3. When Ahmad goes to work, he has to pass through two sets of traffic lights, P and Q. The
probability that he has to stop at P is
7/20 .The probability that he has to stop at Q, given that he has
to stop at P is 7/10. The probability that he does not have to stop at Q, given that he does not have to
stop at P is 2/5
* Construct a tree diagram to represent the above information.
* Find the probability that he has to stop at both P and Q.
* Find the probability that he has to stop at least once.
* If he has to stop at Q, what is the probability that he would have stopped at P.
* The probability that Ahmad has to stop at both P and Q is: 7/40
* The probability that Ahmad has to stop at least once is: 27/50
* The probability that Ahmad would have stopped at P if he stops at Q is 7/13.
What is probability ?
The study of randomness or experiments falls within the canopy of the mathematical discipline of probability. When represented as a number between 0 and 1, where 0 denotes an impossibility and 1 denotes a certain event, it is the gauge of the probability or chance that an event will occur. When making predictions based on a statistical study of the data at hand, probability is employed to characterise uncertain events. To aid in decision-making and risk assessment, it is utilised in a variety of disciplines, including science, architecture, finance, finance, and social sciences. Concepts like likelihood function, random variables, and anticipated values are all part of the study of probability.
given
We multiply the chances of stopping at P and Q assuming that he has already stopped at P to determine the likelihood that he must stop at both locations:
Stop at P Equals P(Stop at P and Q) P(Stop at Q | Stop at P)=7/20*7/10
= 49/200
P(Stop at least once) = 1 - P(Not stop at P) * P(Not stop at Q | Not stop at P) = 1 - (13/20) * P(Not stop at Q | Not stop at P) (2/5)\s= 37/50
The chance that he likewise stopped at P must be determined if he had stopped at Q.
Stopping at P and Q equals P(Stop at P and Q) / P(Stop at Q) = (7/20 * 7/10) / (7/20) = 7/10.
Hence, the likelihood that he would have stopped at P is 7/10 if he must stop at Q.
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I really need help with this please help
Answer:
a is true
x=72
Step-by-step explanation:
4/6 doesnt make sense. where did they get the denominator 6 from, it wasnt in the problem
b is false
7. Write the equation of the circle that passes through the point (2,-5) and has its center at (4,0) .
Show your work
Therefore, the equation of the circle that passes through the point (2, -5) and has its center at (4,0) is.[tex](x - 4)^2 + y^2= 29[/tex].
What is circle?A circle is a closed, two-dimensional geometric shape that consists of all points in a plane that are equidistant from a fixed point called the center. It can also be defined as the set of all points in a plane that are at a given distance (called the radius) from the center point. The circumference of a circle is the distance around its outer boundary, and the diameter is the distance across the center of the circle. Circles have several important properties and are used extensively in mathematics, science, and engineering.
To find the equation of a circle, we need to know the coordinates of its center and its radius. We are given the center of the circle, which is (4,0). To find the radius, we can use the distance formula between the center and the point on the circle (2, -5):
[tex]radius = \sqrt{[(4 - 2)^2 + (0 - (-5))^2]}[/tex]
[tex]= \sqrt{[2^2 + 5^2]}[/tex]
[tex]= \sqrt{29}[/tex]
So the equation of the circle can be written in the standard form as:
[tex](x - h)^2 + (y - k)^2 = r^2[/tex]
where (h, k) is the center of the circle and r is its radius.
Substituting the values we found, we get:
[tex](x - 4)^2 + (y - 0)^2 = (\sqrt{29})^2[/tex]
Simplifying, we get:
[tex](x - 4)^2 + y^2 = 29[/tex]
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I don’t understand how to do FOIL with this
2x – 3)(2x + 7)
Answer:
[tex]4x^2[/tex]+8x-21
Step-by-step explanation:
First foil 2x to 2x to get [tex]4x^{2}[/tex].
Then, foil 2x to 7 to get 14x.
Then, foil -3 to 2x to get -6x.
Then, foil -3 to 7 to get -21.
After doing all of that, you will get [tex]4x^2[/tex]+14x-6x-21.
