5. a square has a vertex at (-15,-9) and is dilated at the origin with a scale factor of 1/3
what is the new coordinate of the of the vertex?


(3,5)
(5,3)
(-3,-5)
(-5,-3)

Answer:

A

Step-by-step explanation:

Using the given formula for SA

SA = 2πr² + 2πrh ( r is the radius and h the height )

    = 2πr(r + h) ← factoring out 2πr from each term

    = 2π × 3 × (3 + 5)

    = 6π × 8

     = 48π in² → A

Answer:

3.3333333333333...

Step-by-step explanation:

5 (2/3) = 3.33333333333 (repeating decimal)

Also,

10 (2/3) = 6.66666666666666666 (repeating decimal)

6.66666666666666 / 2 = 3.33333333333333 (repeating decimal)

∈Answer:

x ≥ 7/2

Step-by-step explanation:

-2x + 7 ≤ 0

(-2x + 7) + (-7) ≤ -7

-2x + 7 - 7 ≤ -7

-2x ≤ -7

2x/2 ≥ 7/2

x ≥ 7/2

x ∈ [7/2,∞)

Answer:

The answer is C because its the only one that adds up correctly

None of the given expressions are equivalent to (4 + 9) - (3 . 2).

An expression contains one or more terms with addition, subtraction, multiplication, and division.

We always combine the like terms in an expression when we simplify.

We also keep all the like terms on one side of the expression if we are dealing with two sides of an expression.

Example:

1 + 3x + 4y = 7 is an expression.com

3 + 4 is an expression.

2 x 4 + 6 x 7 – 9 is an expression.

33 + 77 – 88 is an expression.

We have,

We can simplify the given expression as:

(4 + 9) - (3 . 2) = 13 - 3.2 = 9.8

Now, we can check which of the given expressions is equivalent to 9.8:

A.

(3 . 2) - (2.4) + (2.9) = 3.7

(not equivalent)

B.

(2 + 4) (2 + 9) -3 . 2 = 84.8

(not equivalent)

C.

2.4 +9 - 3.2 = 8.2

(not equivalent)

D.

2.4 + (2.9) - (2.3) = 3.0

(not equivalent)

Therefore,

None of the given expressions are equivalent to (4 + 9) - (3 . 2).

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The complete question.

Which of the expressions is equivalent to the one below?

Check all that apply.

(4 + 9) - (3 . 2)

A. (3 . 2) - (2.4) + (2.9)

B. (2 + 4) (2 + 9) -3 . 2

C. 2.4 + 9 - 3.2

D. 2.4 +  (2.9) - (2.3)

If there are 6 red blocks and 4 blue blocks and a child is arranging them in a row, then there will be total of 210 possible arrangements.

In this scenario, there are a total of 10 blocks (6 red and 4 blue).

To determine the number of different arrangements possible, you'll need to find the combinations of these 10 blocks.

Using the formula for combinations (n! / (r! (n-r)!)), where n is the total number of blocks and r is the number of one type (e.g. red):

Total possible arrangements = 10! / (6!4!) = 210

So, there are 210 different possible arrangements of the 6 red blocks and 4 blue blocks in a row.

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Answer:

\(-8.57\)

Step-by-step explanation:

\(-4.5+(-4.07)\\-4.5-4.07\\-8.57\)

Answer:

-8.57

Step-by-step explanation:

Simplify the expression

Answer:

3(x-1) 2 if x=4,99

3(499-1)2

3(4,98)2

14.94 + 2 =16.94

Step-by-step explanation:

The value of the equation 7a = 28 is a = 4

What is an Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

7a = 28

On simplifying the equation , we get

Divide by 7 on  both sides of the equation , we get

a = 28 / 7

a = 4

Therefore , the value of a is 4

Hence , The value of the equation 7a = 28 is a = 4

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5/7 = 35 kg

1/7 = 7 kg

Peter weighs 49 kg

49 - 8 = 41 kg

Ailen weighs 41 kg

49 + 41 = 90kg

Their total weight is 90 kg

Step-by-step explanation:

Use z-score table to find the z-score that corresponds to .7000   ( 70%)

approx   .525   s.d.  above the mean

  .525  * 10 =  5.25  points above 100   = 105.25

To solve the problem we will calculate the amount of food consumed by Deon's dog in 2.5 weeks.

