Mrs. Nolan hired a painter to paint the exterior of her house. It took the painter 3 days to paint her house. The painter agreed to a rate of $23 per hour with a 12-hour unpaid lunch break each day. The table shows when the painter clocked in and out each day.Before taxes, how much money did the painter make

(x-2)

1) Let's use the Rational Roots Theorem so that we can factor this Polynomial and find the factors that make up this Polynomial.

2) Taking all the factors of the constant and the leading coefficients we have:

Let's enlist these factors:

2.2) Let's pick any number on the numerator and divide it by any number of the denominator, to get possible roots:

Proceeding with that let's do a Synthetic Division, testing 2

Note that we have three factors. After factoring out

3) Hence, the answer is (x-2)

Given the figure of a cyclic quadrilateral

We will check whether the given statements are true or false.

A) Angle CDE measures 80 degrees.

True

Because the sum of the opposite angles has a sum of 180

B) Angle CDE measures 100 degrees

False

C) The sum of the measures of the arcs from E to C, one passing through D and passing through b is 360

True

Because the sum of the central angles of the circle = 360

The two arcs are forming the complete circle.

D)The arcs from E to C passing through D measure 100 degrees

False

Because the measure of the arc = 2 times the angle CBE = 200

E) Angle BCD measures 50 degrees

False

Because the measure of the angle BCD = 180 - 50 = 130

The sum of the opposite angles = 180

F) The arc from B to D passing through C measures 100

True

Because the inscribed angle opposite the arc = 50

So, the measure of the arc = 2 times the opposite inscribed angle

Weare asked to use the "point-slope" form of a line that has slope -5 and goes though the point (1, -7) on the plane.

Therefore we use the form:

y - yp = m (x - xp)

where "m" is the slope, and xp and yp are the coordinates of the point on the plane the line goes through. So in our case we have:

y - (-7) = -5 (x - 1)

now we proceed to remove parenthesis using distributive property:

y + 7 = -5 x + 5

and finally express the equation in slope-intercept form by isolating "y" on the left:

Subtract 7 from both sides and combine:

y = -5 x + 5 - 7

y = -5 x - 2

The difference of a number (y) and 9 is written as

Then, twice the difference of a number and 9 is

Finally, set the later expression to be equal to 6,

The equation is 2(y-9)=6

Using the pythagoras theorem,

areAs given by the question

There are given that the profit function

Now,

The zeros are the x values where the graph intersects the x axis.

Then,

To find the zeroes, replace P(x) with 0 and solve for x.

Then,

The zeroes of the given function is:

Hence, the zeroes of the function is 0, 12, 5.

We know that the equation of the line that pass through the pair of points (3, 3) and (-5, -5) is x = y, so the slope of a paralell line is 1 and a perpendicular line is -1.

So the answe is C. 1, -1.

We are given that a bag contains 1 gold marble, 6 silver marbles, and 21 black marbles. First, we need to determine the total number of marbles. The number of marbles of each color is:

The total number is then:

Substituting the values:

Therefore, there are a total of 28 marbles. Now we determine the probability of getting each of the marbles by determining the quotient of the number of marbles of a given color over the total number of marbles. For the gold marbles we have:

For silver we have:

For the black marbles:

Now, to determine the expected value we need to multiply each probability by the value that is gained for each of the colors. We need to have into account that is it is a gain we use a positive sign and if it is a lose we use a negative sign:

Solving the operations we get:

Therefore, the expected value is -$0.21.

the distance the ship travelled from point A to D is 582 ft

To dtermine the distance from point A to D, we need to find the distance from point A to C and distance from point C to D

To get the distance from point C to D, we will consider triangle BCD:

opposite = 125 ft

DC = ?

angle = 16°

To get DC (adjacent), we will use tan ratio:

To get the distance from point A to C, we will consider triangle ABC:

opposite = 125 ft

AC = ?

angle = 7°

To get AC (adjacent), we will use tan ratio:

Distance AC = Distance DC + Distance AD

The distance the ship travelled from point A to D = Distance AD

To the nearest foot, the distance the ship travelled from point A to D is 582 ft

A standard deck of cards consists of 52 cards with 4 aces.

