Convert 36 inches to feet. There are 12 inches in a foot.
A. 432 feet
B. 3 feet
C. 6 feet
D. 360 feet

Problem 1

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Explanation:

Let's plug 8 into f(x)

\(f(x) = \frac{x+3}{x^2-4x-21}\\\\f(8) = \frac{8+3}{8^2-4(8)-21}\\\\f(8) = \frac{8+3}{64-32-21}\\\\f(8) = \frac{11}{11}\\\\f(8) = 1\\\\\)

Repeat for g(x)

\(g(x) = \log_{4}(x)\\\\g(8) = \log_{4}(8)\\\\g(8) = \frac{\log(8)}{\log(4)}\\\\g(8) = \frac{\log(2^3)}{\log(2^2)}\\\\g(8) = \frac{3*\log(2)}{2*\log(2)}\\\\g(8) = \frac{3}{2}\\\\\)

I used the change of base formula in the third step.

Lastly, we subtract the results like so

\((g-f)(x) = g(x) - f(x)\\\\(g-f)(8) = g(8) - f(8)\\\\(g-f)(8) = \frac{3}{2} - 1\\\\(g-f)(8) = \frac{3}{2} - \frac{2}{2}\\\\(g-f)(8) = \frac{3-2}{2}\\\\(g-f)(8) = \frac{1}{2}\\\\\)

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Problem 2

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Explanation:

Through trial and error (I recommend the rational root theorem), you should find that the roots of R(x) are:  -1, 3, and 8

We'll only focus on positive x values. So we focus on the roots 3 and 8.

It turns out that the R(x) curve dips below the x axis when x is between 3 and 8. When x > 8 is when R(x) is positive and goes upward forever. This represents when the company is making money.

The company does make money when x is between 0 and 3; however, this is a short timespan compared to the other interval. So it's much more effective and realistic to say that the company makes money after 8 days.

In other words, yes the company makes money between day 0 and day 3, but from day 3 to day 8 is when the company loses money. Ultimately the company is profitable again when it's beyond day 8.

The equation 2 (p+ 7) = 4 - 8p has only one solution that is; -9.

We know that solution of an equation refers usually to the values of the variables involved in that equation that if substituted in place of that variable would give a true mathematical statement.

We need to determine the solutions does the equation 2 (p+ 7) = 4 - 8p have;

Now solving for p,

2 (p+ 7) = 4 - 8

Open the bracket,

2p+ 14 = 4 - 8

Combine the like terms,

2p = -4 - 14

2p = -18

p = -18/2 = -9

Therefore, the equation has only one solution which is -9.

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New price = 90 dollars

25% of 120 = 30

Price is reduced 25% from 120 so,

120 - 30 = 90

Amount of discount = 30

Answer:

26.25 gallons

Step-by-step explanation:

\(\frac{30 gallons}{800 miles} = \frac{x}{700 miles}\)

21000 = 800x

x = 26.25 gallons

Apologies, but your questions seem to have errors and incomplete information.

For the first question about Jessica and Melissa sharing 12 pieces of dried pears, it is unclear how much Jessica ate as the fraction is missing. Similarly, information about how many pears Melissa ate is also missing. To answer the question accurately, I need the missing information.

For the second question about the children playing in the park, you mentioned that one-third of the children returned home, but you didn't provide the total number of children initially in the park. Without that information, I cannot determine how many children stayed in the park.

Please provide complete and accurate information for a precise answer.

Answer:

Your answer is x=0

The multiplicative rate of change for the function  is approximately.

To find the multiplicative rate of change for the exponential function f(x) = , we need to calculate the derivative of the function. However, it's important to note that the function you provided is not an exponential function. An exponential function has a base raised to a variable exponent.

The given functioncan be rewritten as. Now, we can proceed to find the multiplicative rate of change by taking the derivative of f(x) with respect to x.

Using the chain rule, the derivative of is:

Here, ln(2/5) is a constant representing the natural logarithm of 2/5. The multiplicative rate of change is given by the derivative, which is

The value of ln(2/5) is approximately -0.916.

It's important to note that the multiplicative rate of change is not constant for this function. It depends on the value of x and decreases exponentially as x increases.

