Question

Select the correct answer from each drop-down menu. Nick bought apples at a farmers market where 5 apples cost $4. 45. If Nick bought 7 apples, he paid $. If Nick paid $9. 79 for some apples, he bought

apples.

Answers

Answer 1

Nick bought 11 apples for $9.79.

Nick paid $6.23 for 7 apples, and he bought 9 apples for $9.79.

Nick bought apples at a farmers market where 5 apples cost $4. 45. If Nick bought 7 apples, he paid $. To find the cost of one apple, we divide $4.45 by 5, which gives us $0.89 per apple.

For 7 apples, we multiply $0.89 by 7, which gives us $6.23.

To find the number of apples Nick bought for $9.79, we set up a proportion:

5 apples/$4.45 = x apples/$9.79

Solving for x, we get x = (9.79 × 5) / 4.45 ≈ 11

Therefore, Nick bought 11 apples for $9.79.

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Related Questions

If one-quart bottles of apple juice have weights that are normally distributed with a mean of 64 ounces and a standard ceviation of3 ounces. What nervent of
bottles would be expected to have less than 58 ounces?

Answers

Approximately 2.28% of the bottles would be expected to have less than 58 ounces.

To determine the proportion (or percentage) of bottles expected to have less than 58 ounces, we need to calculate the z-score and then use the standard normal distribution table.

First, let's calculate the z-score using the formula:

z = (x - μ) / σ

where:

x = 58 ounces (desired value)μ = 64 ounces (mean)σ = 3 ounces (standard deviation)

z = (58 - 64) / 3 = -2

Next, we need to find the corresponding area under the standard normal curve for a z-score of -2.

By referring to a standard normal distribution table or using a calculator, we can find that the area to the left of -2 is approximately 0.0228.

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Consider the following. g(x) = 4x2 - 5; h(x) = 1.6% - (a) Write the product function. f(x) = x (b) Write the rate-of-change function. f'(x) = =

Answers

(a) The product function would be f(x) * g(x) = x(4x^2 - 5) = 4x^3 - 5x.
(b) To find the rate-of-change function, we need to take the derivative of the product function. So, f'(x) = d/dx (4x^3 - 5x) = 12x^2 - 5. This is the rate-of-change function for the product of f(x) and g(x).


Let's define the functions and find the product function and the rate-of-change function.

Given:
g(x) = 4x^2 - 5
f(x) = x

(a) Product function:
To find the product function, we need to multiply g(x) and f(x) together.

Product function = f(x) * g(x) = x * (4x^2 - 5)

Product function = 4x^3 - 5x

(b) Rate-of-change function:
To find the rate-of-change function, we need to find the derivative of the product function with respect to x.

f'(x) = d(4x^3 - 5x) / dx

Using the power rule, we get:

f'(x) = 12x^2 - 5

So, the rate-of-change function is f'(x) = 12x^2 - 5.

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a pair of 6 sided dice are tossed. what is the probability that at least one of the dice has a value greater than or equal to 5?answer

Answers

The probability that at least one of the dice has a value greater than or equal to 5 is 5/9. The probability that at least one of the dice has a value greater than or equal to 5 can be determined by calculating the probability of the complementary event and subtracting it from 1.

In this case, the complementary event is that both dice have a value less than 5. Since each die has six sides, and four of those sides have values less than 5, the probability of a single die having a value less than 5 is 4/6 or 2/3. The probability of both dice having a value less than 5 is then (2/3) * (2/3) = 4/9. Therefore, the probability of at least one die having a value greater than or equal to 5 is 1 - 4/9 = 5/9.

To calculate the probability that at least one of the dice has a value greater than or equal to 5, we can first determine the probability of the complementary event, which is that both dice have a value less than 5. Each die has six sides, so the probability of a single die having a value less than 5 is 4 out of 6, or 4/6, which simplifies to 2/3.

Since we are dealing with two dice, we need to consider the probability of both dice having a value less than 5. We can calculate this by multiplying the probability of one die having a value less than 5 by itself: (2/3) * (2/3) = 4/9.

To find the probability of at least one die having a value greater than or equal to 5, we subtract the probability of the complementary event from 1. So, the probability is 1 - 4/9 = 5/9.

Therefore, the probability that at least one of the dice has a value greater than or equal to 5 is 5/9.

