The cross section of a water bin is shaped like a trapezoid. The bases of the trapezoid are 28 feet and 6 feet long. It has an area of 34 square feet. What is the height of the cross section?

Answer:

  -2.1x +14.4y

Step-by-step explanation:

Use the distributive property to eliminate parentheses. Then combine like terms.

  (12.7y-3.1x)+5.9y-(4.2y-x)

  = 12.7y -3.1x +5.9y -4.2y +x

  = x(-3.1 +1) +y(12.7 +5.9 -4.2)

  = -2.1x +14.4y

The volume of a cube that measures 3 meters on one side is 27 cubic meters.

The volume of a cube is calculated by raising the length of one side to the power of three, which in mathematical notation is written as s^3. If a cube measures 3 meters on one side, you would calculate the volume as follows: 3^3 = 3 * 3 * 3 = 27 cubic meters. So, the volume of this cube is 27 cubic meters.

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Answer:

[tex]240^\circ[/tex]

Step-by-step explanation:

See the attached picture. One possible angle measure is [tex]60^\circ+180^\circ=240^\circ[/tex]

The possible measure of an angle with terminal side in 3rd quadrant and making an angle of 60°with the X-axis is 240°.

When the vertex of an angle is at the origin and one ray is on the positive x-axis, it is said to be in standard position. The ray on the x-axis is known as the starting side, while the ray on the y-axis is known as the terminal side.

The question is shown in the figure below:

The angle made with X - axis = 60°

Angle is lying in 3rd quadrant

If we start moving in the anticlockwise direction then the measure of the total angle will be 180° + 60° = 240°.

Hence, the total angle for an angle lying in 3rd quadrant is 240°.

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Answer:

y= (x-2)^2/4-7

Step-by-step explanation:

Answer:

1.83 units

Step-by-step explanation:

To find we rest the width from the lenght. It would be 4.5 - 2.67 = 1.83, so the lenght was 1.83 units longer than the width.

The length of the rectangle is 1.83 units longer than its width. This value is calculated by subtracting the width (2.67 units) from the length (4.5 units).

The student asked how much longer the length of a rectangle was compared to its width. The length of the rectangle is 4.5 units and the width is 2.67 units. To find how much longer the length is than the width, we subtract the width from the length.

To calculate it:  4.5 - 2.67 = 1.83

So, the length is 1.83 units longer than the width of the rectangle.

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Step-by-step explanation:

Lily goes to gym once every 8 days.

Such that she will visit on 8, 16 , 24, 32 , 40, 48th days

Ann goes once every 12 days

Such that she will visit on 12, 24, 36, 48, 60th days ....

Taylor comes once every 16 days

Such that she will visit on 16, 32, 48, 64th days....

Comparing the common days on which they will visit again after wednesday,

it will be after 48 days, (i.e) after 6 weeks and 5 days, it will be tuesday

Answer:

48 days

Step-by-step explanation:

LCM of 8, 12, 16 is 48.

The mean point of the each group can be calculated using midpoint and mean formula. The mean is sum of all the term divided by number of term.

The mean height of a plant is 30.5.

Given:

The height of plant and frequency is given in table.

Refer the attached table for the calculation of mid point and frequency of midpoint.

Now we have ,

[tex]\rm {Sum \:of\: frequencies} = 20[/tex]

[tex]{\rm Sum \:of\: frequency\: \times midpoint\: product} = 610[/tex]

Calculate the mean of height of a plant.

[tex]\rm Mean=\dfrac{610}{20}\\\rm Mean=30.5[/tex]

Thus, the mean height of a plant is 30.5.

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To estimate the mean height of 20 plants, using midpoints and frequencies, the calculation yields approximately 13.89 cm. This provides a representative value based on the distribution of heights within specified intervals.

To estimate the mean height of the plants using the midpoints of each group, we'll calculate the midpoints for each interval and then find the weighted average.

