There are 30 students in a class. The teacher will choose 2 students at random to represent the class at an assembly. How many groups of 2 students can be chosen? A. 870 B. 435 C. 60 D. 15

Step-by-step explanation:

When the object hits the ground, h = 0.

0 = -21.962x + 114.655

x = 5.2

From the table, the object landed at x = 4.6 seconds.  So the line of best fit predicts a time 0.6 seconds greater than actual.

The original height is when x = 0.

h = -21.962(0) + 114.655

h = 114.7

So the line of best fit predicts the object was dropped from a height of 114.7 meters.  This is higher than the actual 100 meters.

At x = 3.5:

h = -21.962(3.5) + 114.655

h = 37.8

So the line of best fit estimates the object reached a height of 37.8 meters after 3.5 seconds.

We know that at x = 0, h = 114.7.  This is more than 4 meters from the actual initial height of 100 m.

Therefore, the answer must be A.

Answer:

A. According to the line of best fit, the object would have hit the ground 0.6 seconds later than the actual time the object hit the ground.

Step-by-step explanation:

Answer:

Step-by-step explanation:

the slope is 4

y int is 1

Answer:

24

Step-by-step explanation:

(-4) -6? well it equals 24 because a negative plus a negative equals a positive.

Hope my answer has helped you! If not i'm sorry.

Answer:

The correct answer is -10. 24 isn't correct ^^^^.

Step-by-step explanation:

[tex]\bf ~~~~~~ \textit{Simple Interest Earned} \\\\ I = Prt\qquad \begin{cases} I=\textit{interest earned}\\ P=\textit{original amount deposited}\dotfill & \$1250\\ r=rate\to 7.25\%\to \frac{7.25}{100}\dotfill &0.0725\\ t=years\dotfill &5 \end{cases} \\\\\\ I=(1250)(0.0725)(5)\implies 453.125 \\\\\\ \stackrel{\textit{he'll have to repay}}{1250+453.125}\implies 1703.125[/tex]

The volume is 90 if you add

Answer:

[tex]V = 983.73\ cm^3[/tex]  or [tex]V = 983\ ^{11/15}\ cm^3[/tex]

Step-by-step explanation:

By definition the volume of a rectangular prism is the product of its length (l) by its width (w) by its height (h). This is:

[tex]V = lwh[/tex]

In this case we know that

l = [tex]8\ ^{1/2}[/tex] centimeters

l = [tex]8 + \frac{1}{2}=8.5[/tex] centimeters

w=  [tex]9\ ^{1/3}[/tex] centimeters

w = [tex]9 + \frac{1}{3}=9.333[/tex]  centimeters

h=  [tex]12\ ^{2/5}[/tex] centimeters

h = [tex]12 + \frac{2}{5}=12.4[/tex]  centimeters

Then

[tex]V = (8.5)(9.333)(12.4)\ cm^3[/tex]

[tex]V = 983.73\ cm^3[/tex]

[tex]V = 983\ ^{11/15}\ cm^3[/tex]

[tex]f(n+1)=f(n)-8\\f(1)=100\\\\f(2)=100-8=92\\f(3)=92-8=84\\f(4)=84-8=76\\f(5)=76-8=68\\f(6)=68-8=60[/tex]

Answer:

C. [tex]\{y|y\ge 1\}.[/tex]

Step-by-step explanation:

Consider the parent function [tex]f(x)=\sqrt{x}.[/tex]

Now consider given function [tex]h(x)=\sqrt{x+4}+1[/tex] (translated 4 units left and 1 unit up.)

Answer:

The range of the function h(x) is [tex]R=\{y|y\geq 1\}[/tex]

Step-by-step explanation:

Given : The graph of [tex]y=\sqrt{x}[/tex] is translated 4 units left and 1 unit up to create the function h(x).

To find : What is the range of h(x)?

Solution :

When the graph f(x) is translated then

1) f(x)+b shifts the function b units upward.

2) f(x + b) shifts the function b units to the left.

The graph of [tex]y=\sqrt{x}[/tex] is translated 4 units left.

i.e. [tex]y=\sqrt{x+4}[/tex]

The graph of [tex]y=\sqrt{x}[/tex] is translated 1 unit up.

i.e. [tex]y=\sqrt{x+4}+1[/tex]

So, The required function h(x) is [tex]h(x)=\sqrt{x+4}+1[/tex]

The range of a function is set of output values produce by a function.

In the given graph, y value is always greater than and equal to 1.

