Which variable is most important to the following problem?
Evan and Josh play on a basketball team. Evan played the whole first quarter
and the first 4 minutes of the second quarter. Josh played the rest of the
second quarter and all of the third quarter. Evan played the whole fourth
quarter. If each quarter is 10 minutes long, how long did Evan play?

A. the number of minutes Josh played in the fourth quarter
B. the number of players on the team
C. the number of minutes Evan played
D. the number of times Evan was substituted into the game

Answer:

Option D is correct.

Step-by-step explanation:

The first value is 1/32

if we multiply 1/32 with 2 i.e 1/32*2 we get 1/16

So, next value is 1/16

if we multiply 1/16 with 2 i.e 1/16 * 2 we get 1/8

So, next value is 1/8

if we multiply 1/8 with 2 i.e 1/8 * 2 we get 1/4

So, next value is 1/4

if we multiply 1/4 with 2 i.e. 1/4 *2 we get 1/2

so, next value is 1/2

if we multiply 1/2 with 2 i.e 1/2 * 2 we get 1

So, Option D multiply the previous value by 2 is correct.

Answer:

k(x)=5x+2

k(4)=5(4) +2 =22

k(1)= 5(1) +2 =7

k(4) - k(1) = 22 - 7 = 15

The answer is:

A). 15

Answer:

$1,466.23 Will be your answer mate !!!!!!

Step-by-step explanation:

The present value is calculated by discounting each of the cash flows to the present therefore if we assume no salvage value:  

PV = $100 / 1.08 + $100 / 1.08^2 + $100 / 1.08^3 + $200 / 1.08^4 + $300 / 1.08^5 + $600 / 1.08^6  

PV = $923.98  

Technically, as we have assumed there are no salvage value then in the future value will be zero. If you are asking how much remains in the investment. If you are asking how much the investment has yielded, keep in mind that the cash flows are not by definition reinvested so the time value of those cash flows can't be accounted for. If you do not account for the time value of those cash flows then the future value is just:  

$100 * 3 + $200 + $300 + $500 = $1,300  

However if you use the 8% per annum effective rate as a discount rate to take into consideration the time value of the money which is basically saying that you can reinvest the cash flows at 8% per annum effective then the future value would be:  

$100 * 1.08^5 + $100 * 1.08^4 + $100 * 1.08^3 + $200 * 1.08^2 + $300 * 1.08 + 500 = $1,466.23

you'll get your answer as : $1,466.23 !

Final answer:

The present value of the investment with varying cash flows and an 8% discount rate is $943.28. The future value, assuming reinvestment at an 8% interest rate until the end of Year 6, is $1,466.23.

Explanation:

To calculate the present value of the investment with varying cash flows and an 8% discount rate (interest rate), we discount each cash flow to its present value using the formula [tex]PV = FV / (1 + r)^t,[/tex]where PV is present value, FV is future value, r is the annual interest rate, and t is the number of years until the payment.

Year 1:  [tex]\$100 / (1 + 0.08)^1 = $92.59[/tex]

[tex]Year 2: \$100 / (1 + 0.08)^2 = $85.73 \\Year 3: \$100 / (1 + 0.08)^3 = $79.38 \\Year 4: \$200 / (1 + 0.08)^4 = $150.26 \\Year 5: \$300 / (1 + 0.08)^5 = $220.08 \\Year 6: \$500 / (1 + 0.08)^6 = $315.24 \\[/tex]

The sum of these values is the total present value of the investment, which equals $943.28.

For the future value, we grow each cash flow by the interest rate for the remaining period it would be invested until the end of Year 6, since payments are made at the end of each year.

[tex]Year 1: \$100 * (1 + 0.08)^5 = $146.93 \\Year 2: \$100 * (1 + 0.08)^4 = $136.05 \\Year 3: \$100 * (1 + 0.08)^3 = $125.97 \\Year 4: \$200 * (1 + 0.08)^2 = $233.28 \\Year 5: \$300 * (1 + 0.08)^1 = $324.00 \\[/tex]

Year 6: $500 = $500.00

By adding all future values, the total future value of the investment is $1,466.23.

