a student found the volume of a rectangular pyramid with a base area of 92 square meters and a height of 54 Meters to be 4968 cubic meters explain and correct the error

Answer:

  x > 4/3

Step-by-step explanation:

The first inequality can be solved this way ...

  3x -91 > -87

  3x > 4 . . . . . . . add 91

  x > 4/3 . . . . . . divide by 3

__

The second inequality has solution ...

  21x -17 > 25

  21x > 42 . . . . . . add 17

  x > 2 . . . . . . . . . divide by 21

__

The solution set is the union of these overlapping solutions, so will be equal to the first solution:

  x > 4/3

Answer:

The solution is [tex]x>\frac{4}{3}[/tex]

Step-by-step explanation:

A compound inequality is an inequality that combines two simple inequalities.

We want to solve for x the following compound inequality

[tex]3x-91>-87 \:{OR} \:{21x-17>25}[/tex]

Solving the first inequality for x, we get:

[tex]3x-91+91>-87+91\\\\3x>4\\\\x>\frac{4}{3}[/tex]

Solving the second inequality for x, we get:

[tex]21x-17+17>25+17\\\\21x>42\\\\x>2[/tex]

So our compound inequality can be expressed as the simple inequality:

[tex]x>\frac{4}{3}[/tex]

The graph of a compound inequality with an "or" represents the union of the graphs of the inequalities. A number is a solution to the compound inequality if the number is a solution to at least one of the inequalities.

Graphically, we get

Answer:

Perimeter of any figure is given by adding up all the side measurements.

So, when a figure is enlarged by a scale factor then we can multiply all the sides with the scale factor to get the new sides measurements and then we can find the perimeter.

Or simply we can find the perimeter of the original figure and then multiply by the scale factor.

In both the methods, the answer will be the same.

We can take an example:

Lets suppose the original figure to be a rectangle with length 5 cm and width 2 cm. The rectangle is enlarged by a scale factor of 6.

The original perimeter is = [tex]2(5+2)[/tex]

= [tex]2(7)=14[/tex] cm

1st method:

Multiply the length by 6 and width by 6 to get new dimensions.

Length becomes: [tex]5\times6=30[/tex]

Width becomes: [tex]2\times6=12[/tex]

Perimeter becomes: [tex]2(30+12)[/tex]

= [tex]2(42)=84[/tex] cm

2nd method:

Simply multiply 6 with the original perimeter.

[tex]14\times6=84[/tex] cm

We can see that in both methods, the perimeter is same.

Sample Response:

To find the perimeter of an enlarged figure, you can multiply the original figure’s perimeter by the scale factor. You could also multiply each dimension of the original figure by the scale factor to find the dimensions of the enlarged figure, and then add to find the perimeter.

Answer:

the answer is C.

Step-by-step explanation:

83%

The true statement about the given conditional Probability is; The probability that event A occurs, given that event B occurs, is 83%.

We are told that If events A and B are independent, and the probability that event A occurs is 83%.

Now, Conditional probability like p(A|B) is the probability of event A occurring, given that event B occurs. Thus, applying that to our question means we can denote that;

The probability that event A occurs, given that event B occurs, is 83%.

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The ratio of the area of the cross sectional circle and area of the cross sectional square is π : 4

Suppose that we've got two quantities with measurements as 'a' and 'b'

Then, their ratio(ratio of a to b) a:b or [tex]\dfrac{a}{b}[/tex]

We usually cancel out the common factors from both the numerator and the denominator of the fraction we obtained. Numerator is the upper quantity in the fraction and denominator is the lower quantity in the fraction).

Suppose that we've got a = 6, and b= 4, then:

[tex]a:b = 6:2 = \dfrac{6}{2} = \dfrac{2 \times 3}{2 \times 1} = \dfrac{3}{1} = 3\\or\\a : b = 3 : 1 = 3/1 = 3[/tex]

Remember that the ratio should always be taken of quantities with same unit of measurement. Also, ratio is a unitless(no units) quantity.