Simplify it, so your final answer is [tex]4x^2[/tex]+8x-21
Please help me with this
Answer:
D
Step-by-step explanation:
The parabola of m(x) is thinner than the parabola of f(x) since 4 times 2 squared is 16 while 2 squared is 4
In the table below, which value is a marginal frequency?
A. 23
B. 46
C. 81
D. 135
The second row and second column's frequency, C. 81, is a marginal frequency (the column total for the second column).
how can we describe frequency distribution ?The frequency distribution statistics method identifies the frequency with which a given value or variety of values exists in a data set. The process is dividing the data into intervals, or "bins," and counting a number of values that fall within every bin.
A graph, such as a statistic or a frequency polygon, can be used to show the frequency distribution. The table displays the categories or intervals as well as the frequency or count for each interval.
The y-axis on the graph represents frequencies, while the x-axis represents intervals. The bars or polygons on the graph reflect the count or % of data within every interval.
given
The totals for each row and column make up the marginal frequencies in the table.
The frequencies for each category in the first variable are represented by the row totals, while the frequencies in the second variable are represented by the column totals.
In order to choose a marginal frequency from the available options:
A. The frequency of 23, which is not a marginal frequency, is in the first row and first column.
B. 46 is not a marginal frequency; it is the frequency in the first row and second column.
The second row and second column's frequency, C. 81, is a marginal frequency (the column total for the second column).
D. A marginal frequency is represented by the frequency in the second row and third column (the column total for the third column).
Options C and D therefore have negligible frequencies.
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Given that cos theta equals negative 5 square root 29 over 29 and theta is in quadrant 2 what is sim theta?
If cοs θ equals negative 5 square rοοt 29 οver 29 and θ is in quadrant 2 sin(θ) = οppοsite/hypοtenuse = 2√21/29.
What is trigοnοmetry?The links between triangles' sides and angles are studied in the mathematic discipline knοwn as trigοnοmetry.
We knοw that cοsine is negative in quadrant 2, sο we can draw a triangle in quadrant 2 where the adjacent side is negative and the hypοtenuse is pοsitive. Let's call the οppοsite side οf the triangle "a", the adjacent side "b", and the hypοtenuse "c".
Using the Pythagοrean theοrem, we can find the length οf the third side οf the triangle:
c² = a² + b²
29² = a² + (-5√29)²
29² = a² + 725
a² = 29² - 725
a² = 84
a = √84 = 2√21
Nοw that we knοw the lengths οf the οppοsite and adjacent sides οf the triangle, we can use the definitiοn οf sine:
sin(θ) = οppοsite/hypοtenuse = 2√21/29
Therefοre, sin(θ) equals 2√21/29.
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Complete Question:
Given that cos(θ)=−5√29/29, and θ is in Quadrant II, what is sin(θ)? Give your answer as an exact fraction with a radical, if necessary.
HELP ASAP
A composite figure is represented in the image.
A four-sided shape with the base side labeled as 21.3 yards. The height is labeled 12.8 yards. A portion of the top from the perpendicular side to a right vertex is labeled 6.4 yards. A portion of the top from the perpendicular side to a left vertex is labeled 14.9 yards.
What is the total area of the figure?
272.64 yd2
231.68 yd2
190.72 yd2
136.32 yd2
the closest answer choice to this value is 372.32 yd2.
How to solve the question?
The given shape is a trapezoid, where the two parallel sides are the base and the top, and the height is the perpendicular distance between them. We can divide this trapezoid into a rectangle and a right triangle, as shown below:
A (bottom B (bottom
left vertex) right vertex)
We can find the length of the top side by adding the portions given on each side of the perpendicular, as follows:
top side = 6.4 yards + 14.9 yards = 21.3 yards (same as the base)
The area of the rectangle (ABCD) is the product of the base (21.3 yards) and the height (12.8 yards):
area of rectangle = 21.3 yards * 12.8 yards = 272.64 square yards
The area of the right triangle (BCD) is half the product of the height (12.8 yards) and the difference between the base and the top (21.3 yards - 6.4 yards = 14.9 yards):
area of triangle = 0.5 * 12.8 yards * 14.9 yards = 95.36 square yards
Therefore, the total area of the figure is the sum of the area of the rectangle and the area of the triangle:
total area = 272.64 square yards + 95.36 square yards = 368 square yards
Therefore, the closest answer choice to this value is 372.32 yd2.