The new bag of food will last for 2.5 weeks.

Given to us

To know the amount of food consumed by Deon dog in 2.5 weeks, we will multiply the food consumed by Deon dog in 1-week by the Number of weeks for which food is been consumed.

Food consumed by Deon dog in 2.5 weeks

= Food consumed by Deon dog in 1-week x Number of weeks

= 62 cups of dog food x 2.5

= 155 cups of dog food

Thus, the food consumed by Deon's Dog is 155 cups.

As we can see the Dog will consume 155 cups of dog food in 2.5 weeks, therefore, the new bag of food will last for 2.5 weeks.

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The volume of the soup pot is 226.08 cube inches.

Jayla bought the ingredients to make chicken soup, and wanted to make a double batch, which would be 12 cups of soup.

A quick search told her that this was 173.3 cubic inches. she hoped the soup pot below would be big enough.

The soup pot is 8 inches tall with a radius of 3 inches.

We have to find the volume of the soup pot.

Since the cup is in the shape of cylinder.

So the volume of cylinder = πr^2h

from the question, r = 3 inches and h = 8 inches

π = 3.14

The volume of cylinder = πr^2h

The volume of cylinder = 3.14 * (3)^2*(8)

The volume of cylinder = 226.08 cube inches

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The given expression, (2x + 3y), is directly proportional to (x + 5y) if and only if x is directly proportional to y.

To determine if (2x + 3y) is directly proportional to (x + 5y), we need to analyze the relationship between the variables x and y. If x is directly proportional to y, it means that as x increases or decreases, y will increase or decrease in the same ratio.

Let's assume that x is directly proportional to y. In this case, we can write x = ky, where k is the constant of proportionality. Now we substitute this expression into the given equation:

2(ky) + 3y = (ky) + 5y

Simplifying this equation, we get:

2ky + 3y = ky + 5y

Next, we combine like terms:

(2k + 3)y = (k + 5)y

For this equation to hold true for all values of y, the coefficients of y on both sides of the equation must be equal. Therefore, we can conclude that 2k + 3 = k + 5.

Solving this equation, we find:

2k + 3 = k + 5

k = 2

So, x = 2y, which confirms that x is directly proportional to y.

In summary, the expression (2x + 3y) is directly proportional to (x + 5y) if and only if x is directly proportional to y. This relationship holds true when x can be expressed as a constant multiple of y, with the constant of proportionality equal to 2.

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Answer:

The sale price is $12.

Step-by-step explanation:

M.P = $40

Discount % = 70

S.P = M.P - Discount

=> S.P = $40 - (70/100 x 40)

=> S.P = $40 - $28

=> S.P = $12

Hope you understood!!

The solution is given below.

An equation is a  mathematical statement that is made up of two expressions connected by an equal sign.  In its simplest form in algebra, the definition of an equation is a mathematical statement that shows that two mathematical expressions are equal. For instance, 3x + 5 = 14 is an equation, in which 3x + 5 and 14 are two expressions separated by an 'equal' sign.

here, we have,

The perimeter of a rectangle is 40 cm. The length is 14 cm.

Let x = width of the rectangle.

Ravi says he can find the width using the equation 2(x + 14) = 40.

Fran says she can find the width using the equation 2x + 28 = 40.

now, we get,

1. Divide both sides by 2

 2(x+14) = 40

 x+14 = 20

2. Isolate the x term by subtracting 14 from both sides

3. x = 6. The width of the triangle is 6 cm.

4. Isolate the x term by subtracting 28 from both sides

 2x + 28 = 40

 2x = 12

5. Divide both sides by 2

6. x = 6

7. The two equations have the same solution, because by the distributive rule, 2(x+14) = 2x+28.

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The translations to the parent function f(x) = x² to generate the function g(x) = (x - 1)² - 3 are given as follows:

A translation happens when either a figure or a function is moved horizontally or vertically on the coordinate plane.

