What does the variable r represent?The population correlation coefficientThe sample correlation coefficientThe coefficient of determinationThe critical value for the correlation coefficient

ANSWER

A. True

EXPLANATION

Let the complex number be z = a+ ib, so its complex conjugate is z* = a - ib, where a and b are real numbers. Let's find the product,

The product is,

Solve the products,

Simplify: note that the second and third terms are opposites, so they cancel out. Remember that i² is equal to -1,

Since a and b were real numbers, then the sum of their squares is also a real number.

Hence, this statement is true.

3x+2y=10 This is the equation of the new line in standard form

Two parallel lines have the same slope,  to compute the slope (m) of the equation 3x+2y=19.  This can be obtained by converting the equation into slope-intercept form (i.e., y=mx+b, where m is the slope):

by subtracting 3x from both sides, and then simplifying:

3x+2y-3x=19-3x

     2y     =-3x+19

Then, let's divide both sides by 2, to obtain slope-intercept form:

      y      = (-3/2)x+(/2)     From this, we know that the slope (m) is -3/2

To determine the equation of the line we're being asked to solve for.  If we know the slope (in this case m=-3/2) along with any given point on the line ((x0,y0); in this case (4,1)), the equation of the line can be determined as y-y0=m(x-x0)

So substituting, the equation of the line is y-1=(-3/2)(x-5)

We now need to put this into standard form, with both x and y terms on the left side of the equation:

First, distribute the 3/2 on the right side:  y-1=(-3/2)x+(3/2)5  or y-1

= (-3/2)x+6

Next, add (3/2)x to both sides, add 1 to both sides, and simplify:

(3/2) x + y = 5

multiply both sides by 2, to eliminate the fraction (3/2): 3x+2y = 10 This is the equation of the new line in standard form

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To find f(-8), we just need to replace x by -8 on the function f(x) as:

At the same way g(-2) is equal to:

Finally, h(2/3) is equal to:

Answers: f(-8) = 23

g(-2) = 16

h(2/3) = 9

-7

Explanation

Step 1

given

subtrac (1/4)z in both sides

Step 2

add 7/8 in both sides

finally, multiply both sides by -8 in order to isolate z

therefore, the answer is

-7

I hope this helps you

we have the following:

where d is distance, t is time and v is velocity, replacing:

therefore, the distance is 13.2 miles

There are 40 animals in the shelter, 18 of that animals are cats.

We need to find the percent of the animals that are cats.

Then, 40 animals represent 100% in the shelter.

We can use the rule of three to find the cat's percent:

Therefore:

40 animals -------------- 100%

18 cats ------------------------ x

x = (18*100)/40

x =45

So, 45 % of the animals are cats.

The ordered pair which can be plotted according to the given data in graph will be (6,21).

Plotting an ordered pair on graph of speed and time represents the motion of a particle accelerating from a speed at time 0 , u , to a speed v at time t .

According to given graph we have already plotted points as follows

(2, 7), (4, 15), (5,17)

Now by analysis of the given graph pattern we can conclude that the ordered pair which can be added to the given graph if (6, 21).

Note : - The Question is completed as below and the coordinate plane is attached too.

Maggie walks at a constant speed. Maggie plots points on the coordinate plane below to show amounts of time it takes her to walk certain distances.

Which of the following ordered pairs could Maggie add to the graph?

A. (1,3)

B. (3,10)

C. (6,21)

D. (3,1)

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Answer:

[tex]8.808 \times 10^{-6}[/tex]

Step-by-step explanation:

Given expression:

[tex](2.6 \times 10^{-6})+(3.2 \times 10^{-2})(1.94 \times 10^{-4})[/tex]

The grouping of numbers by parentheses in a different way does not affect their product.  Also, changing the order or position of the product of two numbers does not change the end result.

[tex]\implies (2.6 \times 10^{-6})+(3.2 \times 1.94 \times 10^{-2} \times 10^{-4})[/tex]

Multiply the numbers 3.2 and 1.94:

[tex]\implies (2.6 \times 10^{-6})+(6.208\times 10^{-2} \times 10^{-4})[/tex]

[tex]\textsf{Apply the exponent rule} \quad a^b \cdot a^c=a^{b+c}:[/tex]

[tex]\implies (2.6 \times 10^{-6})+(6.208\times 10^{-2-4})[/tex]

[tex]\implies (2.6 \times 10^{-6})+(6.208\times 10^{-6})[/tex]

Factor out the common term 10⁻⁶:

[tex]\implies 10^{-6}(2.6+6.208)[/tex]

Add the numbers 2.6 and 6.208:

[tex]\implies 10^{-6}(8.808)[/tex]

[tex]\implies 8.808 \times 10^{-6}[/tex]

Scientific notation is written in the form a × 10ⁿ , where 1 ≤ a < 10 and n is any positive or negative whole number.  Therefore, the final answer is in scientific notation.