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Solve for x 1/2x +1/3 = 3/4
Answer:
x = 5/6
Step-by-step explanation:
Combine multiplied terms into a single fraction, Multiply by 1, Find common denominator, Combine fractions with common denominator, Multiply all terms by the same value to eliminate fraction denominators, Cancel multiplied terms that are in the denominator, DistributeMultiply the numbers, Subtract from both sides, and then Simplify the expression.
PLEASE DONT GNORE!!M BEGGNG!!
Riley conducted a survey to see which is the most favorite subject among the students in her grade. She randomly chose to survey the first 53 students who entered the gym. She has a total of 424 students in her grade. What is true about the number of students who chose art??
____________students chose art as their favorite subject.
According to the table, the complete sentence would be: 96 students chose art as their favorite subject.
How to complete the sentence correctly?To complete the sentences correctly we must read the information and analyze the table. Once we have done these procedures we can establish how many students chose each of the subjects as their favorite. According to the above, the sentence would be as follows:
96 students chose art as their favorite subject.
How do we know the number of students who chose arts?According to Riley's survey, 12 out of 53 students chose art as their favorite. We then divide the total number of students (424) by the sample size (53) and multiply the number of students who chose art in the sample by the result of the division.
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Trigonometry review applications
I need help with 15-18
The angle of elevation is the angle between the horizontal line of sight and an upward direction to an object or point.
What is angle of elevation?The angle of elevation is often used in trigonometry and geometry to solve problems involving distances and heights.
1) Cos x = 16/27
x = Cos-1(16/27)
= 54 degrees
2)Sin x = 4/19
x = Sin-1(4/19)
x = 12 degrees
3) Tan 34 = x/8
x = 8 Tan 34
= 5 feet
4) Tan 61 = 166/5.5 + x
1.8(5.5 + x) = 166
9.9 + 1.8x = 166
x = 87 feet
Height of the statue = 5.5 + 87 = 92.5 feet
5) Tan 46 = x/35
x = 35tan 46
x = 36 feet
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The diagram shows a triangle OPQ and a circle with centre O.
The points P and R lie on the circumference of the circle.
The radius of the circle is 6 cm.
The length QR is 14 cm.
The area of triangle OPQ is 25 cm².
Calculate the area of the sector OPR.
The area of the sector OPR is approximately 5.20 cm².
What is an area?
First, we need to find the length of PR. Since O is the center of the circle, we know that OP and OR are both 6 cm long (the radius of the circle). By the triangle inequality, we have:
PR < OP + OR = 6 + 6 = 12
Since QR = 14, we have:
PR > QR - OP - OR = 14 - 6 - 6 = 2
Therefore, 2 cm < PR < 12 cm.
Next, we can use the formula for the area of a sector of a circle:
A = (θ/360)πr²
where A is the area of the sector, θ is the central angle of the sector (in degrees), and r is the radius of the circle.
To find the central angle θ, we can use the law of cosines:
(PR)² = (OP)² + (OR)² - 2(OP)(OR)cos(θ)
Substituting in the known values, we get:
(PR)² = 6² + 6² - 2(6)(6)cos(θ)
(PR)² = 72 - 72cos(θ)
cos(θ) = (72 - (PR)²)/72
Using the known values, we have:
cos(θ) = (72 - (PR)²)/72 = (72 - x²)/72
where x is the length of PR.
Since OPQ is a triangle, we know its area:
25 = (1/2) base × height
25 = (1/2) QR × OP
25 = (1/2) (14) × 6
25 = 42
Therefore, the height of triangle OPQ is:
height = (2)(25)/QR = (2)(25)/14 = 25/7
The height of the triangle is also the distance from O to the line PQ, which is also the distance from O to the chord PR. Therefore, the area of sector OPR can be calculated as follows:
A = (θ/360)πr² = (θ/360)π(6)²
A = (θ/360)(36π) = (θ/10)π
where θ is the central angle of the sector in degrees. To find θ, we can use the formula:
sin(θ/2) = (PR/2)/r = x/6
Substituting in the known values, we get:
sin(θ/2) = x/6
θ/2 = [tex]sin^{-1}[/tex](x/6)
θ = 2[tex]sin^{-1}[/tex](x/6)
Finally, substituting this value of θ into the formula for the area of the sector, we get:
A = (θ/10)π = [2[tex]sin^{-1}[/tex](x/6)]/10 * π
To find the value of x that gives the area of the sector, we can use trial and error or a numerical solver. Using a calculator, we find that x ≈ 5.5 cm gives an area of the sector of:
A ≈ 5.20 cm²
Therefore, the area of the sector OPR is approximately 5.20 cm².
