A trapezoid has a base that is 10.2 centimeters long and another base that is 9.8 centimeters long. Its height measures 5 centimeters. What is the area of the trapezoid?

Answer:

You can be 95% confident that the population mean (μ) falls between 0.5837 and 1.3363.

Step-by-step explanation:

Calculation

M = 0.96

Z = 1.96

sM = √(0.96)^2/25) = 0.19

μ = M ± Z(sM)

μ = 0.96 ± 1.96*0.19

μ = 0.96 ± 0.3763

Result

M = 0.96, 95% CI [0.5837, 1.3363].

You can be 95% confident that the population mean (μ) falls between 0.5837 and 1.3363.

Answer:

b) 9

Step-by-step explanation:

Given: Three machines  operating independently, simultaneously, and at the same constant rate can fill a certain production order in [tex]36[/tex] hours.

To Find: If one additional machine were used under the same operating conditions, in how many fewer hours of simultaneous operation could the production order be filled.

Solution:

Let  the time taken by one machine to fill a certain production alone be[tex]=\text{x}[/tex]

Time taken when three machine operate independently and simultaneously

[tex]\frac{1}{\text{x}}+\frac{1}{\text{x}}+\frac{1}{\text{x}}=\frac{1}{36}[/tex]

[tex]\frac{3}{\text{x}}=\frac{1}{36}[/tex]

[tex]\text{x}=108[/tex] [tex]\text{hours}[/tex]

Let time taken when one additional machine is used [tex]=\text{y}[/tex]

Time when when one additional machine is used

[tex]\frac{1}{108}+\frac{1}{108}+\frac{1}{108}+\frac{1}{108}=\frac{1}{\text{y}}[/tex]

[tex]\frac{4}{108}=\frac{1}{\text{y}}[/tex]

[tex]\text{y}=27[/tex] [tex]\text{hours}[/tex]

it takes [tex]27[/tex] [tex]\text{hours}[/tex] when one additional machine is used

Now,

fewer hours taken when one additional  machine is used

[tex]=\text{number of hours taken when three machines are used}-[/tex][tex]\text{number of hours taken when one additional machine is used}[/tex]

[tex]36-27[/tex]

[tex]9[/tex] [tex]\text{hours}[/tex]

in [tex]9[/tex] fewer hours of simultaneous operation the production order can be filled if one additional machine is used

Hence option b) is correct.

Answer:

$9.50

Step-by-step explanation:

Solution is in the attachment . You can see it.

Answer:

21.10 m

Step-by-step explanation:

Given:

Height of the temple above ground is, [tex]H=24\ m[/tex]

Total number of steps is, [tex]N=91[/tex]

Let us assume that each step is of same height, then the height of each step is given as:

[tex]\textrm{Each step height}=\frac{Total\ Height}{Total\ steps}=\frac{H}{N}=\frac{24}{91}\ m[/tex]

Now, height corresponding to 1 step = [tex]\frac{24}{91}\ m[/tex]

∴ Height corresponding to 80 steps = [tex]\frac{24}{91}\times 80=\frac{24\times 80}{91}=21.10\ m[/tex]

So, I would be at a height of 21.10 m above the ground at the [tex]80^{th}[/tex] step.

Answer:  54 mph

Step-by-step explanation:

Speed x Time = Distance

So, Speed = Distance/Time

Speed = 324 miles/6hrs = 54 mph

To calculate the conditional probability of at most 3 men entering the drugstore given that 10 women entered using Poisson Distribution. The gender doesn't influence the probability, therefore the events are treated as independent. Assumption made is that occurrences are independent and happen at a known average rate.

To compute the conditional probability that at most 3 men entered the drugstore, given that 10 women entered in that hour, we would apply Poisson Distribution. Poisson Distribution is used to find the probability of a number of events in a fixed interval of time or space if these events happen at a known average rate and independently of the time since the last event.

