what is the rule for solving proportions? A. The sum of the means is the product of the extremes. B. The product of the means is equal to the product of the extremes. C. The product of the extremes is twice the product of the means.

Answer:

  36

Step-by-step explanation:

36 is a factor of both numbers

_____

If the smaller divides the larger with no remainder, then the smaller number is the greatest common factor.

If there is a remainder, replace the larger number with that and repeat the process.

multiply 4 by 9.99 for cost of the 4 dvd's

9.99 *4 = 39.96

20% discount is: 39.96 *0.20 = 7.99

39.96 - 7.99 = 31.97

now add the sales tax:

31.97 * 1.0675 = 34.13

 total cost is $34.13

The 6 in 600 has a value one tenth the value of the 6 in 34, 761.

The question asks in which number does the 6 have a value that is one tenth the value of the 6 in 34, 761.

To find the answer, we need to compare the place value of the 6 in both numbers. In 34, 761, the 6 is in the thousands place, and its value is 6,000. To have a value that is one tenth of 6,000, the 6 would need to be in the hundreds place in the other number.

So, the number in which the 6 has a value one tenth the value of the 6 in 34, 761 would be 600.

Final answer:

The number 6 in 2,001.06 is one-tenth the value of the 6 in 34,761.

Explanation:

The number 6 in 34,761 has a value that is one-tenth the value of the 6 in the number 2,001.06.

To find this, we can compare the place values of the two 6's. The 6 in 34,761 is in the ones place, while the 6 in 2,001.06 is in the tenths place.

Since the tenths place is one place to the right of the ones place, the value of the 6 in 2,001.06 is one-tenth the value of the 6 in 34,761.

The sum of b and c is equal to 54.

A quadratic equation is an algebraic equation of the second degree in x. The quadratic equation in its standard form is ax² + bx + c = 0, where a and b are the coefficients, x is the variable, and c is the constant term.

Given is the following quadratic equation -

x² - 6x + 66

x² - 6x + 9 - 9 + 66

x² - 3x - 3x + 9 - 9 + 66

x(x - 3) - 3(x - 3) - 9 + 66

(x - 3)² + 57

The given form of resultant is -

(x + b)² + c

On comparing, we get -

b = - 3

c = 57

Therefore -

b + c = -3 + 57 = 54

Therefore, the sum of b and c is equal to 54.

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https://brainly.com/question/1863222

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If the 4 states have to be in a specific order say ABCD, then the total number of different possible routes is:

 43P4 = 2,961,840

So the probability is:

1 / 2,961,840 = 3.38 x 10^-7

But if the 4 states can be in any order such as DBAC, ACBD etc, then the total number of different possible routes is:

 43C4 = 123,410

So the probability is:

1 / 123,410 = 8.1 x 10^-6

No I don’t think it is practical to list all the different possible routes to select the one that is best. We can simply use mathematical models to solve for that one.

2A on 2A + 3B + 3C = 8 pieces

The probability:

[tex]\dfrac{2}{8}=\dfrac{2:2}{8:2}=\dfrac{1}{4}[/tex]

[tex]\dfrac{1}{4}=\dfrac{1}{4}\cdot100\%=25\%[/tex]

To write the given equation in vertex form, we need to complete the square for the x terms. The vertex form of a quadratic equation is y = a(x-h)^2 + k, where (h, k) is the vertex of the parabola. After completing the square and rearranging the equation, we find that the equation in vertex form is y = 171(x + 7391/4) - 17113/4.

To write the given equation in vertex form, we need to complete the square for the x terms. The vertex form of a quadratic equation is given by y = a(x-h)^2 + k, where (h, k) is the vertex of the parabola.

Let's rearrange the equation to isolate the x terms on one side and the y term on the other side: 162x + 9x + y = -731 - 2

Combine like terms: 171x + y = -733

Now, we can complete the square for the x terms. Divide the coefficient of x by 2 and square the result. Add this value to both sides of the equation: 171x + y + (171/2)^2 = -733 + (171/2)^2

Simplify: 171x + y + 7391/4 = 17113/4

Finally, we can rewrite the left side as a binomial squared and simplify the right side: 171(x + 7391/4) + y = 17113/4

Therefore, the equation in vertex form is: y = 171(x + 7391/4) - 17113/4

The given equation is:

x y – 5000 = y

Rewrite this to create an explicit equation:

x y – y = 5000

y ( x – 1) = 5000

y = 5000 / (x – 1)

Derive to get dy / dx:

dy = - 5000 dx / (x – 1)^2

dy / dx = - 5000 / (x – 1)^2

So plugging in x = 6,

dy / dx = - 5000 / (6 – 1)^2

dy / dx = - 200

Answer:

[tex]\frac{dy}{dx}|_{x=6}= -200[/tex]

Step-by-step explanation:

Given : Demand equation [tex]xy − 5,000 = y[/tex]

