Solve for x. Type your answer as a number in the blank without "x=".

C) 36 yards   18*6=108

108ft to yards is 36

Answer:C

Step-by-step explanation:

Each jump rope is 6 feet long, so 18 jump ropes would require a total of:

18 x 6 = 108 feet of rope

Since there are 3 feet in a yard, we can convert 108 feet to yards by dividing by 3:

108 ÷ 3 = 36 yards

Therefore, the football coach should buy 36 yards of rope. The answer is (C).

The operations that are performed with the exponents 2 and 3 in order to simplify the expression include the following:

x²x³ = addition.

(x²)³ = multiplication.

x³/x² = subtraction.

In Mathematics, an exponent is a mathematical operation that is typically used in conjunction with an algebraic expression in order to raise a quantity to the power of another.

This ultimately implies that, an exponent is represented by the following mathematical expression;

bⁿ

Where:

By applying the addition, division, and multiplication law of exponents for powers to each of the expressions, we have the following:

x²x³ = x⁽³⁺²⁾ = x⁵ (addition).

(x²)³ = x⁶ (multiplication).

x³/x² = x⁽³⁻²⁾ = x (subtraction).

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As per the concept of simple interest, the interest amount earned after three years is $306.

To calculate the interest amount earned, we can use the formula:

I = P * r * t

Where:

I = interest earned

P = principal amount

r = interest rate per year (as a decimal)

t = time period in years

Plugging in the values from the problem, we get:

I = $1200 * 0.085 * 3

I = $306

This means that after three years, the bond will be worth the principal amount plus the interest earned, which is:

$1200 + $306 = $1506

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For the data set 29, 20, 15, 13, 35, 20. the mean, median, mode and range are 22, 20, 20, and 22, respectively.

The mean (arithmetic mean), denoted by μ, is a single value defined as the sum of the data values divided by the total number of data values.

[tex]\text{Mean} =\dfrac{x_1+x_2+...+x_n}{\text{N}}[/tex]

[tex]\text{Mean} = \dfrac{29+20+15+13+35+20}{6}[/tex]

[tex]\text{Mean} = 22[/tex]

The median, denoted by , is the single value at the middle of an ordered arrangement of data values according to increasing or decreasing magnitude.

[tex]\text{M}_{\text{d}}=x_{\dfrac{\text{N}+1}{2} }[/tex]     if N is odd, and

[tex]\text{M}_{\text{d}}=\dfrac{^x\frac{\text{N}}{2}^{+x} \frac{\text{N}}{2} +1}{y}[/tex]    if N is even

[tex]\text{N = 8}[/tex]

Data : 13, 15, 20, 20, 29, 35

[tex]\text{M}_{\text{d}}=\dfrac{^x\frac{\text{N}}{2}^{+x} \frac{\text{N}}{2} +1}{y}[/tex]

where [tex]x_\frac{\text{N}}{2}[/tex] = [tex]x_\frac{8}{2}[/tex] = [tex]x_4[/tex] = 20 and [tex]x_\frac{\text{N}}{2}_{+1}=x_\frac{8}{2}_{+1}=x_4_{+1}=x^5[/tex] = 20

[tex]\text{M}_{\text{d}}=\dfrac{20+20}{2}[/tex]

[tex]\text{M}_{\text{d}}=20[/tex]

The mode, denoted by , refers to the most frequent value in the data set.

[tex]\text{Mode = 20}[/tex]

The range (R) is defined as the difference between the maximum and minimum values of a data set.

[tex]\text{R} = \text{MAX} - \text{MIN}[/tex]

[tex]\text{R} = 35- 13[/tex]

[tex]\text{R} = 22[/tex]

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The domain of the expression is all real numbers except -7 and 5. In interval notation, the domain can be expressed as (-∞, -7) U (-7, 5) U (5, ∞).

The simplified form of the expression is:

(12 - X) / (x² + 2x - 35) * (x² + 7x) / (x² - 12x)

And the domain of the expression is all real numbers except for values of x that make the denominators equal to zero, as division by zero is undefined.

To find the values of x that make the denominators equal to zero, we can set the denominators equal to zero and solve for x:

x² + 2x - 35 = 0

(x + 7)(x - 5) = 0

x + 7 = 0 or x - 5 = 0

x = -7 or x = 5

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The function best models the data in the table is y=-0.6x+132 (option a).

