1. Name the geometric solid
associated with each situation.
a. a stack of 100 copies of the
same book
b. a stack of 100 tires, all with the
19 same radius no
c. a stack of 100 stop signs

Answer:

∠A = 48.2

Step-by-step explanation:

Cos^-1(6/9

Use the Cosine with the negative one because you are finding an angle. Then, because Cosine is adjacent/hypotenuse, 6 would be your adjacent side length to theta and 9 would be the hypotenuse as it is across from the right angle.

The probability of people who run red lights is

=0.465

Probability is the measure of the likelihood or chance that an event will occur.

Probability = Possible outcome of an event ÷ Total outcome

Total number of people asked if they had run a red light = number of people that responded 'yes' + number of people that responded 'no'

Total outcome = 348+400

Total outcome = 748

Possible outcome = number of people that responded yes = 394

The probability that if a person is chosen at random, they have run a red light in the last year will be

[tex]=\frac{348}{748}\\\\=0.465[/tex]

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Answer:

Step-by-step explanation:

The sketch is a right-angled triangle.

We can use Pythagoras' theorem.

[tex]z^{2} =x^{2} +y^{2}[/tex]

z=√(50^2+25^2)

z= 25√5

z=25*2.23

z=55.75

z≈56km

the distance between where he started the

journey=56km

tan(90-Θ)=25/50

cotΘ=1/2

tanΘ=2

Θ=[tex]tan^{-1} (2)[/tex]

bearing of his starting point from his end point[tex]tan^{-1} (2)[/tex]

a. Hypotheses are: [tex]\rm H_{0}:p=0.20,H_{a}:p > 0.20[/tex]

b. Z-statistics will be 2.47 and p-value = 0.0068

c. you should proceed with plans to develop and market the upgrade.

d. Confidence interval for population proportion will be (0.23, 0.45)

e. The populations are different because they are frοm different regiοns sο prefrences οf peοple may different.

Probability is a mathematical concept that measures the likelihood or chance of an event occurring. It is a number between 0 and 1, where 0 indicates that the event is impossible and 1 indicates that the event is certain.

a. Hypotheses are:

[tex]\rm H_{0}:p=0.20,H_{a}:p > 0.20[/tex]

b) Here we have following information:

[tex]\rm n=50, \hat{p}=\frac{17}{50}=0.34[/tex]

Standard deviation of the proportion is:

[tex]\rm \sigma=\sqrt{\frac{p\left ( 1-p \right )}{n}}=\sqrt{\frac{0.20\left ( 1-0.20 \right )}{50}}=0.0566[/tex]

Test statistics will be:

[tex]$ \rm z=\frac{\hat{p}-p}{\sigma}=\frac{0.34-0.20}{0.0566}=2.47[/tex]

Alternative hypothesis shows that the test is right tailed so p-value of the test is

[tex]\rm p-value = P(z > 2.47) = 1 - P(z \leq 2.47)=1-0.9932=0.0068[/tex]

c. Since p-value of the test is less than 0.05 so we reject the null hypothesis at 0.05 level of significance. So based on this sample, you should proceed with plans to develop and market the upgrade.

d. For 90% confidence interval [tex]\alpha[/tex] = 0.10 so critical value of z will be[tex]\rm z_{c}=z_{\alpha/2}=1.645[/tex]

Confidence interval for population proportion will be

[tex]\rm \hat{p}\pm z_{c}\sqrt{\frac{\hat{p}\left ( 1-\hat{p} \right )}{n}}=0.34\pm 1.645\sqrt{\frac{0.34\left (1-0.34 \right )}{50}}=0.34\pm 0.11 =(0.23, 0.45)[/tex]

e. The populations are different because they are frοm different regiοns sο prefrences οf peοple may different.

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There are 9 parts to the trail, and each part is the same length.  and hence each part of the trail is 0.2 kilometers long.

The following equation may be used to determine a rectangle's perimeter:

Perimeter is equal to 2 x (length + breadth).

where "length" denotes the rectangle's length and "width" denotes the rectangle's width. In order to account for both sides of the rectangle, we add the length and breadth together and multiply the result by 2, which is the distance around the outside of the rectangle.

The distance ran by Brurt is:

1.8 km ÷ 9 = 0.2 km

Hence, each part of the trail is 0.2 kilometers long.

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Answer: 384 cm cubed

Step-by-step explanation: The first thing you will do is 48 square centimeters times 8 cm. Since 48 is squared you have that 2 right above it. Your 8 technically has a 1 above it. So add the 2 and the 1, and you will get cubed. (AKA 3)

Answer:

A) The histogram is bimodal.