However, in this case, the number of men entering is independent of the number of women entering. Therefore, the fact that we know 10 women entered does not affect the probability regarding the number of men. The gender of the individuals entering the drugstore is irrelevant, and we can consider them as independent events. The result is the same if we simply asked: What is the probability that at most 3 people entered the drugstore?

To calculate this, we would use the formula for Poisson Distribution, summing up the probabilities of 0, 1, 2 and 3 events happening. The assumption made here is that the occurrences are independent of each other and occur with a known average rate, λ, which is 10 in this question.

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Answer:

Step-by-step explanation:

There are at least a couple of ways you could go at this. Here, we'll use an area formula to find m∠A, then use the law of cosines to find BC. Using BC, we can use the law of sines to find another angle.

  Area = (1/2)·AB·AC·sin(∠A)

  65·2/(12·17) = sin(∠A) ≈ 65/102

  ∠A = arccos(65/102) ≈ 39.587°

From the law of cosines, ...

  BC² = AB² +AC² -2·AB·AC·cos(∠A)

  BC² = 12² +17² -2·12·17·cos(39.587°) ≈ 118.5735

  BC ≈ √118.5735 ≈ 10.889

Then ∠C can be found from the law of sines:

  sin(∠C)/AB = sin(∠A)/BC

  ∠C = arcsin(AB/BC·sin(∠A)) ≈ 44.609°

The measure of ∠B will be the angle that makes the total be 180°:

  39.587° +∠B +44.609° = 180°

  ∠B = 95.804°

_____

There is actually another solution, in which ∠A is obtuse. We thought the diagram showed an acute triangle, so we didn't investigate the other alternative. The above calculations show the triangle is obtuse in any event.

See the second attachment for the other solution.

Answer:

[tex]p(x)= -\frac{1}{10}x + 685[/tex]

Step-by-step explanation:

Since, Function of demand is the linear function of quantity.

Let x represents the quantity and p represents the price of each unit.

∵ Manufacture has been selling 1450 television sets a week at $540 each,

i.e. [tex](x_1, p_1) = (1450, 540)[/tex]

Also, for each $13 rebate offered to a buyer, the number of sets sold will increase by 130 per week.

i.e. [tex](x_2, p_2) = (1580, 527)[/tex]

Thus, the linear equation of the price,

[tex]p-p_1 = \frac{p_2-p_1}{x_2-x_1}(x-x_1)[/tex]

[tex]p-540 = \frac{527 - 540}{1580-1450}(x-1450)[/tex]

[tex]p-540 = -\frac{13}{130}(x-1450)[/tex]

[tex]p-540 = -\frac{1}{10}(x-1450)[/tex]

[tex]p = -\frac{1}{10}x + 145 + 540[/tex]

[tex]\implies p = -\frac{1}{10}x + 685[/tex]

Hence, the function representing price as a function of the demand is,

[tex]p(x)= -\frac{1}{10}x + 685[/tex]

Answer: 2432 visitors

Step-by-step explanation:

An employee of a museum surveyed a random sample of 350 visitors that came to the museum. Of the visitors that were surveyed, 266 stopped at the gift shop.

Since 266 out of 350 stopped at the gist shop, we find the fraction or decimal of people who stopped at the gift shop. This will give 266/350 = 19/25 or 0.76.

If 3200 visitors come to the museum, the expected number of people to stop at the gift shop are:

= 0.76 × 3200

= 2432

2432 visitors are expected to stop at the gift shop out of 3200 visitors.

Answer:

The mean and standard deviation of Y are, 94 and 0.28 respectively.

Step-by-step explanation:

Let the random variable , 'Test grades on the last statistics exam' be X.

