A pyramid and a cone are both 12 centimeters tall and have the same
volume. What statement must be true about the two solids?
AA
OA. The horizontal cross-sections of the prisms at the same height
must have the same area.
OB. The vertical cross-sections of the prisms at the same width must
have the same area.
C. The area of the cross-sections of the prisms are multiples of each
other.
D. The cross-sections of the prisms are the same shape.

Check the picture below.

so the pyramid is really 4 triangular faces with a base of 6 and a height of 7, and a 6x6 square at the bottom.

[tex]\stackrel{\textit{\LARGE Areas}}{\stackrel{\textit{four triangular faces}}{4\left[\cfrac{1}{2}(\stackrel{b}{6})(\stackrel{h}{7}) \right]}~~ + ~~\stackrel{square}{(6)(6)}}\implies 84~~ + ~~36\implies 120~yd^2[/tex]

Answer:

127.38

Step-by-step explanation:

The surface area formula for a square pyramid is:

A = a^2 + 2a * sqrt[ (a^2 / 4 ) + h^2 ]

So we input the base height as the a value, and the slant as H)

A = 6^2 + 2(6) * sqrt[ (6^2 / 4 ) + 7^2 ]

When using the exponents we get:

A = 36 + 2(6) * sqrt[ (36) / 4 ) + 49 ]

Then multiply/divide:

A = 36 + 12 * sqrt[ (9) + 49 ]

Then add the value in the sqrt.

A = 36 + 12 * sqrt[ 58 ]

Now, if we find the sqrt of 58, we get:     sqrt[ 58 ] ≅ 7.615

A = 36 + 12 * 7.615

When multiplying we get:

A = 36 + 91.38

Finally, after adding, the surface area of the square pyramid is:

A = 127.38

Answer:

x=6.18

Step-by-step explanation:

[tex]sin(31) = \frac{opp}{hyp} \\ \frac{0.52}{1} = \frac{x}{12} \\ \\ x = 12(0.52) \\ x = 6.18 [/tex]

Answer:

[tex]\large\text{$ f(-2.2)=1 $}[/tex]

Step-by-step explanation:

Given function:

[tex]\large\text{$ f(x)=\left\lceil x \right\rceil+3 $}[/tex]

This is a Ceiling Function, denoted by the square brackets [ ] with the bottom part missing.

When graphing a Ceiling Function:

The Ceiling Function gives us the nearest integer up.

So the ceiling of x = -2.2 is -2,  as the greatest integer that is more than (or equal to) -2.2 is -2

Therefore:

[tex]\large\begin{aligned}f(-2.2) & =\left\lceil -2.2 \right\rceil+3\\& = -2+3\\& = 1\end{aligned}[/tex]

This is confirmed when using the graph to solve.

To find f(-2.2), locate x = -2.2 on the graph.  

Trace up vertically until a step is reached. 

The step in this part is not including -3 and including -2, so this confirms that x = -2.2 is in this interval.  

Trace along horizontally to the y-axis to find the corresponding y-value, which is 1.  

Therefore, f(-2.2) = 1

Let's see

[tex]\\ \rm\Rrightarrow f(x)=[x]+3[/tex]

[tex]\\ \rm\Rrightarrow f(-2.2)[/tex]

[tex]\\ \rm\Rrightarrow [-2.2]+3[/tex]

[tex]\\ \rm\Rrightarrow -2+3[/tex]

[tex]\\ \rm\Rrightarrow 1[/tex]

So

The rate of change is negative 1.25. The negative of 1.25 represents 1.25 feet is drain every hour. The number 1 represents 1 foot of water that is already present in the pool.

A linear system is one in which the parameter in the equation has a degree of one. It might have one, two, or even more variables.

The Gutierrez family and the Kim family both have pools.

The Gutierrez family is filling their pool, which is modeled by the equation

y = x + 1

The Kim family is draining their pool, which is modeled by the equation

y = -1.25x + 5

In both equations, x represents the time in hours and y represents the depth of the water in the pool in feet.

These two situations can be described by the following system of equations:

Then the rate of change for the Kim family's pool will be

Rate of change = -1.25

The negative of 1.25 represents 1.25 feet is drain every hour.

Looking at the equation for the Gutierrez family's pool.

y = x + 1

The number 1 represents 1 foot of water that is already present in the pool.

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Answer:

[tex]x > - 1 \\ the \: answer \: is \: {d}[/tex]

The total volume of the wedding cake would be 620 in³.

A rectangular prism is a three-dimensional shape. It also known as a cuboid.

Volume = length x width x height

The volume of the cake is the sum of the volume of the three layers.

