A water trough has two congruent isosceles trapezoids as ends and two congruent rectangles as sides.


The exterior surface area of the trough is ________.



The volume of the trough is _____.


If a trough is emptied until the water level is even with the midsegment of the trapezoidal ends there will be ______ cubic feet of water left in the trough.

Answer:  The required median of the given data set is 16.5.

Step-by-step explanation:  We are given to find the median of the following set of values :

11,  13,  14,  15,  18,  20,  23,  26.

We know that

(i) If the data contain an odd number of values, then the mid-value is the required median.

(ii) If the data contain an even number number of values, then the average of the two mid-values will be the required median.

Since the given data contains 8 values, which is an even number, so we will consider two mid-values and those are 15 and 18.

The average of 15 and 18 is given by

[tex]A=\dfrac{15+18}{2}=\dfrac{33}{2}=16.5.[/tex]

Thus, the required median of the given data set is 16.5.

Answer:

Step-by-step explanation:

The point-slope form of an equation of a line:

[tex]y-y_1=m(x-x_1)[/tex]

m - slope

(x₁, y₁) - point

The formula of a slope:

[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]

We have the points (9, 1) and (4, 16). Substitute:

[tex]m=\dfrac{16-1}{4-9}=\dfrac{15}{-5}=-3[/tex]

[tex]y-1=-3(x-9)[/tex]

The equation of the line that passes through the points (9, 1) and (4, 16) in point-slope form is y - 1 = -3(x - 9).

To find the equation of a line, we can use the point-slope form, which is y - y₁ = m(x - x₁), where (x₁, y₁) is a point on the line and m is the slope of the line.

Given the points (9, 1) and (4, 16), we can calculate the slope using the formula m = (y₂ - y₁) / (x₂ - x₁).

Substituting the values, we get m = (16 - 1) / (4 - 9) = -3. So, the equation of the line in point-slope form is y - 1 = -3(x - 9).

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Answer:

Step-by-step explanation:

The formula of a distance between two points:

[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

We have the points (5, -7) and (5, 11). Substitute:

[tex]d=\sqrt{(5-5)^2+(11-(-7))^2}=\sqrt{0^2+18^2}=\sqrt{18^2}=18[/tex]

Answer:

AC = 10

Step-by-step explanation:

Two tangents drawn to a circle from the same exterior point are congruent.

AC = AB

Since AB = 10, then

AC = 10

Answer:

>

Step-by-step explanation:

100 is a larger quantity than 20.

Using the is greater than sign shows this relationship between two quantities.

Hope this helps.

-Gumina

For this case we have the following pair of numbers:

100 and 20

We must indicate the correct symbol to relationalize them. That is to say:

<,>, =

So:

[tex]100 <20[/tex]

The relationship is false.

[tex]100> 20[/tex]

The relationship is true. 100 is greater than 20.

Answer:

100 is greater than 20. The opening of the symbol should be pointing to 100. That is: [tex]100> 20[/tex]

Answer: 7 cm

Step-by-step explanation:

You know the lenght of one of the sides of the smaller triangle.

You also know the lengths of two sides of the larger triangle.

You can see that a corresponding angle is equal

Therefore, by similarity, you can write the expression shown below:

[tex]\frac{36cm}{42cm}=\frac{6cm}{x}[/tex]

Now you must solve for x.

Therefore, you obtain that the value of x is the shown below:

[tex]x(\frac{36cm}{42cm})=6cm\\\\x=\frac{6cm*42cm}{36cm}\\\\x=7cm[/tex]

Answer:

[tex]n=2*10^{12}[/tex]

Step-by-step explanation:

we have

[tex](4.8*10^{-3})(n)=9.6*10^{9}[/tex]

Solve for n

That means-----> isolate the variable n

Divide by [tex](4.8*10^{-3})[/tex] both sides

[tex]n=\frac{9.6*10^{9}}{4.8*10^{-3}}\\\\n=\frac{9.6}{4.8}*10^{(9+3)}\\ \\ n=2*10^{12}[/tex]

Answer:

The value of [tex]n=2\times 10^{12}[/tex]  which make equation true.

Step-by-step explanation:

Given : Expression [tex](4.8\times 10^{-3})(n)=9.6\times 10^9[/tex]

To find : What scientific value for n will make this equation true?

Solution :

[tex](4.8\times 10^{-3})(n)=9.6\times 10^9[/tex]

Solve for n,

[tex]n=\frac{9.6\times 10^9}{4.8\times 10^{-3}}[/tex]  

[tex]n=\frac{9.6}{4.8}\times 10^{9+3}[/tex]  

[tex]n=2\times 10^{12}[/tex]  

Therefore, The value of [tex]n=2\times 10^{12}[/tex]  which make equation true.

The height would be 5.

