Can someone help me out with these problems?

The total surface area of the trapezoidal prism is S = 3,296 inches²

Given data ,

Let the total surface area of the trapezoidal prism is S

Now , the measures of the sides of the prism are

Side a = 10 inches

Side b = 32 inches

Side c = 10 inches

Side d = 20 inches

Length l = 40 inches

Height h = 8 inches

Lateral area of prism L = l ( a + b + c + d )

L = 40 ( 10 + 32 + 10 + 20 )

L = 2,880 inches²

Surface area S = h ( b + d ) + L

On simplifying the equation , we get

S = 2,880 inches² + 8 ( 52 )

S = 3,296 inches²

Hence , the surface area of prism is S = 3,296 inches²

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Answer:

30°

Step-by-step explanation:

Step 1:

2x + 10 + 4x + 80 = 180     Sum of a line

Step 2:

6x + 90 = 180      Combine Like Terms

Step 3:

6x = 90     Subtract 90 on both sides

Answer:

x = 30°       Divide

Hope This Helps :)

The solution to the inequality -48 - 3x > 6x - 8 is x < -40/9

From the question, we have the following parameters that can be used in our computation:

-48 - 3x > 6x - 8

Collect the like terms in the above inequality

So, we have

-6x - 3x > 48 - 8

When the like terms are evaluated, we have

-9x > 40

Divide both sides by -9

x < -40/9

Hence, the solution to the inequality is x < -40/9

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Answer:

30 degrees

Step-by-step explanation:

(75 degrees x 2) = 150 degrees

180 degrees - 150 degrees = 30 degrees

angle 1 = 30 degrees

Answer:

The null hypothesis is rejected if the p-value is lower than or equal to the chosen significance threshold; otherwise, it is not. To put it another way, if p, reject  \(H_{0}\); if p>, do not reject \(H_{0}\).

This criterion, known as (alpha) in null hypothesis testing, is often set to 05. The rejection of the null hypothesis is if there is less than a 5% probability that a result as dramatic as the sample result would occur if the null hypothesis is accepted. The outcome is referred to as statistically significant when this occurs.

If a statistical test is run with a threshold of significance = 0.1, 0.05, and 0.01 the null hypothesis was rejected.

The alternative hypothesis is taken into consideration instead of the null hypothesis if the P value is less than alpha, the predetermined level of statistical significance.

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Answer:

30/64 inches.

Explanation:

The size of the converted metric part = 0.473 in.

Now, we know that:

Therefore:

Thus, we have that:

To the nearest 64th of an inch, the closest size will be 30/64 inches.

Answer:

  86%

Step-by-step explanation:

You want the girls' average if the 20 boys in the 30-student class had an average of 62%, and the class average was 70%.

The class average is the weighted average of the boys' score and the girls' score. The weights are the fraction of students of each gender.

  class average = (1/3)(girls' average) +(2/3)(boys' average)

Solving this equation for the girls' average, we get ...

  (1/3)(girls' average) = (class average) -(2/3)(boys' average)

  girls' average = 3(class average) -2(boys' average)

  girls' average = 3(70%) -2(62%) = 210% -124%

  girls' average = 86%

__

Alternate solution

The sum of differences from the class average must be zero. The boys' average is 8 points below the class average, and there are 2 times as many boys as girls. Thus, compared to the girls, the boys contribute a total of 2·8 = 16 points below the class average. The girls must counter by having an average 16 points above the class average: 70+16 = 86.

Answer:

c=27

Step-by-step explanation:

9-c=-18

-c = -18 -9

-c = -27

change the signs

c = 27

Answer:

60

Step-by-step explanation:

divide 39 by 65%,

you will get
39 / ( 65/ 100)
= 39 * (100/65)
= 39 * (20 /13)
= 3*20
= 60

Answer:

f ≥ 5

Step-by-step explanation:

Translating the word problem into an algebraic expression, we have;

2(f - 4) ≥ 2

Opening the bracket, we have;

2f - 8 ≥ 2

Rearranging the equation, we have;

2f ≥ 2 + 8

2f ≥ 10

Dividing both sides by 2, we have;

f ≥ 5

Therefore, the possible values for Felipe’s age is 5, 6, 7, 8, 10 till infinity.

approximately 97.5% of the sample will have values below 600.