So, The range of the function h(x) is [tex]R=\{y|y\geq 1\}[/tex]

Step-by-step explanation:

[tex]\text{The slope-intercept form of an equation of a line:}\\\\y=mx+b\\\\m-slope\\b-y-intercept\\\\\text{We have the equation:}\\\\-3y=15-4x\\\\-3y=-4x+15\qquad\text{ivide both sides by (-3)}\\\\\boxed{y=\dfrac{4}{3}x-5}\\\\\boxed{slope=\dfrac{4}{3}}\\\boxed{y-intercept=-5}[/tex]

[tex]\text{To draw a graph we need only two points.}\\\text{We choose any value of x, put it to the equation of the line}\\\text{and calculate the value of y:}\\\\for\ x=0\\\\y=\dfrac{4}{3}(0)-5=0-5=-5\to(0,\ -5)\\\\for\ x=3\\\\y=\dfrac{4}{3}(3)-5=4-5=-1\to(3,\ -1)\\\\\text{The graph is in attachment}.[/tex]

Answer:

answer in picture

Step-by-step explanation:

[tex]\bf \qquad \qquad \textit{sum of a finite geometric sequence} \\\\ \displaystyle S_n=\sum\limits_{i=1}^{n}\ a_1\cdot r^{i-1}\implies S_n=a_1\left( \cfrac{1-r^n}{1-r} \right)\quad \begin{cases} n=\textit{last term's}\\ \qquad position\\ a_1=\textit{first term}\\ r=\textit{common ratio}\\ \cline{1-1} n=9\\ r=3.8\\ \stackrel{S_n}{S_9}=44240 \end{cases}[/tex]

[tex]\bf 44240=a_1\left( \cfrac{1-3.8^9}{1-3.8} \right)\implies 44240\approx a_1\left( \cfrac{-165215.101}{-2.8} \right) \\\\\\ 44240\approx a_1(59005.393)\implies \cfrac{44240}{59005.393}\approx a_1\implies \stackrel{\textit{rounded up}}{0.75=a_1}[/tex]

When all the terms of a geometric sequence are added, then that expression is called geometric series. The first term of the given geometric series is 0.75.

When all the terms of a geometric sequence are added, then that expression is called geometric series.

Let's suppose its initial term is, the multiplication factor is  r

and let it has total n terms, then, its sum is given as:

[tex]S_n = \dfrac{a(r^n-1)}{r-1}[/tex]

(sum till nth term)

Given the sum of the geometric series is 44,240, while the number of terms is 9. Also, the common ratio of the series is 3.8. Thus, we can write,

Sₙ = a(rⁿ-1)/(r-1)

44240 = a(3.8⁹ - 1)/(3.8 - 1)

44240 = a 59005.3933

a = 0.75

Hence, the first term of the given geometric series is 0.75.

Learn more about the Sum of terms of geometric sequence:

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Answer:

Step-by-step explanation:

Angle 9 = 85 degrees

Angle 9 and < 11 are vertical angles

Vertical angles are equal

<11 = 85 degrees

Answer:

x < -1

Step-by-step explanation:

5 - 3 = 2

-2x < 2

x < -1

Answer:

Answer is x > -1

Step-by-step explanation:

Because -2x + 3 < 5

                       -3   -3 minus 3 on both sides

Then:        -2x  <  5

                  -2      -2 divide negative 2 on both sides

And get  x > -1, Because if you divide by negative numbers the sign always flips.

Sorry i had to reedit it's -1 because you divide my bad.

Hope my answer has helped you and if not i'm sorry.

Answer:

16

Step-by-step explanation:

1/2 the linear term (which in this case is 8x) squared.

The linear term is one which may have a number in front of the x, but there is only 1 x.

x^2 does not qualify as a linear term

So for this question

1/2 8 = 4                    leave off the x.

squared = 4^2 = 16

You would add 16 to both sides.

Answer:

Add 16 to each side

Step-by-step explanation:

x^2 + 8x = 4

To complete the square, we take the coefficient of the x term, divide by 2, and then square it

8

8/2 =4

4^2 = 16

Add 16 to both sides of the equation

x^2 +8x +16 = 4+16

(x+4)^2 = 20

Answer:

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

Step-by-step explanation:

If there is 1500 cellular phones per 1000 people, then the number of phones per person is:

[tex]\frac{1500}{1000} = \frac{15}{10} = \frac{3}{2}[/tex]

Now we know that [tex]\frac{3}{2} = 1 + \frac{1}{2} = 1\frac{1}{2}[/tex]

Answer:

[tex]\large\boxed{y=\dfrac{32}{9}}[/tex]

Step-by-step explanation:

[tex]\underline{+\left\{\begin{array}{ccc}x+3y=1\\2x-3y=-30\end{array}\right}\qquad\text{add both sides of the equations}\\.\qquad3x=-29\qquad\text{divide both sides by 3}\\.\qquad x=-\dfrac{29}{3}\\\\\text{put the value of x to the first equation}\\\\-\dfrac{29}{3}+3y=1\qquad\text{multiply both sides by 3}\\\\3\!\!\!\!\diagup^1\cdot\left(-\dfrac{29}{3\!\!\!\!\diagup_1}\right)+(3)(3y)=(3)(1)\\\\-29+9y=3\qquad\text{add 29 to both sides}\\\\9y=32\qquad\text{divide both sides by 9}\\\\y=\dfrac{32}{9}[/tex]

By adding the system of equations and solving for x, then substantifying back into the first equation, we find that y in this system of equations is approximately 3.5556.

