What number could be a common denominator for these two fractions?
3/10 and 1/5

You can tell if a table shows a proportional relationship by calculating the ratio of each pair of values.

The table depicts a proportionate relationship if all of those ratios are the same.

If all of the ratios of the variables are equal, then there is a proportional link between the two variables.

In proportional relationships, one variable is, in other words, always a constant value multiplied by the other variable. The proportionality constant is the name given to the constant value. A mathematical equation of the form y=kx, where k is the proportionality constant, can be used to model any proportional relationships. The unit rate is another name for the proportionality constant.

Dustin, for instance, spends $8 each month for a music streaming service. The total cost of the service, c, and the number of months Dustin pays for the streaming service, m, are proportionate. 

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Answer:

17

Step-by-step explanation:

add the exponents

The solution to the equation is x = 16/11.

what is algebra?

Algebra is a branch of mathematics that deals with mathematical operations and symbols used to represent numbers and quantities in equations and formulas. It involves the study of variables, expressions, equations, and functions.

Diego's mistake is in the step where he subtracts 3x from both sides of the equation. The correct subtraction should be 28, not 12.

Here's the correct solution:

4(7 - 2x) = 3(x + 4)

28 - 8x = 3x + 12

28 - 12 = 3x + 8x

16 = 11x

x = 16/11

Therefore, the solution to the equation is x = 16/11.

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Answer:

A) = 4.

B) = 25.

C) = 4.

Step-by-step explanation:

We are given that a and b are positive integers and that:

\(a-b=2\)

And we want to evaluate the following expressions.

Expression A)

We have:

\(\displaystyle \frac{2^a}{2^b}\)

This is equivalent to:

\(=2^a\div 2^b\)

Therefore:

\(=2^{a-b}\)

Substitute and evaluate:

\(=2^{(2)}=4\)

Expression B)

We have:

\(\displaystyle \frac{5^a}{5^b}\)

This is equivalent to:

\(=5^{a-b}\)

Again, substitute and evaluate:

\(=5^{(2)}=25\)

Expression C)

Lastly, we have:

\(\displaystyle \frac{4^{0.5a}}{2^b}\)

Note that 4 = 2². Hence:

\(=\displaystyle \frac{(2)^{2(0.5a)}}{2^b}\)

Simplify:

\(=\displaystyle \frac{2^a}{2^b}\)

Using the previous result:

\(=4\)

Answer:

c=4

Step-by-step explanation:

becus rsm said it was correct

To answer this question, we can proceed as follows:

We have that the complete way to obtain this division is that the quotient is equal to 1.38.

However, in a division in which we have the remainder, we can express this division as:

D = d * C + R

Where

D is the dividend (69)

d is the divisor (50)

C is the quotient.

R is the remainder

So having the remainder, and not having decimals part in the division, we can say that this division is equal to:

69 = 50 * 1 + 19.

We can express this as follows:

69 is the Dividend, 50 is the divisor, 1 is the quotient, and 19 is the remainder.

Therefore, the division 69 / 50 = 1 + 19. We can divide the number 69 by 50 and we have that we can divide it in 1, but we have 19 as the remainder, then we have:

69 = 50 * 1 + 19

Answer:

a. center (3,6) –> (h,k)

point (0,-2) –> (x,y)

(x-h)²+(y-k)²=r²

(0-3)²+(-2-6)²=r²

(-3)²+(-8)²=r²

9+64=r²

r²=73

(x-h)²+(y-k)²=r²

(x-3)²+(y-6)²=73

____o_o___

b. center (-4,-2) –> (h,k)

radius =9 –> r

(x-h)²+(y-k)²= r²

(x-(-4))²+ (y-(-2))²= 9²

(x+4)²+(y+2)²=81

____o_o___

c. (2,5) –> (x1 , y1)

(-10,7) –> (x2,y2)

\(( \frac{x1 + x2 }{2} , \frac{y1 + y2}{2} ) \\ \\ ( \frac{2 + ( - 10)}{2} ,\frac{5 + 7}{2} ) \\ \\ ( \frac{ - 8}{2} , \frac{12}{2} ) = ( - 4,6)\)

center (-4,6) –> (h,k)

(2,5) –> (x, y)

\( {(x - h)}^{2} + (y - k)^{2} = {r}^{2} \\ (2 - ( - 4)) ^{2} + {(5 - 6)}^{2} = {r}^{2} \\ ({6})^{2} + {( - 1)}^{2} = {r}^{2} \\ 36 + 1 = {r}^{2} \\ {r}^{2} = 37\)