1. Midpoint for 0 < h < 10:

  - Midpoint = (0 + 10)/2 = 5

2. Midpoint for 10 < h < 20:

  - Midpoint = (10 + 20)/2 = 15

3. Midpoint for 20 < h < 30:

  - Midpoint = (20 + 30)/2 = 25

4. Midpoint for 30 < h < 40:

  - Midpoint = (30 + 40)/2 = 35

5. Midpoint for 40 < h < 50:

  - Midpoint = (40 + 50)/2 = 45\)

6. Midpoint for 50 < h < 60:

  - Midpoint = (50 + 60)/2 = 55

Now, calculate the weighted average using the frequencies:

[tex]\[ \text{Mean height} = \frac{\sum (\text{Midpoint} \times \text{Frequency})}{\sum \text{Frequency}} \]\[ \text{Mean height} = \frac{(5 \times 4) + (15 \times 2) + (25 \times 3) + (35 \times 0) + (45 \times 0) + (55 \times 0)}{4 + 2 + 3 + 0 + 0 + 0} \]\[ \text{Mean height} = \frac{20 + 30 + 75}{9} \]\[ \text{Mean height} = \frac{125}{9} \][/tex]

Therefore, the estimate for the mean height of a plant is approximately 13.89 cm.

Answer:

Yes

Step-by-step explanation:

Mrs. Shelby

$3 for  6 muffins

$3 for every 6 muffins 3 X 6 =18

$3...6

$6...12

$9....18

Mrs. Kloske

$9 for 18        

They are equivalent in the sense that the price break down would be the same.

I think it's $16.432 but I'm not sure.

The price per cap yielding demand of 330 caps when advertising is increased to $3250 is 16.51 per cap.

What is algebra ?

Algebra is a branch of mathematics that deals with various symbols and the arithmetic operations such as division , multiplication , etc.

It is given that at $15 per cap , $2750 is spent each week on ads , and demand is 330 caps.

So , we can find how much money earn if cost is $15 per cap.

As 330 is the demand , then total earning is :

= 330 × 15

= $ 4950

Out of this , $2750 is spent per week on ads. So , total profit is :

= 4950 - 2750

= $ 2200

Now , If advertising is increased to $3250 then , money more spent on ads is :

= 3250 - 2750

= 500

So , total earning will be :

= 3250 + 2200

= 5450

And price per cap for demand of 330 caps will be :

= 5450 ÷ 330

= 16.51 per cap

Therefore , the price per cap yielding demand of 330 caps when advertising is increased to $3250 is 16.51 per cap.

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Answer:

Diameter = 7cm

Radius = 3.5cm

Step-by-step explanation:

The diameter is the distance across the circle; shown as 7cm.

The radius is half the distance of the diameter, or half the distance across the circle.

Answer:

Radius = 3.5

Diameter = 7

Step-by-step explanation:

Radius = half of diameter

Diameter is the 7 cm you see on the image.

Answer:

True

Step-by-step explanation:

Since if you use negative number you can determine the length between -3 and 0.

Answer:

C = 2

Step-by-step explanation:

9c + 14 = 2c^2 + 9c + 6

-9c                     -9c

14 = 2c² + 6

-6           -6

8 = 2c²

4 = c²

c = 2

The value of c on the circle is 4 or -4.

In geometry, the tangent of a circle is a line that intersects the circle at only one point, known as the point of tangency.

The tangent line is perpendicular to the radius of the circle at that point.

We have,

XY and XZ are tangent on the same circle.

So,

XY = XZ

This means,

2c² + 9c + 6 = 9c + 14

Combining like terms.

2c² + 9c - 9c + 6 - 14 = 0

2c² - 8 = 0

2c² = 8

c² = 8/2

c² = 4

c = √4

c = ±4

Thus,

The value of c is 4 or -4.

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Step 1: Simplify both sides of the equation.

28 =  −7 /2 x

Step 2: Flip the equation.

−7 /2 x = 28

Step 3: Multiply both sides by 2/(-7).

