Find the smallest pair of 4-digit numbers such that the difference between them is 303 and their hcf is 101. Show your step.

Option (b) $11004.70 is correct answer. The amount of the Gentrys' annual transportation and taxes budgets combined is approx $11004.70 .

Given,

Total yearly income of the family = $29,742.42

% Expenses for Transportation = 9%

% Expenses for Taxes = 28%

We know that ,

Percentage is from total income of the family,

Expenses for transportation in $ = 9% of $29742.42

                                                      =  0.09 * 29742.42

                                                      =  $2676.8178

Expenses for taxes in $ = 28% of $29742.42

                                       =  0.28 * 29742.42

                                       =  $8327.8776

Total expense Transportation + Taxes =  $2676.8178 + $8327.8776

                                                                = $11004.694

                                                                ≈ $11004.70

Hence, amount of the Gentrys' annual transportation and taxes budgets combined is approximately $11004.70 .

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The complete question is :

What is the dollar amount of the Gentrys' annual transportation and taxes budgets combined?

(a)$2,676. 82

(b) $11,004. 70

(c) $8,327. 88

(d) $18,737.

Gentry Family

Three Children Yearly Budget; Yearly Income - $29,742.42

Item                                      Percentage          

Tithe                                         10%

Taxes                                        28%

Food                                          20%

Housing                                     30%

Clothing                                     6%

Transportation                           9%

Doctor, Medicine, etc.               8%

Answer:

y=8x-25

Step-by-step explanation:

First, you want to find the slope.

Formula: y2-y1 / x2-x1

So, in this case it would be: 7-(-1) / 4-3

Which is the same thing as 7+1 / 4-3 = 8/1 or just 8

Now, when finding the equation of the line, always use the slope-intercept equation: mx + b = y.

If we plug in the slope, we get 8x + b = y. However, we want to find b, since we could use either (3, -1) or (4, 7) for the x and y.

I'm going to use (4, 7), but it doesn't matter what you choose because you'll get the same answer.

8(4) + b = 7.

When you simplify you should get b = -25.

So now, you just have to plug everything in and you get your answer y = 8x - 25.

The number of boxes with three of them are 44.

Two or more expressions with an Equal sign is called as Equation.

Given that Fells had 9 boxes.

Dylan had 2 times minus 1 boxes than Fells.

2(9)-1 which is 18-1= 17 boxes.

Scarlett had 18 boxes but fewer than Dylan

The total number of boxes are 9+17+18

44 boxes

Hence, the number of boxes with three of them are 44.

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3/4 and 5 18 is fraction have a leat common denominator of 36.

3/4 and 5 18 is fraction have a leat common denominator of 36.

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The number of batches of soup that Fabian can make is given as follows:

3 batches.

The number of batches of soup is obtained applying the proportions in the context of the problem.

He has 10 pounds, and sets aside 2.8 pounds of tomatoes to make spaghetti sauce, hence the amount remaining for soup is given as follows:

10 - 2.8 = 7.2 pounds.

He needs 2 and 2/5 = 2 + 0.4 = 2.4 pounds for each batch, hence the number of batches is obtained as follows:

7.2/2.4 = 3.

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An arc having a central angle of 30° and a radius of 15 cm has a length of 225 cm.

The theory used in this question is the formula for calculating the length of an arc, which is θ/360 × circumference. θ is the central angle in degrees and the circumference is the circumference of the circle.

Given:

Determine the circle's circumference.

Circumference of a circle = 2πr

Radius = 15 cm

Circumference of the circle = 2π × 15 cm

Circumference of the circle = 30π cm

Calculate the length of the arc.

Length of an arc = θ/360 × circumference

Central angle = 30°

Length of an arc = 30°/360 × 30π cm

Length of an arc = (30π/360) × 30π cm

Length of an arc = 225 cm

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The value of a is -46 which is the solution of equation  a + 16 = −30.

Two or more expressions with an Equal sign is called as Equation.

The given equation is a+16=-30

a plus sixteen equal to minus thirty

In the equation the variable is a

a+16=-30

Subtract 16 from both sides

a=-30-16

a=-46

Hence, the value of a is -46 which is the solution of equation  a + 16 = −30.

