Kathy found a job listed on an employment web site that pays a yearly salary of $27,630. What is
the biweekly salary based on this annual salary rounded to the nearest cent?
Do not include a dollar sign in your answer.​

Hey there!

The answer is 58 degrees

Since ΔABC ~ ΔDEF, then m∠A ~ m∠D, and m∠B ~ m∠E, and m∠C ~ m∠F. This means we can set m∠A equal to m∠D:

x + 29 = 2x

Subtract x from both sides:

29 = x

Now, we plug into the angle expressions to find their measurement:

m∠A = 29 + 29

m∠A = 58

Since they are equal, m∠A and m∠D are both 58 degrees.

Have a terrificly amazing day! :)

The measure of each interior angle of a regular polygon is \(\frac{180(n-2)}{n}\) degrees, where n is the number of sides.

Question 1

\(144=\frac{180(n-2)}{n}\\\\144n=180(n-2)\\\\144n=180n-360\\\\-36n=-360\\\\n=10 \text{ sides}\)

Question 2

\(\frac{180(n-2)}{n}=135\\\\180(n-2)=135n\\\\180n-360=135n\\\\-360=-45n\\\\n=8 \text{ sides}\)

Answer:

Step-by-step explanation:

A consumer is considering two different purchasing options for the car of their choice. The first option, which is leasing, is described by the equation 250x - y + 4000 = 0 where x represents the number of months of ownership and y represents the total paid for the car after ‘x' months. The second option, which is the financing option, will cost $400 for 0 months of ownership, (0,400), and $4400 for 10 months of ownership, (10, 4400). Part A: Find the equations, in slope/y-intercept form, for each of the purchasing options. Explain the significance of the slope and y-intercept for each purchasing option.

Answer: For the first option which is leasing, it is described by the equation:

250x - y + 4000 = 0

The general equation of a line is y = mx + c, where m is the slope of the line and c is the intercept on the y axis.

Since 250x - y + 4000 = 0, we need to make it in the form of the general equation by making y the subject of the formula.

Therefore:

y = 250x + 4000

This means that the slope is 250 and the y intercept is 4000. That is at 0 months, the amount paid for the car is $4000 for the first option. As the value of the months increase by 1, the amount paid for the car increase by 250

The second option, which is the financing option, will cost $400 for 0 months of ownership, (0,400), and $4400 for 10 months of ownership, (10, 4400). To get the equation of the line, we use the formula:

\(\frac{y-y_1}{x-x_1}=\frac{y_2-y_1}{x_2-x_1}\\ Substituting:\\\frac{y-400}{x-0}=\frac{4400-400}{10-0}\\\frac{y-400}{x} = 400\\y=400x+400\)

The second option has a slope of 400 and an intercept of 400. At 0 months, $400 is paid for ownership. As the value of the months increase by 1, the amount paid for the car increase by 400

Question:

A shop is having a sales all items are reduced by 25%. Work out the sale price of an item normally priced at £60?

Answer:

The new price is £45

Step-by-step explanation:

Given

\(Sales\ price = \pounds 60\)

\(Rate = 25\%\)

First, calculate the reduction

\(Reduction = Rate * Sales\ price\)

\(Reduction = 25\% * \pounds 60\)

\(Reduction = \pounds 15\)

The new price is:

\(New = Sales\ price - Reduction\)

\(New = \pounds 60 - \pounds 15\)

\(New = \pounds 45\)

The motel revenue based on the number of rooms rented and group rental are as follows;

(a) The price for renting three rooms is $195

(b) The formula through which the unit rate of a room is found is aₙ = 71 - 3·(n -1)

(c) The function for the revenue, R(n) = 74·n - 3·n²

(d) The most amount that can be made is $456

The number of rooms that gives the most amount is 12 rooms

A revenue is the total amount received for the sale of goods and services

The number of rooms in the motel = 44

The price for renting one room = $71

The price for renting two rooms = $68

The per room group rate = $71 - $3 for each additional room
(a) The amount made if a family rents three rooms is given as follows;

The unit price for two rooms = $71 - $3 = $68

The unit price for three rooms = $68 - $3 = $65

The price for the three rooms is therefore;

$65 × 3 = $195

(b) The formula that gives the rate charged for each room to an organization is an arithmetic progression, which can be expressed as follows;

aₙ = a₁ + (n - 1)·d

Where;

n = The number of rooms the organization plans to rent

a₁ = The first term of the arithmetic progression = 71

d = The common difference = -3

Which gives;

aₙ = 71 - 3·(n - 1)

The price for each room when an organization rents n rooms is therefore;

aₙ = 71 - 3·(n - 1)

(c) The revenue for renting n room is given by the formula;

Revenue, R(n) = Unit rate × Number of rooms

∴ R(n) = (71 - 3·(n - 1)) × n = 74·n - 3·n²

(d) The -ve coefficient of n² in the formula with which the revenue can be found indicates that the function has a maximum value. The number of rooms that gives the most revenue is obtained at the from the derivative of the R(n) as follows;

R'(n) = 74 - 6·n = 0

n = 74/6 ≈ 12

Which gives;

\(R_{max}\) = R(12) = 74 × 12 - 3 × 12² = 456

The maximum revenue from renting to a single group ≈ $456

The number of rooms to rent that gives the maximum revenue is n ≈ 12

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The distance between the stake from the pole is 6.25 ft.

Pythagorean theorem states that in the right angle triangle, the hypotenuse square is equal to the square of the sum of the other two sides.

According to this statement, the areas of the squares on the other two sides add up to the size of the square whose side is the hypotenuse.

Given that a utility pole is 5 ft high. An 8 ft cable is stretched from the top of the pole to a stake in the ground.

The distance will be calculated as,

B² =  H² - P²

B = √(8² - 6²)

B = √ ( 64 - 36 )

B = √39

B = 6.25 ft

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The value of x is equal to 15°

In Mathematics and Geometry, the sum of the exterior angles of both a regular and irregular polygon is always equal to 360 degrees.

Note: The given geometric figure (regular polygon) represents a pentagon and it has 5 sides.

By substituting the given parameters, we have the following:

3x + 4x + 8 + 5x + 5 + 6x - 1 + 5x + 3 = 360°.

3x + 4x + 5x + 6x + 5x + 8 + 5 - 1 + 3 = 360°.

23x + 15 = 360°.

23x = 360 - 15

23x = 345

x = 345/23

x = 15°.

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The Scale factor was used to enlarge the picture is 7/ 31.5.

A scale factor is a numerical value that can be used to alter the size of any geometric figure or object in relation to its original size. It is used to find the missing length, area, or volume of an enlarged or reduced figure as well as to draw the enlarged or reduced shape of any given figure. It should be remembered that the scale factor only affects how big a figure is, not how it looks.

Given:

A picture is 7 inches wide and 9 inches long.

A photographer enlarges it so it is 31.5 inches wide and 40.5 inches long.

So, scale factor is

= Original dimension / Enlarged dimension

= 9/ 40.5

= 90/ 405

= 10/45

= 2/9

Now, simplifying the scale factor 7/31.5 because it has Nr < Dr.

= 7/ 3.15

= 70/31.5

= 2/9

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The researcher selects the easiest population members from which to obtain information in a quota sample. Option B

In a quota sample, the researcher utilizes their judgment to select population members who are considered good prospects for accurate information.

This approach does not involve random sampling or employing a specific strategy to sample the entire population. Instead, the researcher sets predetermined quotas based on specific characteristics or demographics of interest.

Quota sampling involves dividing the population into various subgroups or strata and determining the desired number of individuals to be included from each subgroup.

The researcher then exercises their judgment to select individuals who meet the criteria until the quotas are fulfilled. This approach aims to ensure that the sample reflects the distribution of certain characteristics within the population.

While quota sampling provides a structured method for achieving representation across various subgroups, it is not based on random selection. This can introduce bias into the sample, as the researcher's judgment may influence the selection process.

Consequently, the generalizability of the findings obtained from a quota sample may be limited, and caution should be exercised when interpreting the results. So Option B is correct.

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Answer:

1764

.

.

.................

....

Step-by-step explanation:

To find a line perpendicular to one another and passing through the point we take the slope of the original line and apply its reciprocal in point slope form.

Reciprocal of \(\frac{1}{4}\) is \(\frac{-4}{1}=-4\)

Now plug the slope into point-slope form with the known x and y values:

\(x-(-2)=-4(y-4)\\x+2=-4(y-4)\\x+2=-4y+16\\x+2+4y=16\\4y=16-x-2\\y=4-\frac{x}{4}-\frac{2}{4}\\y=3.5-\frac{x}{4}\)

Answer:

5 weeks

Step by step

7.80 x 20 = 156

156 x 5 = 780

Answer: B) 5 weeks

Step-by-step explanation: I know your struggling and that's why you need this answer. your welcome cutie.

90 x 120 = 10800

10800/2 = 5400

Answer:

Step-by-step explanation:

so this is the problem:

90x120=x/2

first, you can multiply 90 and 120 to get 10800.

then, your equation looks like this

10800=x/2

you can multiply both sides by 2

2(10800)=(x/2)(2)

then, you get this

21600=x

hope this helped!!!

The union of sets A and B is {m ∈ Z: m ≤ i} ∪ {m ∈ Z: m > j}, and the intersection of sets A and B is {m ∈ Z: m ≤ i and m > j}.

The union and intersection of sets A and B, given A = {m ∈ Z: m ≤ i} and B = {m ∈ Z: m > j}, can be determined as follows:

Union of A and B:

The union of two sets A and B, denoted by A ∪ B, is the set containing all the elements that are present in either A or B (or both). In this case, the union of A and B is the set of all integers that are either less than or equal to i, or greater than j. The union of A and B can be expressed as {m ∈ Z: m ≤ i} ∪ {m ∈ Z: m > j}.

Intersection of A and B:

The intersection of two sets A and B, denoted by A ∩ B, is the set containing all the elements that are common to both A and B. In this case, the intersection of A and B is the set of all integers that satisfy both conditions: m ≤ i and m > j. The intersection of A and B can be expressed as {m ∈ Z: m ≤ i and m > j}.

