A circle has a center at (4, -7) and a radius of 4 units. What is the equation of this circle?
O (4)² + (y + 7)² = 16
O (x + 4)² + (y + 7)² = 4²
O(x-4)² + (y - 7)² = 16
O(x + 4)² + (y - 7)² = 4²

Answer:

  1) 120 units

  2) see attachment

Step-by-step explanation:

Given a figure composed of 21 squares that each have an area of 25 square units, you want to know (1) the perimeter of the figure, and (2) how to rearrange it to have the same perimeter, but with sides that line up.

The perimeter is the sum of the lengths of the sides that form the boundary of the figure. The boundary consists of ...

for a total of 6·4 = 24 edges of the squares shown.

Each of the squares shown has an area of A = s² = 25 units², so a side length of s = √(25 units²) = 5 units.

The perimeter is the length of 24 of these edges, so is ...

  perimeter = 24 × 5 units = 120 units

The 21 squares shown in the figure can only be rearranged into rectangles that are 21 × 1 squares or 7 × 3 squares. These will have perimeters of 44 or 20 edges, respectively. Hence, it is not possible to have "sides of the squares line up" in a rectangle with the same perimeter.

The attached figure is the next best thing. It shows a 6 × 4 rectangle with three squares removed (to keep the total at 21). The number of horizontal and vertical edges total 24, as required to keep the same perimeter.

42 / 15-2^3

First, solve for the exponent:

42 / 15-8

Subtract:

42/7

Divide:

6

We need to solve the inequality:

We can start by sketching the graph of the parabola:

Then, we need to find the points of the parabola below the x-axis.

The zeros of that parabola are given by:

And since the coefficient of x² is positive, the parabola opens upwards. So, its graph looks like this:

Thus, the points on the parabola below the x-axis are those for which:

The graph represents a linear function with negative slope.

How does different type of graph and their equations look like?
1. Linear graph: It is of the form y= mx+ c

First-order variables are present in linear functions, and the graph's placement is determined by two constants. These operations graph into a line in every case. The slope of the line is determined by the constant m. The slope of the line will slope up if it is positive and down if it is negative.

2. Quadratic graph: y= ax^2+ bx+ c

These type of graphs have an U shaped curve and their slope can also be obtained by drawing a tangent.

3. Square root graph : F(x)=x is the parent function of all functions with the formula f(x)=a+b. Keep in mind that f(x)=x has an x0 domain and a y0 range. By translating the graph of f(x)=x to a units to the right and then b units up, the graph of f(x)=root x-a+b can be derived.

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The earnings and deductions, are given as follows:

First we find her gross earning, which is given by the hourly wage multiplied by the number of hours worked, hence:

Gross pay = 40 x 18 = $720.

Hence her yearly income is given by:

Yearly income = 52 x 720 = $37440.

Meaning that her federal tax rate is of $19.76 a week plus 12% of the excess over $197.60, then:

Federal tax = 19.76 + 0.12 x (720 - 197.60) = $82.45.

The social security tax rate is of 6.2% of her gross weekly earnings, hence it is given by:

Social Security = 0.062 x 720 = $44.64.

The medicare tax rate is of 1.45% for Lynn(employee), hence:

Medicare = 0.0145 x 720 = $10.44.

The state tax is 3% of her gross earnings, hence:

State tax = 0.03 x 720 = $21.60.

The local tax is 1.5% of her gross earnings, hence:

State tax = 0.015 x 720 = $10.80.

The medical and union dues are stated in the problem, hence the sum of all discounts is given by:

82.45 + 44.64 + 10.44 + 21.60 + 10.80 + 35 + 17 = $221.93.

The net pay is the gross pay subtracted by the discounts, hence:

Net pay = 720 - 221.93 = $498.07.

The value of an allowance is not stated, hence they are not considered for the calculations.

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The quotient of 33/402 is 0 and the remainder is 369

The division expression is given as

33/402

From the above expression, we have

Numerator = 33

Denominator = 402

As a general rule of quotient, when the denominator is greater than the numeration, then the quotient is 0

The division expression is given as

33/402

From the above expression, we have

Numerator = 33

Denominator = 402

As a general rule of quotient, when the denominator is greater than the numeration, then the remainder is 0

Remainder = Denominator - Numerator

This gives

Remainder = 402 - 33

Evaluate

Remainder = 369

This means that the remainder of 33/402 is 369

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Possible question

Find the quotient and remainder for the following expression using the division algorithm.