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The direction of A for the given indices of the cubic unit cell is:

A = [3 3 -1].

A notation used to pinpoint crystal planes is called a Miller index.

For the direction of A:

Direction of A = [(1 - 0) ,  (1 - 0), (1/3 - 2/3)]

                       = [ 1  1  -1/3]

Multiply each by 3.

                       = [3  3   -1]

Thus, the  direction of A for the given indices of the cubic unit cell is:

A = [3 3 -1].

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The complete question is-

Determine the indices for A, the directions shown in the following cubic unit cell.

The diagram is attached:

Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation:

-4

Work Shown:

[tex]a_1 = -1 = \text{ first term} \\\\d = 0.5 = \text{ common difference} \\\\a_n = a_1 + d(n-1)\\\\a_n = -1 + 0.5(n-1)\\\\a_6 = -1 + 0.5(6-1)\\\\a_6 = -1 + 0.5(5)\\\\a_6 = -1 + 2.5\\\\a_6 = 1.5\\\\[/tex]

A total of $540 being donated to the school.

The formula for calculating the amount of money that will go to the school is as follows: (Selling Price - Cost of Production) x 25% x Number of Sets Sold. In this case, the calculation is (4.55 - 1.75) x 0.25 x 800 = $540. This means that if 800 sets of pens are sold, $540 will go to the school. This can also be expressed as 25% of the profit from each set (the difference between the purchase price and the amount it costs to make) multiplied by the total number of sets sold. Thus, if 800 sets of pens are sold, the school will receive 25% of the profit from each set multiplied by 800. This results in a total of $540 being donated to the school.

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Substance Gallons         % Fruit Juice

Drink A              x                         20%

Drink B              y                          5%

Total         x + y = 30                  10%

To find the number of gallons of Drink A and Drink B that should be used, we can write two equations based on the percentage of fruit juice.

20% * x = 10% * (x + y)

5% * y = 10% * (x + y)

Simplifying and solving for x and y:

x = 1.5 * y

10% * (x + y) = 10% * 30

y = 15

x = 1.5 * 15 = 22.5

So, we would use 22.5 gallons of Drink A and 15 gallons of Drink B to make a 30 gallon mixture that is 10% fruit juice.

Answer:

B

Step-by-step explanation:

Therefore , the solution of the given problem of ratio comes out to be greatest portion of race covered is by Deangelo which is 0.72.

The simple formula "a / b" can be used to create a pair of similar variables "a" and "b," where "b" may also be greater than zero. One ratio is created by combining two ratios. If there were only one man and three women, the ratio would be 1:1. There are 1/4 boys and 3/4 girls in the group. A separation between a or more objects, a numeral, or a piece of a component's volume are all examples of parts.

Here,

Given :

=> Aljendaro  is 65%

=> Beth is 3/5

=> Christina is 0.7

=> Deangelo is 18/25

the greatest portion of the race covered is :

=> 65/100 = 0.65

=> 3/5 = 0.6

=> 0.7

=> 18/25 = 0.72

The greatest portion of race covered is by Deangelo which is 0.72.

Therefore , the solution of the given problem of ratio comes out to be greatest portion of race covered is by Deangelo which is 0.72.

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The complete question is " Four friends are in a marathon. After 3 hours, each friend has completed a different portion of the race.

Given:

Aljendaro  is 65%

Beth is 3/5

Christina is 0.7

Deangelo is 18/25 "

The value of the sample variance rounded to one decimal place is 76.0.

What is the Mean?

The mean is a measure of the central tendency of a set of data, calculated as the sum of the values divided by the number of values in the set.

The sample variance of a set of data is a measure of the spread or dispersion of the data around the mean. To calculate the sample variance, you can follow these steps:

Calculate the mean of the data: First, find the sum of all the data points and divide by the number of data points (n).

For the given data, the mean is: (-11 + -5 + -5 + -11 + 13 + -11 + -5) / 7 = -7

Subtract the mean from each data point: Next, subtract the mean from each data point to get the deviations from the mean.