Volume of the first layer = 2 1/2 x 12 x 10

5/2 x 12 x 10 = 300 in³

Volume of the second layer = 2 1/2 x 10 x 8

5/2 x 10 x 8 = 200 in³

Volume of the third layer = 2 1/2 x 8 x 6

= 5/2 x 8 x 6 = 120 in³

Total volume = 300 + 200 + 120 = 620 in³

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Answer:

1260 inches

Step-by-step explanation:

Calculator

The expressions of the number of radians can be expressed in the ways below.

The radius = 1.9 km

The angular speed = 3.1 radians per hour

a. The expression of t from the number of radians

θ = π/2 + 3.1t

x = rcosθ

= 1.9cos(π/2 + 3.1t)km

= rsinθ

= 1.9sin((π/2 + 3.1t)km

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The sum of supplementary angles is 180 degrees. The measure of angle 7 is 48 degrees

The sum of supplementary angles is 180 degrees.

Let the supplement of the angle be "x", so that;

x + 132 = 180

Subtract 132 from both sides

x + 132 - 132 = 180 - 132
x =. 180 - 132
x = 48 degrees

Hence the measure of angle 7 is 48 degrees

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Answer:

38.1971

Step-by-step explanation:

The formula for diameter is circumference/ pi. So 120/3.14... is 38.1971

∠IKL and ∠IKC and ∠DLH and ∠JLD are pairs by the Transitive Property of Congruency.

This states that, if a pair of lines or angles or triangles are said to be congruent to a third line or angle, therefore, the first line or angle or triangle is said to be congruent to the third line or angle.

∠IKL and ∠IKC and ∠DLH and ∠JLD are pairs by the Transitive Property of Congruency. because the two angles and the other side of the angle/triangle are said to be equal to two angles and other side of the other triangle.

∠IKC ≅ ∠JLD, so m∠IKC = m∠JLD  and as such angle is Applying the  Transitive Property of Congruency because  if A =b, and b = c then A = c and therefore, the above is true.

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The conclusion drawn is not valid. This is as a result of the fact that the sample is inappropriate.

We are told that a restaurant is analyzing its customer satisfaction level. Now, the conclusion drawn was that most of the customers are satisfied with the service they receive.

Now, we can say that the conclusion drawn is not valid. This is as a result of the fact that the sample is inappropriate as it does not deal with the actual response from the customers but only observational.

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Answer:

So for a quadratic function, the axis of symmetry is the line that divides the curved line in the middle, which is the h value, it can be found by using the formula -b/2a, so for here it would be 4/2(1) = 2, so x =2

Hope that answers your question

Step-by-step explanation:

Answer:

Step-by-step explanation:

We'll look for a line with the form of y = mx + b, where m is the slope and b is the y-intercept (the value of y when x = 0).

A parallel line will have the same slope as the reference line,  For y=3x-8, the slope is 3.  We can write:

y =3x + b for the new line.  We need a value of b that will cause the line to include point (6,-4).  To find a b that will work, simple use the given point in the above equation and solve for b:

y =3x + b

-4 =3(6) + b  for (6,-4)

-4 =18 + b

b = -22

The parallel line that goes through point (6,-4) is y = 3x - 22

See the attached graph.

The reason why Fiona cannot make a valid prediction based on the mean of the population is that the variation of Fiona’s samples is too large.

Mean is quite sensitive to outliers so it is best used when the variation between variables is not too much.

In Fiona's case, there variation is quite high with high variable of 95 compared to a low value of 45.

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Answer: just confirming/

Step-by-step explanation:

Answer:

  5x -4y = 4

Step-by-step explanation:

An equation for the perpendicular line can be found by swapping the x- and y-coefficients, and negating one of them. The constant changes to a value so that the equation is satisfied at the given point.

__

Swapping the coefficients gives us ...

  5x +4y = c . . . . . for some constant c

Negating the y-coefficient (so the x-coefficient remains positive) gives ...

  5x -4y = c

Putting (x, y) = (-4, -6) into the equation gives us the value of c:

  5(-4) -4(-6) = c

  -20 +24 = c = 4

The line perpendicular to the given line and through the point (-4, -6) will have equation ...

  5x -4y = 4

Answer:

250.000$

Step-by-step explanation:

so you multiple 2.000 by 25

[tex] \begin{gathered}\\ \large\dashrightarrow\mathsf { \: \: 5 < b = 6 \: \: \: or \: \: \: b - 5 = 6 } \\ \end{gathered}[/tex]

[tex] \begin{gathered}\\ \large\dashrightarrow\mathsf { \: \: b - 5 = 6 } \\ \end{gathered}[/tex]

[tex] \begin{gathered}\\ \large\dashrightarrow\mathsf { \: \: b = 6 + 5 } \\ \end{gathered}[/tex]