The four translation rules for functions are defined as follows:

The changes to the parent function in this problem are given as follows:

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a. The continuous growth rate of the bacteria is 21%

b. The initial population of bacteria is 715

c. The culture will contain 2043 bacteria after 6 × 10⁻⁴ years

Since \(n(t) = 715e^{0.21t}\) represents the number of bacteria in the culture.

This function is similar to an exponential function of the form  \(y(t) = Ae^{\lambda t}\) where λ = growth rate

Comparing n(t) and y(t), we see that λ = 0.21

So, the continuous growth rate of the bacteria is 0.21 = 0.21 × 100 %

= 21%

So, the continuous growth rate of the bacteria is 21%

Since \(n(t) = 715e^{0.21t}\) represents the number of bacteria in the culture, the initial population of bacteria is obtained when t = 0.

So, \(n(t) = 715e^{0.21t}\)

\(n(0) = 715e^{0.21(0)} \\= 715e^{0} \\= 715 X 1\\= 715\)

So, the initial population of bacteria is 715

To find the time when the number of bacteria will be 2043, this means n(t) = 2043.

Since  \(n(t) = 715e^{0.21t}\)

Making t subject of the formula, we have

t = ㏑[n(t)/715]/0.21

So, substituting n(t) = 2043 into the equation, we have

t = ㏑[n(t)/715]/0.21

t = ㏑[2043/715]/0.21

t = ㏑[2.8573]/0.21

t = 1.05/0.21

t = 4.99

t ≅ 5 hours

Converting this to years, we have t = 5 h × 1 day/24h × 1 year/365 days

= 5/8760

= 5.7 × 10⁻⁴ years

≅ 6 × 10⁻⁴ years

So, the culture will contain 2043 bacteria after 6 × 10⁻⁴ years

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Answer:

The interest he will be paid in the first 4 years is $360

Step-by-step explanation:

The rule of the simple interest is I = Prt, where

∵ Bill deposits $3,000 into an account

∴ P = 3000

∵ The account pays simple interest at a rate of 3% per year

∴ r = 3% = 3 ÷ 100 = 0.03

∵ The time is 4 years

∴ t = 4

→ Substitute these values in the rule above

∵ I = 3000(0.03)(4)

∴ I = 360 dollars

∴ The interest he will be paid in the first 4 years is $360

We have shown that cX is exponential with parameter λ/c when X is an exponential random variable with parameter λ and c > 0.

To show that cX is exponential with parameter λ/c when X is an exponential random variable with parameter λ, and c>0, we will use the CDF method:

1. Define the transformation: Let Y = cX be a function of the random variable X, where c > 0.

2. Find the CDF of Y: We want to find P(Y ≤ y), which is equal to P(cX ≤ y) or P(X ≤ y/c).

3. Express CDF of Y in terms of X: Since P(X ≤ y/c) is the CDF of X at y/c, we have FY(y) = FX(y/c).

4. Find the PDF of X: The exponential distribution has the PDF fX(x) = λ * exp(-λx) for x ≥ 0.

5. Differentiate the CDF of Y to find its PDF: To find fY(y), we differentiate FY(y) with respect to y. Using the chain rule, we have:

fY(y) = d(FX(y/c))/dy = fX(y/c) * (1/c)

6. Substitute the PDF of X: Now, we replace fX(y/c) with its exponential form λ * exp(-λ(y/c)):

fY(y) = (λ * exp(-λ(y/c))) * (1/c)

7. Simplify the expression: fY(y) = (λ/c) * exp(-λ(y/c))

This is the PDF of an exponential distribution with parameter λ/c. Therefore, cX is exponential with parameter λ/c when X is an exponential random variable with parameter λ and c > 0.

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Answer:

C) 13x + 5x = 180

Step-by-step explanation:

The angles are supplementary

If they eat 3000 calories per day, the z score will be 3.33

To calculate the z-score, we can use the formula:

z-score = (x - μ) / σ

Where:

x is the value we want to convert to a z-score (in this case, 3000 calories per day)

μ is the mean (average) value of the distribution (in this case, 2000 calories per day)

σ is the standard deviation of the distribution (in this case, 300 calories per day)

Substituting the values, we get:

z-score = (3000 - 2000) / 300

z-score = 1000 / 300

z-score = 3.33

Therefore, if someone eats 3000 calories per day and the average amount of calories eaten per day is 2000, with a standard deviation of 300, their z-score would be 3.33.