\( {(x - h)}^{2} + {(y - k)}^{2} = {r}^{2} \\ (x - ( - 4)) ^{2} + {(y - 6)}^{2} = {r}^{2} \\ (x + 4)^{2} + {(y - 6)}^{2} = 37\)

Answer:

See below for answers and explanations

Step-by-step explanation:

Problem A

The equation of a circle is \((x-h)^2+(y-k)^2=r^2\) where \((h,k)\) is the center and \(r\) is the radius, thus, we need to find \(r^2\) using our center and given point, through which we can find our equation:

\((x-h)^2+(y-k)^2=r^2\\\\(0-3)^2+(-2-6)^2=r^2\\\\(3)^2+(-8)^2=r^2\\\\9+64=r^2\\\\73=r^2\)

This means that the correct equation is \((x-3)^2+(y-6)^2=73\)

Problem B

\((x-h)^2+(y-k)^2=r^2\\\\(x-(-4))^2+(y-(-2))^2=9^2\\\\(x+4)^2+(y+2)^2=81\)

Thus, the correct equation is \((x+4)^2+(y+2)^2=81\)

Problem C

Use the distance formula where \((x_1,y_1)\rightarrow(2,5)\) and \((x_2,y_2)\rightarrow(-10,7)\) to find the diameter of the circle with the given endpoints:

\(d=\sqrt{(y_2-y_1)^2+(x_2-x_1)^2}\\\\d=\sqrt{(7-5)^2+(-10-2)^2}\\\\d=\sqrt{(2)^2+(-12)^2}\\\\d=\sqrt{4+144}\\\\d=\sqrt{148}\\\\d=2\sqrt{37}\)

Since the radius is half the diameter, then \(r=\sqrt{37}\), making \(r^2=37\).

The midpoint of the two endpoints will give us the center, so the center is \(\displaystyle \biggr(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2}\biggr)=\biggr(\frac{2+(-10)}{2},\frac{5+7}{2}\biggr)=\biggr(\frac{-8}{2},\frac{12}{2}\biggr)=(-4,6)\)

Thus, the correct equation is \((x-h)^2+(y-k)^2=r^2\rightarrow(x-(-4))^2+(y-6)^2=37\rightarrow(x+4)^2+(y-6)^2=37\)

Answer:

A

Step-by-step explanation:

the order of letter should resemble the same shape

The average rate of change between x = 1 and x = 1 + h is -3h - 6.

The function given is f(x) = 3 - 3x², x = 1, x = 1 + h; determine the net change and average rate of change between the given values of the variable.

The net change is the difference between the final and initial values of the dependent variable.

When x changes from 1 to 1 + h, we can calculate the net change in f(x) as follows:

Initial value: f(1) = 3 - 3(1)² = 0

Final value: f(1 + h) = 3 - 3(1 + h)²

Net change: f(1 + h) - f(1) = [3 - 3(1 + h)²] - 0

= 3 - 3(1 + 2h + h²) - 0

= 3 - 3 - 6h - 3h²

= -3h² - 6h

Therefore, the net change between x = 1 and x = 1 + h is -3h² - 6h.

The average rate of change is the slope of the line that passes through two points on the curve.

The average rate of change between x = 1 and x = 1 + h can be found using the formula:

(f(1 + h) - f(1)) / (1 + h - 1)= (f(1 + h) - f(1)) / h

= [-3h² - 6h - 0] / h

= -3h - 6

Therefore, the average rate of change between x = 1 and x = 1 + h is -3h - 6.

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Answer:

442

Step-by-step explanation:

Transformation doesn't depend on the shape of the figure if it has an overlap or not

The transformation \(8d\) can be applied to a figure with overlap or not with overlap.

Transformations are operations on a plane that change the position, shape, and size of geometric figures.

When a geometric figure is transformed,

its new image has the same shape as the original figure.

However,

it is in a new position and may have a different size.

Let's talk about different types of transformations.

Rotation:

It occurs when a shape is turned around a point, which is the rotation center.

Translation:

It moves the shape from one point to another on a plane.

Reflection:

It is an operation that results in the mirror image of the original shape.

Scaling:

The shape is transformed by changing the size without changing its orientation.

Transformation on \(8d\):

In the given problem, the transformation of \(8d\) can be applied to the figure with or without overlap.

This means that \(8d\) transformation doesn't depend on the shape of the figure if it has an overlap or not.

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Answer:

−1.9d+3.6h-17

Step-by-step explanation:

You just need to combine like terms ;)

Hope it helps, let me know

Answer:

145

Step-by-step explanation:

Answer:

y=\(\frac{3}{2} x+3\)

Step-by-step explanation:

If PQ=RS, PQ=5x+9, and RS=x-31, then x=-10 can be proven by constructing two-column proof.

