which statement explains why ABC is congruent to A’B’C’?

The volume of the crate if there is no extra space in the crate is 36m³.

From the information illustrated, the prism is 2m by 1m by 1m abd the shipping crate is packed with 18 of these.

In this case, the volume will be:

= Length × Width × Height

= 2 × 1 × 1

= 2m³

Since there are 18 crates, the total volume will be:

= 2m³ × 18

= 36m³

The volume is 36m³.

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Complete question

A rectangular-prism-shaped toy chest is 2m by 1m by 1m. A shipping crate is packed with 18 of these toy chests. There is no extra space in the crate. What is the volume of the crate?

There are 284 number of students and 152 number of adults.

Two or more expressions with an Equal sign is called as Equation.

Given,

The ratio of teachers to students on a field trip is 2:13

Let x be the number of adults

If there are 132 more students than adults on the field trip, then 132+x

To find the number of adults and number of students formulate a equation as below

2/13=(x+132)/x

Apply cross multiplication

2x=13(x+132)

Apply distributive law on RHS

2x=13x+1716

11x=1716

Divide both sides by 11

x=152

x+132=152+132=284

Hence there are 284 number of students and 152 number of adults.

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Step-by-step explanation:

1/2 miles in 1/4 day (Given)

Find the distance of the road built in 1 day:

1/4 day = 1/2 miles

4/4 days 1/2 x 4 = 2 miles =

Answer: The rate is 2 miles per day.

The function is differentiate w.r.t. x get the answer is [tex]40x^7 + 16x^3[/tex]

Given,

In the question:

The function is:
f(x) =  [tex]x^4(5x^4+4)[/tex]

Differentiate the function with respect to x.

Now, According to the question:

f(x) = [tex]x^4(5x^4+4)[/tex]

Expand the expression:

f(x) = [tex]5x^8+4x^4[/tex]

Calculate the derivative

f'(x) =  [tex]\frac{d}{dx}(5x^8+4x^4)[/tex]

f'(x) = [tex]\frac{d}{dx}(5x^8)+\frac{d}{dx} (4x^4)[/tex]

Isolate Coefficients

f'(x) = 5 x [tex]\frac{d}{dx}(x^8)+4 \frac{d}{dx} (x^4)[/tex]

Apply the power rule

f'(x) = 5x [tex]8x^7+4[/tex] x[tex]4x^3[/tex]

f'(x) = [tex]40x^7 + 16x^3[/tex]

Hence, The function is differentiate w.r.t. x get the answer is [tex]40x^7 + 16x^3[/tex]

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For the two similar cuboids A and B,

surface area of A : surface area of B = 16 : 2 then the ratio of their volumes is equal to volume of A : Volume of B = 16√2 : 1.

As given in the question,

Given : Two similar cuboids A and B,

Let x , y , and z be the length , width and height of cuboid A

And l, b, h be the length , width , and height of cuboid B.

As both the cuboids are similar their sides are in proportion.

k is the constant of proportionality then,

x= kl , y = kb, z = kh

Surface area of A : Surface area of B = 16 :2

⇒2k²(lb +bh +hl) : 2(lb +bh +hl) = 16 : 2

⇒k² = 16 :2

⇒k = 4 : √2

Now volume of A : Volume of B

= xyz : lbh

= k³lbh : lbh

= k³

=( 4 : √2)³

=64 : 2√2

= 64√2 : 4

= 16√2 : 1

Therefore, for the two similar cuboids A and B,

surface area of A : surface area of B = 16 : 2 then the ratio of their volumes is equal to volume of A : Volume of B = 16√2 : 1.

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The area of given figure is 93mm².

Since the researcher randomly selected 100 people who exercise regularly and 100 people who do not exercise regularly, and compared how many hours they sleep at night, on average: C. the study is an observational study.

An observational study can be defined as a type of scientific study in which a researcher observes and measures the effect of a diagnostic test, risk factors, and specific treatments on individuals without intervening, manipulating, altering, or changing those who are or aren't exposed to it (controlled conditions).

