1 3
Determine the quotient of 1---
3.5
1-
10
COTA
9
OIN
2-
5

Answer:

A.  A'(32, 16) B'(48, 16) C'(64, 48)

Step-by-step explanation:

Dilation is a transformation in geometry that changes the size of a figure while preserving its shape. It involves multiplying the coordinates of each point by a scale factor relative to a fixed center of dilation to create a new figure that is either larger or smaller than the original. The center of dilation serves as the fixed point around which the figure is expanded or contracted.

To dilate a figure where the center of dilation is the origin (0, 0), simply multiply each coordinate point by the scale factor.

In this case, as we have not been given a center of dilation, so we can assume it is the origin. The given scale factor is 4.

Given coordinates of the vertices of triangle ABC:

To find the new coordinates after dilation with the origin as the center of dilation, multiply each coordinate point by the scale factor of 4.

A' = (8 · 4, 4 · 4) = (32, 16)

B' = (12 · 4, 4 · 4) = (48, 16)

C' = (16 · 4, 12 · 4) = (64, 48)

Therefore, the new coordinates of the dilated triangle are:

Answer:

The answer is below

Step-by-step explanation:

Given that:

mean value (μ) = 12 cm and standard deviation (σ) = 0.04 cm

a) Since a random sample (n) of 16 rings is taken, therefore the mean (μx) ans standard deviation (σx) of the sample mean Xbar is given by:

\(\mu_x=\mu=12\ cm\\\sigma_x=\frac{\sigma}{\sqrt{n} }=\frac{0.04}{\sqrt{16} }=0.01\)

The sampling distribution of Xbar is centered about 12 cm and the standard deviation of the Xbar distribution is 0.01 cm

b) Since a random sample (n) of 64 rings is taken, therefore the mean (μx) ans standard deviation (σx) of the sample mean Xbar is given by:

\(\mu_x=\mu=12\ cm\\\sigma_x=\frac{\sigma}{\sqrt{n} }=\frac{0.04}{\sqrt{64} }=0.005\ cm\)

The sampling distribution of Xbar is centered about 12 cm and the standard deviation of the Xbar distribution is 0.005 cm

c) n = 16 and the raw score (x) = 11.95 cm

The z score equation is given by:

\(z=\frac{x-\mu_x}{\sigma_x} =\frac{x-\mu}{\sigma/\sqrt{n} } \\z=\frac{11.95-12}{0.04/\sqrt{16} }\\ z=-5\)

P(x > 11.95 cm) = P(z > -5) = 1 - P(z < -5) = 1 - 0.000001 ≅ 1 ≅ 100%

d) for n = 64, the standard deviation is 0.01 cm, therefore it is more likely to be within .01cm of 12cm

Using the normal distribution and the central limit theorem, it is found that:

a) The sampling distribution is approximately normal, centered at 12 cm and with a standard deviation of 0.01 cm.

b) The sampling distribution is approximately normal, centered at 12 cm and with a standard deviation of 0.005 cm.

c) 100% probability that the average diameter of piston rings from a sample size 16 is more than 11.95 cm .

d) Due to the lower standard error, the sample of 64 is more likely to be within 0.01 cm of 12 cm.

In a normal distribution with mean \(\mu\) and standard deviation \(\sigma\), the z-score of a measure X is given by:

\(Z = \frac{X - \mu}{\sigma}\)

In this problem:

Item a:

Sample of 16, thus \(n = 16\) and \(s = \frac{0.04}{\sqrt{16}} = 0.01\)

The sampling distribution is approximately normal, centered at 12 cm and with a standard deviation of 0.01 cm.

Item b:

Sample of 64, thus \(n = 64\) and \(s = \frac{0.04}{\sqrt{64}} = 0.005\)

The sampling distribution is approximately normal, centered at 12 cm and with a standard deviation of 0.005 cm.