Given that PQ=RS, PQ=5x+9, and RS=x-31, we have to prove that x=-10. Let's construct a two-column proof to prove this.

Step 1: Write down the given information and the information to be proven.

Given: PQ=RS, PQ=5x+9, and RS=x-31To prove: x=-10

Step 2: Write down the reasons for each statement.                                          

 Given PQ = 5x+9                                            

 Given RS = x-31                                            

  Given 5x+9 = x-31                                        

 Substitution property 4x = -40                                                

Simplification x = -10                                                  

Division property of equality (Divide by 4)

Step 3: Write down the final statement that proves what we want to prove.x = -10    T

Therefore, PQ = RS = -10 + 31 = 21.

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Your monthly payment for this house will be $1689.5 if your mortgage payment is $1345, your annual insurance premium is $678, and your real estate taxes are $3456.

Describe the mortgage payments in brief?

Principal and interest payments make up your monthly mortgage payments. You must purchase private mortgage insurance if your down payment is less than 20%, which raises your monthly payment. Real estate or property taxes are also included in some payments. Early on in the mortgage, the borrower pays more interest, whereas the principle balance is favored in the latter stages. A greater down payment will directly increase your home's equity.

To find the total monthly payment for the home, we need to divide the annual costs by 12.

Total monthly payment = Mortgage payment + (Annual insurance premium / 12) + (Annual real estate taxes / 12)

= $1345 + ($678 / 12) + ($3456 / 12)

= $1345 + $56.5 + $288

= $1689.5

So the total monthly payment for the home is $1689.5

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Your monthly payment for this house will be $1689.5 if your mortgage payment is $1345, your annual insurance premium is $678, and your real estate taxes are $3456.

Principal and interest payments make up your monthly mortgage payments. You must purchase private mortgage insurance if your down payment is less than 20%, which raises your monthly payment. Real estate or property taxes are also included in some payments. Early on in the mortgage, the borrower pays more interest, whereas the principle balance is favored in the latter stages. A greater down payment will directly increase your home's equity.

To find the total monthly payment for the home, we need to divide the annual costs by 12.

Total monthly payment = Mortgage payment + (Annual insurance premium / 12) + (Annual real estate taxes / 12)

= $1345 + ($678 / 12) + ($3456 / 12)

= $1345 + $56.5 + $288

= $1689.5

So the total monthly payment for the home is $1689.5

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Answer:

Area = 153.8 cm/ m

Step-by-step explanation:

Area of circle = 22 ÷ 7 × r²

= 22 ÷ 7 × (7²)

= 22 ÷ 7 × 49

= 3.14 × 49

= 153.8 cm/ m

The promotion rate distribution of employees can be either unimodal or bimodal, depending on the company's policies and the type of employees. Understanding the distribution is important for employees as it provides insight into the likelihood of being promoted and the time it may take to reach the desired promotion.

Promotion Rates for Employees: Promotion is a common goal for employees as it is often associated with career advancement, higher salaries, and increased responsibility. The rate at which employees are promoted can vary from company to company, depending on various factors such as the size of the organization, the industry, and the company's policies.

In this context, it is important to understand the distribution of the promotion rates, which can be either unimodal or bimodal. Unimodal Distribution: A unimodal distribution is a type of distribution that has a single peak or mode. This means that the majority of the employees are promoted at a certain rate, and the frequency of promotions decreases as the rate moves away from the mode.

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The slope can be calculated using the following equation:

Where (x1, y1) and (x2, y2) are two points on the line.

We know that if you buy 6 cans, x = 6, it will cost $3.00, y = 3.

We also know that if we buy zero cans, x = 0, it will cost nothing, y = 0.

So we have the points (0, 0) and (6, 3), so:

So, the slope is 1/2, fourth alternative.

The simplified matrix expression is (I + C^-1) + (C + E)C.

To simplify the matrix expression C(C^-1 + E) + (C^-1 + E)C, we can use the properties of matrix multiplication and the inverse of a matrix.