Answer:

y = -2x - 6

Step-by-step explanation:

4y = -8x - 24

y = -2x - 6

Answer:

y = -6 - 2x

Step-by-step explanation:

8x + 4y = -24

4y = -24 - 8x

y = (-24 - 8x) / 4

  = -[tex]\frac{24}{4}[/tex] - [tex]\frac{8}{4}[/tex]

  = -6 - 2x (ans)  or -(6 + 2x)

Answer:

12

Step-by-step explanation:

Volume of cylinder is pi*r^2*h    (this is equal to 540pi in this case)

So we have 540pi=pi*r^2*h  

this means that 540=r^2*h   (I just divided both sides by pi since both sides were being multiplied by pi)

The height,h, is 15 so plug in 540=r^2*15

Divide both sides by 15 giving 540/15=r^2

So r^2=36

So r=6

The diameter,d, is twice the radius, r.

So d=2(6)=12

Answer:

b. 12

Step-by-step explanation:

The volume of a cylinder is

[tex]\pi {r}^{2} h[/tex]

Let us compose an equality and solve for the radius.

540pi = pi × r^2 × 15.

Divide both sides of the equation by 15pi.

r^2 = 36

r = +/- 6.

Length cannot be negative, so r = 6.

diameter = 2 × r. In this case,

d = 2 × 6 = 12.

The diameter is 12 ft.

Answer:

145,146,147

Step-by-step explanation:

Let x be the first number

x+1 is the next number

x+1 +1 is the next number

The sum of these three number is

x + x+1 + (x+1+1) = 438

Combine like terms

3x +3 = 438

Subtract 3 from each side

3x+3-3 = 438-3

3x= 435

Divide by 3

3x/3=435/3

x = 145

x+1 =146

x+1+1 = 147

Answer:

B

Step-by-step explanation:

24 times 4 is 96 legs

196-96=100 divided by 2 is 50 humans

50 plus 24 is 74

Answer:

B 24 horses and 50 humans

Step-by-step explanation:

Let x = humans

y = horses

Each horse and human has 1 head, for a total of 74 heads

x+y = 74

Each human has 2 leags, 2x  and each horse has 4 legs, 4y for a total of 196 legs

2x+4y = 196

We have a system of equations

x+y = 74

2x+4y = 196

Multiply the first equation by -2

-2(x+y) = -2*74

-2x -2y - 154

Add the modified first equation to the second equation

-2x-2y = -154

2x+4y = 196

-----------------------

2y = 48

Divide by 2

2y/2 = 48/2

y = 24

There are 24 horses

x+y = 74

We know there are 24 horses

x+24 = 74

x+24-24 = 74-24

x=50

There are 50 humans

Answer:

y = 1/4 x - 1.

Step-by-step explanation:

The slope (from the 2 given points) =  (0 - -1) / (4 - 0) = 1/4.

The y-intercept is at y = -1, so the equation is:

y = 1/4 x - 1.

Answer:

=

Step-by-step explanation:

9/10  vs 36/40

Multiply 9/10 by 4/4 so the denominators are equal

9/10*4/4 = 36/40

36/40 vs 36/40

They are equal

Juan needs to sell 18 fruit baskets and 2 pencils to achieve his goal.

The number of items = (total price for the items)/(each price of the required item)

Given that,

Price of a fruit basket = $16.50

Price of a pencil = $1.50

His goal is to achieve $300

So,

The number of fruit baskets required to sell by the Juan = 300.00/16.50

⇒ 18.18 (rounding off)

⇒ 18 fruit baskets

And

Then 2 more pencils are to be sold to achieve his goal.

Therefore, 18 fruit baskets need to be sold by Juan.

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SA = (l x w x 2) + (l x h x 2) + (w x h x 2)

SA = (6 x 4 x 2) + (6 x 2 x 2) + (4 x 2 x 2)

SA = 48 + 24 + 16

SA = 88

The answer is 88 square units.

Answer:

A. 88 square units.

Step-by-step explanation:

Volume formula:

 ↓

[tex]V=L*W*H[/tex]

[tex]6*4*2=48[/tex]

[tex]L*H*2[/tex]

[tex]6*2*2=24[/tex]

[tex]W*H*2[/tex]

[tex]4*2*2=16[/tex]

Add the numbers from left to right.