The probability of getting an ace in a pack of the standard deck is;

Using the slope intercept equation, the equation of the line in fully simplified slope intercepted form is y=4x−4.

In the given question we have to write the equation of the line in fully simplified slope intercepted form.

As we know that slope intercept form of equation of line is given by

y=mx+c

where m=slope

c=intercept of the line (i.e point where line cut y-axis )

From graph we can easily find two point of the line that is (1,0)(0,−4).

From the point x(1)=1, y(1)=0, x(2)=0, y(2)=−4

Slope (m)=(y(2)−y(1))/(x(2)−x(1))

m=(−4−0)/(0−1)

m=-4/−1

m=4

As we know that c is a point where line cut y axis so c=−4

Hence, slope-intercept form of equation is y=4x−4.

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The definition of the inverse function is

In our case,

Then,

We need to verify this result using the other equality as shown below

Therefore,

The inverse function is f^-1(x)=(x+1)/2.

We say that a relation is a function if, for x in the domain of f, there is only one value of f(x).

In our case, notice that for any value of x, there is only one value of (x+1)/2=x/2+1/2.

The function is indeed a function, it is a straight line on the plane that is not parallel to the y-axis.

The inverse f^-1(x) is indeed a function

In order to solve by subdtitution, first, solve the second equation for x:

x - 2y = 4 add 2y both sides

x = 4 + 2y

next, replace the previous expression for x into the first equation and solve for y:

4x + 2y = -14 replace x=4+2y

4(4 + 2y) + 2y = -14 apply distribution property

16 + 8y + 2y = -14 subtract 16 both sides

8y + 2y = -14 - 16 simplify like terms both sides

10y = -30 divide by 10 both sides

y = -30/10

y = -3

next, replace y=-3 into x = 4 + 2y

x = 4 + 2y = 4 + 2(-3) = 4 -6 = -2

x = -2

Hence, the solution to the given system of equations is:

x = -2

y = -3

From the given question

There are given that the equation:

Now,

For finding the value of a, first, add b in both sides of the equation

So,

Then,

Divide by m on both sides the above equation

Hence, the value of a is z + b.

SOLUTION:

Case: Matrices multiplication

Given:

Two matrices can always be multiplied if they have the same dimensions.

Method:

From the image above, if and only if the number of items of columns matches the number of items of the columns, then it is possible to multiply.

Final answer:

True,

Two matrices can always be multiplied if they have the same dimensions

Given:

Sample Size (n) = 425

No. of Success = 121

Find: estimate the proportion of the population

Solution:

Let's calculate first the success proportion in the sample by dividing no. of success over the total number of people then multiply it by 100.

Our sample proportion p = 28.47%.

Then, for the margin of error, the formula is:

where z = critical value, p = sample proportion, and n = sample size.

For our z-value, since we are using a 95% confidence interval, the value of z = 1.645.

Then, solve.

Let's multiply the MOE by 100%.

Therefore, about 28.47% ± 3.6% or between 24.87% to 32.07% of the population would be able to successfully reproduce the rhythm.

ANSWER:

STEP-BY-STEP EXPLANATION:

1.

In this case it means that you actually have $10 or less, so an inequality that represents the situation would be:

2.

In this case it means that you actually have $10 or more, therefore, an inequality that represents the situation would be:

Two perpendicular lines have reciprocal and opposite slopes.

First we have to write the given line in the slope-intercept form:

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

We have this equation:

To write it in the slope-intercept form we have to clear y:

The slope is 1/4 and the y-intercept is -5.

The slope of the perpendicular line will be the opposite and reciprocal of 1/4, that's -4.

For now we have the perpendicular line's equation:

There are a lot of lines that are perpendicular to the given line, but only one that passes through (2, -5). We use this point to find the y-intercept by replacing x = 2 and y = -5 into the expression above and solving for b:

The y-intercept of the perpendicular line is 3.

The equation of a line perpendicular to the given line that passes through the point (2,-5) is

The area of a square is the squared side, it means

It means, for A, which has a side of 5, the area is

For B, which side is 12, its area is

For C, the area is

Andre has to paint (solve each power):

Once we add the areas of A and B we realize that the sum is equal to the area of C, it proves the pythagorean theorem that says that the sum of the squared length of the legs equals the squared length of the hypotenuse

As we see in the figure, BD bisects the right angle ABC and thus, we find out that ∠ABD = 60° and ∠CBD = 30°. Thus, option 1 is correct.