33/402

1) Since we know the decimal places, then we can write out the following number:

Note the 3 decimal places after the dot is the thousandth's place. Note that we can either write the last digit or omit it.

The steps that would be applied to solve the equation are:

multiplying both sides of the equation by 3

substituting 36 for p to check the solution

An equation is a statement in mathematics that consists of two or more expressions that are connected by an equal to sign.

The given equation is:

p / 3 = 12

In order to solve, the equation, p has to be made the subject of the formula.

In order to make the subject of the formula, take the following step:

Multiply both sides of the equation by the denominator of p. The denominator of p is 3.

3 x (p/3) = (12 x 3)

p = 36

Substitute for p using 36 to check the accuracy of the answer derived

36 / 3 =12

Here are the options:

subtracting 3 from both sides of the equation

multiplying both sides of the equation by 3

dividing both sides of the equation by 3

substituting 4 for p to check the solution

substituting 36 for p to check the solution

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The answer is -3 2/3 + 1 = -2 3/5

It's a linear equation form  -3/ 2/3

What is linear equation?

An equation between two variables that, when plotted on a graph, produces a straight line or say first degree equation is known as linear equation.

An addition problem that has a sum of -3 2/3 may take different forms one of which is the answer supplied where; -3 2/3 is added to 1 and the result is -2 3/5

Therefore, the answer of  -3 2/3 is -2 3/5

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The function f(6) has a value of 1./3

The graph that completes the question is added as an attachment

From the graph, we have the following points

(x, y) = (4, 1) and (1, 2)

We start by calculating the slope of the points using the following slope equation

Slope = (y₂ - y₁)/(x₂ - x₁)

Where x and y are defined above

So, we have

Slope = (2 - 1)/(1 - 4)

Evaluate

Slope = -1/3

At f(6), we have

x = 6

So, the point can be represented as (6, y)

Using the slope formula again, we have

Slope = (y₂ - y₁)/(x₂ - x₁)

Where

(x, y) = (4, 1) and (6, y)

This gives

Slope = (y - 1)/(6 - 4)

Evaluate

Slope = (y - 1)/2

So, we have

(y - 1)/2 = -1/3

Evaluate

y = -2/3 + 1

Evaluate

y = 1/3

Hence, the value of f(6) is 1/3

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The image of C under the translation described by this translation rule (x, y) → (x + 11, y - 8) is: (4, -6)

In Geometry, the translation of a geometric figure to the right simply means adding a digit (11) to the value on the x-coordinate (x-axis) of the pre-image while translating a geometric figure down simply means subtracting a digit (8) from the value on the y-coordinate (y-axis) of the pre-image.

Note: Each point on this graph represents 2 units.

Next, we would translate the image of C 11 units to right and 8 units down. Therefore, this transformation can be modeled by this translation rule:

(x, y)                              →               (x + 11, y - 8)

Point at C = (-7, 2)        →      Point at C' = (-7 + 11, 2 - 8) = (4, -6)

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The most appropriate choice for stocks and net proceeds will be given by-

Net proceeds of Erin = $3533.9

What is stock and net proceeds?

Stock

Stock is a part of share set up by the company so that people can buy.

Net proceeds

After deducting all expenses, amount recieved by the seller after selling of stocks is called net proceeds.

Worth of stocks purchased by Erin  = $23510

Percentage paid to her broker = 1%

Amount paid to broker = [tex]\frac{1}{100}\times 23510[/tex]

                                      = $235.1

Now price of stocks increased to $27300

Net profit = $(27300 - 23510)

                = $3790

Net proceeds = $(3790 - 235.1 - 21)

                        =$3533.9

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Question 8

We are to solve

This can be simplified to

Raising both sides of the equation to a power of 5 we have

By raising both sides of the equation to power of 1/14, we get

Simplifying this we get

X<4 means that the chosen number is less than four and probability if the event X<4, P(X<4) 2/5.

Let us say that we have to select one number between 0-9.

