What is the surface area of the prism below

Answer:

The answer is described below.

Step-by-step explanation:

What we should do is follow the next four steps

1. Identify the geometric shape of the garden.

2. Consult various mathematical formulas available for the area and perimeter of different types of geometric shapes.

3. Use the formula according to the geometric shape of the garden.

4. Identify in the formula the values of the given dimensions to calculate the perimeter and area.

In this way you could already find the area and the perimeter of the garden.

Answer:279936

Step-by-step explanation:

Answer:There are 4 serving in the container.

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

Took Edge 2020 Fraction Multiplication and Division Test

Answer:

Step-by-step explanation:

The expression that is always equivalent to sin x when 0° < x < 90° is (1) cos (90° - x). Option 1

To understand why, let's analyze the trigonometric functions involved. In a right triangle, the sine of an angle is defined as the ratio of the length of the side opposite the angle to the length of the hypotenuse. Since we are considering angles between 0° and 90°, we can guarantee that the side opposite the angle will always be the shortest side of the triangle, and the hypotenuse will be the longest side.

Now let's examine the expression cos (90° - x). The cosine of an angle is defined as the ratio of the length of the side adjacent to the angle to the length of the hypotenuse. In a right triangle, when we subtract an angle x from 90°, we are left with the complementary angle to x. This means that the remaining angle in the triangle is 90° - x.

Since the side adjacent to the angle 90° - x is the same as the side opposite the angle x, and the hypotenuse is the same, the ratio of the adjacent side to the hypotenuse remains the same. Therefore, cos (90° - x) is equivalent to sin x for angles between 0° and 90°.

On the other hand, options (2) cos (45° - x) and (3) cos (2x) do not always yield the same value as sin x for all angles between 0° and 90°. The expression cos x (option 4) is equivalent to sin (90° - x), not sin x.

Option 1 is correct.

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Answer:

66

Step-by-step explanation:

the difference of 54 and 32 is 54 - 32 = 22

the difference of 8 and 5 is 8 - 5 = 3

then

22 × 3 = 66

From the resulting solution, the correct linear inequality graph is Graph C.

Given the inequality equation below:

2(2x-1)+7< 13 or -2x+5 ≤ -10.​

Simplify the expression

2(2x-1)+7< 13

Expand

4x - 2 + 7 < 13

4x + 5 < 13

4x < 13 - 5

4x < 8

x < 2

For the inequality -2x+5 ≤ -10.

-2x+5 ≤ -10

-2x  ≤ -15

x  ≥ 7.5

Hence the solution to the given system of inequalities are x < 2 and x  ≥ 7.5

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Answer:

Step-by-step explanation:

You want to show that the point (4, -4) is on the graph of x² +y² = 32, and you want the tangent and normal lines at that point.

The point is on the curve because when x = 4 and y = -4 the resulting statement is 16 +16 = 32, which is a true statement.

The tangent to a circle is most easily found by first considering the normal. The normal line will be the line through the point on the circle and the center of the circle. Here, the center is (0, 0). The slope of the normal line is ...

  m = y/x = -4/4 = -1

The tangent line's slope is the opposite reciprocal of this:

  m = -1/(-1) = 1

The point-slope form of the equation for the tangent line is ...

  y -k = m(x -h) . . . . . equation for line with slope m through point (h, k)

  y -(-4) = 1(x -4) . . . . . equation for line with slope 1 through point (4, -4)

  x -y = 8 . . . . . . . . . . add 4-y to put in standard form

The equation of the tangent line is x - y = 8.

In the section above, we found the slope of the normal line is -1. We also noted that the normal line goes through the point (0, 0). Then the point-slope form of the normal line is ...

  y -0 = -1(x -0)

  y = -x

The equation of the normal line is y = -x.

__

Additional comment

The normal line can also be written as x + y = 0.

The tangent line can also be written as y = x -8.

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Bryan invested $1600 in the first account (earning 11% interest) and $4900 (6500 - 1600) in the second account (earning 7% interest).

Let's assume that Bryan invested an amount of x dollars in the first account, which earns 11% interest, and (6500 - x) dollars in the second account, which earns 7% interest.

The interest earned from the first account can be calculated as 0.11x, and the interest earned from the second account can be calculated as 0.07(6500 - x).

According to the problem, the total interest earned after one year is $519. So we can set up the equation:

0.11x + 0.07(6500 - x) = 519

Simplifying the equation:

0.11x + 455 - 0.07x = 519

0.04x + 455 = 519

0.04x = 64

x = 64 / 0.04

x = 1600

Therefore, Bryan invested $1600 in the first account (earning 11% interest) and $4900 (6500 - 1600) in the second account (earning 7% interest).

