Question 1 of 10
An electric company calculates a person's monthly bill from the number of
kilowatt-hours (kWh), x, used.
The function b(x) = { 0.15(2-200) +20, 200
x <
x>
bill.
determines the
How much is the bill for a person who uses 600 kWh in a month?

Answer:

100$

Step-by-step explanation:

Answer:$100

Step-by-step explanation:

Answer:

\(z = -3\)

Step-by-step explanation:

Given

\(z^2 +11z+9 = 5z\) --- the correct equation

Required

Solve

Equate to 0

\(z^2 +11z-5z+9 = 0\)

\(z^2 +6z+9 = 0\)

Expand

\(z^2 +3z+3z+9 = 0\)

Factorize

\(z(z +3)+3(z+3) = 0\)

Factor out z + 3

\((z +3)(z+3) = 0\)

Split

\(z + 3 =0\) --- twice

\(z = -3\)

Each friend had originally 13 action figures before buying 11 more.

Given that there are 5 friends and each of them has x action figures in his or her collection. When they buy 11 more action figures, the total number of action figures they will have is 120.

a) We need to find an equation that models the problem. Let x be the original number of action figures that each friend had.

Therefore, the total number of action figures that each friend will have after purchasing 11 more is x + 11.

The total number of action figures will be 5(x + 11) = 5x + 55.

Now, according to the problem,5x + 55 = 120

This is our equation that models the problem.

b) We have to solve the equation 5x + 55 = 120 to find the original number of action figures, x, that each friend had before buying 11 more action figures.

5x + 55 = 120

5x = 120 - 55 (subtract 55 from both sides)

5x = 65x = 13

Therefore, each friend had originally 13 action figures before buying 11 more.

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Therefore, the interest portion of the seventh payment is:7,000 x (1 + r + r2 + r3 + r4 + r5 + r6) / r7 - 7,000.

We have the following payments and their corresponding times of payment:At the end of year 1: $1,000At the end of year 2: $2,000At the end of year 3: $3,000At the end of year 4: $4,000At the end of year 5: $5,000At the end of year 6: $6,000At the end of year 7: $7,000

At the end of year 8: $8,000At the end of year 9: $9,000At the end of year 10: $10,000The present value of these payments is:PMT x [(1 - (1 + r)-n) / r]where PMT is the payment, r is the interest rate per year, and n is the number of years till payment.

For the first payment (end of year 1), the present value is:1,000 x [(1 - (1 + r)-1) / r]which equals

1,000 x (1 - 1 / (1 + r)) / r = 1,000 x ((1 + r - 1) / r) = 1,000

For the second payment (end of year 2), the present value is:2,000 x [(1 - (1 + r)-2) / r]which equals 2,000 x (1 - 1 / (1 + r)2) / r = 2,000 x ((1 + r - 1 / (1 + r)2) / r) = 2,000 x (1 + r) / r2

For the seventh payment (end of year 7), the present value is:

7,000 x [(1 - (1 + r)-7) / r]

which equals

7,000 x (1 - 1 / (1 + r)7) / r = 7,000 x ((1 + r - 1 / (1 + r)7) / r) = 7,000 x (1 + r + r2 + r3 + r4 + r5 + r6) / r7

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Answer:

650 x 1.07 = 695.5.......

compute is an electronic devices

Answer:

Step-by-step explanation:

32 out of 40 did not show

8 out of 40 did show

When you ask "What is 8 out of 40?" you want to know what percent 8 is out of 40.

