Use the distributive property to expand the expression. 5(4r2 + 8s2) − (−3s + 5t)

move the decimal point 4 places to the left to get

1.85326 x 10^4

Answer:

The  answer is:

B.  0.4 centimeter = 8 kilometers

C.  0.75 centimeter = 15 kilometers

D.  3 centimeters = 60 kilometers

Step-by-step explanation:

Got it right in 2021

The product of nine and the sum of a number Z and four can be written as 9(Z + 4). For example, if Z = 5, then the expression becomes 9(5 + 4), which equals 81.

The product of nine and the sum of a number Z and four can be written as 9(Z + 4).

For example, if Z = 5, then the expression becomes 9(5 + 4), which equals 9(9) = 81.

So, the product of nine and the sum of a number Z and four is 9(Z + 4), where Z represents any number.

Answer:

C.

Step-by-step explanation:

The ordered pair which represents the point on the line y = 2x + 1 is C. (-1, -1).

Coordinates are the set of points in a geometrical plane or space, which is used to denote the exact point in the coordinate plane or space.

Given equation is y = 2x + 1.

We have to substitute each of the points in the line if the equation holds or not.

A. (0, 3)

2x + 1 = 0 + 1 = 1 ≠ 3

B. (2, 1)

2x + 1 = 4 + 1 = 5 ≠ 1

C. (-1, -1)

2x + 1 = -2 + 1 = -1

D. (1, 2)

2x + 1 = 2 + 1 = 3 ≠ 2

Hence the point on the line is C. (-1, -1).

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Answer:

27.7 or 28

Step-by-step explanation:

 add standard deduction and exemption: 5700 + 3650 = 9350

 subtract from each of their incomes and that will be the taxable income:

 Melvin: 44500 - 9350 = 35150 taxable income

Sylvia: 51200 - 9350 = 41850 taxable income

Melvin's taxable income is $34,150 and Sylvia's taxable income is $42,850.

To calculate Melvin's taxable income, we need to subtract his standard deduction and exemption from his gross income. Melvin's gross income was $44,500 and his standard deduction is $5700. He can also claim himself as an exemption for $3650. Therefore, Melvin's taxable income would be $44,500 - ($5700 + $3650) = $34,150.

In a similar way, to calculate Sylvia's taxable income, we subtract her standard deduction and exemption from her gross income. Sylvia's gross income was $51,200 and her standard deduction is $5700. She can also claim herself as an exemption for $3650. Therefore, Sylvia's taxable income would be $51,200 - ($5700 + $3650) = $42,850.

We would expect the height of women at age 4 and their height as women at age 18 to be the highest correlation since it is rational to think taller children to turn out to be taller adults and shorter children to become shorter adults. The next highest would be the correlation between the father and their adult sons. Tall fathers be likely to have tall sons, but naturally not as tall, and similarly for shorter fathers. The lowest correlation would be between husbands and their wives.  Husbands may be taller than their wives in common, but there is no purpose to expect anything more than a  weak positive correlation.

The heights of fathers and their adult sons have the highest correlation due to genetics, followed by the heights of husbands and wives influenced by assortative mating. Lastly, the correlation between the heights of women at age 4 and their heights at age 18 is weaker due to the intervening growth factors.

To rank the correlation between these pairs of variables, we should consider how closely related they are likely to be based on genetic, environmental, and social factors. Genetics plays a significant role in the height of fathers and their adult sons because height is a highly heritable trait. Therefore, we can expect a high correlation here. Social factors influence the heights of husbands and their wives since people may choose partners similar to themselves in height, a phenomenon known as assortative mating, but the correlation is likely to be weaker than genetic influence. Lastly, for the heights of women at age 4 and their heights at age 18, while early childhood height can be an indicator of adult height, there's substantial growth and development between these ages, affected by environmental and genetic factors, resulting in a lower correlation compared to the direct genetic link between fathers and sons.

If we were to rank the correlation from largest to smallest, it would be:

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Answer:

The point A' lie at (-4,1).

Step-by-step explanation:

From the given figure it is clear that the coordinates of A are (-4,1).