First, let's focus on the term C(C^-1 + E). We can distribute the matrix C into the parentheses:

C(C^-1 + E) = CC^-1 + CE

Since C^-1 is the inverse of matrix C, their product CC^-1 results in the identity matrix I:

CC^-1 = I

Therefore, the term CC^-1 simplifies to the identity matrix I:

C(C^-1 + E) = I + CE

Similarly, for the term (C^-1 + E)C, we can distribute the matrix C into the parentheses:

(C^-1 + E)C = C^-1C + EC

Again, C^-1C results in the identity matrix:

C^-1C = I

Therefore, the term C^-1C simplifies to the identity matrix I:

(C^-1 + E)C = C^-1 + EC

Combining the simplified terms, we get:

C(C^-1 + E) + (C^-1 + E)C = I + CE + C^-1 + EC

We can rearrange the terms and group similar ones:

C(C^-1 + E) + (C^-1 + E)C = (I + C^-1) + (C + E)C

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The denominator is never equal to zero, and the domain of the function is all real numbers: Domain: (-∞, ∞)

The domain of a function is the set of all possible values of the input variable for which the function is defined. In the case of the given function:

f(x) = x / (-2sin(x) - 3)

We know that the denominator cannot be equal to zero, otherwise the function will be undefined. Therefore, we need to find the values of x that make the denominator zero and exclude them from the domain.

-2sin(x) - 3 = 0

sin(x) = -3/2

The sine function is only defined between -1 and 1, so there are no real values of x that make sin(x) equal to -3/2.

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Answer:

2 radians

Step-by-step explanation:

the arc length is calculated as

arc = circumference of circle × fraction of circle

let x be the central angle , then

arc = 2πr × \(\frac{x}{2\pi }\) ( cancel 2π on numerator and denominator )

    = 2r × x

given arc length = 40 , then

2 × 10 × x = 40

20x = 40 ( divide both sides by 20 )

x = 2

the central angle has a measure of 2 radians

Answer: 96

Step-by-step explanation:

A palindrome is a number that is the same when reading in both ways (right to left, and left to right), for example, 121

Then, we have 9 digits, and all the digits need to be even.

the options are: 0, 2, 4, 6, 8.

Now, we can tink a 9 digit number as 9 empty slots, and in each slot, we can put a number.

But because this is a palindrome, the first digit must be equal to the ninth, and the second digit must be equal to the eight, and so on.

So we can tink it as actually only 5 slots, where in each slot, we can put an even number, now let's count the options that we have in each selection.

For the first digit we have 4 options: 2, 4, 6 and 8 (0 is not counted here because if the first digit was a 0, then this would not be a 9 digit number).

for the second digit, we have also 4 options (because we already toked one, but now the 0 can be chosen)

for the third digit, we have 3 options

for the fourth digit, we have 2 options

for the fifth digit, we have only one option.

The total number of combinations is equal to the product of the number of options for each selection:

C = 4*4*3*2*1 = 96

Answer:

96

Step-by-step explanation:

The percentage of the cub scout which are atleast as old as the near scout refers to percentage of the cub scout which are atleast 8 years old. Hence, the percentage is 28%

Cub scouts which are atleast 8 years old :

Hence, the percentage of cub scout which are atleast 8 years old is 28%

Therefore, the percentage of the cub scout that are atleast as old as the Bear scout is 28%

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The probability that the sample mean will be greater than 57.95 is 0.0495.

Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event. The value is expressed from zero to one. This is the basic probability theory, which is also used in the probability distribution.

To solve this question, we need to know the concepts of the normal probability distribution and of the central limit theorem.

Problems of normally distributed samples can be solved using the z-score formula.

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

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

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

The Central Limit Theorem establishes that, for a random variable X, with mean \(\mu\) and standard deviation \(\sigma\), a large sample size can be approximated to a normal distribution with mean \(\mu\) and standard deviation \(\frac{\sigma}{\sqrt{\text{n}} }\).

In this problem, we have that:

The probability that the sample mean will be greater than 57.95

This is 1 subtracted by the p-value of Z when X = 57.95. So

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

By the Central Limit Theorem

\(Z=\dfrac{X-\mu}{\text{s}}\)

\(Z=\dfrac{57.95-53}{3}\)

\(Z=1.65\)

\(Z=1.65\) has a p-value of 0.9505.

Therefore, the probability that the sample mean will be greater than 57.95 is 1-0.9505 = 0.0495

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Answer:

Step-by-step explanation:

Here you go mate

Step 1

14−3x<−1  Question

Step 2

14−3x<−1  Simplify

Step 3

14−3x<−1   Subtract 14 from sides

-3x<-15

Step 4

-3x<-15  Divide sides by -3

x>5

Answer

x>5

Hope this helped

Answer:

Step-by-step explanation:

I can help

Step 1

14−3x<−1  Simplify

Step 2

14−3x<−1  subtract 14 from the sides

-3x<-15

Step 3

-3x<-15  Divide the sides by 3

-3x/-3<-15/-3

Answer

x>5

Hope this helps