For the given data, the deviations are: (-11 - -7) = -4, (-5 - -7) = 2, (-5 - -7) = 2, (-11 - -7) = -4, (13 - -7) = 20, (-11 - -7) = -4, (-5 - -7) = 2

Square the deviations: Square each deviation to get rid of negative values.

For the given data, the squared deviations are: (-4)^2 = 16, (2)^2 = 4, (2)^2 = 4, (-4)^2 = 16, (20)^2 = 400, (-4)^2 = 16, (2)^2 = 4

Sum the squared deviations: Sum all the squared deviations.

For the given data, the sum of the squared deviations is: 16 + 4 + 4 + 16 + 400 + 16 + 4 = 456

Divide the sum by n - 1: Finally, divide the sum of the squared deviations by the number of data points minus 1 (n - 1). This gives us the sample variance.

For the given data, the sample variance is: 456 / (7 - 1) = 456 / 6 = 76

Hence, the value of the sample variance rounded to one decimal place is 76.0.

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The Probabilities are as follows

P(A) = 3/6 = 1/2

P(B) = 3/6 = 1/2

P(A and B) = 1/6

P(A or B) = 5/6

Sample Space (S) of the whole experiment: {1, 2, 3, 4, 5, 6}

Sample Space of Event A: {2, 4, 6}

Sample Space of Event B: {1, 2, 3}

A Venn diagram indicating two circles labeled A and B, and the overlap between the two circles labeled A and B]

Probabilities:

P(A) = |Event A| / |Sample Space| = 3/6 = 1/2

P(B) = |Event B| / |Sample Space| = 3/6 = 1/2

P(A and B) = |Event A and Event B| / |Sample Space| = 1/6

P(A or B) = 1 - P(Neither A nor B) = 1 - (6 - |Event A| - |Event B|) / |Sample Space| = 1 - (6 - 3 - 3) / 6 = 1 - (6 - 6) / 6 = 1/6 = 5/6

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The complete question goes thus:

Consider rolling a fair six-sided die once with the two possible events, Event A: roll an even number Event B: roll a number less than or equal to 3 • State the Sample Space of the whole experiment: State the Sample Space of the Event A: State the Sample Space of the Event B: Draw a Venn diagram: . Find the following probability: P(A)= P(B)= P (A and B) = P (A or B) =

l

The probability that the battery will last for 52 months is approximately 0.928, or 92.8%.

To calculate the probability that a battery will last for 52 months, we need to find the z-score of 52 months, using the formula:

z = (x - μ) / σ

Plugging in the values, we get:

z = (52 - 42.5) / 6.5 = 1.384615

Next, we can use a z-table to find the probability that a battery will last more than 52 months.

In this case, the z-score is positive, so we look up the area to the right of 1.384615 in the z-table. The area to the right of 1.384615 is approximately 0.928.

Therefore, the probability that a battery will last for 52 months or more is approximately 0.928, or 92.8%.

So the answer to the question is: A) 92.8%

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Answer: 3

Step-by-step explanation:

The domain and range of the ordered pair  {(-13, 9), (-7, -5), (5, 14). (11, -10)) is as follows:

domain = [-13, -7, 5, and 11]

range = {9, -5, 14 and -10}

The domain of a function is independent variable of a function. The domain is the input value of the function. The domain lies on the x axis of the function.

Therefore, the domain of the ordered pair {(-13, 9), (-7, -5), (5, 14). (11, -10)) is [-13, -7, 5, and 11]

The range is the dependent value of the function. The range is also called the output value of the function. The range lies on the y-axis of the function.

Therefore, the range of the ordered pair {(-13, 9), (-7, -5), (5, 14). (11, -10)) are {9, -5, 14 and -10}

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In a case whereby Mrs. Carter's famous peanut butter cookies call for 1 cup of peanut butter for every 1 2 of a cup of oil. Today, she wants to make a huge batch with 1 cup of oil the amount of peanut butter she should use can be expressed as  2 cups of peanut butter.