( 2 /−7 )*( −7 /2 x) = (  2 /−7 )*(28)

x=−8

Answer:

x=−8

[tex]28 = - \frac{7}{2} x \\ x = 28 \div ( - \frac{7}{2} ) \\ x = 28 \times ( - \frac{ 2 }{7} ) \\ x = - 8[/tex]

Let's chek

[tex] - 8 \times ( - \frac{7}{2} ) = \frac{8 \times 7}{2} \\ = 28[/tex]

Answer:

[tex]x = - 8[/tex]

Answer: the probability that exactly two of the next five people who apply to that university get accepted is 0.23

Step-by-step explanation:

We would number of people that applies for admission at the university and gets accepted. The formula is expressed as

P(x = r) = nCr × p^r × q^(n - r)

Where

x represent the number of successes.

p represents the probability of success.

q = (1 - p) represents the probability of failure.

n represents the number of trials or sample.

From the information given,

p = 0.6

q = 1 - p = 1 - 0.6

q = 0.4

n = 5

the probability that exactly two of the next five people who apply to that university get accepted is

P(x = 2) = 5C2 × 0.6^2 × 0.4^(5 - 2)

P(x = 2) = 10 × 0.36 × 0.064

P(x = 2) = 0.23

Answer:

0.2304 or 23.04%

Step-by-step explanation:

Please kindly check the attached files for explanation

Answer:

x = -7

Step-by-step explanation:

-6x + 3 = 45  

      - 3    - 3

        -6x = 42

         /-6 = /-6

         x    =  -7

The value of x to satisfy the given equation is 1/17.

Given,

-6x + 3 = 45x

We need to find x that makes that satisfy the equation.

A numeral is a symbol or name that stands for a number.

Find x.

-6x + 3 = 45x

Subtract 45x on both sides

-6x + 3 - 45x = 45x - 45x

-51x + 3 = 0

Subtract -3 on both sides

-51x + 3 - 3 = -3

-51x = -3

Divide both sides by 51

(51/51)x = 3/51

x = 1 / 17

This means we need x = 1/17 to make the equation true.

-6 x 1/17 + 3 = 45 x 1/17

-6/17 + 3 = 45/17

(-6 + 51) / 17 = 45/17

45/17 = 45/17

Thus the value of x to satisfy the given equation is 1/17.

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Answer:

7.7833 × 108

Step-by-step explanation:

Answer:

7.78×10∧8

Step-by-step explanation:

By setting up a system of equations based on the given information, we find that Brenda sewed 12 buttons on 28 dresses.

Since there are 90 dresses in all, Brenda would have sewed 8 buttons on some and 12 buttons on the remaining. We can set up a system of equations to solve this. Let's say the number of dresses that have 8 buttons is 'x' and the number of dresses with 12 buttons is 'y'. Hence, we have two equations:

From the first equation, we get x = 90 - y. Substituting this into the second equation, we have 8*(90 - y) + 12y = 784. Solving this yields, y = 28. Therefore, Brenda sewed 12 buttons on 28 dresses.

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Answer:

58

Step-by-step explanation:

Order of operations.

Additions and subtractions, in the order they appear, from left to right.

30 + 30 - 2 =

= 60 - 2

= 58

Answer:

The 90% confidence interval for the mean time to graduate with a bachelor’s degree is (4.32, 4.84).

Yes, this confidence interval contradict the belief that it takes 4 years to complete a bachelor’s degree.

Step-by-step explanation:

The (1 - α)% confidence interval for population mean μ, when the population standard deviation is not known is:

[tex]CI=\bar x\pm t_{\alpha/2, (n-1)}\times \frac{s}{\sqrt{n}}[/tex]

The information provided is:

[tex]\bar x=4.58\\s=1.10\\\alpha =0.10[/tex]

Compute the critical value of t for 90% confidence interval and (n - 1) degrees of freedom as follows:

[tex]t_{\alpha/2, (n-1)}=t_{0.10/2, (50-1)}=t_{0.05, 49}=1.671[/tex]

*Use a t-table for the probability.

Compute the 90% confidence interval for population mean μ as follows:

[tex]CI=\bar x\pm t_{\alpha/2, (n-1)}\times \frac{s}{\sqrt{n}}[/tex]

     [tex]=4.58\pm 1.671\times \frac{1.10}{\sqrt{50}}\\=4.58\pm 0.26\\=(4.32, 4.84)[/tex]

Thus, the 90% confidence interval for the mean time to graduate with a bachelor’s degree is (4.32, 4.84).