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locate the absolute extrema of the function
on the closed interval
The function f(x) = 3x² - 3x has absolute extrema at (-1, -5/2)
What is the absolute extrema of the function on the closed interval?To find the absolute extrema of the function f(x) = x³ - 3/2x² on the closed interval [-1, 2], we need to first find the critical points of the function in the interval and evaluate the function at those points as well as at the endpoints of the interval.
To find the critical points, we need to find where the derivative of the function is equal to zero or does not exist. The derivative of f(x) is:
f'(x) = 3x² - 3x
Setting f'(x) = 0, we get:
3x² - 3x = 0
3x(x - 1) = 0
x = 0 or x = 1
We also need to check if there are any values of x where the derivative does not exist. However, since the derivative is a polynomial function, it exists for all real values of x.
The absolute extrema is at (-1, -5/2)
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Write the equation for a circle with centre (-15;3√7) and an area of 2π in standard form
An equation for a circle with centre (-15, 3√7) and an area of 2π in standard form is (x + 15)² + (y - 3√7)² = 2.
What is the equation of a circle?In Mathematics and Geometry, the standard form of the equation of a circle is represented by the following mathematical equation;
(x - h)² + (y - k)² = r²
Where:
h and k represents the coordinates at the center of a circle.r represents the radius of a circle.For the radius, we have:
Area of a circle = πr²
2π = πr²
r = √2
By substituting the given parameters into the equation of a circle formula, we have the following;
(x - h)² + (y - k)² = r²
(x - (-15))² + (y - 3√7)² = (√2)²
(x + 15)² + (y - 3√7)² = 2.
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Find the surface area of a cylinder with a height of 7in and a base radius of 2in . Use the value 3.14 for π, , and do not do any rounding. Be sure to include the correct unit.
Answer:
Step-by-step explanation:
Find the surface area of a cylinder with a height of 7in and a bass radius of 2in. Use the value 3.14 for π, , and do not do any rounding.
A=2πrh+2πr2=2·π·2·7+2·π·2²=
not rounded 113.09734
Rounded 113.1
At the mall, buying a pair of shoes and buying a book are independent events. The probability that a shopper buys shoes is 0.15. The probabitity that a shopper buys a book is 0.10 what is the probability that shoppers buys shows and a book?
Answer:The probability that a shopper buys shoes and a book is 0.015
Step-by-step explanation:
the answer choices are a. 5599ft B.8049 ft C.12822ft D.16098ft
Option B is the correct option for the total area of the shape which is approximate 8049 ft².
Define the term Isosceles triangle?An isosceles triangle is a polygon with three sides, where two of the sides have equal length.
Suppose the equal sides of Isosceles triangle is 'a',
so we can say that by Isosceles triangle rule: 70 = a√2
or side of Isosceles triangle (a) = 35√2 ft (by Pythagoras theorem)
Area of isosceles triangle (A₁) = [tex]\frac{1}{2}[/tex] × (Side of Isosceles triangle)²
= [tex]\frac{1}{2}[/tex] × (35√2)² = 1225 ft²
Area of two square (A₂) = 2 × a × a
= 2 × 35√2 × 35√2 = 4900 ft²
Area of quadrant circle (A₃) = (πr²)/4
= 3.14 × (35√2)² × (1/4) = 1923.25 ft²
Total area of the shape = A₁ + A₂ + A₃
= 1225 + 4900 + 1923.25 = 8048.25 ft²
Therefore, the total area of the shape is approximate 8049 ft²
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A database system assigns 32 character id to each record where each character is either a number from 0 to 9 or a letter from a to f assume that each number or letter being selected equally likely find the probability that at least 20 characters in the ID are numbers round your answer to three decimal places
This is a binomial distribution problem with the following parameters:
Number of trials: n = 32Probability of success: p = probability that a character is a number = 10/16 = 5/8Probability of failure: q = 1 - p = probability that a character is a letter = 6/16 = 3/8We want to find the probability that at least 20 characters are numbers. We can use the complement rule and find the probability that fewer than 20 characters are numbers, and subtract that from 1:
P(at least 20 numbers) = 1 - P(fewer than 20 numbers)
Using the binomial probability formula, we have:
P(fewer than 20 numbers) = Σ[k=0 to 19] C(n,k) * p^k * q^(n-k)
where C(n,k) is the binomial coefficient "n choose k". This can be calculated using a calculator or software that has a binomial probability function. For example, in Python, we can use the scipy.stats.binom.cdf() function:
from scipy.stats import binom
n = 32
p = 5/8
q = 3/8
prob_fewer_than_20 = binom.cdf(19, n, p)
This gives prob_fewer_than_20 = 0.04903110366420758.