The empirical rule states that about 68 % of the sample will be within one standard deviation of the mean, approximately 95 % will be within two standard deviations of the mean, and approximately 99.7 % will be within three standard deviations of the mean.

We must determine the z-score for a value of 600 using the following formula in order to determine the proportion of the sample that has values lower than 600.

z = (x - μ) / σ

If x is the value for which we wish to calculate the probability, is the sample mean, and is the sample standard deviation.

When we enter the values we have, we get:

z = (600 - 500) / 50 = 2

The number of 600 is therefore two standard deviations above the mean.

Approximately 95% of the sample will, under the empirical criterion, lie within two standard deviations of the mean. We can infer that since 600 is two standard deviations above the mean, 2.5% of the sample will have values above 600.

Therefore, approximately 97.5% of the sample will have values below 600.

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The derivative of\(y = e^(6−6x)\) is found as \((dy)/(dx) = -6e^(6-6x).\)

In calculus, we often use the chain rule to differentiate complex functions. In this question, we use the chain rule of differentiation to find the derivative of \(y = e^(6−6x).\)

The chain rule states that if we have a function of the form f(g(x)), then the derivative of this function is given by

(df)/(dx) = (df)/(dg) * (dg)/(dx).

The given equation is  \(y = e^(6−6x).\)

Differentiate \(y = e^(6−6x).\)

We can differentiate y with respect to x using the chain rule of differentiation, which is given by

(dy)/(dx) = (dy)/(du) * (du)/(dx)

Where u = 6 - 6x and y = e^u

Hence, we can write

\((dy)/(dx) = e^u * (-6)\)

Now substituting u = 6 - 6x, we get

\((dy)/(dx) = e^(6-6x) * (-6)\)

Therefore, the derivative of\(y = e^(6−6x)\) is given by

\((dy)/(dx) = -6e^(6-6x).\)

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Check the picture below.

Answer:

Increase

Step-by-step explanation:

The number gets larger. Increase means it gets larger, but decrease means it gets lower.

Answer:

D. 0.00003471

Step-by-step explanation:

Answer:

Y=1.88x

Step-by-step explanation:

x1=2 x2=3, y1=3.76 y2=5.64

(2, 3.76) (3, 5.64)

m(slope) =5.64-3.76/3-2

m=1.88

y-3.76=1.88(x-2)

y-3.76=1.88x-3.76

Y=1.88x

Answer:

$39.36

Step-by-step explanation:

Can find how much the sales tax cost:

32 x 0.08 = $2.56

Can also find out how much he tipped:

32 x 0. 15 = $4.80

Total = $32 + sales tax + tip

Total = $32 + $2.56 + $4.80

Total = $39.36

Answer:

$39.36 in total

Step-by-step explanation:

32×0.08= 2.56

32×0.15= 4.8

4.8+2.56= 7.36

32+7.36=39.36

The dimensions of the fenced-in area is given as

either length is 35 yards and width is 80 yards ,  

or length is 40 yards and width is 70 yards .

In the question ,

given that the total length of the fence (perimeter) = 150 yards

let L be the length of the portion to be fenced

let B be the width of the house

Given that , one side of the portion is fenced using the back side of the house

So, the perimeter of the portion to be fenced is 2L+B

equating both the perimeter ,we get

2L+B=150

B=150-2L       ....(i)

Also , given that the area of the  fenced-in portion = 2800 yards

also the formula for area of fenced-in portion = L×B

hence

L*B=2800

Substituting the values of B from equation(i) , we get

L*(150-2L)=2800

150L - 2L² = 2800

2L² - 150L + 2800 = 0

simplifying further , we get

L² - 75L + 1400 = 0

L² -40L -35L +1400 = 0          .....using splitting the middle term

L(L-40) -35(L-40) = 0

(L-35)(L-40) = 0

So , L = 35 yards or L = 40 yards

Using L = 35 yards , we get B = 150-2(35) = 80 yards

and using L =40 yards , we get B = 150-2(40) = 70 yards .

Therefore , the dimensions of the fenced-in area is given as

either length is 35 yards and width is 80 yards ,  

or length is 40 yards and width is 70 yards .