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To calculate the mean absolute deviation (MAD) of the test scores for this sample, follow these steps:

Find the mean (average) of the test scores:

Mean = (95 + 65 + 70 + 70 + 85 + 90 + 100 + 40 + 75 + 80) / 10

= 750 / 10

= 75

Find the absolute deviation for each test score by subtracting the mean from each score and taking the absolute value:

Absolute Deviation = |Score - Mean|

Absolute Deviation for each score:

|95 - 75| = 20

|65 - 75| = 10

|70 - 75| = 5

|70 - 75| = 5

|85 - 75| = 10

|90 - 75| = 15

|100 - 75| = 25

|40 - 75| = 35

|75 - 75| = 0

|80 - 75| = 5

Calculate the sum of the absolute deviations:

Sum of Absolute Deviations = 20 + 10 + 5 + 5 + 10 + 15 + 25 + 35 + 0 + 5

= 130

Find the MAD by dividing the sum of the absolute deviations by the number of scores (10 in this case):

MAD = Sum of Absolute Deviations / Number of Scores

= 130 / 10

= 13

Therefore, the mean absolute deviation (MAD) of the test scores for this sample is 13.

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a. there are 524,288 frames in the system. b. the maximum number of frames is determined by the number of bits required to represent the page number, and the number of pages that can be addressed is limited by the size of the logical address space. c. 3 bits are needed to represent the page number 8, and 12 bits are needed to represent the offset 12.

a) The system has 524,288 frames. This can be calculated by dividing the maximum size of the logical address space (1MB) by the size of each frame (4KB).

1MB = 2^20 bytes

4KB = 2^12 bytes

Number of frames = (1MB / 4KB) = (2^20 / 2^12) = 2^(20-12) = 2^8 = 256

Therefore, there are 524,288 frames in the system.

b) The maximum number of frames that can be allocated to a process in this system is 256. This is because the maximum number of frames is determined by the number of bits required to represent the page number, and the number of pages that can be addressed is limited by the size of the logical address space.

c) i. The page number 8 can be represented using 3 bits. This is because there are 2^3 = 8 possible page numbers (0 to 7).

ii. The offset 12 can be represented using 12 bits. This is because there are 2^12 = 4,096 possible offsets (0 to 4,095).

Therefore, 3 bits are needed to represent the page number 8, and 12 bits are needed to represent the offset 12.

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Total Productive Maintenance (TPM) practices ensure D. equipment downtime is maximized

According to TPM, operators are in charge of sanitizing, enhancing, and maintaining their workstations to guarantee quality and safety throughout production cycles. The objective of TPM is to maintain equipment in top working order to ensure that production processes go without hiccups or delays.

Through the optimization of equipment availability and performance, TPM seeks to increase overall productivity and quality. The 5S methodology, a method of workforce organization that aids in streamlining and standardizing facility procedures, is the foundation on which TPM is based.

Therefore, the correct option is D.

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Answer: x + 1/4 = 1

Step-by-step explanation: the sum of something is to add and if you are adding 1/4 to x they need to be on the same side and “is” is a good indicator of where or when the equal sign needs to go.

Answer:

x + 1/4 = 1

x = 3/4

Step-by-step explanation:

If the directions are to write an equation, then you get:

x + 1/4 = 1

"Sum" means adding.

If you are also asked to solve, then subtract 1/4 from both sides of the equation.

x + 1/4 = 1

x = 1 - 1/4

x = 3/4

Answer:

6

Step-by-step explanation:

it is a8=a1 +(n-1)x d

41=-1+ 7xd

42/7=d

d=6

Answer: 6

Step-by-step explanation:

\(a_1=-1\ \ \ \ \ \ \ \ a_8=41\ \ \ \ \ \ \ \ d=?\\\\\boxed{a_n=a_1+d(n-1)}\\\\Hence,\\\\a_8=-1+d(8-1)\\\\41=-1+7d\\\\41+1=-1+7d+1\\\\42=7d\\\\\)

Divide both parts of the equation by 7:

6=d

Thus, d=6

Answer:

Is this what you meant?