Answer: i used my calculator check this is right

Step-by-step explanation:

Answer:

Infinitely many solutions: [tex]-5x+9y=2[/tex]

One solution: [tex]-10x+5y=4[/tex]

No solution: [tex]-10x+18y=5[/tex]

Step-by-step explanation:

 Solve for y from each equation to obtain the equation of the line in slope-intercept form:

[tex]y=mx+b[/tex]

m: slope

b: y-intercept

EQUATION ON THE TOP:

[tex]-10x+18y=4\\\\y=\frac{5}{9}x+\frac{2}{9}[/tex]

Equation 1:

[tex]5y=10x+4\\\\y=2x+\frac{4}{5}[/tex]

The equation on top and the equation equation 1 has different slopes and different y-intercept, therefore the system will have one solution.

Equation 2:

 [tex]9y=5x+2\\\\y=\frac{5}{9}x+\frac{2}{9}[/tex]

The equation on top and the equation equation 2 are the same, therefore, the system will have infinitely many solutions.

Equation 3:

[tex]18y=10x+5\\\\y=\frac{5}{9}x+\frac{5}{18}[/tex]

The slopes are equal, then both lines will be parallels, therefpre  the system will have no solution.

To form a system with infinite, one or no solutions, a second equation is chosen to be identical or a multiple, have different coefficients, or the same slope but different constants relative to the first equation, respectively.

To address the student's question about creating a system of equations with either infinitely many solutions, one solution, or no solutions, it is important to understand the properties of linear equations. When two equations are combined to form a system, the number of solutions is determined by their graphs on a coordinate plane. Three scenarios are possible:

To create a system with a known outcome, one must write a second equation with either the same coefficients and constant term (for infinitely many solutions), different coefficients (for one solution), or the same coefficients but a different constant term (for no solutions).

For example, if the given equation is y = 2x + 3, an equation for infinitely many solutions could be 2y = 4x + 6, for one solution y = -x + 1, and for no solutions y = 2x + 5.

X, Division symbol, +, -.

Answer:

=, +, or -

Step-by-step explanation:

You can have 3y + 5y. Or 3y - 5y. Or 3y=5y.

Answer:

  65 mL

Step-by-step explanation:

Let x represent the quantity (mL) of 30% acid that should be added to (70-x) mL of pure acid to make 35% acid. The quantity of acid in the mix is ...

  0.30·x + 1.00·(70 -x) = 0.35·70

  -0.70x = 70·(-0.65) . . . . . . simplify, subtract 1.0·70

  x = 65 . . . . . . . . . . . . . . . . . divide by the coefficient of x

65 mL of 30% acid should be added to 5 mL of pure acid to make 70 mL of 35% acid.

_____

Comment on the problem wording

Safety precautions should be observed when working with pure acid. As a chemistry problem (not a math problem), 5 mL of pure acid should be added to 65 mL of 30% acid, not the other way around.

Answer:

Step-by-step explanation:

The formula of a volume of a cube:

[tex]V=a^3[/tex]

a - edge of cube

We have V = 1,953,125 cm³. Substitute:

[tex]a^3=1,953,125\to a=\sqrt[3]{1,953,125}\\\\\begin{array}{c|c}1,953,125&5\\390,625&5\\78,125&5\\15,625&5\\3,125&5\\625&5\\125&5\\25&5\\5&5\\1\end{array}\\\\1,953,125=5^3\cdot5^3\cdot5^3\\\\\sqrt[3]{1,953,125}=\sqrt[3]{5^3\cdot5^3\cdot5^3}\qquad\text{use}\ \sqrt[3]{ab}=\sqrt[3]a\cdot\sqrt[3]b\\\\=\sqrt[3]{5^3}\cdot\sqrt[3]{5^3}\cdot\sqrt[3]{5^3}\qquad\text{use}\ \sqrt[3]{a^3}=a\\\\=5\cdot5\cdot5=125[/tex]

sure !! pretty sure it wants you to distribute in each of your answer choices to get the functions and then match the function to the graph because the answer choices now are factored and harder to work with. to be honest once you find your functions after distributing i would just use a graphing calculator website like desmos.com and input each function to see which graph looks like the one shown

Answer:

(x^-1)(x+3)

Step-by-step explanation:

A

Answer:

the mean is 4.2

Step-by-step explanation:

Answer:

Mean absolute deviation: 1.84.

Step-by-step explanation:

How do you find the mean absolute deviation for a bunch of numbers?

What's the mean of those numbers?

(3 + 5 + 8 + 1 + 4) / 5 = 4.2.

Absolute difference:

What's the average of those absolute differences?

(1.2 + 0.8 + 3.8 + 3.2 + 0.2) / 5 = 1.84. That's the mean absolute deviation of those five numbers.

1/12  the fraction of the garden is planted with carrots.

The Brown family is planting 1/3 of their garden with vegetables, which is further divided into equal parts of carrots, onions, peppers, and tomatoes.

So, the fraction of the garden planted with carrots is 1/4 of the vegetable section, which can be calculated as follows:

1/4 x 1/3 (fraction of the garden planted with vegetables) = 1/12

Therefore, 1/12 of the garden is planted with carrots.

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Final answer:

1/12 of the Brown family's garden is planted with carrots, as the vegetable section is 1/3 of the garden and is equally divided among four types of vegetables.

Explanation:

The Brown family is planting 1/3 of their garden with flowers, 1/3 with berries, and 1/3 with vegetables.

The vegetable section is equally divided into four parts for carrots, onions, peppers, and tomatoes.