The concept that will be used is simplification. Base on the provided information from the question,

(1/2 cup of oil )= (1 cup of peanut butter)

we can represent (1 cup of oil)  as  (x)

The if we perfor a Cross Multipliplication we have:

(1/2x) =( 1 × 1)

x = (1 × 2/1)

x = 2 cups of peanut butter.

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In wage data the correlations between lwage and the three variables education, experience and job tenure (all measured in years) are respectively 0.4, 0.1 and 0.3. So, Regression of lwage on education will have the highest R squared.

R squared is the square of the correlation so the pair that have the highest correlation will also have the highest R squared in a regression involving the two variables.

Regression is a statistical method used to estimate the relationship between a dependent variable and one or more independent variables. This method can also be used to assess the strength of the relationship between variables with future predictions.

Regression analysis includes several variations, namely linear, multiple linear, and nonlinear. The most common models are linear and multiple linear. Meanwhile, nonlinearity is usually used for more complex data groups - because the relationships between variables are not consistent.

Regression analysis can be applied to a variety of disciplines, including finance, investing, and marketing.

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The limit does not exist as x approaches 8 for (√(12−x) − 2)/ (√(24−x) − 4).

Therefore the answer is dne.

The square root of 12 - x approaches 2 as x approaches 8 and the square root of 24 - x approaches 4 as x approaches 8.

The limit fails to exist because both the numerator and the denominator approach 0 as x approaches 8, but the ratio of the two approaches positive infinity. This shows that the limit is undefined or "dne".

As both the numerator and denominator approach 0, the fraction they form can approach any real number or it can oscillate between two values, leading to an undefined limit. In such cases, the limit fails to exist.

--The question is not readable, answering to the question below--

"evaluate the limit, if it exists. (if an answer does not exist, enter dne.)

lim x → 8 (√(12−x) − 2)/ (√(24−x) − 4)"

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Answer:

3 Ducks

Step-by-step explanation:

Two ducks are in front of the last duck; the first duck has two

ducks behind; one duck is between the other two

Hence , there are 3 ducks

Hope it is correct

Answer: I think 7

Step-by-step explanation: Sorry if its wrong.

Answer:

False. The two sides evaluate to different numbers.

Step-by-step explanation:

Let's evaluate each side:

4 × (3 + 5) - 10 = 4 × 8 - 10 = 32 - 10 = 22

4 × 3 + 5 - 10 = 12 + 5 - 10 = 17 - 10 = 7

Upon solving using direct factoring, the value of k = 56i / 3, a = 4i.

The algebraic square and simplify method is used to finish the square in a quadratic equation in order to obtain the required equation roots. The answer to the quadratic equation ax2 + bx + c = 0 is a 0. To obtain the roots, we simplify this equation to read as ax2 + bx + c = 0.

It is referred to as the direct technique since it allows us to solve the given system of linear equations in a finite number of specified steps.

Given the equation are -

9k² + 8 = - 48

9k² = -48 - 8

9k² = - 56

k = -√56 / √9

k = -√56 / 3

5a² + 10 = - 70

5a² = -80

a² = -16

a = 4i

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Answer:

(-3, -5)

Step-by-step explanation:

When reflected over the x-axis, the x remains the same, and the y change to their opposite sign.

So, the answer is (-3, -5)

Answer:

Step-by-step explanation:

10x+y=9(x+y)

10y+x=10x+y-63

now put x alone and solve for x then y and add the values of x and y and you will get your answer

For the given function, the value using limits is ∫h′′(u)du = 127/6 = 21.17

A limit in mathematics is the value that a function gets closer to when the input gets closer to a certain value. Calculus and mathematical analysis are not possible without limits, which are also required to determine continuity, derivatives, and integrals.

A function's second derivative is a measure of how quickly its first derivative, or acceleration, changes over time. If h′ is differentiable and has a continuous rate of change, then h′′ is continuous. The derivative of an integral is equal to the integrand according to the calculus fundamental theorem. Therefore, h′(u) equals h′′(u)du plus C, where C is a free constant.