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Answer:

\(x = 1-10t\\y = -6+16t\\z = 7-12t\)

Step-by-step explanation:

We are given the coordinates of points P(1,-6,7) and Q(-9,10,-5).

The values in the form of (\(x,y,z\)) are:

\(x_1=1\\x_2=-9\\y_1=-6\\,y_2=10\\z_1=7\\z_2=-5\)

\($\vec{PQ}$\) can be written as the difference of values of x, y and z axis of the two points i.e. change in axis.

\(\vec{PQ}=<x_2-x_1,y_2-y_1,z_2-z_1>\)

\(\vec{PQ} = <(-9-1), 10-(-6),(-5-7)>\\\Rightarrow \vec{PQ} = <-10, 16,-12>\)

The equation of line in vector form can be written as:

\(\vec{r} (t) = <1,-6,7> + t<-10,16,-12>\)

The standard parametric equation can be written as:

\(x = 1-10t\\y = -6+16t\\z = 7-12t\)

The transformations which is NOT preserve the size and the shape of the figure is dilate by a scale factor of 4 (B) and dilate by a scale factor of 1 (C).

Dilation of a figure, means the transformation of the figure. The factor by which the given figure dilated, called the scale factor of dilation.

When a figure is dilated, the size of the original figure is changed.

A figure is graphed in the coordinate plane. Let's check all the option for the transformation of original figure.

Hence, the transformations which is NOT preserve the size and the shape of the figure is dilate by a scale factor of 4 (B) and dilate by a scale factor of 1 (C).

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Answer:

ans is 58°

Step-by-step explanation:

it is a straight line so the angle is 180°

so the angle of CED is

CED + 122° = 180°

CED = 180 - 122 = 58°

No, the rank of the product of two n by n square matrices A and B, denoted as AB, cannot be less than n-1 if both A and B have ranks of n-1.

According to the Rank-Nullity theorem, for any matrix M, the sum of its rank and nullity is equal to the number of columns in M. In this case, the number of columns in AB is n, so the sum of the rank and nullity of AB must be n.

If rank(A) = rank(B) = n-1, it means that both A and B have nullity 1. The nullity of a matrix is the dimension of its null space, which consists of all vectors that get mapped to the zero vector when multiplied by the matrix. Since both A and B have rank n-1, their null spaces consist only of the zero vector.

Now, considering AB, if the rank of AB were less than n-1, it would mean that the nullity of AB is greater than 1.

However, this would violate the Rank-Nullity theorem since the sum of the rank and nullity of AB must be n, which is the number of columns.

Therefore,  if rank(A) = rank(B) = n-1, the rank of AB cannot be less than n-1.

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The given equation above written in the form AX = b will be;

\(\left[\begin{array}{ccc}1&2\\2&3\\\end{array}\right] \left[\begin{array}{ccc}x\\y\\\end{array}\right] =\left[\begin{array}{ccc}11\\18\\\end{array}\right]\)

Given the system of equation;

This equation can be represented in matrix form as \(AX = b\)

where:

The given equation above written in the form AX = b will be;

\(\left[\begin{array}{ccc}1&2\\2&3\\\end{array}\right] \left[\begin{array}{ccc}x\\y\\\end{array}\right] =\left[\begin{array}{ccc}11\\18\\\end{array}\right]\)

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The solution is: Piece-wise function

f(x)=x+6 , x≤1

f(x) = x^2 + 3 , x>1, the following functions is graphed below.

Option C is correct.

Explanation:

We are given a graph of piece-wise function which break at x=1

We need to choose correct option for graph.

Function is break at x=1.

We will get two function

For x≤1 and x>1

As we can see x≤1, graph is linear and x>1 graph is parabolic.

Equation of linear graph, x≤1

Take two point of graph (0,6) and (-6,0)

Equation of line:

y-y1/y2-y1 = x-x1/x2-x1

y = x+1

f(x)=x+6 , x≤1

Equation of parabolic graph, x>1

f(x) = x^2 + 3

Piece-wise function

f(x)=x+6 , x≤1

f(x) = x^2 + 3 , x>1

Please see the attached figure.