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the first bike, but spent 5 hours on the second. They have 6 more bikes to do. Determine approximately how much time will be (was) required for: a) The 1st unit = hours (round your response to two decimal places). b) The 8th unit = hours (round your response to two decimal places). c) The total amount of hours to build the 8 units = hours (round your response to two decimal places).

Answers

The time required for the first unit is "x" hours, the time required for the eighth unit is "x + 35" hours, and the total amount of time required for building the eight units is "8x + 140" hours.

To determine the approximate amount of time required for building the remaining bikes, we need to consider the time spent on the first and second bikes as well as the number of remaining bikes. Let's denote the time required for building the first bike as "x" hours and the time required for building the second bike as "5" hours.

(a) To find the approximate time required for building the first unit, we already know that "x" hours spent on it.

(b) For the eighth unit, we can observe that a pattern is emerging. The time required for each unit is increasing by 5 hours. Therefore, for the eighth unit, we can calculate the time as follows:

Time for the eighth unit = Time for the first unit + (7 * 5) hours = x + 35 hours.

(c) To find the total amount of time required for building the eight units, we need to sum up the time required for each unit. Since each subsequent unit takes 5 hours longer than the previous one, we can use the arithmetic series formula to calculate the sum:

Total time for eight units = (Number of units / 2) * (Time for the first unit + Time for the last unit)

                            = (8 / 2) * (x + (x + 35))

                            = 4 * (2x + 35)

                            = 8x + 140 hours.

In summary, the time required for the first unit is "x" hours, the time required for the eighth unit is "x + 35" hours, and the total amount of time required for building the eight units is "8x + 140" hours.

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Find the distance represented by 4.9 inches if 1 inch = 50 miles.
O A. 4.9 miles
B. 49 miles
C. 209 miles
OD. 245 miles
O E. none of these

Answers

Answer:

E. none of these

Step-by-step explanation:

4.9 inches = 7.73359e-5 miles

I need help what is this answer Yesterday, it rained for 335 minutes. The day before that it rained for 5 hours and 10 minutes. On which day did it rain for a longer period of time?

Answers

Answer: Yesterday it rained longer

335 / 60 = Hours

335 minutes

= 5 7/12 hours

≈ 5.58333 hours

335 minutes

= 5 hours & 35 minutes

Hope it helps and have a good day! (:^w^:)

Use the number line to find the difference of 4 1/2-8

Answers

Using the number line, the difference between 4 1/2 and 8 will come to -31/2.

What is a number line?

A number line is a depiction of a graded straight line that serves as a visual representation of real numbers in primary mathematics. Every point on a number line is presumed to be a real number, and every real number is assumed to be a point.

Subtraction on a number line makes it much easier to subtract smaller values. When subtracting numbers from a number line, we must leap (move) to the left side of the number line.

Thus, moving to the left, 8 times from 4.5 will help us arrive at -3.5. See attached Number line.

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Use the number line to find the difference of 4 1/2-8

What is the volume of a cylinder with a height of 7.1 ft and a base with a diameter of 12.8 ft, to the nearest tenth of a cubic foot?

Answers

Answer:

V=π(d

2)2h=π·(12.8

2)2·7.1≈913.62541ft³ Step-by-step explanation: because i said so

Shapes A and B are similar. a) Calculate the scale factor from shape A to shape B. b) Find the value of t. Give each answer as an integer or as a fraction in its simplest form. 5 cm A 7 cm 15 cm 4 cm B tcm 12 cm Not drawn accurately​

Answers

a) The scale factor from shape A to shape B is given as follows: 4/5.

b) The value of t is given as follows: t = 5.6.

What are similar triangles?

Similar triangles are triangles that share these two features listed as follows:

Congruent angle measures, as both triangles have the same angle measures.Proportional side lengths, which helps us find the missing side lengths.

The concepts relating to similar shapes shape can be extended to any, hence the proportional relationship is given as follows:

5/4 = 7/t = 15/12.

Hence the value of t is obtained as follows:

5/4 = 7/t

5t = 28

t = 28/5

t = 5.6.

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Which value of a from the set {16, 18, 20, 22} makes the equation 2(42 - a) = 48 true? A. 16 B. 18 C. 20 D. 22

Answers

Answer:

18

Step-by-step explanation:

We are to determine the value of a

to do this we have to make a the subject of the formula. this can be achieved by taking the following steps

divide both sides of the equation -  2(42 - a) = 48 - by 2

42 - a = 24

take a to the right hand side and bring 24 to the left hand side

a = 42 - 24

a = 18

Not sure what the answer is. Need help.