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Answer:

x is -1/b yw

Step-by-step explanation:

Write an equation in point-slope form of the line that passes through the point (−6, 6) and has a slope of m=3/2.

Area = 1/2 × 24 × 11 × Sin(76)

Area = 12 × 11 × 0.9703

Area = 132 × 0.9703

Area = 128.0796

Area = 128.1 in^2

Answer:

2 students play both

Step-by-step explanation:n(u)=28

n(b)=7,n(b)=5,n(who play neither sport)=18

HERE,

n(u)=n(b)+n(b)-n(BnB)+n(who play neither sport)

28=7+5-n(BnB)+18

28=30-n(BnB)

n(BnB)=30-28

 =2 answer

Answer:

(2,1)

6928ft

59.0813m

26 1/4m

Step-by-step explanation:

Area of a trapezoid = (a+b)*h/2 so (100+150)*80/2

= 10000

Area of a rectangle = l*w so 48*64

=3072

10000-3072 = 6928

The surface area of a square pyramid is A=a^2+2a√a^2/4+h^2 which is A=4^2+2(4)√(4)^2/4+(5)^2 which = 59.08

Volume of a rectangular prism is l*w*h so 3.5*1.25*6 = 26.25 which is equal to 26 1/4

Okay, here we have this:

Considering the provided table, we are going to analize if the table shows direct variation, so we obtain the following:

To identify if there is direct variation then we will calculate the ratios between the points, and if they are all the same then the table does show direct variation, then we have:

y=kx

k=y/x

5/2=2.5

45/18=2.5

80/30=2.66

Since the ratios between the points are not the same, then it does not represent a direct variation.

In the quadrilateral ABCD and LBNM the corresponding angles and line segments are as follow,

∠A = ∠L, ∠D =∠M , ∠C = ∠N , and

AB = LB , CD = NM ,  DA = ML.

Quadrilateral ABCD rotates 180 degrees around point B,

New quadrilateral formed named LBMN

The corresponding angle after rotation of 180 degrees around B is equals to,

B remain at same position.

A rotates and point L take the position of A.

D rotates and point M take the position of D.

C rotates and point N take the position of C.

Corresponding angle to A is angle L.

Corresponding angle to D is angle M.

Corresponding angle to C is angle N.

Similarly corresponding segments are of ABCD and LBNM are

Line segment AB corresponds to line segment LB.

Line segment CD corresponds to line segment NM

Line segment DA corresponds to line segment ML.

Therefore, in the quadrilateral the corresponding angles and line segments are ∠A = ∠L, ∠D =∠M , ∠C = ∠N , AB = LB , CD = NM , and DA = ML.

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Answer:

24 ounces/ 2 packets = 12 ounces/ packet

Step-by-step explanation:

23 (12 ounces/packet) = 276 ounces of water

The the rate of ounces of water needed for each packet of flavoring would be 12.

Given is the packets of flavoring added to an specific amount of water to make soup.

Now, for 24 ounces of water, 2 packets of flavoring are needed.

Then, for 1 packet of flavoring, (24/2) or 12 ounces of water is needed.

For 5 packets of flavoring, (12 x 5) or 60 ounces of water is needed.

So, the rate of ounces of water needed for each packet of flavoring would be -

r = (60 - 24)/(5 - 2)

r = 36/3

r = 12

r = 12

Therefore, the the rate of ounces of water needed for each packet of flavoring would be 12.

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Answer:

Around 11.2

Step-by-step explanation:

The tangent of an angle in a right triangle is equivalent to the opposite side divided by the adjacent side. In this case:

\(\tan 24= \dfrac{5}{x} \\\\x=\dfrac{5}{\tan 24}\approx 11.2\)

Hope this helps!

Answer:

Grapes are less expensive

Step-by-step explanation:

First, find how much money 1 pound of each fruit is:

Bananas: $1.47 / 3 = $0.49

Grapes: $1.18 / 2 = $0.59

Compare:

0.49 < 0.59

So grapes are less expensive

Answer:

1384.7

Step-by-step explanation:

42/2     21^2x3.14=1384.74

Hope this Helps :)

Answer:

3

Step-by-step explanation:

1/5 / 1/15 = 3

Insert a picture, please.

