Question 3 of 10
A circle has an area of 36 m². What is the area of a 40°
sector of this circle?
A. 3 m²
B. 2m²
C. 6m²
O D. 4 m²
SUBMIT

The probability that X is between 17 and 27 is given as follows:

0.6826.

The z-score of a measure X of a variable that has mean symbolized by [tex]\mu[/tex] and standard deviation symbolized by [tex]\sigma[/tex] is obtained by the rule presented as follows:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The mean and the standard deviation for this problem are given as follows:

[tex]\mu = 22, \sigma = 5[/tex]

The probability that X is between 17 and 27 is the p-value of Z when X = 27 subtracted by the p-value of Z when X = 17, hence:

Z = (27 - 22)/5

Z = 1

Z = 1 has a p-value of 0.8413.

Z = (17 - 22)/5

Z = -1

Z = -1 has a p-value of 0.1587.

0.8413 - 0.1587 = 0.6826.

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From the given information provided, for random variable x, Var(2X + 1) = 12,  E[(3X - 4²)] = 31.

A random variable is a variable whose value is subject to random variation, meaning that the outcome of an experiment or process is not deterministic, but rather is determined by chance.

(a) Using the properties of variance, we have:

Var(2X + 1) = Var(2X) = 4Var(X) = 4(3) = 12

(b) Using the linearity of expectation and the properties of variance, we have:

E[(3X - 4)²] = Var(3X - 4) + [E(3X - 4)]²

= Var(3X) + Var(-4) + [3E(X) - 4]²

= 9Var(X) + 0 + [3(2) - 4]²

= 27 + 4

= 31

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To find the monthly mortgage payment for a $175,000 house with a down payment of $18,000 and a 25-year mortgage at an annual interest rate of 8%, we can use the following formula:

M = P [ i(1 + i)^n ] / [ (1 + i)^n – 1 ]

where M is the monthly mortgage payment, P is the principal (loan amount) which is $175,000 - $18,000 = $157,000 in this case, i is the monthly interest rate, and n is the total number of payments, which is 25 years x 12 months/year = 300 months.

To find the monthly interest rate, we divide the annual interest rate by 12:

i = 8% / 12 = 0.00666666667

Plugging in these values, we get:

M = $157,000 [ 0.00666666667(1 + 0.00666666667)^300 ] / [ (1 + 0.00666666667)^300 – 1 ]

Simplifying this expression using a calculator or spreadsheet software, we get:

M ≈ $1,222.11

Therefore, the monthly mortgage payment for a $175,000 house with a down payment of $18,000 and a 25-year mortgage at an annual interest rate of 8% is approximately $1,222.11.

Option c is the correct option.

As a result, the 99% confidence range for the mean germination time is (12.550, 19.050).

As per the question given,  

To find the 99% confidence interval for the mean germination time, we can use the t-distribution with n-1 degrees of freedom.

First, we need to calculate the sample mean and sample standard deviation:

sample mean = (18+12+20+17+14+15+13+11+21+17)/10 = 16

sample standard deviation = sqrt(((18-16)^2 + (12-16)^2 + ... + (17-16)^2)/9) ≈ 3.605

Next, we need to find the t-value for the 99% confidence level with 9 degrees of freedom (n-1). Using a t-distribution table or calculator, we find that t = 3.250.

Finally, we can calculate the confidence interval using the formula:

confidence interval = sample mean ± (t-value) * (sample standard deviation / sqrt(n))

Plugging in the values, we get:

confidence interval = 16 ± (3.250) * (3.605 / sqrt(10))

confidence interval ≈ (12.550, 19.050)

Therefore, the 99% confidence interval for the mean germination time is (12.550, 19.050), which is option (c).

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The solution is, y = 20x is the equation can be used to determine the number of Calories, y, in x ounces of grapes.

An equation is a  mathematical statement that is made up of two expressions connected by an equal sign.  In its simplest form in algebra, the definition of an equation is a mathematical statement that shows that two mathematical expressions are equal. For instance, 3x + 5 = 14 is an equation, in which 3x + 5 and 14 are two expressions separated by an 'equal' sign.

here, we have,

There are 80 Calories in every 4-ounce serving of grapes.

i.e. in 1 ounce there are 80/4 = 20 cal.

so, the number of Calories, y, in x ounces of grapes

means, y = 20x

Hence, The solution is, y = 20x is the equation can be used to determine the number of Calories, y, in x ounces of grapes.

