(08.01 MC)
Find the height of a square pyramid that has a volume of 75 cubic feet and a base length of 5 feet.

A. 5 feet
B. 9 feet
C. 25 feet
D. 45 feet

Answer: [tex]\frac{\sqrt{113}}{7}[/tex]

Step-by-step explanation:

As X is an acute angle, all 6 trigonometric functions with an argument of X are positive.

Using the identity [tex]1+\tan^{2} X=\sec^{2} X[/tex],

[tex]1+\left(\frac{8}{7} \right)^{2}=\sec^{2} X\\\\\sec^{2} X=\frac{113}{49}\\\\\therefore \sec X=\boxed{\frac{\sqrt{113}}{7}}[/tex]

Answer:

516 students eat out 3 times a week

Step-by-step explanation:

22% of 2346 is 516.12 and a person can't be a decimal so it's 516

22 x 2346 = 51612
and 51612÷100 = 516.12

We would expect about 516 WHS students to eat out 3 time

percentage, a relative value indicating hundredth parts of any quantity.

Given that 22% of high school students say they eat out 3 times a week

We need to find the number of students  of the 2346 students who attend WHS would you expect eat out 3 times a week

We can start by using the proportion:

(22/100) = (x/2346)

where x is the number of students we would expect to eat out 3 times a week.

To solve for x, we can cross-multiply:

100x = 22 × 2346

100x = 51612

Divide both sides by 100

x = 516.12

Hence, we would expect about 516 WHS students to eat out 3 time

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The correct answer is option C which is the ratio of the difference in the means of the two teams to the mean absolute deviation of Team B will be 0.25.

Mean is defined as the ratio of the sum of the number of the data sets to the total number of the data.

The difference between the mean times is about 16 times the mean absolute deviation of the data set.

59.32 - 59.1 = 0.22

2.4 - 1.5 = 0.9

0.22 / 0.9 = 0.25

Therefore the correct answer is option C which is the ratio of the difference in the means of the two teams to the mean absolute deviation of Team B will be 0.25.

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A pattern is a recurring arrangement of numbers, forms, colours, and so on.

In mathematics, a pattern is a recurring arrangement of numbers, forms, colours, and so on. The Pattern may be applied to any form of event or object. A pattern is defined as a group of integers that are connected to each other in a specified way.

As per the pattern, Each figure has 3 more squares than the one before it.

Hence, the correct option is C.

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The interest which has to be paid is $28.

Simple Interest amount can be estimated by the product of principal amount, rate of interest, and time in year.

Simple Interest= S.I. =p*t*r/100

where p is the principal amount,

r: interest rate (%)

t: the time (in year).

Here, given,

Margo has taken borrowed $600 with an annual interest of 7% which has to be paid within 8 months.

principal amount P = $600

rate of interest= r=7%

time=t=8 months= 2/3 year

using the above-mentioned formula,

Simple Interest S.I.= p*t*r/100= (600*(2/3)*7)/100= $28

Therefore the interest which has to be paid is $28.

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[tex]\large\orange\implies \rm \large \:f(x) \: = \: 2x[/tex]

We have to find x when f(x) is 8

[tex]\large\orange\implies \rm \large \:8 = \: 2x[/tex]

[tex]\large\orange\implies \rm \large \: \cancel\frac{8}{2} \: = \: x \\ [/tex]

[tex]\large\orange\implies \rm \large \: \: 4 \: = \: x[/tex]

[tex]f(x) \: = \: 2x[/tex]

We have to find x when f(x) is 8

[tex]8 = \: 2x[/tex]

[tex]x = \frac{8}{2} \\ \\ x = 1.[/tex]

The value of x is 4 when f(x) is 8 .

Answer:

20

Step-by-step explanation:

Answer:

20$ For the Roses

Step-by-step explanation:

Think about it like this. For each daisy (1$), the price is double for roses (2$).

Brad has a limit of 33$. And he bought 3 more daisies than roses.

If each daisy is 1$, and he bought 3+ over roses, take away 3$ to get 30$. If he bought 10 (excluding 3+) Daisies, He must have bought 10 roses.