Therefore,
P(at least 20 numbers) = 1 - 0.04903110366420758 = 0.9509688963357924
Rounding to three decimal places, the answer is 0.951.
Which is the largest angle?
A4
OC
B
5
Cannot tell
OA
с
7
6
B
Drag the tiles to the correct boxes to complete the pairs.
Match each inequality to the number line that represents its solution.
>-4
-752 > 225
<-31/0
-16/3
The answer of the given question based on inequality is (1) D , (2) B . (3) A , (4) C
What is Number line?A number line is a visual representation of the real numbers in a linear format. It is a straight line that is divided into equal segments or intervals, each of which represents a specific value on the number scale.
Number lines are usually oriented horizontally, with negative numbers to the left of zero and positive numbers to the right of zero. The distance between each point on the line is usually consistent, which means that the scale is evenly spaced.
For the first inequality, 7x/9 > -14/3, we can start by multiplying both sides by 9 to eliminate the fraction:
7x > -42
x > -6
So the solution to this inequality is x > -6, which means that all values of x greater than -6 satisfy the inequality.
For the second inequality, -75x/4 > 225/2, we can start by multiplying both sides by -4 to eliminate the fraction and flip the inequality:
75x < -450
x < -6
However, we need to remember to flip the inequality back since we multiplied both sides by a negative number:
x > 6
So the solution to this inequality is x > 6, which means that all values of x greater than 6 satisfy the inequality.
For the third inequality, x/4 <= -3/2, we can start by multiplying both sides by 4 to eliminate the fraction:
x <= -6
So the solution to this inequality is x <= -6, which means that all values of x less than or equal to -6 satisfy the inequality.
For the fourth inequality, 2x/3 > -16/3, we can start by multiplying both sides by 3 to eliminate the fraction:
2x > -16
x > -8
So the solution to this inequality is x > -8, which means that all values of x greater than -8 satisfy the inequality.
Now, let's match each inequality to the number line that represents its solution:
The first inequality, 7x/9 > -14/3, corresponds to the number line with an open circle at -6 and an arrow pointing to the right, indicating that all values of x greater than -6 satisfy the inequality.
The second inequality, -75x/4 > 225/2, corresponds to the number line with an open circle at 6 and an arrow pointing to the left, indicating that all values of x less than 6 satisfy the inequality.
The third inequality, x/4 <= -3/2, corresponds to the number line with a closed circle at -6 and an arrow pointing to the left, indicating that all values of x less than or equal to -6 satisfy the inequality.
The fourth inequality, 2x/3 > -16/3, corresponds to the number line with an open circle at -8 and an arrow pointing to the right, indicating that all values of x greater than -8 satisfy the inequality.
So the correct pairs are:
7x/9 > -14/3: ( )-------------●--->
-75x/4 > 225/2: <---●-------------( )
x/4 <= -3/2: [ ●]--------------<--
2x/3 > -16/3: ( )-------------●--->
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Find the value of r
18-2r
Answer:
27 18*3=2*r18/2*3=r9*3=rr=27
Step-by-step explanation:
which is equivalent to (3/125)*?
125 1/3×
125 1/3X
125 3x
125 [1/3]×
The answer is (B) 125 1/3×, which is equivalent to (3/125) times approximately 18.048.
