The Diameter Of A Regulation Soccer Ball Is About 5 Inches. This Number Was Graphed On A Number Line. (2024)

Explanation:

For an exponential growth, the spike in share price must be proportional to what was already on ground.

We conclude that it is not an example of exponential growth.

Given the points (2,4) and (-1,9)

[tex]\begin{gathered} X_1=2;Y_1=4 \\ X_2=-1;Y_2=9 \end{gathered}[/tex][tex]\begin{gathered} \text{Slope, M of a line is given by the equation;} \\ M=\frac{Y_2-Y_1}{X_2-X_1} \\ M=\frac{9-4}{-1-2} \\ M=\frac{5}{-3} \\ M=\frac{-3}{5} \end{gathered}[/tex][tex]\text{Hence the slope of the l}ine\text{ }is\text{ }\frac{-3}{5}[/tex]

Answer:

(c)12th Month

(d)$76.86

Explanation:

Part A

Prize A: $5,000 for the first month with a $100 increase every month thereafter.

[tex]y_1=5,000+100x[/tex]

Prize B: $2,000 for the first month with a 10% increase every month thereafter.

[tex]\begin{gathered} y_2=2000(1+\frac{10}{100})^x \\ y_2=2000(1.1)^x \end{gathered}[/tex]

Part B

The table is completed and attached below:

Part C

As seen from the table, Prize B will earn more than prize A in the 12th Month.

Part D

[tex]\begin{gathered} \text{Difference in the 12th Month=6276.86-6200} \\ =\$76.86 \end{gathered}[/tex]

Prize B will earn $76.86 more than prize A in the 12th month.

Given the equation:

y = 3x + 2

Let's find the equation that passes through the point (3, -1) and is parallel to the given line.

Apply the slope-intercept form of a linear equation:

y = mx + b

Where m is the slope and b is the y-intercept.

Now compare both equations:

y = mx + b

y = 3x + 2

This means the slope of the line m = 3.

y-intercept (b) = 2

The slope of parallel lines are equal.

Hence, the slope of the parallel line is also 3.

Now, let's find the y-intercept of the parallel line.

Given the point:

(x, y) ==> (3, -1)

Substitute 3 for x, -1 for y, then 3 for m in the slope-intercept equation to solve for b.

We have:

y = mx + b

-1 = 3(3) + b

-1 = 9 + b

Subtract 9 from both sides:

-1 - 9 = 9 - 9 + b

-10 = b

b = -10

The y-intercept of the parallel line is -10.

Therefore, the equation of the parallel line is:

y = 3x - 10

Angle between v and w is

Angle A = Angle v - Angle w

then

Angle v= Arctan (-1/4) = -14 °

Angle w= Arctan (5/2) = 68.2 °

Therefore, angle between v and w is

. = -82.2 °

Then answer is

Angle A = -82.2°

The formua for determining simple interest interest is expressed as

I = PRT/100

where

I = interest

P = principal or initial amount

R = interest rate

T = number of years

From the information given,

P = 215

T = 8

R = 8

I = (215 x 8 x 8)/100 = 137.6

The ending balance after 8 years = principal + intereest

Ending balance = 215 + 137.6 = $352.6

To solve the exercise, we are going to find the greatest common factor or GCF of 48 and 63:

• Factors of 48: 1, 2, ,3,, 4, 6, 8, 12, 16, 24, and 48.

• Factors of 63: 1, ,3,, 7, 9, 21, and 63.

Notice that the greatest common factor of 48 and 63 is 3.

Therefore, the greatest number of friends that Jared can invite over is 3.

For the second question, we divide the number of fruit snacks by the number of friends that Jared can invite, and we divide the number of co*kes by the number of friends that Jared can invite:

[tex]\begin{gathered} \frac{48}{3}=16\Rightarrow\text{ Fruit snacks} \\ \frac{63}{3}=21\Rightarrow\text{ co*kes} \end{gathered}[/tex]

Therefore, each friend will receive 16 fruit snacks and 21 co*kes.

The reflected graph of the function y=|x| is shown below.