48+24=72

72+16=88

88 is the correct answer.

Answer:

[(-15, 21), (-6, 12).(-1, 7)}

Step-by-step explanation:

we have

x+y=6

Find the values of y for XE (-15, -6, -1)

so

For x=-15

-15+y=6 --->y=21

therefore

a solution is the point (-15,21)

For x=-6

-6+y=6 --->y=12

therefore

a solution is the point (-6,12)

For x=-1

-1+y=6 --->y=7

therefore

a solution is the point (-1,7)

The set of ordered pairs that are solutions is

[(-15, 21), (-6, 12).(-1, 7)}

Final answer:

The correct set of ordered pairs, which are the solutions to the equation x + y = 6 given x in {-15, -6, -1}, is {(-15, 21), (-6, 12), (-1, 7)}.

Explanation:

To determine which set of ordered pairs are solutions to the given equation x + y = 6, we need to plug the x-values into the equation and solve for y.

The correct set of ordered pairs is therefore {(-15, 21), (-6, 12), (-1, 7)}.

Answer:

The first two terms are √2 and 6.

Step-by-step explanation:

a3^2+4=1604

a3=40

a2^2+4=40

a2=6

a1^2+4=6

a1=√2

The first two terms are approximately a1 ≈ 2.52 and a2 ≈ 6.33.

First Two Terms of the Sequence

To find the first two terms of the sequence defined recursively by the formula an = (an-1)2, given that a4 = 1604, we need to work backwards.

Step-by-Step Explanation:

Therefore, the first two terms of the sequence are approximately a1 ≈ 2.52 and a2 ≈ 6.33.

Step-by-step explanation:

Let's do the volume first. Volume of any prism is the area of the base times the height.

V = Ah

The base is a large square with a smaller rectangle cut from the corner, so its area is:

A = (14)(14) - (7)(10)

A = 126

So the volume is:

V = (126)(6)

V = 756 m^3

Now the surface area of a prism is the area of the bases plus the base perimeter times the height:

S = 2A + Ph

We already found the area of the base. Now we just have to add the perimeter times height.

S = 2(126) + (14 + 14 +7 + 10 + 7)(6)

S = 480 m^2

Answer:

The ratio of their surface areas is 4:49

Step-by-step explanation:

we know that

If two figures are similar, then the ratio of its corresponding sides is equal and this ratio is called the scale factor

In this problem the scale factor is equal to the ratio 2:7

and

Remember that

If two figures are similar, then the ratio of its surface areas is equal to the scale factor squared

therefore

In this problem the ratio of their surface areas is (2:7)^2 = 4:49

The ratio of their surface areas is,

⇒ 4 : 49

A ratio indicates how many times one number contain in another number. The ratio of two number is written as x : y, which is equivalent to x/y.

Where, x and y are individual amount of two quantities.

And, Total quantity gives after combine as x + y.

\

We know that;

If two figures are similar, then the ratio of its corresponding sides is equal and this ratio is called the scale factor.

In this problem the scale factor is equal to the ratio 2/7,

Hence, If two figures are similar, then the ratio of its surface areas is equal to the scale factor squared

therefore,

In this problem the ratio of their surface areas is ,

⇒ (2 / 7)²

⇒ 4 / 49

⇒ 4 : 49

Thus, The ratio of their surface areas is,

⇒ 4 : 49

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Answer:

The product of  [tex](x^2+3x+1)(x^2+x+2)[/tex] is [tex]x^3+4x^3+6x^2+7x+2[/tex]

Step-by-step explanation:

We need to find the product of [tex](x^2+3x+1)(x^2+x+2)[/tex]

We need to multiply the first term with the second term.