So, the total possible outcomes can be 10.

Let us say that a number x is chosen randomly,

The expression x<4 means that is the chosen number is X, then the number should must be less than 4, not even equal, it should be less than 4.

So, The probability of X<4, we should first find total favorable outcomes,

The total number less than 4 are 0,1,2,3.

So, the total favorable outcomes are 4.

We know,

Probability of event E is,

P(E) = total favorable outcomes/total number of outcomes.

So, P(X<4) = 4/10

P(X<4) = 2/5

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The numeric value of the slope of the inverse function at x = -32 is given by:

(h^-1)'(-32) = 0.03.

To find the inverse of a function, we exchange x and y in the original function, then isolate y.

This means that if the original function has a point (x,y) graphed, the inverse will have point (y,x) graphed.

From it's graph, the function h(x) has these two following points:

(-4.552, -32) and (-4.555, -32.1)

Hence the inverse will have these two following points:

(-32, -4.552) and (-32.1, -4.555).

The slope is given by change in y divided by change in x, hence:

(h^-1)'(-32) = (-4.552 - (-4.555))/(-32 - (-32.1)) = 0.03.

Which is also equivalent to the derivative of the inverse function at x = -32.

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Answer: a) 216 beats     b) almost 16 minutes

Step-by-step explanation:

54 beats/minute x 4 minutes = 216 beats

855 beats / 54 beats/minutes = 15.83333 minutes

Hope this helps!

At the CD's maturity in 2 years' time, the future value that you can collect is $4,347.22.

The future value (FV) of CD is the present value compounded at an interest rate of 4.25% for 2 years in the future.

We can compute the future value using the FV formula or an online finance calculator as below.

N (# of periods) = 2 years (24 months)

I/Y (Interest per year) = 4.25%

PV (Present Value) = $4,000

PMT (Periodic Payment) = $0

Results:

FV = $4,347.22 ($4,000 + $347.22)

Total Interest = $347.22

Thus, the 24-month CD purchased for $4000 will yield a future value of $4,347.22 at maturity.

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To solve the exercise, replace in the expression the given values of c and d and then operate:

Therefore, the value of the evaluated expression is 38.1

Answer:

4.58 gallons

Step-by-step explanation:

13$ in 2000 = 8 1/3 gallons

13$ in 2010 = 4.577 gallons

ANSWER

• AB and EF

• BC and FG

• AC and EG

EXPLANATION

The order in which the vertices of the triangles are named gives us which sides are congruent. If ΔABC ≅ ΔEFG, then the pairs of corresponding congruent sides are,

Given set :

154,109,137,115,152,140,154,178,80,103,126,126,137,165,165,129,200,148.

Rewrite the given data set from least to highest values.



80, 103, 109, 115, 126, 126, 129, 137, 137, 140, 148, 152, 154, 154, 165, 165, 178, 200.

Recall that a data point is an outlier if it is over 1.5 times the IQR below the first quartile or 1.5 times the IQR above the third quartile.

We know that

The upper half of the data set is

{137, 140, 148, 152, 154, 154, 165, 165, 178, 200}

The number of data in the set is even.

There are two middle terms in this upper half of the given set. That are 154 and 154.

The lower half of the data set is

{80, 103, 109, 115, 126, 126, 129, 137, 137, 140}

The number of data in the set is even.

There are two middle terms in this lower half of the given set. Which are 126 and 126.

Substitute known values in the IQR formula.

We get IQR=28.

Answer:

[tex]11\frac{14}{48}[/tex]

Step-by-step explanation:

[tex]7\frac{3}{16}+4\frac{5}{48}[/tex]

First, make these improper fractions.

[tex]\frac{115}{16} +\frac{197}{48}[/tex]

And now to add these fractions, make the denominators the same.

For that, multiply both the numerator and denominator of the fraction 115/16 by 3.

[tex]\frac{115*3}{16*3} +\frac{197}{48}\\\\\frac{345}{48} +\frac{197}{48}\\\\\frac{542}{48} \\\\=11\frac{14}{48}[/tex]

Please, give me some minutes to take over your question

Ben run 6 miles in an hour. How many miles does Ben run in nine hours?