The graph of -y=|x| is,

In the question, the vertex of graph is translated 2 units to left implies,

[tex]-y=|x+2|[/tex]

The vertex is shifhted four units above, implies,

[tex]-y=|x+2|-4[/tex]

Therefore, the equation is

y=-|x+2|+4

Answer:

[tex]\begin{gathered} a)\text{ log}_{10}x\text{ =3 }\rightarrow\text{ 1000} \\ b)\text{ log}_2x\text{ = 5}\rightarrow\text{ 32} \\ c)\text{ log}_4x\text{ = 2 }\rightarrow\text{ 16} \\ d)\text{ log}_5x\text{ = 4}\rightarrow\text{ 625} \end{gathered}[/tex]

Explanation:

Here, we want to select the appropriate logarithmic relationship

We have the general rule as:

[tex]\begin{gathered} Log\placeholder{⬚}_aB\text{ = c} \\ B\text{ = a}^c \end{gathered}[/tex]

This is the rule we are going to use. Since there are 4 tiles, we shall be selecting the 4 logarithmic expressions and use their number equivalent on the right side

a)

[tex]\begin{gathered} log\placeholder{⬚}_{10}\text{ x = 3} \\ x\text{ = 10}^3 \\ x\text{ = 1000} \end{gathered}[/tex]

b)

[tex]\begin{gathered} log\placeholder{⬚}_2x\text{ = 5} \\ x\text{ = 2}^5 \\ x\text{ = 32} \end{gathered}[/tex]

c)

[tex]\begin{gathered} log\placeholder{⬚}_4x\text{ = 2} \\ x\text{ = 4}^2 \\ x\text{ = 16} \end{gathered}[/tex]

d)

[tex]\begin{gathered} log\placeholder{⬚}_5x\text{ = 4} \\ x\text{ = 5}^4 \\ x\text{ = 625} \end{gathered}[/tex]

Notice that:

[tex]-3+3=0.[/tex]

Therefore:

[tex]8x-3+4x+3=12x+0.[/tex]

Answer: ?=0.

SOLUTION

Given the question, the following are the solution steps to answer the question.

STEP 1: Interpret the statement

Let the number be y

From first statement,

[tex]\begin{gathered} twice\text{ the number}=2y \\ 2y+\frac{5}{6}=3y-\frac{2}{3} \end{gathered}[/tex]

STEP 2: Evaluate the equation to get y

[tex]\begin{gathered} \mathrm{Subtract\:}\frac{5}{6}\mathrm{\:from\:both\:sides} \\ 2y+\frac{5}{6}-\frac{5}{6}=3y-\frac{2}{3}-\frac{5}{6} \\ 2y=3y-\frac{3}{2} \\ \mathrm{Subtract\:}3y\mathrm{\:from\:both\:sides} \\ 2y-3y=3y-\frac{3}{2}-3y \\ -y=-\frac{3}{2} \\ \mathrm{Divide\:both\:sides\:by\:}-1 \\ \frac{-y}{-1}=\frac{-\frac{3}{2}}{-1} \\ y=\frac{3}{2} \end{gathered}[/tex]

Hence, the number is 3/2

The symbol U means that we are going to do the Union of two sets, which means that we will take the elements of set A, and the elements of set B, and create a new set C that contains all the elements of A and B.

Therefore, if A = [-14, -8] and B = (-8, 10), the union of that two sets, represented by [-14, -8] U (-8, 10) will be

[tex]C=\lbrack-14,10)[/tex]

Final answer:

[tex]C=\lbrack-14.10)[/tex]

[tex]a+2a-3=30[/tex]

solve the first squation by simplifying all common factors

[tex]3a-3=30[/tex]

add 3 on both sides

[tex]\begin{gathered} 3a-3+3=30+3 \\ 3a=33 \end{gathered}[/tex]

divide by 3 on both sides

[tex]\begin{gathered} a=\frac{33}{3} \\ a=11 \end{gathered}[/tex]

for the second equation

[tex]0.10c+0.25(c+3)=10.90[/tex]

simplify left side of the equation

[tex]0.10c+0.25c+0.75=10.90[/tex][tex]0.35c+0.75=10.90[/tex]

substract 0.75 on both sides

[tex]\begin{gathered} 0.35c+0.75-0.75=10.90-0.75 \\ 0.35c=10.15 \end{gathered}[/tex]

divide by 0.35 on both sides

[tex]\begin{gathered} c=\frac{10.15}{0.35} \\ c=29 \end{gathered}[/tex]

Given

[tex]\frac{x^3+2x^2+3x+2}{x+1}[/tex]

To rewrite the expression using synthetic division.

Explanation:

It is given that,

[tex]\frac{x^3+2x^2+3x+2}{x+1}[/tex]

That implies,

Set x + 1 = 0.

