - P(Z < 0.977) (as the standard normal distribution is a continuous distribution)
Using the standard normal distribution table, we get P(Z < 0.977) = 0.8365 (approx) Therefore, P(Y > 14) = 1 - P(Z < 0.977) = 1 - 0.8365 = 0.1635 (approx)
Therefore,
The probability that the average size of the fish you caught is more than 14 inches is 0.1635 or 0.164 (approx).
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Problems 9 & 10. Determine whether the triangles are similar by AA~, SSS~, SAS~, or not similar. If the triangles are similar, write a valid similarity statement.
On the basis of similarity of triangles, the triangles in Q9 are similar by AA similarity whereas in Q10 the triangles are similar by SAS similarity.
What is similarity?
Any Two triangles are said to be same or similar if they have the same ratio of the corresponding sides in the triangles and equal pair of corresponding angles in the triangles. If two or more figures or polygons having the same shapes, but their sizes are not same, then those figures or polygons are called similar. To be congruent, the shapes or polygons must have equal angles and equal sides.
Q9)Consider the ΔTUS and ΔUVW
∠STU=∠UVW=(72°)
∠TUS=∠VUW {vertically opposite angles}
The given triangles are similar by AA criteria.
Q10)Consider the ΔKDH and ΔBAD
∠H = ∠A = 38 °
[tex]\frac{KH}{BA} =\frac{DH}{AD}[/tex]
[tex]\frac{20}{28} = \frac{15}{21} = \frac{5}{7}[/tex]
The above triangles are similar by SAS
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square root of 31-4√21
Answer:
-12.762538417
Step-by-step explanation: