Graph the line with the given slope m and y-intercept b.
m = 4, b = -5

Given:

The initial mean weekly wage is $ 789.35.

The growth rate is 5.125 %.

Aim:

We need to find a new annual wage.

Explanation:

Consider the equation

Let A be the new annual wage.

Here R is the growth rate and P is the initial mean weekly wage and T is the number of weeks in a year.

The number of weeks in a year = 52 weeks.

Substitute P=789.35 , R =5.125 % =0.05125 and T =52 in the equation.

The new mean annual wage is $ 43,149.82.

Final answer:

The new mean annual wage is $ 43,149.82.

Answer:

Explanation:

Given:

To find:

We can find g(d) by substituting x in g(x) with d, so we'll have;

We can find f(d) by substituting x in f(x) with d, so we'll have;

We can now go ahead and subtract f(d) from g(d) and simplify as seen below;

Therefore, g(d) - f(d) = -d^2 - d -2

Since the function describing the height is a quadratic function with negative leading coefficient this means that this is a parabola that opens down. This also means that the maximum height will be given as the y component of the vertex of the parabola, then if we want to find the maximum height, we need to write the function in vertex form so let's do that:

Hence the function can be written as:

and its vertex is at (1.9,19.9) which means that the maximum height of the ball is 19.9 m

Given:

The inside diameter of the pope, I.D.=0.599 in.

The outside diameter of the pope, O.D.=1.315 in.

The inside radius of the pope is,

The outside radius of the pope is,

The wall thickness of the pope can be calculated as,

Therefore, the wall thickness of the pope is t=0.358 in.

The standard equation of a vertex is given by:

where (h,k) is the vertex.

Comparing with the given equation after re-arranging:

The vertex of the function is (-1, 4)

the perimeter is the sum of the outside sides. So in this case is 4+4+2+2+2+2=16

so the answer is 16cm

We know that the equation of a line is given by

y = mx + b,

where m and b are numbers: m is its slope (shows its inclination) and b is its y-intercept.

In order to find the equation we must find m and b.

In all cases, m is given, so we must find b.

We use the equation to find b:

y = mx + b,

↓ taking mx to the left side

y - mx = b

We use this equation to find b.

We have that the line passes through

(x, y) = (-10, 8)

and m = -1/2

Using this information we replace in the equation we found:

y - mx = b

↓ replacing x = -10, y = 8 and m = -1/2

Then, the equation of this line is:

y = mx + b,

↓

y = -1/2x + 3

Equation 1: y = -1/2x + 3

Similarly as before, we have that the line passes through

(x, y) = (-1, -10)

and m = 0

we replace in the equation for b,

y - mx = b

↓ replacing x = -1, y = -10 and m = 0

-10 - 0 · (-1) = b

↓ 0 · (-1) = 0

-10 - 0 = b

-10 = b

Then, the equation of this line is:

y = mx + b,

↓

y = 0x - 10

y = -10

Equation 2: y = -10

Similarly as before, we have that the line passes through

(x, y) = (-6, -9)

and m = 7/6

we replace in the equation for b,

y - mx = b

↓ replacing x = -6, y = -9 and m = 7/6

Then, the equation of this line is:

y = mx + b,

↓

y = 7/6x - 2

Equation 3: y = 7/6x - 2

The line passes through

(x, y) = (6, -4)

and m = does not exist

When m does not exist it means that the line is vertical, and the equation looks like:

x = c

In this case

(x, y) = (6, -4)

then x = 6

Then

Equation 4: x = 6

The line passes through

(x, y) = (6, -6)

and m = 1/6

we replace in the equation for b,

y - mx = b

↓ replacing x = 6, y = -6 and m = 1/6

Then, the equation of this line is:

y = mx + b,

↓

y = 1/6x - 7

Equation 5: y = 1/6x - 7

we have that

therefore

If b is a positive real number

then

Given the points:

You need to use the formula for calculating the distance between two points:

Where the points are:

In this case, you can set up that:

Then, you can substitute values into the formula and evaluate:

Hence, the answer is:

we have

Multiply in cross

square root both sides

see the attached figure to better understand the problem

the solution is the interval {-6,6}

the solution in the number line is the shaded area at right of x=-6 (close circle) and the shaded area at left of x=6 (close circle)

Considering the given dot plot for the distribution, it is found that:

a) The distribution is right skewed.

b) There is an outlier at 9.

c) Since there is an outlier, the best measure of center is the median.

A dot plot shows the number of times that each measure appears in the data-set, hence the data-set is given as follows:

1, 1, 1, 1, 2, 2, 2, 2, 2 3, 3, 3, 3, 4, 4, 4, 5, 5, 5, 9.

To find the skewness of the data-set, we need to find the mean and the median.

The mean is the sum of all values divided by the number of values of 20, hence:

Mean = (4 x 1 + 5 x 2 + 4 x 3 + 3 x 4 + 3 x 5 + 9)/20 = 3.1.

The median is the mean of the 9th and the 10th elements(even cardinality) of the data-set, hence:

Median = (2 + 3)/2 = 2.5.

The mean is greater than the median, hence the distribution is right skewed.

To identity outliers, we need to look at the quartiles, as follows:

The interquartile range is:

IQR = 4 - 2 = 2.

Outliers are more than IQR from the quartiles, hence:

4 + 1.5 x 2 = 4 + 3 = 7 < 9, hence 9 is an outlier in the data-set, and hence the median will be the best measure of center.

The questions are as follows:

Part A: Describe the dotplot. (4 points)

Part B: What, if any, are the outliers in these data? Show your work. (3 points)

Part C: What is the best measure of center for these data? Explain your reasoning. (3 points) (10 points)

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Given the equation

To apply the subtraction property of equality, we subtract 20 from both sides.

The missing reasons are

ΔCDA ≅ ΔBDA  by SSS [side side side]

ΔCED ≅ ΔBED by SAS [side angle side]

What is Kite?

A kite is a quadrilateral having reflection symmetry across a diagonal in Euclidean geometry. A kite has two equal angles and two pairs of adjacent equal-length sides as a result of its symmetry.

Given,

ABCD is a kite, with the diagonal AD and BC

We have,

               AC = AB

and

               CD = BD                [Property of Kite]

In ΔACD and ΔABD

                AC = AB

and

               CD = BD               [Property of Kite]        

               AD = AD               [Common]

By rule SSS Criteria [Side Side Side ]

              ΔACD ≅ ΔABD

 ∴           ∠CDA = ∠BDA         [CPCT]

Now,

         In ΔCDE and ΔBDA

                 CD = BD

            ∠CDE = ∠BDE

                 DE = DE                [Common]

By rule SAS Criteria [Side Angle Side]  

            ΔCDE ≅ ΔBDA

∴                CE = BE                [CPCT]  

Hence, AD bisects BC into equal parts

The missing reasons are

ΔCDA ≅ ΔBDA  by SSS [side side side]

ΔCED ≅ ΔBED by SAS [side angle side]

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We have to select a point that is the best representative of the square root of 15.

We can calculate the square root of 15 with a calculator, but we can aproximate with the following reasoning.

We know that 15 is the product of 3 and 5. If we average them, we have 4.

If we multiply 4 by 4, we get 16, that is a little higher than 15.

If we go to the previous number (3) and calculate 3 by 3 we get 9, that is far from 15 than 16.

So we can conclude that the square root of 15 is a number a little less than 4.

In the graph, the point B is the one that satisfy our conclusion, as it is a point in the scale that is between 3 and 4, and closer to 4.

The answer is Point B

Notice that the polar coordinates of the point on the simplest form are (2,30). Then, the only option that does not match a proper transformation of coordinates is the point (-2,30)

Given data:

The given expression is 1 4/5 + (2 3/20 + 3/5).

The given expression can be written as,

Thus, the value of the given expression is 91/20.

a) Let's say initial population is po and p = p(t) is the function that describes that population at time t. If it increases 10% each hour then we can write:

t = 0

p = po

t = 1

p = po + 0.1 . po

p = (1.1)¹ . po

t = 2

p = 1.1 . (1.1 . po)

p = (1.1)² . po

t = 3

p = (1.1)³ . po

and so on

So it has an exponential growth and we can write the function as follows:

p(t) = po . (1.1)^t

p(t) = 500 . (1.1)^t

Answer: p(t) = 500 . (1.1)^t

b)

We want the population for t = 2 hours, then:

p(t) = 500 . (1.1)^t

p(2) = 500 . (1.1)^2

p(2) = 500 . (1.21)

p(2) = 605

Answer: the population at t = 2 hours is 605 algae.

c)

Let's plug t = 4 in our function again:

p(t) = 500 . (1.1)^t

p(4) = 500 . (1.1)^4

p(4) = 500 . (1.1)² . (1.1)²

p(4) = 500 . (1.21) . (1.21)

p(4) = 500 . (1.21)²

p(4) = 732.05

Answer: the population at t = 4 hours is 732 algae.

A group of numbers' greatest common factor (GCF) is the biggest factor that all the numbers have in common. For instance, the numbers 12, 20, and 24 share the components 2 and 4.

Therefore, 12 and 24 have the most things in common. Figure 2: LCM = 24 and GCF = 12 for two numbers.