Item c:

This probability is 1 subtracted by the p-value of Z when X = 11.95, thus:

\(Z = \frac{X - \mu}{\sigma}\)

By the Central Limit Theorem:

\(Z = \frac{X - \mu}{s}\)

\(Z = \frac{11.95 - 12}{0.01}\)

\(Z = -5\)

\(Z = -5\) has a p-value of 0.

1 - 0 = 1.

100% probability that the average diameter of piston rings from a sample size 16 is more than 11.95 cm .

Item d:

Due to the lower standard error, the sample of 64 is more likely to be within 0.01 cm of 12 cm.

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Answer:

27 minuets

Step-by-step explanation:

Answer:

5000=2000/1 hshshsjsnndjskbdjs

Answer:

r = 4.95046%              

r ≈ 4.95%                      

Answer:

d

Step-by-step explanation:

Luis traveled approximately 31,736.8 inches on his bicycle.

We have,

To find the distance that Luis traveled on his bicycle, we need to calculate the circumference of the tires and then multiply it by the number of complete turns.

Given:

Radius of the tires (r) = 20p (2.54) inches

Number of complete turns (n) = 50

The circumference of a circle can be calculated using the formula:

Circumference = 2πr

Substituting the given radius into the formula, we have:

Circumference = 2π * (20p) inches

Now we can calculate the distance traveled (d):

Distance = Circumference x Number of complete turns

Distance = 2π x (20p) x 50 inches

To simplify the calculation, we can approximate π as 3.14:

Distance ≈ 2 x 3.14 x (20 x 2.54) x 50 inches

Calculating this expression, we find:

Distance ≈ 31736.8 inches

Therefore,

Luis traveled approximately 31,736.8 inches on his bicycle.

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The complete question.

What is the distance that Luis traveled on his bicycle rolled 20p (2.54) after the tires gave 50 complete turns

Answer:

$45.60 per month

Step-by-step explanation:

She owes the dentist $342.00

you take $342.00 divided by 7.5(the amount of months)

and get $45.60 per month

Both planes have a speed of 340 miles per hour and 510 miles per hour, respectively.

In its most basic form, an equation is a mathematical statement that indicates that two mathematical expressions are equal. 3x + 5 = 14, for example, is an equation in which 3x + 5 and 14 are two expressions separated by a 'equal' sign. A mathematical statement made up of two expressions joined by an equal sign is known as an equation. 3x - 5 = 16 is an example of an equation. We get the value of the variable x as x = 7 after solving this equation.

Here,

Let tc be the time of commercial jet and tp be the time of private airplane.

Let vc be the speed of commercial jet and vp be the speed of private airplane.

Let dc be the distance of commercial jet and dp be the distance of private airplane.

now,

dc=dp

vc=vp+170

vc*tc=vp*tp

(vp+170)*1.2=vp*1.8

(vp+170)*2=vp*3

2vp+340=3vp

vp=340 miles/hour

vc=340+170

vc=510 miles/ hour

The speed, in miles per hour, of both airplanes is 340 miles per hour and 510 miles per hour.

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Case 1: a = 0; b = 0 --> Real Number

Case 2: a = 0; b ≠ 0 --> Non-Real Complex Number

Case 3: a ≠ 0; b = 0 --> Real Number

Case 4: a ≠ 0; b ≠ 0 --> Non-Real Complex Number

For each case, we can determine whether the expression a + bi represents a real number or a non-real complex number based on the values of a and b.

Case 1: a = 0; b = 0

In this case, both a and b are zero. The expression a + bi simplifies to 0 + 0i, which is equal to 0. Therefore, the expression represents a real number.

Case 2: a = 0; b ≠ 0

Here, a is zero, but b is nonzero. The expression a + bi becomes 0 + bi, where b is a nonzero real number multiplied by the imaginary unit i. Since the expression contains a nonzero imaginary part, it represents a non-real complex number.

Case 3: a ≠ 0; b = 0

In this case, a is nonzero, but b is zero. The expression a + bi simplifies to a + 0i, which is equal to a. As there is no imaginary part in the expression, it represents a real number.