Then according to the question,

E(X) = 78 ------------(1)

and

[tex]\sigma_{X}[/tex] = 0.14------------(2)

Now, according to the question,

Y = 2(X - 31)

⇒E(Y) = 2(E(X) - 31)

          = [tex]2 \times (78 - 31)[/tex]

          = 94  ----------------(4)

and

V(Y) = 4V(X)

⇒[tex]\sigma_{Y} = 2 \times \sigma_{X}[/tex]

⇒[tex]\sigma_{Y} = 2 \times 0.14[/tex] = 0.28

So, the mean and standard deviation of Y are, 94 and 0.28 respectively.

Answer: P = 0.156

Step-by-step explanation:

Initially in the jar, we have 9 red and 13 blue marbles, so we have a total of 22 marbles in the jar.

If we want to take a red ball for the jar, the probability of getting one is equal to the number of red balls divided by the total number of balls, so:

P1 = 9/22 .

Now, suppose you already took one red ball, we want to take the second one; the probability is calculated in the same way, but now we already took a red ball, so we have 8 red balls and 21 balls in total; so:

P2 = 8/21

Now the probability of both events to happen is equal to the product of their probabilities:

P = P1*P2 = (9/22)*(8/21) = 0.1558

Now we want to round it to the nearest thousandth.

The thousandth is the second number after the decimal point, and the number that comes after is an 8, so we need to round it up; then we get:

P = 0.156, or 15.6% in percentage form.

To calculate the area between the birth rate and death rate curves for a given time interval, find the net growth rate function by subtracting the death rate from the birth rate, and then integrate this function over the time interval. The result reflects the population surge due to the rates of births and deaths.

The student's question involves calculating the area between two exponential growth curves, birth rate and death rate, over a given time interval. To find the area between the curves b(t) = 2300e0.024t and d(t) = 1450e0.019t from t = 0 to t = 10, we need to integrate the difference between them with respect to time over the given interval.Step-by-step Solution:

Subtract the death rate from the birth rate to get the net growth rate function: g(t) = b(t) - d(t) = 2300e0.024t - 1450e0.019t.

Integrate the net growth rate function with respect to t from 0 to 10 to find the total area.

Use a calculator or computer software to perform the integration and round the final answer to the nearest integer.

This computation will give the total number of people added to the population over the 10-year period, which reflects the population surge resulting from the different rates of increase in births and deaths.

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m=16t can be used to determine the distance in miles Han has gone after t hours.

Step-by-step explanation:

Speed of Han = 16 miles per hour

Let,

m be the distance covered by Han in miles;

t be the number of hours Han has been biking,

According to formula,

Distance = Speed*Time

[tex]m=16*t\\m=16t[/tex]

m=16t can be used to determine the distance in miles Han has gone after t hours.

Keywords: distance, speed

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Answer:

y = mx + b ( y = 16t + 0

Step-by-step explanation:

Answer:

y-intercept: when x = 0

For Line A:

y = 0 + 7 = 7

For line B:

when x = 0, the value is -5

7 > -5, so y-intercept of line A is greater than line B's.

Answer:

5^20

Step-by-step explanation:

For each comic book, there are five different choices for which kid will receive that comic book. 20 decisions are made, one for each comic book with five different possibilities for each choice. The number of ways to distribute the comic books to the five kids is 5^20.

Final answer:

The formula for distributing 20 comic books among five kids with no restrictions is C(24, 5) = 42,504 ways.

Explanation:

To distribute the 20 comic books to five kids with no restrictions on how many each kid receives, we can use the concept of distributing identical items among distinct groups.

The number of ways to distribute the comic books in this scenario is represented by the formula: C(n+r-1, r) where n is the number of items (in this case, 20 comic books) and r is the number of groups (5 kids).

Therefore, the number of ways to distribute the comic books to the five kids is: C(20+5-1, 5) = C(24, 5) = 42,504 ways.

Answer: The inner diameter of the ring is 16 mm.

Step-by-step explanation:

As we know that ,

Circumference of a circle = [tex]\pi d[/tex] , where d = diameter of the circle .

We are given that ,

The circumference of the outside of a ring is 66 mm and it has an outer diameter of 21 mm .