Answer:

To create a frequency distribution, we first need to determine the range of the data. The smallest measurement is 3.4 inches and the largest is 5.4 inches, so the range is 5.4 - 3.4 = 2 inches. To create 6 classes with a width of 0.4 inches, we divide the range by 0.4 and round up to the nearest integer:

Number of classes = (range / class width) rounded up = 2 / 0.4 = 5

So we will use 5 classes with a width of 0.4 inches each. The classes and their corresponding frequency counts are:

Class 1: 3.4 - 3.8 | Frequency: 3

Class 2: 3.9 - 4.3 | Frequency: 8

Class 3: 4.4 - 4.8 | Frequency: 6

Class 4: 4.9 - 5.3 | Frequency: 7

Class 5: 5.4 - 5.8 | Frequency: 1

To create a histogram, we can plot the frequency counts on the y-axis and the class intervals on the x-axis. The shape of the histogram can give us information about the distribution of the data. In this case, the histogram is bimodal, meaning there are two peaks in the data. This suggests that the data may be composed of two separate subpopulations.

Answer: The actual answer is 7/12, but the closest match is (A) 1/2.

Answer:

c. greater than​

Step-by-step explanation:

[tex]\frac{1}{2}[/tex] + [tex]\frac{2}{3}[/tex] = [tex]\frac{3}{6}[/tex] + [tex]\frac{4}{6}[/tex] = [tex]\frac{7}{6}[/tex] ≈ 1.167

1.167 > 1

So, the answer is c. greater than​

The difference in centigrade degrees between a temperature of 60°F and a temperature of 78°F is 10°C.

To convert Fahrenheit (°F) to Celsius (°C), you can use the following formula:

°C = (°F - 32) / 1.8

Using this formula, we can first convert 60°F to Celsius:

°C = (60°F - 32) / 1.8

°C = (28°F) / 1.8

°C = 15.56°C

Similarly, we can convert 78°F to Celsius:

°C = (78°F - 32) / 1.8

°C = (46°F) / 1.8

°C = 25.56°C

The difference in Celsius degrees between these two temperatures is:

Δ°C = 25.56°C - 15.56°C

Δ°C = 10°C

Therefore, the difference in centigrade degrees between a temperature of 60°F and a temperature of 78°F is 10°C.

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By iterating through different alpha values, you can identify the optimal alpha for this data set that results in the smallest MSE.

a. To construct a time series plot, you would typically use software like Excel or programming languages like Python or R.

However, I can describe the general trend based on the given data points.

Week 1: 7.35

Week 2: 7.40

Week 3: 7.55

Week 4: 7.56

Week 5: 7.60

Week 6: 7.52

Week 7: 7.52

Week 8: 7.70

Week 9: 7.62

Week 10: 7.55

Based on the data, there seems to be a slight overall upward trend in the Commodity Futures Index over the ten weeks, but there are also small fluctuations up and down throughout the period.

b. To find the best exponential smoothing coefficient (alpha) using the trial and error method, you would typically use software or programming languages to calculate the Mean Squared Error (MSE) for each alpha value.

Choose an initial value for alpha (e.g., 0.1).

Apply the exponential smoothing formula to the data series: St = α * Xt + (1 - α) * St-1, where St is the smoothed value at time t, α is the smoothing coefficient, Xt is the observed value at time t, and St-1 is the smoothed value at time t-1.

Calculate the forecast errors (Et) as the difference between the observed value and the smoothed value for each time period: Et = Xt - St-1.

Compute the Mean Squared Error (MSE) by taking the average of the squared forecast errors.

Repeat steps 2-4 with different values of alpha (e.g., 0.2, 0.3, 0.4, etc.) until you find the alpha value that minimizes the MSE.

By iterating through different alpha values, you can identify the optimal alpha for this data set that results in the smallest MSE.

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A 95.2% confidence interval in z-score is a range of values that is likely to contain the true population mean with a probability of 95.2%. The z-score for a 95.2% confidence interval is approximately ±1.97.

To calculate the 95.2% confidence interval in z-score, we can use the following formula:

CI = X ± z × (σ/√n)

where X is the sample mean, σ is the population standard deviation, n is the sample size, and z is the critical value from the standard normal distribution table.

For a 95.2% confidence interval, the area in the tails of the standard normal distribution is 0.024 (0.5 - 0.952/2). Therefore, the critical z-value for a 95.2% confidence interval is approximately ±1.97.