From the given figure, we have

∠ABD = 4x° ---- (1)

∠CBD = 2x° ---- (2)

∠ABC = 90° ---- (3)

We have to find out the values of the ∠ABD and ∠CBD.

As given in the figure, we can see that BD bisects ∠ABC into ∠ABD and ∠CBD. So, we can say that -

∠ABD + ∠CBD = ∠ABC

=> 4x° + 2x° = 90° [From equation (1), (2), (3)]

=> 6x° = 90°

=> x° = 15° ---- (4)

Substituting equation (4) in equations (1) and (2), we get

∠ABD = 4x° and ∠CBD = 2x°

=> ∠ABD = 4*15° and ∠CBD = 2*15°

=> ∠ABD = 60° and ∠CBD = 30°

Since BD bisects the right angle ABC, we find out that ∠ABD = 60° and ∠CBD = 30°. Thus, option 1 is correct.

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We have the expression:

We can apply logarithm to both sides. We would use it in order to get "4d+1". Then, we would apply logarithm with base c. This is beacuse of the definition of logarithm:

If we apply this to our expression, we get:

If we rearrange both sides, we get the expression in Option B (we have to switch the sides):

Answer: Option B

Answer to part A :

The school that gets the award for the highly consistent attendance among its students is school B . Because its range is the smallest that is there exists a smaller variation in the highest and the lowest value and also because the interquartile range is the smallest means that the data is spread out the least.

Answer to part B :

The school that gets the award for the highest average attendance among its students is High school A . This is because its mean and median are the highest which means that there are more kids attended school on average.

Answer:

Step-by-step explanation:

10(7p + 6) – 5(5p + 4)=70p+60-25p-20=45p+40=5(9p+8)

Answer

Use the distributive property to remove the parenthesis

Now , Given

The final answer

Given the numbers : 7 1/2 and 1 1/8

We will divide them

so,

The probability that among these 11 people, the number passing the test is between 2 and 4 inclusive is 0.0665

What is Probability?

Probability gives us the information about how likely an event is going to occur

Probability is calculated by Number of favourable outcomes divided by the total number of outcomes.

Probability of any event is greater than or equal to zero and less than or equal to 1.

Probability of sure event is 1 and probability of unsure event is 0.

Now

Binomial distribution of probability will be used

Here, n = 11, p = 0.63,

P(X = x) = [tex]{n\choose x} p^x(1-p)^{n-x}[/tex]

P(X= 2) = [tex]{11\choose 2} 0.63^2(1-0.63)^{11-2}[/tex]

            = 0.0028

P(X = 3) = [tex]{11\choose 3} 0.63^3(1-0.63)^{11 - 3}\\[/tex]

             = 0.0144

P(X = 4) = [tex]{11\choose 4} 0.63^4(1-0.63)^{11 - 4}\\\\[/tex]

             = 0.0493

The probability that among these 11 people, the number passing the test is between 2 and 4 inclusive =  0.0028 + 0.0144 + 0.0493

                                                = 0.0665

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The equation of consideration is:

Since two unknowns ( x and y) are given in just one equation, to get each set of the solutions, we are going to choose a value of x and get a corresponding value of y

Let x = 0, to get the value of y at point x = 0, substitute this value of x into the given equation:

The first set of solutions is therefore:

To get the second set of solution, let us choose x = 3 and substitute this value into the given equation:

The second set of equation is:

The above is the graph showing the two sets of solutions

Given

Quadratic equation

Find

Explain best method to solve equation

Explanation

I prefer the factorisation method to solve the equation.

to solve the equation with this method we take following steps

1. Put all the terms on one side.

2. then factor

3. now, set every factor equal to zero

4. next, solve the new equation which obtained by taking equal to zero

5. atlast, check the solution by puting values in main equation

Now, let us take an example

now, use step 1st

next, factor

now, put each factor equal to 0 and solve for x

Final Answer

Factorisation is the best method to solve quadratic equation