Case 4: a ≠ 0; b ≠ 0

Here, both a and b are nonzero. The expression a + bi contains both a real part (a) and an imaginary part (bi). Thus, it represents a non-real complex number.

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The surface area of the cylinder is 905 square centimeters

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

Diameter, d = 12 cm

Height, h = 18 m

This means that

Radius, r = 12/2 = 6 cm

Using the above as a guide, we have the following:

Surface area = 2πr(r + h)

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

Surface area = 2π * 6 * (6 + 18)

Evaluate

Surface area = 905

Hence, the surface area is 905 square centimeters

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Answer:

b = -3 so A is answer

good luck

Answer:

option C is the correct answer

Answer: 83.2

x

11

−

166.4

x

Step-by-step explanation: Multiply  

104

by  

0.2

.

20.8

x

(

4

x

10

−

8

)

Apply the distributive property.

20.8

x

(

4

x

10

)

+

20.8

x

⋅

−

8

Simplify the expression.

Answer:

59

Solution

Equation 7x^2 + 2y=0

Where x=1,y=5

Put the value of x and y in equation

⟹(7×1)^2 + 2×5

⟹49+10

=59

Parallelograms and trapezoids are both two-dimensional shapes with four sides. While they share similarities, there are some key differences between the two that help to distinguish them from each other. In this essay, we will discuss the key differences between parallelograms and trapezoids and explore how these differences can help us to identify each shape.

A parallelogram is a two-dimensional shape with four sides and two sets of parallel lines. It is a quadrilateral with opposite sides parallel to each other and opposite angles equal. A parallelogram can also have opposite sides of equal length, which is known as a rhombus. Examples of shapes that are parallelograms include squares, rectangles, and rhombuses.

A trapezoid is also a two-dimensional shape with four sides. However, unlike a parallelogram, a trapezoid only has one set of parallel lines. The two non-parallel sides of a trapezoid are called the legs, while the two parallel sides are called the bases.

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Answer:

125

Step-by-step explanation:

it is the multiflication of 5 by itself 3 times (5×5×5=125)

The roster method of the set A' = {14, 15, 20}

The roster method is defined as a way to show the elements of a set by listing the elements inside of brackets.

A typical example of the roster method is to write the set of numbers from 1 to 5 as {1, 2, 3, 4, 5}.

Therefore,

U = universal sets = {14, 15, 16, 17, 18, 19, 20}

A = {16, 17, 18, 19}

Therefore, let's find A' as follows:

A' is the value not in A. Hence, in roster method.

A' = {14, 15, 20}

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The quantity of salt in the tank at time t is given by Q(t) = 640 (1 - e^(-t/40)) for 0 ≤ t ≤ 90.

To solve this problem, we need to use a differential equation to model the rate of change of the quantity of salt in the tank. Let Q(t) be the quantity of salt in the tank at time t.

Then, the rate of change of Q is given by:

dQ/dt = (rate of salt in) - (rate of salt out)

The rate of salt in is given by the concentration of salt in the incoming water, multiplied by the rate at which water is added to the tank:

rate of salt in = c * 2

The rate of salt out is given by the concentration of salt in the solution in the tank, multiplied by the rate at which water is leaving the tank:

rate of salt out = (Q(t) / (160 + 2t)) * 1

Putting these together, we get the following differential equation:

dQ/dt = 2c - (Q(t) / (160 + 2t))

To solve this differential equation, we can use separation of variables. Rearranging the equation, we get:

(160 + 2t) dQ/dt + Q(t) = 2c(160 + 2t)

Multiplying both sides by the integrating factor e^(2t/160), we get:

d/dt (e^(2t/160) Q(t)) = 2c e^(2t/160)

Integrating both sides with respect to t, we get:

e^(2t/160) Q(t) - Q(0) = 160c (e^(2t/160) - 1)

Solving for Q(t), we get:

Q(t) = Q(0) e^(-2t/160) + 160c (1 - e^(-2t/160))

Substituting Q(0) = 0, since there is no salt initially in the tank, we get:

Q(t) = 160c (1 - e^(-2t/160))

Finally, we can substitute c = 4, since the concentration of salt in the incoming water is 4 pounds per gallon.