The table shows the minimum target heart rates by age, which implies that as a person ages, their heart rate should be maintained within a certain range during exercise to achieve optimal cardiovascular benefits. In order to determine the target heart rate for a given age, we need a mathematical function that can accurately model the data in the table.

This is a linear function, which means that it assumes a constant rate of change in the target heart rate as age increases.

However, the data in the table shows that the target heart rate decreases gradually with age. Therefore, this function does  accurately model the data and is a suitable option.

Hence (a) is the right one.

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Complete Question:

Age x (year)                           Minimum Target Heart Rates by Age

30                                                                114

35                                                                 111

40                                                                108

45                                                                105

50                                                                102

Which function best models the data in the table?

a) y=-0.6x+132

b) y=(x-30)²+114

c) y= 19/30x

The number that could be expected to have ordered a medium was 64 people.

The number that could be expected to have ordered a small would be 108 people.

The number that could have been expected to have ordered a small, medium, or large was 75 people.

The number that could have been expected to have ordered a medium was :

= 16 / ( 9 + 16 + 5 + 10 ) x 160 people

= 64 people

The number that could have been expected to have ordered a small would be :

= 9 / ( 9 + 16 + 5 + 10 ) x 480 people

= 108 people

The number that could have been expected to have ordered a small, medium, or large was :

= ( 9 + 16 + 5 ) / ( 9 + 16 + 5 + 10 ) x 100

= 75 people

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the earned interest after 3 years is $1,608.75.

What is simple interest?

Before delving further into the concept of simple interest, it is worth noting that it is a straightforward method for calculating interest on money, whereby interest is added at a constant rate for each time period and always to the initial principal amount. When we deposit our money into a bank, we can earn interest on our investment. Simple interest is one type of interest that banks may offer.

The formula for simple interest is:

I = P * r * t

where:

I = interest earned

P = principal (initial amount)

r = interest rate per year (as a decimal)

t = time (in years)

Substituting the given values, we have:

P = $9,750

r = 0.055 (since the interest rate is 5.5%)

t = 3

I = $9,750 * 0.055 * 3

I = $1,608.75

Therefore, the earned interest after 3 years is $1,608.75.

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The journal entries fro the transaction for October 31 and November 19 are as follows:

Oct. 31: Cash                                              $3,840,000

             ($12 x 320,000)

                       Common Stock                                      $1,600,000

                       ($5 x 320,000)

                       Paid-In Capital in Excess of Par-com.   $2,240,000  

                       ($3,840,000 - $1,600,000)

Nov. 19: Cash                                            $3,240,000

              ($72 x 45,000)

                       Preferred Stock                                     $2,700,000

                        ($60 x 45,000)

                       Paid-In Capital in Excess of Par-Pre.    $540,000

                        ($3,240,000 - $2,700,000)

Full question "On October 31, Pidgeon Stones Inc. , a marble contractor, issued for cash 320,000 shares of $5 par common stock at $12, and on November 19, it issued for cash 45,000 shares of preferred stock, $60 par at $72. Journalize the entries for October 31 and November 19".

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The equation that can be used to represent number of people who can go to the amusement park is 12 + 33.75x = 215.50.

We have,

the total amount to spent on amusement park = $214.50

And the parking fees = $12

The ticket cost per person = $33.75

let the number of person be x.

Then, the equation can become as

12 + 33.75x = 215.50

Simplifying the equation we get

33.75x = 215.5 - 12

33.75x = 203.5

x= 6.02

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Answer:

  x ∈ {6, 7, 8, 9, 10}

Step-by-step explanation:

You want possible values of whole number x such that ...

  4 ≤ √3 +√x < 5

We can solve this inequality by first subtracting √3 from all sides:

  4 -√3 < √x < 5 -√3

Squaring these positive numbers does not change their order:

  19 -8√3 < x < 28 -10√3

  5.14 < x < 10.67

The value of x may be any whole number in the range 6–10, inclusive.

Using mathematical operations of division and multiplication, the total weight of the order in pounds is 3 pounds.

The total weight is firstly computed in ounces before being converted into pounds.

The computation follows the mathematical operations of multiplication and division, respectively.