A collection of paired data consists of the number of years that students have studied Spanish and their scores on a Spanish language proficiency test. A computer program was used to obtain the least squares linear regression line and the computer output is shown below. Along with the paired sample data, the program was also given an x value of 2 (years of study) to be used for predicting test score.

Equation: y = mx + b

Statistics:

r2 = 0.83
r = 0.91
Parameters:

m = 10.90
b = 31.55
Answer the following questions based on the information given above.

Use the information in the display to find the value of the linear correlation coefficient r. Determine whether there is significant linear correlation between years of study and test scores. Use a significance level of 0.05. There are 10 pairs of data.

A. r = 0.91; There is significant linear correlation.

B. r = 0.83; There is significant linear correlation.

C. r = 0.91; There is no significant linear correlation

D. r = 0.83; There is no significant linear correlation.

Answers

A collection of paired data consists of the number of years that students have studied Spanish and their scores on a Spanish language proficiency test.  r = 0.91; There is a significant linear correlation. Option A

What is linear correlation coefficient r.?

Generally, The value of the linear correlation coefficient r is given in the display as 0.91. To determine whether there is significant linear correlation between years of study and test scores, we need to conduct a hypothesis test.

The null hypothesis for this test is that there is no linear correlation between years of study and test scores, and the alternative hypothesis is that there is linear correlation.

To test the null hypothesis, we can use the value of r and the sample size (10 pairs of data) to calculate a p-value. If the p-value is less than our significance level of 0.05, we can reject the null hypothesis and conclude that there is significant linear correlation between the variables.

Since r is given as 0.91 and the sample size is 10, we can conclude that there is significant linear correlation between years of study and test scores.

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Find the present value of $5,325 to be received in one period if the rate is 6.5%: Select one: a. 5,644 b. 5,671 c. 5,023 d. 5,000

Answers

The correct option of the given statement "The present value of $5,325 to be received in one period at a rate of 6.5%" is d. 5,000.

it can be found using the formula:

PV = FV/(1 + r),

where

PV is the present value,

FV is the future value,

and r is the interest rate expressed as a decimal.

Here, FV = $5,325 and r = 0.065 (6.5% expressed as a decimal).

Substituting these values into the formula gives:

PV = $5,325/(1 + 0.065)PV

    = $5,325/1.065PV

     ≈ $5,000

Therefore, the present value of $5,325 to be received in one period if the rate is 6.5% is approximately $5,000.

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The scores earned in a flower-growing competition are represented in the stem-and-leaf plot.



2 0, 1, 3, 5, 7
3 2, 5, 7, 9
4
5 1
6 5
Key: 2|7 means 27


What is the appropriate measure of variability for the data shown, and what is its value?
The IQR is the best measure of variability, and it equals 16.
The range is the best measure of variability, and it equals 45.
The IQR is the best measure of variability, and it equals 45.
The range is the best measure of variability, and it equals 16.

Answers

The appropriate measure of variability for the given data is the IQR, and its value is 16.

Based on the given stem-and-leaf plot, which represents the scores earned in a flower-growing competition, we can determine the appropriate measure of variability for the data.

The stem-and-leaf plot shows the individual scores, and to measure the spread or variability of the data, we have two commonly used measures: the range and the interquartile range (IQR).

The range is calculated by subtracting the smallest value from the largest value in the dataset. In this case, the smallest value is 20, and the largest value is 65. Therefore, the range is 65 - 20 = 45.

The interquartile range (IQR) is a measure of the spread of the middle 50% of the data. It is calculated by subtracting the first quartile (Q1) from the third quartile (Q3). Looking at the stem-and-leaf plot, we can identify the quartiles. The first quartile (Q1) is 25, and the third quartile (Q3) is 41. Therefore, the IQR is 41 - 25 = 16.

In this case, both the range and the IQR are measures of variability, but the IQR is generally preferred when there are potential outliers in the data. It focuses on the central portion of the dataset and is less affected by extreme values. Therefore, the appropriate measure of variability for the given data is the IQR, and its value is 16.

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Find the measurement of angle x.

Find the measurement of angle x.