[tex] \begin{gathered}\\ \large\dashrightarrow \: \: \underline{ \boxed{\mathbf \red{ \: \: b = 11 \: \: }}} \\ \end{gathered}[/tex]

▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬

[tex]\begin{gathered}\begin{gathered}\begin{gathered}\: \: \: \: \: \: \begin{gathered}\begin{gathered} \small \color{blue}{ \underline{\boxed{ \begin{array}{cc} \small \underline{\underline{\bf{ \color{red}{{ \orange \bigstar \: MᴏʀE \: IᴅᴇɴᴛɪᴛɪᴇS \: \orange \bigstar}}}}} \\ \\ \: \frak{ {(x + y)}^{2} = {x}^{2} + 2xy + {y}^{2} }\:\\ \\ \: \frak{ {(x - y)}^{2} = {x}^{2} - 2xy + {y}^{2} }\:\\ \\ \: \frak{ {x}^{2} - {y}^{2} = (x + y)(x - y)}\:\\ \\ \: \frak{ {(x + y)}^{2} - {(x - y)}^{2} = 4xy}\:\\ \\ \: \frak{ {(x + y)}^{2} + {(x - y)}^{2} = 2( {x}^{2} + {y}^{2})}\:\\ \\ \: \frak{ {(x + y)}^{3} = {x}^{3} + {y}^{3} + 3xy(x + y)}\:\\ \\ \: \frak{ {(x - y)}^{3} = {x}^{3} - {y}^{3} - 3xy(x - y) }\:\\ \\ \: \frak{ {x}^{3} + {y}^{3} = (x + y)( {x}^{2} - xy + {y}^{2} )}\: \\ \: \end{array} }}}\end{gathered}\end{gathered}\end{gathered}\end{gathered}\end{gathered} \: \: [/tex]

▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬

^०^

Answer:B

Step-by-step explanation:

"the quantity of can be ignored".

(x+4)/3=2

(x+4)=6

x=2

Answer:

4 days

Step-by-step explanation:

8 pints = 1 gallon

2 pints = 1 day

1 gallon = 4 days

Step-by-step explanation:

Susan drinks milk each day = 2 pints

1 gallon = 8 pints

Now, Susan take days to drink 1 gallon of milk

= 8 ÷ 2

= 4 answer

Hence, Susan takes 4 days to drink 1 gallon of milk .

Answer:

$900

Step-by-step explanation:

x = the cost of the tickets

y = the cost of dj & decorations

In the first situation, the profit of -$150 = 75x - y

In the second situation, the profit of $100 = 100x - y

Using the first situation, we isolate y as follows:

-150 = 75x - y

Add y to each side: y-150 = 75x

Add 150 to each side to isolate y

y = 75x + 150

Use this formula in the second situation in place of the y

Original formula: 100 = 100x - y

With substitution: 100 = 100x - (75x + 150)

Simplify to: 100 = 25x - 150

Add 150 to both sides: 250 = 25x

Divide both sides by 25: 10 = x

Input the 10 in for x in either formula above

-150 = 75(10) - y

-150 = 750 - y

Add y to both sides

y - 150 = 750

Add 150 to both sides

y = 900

Answer:

Hi,

Step-by-step explanation:

The playground 's area is the difference of 2 squares:

20²-10²=(20+10)*(20-10)=30*10=300 (ft²)

Probability that the mean childhood asthma prevalence for the sample is greater than 2.6% is 0.0357 or 3.57 %.

What is Probability ?

Probability is the measure of likelihood of an event.

For a Normal Distribution ,

the z-score formula is given by

[tex]\rm Z = \dfrac{X - \mu }{\sigma}[/tex]

Here [tex]\rm \mu\\[/tex] is the mean and [tex]\rm \sigma\\[/tex] is the standard deviation .

It is the measure of the deviation of the data from its central tendency.

Each z-score has a probability value.

It is given in the question that

Mean of 2.16% =  [tex]\rm \mu\\[/tex] = 2.16

Standard deviation of 1.36% means that  [tex]\rm \sigma\\[/tex] = 1.36

For Sample of 31 the value of standard deviation is [tex]\rm s = \dfrac{\sigma}{\sqrt{n}}[/tex]

s = 1.36/√31

s = 0.2442

Substituting the values

Z = (2.6 -2.16)/0.2442

Z =1.8

the p value from the graph of z and p , 0.9643

To determine value of probability  more than X is 1 - 0.9643= 0.0357

the

Probability that the mean childhood asthma prevalence for the sample is greater than 2.6% is 0.0357.

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Answer:

The first option.  See attachment.

Step-by-step explanation:

Explained on attached image.

The translated vertices are:

The vertices of the original figure are:

Now we want to apply a translation of four units to the right and 2 units down, then each point (x, y) becomes (x + 4, y - 2).

This means that the translated vertices are:

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