To Find [tex]\frac{dy}{dx}|_{x=6}[/tex]

Solution :

[tex]xy- y= 5000[/tex]

[tex]y(x-1)= 5000[/tex]

[tex]y= \frac{5000}{x-1}[/tex]

Differentiating with respect to x

[tex]\frac{dy}{dx}= \frac{-5000}{(x-1)^2}[/tex]

Now substitute x = 6

[tex]\frac{dy}{dx}|_{x=6}= \frac{-5000}{(6-1)^2}[/tex]

[tex]\frac{dy}{dx}|_{x=6}= \frac{-5000}{5^2}[/tex]

[tex]\frac{dy}{dx}|_{x=6}= \frac{-5000}{25}[/tex]

[tex]\frac{dy}{dx}|_{x=6}= -200[/tex]

Hence [tex]\frac{dy}{dx}|_{x=6}= -200[/tex]  =T-shirts per dollar

The data on student heights and weights suggests a strong positive correlation, implying that as a student's height increases, their weight tends to increase as well.

The data provided on student's heights and weights suggests a linear relationship. To complete the sentences based on the data:

The data seems to have a correlation coefficient close to positive one. This indicates that the weight of a student increases as the height of the student increases.

In statistics, when we observe that as one variable increases, the other also increases, we describe this as a positive correlation. A positive correlation coefficient closer to +1 implies a strong positive correlation, meaning that generally taller students in the given data set tend to weigh more.

Final answer:

The correlation coefficient for the given data is approximately 0.86, indicating a positive correlation between height and weight.

Explanation:

The data seems to have a correlation coefficient close to 0.86. This indicates that the weight of a student increases as the height of the student increases.

I believe we are to find for values in this problem.

a. The graph of the function

b. The domain and range

c. The slope

d. The c intercept value

Answers:

a. see the graph photo attached

b. The domain is the set of all x that can be input to the function. Since x is the distance and we know that distance cannot be negative hence the domain is:

x ≥ 0

So the range starts from x = 0:

c (x) = 0.5 * 0 + 70 = 70

Therefore the range is:

c ≥ 70

Domain: x ≥ 0                     Range: c ≥ 70

c. A linear equation has a general form of:

y = mx + b

where m is the slope

From the given equation, the slope is 0.5.

slope = 0.5

d. The c intercept is simply the value of c when x is equal to 0

c intercept = 70

Answer:Given function: c(x) = 0.5x+70.Where c is the cost (in dollars) and x is the number of miles you drive the truck.If we compare given function by slope-intercept form y=mx+b, we get Slope m = 0.5 in fractions could be written as 1/2.And y-intercept b =70.So, in order to graph it, we need to plot y-intercept at 70 first and then plot some more points using rise/run = 1/2.The red line is the graph for the given function.We can see that starting value of cost is $70 for 0 number of miles.x values represents domain and C(x) represents range.We can take x values greater than or equal to 0 and C values greater than equal to 70.Therefore, Domain: x≥0 and Range : C(x) ≥ 70.

Step-by-step explanation:Credit:User named PiaDeveau thanks for providing the answer and hope this helps

:)

Step-by-step explanation:

We have been given that [tex]\frac{2}{3}a=16[/tex].

Since multiplicative inverse property states that any number multiplied by its reciprocal is equal to one.

[tex]\frac{2}{3}\times \frac{3}{2} =1[/tex]

To solve for a let us divide 16 by [tex]\frac{2}{3}[/tex].

[tex]a=16\div \frac{2}{3}[/tex]

Since dividing a number by fraction is same as multiplying the number by the reciprocal of fraction. So we will multiply 16 by [tex]\frac{3}{2}[/tex].

[tex]a=16\times\frac{3}{2}[/tex]

[tex]a=8\times 3[/tex]

[tex]a=24[/tex]

We can see that to solve for a we have multiplied 16 by [tex]\frac{3}{2}[/tex] and [tex]\frac{3}{2}[/tex] is reciprocal of [tex]\frac{2}{3}[/tex].

Let us verify our answer by substituting a=24 in our given equation.

[tex]\frac{2}{3}\times 24=16[/tex]

[tex]2\times 8=16[/tex]

[tex]16=16[/tex]

Hence, to find the value of a we used multiplicative inverse property.

Answer:

a = -15

Step-by-step explanation:

Let's rewrite the exercise in math language.

We have to subtract a-4 from 4a+16 to get -25, that is

4a+16 - (a-4) = -25

The minus sign that is just before the parenthesis changes all the signs inside it. Therefore, if we want to delete the parenthesis, we need to change the signs before.

4a + 16 - a + 4 = -25

Now we can associate the terms with an a between them and the terms without it from the left side of the equation.

3a + 20 = -25

Let's subtract 20 on both sides.

3a + 20 - 20 = -25 - 20

3a = -45

Finally, we divide by 3 on both sides

3a/3 = -45/3

a = -15