Answers

The measure of angle x in the right triangle is approximately 14.6 degrees.

What is the measure of angle x?

The figure in the image is that of two right angles.

First, we determine the hypotenuse of the left-right angle.

Angle θ = 30 degrees

Adjacent to angle θ = 10 cm

Hypotenuse = ?

Using the trigonometric ratio.

cosine = adjacent / hypotenuse

cos( 30 ) = 10 / hypotenuse

hypotenuse = 10 / cos( 30 )

hypotenuse = \(\frac{20\sqrt{3} }{3}\)

Using the hypotenuse to solve for x in the adjoining right triangle:

Angle x =?

Adjacent to angle x = \(\frac{20\sqrt{3} }{3}\)

Opposite to angle x = 3

Using the trigonometric ratio.

tan( x ) = opposite / adjacent

tan( x ) = 3 / \(\frac{20\sqrt{3} }{3}\)

tan (x ) = \(\frac{3\sqrt{3} }{20}\)

Take the tan inverse

x = tan⁻¹(  \(\frac{3\sqrt{3} }{20}\) )

x = 14.6 degrees

Therefore, angle x measures 14.6 degrees.

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What is the y-intercept of y = -32?

A) (-3,-3)

B) (-3,0)

C) (0,-3)

D) (0,0)

Answers

D I hope this helps

Solve for x: 3(x - 5) = -9
PLEASE HELP MEEEE

Answers

Answer:

X=2

Step-by-step explanation:

X = 7
first you need to equivalent the expression that have equal bases then make the exponents equal that turned into x-5=2 and move all terms not containing x to the right side that’s makes x=7

I need help please, I will give brainliest to the first person that answers

I need help please, I will give brainliest to the first person that answers

Answers

Answer:

it is C

Step-by-step explanation:

what does most specifically describe? a. a minor arc b. a major arc c. a semicircle d. a chord

Answers

The term "most specifically" is used to indicate the option that is the most specific or narrowest in meaning among the choices is d. chord.

The term "most specifically" is used to indicate the option that is the most specific or narrowest in meaning among the choices. Let's examine each option in the context of geometry:

a. A minor arc: A minor arc is a portion of a circle that measures less than 180 degrees. It is not the most specific term because it encompasses a range of arc sizes smaller than a semicircle, but it does not provide a narrower definition than other options.

b. A major arc: A major arc is a portion of a circle that measures more than 180 degrees. Similar to a minor arc, it does not provide the narrowest definition among the options.

c. A semicircle: A semicircle is a half of a circle, dividing it into two equal halves. This option is more specific than both minor and major arcs because it refers to a precise geometric shape with a 180-degree angle. However, there is one more option left to consider.

d. A chord: A chord is a straight line segment that connects two points on a circle. It is the most specific option among the choices because it refers to a specific geometric element—a line segment—within a circle.

So, The option that most specifically describes a geometric concept is:d. a chord.

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In circle Y, the measure of arc CD is f radians. The length of diameter segment ED is 24.
What is the area of sector CYD in terms of f?

Answers

The area of the sector is 72f

How to determine the area of the sector?

The given parameters are:

Angle = f

Diameter = 24

Start by calculating the radius

r = Diameter/2

r = 24/2

r = 12

The area of the sector is

A = (θ/2) × r^2

So, we have

A = (f/2) * 12^2

Evaluate

A = 72f

Hence, the area of the sector is 72f

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Calculate the present value annuity of 5000per annum for 12years and interested being 4% per annually compounded annually

Answers

\(~~~~~~~~~~~~\underset{\textit{payments at the end of the period}}{\textit{Future Value of an ordinary annuity}}\\ \\\\ A=pymnt\left[ \cfrac{\left( 1+\frac{r}{n} \right)^{nt}-1}{\frac{r}{n}} \right] \\\\\\ ~~~~~~ \begin{cases} A=\textit{accumulated amount} \\ pymnt=\textit{periodic payments}\dotfill &\$5000\\ r=rate\to 4\%\to \frac{4}{100}\dotfill &0.04\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{annually, thus once} \end{array}\dotfill &1\\ t=years\dotfill &12 \end{cases}\)

\(A=5000\left[ \cfrac{\left( 1+\frac{0.04}{1} \right)^{1\cdot 12}-1}{\frac{0.04}{1}} \right]\implies A=5000\left( \cfrac{1.04^{12}~~ - ~~1}{0.04} \right) \\\\[-0.35em] ~\dotfill\\\\ ~\hfill A\approx 75129.03~\hfill\)

please help will mark brainliest

please help will mark brainliest

Answers

Answer:

A. (-4,2)

Step-by-step explanation:

the program committee of a bluegrass music festival must arrange 5 numbers for an evening performance. eight numbers are available. how many different arrangements of the evening performance are possible?