To find the value of y in the given system of equations, you can add the two equations together. The first equation is x+3y=1 and the second equation is 2x – 3y = -30. Here are the steps:

This value, 3.5556, is the value of y in the solution for the system of equations.

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Answer:

Option 4 (If it is fall, then the trees have no leaves).

Step-by-step explanation:

Conditional Statements are the statements which involve "if" and "then". It contains two sets of statements in it. The statement after the word "if" is the hypothesis, and the statement after the word "then" is the conclusion. Conditional statements are written in the form "If A, then B"; where A is the hypothesis, and B is the conclusion. The converse of a conditional statement is the opposite of the original statement: hypothesis and conclusion replace each other. So the converse of the above statement will be "If B, then A".

In this case, A=The trees have no leaves and B=It is fall. Therefore, the converse will be:

If it is fall, then the tress have no leaves. Option 4 is the right answer!!!

Answer:

all work is shown and pictured

Answer:

  x^4 +8/7x^3  + 6x +1

Step-by-step explanation:

8/7x^3 + x^4 + 6x +1

Standard from is from the largest power to the smallest power

  x^4 +8/7x^3  + 6x +1

$16,462.58 (rounded from $16462.575)

By subtracting 13%, you leave 87%, because [tex]100-13=87[/tex].

So, the expression we need to simplify is [tex]25000 * 0.87^3[/tex], because you need to multiply 25000 by 87% three times.

Answer:

$16,462.58

Step-by-step explanation:

100 - 13 = 87

So, then it becomes 87% of its value each year.

25000 * 0.87 = 21,750

21750 * 0.87 = 16,462.575

16,462.575 = $16,462.58 (round up)

Answer is $16,462.58

Answer:

g(x) = 3 square root of x + 7 is "The graph of the parent function is shifted 7 units up"

j(x) = 3 square root of x + 7 is "The graph of the parent function is shifted 7 units left"

h(x) = 3 square root of x - 7 is "The graph of the parent function is shifted 7 units down"

k(x) = 3 square root of x - 7 is "The graph of the parent function is shifted 7 units right"

Explantion:

Got this right on the test. And for square root of is supposed to mean the symbol for anyone who doesn't know that, I didn't have that thing on my keyboard.

The graph of the parent function f(x)=x^3 can be shifted up, down, left, or right by adding or subtracting constants to the function or its variables. The four variations of the function provided will result in vertical or horizontal shifts.

The graph of a parent function f(x)=x3, can be shifted in various ways by altering the function equation. When a positive or negative constant is added to the function, such as f(x)=x3+7 or f(x)=x3-7, it results in vertical shifts. Adding the constant shifts the function upward, while subtracting the constant shifts it downwards. On the other hand, if the constant alters the x-value (inside the parentheses), like in f(x-7)=x3 or f(x+7)=x3, it results in horizontal shifts. Adding the constant shifts the function to the left, while subtracting the constant shifts it to the right.

Match each function to the graph's shift:

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Answer:

x = 30

Step-by-step explanation:

The sum of the 3 interior angles of a triangle = 180°, hence

x + x + 10 + 3x + 20 = 180

5x + 30 = 180 ( subtract 30 from both sides )

5x = 150 ( divide both sides by 5 )

x = 30

Answer:  b. 6

Step-by-step explanation:

The maximum value is the y-value of the vertex.

Step 1: Find the x-value (aka Axis Of Symmetry) using the formula: [tex]x=\dfrac{-b}{2a}[/tex]

[tex]x=\dfrac{-(2)}{2(-1)}=\dfrac{-2}{-2}=1[/tex]

Step 2: input the x-value (above) into the given equation to solve for y:

[tex]y=-x^2+2x+5\\y=-(1)^2+2(1)+5\\y=-1 + 2 + 5\\y = 6[/tex]

Answer:

(x-2)/3 = g

Step-by-step explanation:

First you move the 2 over to the same side as the x by subtracting it on both side, because you are trying to make the g "alone". Then you move the 3 by doing the inverse, just like with the 2. Since you are multiplying 3 on one side to move to the other side you have to divide both sides by 3.

Answer:

g= (x-2)/3

Step-by-step explanation:

x=3g+2

Subtract 2 from each side

x-2=3g+2-2

x-2 = 3g

Divide each side by 3

(x-2)/3 = 3g/3

(x-2)/3 =g

g= (x-2)/3

Answer:

The answer is option D.