Find the other number if one is 12, then. What does 12 and 24's GCF stand for?

Example of an image for 12 + 24 = ( + ) Locate the GCF. You should distribute your GCF as the first number.

12 is the GCF of 12 and 24. We must factor each number individually in order to determine the highest common factor of 12 and 24 (factors of 12 = 1, 2, 3, 4, 6, 12; factors of 24 = 1, 2, 3,.

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The x variable represents the year in question. The year 2000 is represented by x = 0, 2001 would be repreented by x = 1, and so on.

The year in which both states would have the same population can be determined by the value of x which satisfies both equations.

We would now solve these system of equations as follows;

Note that x = 19 represents the year 2019

ANSWER:

The two states will have the same population in the year 2019

Let the amount of 30% acid solution be a

Let the amount of 60% acid solution be b

Given, "a" and "b" mixed together gives 570 liters of 31% acid. We can write:

Also, we know 30% acid and 60% acid amounts to 570 liters, thus:

The first equation becomes:

We can solve the second equation for a:

Putting this into the first equation, we can solve for b. The steps are shown below:

So, a will be:

a = 570 - b

a = 570 - 19

a = 551

Thus,

551 Liters of 30% acid solution and 19 Liters of 60% acid solution need to be mixed.

Answer:

23z-66x

Step-by-step explanation:

Look at the attachment please :D

We have to solve for c:

When we have quadratic expressions, we have to take into account that each number has two possible square roots: one positive and one negative.

We can see it in this example: the square root of 4 can be 2 or -2. This is beacuse both (-2)² and 2² are equal to 4.

Then, taking that into account, we can solve this expression as:

We then calculate the first solution for the negative value -8:

And the second solution for the positive value 8:

Then, the two solutions are c = -17 and c = -1.

We can check them replacing c with the corresponding values we have found:

Both solutions check the equality, so they are valid solutions.

Answer: -17 and -1.

c = price of a slice of Cheese pizza

m= price of a slice of mushroom pizza

Jack bought 3 slices of cheese pizza and 4 slices of mushroom pizza fora total cost of $12.50

3c + 4 m = 12.50

Grace bought 3 slices of cheese pizza and 2 slices of mushroom pizza for a total cost of $8.50.

3c + 2m = 8.50

We have the system of equations:

3c + 4 m = 12.50 (a)

3c + 2m = 8.50 (b)

Subtract (b) to (a) to eliminate c

3c + 4m = 12.50

-

3c + 2m = 8.50

_____________

2m = 4

Solve for m:

m = 4/2

m=2

The cost of one slice of mushroom pizza is $2

Answer

The error in the solution is circled (red) in the picture below.

The equation can be solved correctly as follows

The most appropriate choice for perimeter of rectangle will be given by -

Perimeter of rectangle = (22v + 14w) cm

What is perimeter of rectangle?

At first it is important to know about rectangle.

Rectangle is a parallelogram in which every angle of the parallelogram is 90°.

Perimeter of rectangle is the length of the boundary of the rectangle.

If l is the length of the rectangle and b is the breadth of the rectangle, then perimeter of the rectangle is given by

Perimeter of rectangle = [tex]2(l + b)[/tex]

Length of rectangle = (5v - w) cm

Breadth of rectangle = (6v + 8w) cm

Perimeter of rectangle = 2[(5v - w) + (6v + 8w)]

                                      = 2(11v + 7w)

                                      = (22v + 14w) cm

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Complete Question

The width of a rectangle measures (5v−w) centimeters, and its length measures(6v+8w) centimeters. Which expression represents the perimeter, in centimeters, of the rectangle?

Answer:

5(5m + 2)

Explanation:

To factor out the expression, we first need to find the greatest common factor between 25m and 10, so the factors if these terms are:

25m: 1, 5, m, 5m, 25m

10: 1, 2, 5, 10

Then, the common factors are 1 and 5. So, the greatest common factor is 5.

Now, we need to divide each term by the greatest common factor 5 as:

25m/5 = 5m

10/5 = 2

So, the factorization of the expression is:

25m + 10 = 5(5m + 2)

Answer:

Explanation:

Given: interval [1,5]

Based on the given functions, we start by computing the function values at each endpoint of the interval.

For:

Now we compute the average rate of change.

For:

For:

For:

Therefore, the function that has the greatest average rate is

From the information provided, the triangle HXI can be mapped onto triangle PSL. This means the vertices of the reflected image would now have the following as same measure angles;

Measure of angle S cannot be determined from the information provided because there is insufficient information given to determine the measure of angle X, hence the angle congruent to it (angle S) likewise cannot be determined.