If parallelogram ABCD was reflected over the y-axis, then

[tex](x,y)\rightarrow (-x,y)[/tex]

[tex]A(-4,1)\rightarrow A_1(4,1)[/tex]

Then it reflected over the x-axis,

[tex](x,y)\rightarrow (x,-y)[/tex]

[tex]A_1(4,1)\rightarrow A_2(4,-1)[/tex]

After that, it rotated 180° about the origin,

[tex](x,y)\rightarrow (-x,-y)[/tex]

[tex]A_2(4,-1)\rightarrow A'(-4,1)[/tex]

Therefore the point A' lie at (-4,1).

Answer:

Your answer is B

The number of batches you can make if you use all the sugar is 12.61 batches.

The cost of sugar used per batch is $0.28.

A 4-pound bag of sugar = 454 one-teaspoon

Sugar used for a batch of muffins = ¾ cup

If 1 cup = 48 teaspoons

3/4 cup = 3/4 × 48

= 36 teaspoons

Number of batches to make = 454 one-teaspoon / 36 teaspoons

= 12.61 batches

Cost of sugar teaspoons= 3.49/454

= $0.007687224669603 per teaspoon

Cost of sugar per batch = 0.007687224669603 × 36

= $0.276740088105726 per batch

Hence, the cost of sugar used per batch is approximately $0.28

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A 4-pound bag of sugar contains 454 one-teaspoon servings and costs $3.49. A batch of muffins uses ¾ cup of sugar. How many batches can you make if you use all the sugar? What is the cost of sugar for each batch? (1 cup = 48 teaspoons)

To find out how many batches of muffins can be made and the cost per batch, convert the total servings of sugar to cups, then divide by the amount of sugar used per batch, and finally, divide the total cost by the number of batches. which results in approximately $0.29 per batch.

The subject of this question is Mathematics, and it appears to be at the High School level due to the application of ratios, conversions, and basic algebraic skills to solve real-world problems.

Calculating Batches of Muffins from a Sugar Bag

Firstly, we determine the total amount of sugar in the bag in terms of cups. Since 1 teaspoon is equivalent to 4 grams of sugar, and we have 454 servings, we multiply 454 by 4g to get 1816g of sugar in total. To convert grams to cups (given 1 cup of sugar is 200g), we divide 1816g by 200g/cup, which gives us 9.08 cups.

Since a batch of muffins uses 3/4 cup of sugar, we divide the total cups of sugar by 3/4 to find the number of batches. 9.08 cups divided by 3/4 cups per batch results in approximately 12.1 batches; however, since you can't make a partial batch with the remaining sugar, it is safe to say you can make 12 full batches. To find the cost per batch, divide the total cost of the bag ($3.49) by the number of batches (12), which results in approximately $0.29 per batch.

A prototype is unique in that it is designed to have functional features similar to the final product, allowing designers and engineers to test and refine the design. Option D.

The main difference between a prototype and other kinds of models is that a prototype is designed to have some features that work like the real thing (Option D).

7 cups

4 1/5= 21/5

3+3+3+3+3+3+3= 21

             7

Jessica can fill 7 glasses with water, by dividing the total amount of water ([tex]4\frac{1}{5}[/tex] cups) by the amount that each glass holds ([tex]\frac{3}{5}[/tex] cup).

The question asks us to determine how many glasses Jessica can fill with water when each glass holds [tex]\frac{3}{5}[/tex] cup of water and she has 4 1/5 cups of water in total. To solve this, we need to divide the total amount of water by the amount each glass holds.

Firstly, we need to convert the mixed number 4 1/5 cups to an improper fraction. This is done by multiplying the whole number by the denominator and adding the numerator, like this: (4 times 5) + 1 = 21, so 4 1/5 cups is the same as [tex]\frac{21}{5}[/tex]cups.

Next, we divide the total amount of water (21/5 cups) by the amount each glass holds ([tex]\frac{3}{5}[/tex] cup), which can be written as a fraction division problem:

[tex]\frac{\frac{21}{5} }{\frac{3}{5} }[/tex] = [tex]\frac{21}{5}[/tex] x [tex]\frac{5}{3}[/tex] = [tex]\frac{21}{3}[/tex] = 7

So, Jessica can fill 7 glasses with water.