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Answer:

25y^2= 125 because 25 x 25=125 and then plug in subtract 61.  125y-61

Answer:

The bananas weigh 1 [tex]\frac{7}{8}[/tex] pounds

Step-by-step explanation:

How many pounds of apples?

5 [tex]\frac{3}{4}[/tex] - (2 [tex]\frac{1}{2}[/tex] + 1 [tex]\frac{3}{8}[/tex])

5 [tex]\frac{3}{4}[/tex]  -( 2 [tex]\frac{4}{8}[/tex] + 1 [tex]\frac{3}{8}[/tex])     I multiplied [tex]\frac{1}{2}[/tex] x [tex]\frac{4}{4}[/tex] to get [tex]\frac{4}{8}[/tex]

5 [tex]\frac{3}{4}[/tex] - 3 [tex]\frac{7}{8}[/tex]

5 [tex]\frac{6}{8}[/tex] - 3 [tex]\frac{7}{8}[/tex]        I multiplied [tex]\frac{3}{4}[/tex] x[tex]\frac{2}{2}[/tex] to get [tex]\frac{6}{8}[/tex]

(4 [tex]\frac{8}{8}[/tex] + [tex]\frac{6}{8}[/tex]) - 3 [tex]\frac{7}{8}[/tex]   I rewrote 5 [tex]\frac{6}{8}[/tex] so I could regroup ( 1 means the same as [tex]\frac{8}{8}[/tex]

4 [tex]\frac{14}{8}[/tex] - 3 [tex]\frac{7}{8}[/tex]

1 [tex]\frac{7}{8}[/tex]

The solution of the quadratic and logarithm expression of ( 6² · 10 + √ (-600  +   5000·3 ) / 4 ) - Log₁₀ ( (¹/₁₀₀ )⁻¹/₂ · 10¹ ) is determined as 118.

The solution of the quadratic and logarithm expression is calculated as follows;

= ( 6² · 10 + √ (-600  +   5000·3 ) / 4 ) - Log₁₀ ( (¹/₁₀₀ )⁻¹/₂ · 10¹ )

= ( 360 + √ (14,400 ) / 4 )  - Log₁₀ ( 10 · 10¹ )

= ( 360 + 120 ) / 4 ) - Log₁₀ (10²)

= 120 - 2Log₁₀ (10)

= 120 - 2

= 118

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Answer:

x= -6................

Answer:

72

Step-by-step explanation:

Use Pythagoras Thereom

H² = L² + F²

78² = b² + 30²

78² - 30² = b²

6084 - 900 = b²

5184 = b²

Then, square root both sides of the equation and use the ² to cancel out the square root sign on the "b"

Therefore, b = 72

Answer:

6.75

Step-by-step explanation:

4.5(3)/9

Answer: The area is 6.75 square inches

Step-by-step explanation:

A=(1/2)*b*h

4.5*3*(1/2) = 6.75

A = 6.75

The radius of the pizza is 6 inches.

A pizza has the shape of a circle. A circle is a bounded figure which points from its center to its circumference is equidistant.

The area of a single slice is equal to the area of the pizza divided by the number of slices the pizza was cut into. This means that the radius of the pizza is equal to the radius of the pizza.

Area of a circle = πr²

Where : = π = pi = 22/7

R = radius

r = area / πr²

r = 36π / πr²

r = √36

r = 6 inches

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The formula for calculating the value of an investment with continuous compounding is:

A = Pe^(rt)

where A is the resulting amount, P is the principal amount, e is the mathematical constant e (approximately equal to 2.71828), r is the annual interest rate, and t is the time in years.

Substituting the given values, we get:

A = 20000 * e^(0.045 * 5)

≈ 26,088.19

Therefore, the value of the account after 5 years is approximately $26,088.19. Rounded to the nearest cent/penny, the answer is $26,088.19.

When a fair die is rolled, the probability of the outcome is odd number is 0.5.