To find the fraction of the garden planted with carrots, you would divide the vegetable section's fraction by the number of vegetable types.

Since 1/3 of the garden is planted with vegetables, and there are 4 types of vegetables, the fraction of the garden with carrots is:
1/3 ÷ 4 = 1/3 × 1/4 = 1/12.
Therefore, 1/12 of the garden is planted with carrots.

Answer:

A. Add both sides

Step-by-step explanation:

jus did it on usa prep test

The solution of the equation is obtained by adding 4 on both sides. Then the correct option is A.

The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.

A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.

The linear equation with a single variable is given below.

x - 4 = 12

Add 4 on both sides of the equation, then we have

x - 4 + 4 = 12 + 4

           x = 16

The arrangement of the situation is acquired by including 4 the two sides. Then the right choice is A.

More about the solution of the equation link is given below.

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Answer:

8

Step-by-step explanation:

see attached for questions 3's answer

Answer:

D.)1.7

Step-by-step explanation:

it's positive and above the 1 point

Answer:

A 8+9+(-3)+4+21 is positive

C  2+16+9-5)+(-3) is also positive

Step-by-step explanation:

The sequence of four plays that the team keeps the ball is,

A. 8, -3, 4, 21.

C. 2, 16, -5, -3.

A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.

Given, If they don't gain at least ten yards, the other team gets the ball.

Therefore, the sequences of four plays that result in the team getting to keep the ball should be more than 10 yards when we take the sum of the sequences.

So, 8 - 3 + 4 + 21 = 30 yards.

30 - 7 - 8 - 12 = 3 yards.

2 + 16 - 5 - 3 = 10 yards.

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C)21-YEARS OLD WOMAN CHARGED WITH FRAUD.

The answer is A.

15 year-old girl with shoplifting

Answer:

B. -28

Step-by-step explanation:

7 times the value -4 is "added", yielding the result of -28.

So we're looking for an answer with -28 as an answer, and a "times 7". That's answer B. Answer D is not the right one since clearly, the model shows -4 being repeatedly (7 times) added. -7 added 4 times would be a different model.

The answer is be -28

Answer:

$3.36

Step-by-step explanation:

1 pound is 4 times 0.25 pounds.

$0.84 = 0.25 pounds

1 pound = $0.84 times 4

1 pound = $3.36

The cost of one pound should be $3.36

Arthur paid $0.84 for 0.25 pounds of potato salad.

Since we know that

1 pound is 4 times 0.25 pounds.

So,

$0.84 = 0.25 pounds

Now

1 pound = $0.84  (4)

1 pound = $3.36

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I believe it would be Steel so B

Answer: both steel and nickel are magnetic but in this case i would go with  B.steel

Answer:

A

Step-by-step explanation:

If a parallel line is perpendicular to the other line, the line parallel to the first line is also perpendicular to that line.

Answer:

32

Step-by-step explanation:

Give each player a letter.

a, b, c, d, e, f, g, h, i

Each player high fives each other once.

a: b, c, d, e, f, g, h, i

b: c, d, e, f, g, h, i

c: d, e, f, g, h, i

d: e, f, g, h, i

f: g, h, i

g: h, i

h: i

Remember that you do not recount high-fives (as each player only gives it to another player once). Add the amount of high fives by counting.

32 is your answer.

~

An acorn is most likely to be weighed in Ounces. Hope this helps! =^-^=

Answer:

ounces

Step-by-step explanation:

tons is what you would weigh a elephant

pounds is what you would measure how heavy a person is

Answer:

I believe the correct answer is B.

Answer: A

Step-by-step explanation: Just because it landed on black more times doesn't mean it will land on it again also i know its correct because i took the same FLVS exam :)

Answer:

P(blue) = 3/7

So '7' belongs in the box

Step-by-step explanation:

There are 14 total marbles, 6 of which are blue.  The probability of pulling a blue marble out of the bag is

P(blue) = 6/14, which reduces to 3/7

The probability of drawing a particular marble from a bag depends on the number of that marble initially in the bag and whether the marbles are replaced after being drawn. Probabilities are calculated based on these conditions, including removing a marble of a particular color after another specific color has been removed.

The subject of the question is probability, a concept in mathematics. The possibility of drawing a particular color of marble from a bag depends on how many of that color is in the bag to start with, as well as whether or not the marbles are replaced after being drawn.

In the case of James and his bag of four blue and three white marbles, the probability of drawing a blue marble is 4 out of 7 the first and second time he draws because the blue marble is replaced each time.

On the other hand, if the first drawn marble is not replaced (like in the second example), the total number of marbles, and thus the probabilities, change. For instance, after drawing and setting aside one blue marble from a bag containing four blue and three white marbles, the probability of drawing another blue marble becomes 3 out of 6, or 1/2.

Finally, in the case of Mark and his bag of green, red, and yellow marbles, the probability of drawing a yellow marble and then a green marble without replacement can be calculated as the product of the possibility of attracting a yellow marble first, and then the conditional probability of drawing a green marble given that a yellow one has already been removed. This shows how probabilistic events can be dependent on one another.

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