To determine C, we can use the given values of h′(1) and h′(6). We have h′(1) = ∫h′′(u)du + C and h′(6) = ∫h′′(u)du + C. Subtracting the two equations yields

h′(6) − h′(1) = ∫h′′(u)du + C − ∫h′′(u)du − C = 0

And, since h′(6) − h′(1) = −15 − 4 = −19, we have −19 = 0, which means that C = −19. Hence, h′(u) = ∫h′′(u)du − 19.

Finally, to determine the integral of h′′, we can integrate both sides of this equation with respect to u:

h(u) = ∫h′(u)du = ∫(∫h′′(u)du − 19)du = ∫h′′(u)du * u - 19 * u + C

To determine C, we can use the given values of h(1) and h(6). We have h(1) = ∫h′′(u)du * 1 - 19 * 1 + C and h(6) = ∫h′′(u)du * 6 - 19 * 6 + C. Subtracting the two equations yields

h(6) − h(1) = ∫h′′(u)du * 6 - 19 * 6 + C − ∫h′′(u)du * 1 - 19 * 1 + C = 3 + 9 - (-9 - 114) = 127

Hence,  ∫h′′(u)du = 127/6 = 21.17

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Since C is any arbitrary constant,  [tex]y^{2} = \frac{1}{5} ln (3 + x^{10}) + 2C[/tex] is the final solution of the differential equation.

The equation given to us is:

[tex](3 + x^{10})\frac{dy}{dx} = \frac{x^{9}}{y}[/tex]

We can re-write the above equation:

[tex]y dy = \frac{x^9}{3 + x^{10}} dx[/tex]

This is separation of variables.

A separable differential equation is any equation that can be written in the form y′=f(x)g(y). The method of separation of variables is used to find the general solution to a separable differential equation.

Now, if we differentiate the denominator,

[tex]\frac{d}{dx} (3 + x^{10} ) = 10x^9[/tex]

Integrating both sides,

[tex]\frac{y^2}{2} = \frac{1}{10} ln (3 + x^{10})[/tex] + C

⇒ [tex]y^{2} = \frac{1}{5} ln (3 + x^{10})[/tex] + 2C

Since C is any arbitrary constant,  [tex]y^{2} = \frac{1}{5} ln (3 + x^{10}) + 2C[/tex] is the final solution of the differential equation.

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The proportionate equation for each problems are:

Let's discuss each problem we have:

1. Liv earns $9.50 for every 2 bracelets she sells.

y = 4.75x

because y = kx, then:

y = $9.50

x = 2

4.75 --> constant of proportionality

--> price per unit of bracelet sold

2. John ran 3 miles in 25.5 minutes

y = 8.5x

y = 25.5 minutes

x = 3 miles

8.5 --> constant of proportionality

--> minuntes per miles

--> times per distance

3. Lincoln bought 3 bottles of energy drink for $4.50

y = kx

y = $4.50

x = 3

$4.50 = k (3)

k = $1.50 --> price of a bottle of energy drink

4.  Total cost of 4 hours renting a cotton candy machine is $72.

y = kx

y = $72

x = 4 hours

$72 = k(4)

k = $18 --> price of renting per hour

5. 7 cups of water are used to make 4 loaves of French bread.

y = kx

y = 7

x = 4

7 = k(4)

k = 7/4

Proportionate equation: y = 7/4 x

(x = 6)

y = 7/4 (6)

y = 21/2 = 10.5 cups of water

6. 6 3/4 yards of fabrics are used to make 3 elf costumes

y = kx

y = 6 3/4

x = 3

6 3/4 = k (3)

27/4 = 3k

--------------- x 4

27 = 12k

k = 9/4

Proportionate equation: y = 9/4 x

(x = 7)

y = 9/4 (7)

y = 63/4

y = 15 3/4 yards of fabric

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The y-intercept of each equation represents the height of the flowers when x = 0, i.e., after 0 days.

For equation (1), the y-intercept is 2:

y = 0.7x + 2

For equation (2), the y-intercept is also 2:

y = 0.4x + 2

The y-intercepts of both equations are the same, meaning that both flowers started at the same height.

However, the slopes of the equations are different, meaning that the rate of growth of the flowers is different.

Since the rate of growth is different, the flowers will not be the same height after any number of days.

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