If a hypothesis test is conducted to determine whether it takes 4 years to complete a bachelor’s degree or not, the hypothesis will be:

Hₐ: The mean time it takes to complete a bachelor’s degree is 4 years, i.e. μ = 4.

Hₐ: The mean time it takes to complete a bachelor’s degree is different from 4 years, i.e. μ ≠ 4.

The decision rule based on a confidence interval will be:

Reject the null hypothesis if the null value is not included in the interval.

The 90% confidence interval for the mean time to graduate with a bachelor’s degree is (4.32 years, 4.84 years).

The null value, i.e. μ = 4 is not included in the interval.

The null hypothesis will be rejected at 10% level of significance.

Thus, it can be concluded that that time it takes to complete a bachelor’s degree is different from 4 years.

Final answer:

The 90% confidence interval for the mean time to graduate ranges from approximately 4.32 to 4.84 years, indicating it may take longer than 4 years to complete a bachelor's degree on average.

Explanation:

To calculate the 90% confidence interval for the mean time to graduate, we'll use the sample mean (Ü), standard deviation (s), and the sample size (n).

The formula for the confidence interval is:

Ü ± (t* × (s/√n))

Where

t* is the t-score that corresponds to the 90% confidence level and n-1 degrees of freedom.

Since our sample size (n) is 50, we have 49 degrees of freedom.

Using a t-distribution table or calculator, we can find the appropriate t* value.

Now, let's use the provided information: Ü = 4.58 years, s = 1.10 years, and n = 50.

Assuming that the t-score (t*) is approximately 1.676 for 49 degrees of freedom at the 90% confidence level, we can compute the margin of error (ME):

ME = 1.676 × (1.10/√50) ≈ 0.26 years

Thus, the 90% confidence interval is:

4.58 ± 0.26 years

This interval ranges from approximately 4.32 to 4.84 years. It suggests that we can be 90% confident that the true mean time for graduates to complete a bachelor's degree is within this range.

The confidence interval does not contain the value of 4 years. Thus, this may indicate that it takes longer than 4 years on average to complete a bachelor's degree, contradicting the belief that it takes exactly 4 years.

Answer:

(m,n)

Step-by-step explanation:

Since O is at the origin, we can take the coordinates of point A and divide them by 2 to find the midpoint

( 2m/2,2n/2)

The midpoint is at (m,n)

Answer:

Is is Infinitely many solutions so 0=0

Step-by-step explanation:

Equation 1: 4y - 3x = -20

Equation (2):  y - 3x/4  = -5

Multiply equation (2) by 4

Equation 1: 4y - 3x = -20

Equation (2): 4y - 3x = -20

y = 3x/4 - 5

4•(3x/4-5) - 3x = -20

Therefore the answer leads to:

Infinitely many solutions, 0=0

Hope this helped :')

Answer:

7.5 Quarts

Step-by-step explanation:

D'Naisa mixed the following:

We are to determine in total, the number of quarts of paint that she mixed. this is done by converting each of the volume to quart.

1 gallon of orange paint

3 pints of red paint.

Therefore,

Total Volume of Paint Mixed in quart= Volume of Orange+Yellow+Red

=4+2+1.5

=7.5 Quarts

Answer:

A= It takes Solomon 16 minutes to print each chess piece.

Step-by-step explanation: Its the first one

The number 16 in this scenario signifies the amount of 3D printed chess pieces. The number indicates the quantity Solomon can print within a particular span of time.

In this given context, 16 refers to the number of 3D printed chess pieces. This is a common type of mathematical problem dealing with ratios or rates. Here, the table suggests a ratio that compares the number of pieces printed to the time it takes to print them. Therefore, 16 essentially represents the quantity of chess pieces that Solomon can print using his 3D printer within a certain amount of time.

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Answer:

The input force needed is 225 Newtons

Step-by-step explanation:

From hydraulic pressure laws,  we have that the pressure at the same level throughout the body of a fluid is equal.  

This means that for the Hydraulic Jack, input pressure = output pressure

Recall,Pressure is a ratio of force and area

i.e pressure = Force / Area

For the hydraulic jack to work properly, the pressure at the input end must be equal to the pressure at the output end.