Now , if circumference of the inside the ring is 50 mm, then we have

[tex]50 = \pi d[/tex] , where d= diameter of the inner circle .

Then , [tex]d=\dfrac{50}{\pi}=\dfrac{50}{\dfrac{22}{7}}=\dfrac{50\times7}{22}\approx15.909090909\approx16\text{ mm}[/tex]

Hence , the inner diameter of the ring is 16 mm.

The diameter of the inner ring is 15.92mm

The formula for calculating the circumference of a circle is expressed as:

C = πd

d is the diameter

Given the following parameters

C = 50mm

The diameter of the inner ring is given as:

d = C/π

d = 50/3.14
d = 15.92mm

Hence the diameter of the inner ring is 15.92mm

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Answer:

Sample 2

Step-by-step explanation:

Correlation  is a technique that show strongly pairs of variables.

For example height and width .There are several different correlation techniques .Correlation is determined by dividing  product of two variables. standard deviation.Standard deviation is a dispersion of  data. Co relation between two variable could be positive or negative or both.

Correlation between two sample is computed. if test statistic is larger in sample 1 then sample 2 will have the larger value of correlation coefficient.

Answer:

c. probably understates the percent of people who favor a system of national health insurance.

Answer:

[tex]y=Ae^{-2x}[/tex]

Step-by-step explanation:

Given that the functions f(x) that have the property that the tangent lines to the graphs of f(x)pass through the point (x+2,0).

Let (x,y) be any arbitrary point of contract

The tangent line passes through two points (x,y) and (x+2,0)

Slope of tangent line = f'(x) = change in y/change in x= [tex]\frac{-y}{2}[/tex]

i.e. we have

[tex]\frac{dy}{dx} =\frac{-y}{2}[/tex]

Separate the variables

[tex]\frac{dy}{y} =-2x\\lny =-2x+c[/tex]

Raise to power e

[tex]y=Ae^{-2x}[/tex]

Thus the functions would have the above form for various values of A

Answer:

C

Step-by-step explanation:

Rearranging x - y ≤ 2

- y ≤ 2 - x ( multiply through by - 1 )

y ≥ - 2 + x ← change direction of inequality symbol

This region is above the yellow line

y ≥ 0 is above the x- axis

x ≥ 0 is to the right of the y- axis

Thus the solution is the indicated blue region

The inequalities from C satisfy the given graph

Answer:

Area = 2500 square feet is the largest area enclosed

Step-by-step explanation:

A rectangular piece of land borders a wall. The land is to be enclosed and to be into divided 3 equal plots with 200 feet of fencing

Let x be the length of each box and y be the width of the box

Perimeter of the box= 3(length ) + 4(width)

[tex]200=3x+4y[/tex]

solve for y

[tex]200=3x+4y[/tex]

[tex]200-3x=4y[/tex]

divide both sides by 4

[tex]y=50-\frac{3x}{4}[/tex]

Area of the rectangle = length times width

[tex]Area = 3x \cdot y[/tex]

[tex]Area = 3x \cdot (50-\frac{3x}{4})[/tex]

[tex]A=150x-\frac{9x^2}{4}[/tex]

Now take derivative

[tex]A'=150-\frac{9x}{2}[/tex]

Set it =0 and solve for x

[tex]0=150-\frac{9x}{2}[/tex]

[tex]150=\frac{9x}{2}[/tex]

multiply both sides by 2/9

[tex]x=\frac{100}{3}[/tex]

[tex]A''=-\frac{9}{2}[/tex]

For any value of x, second derivative is negative

So maximum at x= 100/3

 [tex]A=150x-\frac{9x^2}{4}[/tex] , replace the value of x

[tex]A=150(\frac{100}{3})-\frac{9(\frac{100}{3})^2}{4})[/tex]

Area = 2500 square feet is the largest area enclosed

Final answer:

To find the largest enclosed area with 200 feet of fencing divided into 3 plots, solve the equation 2l + 4w = 200 and substitute the value of l into the area formula.