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The statement "If A is 3 times 3, with columns a_1, a_2, a_3, then det A equals the volume of the parallelepiped determined by a_1, a_2, a_3"  is true as the determinant of a 3x3 matrix equals the volume of the parallelepiped determined by its columns.  The correct option is B).  The second statement "det A^T = (- 1)det A" is false as det A^T = (-1)^(number of row interchanges) det A for any n x n matrix A. So, the correct option is B).

The first statement is true, and the correct answer is: "The statement is true because if A is 3 times 3, with columns a_1, a_2, a_3, then det A equals the volume of the parallelepiped determined by a_1, a_2, a_3. Because det A greater than or equal to 0 for all 3 times 3 matrices A, it follows that |det A| = det A." So, the correct answer is B).

The second statement is also false, and the correct answer is: "The statement is true because a row interchange is needed to turn a matrix into its transpose. A row interchange changes the sign of the determinant." So, the correct ansnwer is B).

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Answer:

\(x^{3} \\\) + \(y^{3} = z^{3}\)

Any variable/number can be replaced by z because its just an assumption.

Step-by-step explanation:

Step-by-step explanation:

Both function are always increasing so D is correct.

Solution

Given x-intercept as 6 => a = 6

and y-intercept as -2 => b = -2

the equation is;

The answer is:

The additive inverse of a number gives zero. The additive inverse of the complex number -8+3i is 8-3i.

The additive inverse of a number is the other number which when added to the initial number gives the output as zero.

As we know about the additive inverse, therefore, we need a number that will return zero when added to the complex number.

The additive inverse of the complex number -8+3i will be,

\((-8+3i) + (8-3i) = 0\)

Thus, the additive inverse of the complex number -8+3i is 8-3i.

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Answer:

8-3i

Step-by-step explanation:

got it right

The length of the missing side (hypothenuse) is equal to 5

"Information available from the question"

Opposite side of the triangle(y) = 3

Adjacent side of the triangle (z)= 4

Hypothenuse side of the triangle = x

Pythagorean Theorem

This formula is used to find the missing side of a right angle triangle if two sides are given.

\(x^{2} =y^2+z^2\)

Let's substitute the values into the formula and solve for the hypothenuse

\(x^{2} =3^2+4^2\)

\(x^{2}\) = 9 + 16

\(x^{2}\) = 25

\(x=\sqrt{25}\)

x = 5

The length of the missing side (hypothenuse) is equal to 5.

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These lines will be parallel to the initial line and will intersect the final velocity line at the corresponding values (122 for the lower estimate and 298 for the upper estimate)

To sketch the velocity against time, you can take the following steps:

First, calculate the acceleration using the given data by using the formula;

acceleration = (final velocity - initial velocity)/time

Where; Initial velocity is the velocity before applying the brakes

Final velocity is the velocity at which the car comes to stop

Time is the time it takes to stop the car (6 seconds in this case)

Now, calculate the lower and upper estimates using the formula;

Lower estimate = initial velocity + (acceleration x time)

Upper estimate = initial velocity + (2 x acceleration x time)

Sketch the graph using the following steps;

On the vertical axis, plot the velocity of the car

On the horizontal axis, plot the time

Start from the initial velocity and draw a straight line with the calculated acceleration until the end of the time (6 seconds)This straight line will give you the final velocity (0 in this case)

Now, draw two more lines, one with the lower estimate and the other with the upper estimate

Finally, label the axes and the lines with their corresponding values.'

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The maibag reaches the ground at the same instant it is released from the helicopter, which is at t = 1.85 seconds.

So, the maibag reaches the ground immediately.

To find the time it takes for the maibag to reach the ground after it is released from the helicopter, we need to set the height equation equal to zero (since the ground is at height 0).

Let's calculate the time using the given height equation:

\(h = 3.25t^3\)

Setting h to 0, we get:

\(0 = 3.25t^3\)

Dividing both sides by 3.25:
\(t^3 = 0\)

Since any number raised to the power of 3 is still that number (cubed), we have:

t = 0

This means that the maibag reaches the ground at the same instant it is released from the helicopter, which is at t = 1.85 seconds.

So, the maibag reaches the ground immediately.

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