Let amount of water that , my dog's water bowl can hold=x cubic unit

Level of water upto which my dog's water bowl is filled

                                 [tex]=\frac{3x}{4} \text{Cubic unit}[/tex]

Let amount of water drank by my Dog in a drink=y cubic unit

   Writing the statement in terms of equation

    [tex]\frac{3x}{4}-y=\frac{x}{3}\\\\y=\frac{3x}{4}-\frac{x}{3}\\\\y=\frac{9x-4x}{4 \times 3}\\\\y=\frac{5x}{12}[/tex]

Fraction of the bowl did my dog drank is equal to [tex]\frac{5}{12}[/tex]

Answer:

Point-slope form: An equation of a straight line in the form [tex]y -y_1 = m(x -x_1)[/tex];  

where

m is the slope of the line and [tex](x_1, y_1)[/tex] are the coordinates of a given point on the line.

Given the equation: [tex]y-2=-\frac{3}{4}(x-6)[/tex]         ......[1]

On comparing with Point slope form equation we have;

m = [tex]-\frac{3}{4}[/tex] and point (6 , 2)

Now, find the Intercept of the given equation:

x-intercept: The graph crosses the the x-axis i.e,

Substitute y =0 in [1] and solve for x;

[tex]0-2=-\frac{3}{4}(x-6)[/tex]

[tex]-2=-\frac{3}{4}(x-6)[/tex]

Using distributive property:  [tex]a\cdot(b+c) = a\cdot b +a\cdot c[/tex]

[tex]-2 = -\frac{3}{4}x + \frac{18}{4}[/tex]

Subtract [tex]\frac{18}{4}[/tex] on both sides we get;

[tex]-2-\frac{18}{4}= -\frac{3}{4}x + \frac{18}{4} -\frac{18}{4} [/tex]

Simplify:

[tex]-\frac{26}{4} = -\frac{3}{4}x[/tex]

or

-26 = -3x

Divide both sides by -3 we get;

x = 8.667

x-intercept: (8.667, 0)

Similarly, for

y-intercept:

Substitute x = 0 in [1] and solve for y;

[tex]y-2=-\frac{3}{4}(0-6)[/tex]

[tex]y-2=\frac{18}{4}[/tex]

Add 2 on both sides we get;

[tex]y-2+2=\frac{18}{4}+2[/tex]

Simplify:

 [tex]y=\frac{26}{4} =6.5[/tex]

y-intercept: (0, 6.5)

Now, using these two points (8.667, 0) and (0, 6.5) you can plot the graph using line tool as shown below.

Answer-

Correlation coefficient for the data in the table was found to be 0.93.

Solution-

Taking the independent variable or input variable as, the time a patient spends at the dentist and the dependent variable or output variable as the amount of the bill.

We know that,

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

Calculating the values from the table, then putting it in the formula

[tex]r=\frac{4 \times 3130.9 \ - \ 6.45 \times 1473}{\sqrt{[4\times 12.3725 \ - \ 6.45^{2}][4 \times 877475 \ - \ 1473^2]}}[/tex]

[tex]\Rightarrow r=0.929720561 \approx 0.93[/tex]

∴  Correlation coefficient for the data is 0.93.

The correlation coefficient for the data in the table would be 0.93. So, the correct option is A.

The correlation coefficient is used to measure the strong relationship between the two variables.

It is given that the first column is labeled time spent at the dentist (in hours) with entries 1.4, 2.7, 0.75, and 1.6.

The second column is labeled bill amount (in dollars) with entries 235, 867, 156, and 215.

The numbers between -1 and 1 should be one of the values related to the bill amount.

By assuming the independent variable or input variable as, the time a patient spends at the dentist and the dependent variable as the amount of the bill.

Hence, The correlation coefficient for the data in the table was found to be 0.93.

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Answer:  The required solution for [tex]d_1[/tex] is [tex]d_1=2m-d_2.[/tex]

Step-by-step explanation:  We are given to solve the following equation for [tex]d_1:[/tex]

[tex]m=\dfrac{1}{2}(d_1+d_2)~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]

To solve the given equation for [tex]d_1,[/tex] we must take all the other terms on the right side of the equation.

From equation (i), we get

[tex]m=\dfrac{1}{2}(d_1+d_2)\\\\\\\Rightarrow 2m=d_1+d_2\\\\\Rightarrow d_1=2m-d_2.[/tex]

Thus, the required solution for [tex]d_1[/tex] is [tex]d_1=2m-d_2.[/tex]