Here are step-by-step instructions showing you how we calculated 8 out of 40 as a percentage:

The first step is to divide 8 by 40 to get the answer in decimal form:

8 / 40 = 0.2000

Then, we multiplied the answer from the first step by one hundred to get the answer as a percentage:

0.2000 * 100 = 20.00%

Answer:

20 %

Step-by-step explanation:

Answer: 0.4. Because 2 divided by five is 0.4

Answer:

y = 1 and y = 5

Step-by-step explanation:

\(( 3 y -9)^2 + 7 = 43\\\\((3y)^2 + (-9)^2 + 2(3y)(-9)) = 43 - 7\\\\(9y^2 + 81 -54y) = 36\\\\9y^2 -54y + 81 -36 = 0\\\\9y^2 -54y + 45 = 0\\\\9(y^2 -6y + 5) = 0\\\\y^2 - 6y + 5 = 0\\\\y^2 - 5y - y + 5 = 0\\\\y(y - 5) -1(y - 5 ) = 0 \\\\( y - 1 )( y - 5) = 0\\\\y = 1 \ , \ y = 5\)

The values of y in the equation (3y-9)^2+7 = 43 are 1 and 5

The equation is given as:

(3y-9)^2+7 = 43

Subtract 7 from both sides of the equation

(3y - 9)^2 = 36

Take the square root of both sides

3y - 9 = ±6

Add 9 to both sides

3y = 9 ± 6

Divide through by 3

y = 3 ± 2

Expand

y = (3 - 2 or 3 + 2)

Evaluate

y = 1 or 5

Hence, the values of y are 1 and 5

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Answer:

The perimeter of a rectangle is the sum of twice the length and twice the width. If the perimeter is at least 48 cm, then the minimum perimeter is 48 cm.

Let width = x

Let length = x + 4

Perimeter = 48

We can set an inequality for perimeter using the variables.

2x + 2(x + 4) ≥ 48

Solve for x.

2x + 2x + 8 ≥ 48

4x + 8 ≥ 48

4x ≥ 40

x ≥ 10

Substitute this value of x into the variable to get your width and length.

width = 10 cm

length = 14 cm

Step-by-step explanation:

hope it helps

The image of the points are X'(3, 0), Y'(-4, -1), Z'(2, -5)

From the question, we have the following parameters that can be used in our computation:

(90°, 0) (AXYZ) for X(0, 3), Y(1, -4), Z(5, 2)

This means that we rotate the points clockwise by 90 degrees

This is represented as

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

Substitute the known values in the above transformation rule, so, we have the following representation

X'(3, 0), Y'(-4, -1), Z'(2, -5)

So, the image are X'(3, 0), Y'(-4, -1), Z'(2, -5)

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The area of a square inscribed in a circle is 25, then the area of the circle is 25π/2 or approximately 39.27 square units.

To solve this problem, we can use the relationship between the area of a square inscribed in a circle and the area of the circle itself.

When a square is inscribed in a circle, the diagonal of the square is equal to the diameter of the circle. Let's assume that the side length of the square is 's' and the radius of the circle is 'r'.

We are given that the area of the square is 25, so we can find the side length of the square:

Area of square = \(s^2 = 25\)

Taking the square root of both sides, we get:

s = √25 = 5

Since the diagonal of the square is equal to the diameter of the circle, we can find the diameter of the circle:

Diagonal = Diameter = s√2 = 5√2

The radius of the circle is half the diameter, so:

Radius = 5√2 / 2 = (5√2)/2

Now, we can calculate the area of the circle using the formula:

Area of circle = \(\pi r^2\)

Substituting the value of the radius, we get:

Area of circle = π((5√2)/\(2)^2\) = π(25/2) = 25π/2

Therefore, the area of the circle is 25π/2 or approximately 39.27 square units.

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Answer:

320

Step-by-step explanation:

4,800 ÷ 15 = 320

Checking this

15 × 320 = 4,800

Given:

Amount he earns per hour = $17

Cost of new shirt = $25

Amount left = $825

Let's find the number of hours Stephen worked this week.

Let's first write a linear equation representing this situation.

Apply the slope-intercept form:

y = mx + b

Thus, we have the equation:

825 = 17h - 25

Now, let's solve for h.

Add 25 to both sides of the equation:

825 + 25 = 17h - 25 + 25

850 = 17h

Divide both sides by 17:

Therefore, Stephen worked 50 hours this week.