(10 Daisies = 10$) + (10 Roses = 20$) = 30$

30$ + (3 Daisies = 3$) = 33$

Answer:

[tex]1)\text{ Friday}\\2)\text{ }7:00\\3a)\text{ }0\\3b)\text{ }4\\3c)\text{ }0\\4a)\text{ }6\\4b)\text{ }4\\4c)\text{ }2[/tex]

Answer: 20

Step-by-step explanation:

Let [tex]f(y)=x[/tex]

[tex]x=\frac{1}{2}y+10\\\\x-10=\frac{1}{2}y\\\\y=h(x)=2x-\boxed{20}[/tex]

Answer:

-x^2-2

Step-by-step explanation:

So by looking at the two curves it appears that g(x) is simply a reflection of f(x) over the x-axis and then shifted 2 units down. So to reflect the parabola you simply make the x^2 negative to get -x^2 and then to go 2 units down you subtract 2 from the -x^2. This gives you the equation

[tex]g(x)=-x^2-2[/tex]

Answer:

43

Step-by-step explanation:

63-3/3=20 63-20

Answer:

mark has 18

don has 45

Step-by-step explanation:

Answer:

the interior angle of a triangle = 180- 89 ( forming linear pair)

= 91°

y = 91 + 23

Y = 114° ( sum of interior angle of a triangle ls equal to its outer angle)

Answer:

114

Step-by-step explanation:

Angle A + 89 = 180 (Sum ofAngles in a straight line)

Angle A = 180 - 89 = 91

Angle B + Angle A + 23 = 180 (Sum of angles in a triangle)

Angle B + 91 + 23 = 180

Angle B = 180 - 114 = 66

Angle B + y = 180 (Sum of angles in a straight line)

66 + y = 180

y = 180 - 66 = 114

Refer to the attached picture.

Answer: x-1

Step-by-step explanation:

Answer:

5:11:9

Step-by-step explanation:

Change the decimal to fractions

45/10:99/10:81/10

Multiply through by the Lowest Common Factor 10

10×45/10:10×99/10:10×81/10

Which makes it

45:99:81

They have a common factor which is 9, so divide through by 9

45/9:99/9:81/9

Your answer is

5:11:9

Hope it helps

Answer:

there is no answer

Step-by-step explanation:

If you multiply 15^x by 15^y, the answer is 15^(x+y) so 2 plus -7 is negitive 5.

but there is no answer equal to this.

The equivalent expression will be;

⇒ 15⁻⁵

Subtraction in mathematics means that is taking something away from a group or number of objects. When you subtract, what is left in the group becomes less.

Given that;

The expression is,

⇒ (15²) × (15⁻⁷)

Now,

Since, The expression is,

⇒ (15²) × (15⁻⁷)

Hence, We solve as;

⇒ (15²) × (15⁻⁷)

⇒  15²⁻⁷

⇒ 15⁻⁵

⇒ 1 / 15⁵

Thus, The equivalent expression is,

⇒ 15⁻⁵

⇒ 1 / 15⁵

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Answer:

Answers are 20, 12 and 16

Step-by-step explanation:

Y=4x

for x = 5

y=4(5)

y=20

for x = 3

y=4(3)

y=12

for x = 4

y=4(4)

y=16

Answer:

X I Y

5 20

3 12

4 16

Step-by-step explanation:

since y=4 multiplied by x

so, 5x4=20

3x4=12

4x4=16

Answer:

(1, 1)  (1, 2)  (1, 3) (1,4)

(1,5)  (2,1)   (2,2) (2,3)

(2,4)  (3,1)  (3,2)   (3,3)

(4,1)   (4,2) (5,1)

Step-by-step explanation:

An event is a specified set of results of a random experiment in probability theory. The number of possible outcomes that Event E has is 21.

An event is a specified set of results of a random experiment in probability theory. Because the sample space is the collection of all potential outcomes of a random experiment, another definition of an event is any subset of a sample space.

Let E be the event where the sum of two rolled dice is greater than or equal to 7. Therefore, the outcomes in E are represented in red in the given table below.

(1, 6)

(2, 6)

(3, 6)

(4, 6)

(5, 6)

(6, 6)

(2, 5)

(3, 5)

(4, 5)

(5, 5)

(6, 5)

(3, 4)

(4, 4)

(5, 4)

(6, 4)

(4, 3)

(5, 3)

(6, 3)

(5, 2)

(6, 2)

(6, 1)

Hence, the number of possible outcomes that Event E has is 21.