Step-by-step explanation:

Answer:

D: Answer:(x-9)(x-3)

Step-by-step explanation:

Answer:

112 adults

20 children

Step-by-step explanation:

In order to solve this problem, we must create system of equations. By definition, system of equations are two equations which help you find unknown variables.

As for this problem, we need to set two variables for each type of person.

Let x represent adults

Let y represent children

We can break the question apart, and form equations based on the information given.

"tickets for adults cost $3.25 while tickets for children cost $2.25 and total receipts for the concert was $364"

$3.25x + $2.25y = $364

Now, we must form our second equation based on the information given.

"If 132 people attend a concert" "how many of each went to the concert"

x + y = 132

Solve for x, or the total number of adults

x = -y + 132

3.25(-y + 132)+ 2.25y = $364

Distribute 3.25

3.25 * -y = -3.25y

3.25 * 132  = 429

-3.25y + 429 = $364

Subtract 429 from both sides

364 - 429 = -65

-3.25y = -65

Now divide both sides by -3.25 to find the value of y.

y = 20

Therefore, 20 children attended the concert.

In order to find the total amount of adults who attended, subtract 20 from the total number of people that attended.

132 - 20 = 112

So, 112 adults attended as well as 20 children.

To find the number of adults and children who attended the concert, we can set up a system of equations and solve for the variables. Using the given information, we can determine that there were 67 adults and 65 children at the concert.

To solve this problem, we can use a system of equations. Let's assume that the number of adults who attended the concert is 'a' and the number of children is 'c'. We can form two equations from the given information:

Now, we can solve the system of equations to find the values of 'a' and 'c'.

Solving Equation 1 for 'a', we get a = 132 - c.

Substituting this value of 'a' into Equation 2, we get 3.25(132 - c) + 2.25c = 364.

Expanding and simplifying the equation gives us 429 - 3.25c + 2.25c = 364.

Combining like terms, we get -c = -65.

So, c = 65.

Substituting this value of 'c' into Equation 1, we get a + 65 = 132.

Solving for 'a', we get a = 67.

Therefore, there were 67 adults and 65 children at the concert.

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Answer:

C. 0.36

Step-by-step explanation:

There is already a 45% chance of having oil on the land.

The oil kit has an 80% accuracy rate.

Therefore the kit has an 80% chance, of that 45% chance, of detecting oil. (Assume the owners in the area are correct in their 45% assumption)

This can be expressed as 80%*40% or 0.8*0.45

= 0.36 or 36%

Hope this helps!

Answer:

C. 0.36

Step-by-step explanation:

Answer:

B.

The system represents the maximum amount that Susan can spend on marigolds, x, and impatiens, y, and the relationship between the number of marigolds and impatiens.

Answer:

B.

The system represents the maximum amount that Susan can spend on marigolds, x, and impatiens, y, and the relationship between the number of marigolds and impatiens.

If r(x) = 3x - 1 and s(x) = 2x + 1, which expression is equivalent to (r/s)(6) is: A. [tex]\frac{3(6) - 1}{2(6)+1}[/tex]

In Mathematics, an algebraic expression is a type of mathematical equation which is typically used for showing the relationship existing between two (2) or more variables, numerical quantities (constants), accompanied with the use of different mathematical operations.

Based on the information provided, the quotient of the two expressions can be computed as follows;

[tex]\frac{r(x)}{s(x)} =\frac{3x - 1}{2x+1} \\\\[/tex]

When the value of x is 6, the output value of the expression

[tex]\frac{r}{s}(6) =\frac{3(6) - 1}{2(6)+1}[/tex]

Complete Question;

If r(x) = 3x - 1 and s(x) = 2x + 1, which expression is equivalent to (r/s)(6)?

Answer:

To find the value of missing exponent, we have to split the number which is in other side of equal sign (which is not having power) as the multiple of base of the missing exponent.

On both sides, powers have the same base, so their exponents must be equal.

Step-by-step explanation:

Write the missing exponent:

25=5^x

Let x be the missing exponent.

To find the value missing exponent, we have to split the number which is in the left side as the multiple of the base of the missing exponent.

That is,

25=5*5 or 5^2

Now,

5^2=5^x

Powers have the same base so their exponent must be equal.

Hence the missing exponent is 2

Answer:

[tex]\large\boxed{D.\ (x-3)^2+(y+2)^2=81}[/tex]

Step-by-step explanation:

The standard form of an equation of a circle:

[tex](x-h)^2+(y-k)^2=r^2[/tex]

(h, k) - center

r - radius

We have the center at (3, -2) and the radius r = 9. Substitute:

[tex](x-3)^2+(y-(-2))^2=9^2\\\\(x-3)^2+(y+2)^2=81[/tex]