ANSWER:

• Equation:

17h - 25 = 825

• Number of hours worked:

50 hours

Step-by-step explanation:

1 15625 m

2 13824 m

3 343 m

4 14167 m

5 cube with 25 m

A. P(6, then 1) = 1/90

B. P(even, then 5) = 1/18

C. P(8, then odd) = 1/18

D. P(3, then prime) = 2/45

E. P(prime, composite) = 4/15

F. P(even, then 3, then 5) = 1/144

Given:

Total number of cards: 10

A. P(6, then 1):

P(6, then 1) = 1/10 x 1/9

= 1/90

B. P(even, then 5):

Number of favorable outcomes: 5 x 1 = 5

P(even, then 5) = 5/10 x 1/9

= 1/18

C. P(8, then odd):

Number of favorable outcomes: 1 x 5 = 5

P(8, then odd) = 1/10 x 5/9

= 1/18

D. P(3, then prime):

Number of favorable outcomes: 1 x 4 = 4

P(3, then prime) = 1/10 x 4/9

= 2/45

E. P(prime, composite):

Number of favorable outcomes: 4 x 6 = 24

P(prime, composite) = 4/10 x 6/9

= 4/15

F. P(even, then 3, then 5):

Number of favorable outcomes: 5 x 1 x 1 = 5

P(even, then 3, then 5) = 5/10 x 1/9 x 1/8

= 1/144

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Answer:

Line A.

Step-by-step explanation:

When you put x as zero into 3x-2, you get 3(0)-2. That equals -2. Therefore, y = -2. When x=0, that is the y-intercept, so the y-intercept is -2. Line A crosses the y-axis at -2, so line A has that y-intercept.

Slope is always y/x. On a graph, that is the number of squares UP over the number of squares ACROSS. Counting, we get, 3 squares up over 1 square across for line A. 3/1= 3. The slope is the number we multiply by x. In the equation, that is 3, because we see 3x, and no sign or space between 2 numbers automatically means we multiply. So line A also has the correct slope.

In linear equations (straight lines), the same slope and y-intercept are enough to tell you that the equation matches the line.

Therefore, the answer is A!

Answer:111

Step-by-step explanation:

1111

Answer:

n=20 \( \sum x = 493, \sum y = 60.5, \sum xy= 1553.01, \sum x^2 =12775, \sum y^2 =192.021\)  

And in order to calculate the correlation coefficient we can use this formula:

\(r=\frac{n(\sum xy)-(\sum x)(\sum y)}{\sqrt{[n\sum x^2 -(\sum x)^2][n\sum y^2 -(\sum y)^2]}}\)

\(r=\frac{20(1553.01)-(493)(60.5)}{\sqrt{[20(12775) -(493)^2][20(192.021) -(60.5)^2]}}=0.8237\)

And then the determination coeffcient would be:

\( r^2 = 0.8237^2= 0.6785 \approx 0.679\)

Step-by-step explanation:

College GPAs ACT Score, x

16 18 24  25  34  27  29  25  30  21  17  21  28  31  35  18  17  26  28 23

College GPA, y

1.85  2.20  2.80  3.50  4.00  3.18  3.90  2.90  4.00  2.60  2.50  3.65  3.10  3.72  3.24  2.30  1.70  3.10  3.50  2.76

From the info given we can calculate the following sums:

n=20 \( \sum x = 493, \sum y = 60.5, \sum xy= 1553.01, \sum x^2 =12775, \sum y^2 =192.021\)  

And in order to calculate the correlation coefficient we can use this formula:

\(r=\frac{n(\sum xy)-(\sum x)(\sum y)}{\sqrt{[n\sum x^2 -(\sum x)^2][n\sum y^2 -(\sum y)^2]}}\)

\(r=\frac{20(1553.01)-(493)(60.5)}{\sqrt{[20(12775) -(493)^2][20(192.021) -(60.5)^2]}}=0.8237\)