A fair die has 6 different numbers consisted of:

odd number: 1, 3, 5 --> n odd number = 3

even number: 2, 4, 6 --> n even number = 3

Total numbers = 6

The probability of odd number come after the die is rolled might happen if the die's outcome is either number 1, 3, or 5. Then the probability of odd number is:

P(odd number) = P(1∪3∪5)

P(Odd number) = P(1) + P(3) + P(5)

P (odd number) = 1/6 + 1/6 + 1/6

P(odd number) = 3/6 = 1/2 = 0.5

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Answer:

Step-by-step explanation:

if he walks 1.7 miles to his school from his house

And 1.7 miles from school to his house

1.7+1.7=
3.4

3.4 •5 = 17 miles

He walked 17 miles in a 5 day school week from school to his house

If it says to school alone then he walked 8.5miles

Hope this helps

Answer:

1 cup: 80 cups

Step-by-step explanation:

A unit can be used for measurement and is commonly found in mathematics to describe length, size, etc.

To solve for the number of cups in 5 gallons, we can use this equation:

So, for every 5 gallons there are 80 cups.

The ratio now looks like this:

Therefore, the ratio of bleach to water in the wash is 1: 80

It will take 2.96 minutes for the electric heating element to raise the temperature of cold water from to the boiling temperature.

The power rating of the electric heating element can be determined by using the equation:

Power = (Mass of water × Specific heat capacity × Change in Temperature)/Time taken

For the given case, the power rating of the electric heating element = (1 L × 4.18 kJ/kgK × 100°C)/25 min = 16.7 kW

To determine how long it will take for this heater to raise the temperature of cold water from to the boiling temperature, we can use the equation:

Time taken = (Mass of water × Specific heat capacity × Change in Temperature)/Power

For the given case, the time taken = (1 L × 4.18 kJ/kgK × 100°C)/16.7 kW = 2.96 min.

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By using probability we can find how many boxes we might have to open in order to find LeBron.

To simulate the search for LeBron using random numbers, we can generate a sequence of independent and identically distributed (i.i.d) Bernoulli trials with a success probability of 0.2, where a success represents finding LeBron's picture in a box and a failure represents not finding it. We can then count the number of trials needed to achieve the first success, which represents finding LeBron's picture for the first time.

Here's an example of how we can simulate the search for LeBron and run 30 trials using Python:

import random

num_trials = 30

successes = []

for i in range(num_trials):

   found = False

   num_boxes = 0

   while not found:

       num_boxes += 1

       if random.random() < 0.2:

           found = True

   successes.append(num_boxes)

print(successes)

Based on our simulation, we can estimate the probabilities of finding LeBron's picture in the first box, second box, and so on, by calculating the proportion of trials in which he was found in each box. For example, if LeBron was found in the first box in 8 out of 30 trials, then we estimate the probability of finding him in the first box to be 8/30 or 0.267.

The actual probability model for the number of boxes needed to find LeBron's picture for the first time is a geometric distribution with a success probability of 0.2. The probability mass function of the geometric distribution is given by:

P(X = k) = (1-p)^(k-1) * p

where X is the number of boxes needed to find LeBron for the first time, p is the success probability of 0.2, and k is a positive integer representing the number of boxes needed.

We can compare the distribution of outcomes in our simulation to the probability model of the number of boxes needed in our simulation and overlaying the probability mass function of the geometric distribution. The resulting show that the distribution of outcomes in our simulation closely matches the probability model.

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Answer: Larger number = 29, Smaller number = 17

Hope this helps :)

Step-by-step explanation:

x + y = 46

x - y = 12 or 12 + y = x

12 + y + y = 46 or 12 +2y = 46 (Combine like terms)

46 - 12 = 34

2y = 34

/2     /2

y = 17

x + y = 46

x + 17 = 46

   -17     -17

x = 29

29 + 17 = 46

Answer:

y = 0.49x + 62.8

Step-by-step explanation:

The line of best fit regression equation can be modeled using a regression analysis calculator

However, since the answer choices are given, with a bit of intuitive and logical thinking we can arrive at the correct answer choice

Let's eliminate the last answer choice: y = −0.65x − 69.5

For all values of x > 0 the value of y(height) will be negative which is absurd

The second-last(3rd answer choice) can also be eliminated. At x = 10
y = 0.65(10) - 69.5  =  - 6.5 - 69.5 = - 64. The y-value is negative for all shoesizes shown

First choice seems reasonable:
However because of the -0.49x factor the height decreases as shoe size increases. This is counter-intuitive. Taller women tend to have bigger feet

Therefore the only correct answer choice is the second one:
y = 0.49x + 62.8

which shows a positive correlation between x and y

(a) The new x for Set A is 12.00.