Then, x = -1.

Therefore, by using synthetic division,

Hence, the expression is rewritten as,

[tex]x^2+x+2[/tex]

Answer: The lengths of the triangles with the sides a b and c can be visualized as follows:

Using the Pythagorean theorem, we can construct the following equation related to the triangle shown:

[tex]\begin{gathered} a^2+b^2=c^2 \\ \\ \\ a=\sqrt{9} \\ b=? \\ c=9 \\ \\ \\ (\sqrt{9})^2+b^2=9^2 \\ \\ \\ b^2=9^2-(\sqrt{9})^2 \\ \\ b=\sqrt{81-9}=\sqrt{72}\approx8.4853 \end{gathered}[/tex]

Answer: 35 days

Explanation:

We have that 2/7 of a jar are use per day to feed the gecko. If she has 10 jars, what we need to do is divide 10 days by 2/7 per day, and we will find the number of days that she can feed her gecko.

-Divide 10 by 2/7:

10 ÷ 2/7

this is equal to the following:

[tex]\frac{10\cdot7}{2}[/tex]

we multiply 10 by the denominator 7 and divide by 2.

solving the operations:

[tex]\frac{10\cdot7}{2}=\frac{70}{2}=35[/tex]

How many days can she feed her gecko with this food ? 35

We are only tasked to count the total number of heads and tails provided by the table. Each X represents a flip that resulted in heads/tails. Based on the given table, the number of heads and tails are

Head - 28

Tails - 22

The given expression is

[tex](9.6\times10^3)\times(6.7\times10^2)[/tex]

First, we group factors and powers.

[tex](9.6\times6.7)(10^3\times10^2)[/tex]

Then, we multiply.

[tex]\begin{gathered} 64.32\times10^{3+2} \\ 64.32\times10^5 \end{gathered}[/tex]Therefore, the right answer is C.

The correlation coefficient gives information about the behavior of two variables and it should always be between -1 and 1.

Since the value of the correlation coefficient is 1.18, then the student made an error computing the correlation coefficient, because the number has to be between -1 and 1.

When the coefficient is near the value of 1, it means that there is a strong positive relationship between the variables (y increases as x increases).

When the coefficient is near the value of -1, it means that there is a strong negative relationship between the variables (y decreases as x increases).

When the value is not near 1 or -1, and it's rather near to 0, then there is a weak relationship (it will be a positive or negative relationship depending on the sign).

Either case, the coefficient cannot be greater than 1 or lower than -1.

The given triangle, is TUV

As E, D, H are the midpoints, we have,

HE=1/2 UV

Similarly,

[tex]\begin{gathered} HD=\frac{1}{2}TU \\ 62=\frac{1}{2}TU \\ TU=2\times62=124 \end{gathered}[/tex]

The product is:

[tex](-x^3y^2)(4x^2y+3xy-x^2)[/tex]

What we have to do is to distribute the -x^3 y^2 term over the other three terms:

[tex]-4x^5y^3-3x^4y^3+x^5y^2[/tex]

In the first term I did:

[tex]-x^3y^2\times4x^2y=-4x^5y^3[/tex]

The second term was:

[tex]-x^3y^2\times3xy=-3x^4y^3[/tex]

And finally, the third term:

[tex]-x^3y^2\times-x^2=x^5y^2[/tex]

Then the answer is:

[tex]-4x^5y^3-3x^4y^3+x^5y^2[/tex]

Answer:

[tex]0.\bar{9}=1[/tex]

Explanation:

The fractions are formed with a 9 as a denominator and the numerator is the number that repeats. So, following the same rule, we can say that 0.999... is equivalent to:

[tex]0.\bar{9}=\frac{9}{9}[/tex]

However, 9/9 is equal to 1, so:

[tex]0.999\ldots=0.\bar{9}=1[/tex]

Therefore, the answer is:

[tex]0.\bar{9}=1[/tex]

Given

Find

Value of x

Explanation

Here , we use trigonometric ratio

[tex]\begin{gathered} \tan C=\frac{P}{B} \\ \\ \tan65\degree=\frac{AB}{BC} \\ \\ \tan65\degree=\frac{x}{7} \\ \\ x=7\tan65\degree \\ \\ x=15.0115484436\approx15 \end{gathered}[/tex]

Final Answer

Hence , the value of x is 15

We know that the tip was $22, which represents 20% of the total, Ti dubs the bill subtotal, we have to solve the following proportion

[tex]\frac{22}{0.20}=\frac{x}{1}[/tex]

Let's solve for x

[tex]x=110[/tex]Hence, the bill subtotal was $110.