Hence, The option C is correct.

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\(\sf \longmapsto \frac{5}{8} \div6\)

\(\sf \longmapsto \frac{5}{8} \times \frac{1}{6} \)

\(\sf \longmapsto \frac{5 \times 1}{8 \times 6} \)

\(\sf \longmapsto \frac{5}{48} \)

Answer In DECIMAL:

\(\sf \longmapsto0.1041\)

Answer:

The binomial probability distribution is shown below.

Step-by-step explanation:

The probability mass function of X is:

\(P(X=x)={n\choose x}p^{x}(1-p)^{n-x};x=0,1,2,3..\)

It is provided that n = 6 and p = 0.25.

Construct a binomial probability distribution with the given parameters as follows:

X                                       P (X = x)

0        \(P(X=0)={6\choose 0}(0.25)^{0}(1-0.25)^{6-0}= 0.1780\)

1         \(P(X=1)={6\choose 1}(0.25)^{1}(1-0.25)^{6-1}= 0.3560\)

2        \(P(X=2)={6\choose 2}(0.25)^{2}(1-0.25)^{6-2}= 0.2966\)

3        \(P(X=3)={6\choose 3}(0.25)^{3}(1-0.25)^{6-3}= 0.1318\)

4       \(P(X=4)={6\choose 4}(0.25)^{4}(1-0.25)^{6-4}= 0.0330\)

5       \(P(X=5)={6\choose 5}(0.25)^{5}(1-0.25)^{6-5}= 0.0044\)

6       \(P(X=6)={6\choose 6}(0.25)^{6}(1-0.25)^{6-6}= 0.0002\)

Compute the mean and standard deviation as follows:

\(\mu=np=6\times0.25=1.50\\\\\sigma=\sqrt{np(1-p)}=\sqrt{6\times 0.25\times (1-0.25)}=1.0607\)

Binomial probability distribution was constructed, and the mean and standard deviation comes to be 1.5 and 1.061 respectively.

As we know that binomial probability distribution is given by

\(P(x) = ^nC_xp^x(1-p)^{n-x}\)

The binomial distribution is a probability distribution that depicts the likelihood that a value will take one of two independent values under a given set of parameters.

Given n=6 & p=0.25

\(P(0) = ^6C_0(0.25)^0(1-0.25)^{6-0}\) = 0.1780

\(P(1) = ^6C_1(0.25)^1(1-0.25)^{6-1}\)=0.3560

\(P(2) = ^6C_2(0.25)^2(1-0.25)^{6-2}\) = 0.2966

\(P(0) = ^6C_3(0.25)^3(1-0.25)^{6-3}\) =0.1318

\(P(0) = ^6C_4(0.25)^4(1-0.25)^{6-4}\)=0.0330

\(P(5) = ^6C_5(0.25)^5(1-0.25)^{6-5}\)=0.0044

\(P(6) = ^6C_6(0.25)^6(1-0.25)^{6-6}\)= 0.0002

Mean = np

Mean = 6*0.25

Mean = 1.5

Standard deviation σ = \(\sqrt{np(1-p)}\)

σ = \(\sqrt{6*0.25(1-0.25)}\)

σ = 1.061

Hence, binomial probability distribution was constructed, and the mean and standard deviation comes to be 1.5 and 1.061 respectively.

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Answer:

B: r =n/2

Step-by-step explanation:

Recondition only mean is that half of what the new is so recondition equals the new over half because recondition is half the price of the new

Answer:

W and X

Y and Z arent functions because some of their domains (x value) have different inputs. Each domain can only have one input.

The required rate of simple interest is 1.75%.

Here, we have,

(Principal + Interest) is a straightforward interest equation.

A = P(1 + rt)

Where: A is the sum of the accrued principal and interest.

Principal Amount is P.

I is the interest rate.

r is the annual percentage rate of interest, or R/100.

R is the annual percentage rate of interest; R = r * 100 t is the length of time involved in months or years.

Since I = Prt,

the initial formula A = P(1 + rt) evolved from A = P + I to A = P + Prt,

which may be represented as A = P(1 + rt).