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An equation that mode the relationship between thee two variable is y=2x+3 .

Let x represent the number of 6-month period worked

Let y represent the total number of paid vacation day

According to the question,

When he started work, he was given three paid day of vacation. For each six-month period he pay at the job, his vacation is increased by two day.

Each year has 2 six-month periods. After 4.4 years Roberto will have worked 8.8 six-month periods. He will have been given vacation days for each of the 8 whole working periods he has completed. x=8 y=2*8+3 y=19

An equation that mode the relationship between thee two variable is y=2x+3 (Total vacation time equals 2 days times x plus the 3 days he was given at the start).

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Answer:Answer B

Step-by-step explanation:

You get more money that way.

Answer:

It would be $13 as the original bill

But the correcy answer is D  

Step-by-step explanation:

Answer:

\(y=5\)

Step-by-step explanation:

Equation in point slope form is given as

\(y-y_1=m(x-x_1)\)

Here

\(m=0 \ and \ (x_1, y_1)=(-2, 5)\)

Therefore

\(y-5=0(x+2)\)

\(y=5\)

Answer:

7 miles.

Step-by-step explanation:

6+8+7+6+7+8/6

42/6

= 7 miles

The answer is 7 miles.

The largest eigenvalue of normalized sample covariance matrices converges to 1 as both the dimension (p) and the sample size (n) tend to infinity.

The sample covariance matrix is computed from a dataset with p variables and n observations. It measures the relationship between variables and provides information about their covariance.

To normalize the sample covariance matrix, each entry is divided by a factor of (1/n), ensuring that the matrix is scaled properly.

As p and n tend to infinity, the eigenvalue distribution of the normalized sample covariance matrix follows the Marčenko-Pastur distribution, a probability distribution describing the eigenvalues of large random matrices.

In this distribution, the largest eigenvalue approaches 1, while the remaining eigenvalues are close to 0. This result is known as the Tracy-Widom law and is applicable to high-dimensional statistics.

Thus, in the limit of increasing p and n, the largest eigenvalue of the normalized sample covariance matrix converges to 1, indicating that it carries little information about the underlying structure of the data.

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Answer:

zx=115'

Step-by-step explanation:

supplementary angles add up to 180'

180-65=115

Answer:

115°

Step-by-step explanation:

Given

Zy = 65°

Zx = ?

we know

Zx + Zy = 180° { being supplementary angles }

Zx + 65° = 180°

Zx = 180° - 65°

Zx = 115°

Hope it will help :)❤

Answer:

4 yards

Step-by-step explanation:

11 1/2 feet is equal to 3.833333 and 4 yards is more than that.

Answer:

11 1/2 ft. < 4 yd

Step-by-step explanation:

I'm not sure if thats what your asking.

But 1 yard is 3 ft, so 4 yards is equal to 12 ft. Therfore 11 1/2 ft. < 4 yd.

Step-by-step explanation:

Tax charge

80 × 6.75/100 = 5.4

Cost + tax charge

80 + 5.4 = 85.4

Tip (15% of cost and tax)

85.4 × 15/100 = 12.81

(Cost + tax charge + tip)

85.40 + 12.81 = 98.21

therefore, $95 is not enough.

Divide all numbers by prime factors

14 21 40 | 2

7 21 20 | 2

7 21 10 | 2

7 21 5 | 5

7 21 1 | 7

1 3 | 3

1 |

Now, multiply all this numbers to find the least common multiple

The least common multiple is 840

Answer:

AB = BC = 4\(\sqrt{2}\)

Step-by-step explanation:

This is a 45-45-90 triangle (right isosceles). This means that the side ratio is

1:1:\(\sqrt{2}\), where AC is sqrt 2, and AB and BC are 1. Now, we need to plug this into our ratio. If sqrt 2 is 8, then 1 is x.

8/\(\sqrt{2}\) = x/1 = x

x = 8/\(\sqrt{2}\) = 4\(\sqrt{2}\) (rationalized)

AB and BC are both 4 * sqrt 2

The answer is AB = BC = 4√2

If T is the midpoint of PQ and PT = 3x+3, TQ = 7x-9, then PT = 12 units.

Determining the Value of PT

It is given that,

T is the midpoint of PQ ........ (1)

PT=3x+3 ......... (2)

TQ=7x-9 .......... (3)

From (1), the distance from P to T and the distance from T to Q will be equal.

⇒ PT = TQ [Since, a midpoint divides a line into two equal segments]

Hence, equating the equations of PT and TQ given in (2) and (3) respectively, equal, we get the following,

3x + 3 = 7x - 9

or 7x - 9 = 3x + 3

or 7x - 3x = 9 + 3

or 4x = 12

or x = 12/4

⇒ x = 3

Substitute this obtained value of x in equation (2)

PT = 3(3) + 3

PT = 9 + 3

PT = 12 units

Thus, if T is the midpoint of PQ, then the measure of PT and TQ is equal to 12 units.

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