Multiplying:

[tex](x^2+3x+1)(x^2+x+2)\\=x^2(x^2+x+2)+3x(x^2+x+2)+1(x^2+x+2)\\=x^4+x^3+2x^2+3x^3+3x^2+6x+x^2+x+2\\Adding\,\,like\,\,terms\,\,\\=x^4+x^3+3x^3+2x^2+3x^2+x^2+6x+x+2\\=x^3+4x^3+6x^2+7x+2\\[/tex]

So, the product of  [tex](x^2+3x+1)(x^2+x+2)[/tex] is [tex]x^3+4x^3+6x^2+7x+2[/tex]

Answer:

f(2) = -4

Step-by-step explanation:

Plug in 2 for x:

f(x) = 4x - 12

f(2) = 4(2) - 12

Remember to follow PEMDAS. (PEMDAS = Parenthesis, Exponents (& roots), Multiplication, Division, Addition, Subtraction) PEMDAS is what you follow to solve these questions.

First, Multiply:

f(2) = 4(2) - 12

f(2) = (4 * 2) - 12

f(2) = 8 - 12

Next, subtract:

f(2) = 8 - 12

f(2) = -4

f(2) = -4 is your answer.

~

Answer:

-4

Step-by-step explanation:

put 2 into all the x values in the equation.

4(2) - 12 = -4

Answer:

B

Step-by-step explanation:

edge 2021

The polynomial that is in standard form is 13x^5 + 11x - 6x^2 + 5.

The polynomial that is in standard form is 13x5 + 11x - 6x2 + 5. In standard form, the polynomial is arranged by descending order of exponents. The terms are written with the coefficient in front of each variable.

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Answer:

10/60 as a decimal is:

0.166666667

Step-by-step explanation:

To get 10/60 converted to decimal, you simply divide 10 by 60.

Please mark brainliest and have a great day!

Answer:

0.166666666666667

Step-by-step explanation:

Answer:

The 99.7% confidence interval for the mean here is

[tex]\rm (11.2, 12.8)\; \mu g\cdot m^{-3}[/tex].

Step-by-step explanation:

The data in this question comes from random samples. In other words, the true population data are not known. Assume that both the sample average and the sample stdev are unbiased estimates for the population mean and stdev.  

The sample size 196 is sufficient large, such that the central limit theorem will apply. By the central limit theorem, the distribution of the mean (as well as the sum) of a sufficiently large samples resembles normal distributions. However, since stdev is only an estimate, the confidence interval can only be found using the Student's t-distribution.

What is the confidence interval for the mean of a random variable that follows the t-distribution?

[tex]\displaystyle \left(\bar{x} - t\cdot \frac{s_{n-1}}{\sqrt{n}}, \; \bar{x} + t\cdot \frac{s_{n-1}}{\sqrt{n}}\right)[/tex],

where

What is not given is

Start by determining the degree of freedom [tex]df[/tex] of [tex]t[/tex]. The degree of freedom for a one-variable estimate is usually equal to [tex]n -1[/tex] (that is: sample size minus one.) For this question, [tex]n = 196[/tex] so [tex]df = 196 - 1 = 195[/tex].

If [tex]T[/tex] represent a random variable that follows the [tex]t_{195}[/tex]-distribution, the value of t shall ensure that

[tex]P(-t \le T \le t) = \text{Confidence Interval} = 0.997[/tex].

The t-distribution is symmetric. As a result,

[tex]\displaystyle P(T > t) = 0.997 + \frac{1}{2}\times (1 - 0.997) = 0.9985[/tex].

Find the value of [tex]t[/tex] either with a t-distribution table or with technology. Keep in mind that for this question, [tex]df = n - 1 = 195[/tex].

[tex]t \approx 3.00549[/tex].

Apply the formula for the confidence interval:

[tex]\displaystyle \left(\bar{x} - t\cdot \frac{s_{n-1}}{\sqrt{n}}, \; \bar{x} + t\cdot \frac{s_{n-1}}{\sqrt{n}}\right)[/tex].

Lower bound:

[tex]\displaystyle \bar{x} - t\cdot \frac{s_{n-1}}{\sqrt{n}} &= 12 - 3.00549\times \frac{3.5}{\sqrt{196}}\approx 11.2[/tex].

Upper bound:

[tex]\displaystyle \bar{x} + t\cdot \frac{s_{n-1}}{\sqrt{n}} &= 12 + 3.00549\times \frac{3.5}{\sqrt{196}}\approx 12.8[/tex].