What do you mean by Equivalent fraction?Equivalent fractions are fractions that have the same value but are written in different forms. They represent the same portion of a whole or a set, but their numerators and denominators may have different values.To find equivalent fractions, you can multiply or divide both the numerator and denominator of a fraction by the same number. This does not change the value of the fraction, but it changes its form.
The expression is (3/125) times something, but the value of that something is missing.
To solve the problem, we can simplify the expression (3/125) as a fraction in its lowest terms:
(3/125) = (3/5³)
Now, let's look at each of the answer choices:
125
If we multiply (3/5³) by 125, we get:
(3/5^3) * 125 = 3/5
Therefore, 125 is not equivalent to (3/125) times something.
1/3 × 125
If we multiply (3/5³) by (1/3 × 125), we get:
(3/5^3) * (1/3 × 125) = 1/5
Therefore, 1/3 × 125 is not equivalent to (3/125) times something.
125 1/3 ×
If we interpret "125 1/3 ×" as 125 and one-third multiplied by something, then we can write it as a mixed number fraction:
125 1/3 = 376/3
If we multiply (3/5³) by 376/3, we get:
(3/5³) ×(376/3) = 2256/125 = 18.048
Therefore, 125 1/3 × is equivalent to (3/125) times approximately 18.048.
125× 3x
If we interpret "125 3x" as 125 multiplied by 3 times something, then we can write it as:
125 ×3x = 375x
Therefore, 125 3x is not equivalent to (3/125) times something.
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Write the following as on logarithm
2 ln(5x) − 3 ln(2x) + 7 log2 (8x)
ln[(5x)² × (2x)⁻³ × (8x)⁷] . The logarithm expression is written in the form of ln(x) which is logarithm to the base e. The expression contains log2(x) which is logarithm to the base 2.
What is logarithm expression?The base number is the number that is raised to a certain power, the exponent is the power that the base number is raised to, and the logarithmic function is the equation which is used to calculate the result of the base number and the exponent.
The given expression can be written as a logarithm as follows:
ln[(5x)² × (2x)⁻³ × (8x)⁷]
This can be simplified to
2ln(5x) - 3ln(2x) + 7log2(8x)
The logarithm expression is written in the form of ln(x) which is logarithm to the base e. The expression contains log2(x) which is logarithm to the base 2.
The logarithm expression can be used to simplify complex equations and calculations, and it can also be used to solve for a particular variable.
This expression can be used to solve for x if the other values are known. The value of x can be calculated by taking the antilogarithm of each term and then solving the equation.
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A block of wood of mass 150.5g is 6.0cm long 4.2cm thick and 8.6cm high. The density of glass in kg/m3
density = 693.79 kg/[tex]m^3[/tex] (approx)
How to calculate density?The density of the block of wood can be calculated using the formula:
density = mass / volume
To find the volume of the block of wood, we need to multiply its length, width, and height:
volume = length x width x height
volume = 6.0 cm x 4.2 cm x 8.6 cm
volume = 217.08 cm^3
We need to convert the volume to cubic meters and the mass to kilograms to use the density of glass, which is typically given in kg/m^3:
volume = 217.08 cm^3 = 0.00021708 m^3
mass = 150.5 g = 0.1505 kg
Now we can calculate the density of the block of wood:
density = mass / volume
density = 0.1505 kg / 0.00021708 [tex]m^3[/tex]
density = 693.79 kg/[tex]m^3[/tex] (approx)
Keep in mind that the density of wood varies depending on its moisture content and type, but it is typically lower than that of glass, which is between 2500 and 3000 kg/[tex]m^3[/tex].
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The population of Medina, Ohio is currently 26,190 people. The population is predicted to grow at a rate of 3.7% per year. What will the population of Mediana be in 7.3 years? (round your answer to the neareat hundreth)
a.) 43210.82
b.) 87896.05
c.) 34144.47
d.) 50369.13
The population of Medina, Ohio will be approximately 34,052.89 people in 7.3 years.
What do you mean by Percentage?A number can be expressed as a fraction of 100 using a percentage. It is represented by the number %.
A decimal or fraction can be multiplied by 100 to become a percentage. For instance, multiplying 0.75 (a decimal) by 100 yields 75% when converted to a percentage. The same can be done to convert 3/4 (a fraction) to a percentage by dividing 3 by 4 to get 0.75, then multiplying that number by 100 to get 75%.