This formula assumes that the sample follows a normal distribution, or that the sample size is large enough to satisfy the central limit theorem.

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the probability of exactly 4 successes in 7 trials of a binomial experiment in which the probability of success is 55% is 0.29 = 29%

A binomial experiment is an experiment that has the following four properties:

The experiment consists of n repeated trials

Each trial has only two possible outcomes

The probability of success, denoted p, is the same for each trial

Each trial is independent

the probability of exactly 4 successes in 7 trials of a binomial experiment in which the probability of success is 55%

We know that the binomial distribution

[tex]^nc_rp^rq^{n-r[/tex]

Where n is the number of trails

p is the probability of success in each trial

q =1-p which is the probability of failure

Here r=4

n=7

p= 55 % =0.55

then by the formula

[tex]p(4)=^7c_4(o.55)^4(0.45)^3\\\\p(4)=35*0.091*0.091\\p(4)=0.29[/tex]

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To prove: Area of triangle MAP = 1/2 area of trapezium MNOP

Given: MN//OP and A is the midpoint of NO

Proof:

Let h be the height of trapezium MNOP.

The area of trapezium MNOP is given by:

Area of trapezium MNOP = (1/2) × (MN + OP) × h

Since MN//OP, we have MN = OP.

Therefore, Area of trapezium MNOP = (1/2) × 2MN × h = MN × h

Now, consider triangle MAP.

The base of triangle MAP is MA, which is half of NO.

Therefore, the base of triangle MAP is (1/2) × NO.

The height of triangle MAP is h, which is the same as the height of trapezium MNOP.

Therefore, the area of triangle MAP is given by:

Area of triangle MAP = (1/2) × (base) × (height) = (1/2) × (1/2NO) × h

Substituting NO = 2OA, we get:

Area of triangle MAP = (1/2) × (1/2 × 2OA) × h = (1/2) × OA × h

Since A is the midpoint of NO, we have OA = 1/2NO.

Therefore, Area of triangle MAP = (1/2) × (1/2NO) × h = (1/2) × (base of trapezium MNOP) × h

Hence, Area of triangle MAP = 1/2 Area of trapezium MNOP.

Therefore, the given statement is proved.

Answer: Given that MNOP is a trapezium with MN parallel to OP and A is the midpoint of NO.

To prove that the area of triangle MAP is half the area of trapezium MNOP, we need to use the following theorem:

Theorem: If a line segment joins the midpoint of one side of a triangle to a vertex opposite to that side, then the segment divides the triangle into two equal areas.

Proof:

Since A is the midpoint of NO, we can draw a line segment AP from vertex P to point A on NO as shown in the figure below:

css

Copy code

      M _______N

       |\      |

       |  \    |

       |    \  |

       |      \|

      O--------P

            A

We can see that triangle MAP is formed by the line segment AP and side MP of the trapezium.

Also, we can see that triangle MAN is congruent to triangle NOP because they are both right triangles with corresponding sides parallel. Therefore, they have the same area.

Since MNOP is a trapezium, the area of trapezium is given by:

Area of trapezium MNOP = (1/2)(MN+OP) × height

Since MN is parallel to OP, the height of the trapezium is the same as the height of triangle MAN and NOP.

Therefore, the area of trapezium MNOP can be written as:

Area of trapezium MNOP = (1/2)(MN+OP) × height

= (1/2)(MA+AP+OP) × height

= (1/2)(MA+MP) × height (Since AP = NO/2 = height)

So, we have proved that:

Area of trapezium MNOP = (1/2)(MA+MP) × height

Using the theorem, we know that AP divides triangle MAP into two equal areas. Therefore,

Area of triangle MAP = (1/2) × Area of triangle MAP

Substituting the above in the expression for the area of trapezium, we get:

Area of trapezium MNOP = Area of triangle MAP + (1/2) × Area of triangle MAP

= (3/2) × Area of triangle MAP

Therefore, we have:

Area of triangle MAP = (1/2) × Area of trapezium MNOP

Thus, we have proved that the area of triangle MAP is half the area of trapezium MNOP.

Step-by-step explanation:

The  price (in cents) should he charge for each of the remaining candy bars 49

First, we would want to calculate how much the box would sell for before the sister ate some.

We would get 24*63(in cents) and we can further get 1512 cents before the sister ate the candy bars.