Explanation:

To find the largest area that can be enclosed with 200 feet of fencing and divided into 3 equal plots, we can first find the length of each side of the rectangular piece of land. Let's assume the length of the land is 'l' and the width is 'w'.

Since the land is divided into 3 equal plots, each plot will have a length of l/3 and a width of w.

From the information given, we can form the equation 2l + 4w = 200 (each length side is counted twice and each width side is counted once). We can solve this equation for l and substitute it back into the area formula (A = l * w) to find the largest possible area.

The inclination angle is 10°

Step-by-step explanation:

The given scenario forms a right angled triangle where the length of ramp is hypotenuse and the rise of ramp is the perpendicular

Given

H = 4.2m

P = 0.7m

We have to use the trigonometric ratios to find the angle. The ratio that has to be used should involve both perpendicular and hypotenuse

Let x be the angle

then

[tex]sin\ x = \frac{P}{H}\\sin\ x = \frac{0.7}{4.2}\\sin\ x = 0.1666\\x = sin^{-1} (1.666)\\x = 9.59 => 10[/tex]

Hence,

The inclination angle is 10°

Keywords: Trigonometric ratios, Right angled triangle

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The angle of inclination of the wheelchair ramp to the nearest degree is 9 degrees.

[tex]\[ \theta = \arctan\left(\frac{\text{rise}}{\text{run}}\right) \][/tex]

Given the rise of the ramp is 0.7 m and the run (length) is 4.2 m, we can plug these values into the formula:

[tex]\[ \theta = \arctan\left(\frac{0.7}{4.2}\right) \][/tex]

Now, we calculate the value of θ:

[tex]\[ \theta = \arctan\left(\frac{1}{6}\right) \][/tex]

Using a calculator, we find:

[tex]\[ \theta \approx \arctan(0.1667) \] \[ \theta \approx 9.4623 \text{ degrees} \][/tex]

Rounding to the nearest degree, we get:

[tex]\[ \theta \approx 9 \text{ degrees} \][/tex]

Therefore, the angle of inclination of the wheelchair ramp is approximately 9 degrees to the nearest degree.

Answer:

She have $1133.33 in account which pays  5% annual interest and he have $1933.33 in account which pays 10% annual interest

Step-by-step explanation:

Let x be the amount she invested at 5% annual interest

She invested $800 more in 10%

So, she invested x+800 at 10% annual interest

Case 1:

Principal = x

Time = 1 year

Rate of interest = 5%

[tex]Si =\frac{P \times R \times T}{100}[/tex]

[tex]SI=\frac{x \times 5 \times 1}{100}[/tex]

[tex]SI=\frac{5}{100}x[/tex]

Case 2:

Principal = x+800

Time = 1 year

Rate of interest = 10%

[tex]Si =\frac{P \times R \times T}{100}[/tex]

[tex]SI=\frac{(x+800) \times 10 \times 1}{100}[/tex]

[tex]SI=\frac{10}{100}(x+800)[/tex]

Interest = Amount - principal = 880+1.1x-x=880+0.1x

Her total interest for a year is $250

So, [tex]\frac{5}{100}x+\frac{10}{100}(x+800)=250[/tex]

[tex]\frac{5}{100}x+\frac{10}{100}(x+800)=250[/tex]

[tex]\frac{5}{100}x+\frac{10}{100}x+80=250[/tex]

[tex]\frac{15}{100}x+80=250[/tex]

[tex]\frac{15}{100}x=250-80[/tex]

[tex]x=170 \times \frac{100}{15}[/tex]

[tex]x=1133.33[/tex]

So the amount she invested at 5% annual interest is $1133.33

She invested at 10% annual interest=x+800=1133.33+800=1933.33

Hence she have $1133.33 in account which pays  5% annual interest and he have $1933.33 in account which pays 10% annual interest

The amount she has in the account that an annual interest of 5% is $3400.