ANSWER

4(x + 3)(x + 4)

EXPLANATION

We want to factorise:

4x² + 28x + 48​

We simply want to write the expression as a product of its factors.

First, because each of the coefficients in the expression and the constant are divisible by 4, we will factor out 4:

[tex]4(x^2\text{ + 7x + 12)}[/tex]

Now, we have to look for two numbers such that adding them will yield 7 and their product will yield 12.

The two numbers we need are:

3 and 4

So, we have that the expression becomes:

[tex]\begin{gathered} 4(x^2\text{ + 3x + 4x + 12)} \\ \Rightarrow\text{ 4\lbrack{}x(x + 3) + 4(x + 3)\rbrack} \\ \Rightarrow\text{ 4(x + 3)(x + 4)} \end{gathered}[/tex]

We have factorised it.

Given:

The table of the frequency distribution of the weights​ (in grams) of​ pre-1964 quarters is given.

Required:

Find the correct histogram from the given histogram.

Explanation:

We can observe from the given histogram that the frequency from 6.150-6.199 to 6.200-6.249 is decreasing. In histogram B it is increasing So option B is not the correct answer.

In histograms A and C we will observe that the frequency is 6.000-6.049

3 and 6.350-6.399 are 1.

But by observation in histogram A it is not correct.

It is correct in histogram C.

Final Answer:

Option C is the correct answer.

74.97 revolutions

Explanation

Step 1

The number of revolutions made by a tire traveling over a fixed distance varies inversely to

the radius of the tire

Let

The number of revolutions=n

the radius of the tire:r

then

[tex]n=\frac{\lambda}{r}[/tex]

where

[tex]\lambda\text{ is a constant}[/tex]

A 12-inch radius tire makes 100 revolutions to travel a certain,Hence

[tex]\begin{gathered} n=\frac{\lambda}{r} \\ 100=\frac{\lambda}{12} \\ \text{Multiply both sides by 12} \\ 100\cdot12=\frac{\lambda}{12}\cdot12 \\ 1200=\lambda \end{gathered}[/tex]

so, the constant is 1200, the equation is

[tex]\begin{gathered} n=\frac{\lambda}{r} \\ n=\frac{1200}{r}\text{ equation} \end{gathered}[/tex]

then, we need to find the distance

then

[tex]\begin{gathered} a\text{ revolution=2}\cdot\pi\cdot radius \\ a\text{ revolution=2}\cdot\pi\cdot12\text{ inche( for the first tire)} \\ a\text{ revolution=75.38 inches} \\ \text{then 100 revolutions = 100}\cdot75.38\text{ inches} \\ 100\text{ revolutionss=7539 inches} \end{gathered}[/tex]

then,the distance is 7539 inches

Step 2

Let

n= unknown

radius=r=16 inch

distance=7539 inches

[tex]\begin{gathered} 2\cdot\pi\cdot r=2\cdot\pi\cdot16 \\ 32\cdot\pi=100.53\text{ inches} \end{gathered}[/tex]

it means

[tex]1\text{ revolution}\Rightarrow100.53\text{ inches}[/tex]

then

[tex]\nu\text{mber of revolutions}\cdot100.553=same\text{ distance}[/tex]

replacing

[tex]\begin{gathered} N\cdot100.553=7539\text{ inches} \\ \text{divide both sides by 100.553} \\ \frac{N\cdot100.553}{100.553}=\frac{7539}{100.553} \\ N=74.97\text{ revolutions} \end{gathered}[/tex]

EXPLANATION

Vacuum cleaner = $15

Coupon discount [For Veterans]= 20%

Seniors discount = $50

To compare both we can do:

Veterans---> $115 * 0.80 = $92

Seniors-----> $115 -50 = $65

Answer: Seniors get the better deal.

Find calculation of fractions

we have the function

[tex]y=\frac{x^2+7x+10}{x+3}[/tex]

Remember that

The zeros of the function, are the values of x when the value of y=0

so

For y=0

[tex]x^2+7x+10=0[/tex]

Solve the quadratic equation

we have that

x^2+7x+10=(x+5)(x+2)

therefore

the zeros of the function are

(-5,0) and (-2,0)