In Science, a controlled variable must always be held constant and unchanged in an experiment in order to prevent it from affecting or influencing the result, which is not applicable to this research.

In conclusion, we can logically deduce that this research is an observational study because people (participants) were chosen through an appropriate process, however, no attempt was made to control any aspect of the people (participants), even though the variable of interest (exercise) was recorded for one of the group.

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The reflection of the point (2,3) over the x-axis is (2,-3). The reflection of the point (7,-2) over the y-axis is (-7,-2).

A reflection is referred to as a flip in geometry. A reflection is the shape's mirror image. A line, called the line of reflection, will allow an image to reflect through it. Every point in a figure is said to reflect the other figure when they are all equally spaced apart from one another.

The reflection of the point (2,3) over the x-axis is calculated as,

(2,3) ⇒  (2,-3)

The reflection of the point (7,-2) over the y-axis is calculated as,

(7,-2) ⇒ (-7,-2)

Therefore, the reflection of the point (2,3) over the x-axis is (2,-3). The reflection of the point (7,-2) over the y-axis is (-7,-2).

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y = -4x²+24x-30 is the standard form of parabola whose equation is  y = -4(x - 3)² + 6

Parabola is a plane curve which is mirror-symmetrical and is approximately U-shaped.

The given equation is y = -4(x - 3)² + 6.

We need to write this equation as standard form of parabola.

the equation of a parabola in  standard form is.

y=ax² +bx+c

The given equation should be expanded y = -4(x - 3)² + 6.

y = -4(x²+9-6x)+6

Now apply distributive property

y = -4x²-36+24x+6

y = -4x²+24x+6-36

y = -4x²+24x-30

Hence y = -4x²+24x-30 is the standard form of parabola whose equation is  y = -4(x - 3)² + 6

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Step-by-step explanation:

Percentage means to be out of 100 . So, 20% is equivalent of being 20100 . That evaluates out to 0.20 . Removing the unnecessary 0 at the end gives us the decimal 0.2 , which is the correct answer.

Trey, Raina, and Deandre have $21,$31, and $93 in their wallets respectively.

From the question the sum of the money in their wallets is:

Raina  +  Trey +Deandre=$145

      R   +    T    +       D      =$145................(i)

Raina has $10 more than Trey= ($10 + T)

Deandre has 3 times more Raina =3($10 + T)

substituting the values of Raina and Deandre in Eqn (i) we have

R   +    T    +       D      =$145

($10 + T) +  T  +{3$(10 + T)}=$145

$10 +T   +T+  $30   + 3T    =$145

                     5T   +$40    =  $145

                                5T   =   $145   -  $40

                                 5T     =    $105

                                    T      = $105/5

                                     T     =   $21

i.e  Trey   =  $21

Raina has $10 more than Trey= ($10 + T)

i.e                                               = ($10 + $21)    

                                      Raina  =$31    

Deandre has 3 times more Raina =3($10 + T)

                                                        =3($10 + $21)

                                                        =$30   +$63

                                       Deandre  =$93

Therefore the total sum of money in thier wallet is:

        Raina  +  Trey +Deandre=$145

             $31  + $21   +  $93=    $145

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If you do not pay anything on that loan during the year and assuming there is no compounding, the total sum owing is $1,216.50.

When money is given to someone else with the knowledge that it would be returned with interest, it is referred to as a loan. . Lenders will consider a borrower's income, credit rating, and level of debt before deciding to grant a loan.

Money borrowed from a bank or other financial organization is known as a loan. The borrower consents to repay the loan's principal plus interest. There are many different kinds of loans, such as auto loans, student loans, and mortgages.

The amount is 1000(1 + 0.0765), or 1000 x 1.0765, or 1,076.50.

Punishment equals 12(0.02 x 1000) = 12(20) = 240.

The total sum owing is $1,216.50 (1,076.50 plus 240).

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The solution of the given statement will be inequality c > -60.

Inequality is defined as mathematical statements that have a minimum of two terms containing variables or numbers is not equal.