The number of Orange You Fresh soap bars ordered by a customer = 12

The weight of each bar of soap = 4 ounces

The total weight of 12 bars in ounces = 48 ounces (4 x 12)

1 pound = 16 ounces

3 pounds = 48 ounces (48 ÷ 16)

Thus, based on mathematical operations, the number of pounds this order will weigh is 3 pounds.

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Given statement: Diversification can reduce portfolio risk even when correlations across stock returns equal zero.

Given statement is true.

Because, By diversifying, you spread your investments across various assets, which can help reduce the overall risk of your portfolio. When correlations are zero, it means that the stock returns move independently of each other, further supporting the benefit of diversification in this case.

Diversification can reduce portfolio risk by combining assets with different return patterns, but even when the correlations between the returns are zero, there is still systematic risk (market risk) that cannot be diversified away.

This is because all stocks are subject to macroeconomic factors such as inflation, interest rates, and changes in consumer confidence, which can affect the entire market.

Therefore, even if the correlations across stock returns are zero, diversification cannot completely eliminate portfolio risk.

However, it can still reduce it to a certain extent by spreading the risk across different assets.

The more uncorrelated the assets are in a portfolio, the greater the potential for risk reduction.

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The value of | a b c 7d + a 7e + b 7f + c g h i| is given by -35 + b(ch - di) + c(gi - eh) + a(hk - fg).

Expanding the determinant using the first row, we get:

| a b c 7d + a 7e + b 7f + c g h i|

= a | b c 7d + 7e b 7f + g h i| - b |a c 7d + 7e c 7f + g h i| + c |a b 7d + 7e 7f + g h i|

= a | b c 7d + 7e b 7f + g h i| + b |a c 7d + 7e c 7f + g h i| - c |a b 7d + 7e 7f + g h i|

Now, we can expand each of the three determinants on the right-hand side using the first row and simplify:

| b c 7d + 7e b 7f + g h i| = b | c 7f h i| - 7e |b 7f h i| + g |b c h i|

= -7e b |7f h i| + g |b c h i| - h |b c 7f i| + i |b c 7f h|

= -7e bi + gh - bhf + chi

|a c 7d + 7e c 7f + g h i| = a |c 7f h i| - 7e |c 7d h i| + g |c 7d 7f i|

= 7e ac - gci + chd - ahf

|a b 7d + 7e 7f + g h i| = a |b 7f h i| - 7e |b 7d h i| + g |b 7d 7f i|

= -7e ab + ghi - bgd + aef

Substituting these expressions back into the expanded determinant and simplifying, we get:

| a b c 7d + a 7e + b 7f + c g h i|

= a(-7e bi + gh - bhf + chi) + b(7e ac - gci + chd - ahf) + c(-7e ab + ghi - bgd + aef)

= -7abe - 7bdf - 7cfg + 7aef + bch + cgi + ahk - ceh - afg - bdi

= -7(abe + bdf + cfg - aef) + (bch + cgi + ahk - ceh - afg - bdi)

Since |a b c d e f g h i| = 5, we have:

abe + bdf + cfg - aef = 5

Therefore, we can simplify the expression further:

| a b c 7d + a 7e + b 7f + c g h i|

= -7(5) + (bch + cgi + ahk - ceh - afg - bdi)

= -35 + b(ch - di) + c(gi - eh) + a(hk - fg)

Hence, the value of | a b c 7d + a 7e + b 7f + c g h i| is given by -35 + b(ch - di) + c(gi - eh) + a(hk - fg).

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The simplified expression for | a b c 7d + a 7e + b 7f + c g h i| is 7| a b c d g h i| + 7| a b c e g h i| - 35.

First, factor out the 7 from the second row:

| a b c 7(d + e + f) g h i| = 7| a b c d + e + f g h i|

Expand the second row using the property of determinants that allows us to break up a row sum:

7(| a b c d g h i| + | a b c e g h i| + | a b c f g h i|)

Now, use the property of determinants that allows us to switch rows and multiply by -1:

7(| a b c d g h i| + | a b c e g h i| - | d e f a b c g h i|)

Recognize that the third determinant is equivalent to the given determinant, but with rows 1 and 3 switched, which

gives us:

7(| a b c d g h i| + | a b c e g h i| - 5)

Finally, multiply 7 by the expression inside the parentheses:

7| a b c d g h i| + 7| a b c e g h i| - 35

So, the simplified expression for | a b c 7d + a 7e + b 7f + c g h i| is 7| a b c d g h i| + 7| a b c e g h i| - 35.