Thus, the quantity of salt in the tank at time t is:

Q(t) = 640 (1 - e^(-t/40))

We can now use this formula to find Q(t) for 0 ≤ t ≤ 90:

Q(0) = 0

Q(90) = 640 (1 - e^(-90/40)) ≈ 908.22 pounds

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Kevin's error is that he incorrectly identified the vertex of the parabola as (3, 2) instead of (2, 3), which resulted to the parabola opens downward. The correct vertex is at (2, 3) and the parabola opens upward.

You are correct that the vertex of the parabola can be determined using the equation f(x) = a(x - h)² + k, where the vertex is at (h, k). In this case, we have f(x) = -(x-2)² + 3, so the vertex can be found by setting x - 2 = 0, which gives x = 2. Plugging this value into the equation,

we get f(2) = -(2-2)² + 3 = 3, so the vertex is at (2, 3).

However, your reasoning for why h is positive is not correct. The expression x - h represents the horizontal distance from the vertex to any point on the parabola. So if x is greater than h, then the expression x - h will be positive, and if x is less than h, then the expression x - h will be negative. In this case, the vertex is at (2, 3), so we have h = 2. This means that any point to the right of the vertex will have a positive value of x - h, while any point to the left of the vertex will have a negative value of x - h.

Therefore, the correct explanation of Kevin's error is that he incorrectly identified the vertex as (3, 2) instead of (2, 3), and as a result, he also incorrectly concluded that the parabola opens downward. In fact, the parabola opens upward because the coefficient of the x² term, -1, is negative.

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Dilation involves changing the size and the position of a shape

The value of x is 20

The scale factor from A to B is given as:

\(k = \frac 12\)

The corresponding side lengths of both figures are:

So, we have:

\(\frac{10}{x} = k\)

Substitute 1/2 for k

\(\frac{10}{x} = \frac{1}{2}\)

Cross multiply the above equation

\(x \times 1 = 10 \times 2\)

Multiply 2 by 10

\(x \times 1 =20\)

Multiply 1 and x

\(x =20\)

Hence, the value of x is 20

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After substituting the values as x=3 and y=7, the value of the expression "2x²-y¹+3x⁰" is 14.

In mathematics, an expression is a combination of numbers, variables, and mathematical operations (such as addition, subtraction, multiplication, and division) that can be simplified or evaluated to a numerical value.

To evaluate the expression 2x²-y¹+3x⁰ for x=3 and y=7, we substitute the given values, which are x=3 and y=7 into the expression and simplify:

On substituting the values,

We get,

= 2x² - y¹ + 3x⁰

= 2(3)² - 7¹ + 3(1)

= 2(9) - 7 + 3

= 18 - 7 + 3

= 14

Therefore, when x=3 and y=7, the value of the expression 2x²-y¹+3x⁰ is 14.

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The pattern for the sequence 1.3, 8.3, 27.3, 64.3,… is f(n) = (n)³.3

The pattern in the question is given as

1.3, 8.3, 27.3, 64.3,…

In the above expressions and pattern, we can see that

From the above, we have the following

Current term = (n)³.3

Note that the decimal does not represent product

And also the pattern is a geometric sequence

Hence, the pattern for the sequence is f(n) = (n)³.3

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Answer:

5 hours

Step-by-step explanation:

Subtract the amount the accountant charged for the 1st hour worked from the total earned:

127 - 35 = 92

Now divide 92 by 23 to find the number of hours he worked at the rate of $23 per hour:

92 ÷ 23 = 4 hours

Therefore, the account worked the 1st hour plus 4 more hours = 5 hours in total

Answer:

He got 1.9 pounds of sugar per dollar.