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The reflection over the line y = x - 3 will take figure M onto its congruent image, figure N.

It is defined as the change in coordinates and the shape of the geometrical body. It is also referred to as a two-dimensional transformation. In the geometric transformation, changes in the geometry can be possible by rotation, translation, reflection, and glide translation.

As we can see in the graph there are two shapes are shown.

Figure M and Figure N

The sequence of transformations that will take figure M onto its congruent image, figure N is:

First, we need to draw a line that passes through (3, 0) and (0, -3)

The equation of the line is:

[tex]\rm y+3=\dfrac{\left(-3\right)}{-3}\left(x\right)[/tex]

y + 3 = x

y = x - 3

The reflection over the above line will take figure M onto its congruent image, figure N.

Thus, the reflection over the line y = x - 3 will take figure M onto its congruent image, figure N.

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The preimage was shifted to the image by a translation 2 units right and 2 units up, so the answer is [tex](x,y) \longrightarrow (x+2, y+2)[/tex]

Answer:

Step-by-step explanation:

I can give you the meaning of Y

Y is the vertical value in a pair of coordinates. In other words how far up or down the point is. The Y coordinate is always written second in an ordered pair of coordinates (x,y) when used. A example from the internet is:

Answer:

5.0

Step-by-step explanation:

0.16÷0.03220=4.9689

=5.0

Answer:

≈ 14.6%

Step-by-step explanation:

percentage increase is calculated as

[tex]\frac{increase}{original}[/tex] × 100%

increase = 2.75 - 2.40 = 0.35 , then

percentage increase = [tex]\frac{0.35}{2.40}[/tex] × 100% ≈ 14.6% ( to the nearest tenth )

Answer:

Yes, k = 1/3 and y = 1/3x

Step-by-step explanation:

[tex]\text{The given line passes through the origin, hence it has equation of the form:}\\y=kx[/tex]

[tex]\text{Therefore y varies directly as x.}The line passes through the point (3,1)}[/tex]

[tex]\text{This implies that,}[/tex]

[tex]1=k(3)\\k=\frac{1}{3}[/tex][tex]\text{Hence the constant of variation is}[/tex] ⇒ [tex]\frac{1}{3}[/tex]

The equation would be ⇒ [tex]y=\frac{1}{3} x[/tex]

Answer:

? = 12

Step-by-step explanation:

[tex]\frac{7}{12} +\frac{10}{12} =\frac{7+10}{12} =\frac{17}{12}[/tex]

[tex]\frac{17}{12} =\frac{12}{12} +\frac{5}{12} =1+\frac{5}{12} =1\frac{5}{12}[/tex]

Hope this helps

The volume of the given figure is 210 cubic in..

We need to find the volume of the given figure.

Volume is a scalar quantity expressing the amount of three-dimensional space enclosed by a closed surface.

Divide the given figure into two convenient cuboids. That is one with dimensions length=4 in., breadth=2 in. and height=3 in. Another with length=4 in., breadth=4 in. and height=12 in.

We know that, the volume of cuboid =l×b×h cubic units.

Now, the volume of the cuboid=4×2×3=18 cubic in. and the volume of another

cuboid=4×4×12=192 cubic in.

The volume of the given figure=18+192=210 cubic in.

Therefore, the volume of the given figure is 210 cubic in.

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Answer:

○ Length = 20 centimeters and Width = 5 centimeters

Step-by-step explanation:

Let the length = L

Then the width is L - 15

A = lw

100 = L(L - 15)

L² - 15L - 100 = 0

(L - 20)(L + 5) = 0

L - 20 = 0  or  L + 5 = 0

L = 20  or  L = -5

Since a length of a rectangle cannot be negative, we discard the solution L = -5 and keep the solution L = 20.

L = 20

width = L - 15 = 20 - 15 = 5

Answer:  ○ Length = 20 centimeters and Width = 5 centimeters

Answer:

The answer is A. 21

i hope this can help you! :)

Answer:

a)21

-step explanation:

Answer:

Step-by-step explanation:

The domain is the set of x-values and the range is the set of y-values.