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We need to round up to the nearest integer, the required sample size is 76 households.

To estimate the required sample size, we can use the formula:

[tex]n = (z^2 * s^2) / E^2[/tex]

Where:

z is the z-score corresponding to the confidence level (90% = 1.645)

s is the standard deviation of the population (square root of the variance, so s = sqrt(3.61) = 1.898)

E is the maximum error allowed (0.15 gallons)

Plugging in the values, we get:

[tex]n = (1.645^2 * 1.898^2) / 0.15^2[/tex]

n = 75.57

Since we need to round up to the nearest integer, the required sample size is 76 households.

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Answer:

[tex]x^{2} + y^{2} = 36[/tex]

Step-by-step explanation:

The form of the equation for a circle is [tex](x-h)^{2} + (y-k)^{2} = r^{2}[/tex], where [tex](h, k)[/tex] is the center and [tex]r[/tex] is the radius. Here, (h, k) is (0,0) and r is 6, so the equation would just be [tex]x^{2} + y^{2} = 36[/tex].

Answer:

x² + y² = 36 (top right answer)

Formula for the circle:

(x - h)² + (y - k)² = r²

h = X center point  

k = Y center point

Answer:

The area of the shaded sector is

(π/4)(6^2) = (π/4)(36) = 9π

Answer:

100ft²

Step-by-step explanation:

to find the area of the figure you must do the area of the small rectangle plus the area of the large rectangle

area = length* width

so the area of the small rectangle equals

7ft * 4ft = 28ft²

then the large rectangle

9ft*8ft=72ft²

28ft²+72ft²=100ft²

Answer:

x = 8/3

Step-by-step explanation:

y = mx + b

y = -3x + 16

8 = -3x + 16

Subtract 16 from both sides

-8 = -3x

Divide both sides by -3

8/3 = x

The final expression that gives us the cost of x skirts and y hats in pounds is 24x + 15y.

In this case, our variables are x and y, which represent the number of skirts and hats, respectively. Our constants are 24 and 15, which represent the cost of one skirt and one hat, respectively. And our operations are multiplication and addition.

The cost of x skirts is simply the cost of one skirt (which is 24) multiplied by the number of skirts (which is x). So, the expression for the cost of x skirts would be:

24x

Similarly, the cost of y hats is the cost of one hat (which is 15) multiplied by the number of hats (which is y). So, the expression for the cost of y hats would be:

15y

To find the total cost of x skirts and y hats, we simply add the two expressions together. Thus, the expression for the cost in pounds of x skirts and y hats is:

24x + 15y

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The number of students in class a is 15, the mean score of class c is 5.5, and the mean score of all three classes is 6.5.

In mathematics, the mean or average is a measure of central tendency that represents the typical value or a central value of a set of numbers. It is calculated by adding up all the values in the set and then dividing by the number of values in the set. The mean is commonly used in statistics to summarize a large amount of data into a single value that is more easily understood. It is often used to represent the "average" or "typical" value of a set of data. For example, the mean score of a class on a test can give an idea of how well the class performed overall.

We can use the formula for the mean to set up two equations, one for the mean score of class a and one for the mean score of all three classes:

For class a and b combined:

(6x + 25 × 8)/ (x + 25) = 7.25

Simplifying this equation gives us:

6x + 200 = 7.25(x + 25)

Expanding the brackets and simplifying further gives:

6x + 200 = 7.25x + 181.25

Subtracting 6x and 181.25 from both sides gives:

18.75 = 1.25x

Therefore, x = 15

For all three classes:

(6x + 25 × 8 + 20y) / (x + 25 + 20) = 6.5

Substituting x = 15 into this equation gives:

(6 ×15 + 25 × 8 + 20y) / (15 + 25 + 20) = 6.5

Simplifying and solving for y gives:

(90 + 200 + 20y) / 60 = 6.5

Simplifying further gives:

y = 5.5

Therefore, the number of students in class a is 15, the mean score of class c is 5.5, and the mean score of all three classes is 6.5.

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The time since the rock reached its closure temperature is approximately 579.8 years. When the rock was discovered, it had 4.375 grams of europium-151.