Given the rectangular coordinates of point Q:

You need to remember that the form from rectangular oordinates to polar coordinates is:

By definition:

In this case, you can identify that:

Then, you can determine that:

Therefore, the polar coordinates are:

Hence, the answer is: Second option.

The distance between Destinee's house and Anna's house is 15.62 miles

To find the coordinate of the Anna's house, we can use the formula of midpoint on this. This is given as

[tex]midpoint(x,y) = \frac{x_2 + x_1}{2}, \frac{y_2 + y_1}{2}[/tex]

In the question, El Ticonzito's house is at midpoint between Destinee's house and Anna's house.

[tex]midpoint(x,y) = \frac{x_2 + x_1}{2}, \frac{y_2 + y_1}{2}\\-4 = \frac{2 + x_1}{2} = -8 = 2 + x_1\\x_1 = -8 - 2 = -10\\\\-2 = \frac{3 + y_1}{2} \\-4 = 3 + y_1\\-4 - 3 = y_1\\y_1 = -7[/tex]

The coordinate's of Anna's point is (-10, -7).

Let's use this to calculate the distance (d) between the two points.

[tex]d = \sqrt{(y_2 - y_1)^2 + (x_2 - x_1)^2} \\d = \sqrt{(-10-2)^2 + (-7 - 3)^2} \\d = \sqrt{(-12)^2 + (-10)^2} \\d = \sqrt{244}\\ d = 15.62 miles[/tex]

The distance between the two points is 15.62 miles

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ANSWER

EXPLANATION

We want to find the domain and range of the function.

The domain of a function is the set of all input values of the function. Basically, the set of all x values of a function.

The range of a function is the set of all output values of the function. Basicallly, the set of all y values of a function.

To find the domain of the function, we have to look at the smallest and largest values of x.

The smallest value of x is -7.

The largest value of x is 3.

So, the domain is:

To find the range of the function, we have to look at the smallest and largest values of y.

The smallest value of y is -1.

The largest value of y is 9.

So, the range is:

Given:

Radius of the cirle = 11 ft

Angle = 150 degrees

π = 3.14

Let's find the area of the sector of the cicle.

To find the area of the sector, apply the formula:

Where:

π = 3.13

θ = 150 degrees

r = 11

Thus, we have:

Solving further:

Therefore, the sector area of the circle is 158.3 square feet.

ANSWER:

158.3 square feet.

Answer:

64

Step-by-step explanation:

9+7=16

16(4)=64

Applying the quotient rule, the derivative of the given function at x = 3 is of -2/3.

A quotient function is defined as follows:

i(x) = g(x)/f(x)

Applying the quotient rule, the derivative of the function defined above is of:

i'(x) = [g'(x)f(x) - f'(x)g(x)]/f(x)².

Hence, at x = 3, the numeric value of the derivative is given as follows:

i'(3) = [g'(3)f(3) - f'(3)g(3)]/f(3)².

Function f(x) is a linear function with slope of -3/2, hence:

Function g(x) is a linear function with slope of -1/2, hence:

Then the derivative is given as follows:

[tex]g^{\prime}(3) = \frac{-\frac{1}{2} \times \frac{3}{2} - \frac{3}{2} \times \frac{1}{2}}{\left(\frac{3}{2}\right)^2} = -\frac{\frac{6}{4}}{\frac{9}{4}} = -\frac{6}{9} = -\frac{2}{3}[/tex]

Hence the numeric value of the derivative at x = 3 is of -2/3.

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The like terms in the expression are 12n and 6n

Like terms are terms that have the same coefficients and in the same order of degrees.

In the expression:

12n - 6 + p + 6n

The like terms are 12n and 6n

The value of t must be less than -2/3, that is, the correct answer must be a negative number, in this case it would be the letter C) -3

The value of x in the linear equation −0.28x − 15.3 = 1.92 is -61.5 option (B) -61.5 is correct.

It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.

The linear equation one variable is:

−0.28x − 15.3 = 1.92

-0.28x = 1.92 + 15.3

-0.28x = 17.22

x = -17.22/0.28

x = -61.5

Thus, the value of x in the linear equation −0.28x − 15.3 = 1.92 is -61.5 option (B) -61.5 is correct.

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Answer:

its B -61.5

Step-by-step explanation:

i attched pictures to show you

Answer:

Yes, 21.23 is a rational number.