And then the determination coeffcient would be:

\( r^2 = 0.8237^2= 0.6785 \approx 0.679\)

Answer:

volume = 33.5 in³

Step-by-step explanation:

Formula:

\(\sf volume \ of \ a \ cone=\dfrac13\pi r^2h\)

Given:

Substituting the given values into the formula:

\(\sf \implies volume=\dfrac13 \times 3.14 \times 2^2 \times 8\)

                  \(=\dfrac13 \times 3.14 \times 4 \times 8\)

                  \(\sf =33.49333333...\)

                  \(\sf =33.5 \ in^3 \ (nearest \ tenth)\)

The interval of the graph at which Susan is running fastest is from point A ( 0 , 0 ) to B ( 10 , 3 )

Given data ,

Susan is running a 5k race. The graph of distance vs. time is shown

So , the slope of the first line is m₁

And , the slope of the second line is m₂

where the points are A ( 0 , 0 ) , B ( 10 , 3 ) , C ( 20 , 4 )

Now , slope of AB is

m₁ = ( 3/10 ) = 0.3

And , m₁ = 0.3 kilometers per minute

And , slope of BC is

m₂ = ( 4 - 3 ) / ( 20 - 10 )

m₂ = 1/10

m₂ = 0.1 kilometers per minute

Therefore , the interval is fastest at second line from B ( 10 , 3 ) , C ( 20 , 4 )

Hence , Susan is running fastest is from point A ( 0 , 0 ) to B ( 10 , 3 )

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The value of p is 15

The unitary method is a method in which you find the value of a unit and then the value of a required number of units.

Given here: Davey reads 58 pages on Saturday and on rest of the days p pages per day

Therefore everyday he reads 58+p pages per day

If he reads for 10 days and he reads a total 1408 pages then we have

In a week there is one Saturday

thus

9p+58=1408

9p=1350

p=15

Thus on the other days p is equal to 15 pages per day.

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The complete question is Davey reads 58 pages on Saturday and p pages on other days and on a span of 10 days he reads 1408 pages. Find the value of p.

A line segment cannot have two distinct mid points.

The midpoint of a line is the middle point of a line segment.

It is equidistant from both endpoints, and it is the centroid both of the segment and of the endpoints.

for external division: (x,y) = ([(mx2 + nx1) / (m + n )], [(my2 + ny1)/(m+n)])

for internal division: (x, y) = ([(mx2 - nx1) / (m -n)], [(my2 - ny1)/(m - n)])

where;

Thus, a line segment cannot have two distinct mid points.

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For a given function f(x) we define the domain restrictions as values of x that we can not use in our function. Also, for a function f(x) we define the inverse g(x) as a function such that:

g(f(x)) = x = f(g(x))

The restriction is:

x ≠ 4

The inverse is:

\(y = 4 + \sqrt{\frac{11}{x} }\)

Here our function is:

\(f(x) = \frac{11}{(x - 4)^2}\)

We know that we can not divide by zero, so the only restriction in this function will be the one that makes the denominator equal to zero.

(x - 4)^2 = 0

x - 4 = 0

x = 4

So the only value of x that we need to remove from the domain is x = 4.

To find the inverse we try with the general form:

\(g(x) = a + \sqrt{\frac{b}{x} }\)

Evaluating this in our function we get:

\(g(f(x)) = a + \sqrt{\frac{b}{f(x)} } = a + \sqrt{\frac{b*(x - 4)^2}{11 }}\\\\g(f(x)) = a + \sqrt{\frac{b}{11 }}*(x - 4)\)

Remember that the thing above must be equal to x, so we get:

\(g(f(x)) = a + \sqrt{\frac{b}{11 }}*(x - 4) = x\\\\{\frac{b}{11 }} = 1\\{\frac{b}{11 }}*4 - a = 0\)

From the two above equations we find:

b = 11

a = 4

Thus the inverse equation is:

\(y = 4 + \sqrt{\frac{11}{x} }\)

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Answer:

B

Step-by-step explanation:

E2021 on god

Answer:

Step-by-step explanation:

it would be "c" because the question asks for the number that makes the inequality true

4x≤ x+3

the graph in c is saying that every number that is 1 or less than 1 makes the inequality true. so lets take -7 as an example

4 x -7=-28

-28+3=-25

-25 is greater than -28 so the inequality is true. the reason why graph d doesnt work is because if we plug in 2 into the equation, then 4x =8 and x+3=5

5 is not greater than 8 so it doesnt work

480 m³ is the volume of the given solid.

What is Volume?

The space that any three-dimensional solid occupies is known as its volume. These solids can take the form of a cube, cuboid, cone, cylinder, or sphere.

The dimensions of the trapezoidal prism are given in the diagram.

The dimensions of the cuboidal cavity are also given.

Volume of the solid = Volume of trapezoidal prism - Volume of cuboidal cavity

Volume of trapezoidal prism = (1/2)[Sum of parallel sides][h]×length

= (1/2)×[13+8]×[5]×10

= 525 m³

Volume of cuboidal cavity = l×b×h

= 10×3×1.5

= 45 m³

Volume of the solid = 525 - 45 m³

= 480 m³

The volume of the solid is 480 m³.

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The coordinates of point P are (5, -3.5). The equation of the circle is \((x - 5)^2 + (y + 3.5)^2 = 1.5^2\). The equation of KL is y = (-4/3)x + 22/3.

To find the coordinates of point P, we can first find the midpoint of MN, which is the center of the circle. The midpoint formula is given by:

Midpoint = ( (x1 + x2) / 2 , (y1 + y2) / 2 )

Using the coordinates of M(3,-5) and N(7,-2), we can calculate the midpoint:

Midpoint = ( (3 + 7) / 2 , (-5 + -2) / 2 ) = (5, -3.5)

Since the midpoint of MN is the center of the circle, the coordinates of P will be the same as the coordinates of the center, which are (5, -3.5).

i. To determine the equation of the circle in the form of \((x-a)^2\) + \((y-b)^2\) = \(r^2\), we can use the center and any point on the circle. We can use point N(7,-2), which lies on the circle.

The radius of the circle is half the length of PN. Therefore, the radius is given by:

Radius =\(1/2 * \sqrt((7 - 5)^2 + (-2 - (-3.5))^2) = 1.5\)

Substituting the values into the equation, we get:

\((x - 5)^2 + (y + 3.5)^2 = 1.5^2\)

ii. To determine the equation of KL in the form of y = mx + c, we can use the slope of the tangent line.

The slope of KL can be calculated as the negative reciprocal of the slope of the radius line MN. The slope of MN is given by:

m = (y2 - y1) / (x2 - x1) = (-2 - (-3.5)) / (7 - 5) = 1.5 / 2 = 0.75

The negative reciprocal of 0.75 is -4/3, which represents the slope of KL.

Using the point N(7,-2) and the slope -4/3, we can use the point-slope form of a line to find the equation of KL:

y - (-2) = (-4/3)(x - 7)

y + 2 = (-4/3)x + 28/3

y = (-4/3)x + 22/3

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Answer:

\(k = \frac{1}{5}\)

Step-by-step explanation:

Given

The attached triangles

Required

The scale factor

From the attachment, we have:

\(TU = 4\)

\(QR = 20\)

So, the scale factor from PQR to STU is:

\(k = \frac{TU}{QR}\)

\(k = \frac{4}{20}\)

\(k = \frac{1}{5}\)

Another name for the set of all x-values for a relation is: domain.

The domain of a relation can be defined as all the x-values that corresponds to the y-values that are plotted on a graph.

They are referred to as the input or the domain of the relation. Therefore, another name for the set of all x-values plotted for a relation on a graph is: domain.

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