Ratio

6 miles / 1 hour

6 miles/ 1 hour = x miles / 9 hours

x= 6 * 9 = 54 miles

Ben runs 54 miles in 9 hours.

Interquartile range of the scores is 7.

When values are ranked from lowest to highest, the IQR designates the middle 50% of those values. Find the median (middle value) of the bottom half and upper half of the data before calculating the interquartile range (IQR). Quartile 1 (Q1) and Quartile 3 are these values (Q3). The IQR represents the variation between Q3 and Q1. The strongest indicator of variability in data sets with outliers or skewed distributions is the interquartile range. It's unlikely to be impacted by outliers because it's based on numbers that come from the center half of the distribution.

Given Set

16, 12, 20,35,21,17,19,20,13,12,15

12, 12, 13, 15, 16, 17, 19, 20, 20, 21, 35

25 percentile(Q₁) = 13

50 percentile(Q₂) = 17

75 percentile(Q₃) = 20

Interquartile range = Q₃ - Q₁

Interquartile range = 20-13

Interquartile range = 7

Interquartile range of the scores is 7.

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Answer:

  (b)  4.65×10⁹

Step-by-step explanation:

You want 4,650,000,000 written in scientific notation.

A number is written in scientific notation in the form shown in the second attachment. The coefficient has one digit to the left of the decimal point. The remaining significant digits of the number are to the right of the decimal point.

The exponent is the same as the exponent of the place value of the most significant digit of the number. Some of those exponents are shown in the first attachment.

The given number has its most significant digit (4) in the "billions" place. The corresponding exponent of 10 is 9. Putting 4 to the left of the decimal point, the number is written in scientific notation as ...

  4.65×10⁹

__

Additional comment

In the above, we have used the superscript font to indicate the exponent. In plain text, an exponent is indicated with a caret (^), as in 4.65·10^9.

If you use an "x" character for a multiplication symbol, you need to make sure it cannot be confused with a variable named "x".

In spreadsheets and some calculators, the base and exponent are written as "E". Here, the number would be 4.65E9. (This is a carryover from one of the earliest high-level computer programming languages.)

(You will notice that the number in the second attachment is similar to, but not the same as, the one given in this problem statement. We intend that attachment to show the format, not the answer to this question.)

The methods which can be used to prove that the two triangles are congruent are:

Prove all three sets of corresponding angles are congruent.

Prove all three sets of corresponding sides are congruent.

Option C and Option D are the correct answer.

Corresponding angles are angles that occur on the same side of the transversal line and are equal in size.

We have,

To prove that two triangles are congruent, we need to show that the corresponding sides and corresponding angles are congruent.

So,

Prove all three sets of corresponding angles are congruent.

Prove all three sets of corresponding sides are congruent.

These two methods can be used to prove that the two triangles are congruent.

Thus,

The methods which can be used to prove that the two triangles are congruent are:

Prove all three sets of corresponding angles are congruent.

Prove all three sets of corresponding sides are congruent.

Option C and Option D are the correct answer.

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Answers:

a) 32500

b) 0.00604

c)  2.4 * 10^6

d) 1.47 * 10^(-3)

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

Explanation:

The exponent over the 10 tells us how many spaces to move right or left.  If the exponent is positive, we move right. If negative, we move left. Think of a number line.

For part (a), the exponent is 4. So we move the decimal point 4 spaces to the right.

The 3.25 then becomes 32500

--------------

In part (b), the exponent -3 means we move 3 spots to the left to go from 6.04 to 0.00604

---------------

Part (c)

Place the decimal point between the first two digits and erase the zeros to get 2.4

Then we need to move the decimal point 6 spots to the right to get back to 2,400,000 again

Therefore we can say 2,400,000 = 2.4*10^6

---------------

Part (d)

Place the decimal point just after the first nonzero digit, and erase the zeros to the left to get 1.47

We must move the decimal point 3 spots to the left to go from 1.47 back to 0.00147 again

It means 0.00147 = 1.47*10^(-3)

Answer: he is right

Step-by-step explanation:

ANSWER

36°

EXPLANATION

A full circle has a central angle of 360°. If this figure represents 1/10 of a full circle, then its central angle is 1/10 of the central angle of the full circle:

Hence, the measure of the central angle in this figure is 36°.