To find the time since the rock reached its closure temperature, we can use the following formula

t = t(1/2) * log(N0/Nt)

where t is the time elapsed, t(1/2) is the half-life, N0 is the initial amount of the isotope, and Nt is the amount of the isotope at the time it was discovered.

Substituting the given values, we get

t = 96.6 * log(5/0.625) ≈ 579.8 years

Therefore, the time since the rock reached its closure temperature is approximately 579.8 years.

To find the amount of europium-151 in the rock when it was discovered, we can use the fact that the total amount of samarium-151 and europium-151 in the rock is constant.

Since the rock originally contained 5 grams of samarium-151, it must have contained 5 - 0.625 = 4.375 grams of europium-151 when it was discovered.

Therefore, the rock had 4.375 grams of europium-151 when it was discovered.

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Answer: B and D.

Step-by-step explanation: We can simplify the expression -3.75+ 2(-4x +6.1) - 3.25x as follows:

-3.75+ 2(-4x +6.1) - 3.25x

= -3.75 - 8x + 12.2 - 3.25x (distributing the 2)

= -11.25x + 8.45 (combining like terms)

Now, let's check each expression to see if it is equivalent to -11.25x + 8.45:

A. 7x-2x +8.2

= 5x + 8.2

Not equivalent to -11.25x + 8.45

B. 8.45-8x-3.25x

= 8.45 - 11.25x

Equivalent to -11.25x + 8.45

C. -1.75-7.25x=6.1

This is not an expression, it is an equation. It is not equivalent to -11.25x + 8.45.

D. -11.25x +12.2 - 3.75

= -11.25x + 8.45

Equivalent to -11.25x + 8.45

Therefore, the expressions that are equivalent to -3.75+ 2(-4x +6.1) - 3.25x are B and D.

We can start by drawing a diagram of the situation:

From shortest to longest is:  C. Marisol, Juan, Lucia, Jamal.

By comparing the lengths of the students' walks, it is possible to determine the correct order of the students based on their walks.

Marisol walks 0.62 miles, while Juan walks one mile. So Juan's walk isn't the most limited.

Lucia walks one mile, which is shorter than Jamal's walk of 0.78 miles but longer than Marisol's walk of 0.62 miles. Therefore, neither the shortest nor longest walk is Lucia's.

Therefore, Jamal and Marisol remain choices. The correct order, from shortest to longest, is as follows because Jamal's walk is longer than Marisol's:

C. Marisol, Juan, Lucia, Jamal.

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The account value after forty (40) years is approximately $2,789,525.

We can use the formula for future value of an annuity to solve this problem:

FV = PMT * ((1 + r)^n - 1) / r

where FV is the future value, PMT is the annual deposit amount, r is the annual interest rate, and n is the number of periods (years in this case).

For the first year, the deposit amount is $3,000, so:

FV1 = 3000 * (1 + 0.0835)^40 = $65,470.22

For the subsequent years, the deposit amount increases by $300, so:

PMT = 3000 + 300 + 300 + ... = 3000 + 300 * 39 = $15,300

Using this value for PMT, we can calculate the future value for the remaining 39 years:

FV2 = 15300 * ((1 + 0.0835)^39 - 1) / 0.0835 = $2,724,054.54

Adding the two future values together, we get the total account value after forty years:

FV = FV1 + FV2 = $2,789,524.76

Therefore, the account value after forty years is approximately $2,789,525.

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Answer: There is an approximate 10.7% probability that it will snow on Sunday, making it the day with the lowest likelihood of snow.

Step-by-step explanation: Snow is highly likely on Friday with an 80% probability. The likelihood of no snowfall occurring on Friday is 20%, which can be calculated by subtracting 0.8 (or 80%) from 1.

There is a high probability of snowfall on Saturday with a 7 in 9 likelihood. In simpler terms, the probability can be reduced to 7 out of 9 or around 0.78. The likelihood of snowfall on Saturday is 78%, therefore the chance of no snow on that day is 22% which is equivalent to 1 minus 0.78.

There is a high likelihood of snow on Sunday with a probability of 75 out of 100 or 14 out of 19. It is possible to reduce this to a likelihood of 0.7514, or about 0.107. The likelihood of Sunday not having snow is equivalent to subtracting 0.107 from 1, resulting in a 0.893 or 89.3% probability.