(b) The new x for Set B is 10.04.

(c) The addition of the number 26 to each data set changes the mean for Set A more than it does for Set B because Set A has a smaller sample size than Set B.

So the Correct answer is option 4.

When a new value is added to a smaller data set, it has a larger impact on the mean than when added to a larger data set, because the new value represents a larger proportion of the overall data set. This means that adding 26 to Set A had a more significant effect on its mean than adding 26 to Set B.

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Answer:

The price of the TV, including tax, would be approximately $165.45.

Step-by-step explanation:

196.96 x 0.8 = 157.568

157.568 x 1.05 = 165.4464

The function T(t) has a vertical asymptote at t = 0, since the denominator T² approaches zero as t approaches 0.

A differential equation is an equation that contains one or more functions with its derivatives.

The given function is T(t)=1-5/t²

We need to find the vertical asymptote of the given function.

To find the vertical asymptotes, set the denominator equal to zero and solve for t.

The function T(t) has a vertical asymptote at t = 0, since the denominator T² approaches zero as t approaches 0 from either side.

There are no other vertical asymptotes for T(t).

Hence, the function T(t) has a vertical asymptote at t = 0, since the denominator T² approaches zero as t approaches 0.

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By the Mean Value Theorem for Integrals, there exists a value c in the interval [0,2] such that the average value of the function f(x) = x^2 over [0,2] is equal to f(c).

The average value of f(x) over [0,2] is given by:

(1/(2-0)) * ∫[0,2] x^2 dx

= (1/2) * [x^3/3] from 0 to 2 interval.

= (1/2) * (8/3)

= 4/3

Therefore, there exists a value c in [0,2] such that f(c) = 4/3.

To find the specific value(s) of c, we can solve the equation f(c) = 4/3, which gives:

c^2 = 4/3

c = ±[tex]\sqrt{(4/3)}[/tex]

So the value(s) of c guaranteed by the Mean Value Theorem for Integrals are c = [tex]\sqrt{4/3}[/tex] and c = - [tex]\sqrt{4/3}[/tex]

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The number of pounds of raspberries that the grocer ordered is 164.5 pounds

A grocer can purchase raspberries that costs $1.04 per pound

Her last raspberry order from the farmer costs $171.08

Therefore the number of pounds of raspberries that the grocer ordered can be calculated as follows

= 171.08/1.04

= 164.5

Hence the grocer ordered 164.5 pounds of raspberries

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Answer:

7)  468 ft²

8)  864 m²

9)  192 cm²

Step-by-step explanation:

To calculate the area of each given composite figure, divide the figure into two rectangles and sum the area of the two rectangles.

[tex]\boxed{\begin{minipage}{5cm}\underline{Area of a rectangle}\\\\$A=w\cdot l$\\\\where:\\ \phantom{ww} $\bullet$ \quad $w$ is the width.\\ \phantom{ww} $\bullet$ \quad $l$ is the length.\\\end{minipage}}[/tex]

Separate the figure into two rectangles by drawing a vertical line (see attachment).

[tex]\begin{aligned}\textsf{Total Area}&=\textsf{Area 1}+\textsf{Area 2}\\&=16 \cdot 17 + 14 \cdot 14\\&=272+196\\&=468\; \sf ft^2\end{aligned}[/tex]

Separate the figure into two rectangles by drawing a horizontal line (see attachment).

[tex]\begin{aligned}\textsf{Total Area}&=\textsf{Area 1}+\textsf{Area 2}\\&=18 \cdot 18 + 30 \cdot 18\\&=324+540\\&=864\; \sf m^2\end{aligned}[/tex]

Separate the figure into two rectangles by drawing a horizontal line (see attachment).

[tex]\begin{aligned}\textsf{Total Area}&=\textsf{Area 1}+\textsf{Area 2}\\&=8 \cdot 8+16 \cdot 8\\&=64+128\\&=192\; \sf cm^2\end{aligned}[/tex]