For this case, we're specified that:

Then, the area of the circle is:

[tex]\pi r^2 \: \rm unit^2[/tex]

and the area of the square is: [tex]\rm side^2 = (2r)^2= 4r^2 \: \rm unit^2[/tex]

The ratio of the area of the circle to the area of the square is:

[tex]\dfrac{\pi r^2}{4r^2} = \dfrac{\pi}{4} = \pi : 4[/tex]

Thus, the ratio of the area of the cross sectional circle and area of the cross sectional square is π : 4

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Answer:

The inverse function is [tex]y=\sqrt{\frac{x+4}{2}}[/tex]

Step-by-step explanation:

The given function is [tex]y=2x^2-4[/tex].

This function is only invertible on the interval, [tex]x\ge 0[/tex].

To find the inverse on this interval, we interchange [tex]x[/tex] and [tex]y[/tex].

[tex]x=2y^2-4[/tex]

We now make [tex]y[/tex] the subject to get,

[tex]x+4=2y^2[/tex]

[tex]\Rightarrow \frac{x+4}{2}=y^2[/tex]

[tex]\Rightarrow \pm \sqrt{\frac{x+4}{2}}=y[/tex]

But the given interval is [tex]x\geq 0[/tex], This implies that, [tex]y\geq 0[/tex].

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

First, we have to look at the equation that models this situation. We learn that the price per hour of babysitting is $8. On Friday, Leticia babysat for 4 hours, and on Saturday, she babysat an unknown amount of time. In total, she earned $72. Therefore:

8 ( 4 + x ) = 72

( 4 + x ) = 72 / 8

4 + x = 9

x = 9 - 4

x = 5

Leticia babysat 5 hours on Saturday.

Answer:

[tex]y=2x^2[/tex]

B is correct

Step-by-step explanation:

Given: We are given equation of parabola ans to choose narrowest graph.

[tex]y=ax^2[/tex]

Parabola form narrowest and widest.

Larger value of a most narrowest graph.

Smaller value of a most widest graph.

Now, we will see the coefficient of x²

[tex]y=\dfrac{1}{6}x^2,\ \ \ a=\dfrac{1}{6}[/tex]

[tex]y=2x^2,\ \ \ a=2[/tex]

[tex]y=-x^2,\ \ \ a=-1[/tex]

[tex]y=\dfrac{1}{8}x^2,\ \ \ a=\dfrac{1}{8}[/tex]

Now, we arrange the value of a in descending order.

[tex]2>1>\dfrac{1}{6}>\dfrac{1}{8}[/tex]

2 is largest value of these.

Hence, The narrowest graph is [tex]y=2x^2[/tex]

Answer:

The answer is Z equals negative 3/2

Step-by-step explanation:

In a standard normal distribution, the probability of getting a positive number is 0.5.

Probability of Getting a Positive Number in a Standard Normal Distribution

In a standard normal distribution, the probability of getting a positive number is 0.5. This is because the standard normal distribution is symmetric around 0, and half of the distribution lies to the right of 0, which corresponds to positive numbers.

Since the bag contains 15 green, 18 yellow, and 16 orange balls, the total number of balls in the bag are 15+18+16=49.

Therefore, the probability of the event that the drawn ball is yellow is given by:

P(yellow)=[tex] \frac{Number of Yellow Balls}{Total Number of Balls} [/tex]

[tex] \therefore P(Yellow)=\frac{18}{49}\times 100\approx36.73\approx37 [/tex]%

Thus, the the probability of the event, to the nearest percent, that the drawn ball is yellow is 37%.

Answer:

4.9

Step-by-step explanation:

The vector [tex]\( \mathbf{v} = 6\mathbf{i} - 3\mathbf{j} \)[/tex].

Its magnitude is [tex]\( \sqrt{45} \)[/tex] in reduced radical form.