Step-by-step explanation:

Divide the amount of sugar by the amount of dollars paid.

Answer:

36

Step-by-step explanation:

By using Percentage , Profit distributed to Charity A is £ 624 and Charity B is £ 336

A figure or ratio stated as a fraction of 100 is called a percentage. Although the abbreviations "pct.", "pct.", and occasionally "pc" are also used, the percent symbol, "%," is frequently used to indicate it. A % is a number without dimensions and without a standard measurement.

The Latin phrase "per centum," which meaning "by the hundred," was the source of the English word "percentage." Fractions having a denominator of 100 are called percentages. In other words, it is a relationship where the value of the entire is always assumed to be 100.

Finding the percentage of a whole in terms of 100 is what percentage calculation refers to. A percentage can be found in one of two ways:

Total ticket sold = 800

Cost of each ticket is £ 2

Total fund raised (raw) = 2 * 800 = £1600

4% of the ticket won a prize of £20 each

so total number of tickets winning a prize = 4 % of 800 = 32

Total prize money distributed = 32 * 20 = £ 640

Total amount to distribute to charity = 1600 - 640 = £ 960

Total profit that goes to Charity A is = 65 % of 960 = £624

And rest to charity B is = £ 336

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Step-by-step explanation:

The formula:

�

�

=

�

2

(

�

1

+

�

�

)

S

n

=

2

n

(a

1

+a

n

)

is used to solve for the sum of the arithmetic sequence given the first term a₁, the number of terms n, and the last term in an.

Example:

3, 6, 9, 12, 15,...,123

The first term, a₁ = 3

The last term an = 123

Common difference, d = 3 (because the sequence are multiples of 3)

Number of terms, n= ?

Find the number of terms, n:

an = a₁ + (n-1) (d)

123 = 3 + (n-1) (3)

123 = 3 - 3 + 3n

123/3 = 3n/3

n = 41

To find the sum of the given sequence without adding 3 + 6 + 9, ... + 123, we use the formula:

S₄₁ = (41/2) (3 + 123)

S₄₁ = (41/2) (126)

S₄₁ = (41)(63)

S₄₁ = 2,583 ⇒ the sum of the given sequence

The exponential growth function is given as P(t) = P₀ * e^(rt). The estimated population of the city in 2018 is 7.74 million. The population of the city will be 10 million in approximately 16.7 years. The doubling time for the city population is 40.2 years

a) The exponential growth function is given as:

P(t) = P₀ * e^(rt)

where

P(t) is the population at time t,

P₀ is the initial population,

r is the growth rate (in decimal form), and e is Euler's number (approximately 2.71828).

Using the given values, we have:

P₀ = 6.54 million

r = 0.0172 per year

Therefore, the exponential growth function for the city's population is:

P(t) = 6.54 * e^(0.0172t)

b) To estimate the population of the city in 2018, we need to find the value of P(t) for t = 6 years (since 2012 to 2018 is a period of 6 years).

P(6) = 6.54 * e^(0.0172*6) = 7.74 million (rounded to two decimal places)

Therefore, the estimated population of the city in 2018 is 7.74 million.

c) To find when the population of the city will be 10 million, we need to solve the equation:

10 = 6.54 * e^(0.0172t)

Dividing both sides by 6.54, we get:

e^(0.0172t) = 10/6.54

Taking the natural logarithm of both sides, we get:

0.0172t = ln(10/6.54)

Solving for t, we get:

t = ln(10/6.54)/0.0172 = 16.7 (rounded to one decimal place)

Therefore, the population of the city will be 10 million in approximately 16.7 years.

d) The doubling time can be found using the formula:

t_double = ln(2)/r

where t_double is the doubling time and r is the growth rate.

Substituting the given value of r, we get:

t_double = ln(2)/0.0172 = 40.2 (rounded to one decimal place)

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