Given: Principal is $1,300

Rate is 7% and the amount earned that is A-P is $159.25.

A = P(1 + rt)

Therefore substituting the values in the above mentioned equation, we get:

159.25= 1300(1+r×7)

On solving we get,

r= 1.75%

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complete question:

At the Blue Bank, Barry would earn $159.25 in simple interest in 7 years after depositing $1,300.

What rate of simple interest is offered at the

Blue Bank?

the value of the test statistic for testing whether there is a linear relationship between the and the estimated number is 0.3506905

Using a correlation Coefficient calculator, the correlation Coefficient, r for the data = 0.127

The test statistic :

T = r² / √(1 - r²) / (n - 2)

Sample size, n = 10

Hence,

T = 0.127² / √(1 - 0.127²) / (10 - 2)

T = (0.016129 / 0.3506905)

T = 0.3506905

The value of the test statistic to 2 decimal places is 0.35

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The median number of hours slept by boys the previous night is 6.5 hours, while the median number of hours slept by girls the previous night is 7 hours.

The given line plots display the results of a survey of 10 boys and 10 girls regarding the number of hours they slept the previous night. To find the median, follow these steps:Put the observations in ascending order.Divide the data into two equal parts.

To locate the median of the data, find the value that is at the center of the data when ordered.To calculate the medians of the given line plots, we must first arrange the observations in ascending order and divide them into two equal parts.

We have 10 boys and 10 girls in total, so we will have 20 observations for each line plot: Boys’ line plot: 4, 5, 6, 6, 6, 7, 7, 8, 9, 10Girls’ line plot: 5, 5, 6, 7, 7, 7, 7, 8, 8, 10When arranged in ascending order,

the observations are as follows: Boys’ line plot: 4, 5, 6, 6, 6, 7, 7, 8, 9, 10Girls’ line plot: 5, 5, 6, 7, 7, 7, 7, 8, 8, 10 Now,

we must determine the medians for each data set. Since each data set has an even number of observations, the median is the average of the two middle values.

The medians for each data set are as follows: Boys’ line plot: (6 + 7) / 2 = 6.5Girls’ line plot: (7 + 7) / 2 = 7

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Answer:

x = 3

\(x=-1\frac{1}{3}\) or \(x=-\frac{4}{3}\)

Step-by-step explanation:

3x² - 5x - 12 = 0

Method 1: Factoring

3x² + 4x - 9x - 12 = 0

(3x² + 4x) + (- 9x - 12) = 0

x(3x + 4) - 3(3x + 4) = 0

(x - 3)(3x + 4) = 0

Two separate equations

x - 3 = 0

3x + 4 = 0

x - 3 = 0

x - 3 + 3 = 0 + 3

3x + 4 = 0

3x + 4 - 4 = 0 - 4

3x = - 4

\(\frac{3x}{3} :-\frac{4}{3}\)

\(x=-1\frac{1}{3}\)

Method 2: Quadratic Formula

Ignore the A before the ±, it wouldn't let me type it correctly.

\(x=\frac{-b±\sqrt{b^{2} -4ac} }{2a}\)

3x² - 5x - 12 = 0

a = 3

b = - 5

c = - 12

\(x=\frac{-(-5)±\sqrt{(-5)^{2} -4((3)(-12))} }{2(3)}\)

\(x=\frac{-(-5)±\sqrt{25 -4((3)(-12))} }{2(3)}\)

\(x=\frac{-(-5)±\sqrt{25 +144} }{2(3)}\)

\(x=\frac{-(-5)±\sqrt{169} }{2(3)}\)

\(x=\frac{-(-5)±13}{2(3)}\)

\(x=\frac{5±13}{6}\)

Two separate equations

One must have a + (positive) and the other will have a - (negative).