To find vector [tex]\( \mathbf{v} \)[/tex] from point [tex]\( P_1 \)[/tex] to point [tex]\( P_2 \)[/tex], we subtract the coordinates of [tex]\( P_1 \)[/tex] from the coordinates of [tex]\( P_2 \)[/tex]:

[tex]\[\mathbf{v} = \begin{pmatrix} x_2 - x_1 \\ y_2 - y_1 \end{pmatrix}\][/tex]

Given [tex]\( P_1 = (-2, 5) \) and \( P_2 = (4, 2) \), we can calculate \( \mathbf{v} \):[/tex]

[tex]\[\mathbf{v} = \begin{pmatrix} 4 - (-2) \\ 2 - 5 \end{pmatrix} = \begin{pmatrix} 6 \\ -3 \end{pmatrix}\][/tex]

So, [tex]\( \mathbf{v} = 6\mathbf{i} - 3\mathbf{j} \)[/tex].

To find the magnitude of [tex]\( \mathbf{v} \)[/tex], we use the formula:

[tex]\[|\mathbf{v}| = \sqrt{v_x^2 + v_y^2}\][/tex]

Where [tex]\( v_x \)[/tex] and [tex]\( v_y \)[/tex] are the components of [tex]\( \mathbf{v} \)[/tex]

For [tex]\( \mathbf{v} = 6\mathbf{i} - 3\mathbf{j} \), \( v_x = 6 \) and \( v_y = -3 \)[/tex]:

[tex]\[|\mathbf{v}| = \sqrt{(6)^2 + (-3)^2} = \sqrt{36 + 9} = \sqrt{45}\[/tex]

Thus, the magnitude of vector [tex]\( \mathbf{v} \) is \( \sqrt{45} \)[/tex] in reduced radical form.

Correct question is:

Let v be the vector from initial point P1 to terminal point P2.

Write v in terms of i and j, and find the magnitude of vector v.

Leave the magnitude in reduced radical form.

P1 = (-2,5) , P2 = (4,2)

Answer:

[tex]y=(x+4)^{2}-37[/tex]

Step-by-step explanation:

we know that

The equation of a vertical parabola into vertex form is equal to

[tex]y=a(x-h)^{2}+k[/tex]

where

(h,k) is the vertex of the parabola

if a> 0 then the parabola open upward (vertex is a minimum)

if a< 0 then the parabola open downward (vertex is a maximum)

In this problem we have

[tex]y=x^{2}+8x-21[/tex]

Convert to vertex form

Complete the square

[tex]y+21=x^{2}+8x[/tex]

[tex]y+21+16=(x^{2}+8x+16)[/tex]

[tex]y+37=(x^{2}+8x+16)[/tex]

[tex]y+37=(x+4)^{2}[/tex]

[tex]y=(x+4)^{2}-37[/tex] --------> equation in vertex form

The vertex is the point [tex](-4,-37)[/tex]

the parabola open upward (vertex is a minimum)

Answer:

the answer is y=(x+4)^2-37

Step-by-step explanation:

The Circle's radius is roughly 3 kilometers.

To find the compass of a circle when given the circumference, we can use the formula

C = 2πr

where C is the circumference, and r is the compass.

Given that the circumference is18.84 kilometers, we can substitute these values into the formula and break for the compass

18.84 = 2 x3.14 x r

Dividing both sides of the equation by 2 x 3.14

18.84  /( 2 x 3.14) = r

Simplifying the right side

r ≈18.84/6.28

r ≈ 3 kilometers.

Thus, the circle's radius is roughly 3 kilometers.

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Final answer:

The fourth rule of probability in statistics is the sum rule, which states that the probability of the occurrence of one event or the other event, of two mutually exclusive events, is the sum of their individual probabilities.

Explanation:

The fourth rule of probability in statistics is the sum rule. The sum rule is used when considering two mutually exclusive outcomes that can come about by more than one pathway. It states that the probability of the occurrence of one event or the other event, of two mutually exclusive events, is the sum of their individual probabilities.

For example, if we flip a penny (P) and a quarter (Q), the probability of getting one coin coming up heads and one coin coming up tails can be calculated as [(PH)  (QT)] + [(QH) × (PT)]

=( [tex]\frac{1}{2}[/tex] × [tex]\frac{1}{2}[/tex] ) + ( [tex]\frac{1}{2}[/tex] ×[tex]\frac{1}{2}[/tex] )

[tex]= \frac{1}{2}[/tex]

Answer:

It is D.x=4+√73

Step-by-step explanation:

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