The sister ate 7 candy bars leaving us with 31 candy bars. To deduct the price for each candy bar, it would be a situation like the following:

$6 for 3 boxes of 500 cookies (i know that's cheap)

6/3...

$2 per box.

Using our situation we get 1512 cents for 31 candy bars.

1512÷31

=48.77

That does seem unrealistic, so we round to the nearest whole number and we get...

49 cents

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According to the assumption the translated triangle would have vertices at (4,0), (6,2), and (5,-1).

Given,

To translate a triangle 3 units to the right and 2 units down, we would take each point of the original triangle and add 3 to the x-coordinate and subtract 2 from the y-coordinate.

For example, if the original triangle has vertices at (1,2), (3,4), and (2,1), the translated triangle would have vertices at:

(1+3, 2-2) = (4,0)

(3+3, 4-2) = (6,2)

(2+3, 1-2) = (5,-1)

So, the translated triangle would have vertices at (4,0), (6,2), and (5,-1).

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The equation of a circle given by the graph is (x-3)²+(y+2)²=29,

hence option b is correct.

A circle is a closed curve that extends outward from a set point known as the center, with each point on the curve being equally spaced from the center. A circle with an (h, k) center and a radius of r has the equation:

(x-h)² + (y-k)²= r²

This is the equation's standard form. Hence, we can quickly determine the equation of a circle if we know its radius and center coordinates.

We know that the equation of the circle is -

[tex](x-h)^2+(y-k)^2=r^2[/tex]

where (h,k) is the center of the circle and r is the radius,

given that,

center of the circle is = (3,-2)

and the radius is=√29

Hence the equation of a circle is

[tex](x-3)^2+(y+2)^2=(\sqrt29)^2\\\\(x-3)^2+(y+2)^2=29[/tex]

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To fold and tape a net into a solid shape, cut out the net, fold it along the lines, tape the edges together, and flatten the edges

The net cannot be fold and tape as it is given as a picture, however the general steps to fold and tape a net into a solid shape:

When the above stapes are followed, some of the nets that can be gotten from the given shape are triangular pyramids and triangles

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a) The plumber should buy 13 sections of 6-meter lengths of PVC pipes.

b) Assuming that there are no errors, the left-over pipe after satisfying Jobs A and B should be 3 meters.

We can use mathematical operations of addition, division, multiplication, and subtraction to determine the two quantities above.

In the first place, the total quantity of PVC pipes required is 75 meters.

This sum is divided by 6 to obtain the sections required, which is approximated to the nearest whole number.

Finally, 75 meters are subtracted from the total quantity bought.

PVC pipes required by Job A = 45 meters

PVC pipes required by Job B = 30 meters

The total quantity of PVC pipes required = 75 meters

The length of each PVC pipe = 6 meters

The number of pipes to buy = 13 sections (75 ÷ 6)

13 sections of pipes = 78 (6 x 13)

Leftover PVC pipes = 3 meters (78 - 75)

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Answer:

20 kilograms.

Step-by-step explanation:

First, we need to find the cost per kilogram.

We can do this by dividing 374 by 34.

That gives us 11. So, our cost per kilogram is $11.

Next, to find how many kilograms we can get with $220 dollars, we need to divide 220 by 11.

That leaves us with a final answer of 20 kilograms.

The random variable x is normally distributed with mean u=89 and standard deviation o=4. The indicated probability, ​P(x<8​7)= 0.3085.

In statistics, standard deviation is a measure of the amount of variation or dispersion in a set of data. It is a commonly used measure of the spread of a distribution and is calculated as the square root of the variance.

A higher standard deviation indicates that the data points are more spread out from the mean, while a lower standard deviation indicates that the data points are more tightly clustered around the mean.

Standard deviation is an important concept in statistics and is used in many statistical analyses, such as hypothesis testing and confidence interval estimation. It is also used in finance and economics to measure the risk associated with investments and to assess the variability of economic data.

To solve this problem, we need to standardize the value using z-score formula.

z = (x - mu) / sigma

Here, x = 87, mu = 89, and sigma = 4.

z = (87 - 89) / 4 = -0.5

We can look up the corresponding area under the standard normal distribution curve using a table or calculator. The area to the left of z = -0.5 is 0.3085.

Therefore, P(x < 87) = P(z < -0.5) = 0.3085.

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The answer to the given question about probability of Bob's shop is option 7) 79.4%.

Out of 700 cars, 144 require more than one day to repair. So the number of cars that can be fixed in one day is

700 - 144 = 556.