Answers

56 different arrangements are possible for the evening

Selections and combinations are synonyms. Combinations represent the choice of items from a predetermined group of items. We're not trying to arrange anything here. We're going to pick them. Out of a set of n objects, we count the number of unique r-selections or combinations. It is given by the formula ⁿCr. Utilizing the combinations formula, it is simple to determine how many distinct groups of r objects each may be created from the provided n unique objects.

Required numbers = 5

Numbers available = 8

The number of arrangements possible:

⁸C₅ = 56

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What is (-8) x (-2/3)

Answers

Answer:

16/3 or 5.3 recurring

Step-by-step explanation:

-8 times -2/3 is 16/3, and 16/3 is 5.3 recurring

fhe measures of the angles of a triangle are shown below. find the value of x.

fhe measures of the angles of a triangle are shown below. find the value of x.

Answers

The measure of three angles are : x, 60 & 100

Sum of all angles in a triangle is 180 degree

So, x + 60 + 100 = 180

x + 160 = 180

x = 180 -160

x = 20

Answer : x = 20

shows the current as a function of time through a 20-cm-long, 4.0-cm-diameter solenoid with 400 turns.

Answers

The current is constant over time as long as the magnetic field strength and other parameters remain constant.

The current through a solenoid can be calculated using the formula:

I = (B * A * N) / R

where I is the current, B is the magnetic field, A is the cross-sectional area of the solenoid, N is the number of turns, and R is the resistance of the solenoid.

Assuming that the solenoid is made of a material with negligible resistance, the resistance can be ignored and the formula reduces to:

I = (B * A * N) / R

The magnetic field inside the solenoid can be calculated using the formula:

B = (μ * N * I) / L

where μ is the permeability of free space, N is the number of turns, I is the current, and L is the length of the solenoid.

Assuming that the magnetic field is uniform across the cross-sectional area of the solenoid, the formula for current can be further simplified to:

I = (μ * A * N^2 * V) / (L * R)

where V is the volume of the solenoid.

Plugging in the given values for the solenoid (A = πr^2, r = 2.0 cm, N = 400, L = 20 cm) and assuming a magnetic field strength of 1 tesla, the current through the solenoid can be calculated to be approximately 0.63 A. The current is constant over time as long as the magnetic field strength and other parameters remain constant.

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please help! provide step by step, clear explaination! algebra 1 work. thanks

please help! provide step by step, clear explaination! algebra 1 work. thanks

Answers

A) H=2C-3
B) 201=3H+1.5C
C) 28=C and 53=H
please help! provide step by step, clear explaination! algebra 1 work. thanks

Solve the system, by elimination please show all the steps!
-2x+2y+3z=0
-2x-y+z=-3
2x+3y+3z=5

Answers

Answer:

x = 1 , y = 1 , z = 0

Step-by-step explanation:

Solve the following system:

{-2 x + 2 y + 3 z = 0 | (equation 1)

-2 x - y + z = -3 | (equation 2)

2 x + 3 y + 3 z = 5 | (equation 3)

Subtract equation 1 from equation 2:

{-(2 x) + 2 y + 3 z = 0 | (equation 1)

0 x - 3 y - 2 z = -3 | (equation 2)

2 x + 3 y + 3 z = 5 | (equation 3)

Multiply equation 2 by -1:

{-(2 x) + 2 y + 3 z = 0 | (equation 1)

0 x+3 y + 2 z = 3 | (equation 2)

2 x + 3 y + 3 z = 5 | (equation 3)

Add equation 1 to equation 3:

{-(2 x) + 2 y + 3 z = 0 | (equation 1)

0 x+3 y + 2 z = 3 | (equation 2)

0 x+5 y + 6 z = 5 | (equation 3)

Swap equation 2 with equation 3:

{-(2 x) + 2 y + 3 z = 0 | (equation 1)

0 x+5 y + 6 z = 5 | (equation 2)