\(x=\frac{5+13}{6}\)

\(x=\frac{18}{6}\)

x = 18 ÷ 6

x = 3

\(x=\frac{5-13}{6}\)

\(x=\frac{-8}{6}\)

x = - 8 ÷ 6

\(x=-1\frac{1}{3}\)

Answer:

D

Step-by-step explanation:

sin  (  3pi / 4 )

 =  sin   (   pi   -   pi  /  4   )

 =  sin   (   pi / 4  )

 = 1/root(2)

  =  root(2) / 2

A. The consumers interviewed in this manner can be considered a random sample of the population as a whole.

B. The sample is a random sample of people who go to malls.

C. It should be noted that the sample applies for just for people who go to that mall.

It should be noted that in a random sample, everyone has an equal chance of being selected.

In this case, the consumers interviewed in this manner can be considered a random sample of the population as a whole. Here, everyone had an equal chance of being picked.

In this case, the sample is a random sample of people who go to malls.

It should be noted that 95% of American households shop at malls at least once a year and that two-thirds shop at malls at least once every 2 weeks. This will give the random sample of the people.

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Answer:

The annual percentage rate of change for the population of Oregon is of 8.125%.

Step-by-step explanation:

Total percentage change:

Change multiplied by 100 and divided by the initial value.

Change: 8.7 - 4.8 = 3.9 million

Initial value: 4.8

Percentage change: 3.9*100/4.8 = 81.25%

Annual percentage rate of change

81.25% during 10 years(from 2000 to 2010).

So, per year

81.25%/10 = 8.125%

The annual percentage rate of change for the population of Oregon is of 8.125%.

Using an online finance calculator, the yield to maturity (YTM) of the Ashburn Company's bond at a coupon rate of 8.9 percent paying semiannual interest and selling at 113% of par value is 7.45%.

The Yield to maturity (YTM) is the total return, expressed as an annual rate, anticipated by a bondholder on a bond if it is held until its maturity date.

The maturity date refers to the date when the principal of a fixed investment is repaid at the maturity value.

The yield to maturity can also be computed using the following formula:

YTM = [(Face value/Bond price)1/Time period]-1.

Face (par) value = $100

Bond current price = $113 ($100 x 113%)

Annual coupon rate = 8.9%

Coupon frequency = Semi-annually

Years to maturity = 15 years

Result:

Yield to maturity (YTM) = 7.45%

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Answer:

16/24

Step-by-step explanation:

9/12–> simplify to 3/4

3/4=15/20

24/32=3/4

6/8=3/4

16/24 is not equal

Answer:

16/24 isn't equivalent to 9/12

Step-by-step explanation:

9/12 = 0.75

Let's see what all the fractions equal to first.

15/20 = 0.75

24/32 = 0.75

6/8 = 0.75

16/24 = 0.667

As you can see, the fraction 16/24 doesn't equal 0.75.

The ordered pairs in which each of the least corrupt countries corresponds to a corruption rating will be {(A,9.7),(B,9.6),(C,9.6),(D,9.1)}.

It should be noted that an ordered pair is the pair of two numbers or variables that are written inside brackets and are separated by a comma.

An example, (1, 2) is an ordered pair. It should be noted it can represent a point. In this case, the pair should be in the form of:

(Country, corruption rating)

(A, 9.7)

(B, 9.6)

(C, 9.6)

(D, 9.1)

Therefore, this will be {(A,9.7),(B,9.6),(C,9.6),(D,9.1)}.

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Answer:

x = -5

Step-by-step explanation:

2x = -10

x = -10/2

x = -5

The value of x is 64 for the given logarithmic expression.

What is logarithm?

In arithmetic, the exponent is that the mathematical function to mathematical operation. meaning the exponent of variety x to the bottom b is that the exponent to that b should be raised, to supply x.

Main body:

You must first put in the same base. This can be started out by using the log rule

logₐ n=logn/loga

Explanation:

logx/log2−logx/log8=4

Now, rewrite the terms in the denominator by using the rule

logaⁿ=nloga

logx/1log2−logx/log2³=4

logx1/log2 − logx/3log2=4

Place on an equal denominator.

3 logx/3 log2 − logx/3log2=4

log₈(x³)−log₈(x)=4

Now, you must use the rule

logₐ n−logₐ m=logₐ (nm).

log₈(x³/x)=4

Convert to exponential form:

x²=8⁴

x²=4096

x=64

Hence the value of x is 64.

the correct statement for question is log₂x−log₈x=4

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