[tex]21.23=\dfrac{2123}{100}[/tex]

Step-by-step explanation:

Terminating decimal numbers are decimals that have a finite number of decimal places.

A Rational Number is the division of an integer by another integer.

Therefore, 21.23 is a terminating decimal since it has a finite number of decimal places.

Let x be the rational number.

[tex]\implies x=21.23[/tex]

Multiply both sides by 100 so that the right side is an integer:

[tex]\implies 100x=2123[/tex]

Divide both sides by 100:

[tex]\implies x=\dfrac{2123}{100}[/tex]

(This fraction cannot be reduced any further).

Therefore, we have proved that 21.23 is a rational number.

Answer:

It is a rational number.

Step-by-step explanation:

Given value,

→ 21.23

Converting into rational number,

→ (21.23/1) × (100/100)

→ (21.23 × 100)/(1 × 100)

→ 2123/100

Hence, it is a rational number.

If two lines of slopes m1 and m2 are perpendicular, then:

The slope of a line passing through points (x1, y1) and (x2, y2) is:

We are given the points of the first line (-4, 7) and (1, 3). Calculate the slope

The slope of the perpendicular line is:

The equation of the perpendicular line has the form:

None of the options has the correct answer.

Let be "x" Jon's current salary.

According to the information given in the exercise, the salary at the new job is 68,000 and this is 12% more than his salary at his current job.

To convert from percent to a Decimal number, you can divide by 100. Then:

Therefore, knowing that information, you can set up the following equation:

Now you can solve for "x" in order to find its value:

The answer is:

Problem #1

budget rent a car rented a basic car at a daily rate of $45.95 plus 40 cents per mile. Another company rents a basic car for $46.95 plus 20 cents per mile. For what mileage is the cost the same.

Define the variables

Let

x -----> number of miles

y -----> the total cost

we have

budget rent a car

y=40x+45.95 ------> equation 1

Another company

y=20x+46.95 -------> equation 2

Solve the system of equations

equate equation 1 and equation 2

40x+45.95=20x+46.95

solve for x

40x-20x=46.95-45.95

20x=1

x=0.05 miles

therefore

Let l and w be the length and width of the rectangle, respectively.

Therefore, according to the question,

Therefore, solving for l and w,

given data:

The cost of house is $176000.

The percentage the house realtor requires is 5%.

That is,

Thus 5% of 176000 is 8800.

Thus, you need to give $8800 to the local realtor.

The sum of complemenatry angles = 90

The sum of supplementary angles = 180

SOLUTION:

Step 1:

In this question Number 15, we are given the following:

1. The lower limit of this confidence interval is $587.13.

2. The upper limit of this confidence interval is $841.25.

The lower limit describes the lowest price that entry-level road bikes will cost.

The upper limit refers to the highest price that entry-level road bikes can command.

Using the lower and upper limits, Randy can confidently estimate the range of the asking price of the used entry-level road bikes.

N = 14

Mean price, µ = $714.19

Sample deviation = $184.56

Confidence interval = 99%

The z-score of 99% confidence interval = 2.576

The margin of error = z-score x (standard deviation/√n)

= 2.576 x ($184.56/√14)

= $127.06

Lower Limit =  µ - margin of error

= $714.19 - $127.06

= $587.13

Upper Limit = µ + margin of error

= $714.19 + $127.06

= $841.25

Thus, Randy can estimate that the price of used entry-level road bikes is $714.19 ±$127.06 at a 99% confidence level.

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Answer:

This is impossible.

Step-by-step explanation:

You didn't give us how much 1 yard is.

Answer: How much is one yard?

Step-by-step explanation:

Answer:  Choice A

x^2-12x+36; is a polynomial

===================================================

Explanation:

Use the rule that (A-B)^2 = A^2 - 2AB + B^2 to show (x-6)^2 = x^2-12x+36 is an identity. In this case, A = x and B = 6

You could also use the FOIL rule or the distributive property as two alternatives.

The result is a polynomial because it consists of summing or subtracting various monomials. If we had terms that had say exponents of decimal numbers or negative values, then we wouldn't have a polynomial.

Answer:

x = [tex]\frac{23}{8}[/tex] or 2 [tex]\frac{7}{8}[/tex]

Step-by-step explanation:

1. Add the numbers

10 + 2 = 12

5x+12+11x = 58

2. Combine like terms

5x + 11x = 16x

16x+12 = 58

3. Subtract 12 from both sides

16x + 12-12 = 58-12

x = [tex]\frac{23}{8}[/tex]