We have been given the statement "number c divided by 3 is greater than -20".

As per the given statement, we can represent this algebraic form with inequality as:

⇒ c / 3 > -20

Inequality by multiplying both sides of the inequality by 3:

⇒ 3 × c / 3 > 3 × -20

⇒ c > -60

Thus, the solution of the given statement will be inequality c > -60.

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The question seems to be incomplete the correct question would be

Find the solution if a number c divided by 3 is greater than -20.

The midpoint of the line joining (6,-5) and (-1,-6) is (-5/2,-11/2).

How to determine the midpoint of the line joining two points (a,b) and (p,q)?

To get the midpoint of the line joining two points (a,b) and (p,q), we first have to add the x coordinates of two points and divide it by 2. So the midpoint's x coordinate will be (a+p)/2 . Similarly, we have to do the same with y. Then the midpoint of the line joining two points (a,b) and (p,q) will be [(a+p)/2,(b+q)/2}.

To get the midpoint of (6,-5) and (-1,-6) , first, we have to add the x coordinates and divide it by 2 . And have to do the same with y.

so, the midpoint will be [(6+(-5)]/2,[-5+(-6)]/2.

Hence ans will be ,(-5/2,-11/2)

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Answer: 0.5

Step-by-step explanation:

1.45*0.34 = 0.493

Rounded to the tenth place is 0.5

The order of the energy levels starting from the highest is:

3. Can hold a maximum of 32 electrons

1. Can hold a maximum of 18 electrons.

2. Can hold a maximum of eight electrons.

4. Can hold a maximum of two electrons.

When a shell gets bigger, it can retain more electrons, and has greater electron energies the further it is from the nucleus.

Two electrons can fit in the first shell, which is closest to the nucleus. Eight electrons can fit in the second shell. 18 electrons can fit in the third shell then 32 electrons can fit inside of the last shell.

The shell that can contain 32 electrons has the highest energy level

Following this relationship, it shows that the arrangement is done using the number of electrons to arrive at 3,  1,  2,and 4

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Answer:

find the increased dollar amount by finding the percentage amount first:

$ 39,400 * .13

= $ 5,122

then take $ 5,122 and add it to the original price

$ 39,400 + $ 5,122 = $ 44,522 (new price)

Step-by-step explanation:

The average rate of change in the number of cars the manufacturer sold between 2002 and 2006 is B. 225 cars per year.

The average rate of change shows the slope line over the stated interval.

We can find the average rate of change by dividing the change in y-values by the change in x-values.

Year        No. of cars sold

                in (hundreds)

2000                 45

2002                 51

2004                53

2006                60

2008                77

The total number of cars sold between 2002 and 2006 = 16,400

The number of cars sold in 2002 = 5,100

The number of cars sold in 2006 = 6,000

The increase in car sold between 2002 and 2006 = 900 (6,000 - 5,100)

OR:

Increase in the number of cars sold in 2004 = 200 (5,300 - 5,100)

Increase in the number of cars sold in 2006 = 700 (6,000 - 5,300)

Total change in y-values = 900 (6,000 - 5,100)

Total change in x-values = 4 (2006 - 200)2

Average rate of change = 225 (900/4)

Thus, we can conclude that for 4 years, car sales increased on, average, by 225 each year.

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The value of the function (fg(x) is 2x⁵ + 2x⁴ + x³ + x ² +5x +3 and the value of f(g)(-4) is -1089.

A polynomial is a mathematical expression made up of coefficients and indeterminates that uses only the operations addition, subtraction, multiplication, and powers of positive integers of the variables.