The amount she has in the account that an annual interest of 10% is  $4,200.

x - y = $800 equation 1

0.1x + 0.05y = $250 equation 2

Where:

Multiply equation 1 by 0.1

0.1x - 0.1y = 80 equation 3

Subtract equation 3 from equation 2

0.05y = 170

Divide both sides by 0.05

y = $3,400

Substitute for y in equation 1

x - 3400 = 800

x = 3400 + 800

x = $4,200

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Answer:

A. 20%

Step-by-step explanation:

These events are independent, because if David eats a healthy breakfast cannot influence on would be rain or not.

"And" for probabilities  of independent events means "x" (times).

80% = 0.8

25% = 0.25

0.8*0.25 = 0.2 = 20%

Answer:

120 calories and 9 grams of fiber.

Step-by-step explanation:

We are told that 1/3 cup serving contains 80 calories and 6 grams of fiber.

Let's multiply everything by 3. So,

1 cup serving has 3*80 = 240 calories and 3*6 = 18 grams of fiber.  

But, we want to really know about 1/2 cup. So, now we multiply everything by 1/2.  

1/2 cup has (1/2) (240) = 40 calories and (1/2) (18 grams) = 9 grams of fiber.

Answer:

240 calories and 9 grams of fiber

Step-by-step explanation:

Answer:

I will forward the challenge to the ISCAP.

Step-by-step explanation:

If the classifying agency does not provide a full response within 120 days, then as per my responsibility, I will forward the challenge to the ISCAP.

ISCAP is the Inter agency security classification appeals panel.

ISCAP is a deciding panel that decides on certain classification or declassification issues to its users, with a forum for further review.

Answer:

Step-by-step explanation:

The function goes up to the right until it gets to the vertex at x=0. Then it goes down to the right. That is, it is ...

  increasing from -∞ to 0 (not including 0)

  decreasing from 0 to +∞ (not including 0)

_____

At x=0, the function is neither increasing nor decreasing, so x=0 is not part of either interval.

Answer:

1 : -1

2:2

3:-5

4: 1/2

5: -3

6: -3/2

7: 1/2

8: -1/2

9: 1

10: 1/3

Step-by-step explanation:

well all u have to do is do rise over run, rise/run. find 2 points and go up according to how much it goes up and go left or right based on the graph. AND sometimes the slope will be negative like number 1.

they use 12 oranges

4•4=16-4=12 which is 3 of the 4/4

The fraction 3/4 of 16 will be the number of oranges and it will be the 12 oranges.

In such a fraction, the value that appears above the horizontal line is referred to as the numerator.

In another word, the fraction is the division of the two numbers but the division is not wholly complete.

As per the given,

They make orange juice using 3/4 of the oranges.

3/4 of 16

(3/4)16 = 3 x 4 = 12 oranges

Hence "The fraction 3/4 of 16 will be the number of oranges and it will be the 12 oranges".

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Ground: y = 0

- 16t² + 128t + 50 = 0

Apply quadratic equation.

t = 0, 8 (rounded to the nearest second)

8 seconds

The time it will take for the object to hit the ground is approximately 4 seconds (rounded to the nearest second).

The given function a(t) = -16t^2 + 128t + 50 represents the approximate altitude, in feet, of an object released from the top of a building t seconds after it is released. To find the time it will take for the object to hit the ground, we need to find the value of t when the altitude is 0.

Setting a(t) = 0, we get:

-16t^2 + 128t + 50 = 0

Using the quadratic formula, we can solve for t.

t = (-b ± √(b^2 - 4ac)) / (2a)

Substituting the values a = -16, b = 128, and c = 50, we get t = 0.54 s or t = 3.79 s. Since the object is already at a height of 0 at t = 0 (the time of release), the time it will take for the object to hit the ground is approximately 4 seconds (rounded to the nearest second).

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