[tex]\frac{F_{1}}{A{1}} = \frac{F_{2}}{A_{2}}[/tex]

[tex]\frac{9000}{4}=\frac{Force}{0.1}[/tex]

From this we can compute that the Input force = 225 Newtons

Answer:

Step-by-step explanation:

Since the pipe is an enclosed container, we would apply Pascal's law which states that a pressure applied to a fluid in a closed container is transmitted equally to every point of the fluid and the walls of the container,

This means that pressure at input = pressure at output

Pressure = force /area

Input force = unknown

Input area = 0.1 m²

Output force = 9000N

Output area = 4m²

Therefore

Input force/0.1 = 9000/4

Input force = 0.1 × 9000 /4 = 225N

3y-y =2y

you have 3 ys and you are taking one y away so  the answer is 2y.

think it as 3 yogurts and you eat one, then you have 2 yogurts

hope this helps!  

Step-by-step explanation:

sin(2x) + cos(3x)

Use double angle formula sin(2x) = 2 sin x cos x.

Use triple angle formula cos(3x) = 4 cos³x − 3 cos x.

Substitute:

2 sin x cos x + 4 cos³x − 3 cos x

Answer: A)There are 5 nonfiction books for every 9 fiction books in the library.  

Step-by-step explanation: If you do the math you realize that there are clearly less nonfiction books than fiction books.

105/5=21 and after 21*9 lines up and to check your work than

5*21=105 and 9*21=189 it is not B because the smaller number 105 is in front of the ratio 105:189 and 5:9

Per 5 nonfiction books there are 9 fiction books in the given library.

Given that;

Ratio of nonfiction books to fiction books = 105:189

Computation:

Ratio of nonfiction books to fiction books = 105:189

[tex]Ratio\ of\ nonfiction\ books\ to\ fiction\ books = \frac{105}{189}\\\\Ratio\ of\ nonfiction\ books\ to\ fiction\ books = \frac{35}{63}\\\\Ratio\ of\ nonfiction\ books\ to\ fiction\ books = \frac{5}{9}\\\\[/tex]

So,

we say that;

Per 5 nonfiction books there are 9 fiction books

Option "A" is the correct answer to the following question.

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Answer:

A. Stock XYZ shows the best performance. The scale of Stock ABC makes the graph appear to be rising more slowly.

Step-by-step explanation:

We can find a and b using inverse trig functions,

[tex]

\cos(a)=\frac{4}{5}\implies a=\arccos\Big(\frac{4}{5}\Big)\approx36.87 \\

\sin(b)=-\frac{5}{13}\implies b=\arcsin\Big(-\frac{5}{13}\Big)\approx-22.62

[/tex]

[tex]\tan(36.87-(-22.62))\approx1.7[/tex]

Hope this helps.

Answer:

The sample should be as large as 480

Step-by-step explanation:

Probability of having a flu, p = 43/334

p = 0.129

Margin Error, E = 0.03

Confidence Interval, CI= 95%

At a CI of 95%, [tex]z_{crit} = 1.960[/tex]

The sample size can be given by the relation:

[tex]n = p(1-p)(z/E)^{2}[/tex]

[tex]n = 0.129(1-0.129)(1.960/0.03)^{2} \\n = 479.59\\n = 480[/tex]

To determine the sample size needed to estimate the population proportion with a desired margin of error, we can use the formula n = (z^2 * p * (1-p)) / (E^2), where n is the required sample size, z is the z-score corresponding to the desired level of confidence, p is the estimated proportion of the population with the characteristic, and E is the desired margin of error. Plugging in the given values, the epidemiologist should take a sample size of approximately 3245 in order to achieve her desired margin of error.

To determine the sample size needed to estimate the population proportion with a desired margin of error, we can use the formula:

n = (z^2 * p * (1-p)) / (E^2)

Where:

Plugging in the given values:

n = (z^2 * p * (1-p)) / (E^2) = (1.96^2 * 0.129 * 0.871) / (0.03^2) ≈ 3244.42

So, the epidemiologist should take a sample size of approximately 3245 in order to achieve her desired margin of error.

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