Given function is f(x) = 2x⁴ + 2x³− x²+ 2x + 3

The value of the function is calculated as,

f(x) = 2x⁴ + 2x³− x²+ 2x + 3

(fg)(x) = (2x⁴ + 2x³− x²+ 2x + 3)(x+1)

(fg)(x) = (2x⁵ + 2x⁴ + x³ + x ² +5x +3)

The value of (fg)(x) is calculated as,

(fg)(x) = (2x⁵ + 2x⁴ + x³ + x ² +5x +3)

(fg)(-4) = (2(-4)⁵ + 2(-4)⁴ + (-4)³ + (-4)² +5x-4 +3)

(fg)(-4) = -2048 +1024-64+16-20+3

(fg)(-4) = -1089

Therefore, the value of the function (fg(x) is 2x⁵ + 2x⁴ + x³ + x ² +5x +3 and the value of f(g)(-4) is -1089.

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Answer:

[tex]y= \frac 12 x -3\\y=0.5x -3[/tex]

Depending if you can imput fractions, or decimal numbers.

Step-by-step explanation:

The slope can easily calculated as [tex]m=\frac{\Delta y}{\Delta x} = \frac {0-(-3)}{6-0} = \frac 36 = \frac12[/tex]

The y intercept can be easily read from the graph as and is -3

[tex](\stackrel{x_1}{5}~,~\stackrel{y_1}{-2})\qquad (\stackrel{x_2}{7}~,~\stackrel{y_2}{-1}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-1}-\stackrel{y1}{(-2)}}}{\underset{run} {\underset{x_2}{7}-\underset{x_1}{5}}} \implies \cfrac{-1 +2}{2} \implies \cfrac{ 1 }{ 2 }[/tex]

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-2)}=\stackrel{m}{ \cfrac{1 }{ 2 }}(x-\stackrel{x_1}{5}) \implies y +2 = \cfrac{1 }{ 2 } ( x -5) \\\\\\ y+2=\cfrac{1 }{ 2 }x-\cfrac{5 }{ 2 }\implies y=\cfrac{1 }{ 2 }x-\cfrac{5 }{ 2 }-2\implies {\Large \begin{array}{llll} y=\cfrac{1 }{ 2 }x-\cfrac{9}{2} \end{array}}[/tex]

Answer:

y=1/2x-9/2

Step-by-step explanation:

First you want to find the slope by doing -2-(-1)/5-7

Therefore the slope is 1/2

Next you want to add in any set of points, either (5, -2) or (7, -1)

Substitute the x- point in place of x and the y in place of y in y=1/2x+b

Once you do this you should get -2=1/2(5)+b

You should get -2=2 1/2+b

Then subtract 2 1/2 from -2

You should get -4 1/2

Once you have the slope and y- intercept you can put together your problem

y=1/2x-4 1/2

don't forget to convert, y=1/2x-9/2

Hope this helps  

The probability that Pat’s second pick will be a blue marble is the fracion 5/3 considering choosing marbles without replacement.

Probability of an event without replacement simply means once an item is drawn, then we do not replace it back to the sample space before drawing a second item.

For the fact that a red marble was first drawn without replacement with the probability of 55/100, given that there are 55 red marbles and a total of 100 marbles in the Urn.

Hence, there will be 99 samples left for the second draw to be made.

The probability that the second pick will be a blue marble = 15/99.

Therefore, the probability that the second pick is a blue marble after the first pick without replacement is the fraction 5/33 reduced to its lowest term from 15/99.

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One bag of cat food costs $6 and one bag of dog food costs $9.

What is system of equations?

A finite set of equations for which common solutions are sought is referred to in mathematics as a set of simultaneous equations, often known as a system of equations or an equation system.

The problem states that c equals the cost of bag of cat food and d equals the cost of bag of dog food.

Last week she paid $117 for 6 bags of cat food and 9 bags of dog food.

Therefore, the equation becomes,

6c + 9d = 117         ..(1)

This week she paid $87 for 4 bags of cat food and 7 bags of dog food.

Therefore, the equation becomes,

4c + 7d = 87         ..(2)

Now to solve the system of equations

To solve the first equation for c.

6c + 9d = 117

6c = 117 - 9d

[tex]c = \frac{117}{6}-\frac{9d}{6}[/tex]

Plug value of c in equation (2).