(2x + 3x) × (3 + 15) = 12x + 36

(5x) × (18) = 12x + 36

90x = 12x + 36

78x = 36

x = 36 / 78

x = 18 / 39

_____________________

or

3(2x+3x) + 15 = 12x + 36

10x + 15 = 12x + 36

-21 = 2x

2x = -21

x = -21/2

Answer:

Hence the greatest number of books that could be on the shelf is 30.

Step-by-step explanation:

Step 1:-

Here the given number of books is m,  

m < 45.  

If they are arranged into piles of five books, each no books would remain.  

m is divisible by 5.  

The last digit of m would be 5 or 0.    

The same number of books, when arranged with piles of 7 books each, two books remain.  

m-2 is divisible by 7.  

Step 2:-  

The last digit of m is 5 or 0.  

m-2 will have the last digit 3 or 8.    

Multiples of 7 are 7,14,21,28,35, 42;  

among which only number 28 has the last digit 8 or 3.    

m - 2 = 28  

m = 30  

The greatest number of books that could be on the shelf is 30.

1. The volume of the given solid is ∫[0,1] (3 - tan^(-1)(-x))² dx. 2. The volume of the given solid is (√3/4) × (b - a)³. 3. The volume of the given solid is (π/12) × [(8 - b)³ - (8 - a)³].

1. To find the volume of the solid with square cross sections, we need to integrate the area of the square cross sections over the interval from x = 0 to x = 1.

The equation y = tan⁻¹(-x) bounds the upper side of the square, while the line y = 3 bounds the lower side. Since each cross section is a square, the side length of the square is given by the difference between these two y-values.

The height of the square cross section is dx, as the cross sections are perpendicular to the x-axis.

Therefore, the volume (V) of the solid can be calculated by integrating the area of the square cross sections:

V = ∫[0,1] (3 - tan⁻¹(-x))² dx

Simplifying the integral is not straightforward, and there isn't a closed-form solution. However, you can approximate the integral using numerical methods such as the trapezoidal rule or Simpson's rule.

2. To find the volume of the solid with equilateral triangle cross sections, we need to integrate the area of the equilateral triangles over the given region.

The equation y = 2x - x² bounds the upper side of the equilateral triangle, while the x-axis bounds the lower side. The height of the equilateral triangle is the y-value of the curve at a given x.

The base of the equilateral triangle is given by the difference between the x-values of the region.

Therefore, the volume (V) of the solid can be calculated by integrating the area of the equilateral triangle cross sections:

V = ∫[a,b] [(side length)² × (√3)/4] dx

The side length of the equilateral triangle can be determined by taking the difference between the x-values of the region

side length = b - a

Substituting the values into the equation, we have:

V = ∫[a,b] [(b - a)² × (√3)/4] dx

= (√3/4) × (b - a)² × (b - a)

Therefore, the volume of the solid is (√3/4) × (b - a)³ cubic units.

3. Since the cross sections perpendicular to the x-axis are semicircles, the volume of the solid can be calculated by integrating the area of the semicircle cross sections over the given region.

The equation x + 2y = 8 can be rewritten as y = (8 - x)/2, which represents the upper boundary of the semicircle.

The x-axis represents the lower boundary of the semicircle.

The radius of the semicircle at a given x is given by the y-value of the upper boundary.

Therefore, the volume (V) of the solid can be calculated by integrating the area of the semicircle cross sections:

V = ∫[a,b] [(π × r²)/2] dx

The radius of the semicircle can be determined by taking the y-value of the upper boundary:

r = (8 - x)/2

Substituting the values into the equation, we have:

V = ∫[a,b] [(π × (8 - x)²)/4] dx = (π/4) × [(8 - x)³/3] evaluated from a to b = (π/4) × [(8 - b)³/3 - (8 - a)³/3]

Therefore, the volume of the solid is (π/12) × [(8 - b)³ - (8 - a)³] cubic units.

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-- The given question is incomplete, the complete question is

"1. The base of a solid is the region in the first quadrant bounded by the y-axis, the graph of