Answer:

\(10 \div \frac{3}{7} \times \frac{4}{7} \)

\(10 \times \frac{7}{3} \times \frac{4}{7} \)

40/3

13.33 min

The sum of the arithmetic sequence 1, 3, 5, 7, … , 99 is 2525

Sequence is an enumerated collection of objects in which repetitions are allowed and order matters.

Given sequence is 1, 3, 5, 7, … , 99.

It is a arithmetic sequence, the difference between two consecutive terms will be same

d=3-1=2

first term a=1

l=last term =99

We need to find 99 is which term in the sequence

Aₙ = a + ( n - 1 ) d

99=1+(n-1)2

99=1+2n-2

99=2n-1

100=2n

Divide both sides by 2

50=n

Now we need to find the sum of 50 terms

Sₙ=n/2(l+d)

=50/2(99+2)

=25(101)

=2525

Hence, the sum of the arithmetic sequence 1, 3, 5, 7, … , 99 is 2525

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The probability that a randomly selected graduate of this state college system does not have a STEM degree and does not identify as female is 0.219

According to the question,

Let event of female graduates in the college be W and Graduates with STEM be "X"

Given , Percentage of female graduates  :52.5%

P(W) = 0.522

Percentage of  graduates with STEM degree = 37.7%

P(X)  = 0.377

Percentage of female graduating with STEM degree = 11.8%

P(W∩X) = 0.118

We have to calculate,

Probability that random selected graduate doesn't have STEM degree and not a female : P( male with not a degree of STEM)

=> 1 - P(W ∪ X)

=> 1 - P(W) - P(X) + P(W∩X)

=> 1 - 0.522 - 0.377 + 0.118

=> 0.219

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Step-by-step explanation:

Because straight lines (that are not the 'same line') can have at most, only one point of intersection...the unique solution.

Answer:

no it not have a unique solution.

Answer:

The speed of the cruise ship relative to the current is approximately 9.424 kilometers per hour.

The cruise ship's will need 2.425 hours for its upstream journey.

Step-by-step explanation:

The total time of the cruise (\(t\)), in hours, is the sum of the times for the upstream (\(t_{u}\)) and downstream journeys (\(t_{d}\)), in hours. Let suppose that both river and cruise ship travel at constant velocity, the cruise ship travels against the current in its upstream journey, whereas it is in favor of the current in the downstream journey, meaning that:

\(t = t_{u} + t_{d}\)

\(t = \frac{x}{v_{S/C} - v_{C}} + \frac{x}{v_{S/C} + v_{C}}\) (1)

Where:

\(v_{C}\) - Speed of the current, in kilometers per hour.

\(v_{S/C}\) - Speed of the cruise ship relative to the current, in kilometers per hour.

If we know that \(t = 4\,h\), \(x = 18\,km\) and \(v_{C} = 2\,\frac{km}{h}\), then we have the following expression:

\(4\,h = (18\,km)\cdot \left(\frac{1}{v_{S/C} - 2\,\frac{km}{h} } + \frac{1}{v_{S/C}+2\,\frac{km}{h} }\right)\)

\(\frac{2}{9} = \frac{1}{v_{S/C}-2} + \frac{1}{v_{S/C}+2}\)

\(\frac{2}{9} = \frac{2\cdot v_{S/C}}{v_{S/C}^{2}-4}\)

\(2\cdot v_{S/C}^{2} - 8 = 18\cdot v_{S/C}\)

\(2\cdot v_{S/C}^{2}-18\cdot v_{S/C}-8 = 0\)

The roots of the second order polynomial are, respectively:

\(v_{S/C,1} \approx 9.424\,\frac{km}{h}\), \(v_{S/C,2} \approx -0.424\,\frac{km}{h}\). Since the speed is the magnitude of the velocity, a realistic solution must be a positive quantity and the solution is:

\(v_{S/C} \approx 9.424\,\frac{km}{h}\)

The speed of the cruise ship relative to the current is approximately 9.424 kilometers per hour.

And the time needed for the upstream journey is:

\(t_{u} = \frac{x}{v_{S/C}- v_{C}}\) (2)

If we know that \(x = 18\,km\), \(v_{S/C} \approx 9.424\,\frac{km}{h}\) and \(v_{C} = 2\,\frac{km}{h}\), then time for the upstream journey is:

\(t_{u} = \frac{18\,km}{9.424\,\frac{km}{h}-2\,\frac{km}{h} }\)

\(t_{u} = 2.425\,h\)

The cruise ship's will need 2.425 hours for its upstream journey.