[tex]4(\frac{117}{6}-\frac{9d}{6}) +7d = 87\\78 - 6d + 7d = 87\\d = 87-78\\d = 9[/tex]

Plug d = 9 in equation (1)

6c + 9(d) = 117

6c + 9(9) = 117

6c + 81 = 117

6c = 117 - 81

6c = 36

c = 6

Hence, one bag of cat food costs $6 and one bag of dog food costs $9.

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Using the z-distribution to test the hypothesis, it is found that:

1. You would not like to continue the game, as in each trial you are losing.

2. The p-value is of 0.0023.

3. The low p-value means that there is enough evidence to conclude that the coin is biased.

At the null hypothesis, it is tested if there is not enough evidence that the coin is biased, that is, the proportion of heads is of 0.5, hence:

[tex]H_0: p = 0.5[/tex]

At the alternative hypothesis, it is tested if there is enough evidence that the coin is biased, that is, it has a proportion of heads lower than 0.5, hence:

[tex]H_1: p_1 < 0.5[/tex]

The test statistic is given by the equation as follows:

[tex]z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}[/tex]

In which the variables are listed and explained as follows:

The values of these parameters are given as follows:

[tex]\overline{p} = \frac{0}{8} = 0, n = 8, p = 0.5[/tex]

Hence the test statistic is:

[tex]z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}[/tex]

[tex]z = \frac{0 - 0.5}{\sqrt{\frac{0.5(0.5)}{8}}}[/tex]

z = -2.83.

Using a z-distribution calculator, and considering a left-tailed test, as we are testing if the proportion is less than a value, with z = -2.83, the p-value is of 0.0023.

Since this p-value is less than the standard significance level of 0.05, it means that there is enough evidence to conclude that the coin is biased towards tails.

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Explanation:

The equation y = 3x-1 is in slope-intercept form y = mx+b

Parallel lines have equal slopes, but different y intercepts.

The answer will also have a slope of m = 3.

Plug that slope value, and the coordinates of the given point [tex](x_1,y_1) = (1,5)[/tex] , into the point-slope formula below.

Solve for y.

[tex]y - y_1 = m(x - x_1)\\\\y - 5 = 3(x - 1)\\\\y - 5 = 3x - 3\\\\y = 3x - 3+5\\\\y = 3x + 2\\\\[/tex]

That's how we arrive at the answer of y = 3x+2

As a check, plugging x = 1 into that answer should get us y = 5.

It confirms that the point (1,5) is on this line.

Answer:

[tex]y+10=\frac{13}{8}(x-20)[/tex]

Step-by-step explanation:

The equation of the line passing through the point [tex](x_1, y_1)[/tex] and slope [tex]m[/tex] is [tex]y-y_1=m(x-x_1)[/tex].

Answer:

a: 0.3125kg

b: 4

Step-by-step explanation:

for a we simply calculate 5 * 0.5 ^ 4.
we then see that the weight after 4 minutes is smaller than 0.5kg, but if we go back to 3 minutes (by multiplying our solution to a by 2), giving us 0.625kg, which is now bigger than 0.5kg. meaning 4 minutes is the first whole amount that will give us a weight smaller than 0.5kg.

Step-by-step explanation:

the area of a triangle is

base × height / 2

in our case

base × height / 2 = 196 mm²

base × height = 392

base = height / 2

so, using that in our main equation :

(height / 2) × height = 392

height² = 784

height = sqrt(784) = 28 mm

base = height / 2 = 28/2 = 14 mm

N × (-5/6) ≥ -1/2 is the inequality for the statement

An inequality compares two values, showing if one is less than, greater than, or simply not equal to another value e.g 5 < 6, x ≥ 2, etc.

Given the statement: negative one half is a minimum of the product of a number and negative five sixths.

This statement can also be written as the product of a number and negative five sixths is greater than or equal to negative one half

Let N represent the number. Thus, the inequality of the statement is:

N × (-5/6) ≥ -1/2    

Note: The symbol ≥ is pronounced as greater than or equal to

Therefore, the inequality for the statement is N × (-5/6) ≥ -1/2

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