In other words, the 99.7% confidence interval for the actual concentration is [tex]\rm (11.2, 12.8)\; \mu g\cdot m^{-3}[/tex].

Answer:

The four answers in the attached figure

Step-by-step explanation:

Part 1) we have

[tex]x-99\leq-104[/tex]

Solve for x

Adds 99 both sides

[tex]x-99+99\leq-104+99[/tex]

[tex]x\leq-5[/tex]

The solution is the interval ----> (-∞, -5]

All real numbers less than or equal to -5

In a number line, the shaded area at  left of x=-5 (close circle)

Part 2) we have

[tex]x-51\leq-43[/tex]

Solve for x

Adds 51 both sides

[tex]x-51+51\leq-43+51[/tex]

[tex]x\leq 8[/tex]

The solution is the interval ----> (-∞, 8]

All real numbers less than or equal to 8

In a number line, the shaded area at  left of x=8 (close circle)

Part 3) we have

[tex]150+x\leq144[/tex]

Solve for x

Subtract  150 both sides

[tex]150+x-150\leq144-150[/tex]

[tex]x\leq -6[/tex]

The solution is the interval ----> (-∞, -6]

All real numbers less than or equal to -6

In a number line, the shaded area at  left of x=-6 (close circle)

Part 4) we have

[tex]75<69-x[/tex]

Solve for x

Subtract 69 both sides

[tex]75-69<69-x-69[/tex]

[tex]6<-x[/tex]

Multiply by -1 both sides

[tex]-6> x[/tex]

Rewrite

[tex]x < -6[/tex]

The solution is the interval ----> (-∞, -6)

All real numbers less than -6

In a number line, the shaded area at  left of x=-6 (open circle)

Answer:

my bad if im wrong but im pretty sure its b

Step-by-step explanation:

Range is all the y values in this case that would be...

{-1, 4, 11, 13}

Keep in mind that there are different ways to show range. The one I showed it just one of them

Hope this helped!

~Just a girl in love with Shawn Mendes

Answer:

a = 5, b=1

Step-by-step explanation:

We can rewrite a whole number as a fraction by putting it over 1

5/1 = 5

a = 5, b=1

5/1 is a rational number since it can be written in the form a/b

Answer:

a = 16

First exclude any restricted values of y.

6/y = 9/24 , y is not equal 0

Simplify the right side of the equation using 3.

6y = 3/8

Cross multiply.

6 x 8 = 3

3 x y = 3y

6 x 8 = 3y

48 = 3y

Switch the sides of the equation.

3y = 48

Divide both sides by 3.

3y/3 = y

48/3 = 16

Answer:

2x - (x/2) >12

Step-by-step explanation:

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Answer:

-0.89 < -0.51

B. Felipe's Restaurant has less value than Ming's Lodge.

Step-by-step explanation:

If you have a big debt you're going to have less money.

Answer:

[tex]x=3\\y=-1\\\\(3,-1)[/tex]

Step-by-step explanation:

We have the following system of equations

[tex]4x-3y=15\\2x+2y=4[/tex]

To solve the system of equations multiply the second equation by -2 and add it to the first equation

[tex]-2*(2x+2y)=-2*4[/tex]

[tex]-4x - 4y=-8\\4x-3y=15[/tex]

-------------------

[tex]-7y = 7\\y=-1[/tex]

Now substitute the value of y in any of the two equations and solve for the variable x

[tex]4x-3(-1)=15[/tex]

[tex]4x+3=15[/tex]

[tex]4x=15-3[/tex]

[tex]4x=12[/tex]

[tex]x=\frac{12}{4}[/tex]

[tex]x=3[/tex]

Finally the solution is:

(3, -1)

The answer is going to be 19.

Answer:

C. 19

Step-by-step explanation:

PEMDAS

Parenthesis

Exponent

Multiply

Divide

Add

Subtract

[tex]|-7|=7[/tex]

[tex]3|4|=3*4=12[/tex]

Add.

[tex]7+12=19[/tex]

[tex]19[/tex], is the correct answer.