The probability that the next car brought to the shop can be fixed in a day is the ratio of the number of cars that can be fixed in a day to the total number of cars:

probability = 556/700

= 0.794 or 79.4%

Therefore, the correct answer is option 7) 79.4%.

Probability is a branch of mathematics that deals with the study of random events or phenomena. It is used to quantify the likelihood of an event occurring, and it is expressed as a number between 0 and 1, with 0 indicating that the event is impossible and 1 indicating that the event is certain. Probability theory is widely used in various fields, such as statistics, physics, economics, and finance, to make predictions and decisions based on uncertain or incomplete information. It provides a powerful tool for analyzing and understanding uncertainty, risk, and randomness in real-world situations, and it has numerous practical applications in diverse areas of research and industry

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Answer:

modes

Step-by-step explanation:

The only one of the three (median, mode, mean) that there can be more than one for a set is the mode, and in fact it has two modes: 5 and 9.

Answer: modes

Answer:

C) Stock Market.

Brainly wants me to put at least 20 characters and since I only provided the answer choice and was too lazy to do an explanation I am putting this here.

Answer:

C) Stock Market.

Step-by-step explanation:

The term stock market refers to several exchanges in which shares of publicly held companies are bought and sold.

There are approximately 78 trees on each acre of land when the trees are spread out evenly.

To find the number of trees on each acre of land mathematically, we can use the formula for average or mean.

The average number of trees per acre can be found by dividing the total number of trees by the total number of acres. In this case, we have 2808 trees and 36 acres:

Average number of trees per acre = Total number of trees / Total number of acres

Average number of trees per acre = 2808 / 36

Average number of trees per acre = 78

Therefore, there are approximately 78 trees on each acre of land when the trees are spread out evenly.

This means that if the land is divided into 36 equal sections, each section will have approximately 78 trees.

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the length of the missing side is approximately 4.73 units. Rounded to two decimal places, the answer is 4.73.

To solve this problem, we can use the Law of Sines, which states that the ratio of the length of a side of a triangle to the sine of the angle opposite that side is the same for all sides and angles in the triangle.

Let's label the missing side as b, and use sin(A) = opposite/hypotenuse to find the length of the side opposite angle A:

sin(A) = opposite/hypotenuse

sin(33.7°) = b/8

b = 8 × sin(33.7°)

b ≈ 4.726

Therefore, the length of the missing side is approximately 4.73 units. Rounded to two decimal places, the answer is 4.73.

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After descending [tex]21.5[/tex] feet, the scientist's new position in the submarine would be  [tex]30.8[/tex] feet below sea level.

The scientist was initially in a submarine, located 52.3 feet below sea level. This means that her position was  [tex]52.3[/tex]feet lower than the surface of the sea.

Over the next ten minutes, the scientist descended further into the ocean by [tex]21.5[/tex] feet. This means that she traveled down an additional [tex]21.5[/tex]feet from her initial position.

To calculate her new position below sea level, we can subtract the distance she traveled downward (21.5 feet) from her initial position (52.3 feet below sea level).

[tex]52.3 feet - 21.5 feet = 30.8 feet[/tex]

Therefore, after descending 21.5 feet, the scientist's new position in the submarine would be 30.8 feet below sea level.

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The value of m∠N is 21° ,the value of m∠M is 55° and the value m∠O is 106°.

To find the value of x, we can use the fact that the sum of the angles in a triangle is 180 degrees. Therefore:

m∠M + m∠N + m∠O = 180

Substituting the given angle measures, we get:

(4x-13) + (2x-13) + (5x+19) = 180

Simplifying the equation, we get:

11x - 7 = 180

11x = 187

x = 17

Now that we know the value of x, we can find the measure of each angle. Substituting x = 17, we get:

m∠M = (4x-13) = (417-13) = 59 degrees

m∠N = (2x-13) = (217-13) = 21 degrees

m∠O = (5x+19) = (5*17+19) = 106 degrees

Therefore, the measure of ∠MNO is:

m∠N = 21 degrees

Note: The question also asks for the measure of ∠P, but there is no information given about ∠P in the problem.

In AMNO, m angle M = (4x - 13) deg m angle N = (2x - 13) deg and m angle O = (5x + 19) deg Find m/N.

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Answer:

The area is (9^2)π = 81π.

Answer: Sampling is very often used in our daily life. For example, while purchasing fruits from a shop, we usually examine a few to assess the quality. A doctor examines a few drops of blood as a sample and draws a conclusion about the blood constitution of the whole body.