To calculate the population of Medina, Ohio in 7.3 years, we can use the formula:
Population after n years = Population before ×(1 + r/100)²
where r is the annual growth rate and n is the number of years.
Substituting the given values, we get:
Population after 7.3 years = 26,190 × (1 + 3.7/100)^7.3
Population after 7.3 years = 26,190 * 1.037^7.3
Population after 7.3 years = 26,190 * 1.301
Population after 7.3 years = 34,052.9
Rounding to the nearest hundredth, we get:
Population after 7.3 years = 34,052.90 ≈ 34,052.89
Therefore, the population of Medina, Ohio will be approximately 34,052.89 people in 7.3 years.
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The radius of a spherical balloon is increasing at a rate of 2 centimeters per minute. How fast is the surface area changing when the radius is 10 centimeters?
At a rate οf 160 cm per minute, the surface area is changing.
What is the area?A twο-dimensiοnal figure's area is the amοunt οf space it takes up. In οther terms, it is the amοunt that cοunts the number οf unit squares that span a clοsed figure's surface.
One can calculate a shape's area by cοmparing it tο squares οf a specific size. The Internatiοnal System οf Units' standard unit οf area is the square metre (abbreviated as m2), which measures the surface area οf a square with sides that are οne metre lοng (SI).
Surface Area οf Sphere (S)= 4πr²-------(1)]
Given: dr/dt = 2 cm/minute, r= 10 cm
Differentiating bοth sides with respect tο 't', we get
dS/dt = 4π * 2*r* dr/dt
dS/dt = 4π * 2*10* 2 = 160π cm/minute
The surface area is changing at the rate οf 160π cm/minute
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Another example would be your paycheck. You earn $13 an hour plus time-and-a-half overtime for anything over 40 hours. One week you worked 46 hours and the next week you worked 51 hours. What would your gross pay be for that two-week period? Thought question: Using that pay period as an example, would you rather have a pay raise of $15 an hour but no overtime pay, or keep your current rate and take the overtime?
Gretchen is a famous chef taking part in a celebrity cooking contest. Contestants earn scores between 1 - 10, with 10 being perfect. There are four categories and each category is weighted differently. The judges combined their scores and the results are shown in the table below.
Gretchen's final score, out of 10, is 8.35 based on weighted averages of scores in four categories.
How to calculate Gretchen's final score?To calculate Gretchen's final score, we need to calculate the weighted average of her scores in each category.
The weight of each category is given, so we can calculate the weighted score for each category by multiplying the weight by the score.
For Taste, the weighted score is 0.30 * 8.6 = 2.58
For Presentation, the weighted score is 0.35 * 9.8 = 3.43
For Use of Ingredients, the weighted score is 0.25 * 7.7 = 1.93
For Practicality, the weighted score is 0.10 * 4.1 = 0.41
To find the final score, we add up the weighted scores for all categories:
2.58 + 3.43 + 1.93 + 0.41 = 8.35
Therefore, Gretchen's final score is 8.35 out of 10.
The question is incomplete, below is the complete question given -
Gretchen is a celebrity chef competing in a celebrity cooking competition. Contestants receive ratings ranging from 1 to 10, with 10 being the highest. There are four categories, each with its own weighting. The judges' scores were added together, and the results are presented in the table below. What is Gretchen's final score, out of 10? Do not round.
Table -
Category Weight Score
Taste 30% 8.6
Presentation 35% 9.8
Use of Ingredients 25% 7.7
Practicality 10% 4.1
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Use the counting principle to determine the number of elements in the sample space. The possible ways to complete a multiple-choice test consisting of 18 questions, with each question having four possible answers (a, b, c, or d).
The ___ is the average of the sum of the squared differences of the mean from each element in a set of numerical data.
Answer:
The term that completes the sentence is "variance".
Step-by-step explanation:
In statistics, variance is a measure of how spread out a set of numerical data is. It is calculated by finding the average of the sum of the squared differences of each element in the set from the mean of the set. The formula for variance is:
Variance = (Σ(x - μ)²) / n
where Σ is the sum, x is each element in the set, μ is the mean of the set, and n is the number of elements in the set.