0 x+3 y + 2 z = 3 | (equation 3)

Subtract 3/5 × (equation 2) from equation 3:

{-(2 x) + 2 y + 3 z = 0 | (equation 1)

0 x+5 y + 6 z = 5 | (equation 2)

0 x+0 y - (8 z)/5 = 0 | (equation 3)

Multiply equation 3 by 5/8:

{-(2 x) + 2 y + 3 z = 0 | (equation 1)

0 x+5 y + 6 z = 5 | (equation 2)

0 x+0 y - z = 0 | (equation 3)

Multiply equation 3 by -1:

{-(2 x) + 2 y + 3 z = 0 | (equation 1)

0 x+5 y + 6 z = 5 | (equation 2)

0 x+0 y+z = 0 | (equation 3)

Subtract 6 × (equation 3) from equation 2:

{-(2 x) + 2 y + 3 z = 0 | (equation 1)

0 x+5 y+0 z = 5 | (equation 2)

0 x+0 y+z = 0 | (equation 3)

Divide equation 2 by 5:

{-(2 x) + 2 y + 3 z = 0 | (equation 1)

0 x+y+0 z = 1 | (equation 2)

0 x+0 y+z = 0 | (equation 3)

Subtract 2 × (equation 2) from equation 1:

{-(2 x) + 0 y+3 z = -2 | (equation 1)

0 x+y+0 z = 1 | (equation 2)

0 x+0 y+z = 0 | (equation 3)

Subtract 3 × (equation 3) from equation 1:

{-(2 x)+0 y+0 z = -2 | (equation 1)

0 x+y+0 z = 1 | (equation 2)

0 x+0 y+z = 0 | (equation 3)

Divide equation 1 by -2:

{x+0 y+0 z = 1 | (equation 1)

0 x+y+0 z = 1 | (equation 2)

0 x+0 y+z = 0 | (equation 3)

Collect results:

Answer: {x = 1 , y = 1 , z = 0

Answer:

x= 1, y = 1, z=  0

Step-by-step explanation

-2x + 2y + 3z = 0

2x + 3y + 3z = 5

-2x - y + z = -3

2x + 3y + 3z = 5

(solving systems)

5y + 6z = 5

2y + 4z = 2

(rewriting)

z = 0

y = 1

-2x + 2 x 1 + 3 x 0

x=1

How many sides does a regular polygon have when each side is 30 degrees

Answers

The total number of sides of a regular polygon with each exterior angle of measure 30 degrees is equal to 12.

Let us consider 'n' be the number of sides of the regular polygon.

Let 'y' be the measure of each of the exterior angle of regular polygon.

y = 30 degrees

Measure of each of the exterior angle of regular polygon 'y'

= ( 360° ) / n

⇒ n = ( 360° / y )

Substitute the value we get,

⇒ n = ( 360° / 30° )

⇒ n = 12

Therefore, the number of sides of a regular polygon with each of the exterior angle 30 degrees is equal to 12.

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The above question is incomplete, the complete question is:

How many sides does a regular polygon have when each exterior angle measures 30 degrees?

The side of an equilateral triangle is 22. Find the exact length of the altitude.
Use the exact value, meaning leave your answer with a radical.
PLEASE HELP THE TEST IS DUE IN 5 MINS

Answers

Step-by-step explanation:

here's the answer to your question

The side of an equilateral triangle is 22. Find the exact length of the altitude.Use the exact value,

What happens to the t distribution as degrees of freedom increase? question 6 options: it approaches the uniform disribution it approaches the normal disribution it approaches the exponential disribution it approaches the binomial disribution

Answers

As the degrees of freedom increase, the t distribution b. approaches the normal distribution, which is a key assumption in many statistical tests. Understanding this relationship is important for making accurate statistical inferences and drawing valid conclusions from data.

The t distribution is a probability distribution that is commonly used in hypothesis testing. It is similar to the normal distribution but with heavier tails. As the degrees of freedom increase, the t distribution approaches the normal distribution. This means that the shape of the t distribution becomes more and more like the normal distribution as the sample size increases.
The reason for this is that the t distribution is based on the sample mean, which becomes more normally distributed as the sample size increases due to the central limit theorem. As the sample size increases, the standard error of the mean decreases, and the t distribution becomes less spread out and more peaked. This is why we use the t distribution instead of the normal distribution when we have a small sample size.

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