distinguish the number of solutions . show your work. explain how you know the number of solutions. -6x-4y=-4, 3x +2y=6

The value of the absolute difference can be expressed as | x - 2 | ≤ 0.01.

The tolerance for the ball bearing is given as 0.01 inches.

Let x = measured value of the diameter in inches

The absolute difference between x and the true diameter of 2 inches of the ball bearing must be less than or equal to the tolerance of 0.01 inches.

The value of the absolute difference can be expressed using absolute value notation as follows;

| x - 2 | ≤ 0.01

Thus, the inequality above, express the absolute value of the difference between x and 2, which is less than and equal to 0.01.

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The statement that best supports the information in the box plots is: D. the interquartile range value of the data for men 20 - 40 years old is greater than that of men of 50 - 70 years old.

The interquartile range of a data set is the difference between the values that are located on both edges of the rectangular box that is displayed in a box plot.

Interquartile range for the men between 20 - 40 years old = 150 - 110 = 40

Interquartile range for the men between 50 - 70 years old = 125 - 95 = 30

This shows that, D. the interquartile range value of the data for men 20 - 40 years old is greater than that of men of 50 - 70 years old.

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Here is a possible dataset with variables for which the central limit theorem could be applied:

A dataset of customer spending at different retail stores.

Variable for which CLT for mean could be applied:

Average monthly spending per customer. As the number of customers at each store increases, the sample mean spending will approach a normal distribution.

Variable for which CLT for proportions could be applied:

Proportion of customers who spend over $200 per month. Even with a small number of customers at each store, the proportion will be approximately normally distributed as the sample size increases due to the CLT for proportions.

The central limit theorem states that the sampling distribution of the sample mean and sample proportion will be normally distributed for large sample sizes, regardless of the original distribution. So these variables from the retail dataset would satisfy that condition. Please let me know if you would like any clarification or have a different dataset in mind. I can provide additional examples.

The volume is D) 84[tex]m^3[/tex].

What is volume?

The space taken up by any three-dimensional solid constitutes a  volume, to put it simply. A cube, cuboid, cone, cylinder, or sphere can be one of these solids. Cubic units are used to measure the volume of solids. The volume will be given in cubic metres, for instance, if the dimensions are given in metres.

Here the given rectangular prism length = 7m , Width = 4m and Height = 3m.

Now using Volume of rectangular prism formula then,

V = lwh cubic unit.

=> V = 7×4×3

=> V = 84[tex]m^3[/tex]

Hence the volume is D) 84[tex]m^3[/tex].

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[tex](2,1)[/tex], [tex](1,2)[/tex] is your base step

if [tex](a,b)[/tex] is in the set [tex](a+1,b+1)[/tex] will be in  the set

if  [tex](a,b)[/tex] is in the set [tex](a+2,b)[/tex] will be in the set

if [tex](a,b)[/tex] is in the set [tex](a,b+2)[/tex] will be in the set.

Think about how to solve this problem in general. How can you assure that the sum [tex]a+b[/tex] is odd?

Think about this, what happens when you sum two even numbers? The result is even or odd?

[tex]2+6 = 8 \ \text{(even)}[/tex]

[tex]10+12 = 22 \ \text{(even)}[/tex]

And what happens when you sum two odd numbers ? The result will be even or odd?  Look

[tex]3+7 = 10 \ \text{(even)}[/tex]

[tex]5+11 = 16 \ \text{(even)}[/tex]

Therefore to assure that [tex]a+b[/tex] is odd, one of them has to be odd and one of them has to be even, that is why

[tex](2,1)[/tex], [tex](1,2)[/tex] is your base step

if [tex](a,b)[/tex] is in the set [tex](a+1,b+1)[/tex] will be in  the set

if  [tex](a,b)[/tex] is in the set [tex](a+2,b)[/tex] will be in the set

if [tex](a,b)[/tex] is in the set [tex](a,b+2)[/tex] will be in the set.

Answer:  x=1   y=2  z=1

Step-by-step explanation:

Add the first 2 equations to eliminate y (easiest to eliminate)

2x + y - 3z = 1

x - y + 2z = 1

3x        -z  = 2      =>       3x - z = 2    

Multiply the 2nd equation by 3 to eliminate y again with the 3rd equation

(You want to eliminate same variable but using the 3rd equation)

3(x - y + 2z = 1)

3x - 3y + 6z = 3

Now add that to 3rd equation

3x - 3y + 6z = 3

 x + 3y -  z =  6

4x         + 5z = 9       =>      4x + 5z =9

Now you want to eliminate another variable from the 2 equations you just found(equations in bold above

To do that I will multiply the top one by 5

5(3x - z = 2)    

15x - 5z = 10

Now add that to the other equation

15x - 5z = 10

4x + 5z =  9

19x         =19

19x=19           solve for x

x=1

Now substitute that into one of the added equations to solve for z

3x - z = 2        

3(1) - z = 2   simplify

3 - z = 2

-z = -1

z = 1    

Now subsitute x and z into one of the original equations

2(1) + y - 3(1) = 1    simplify

2 + y - 3 = 1

-1 + y = 1

y=2

Sure, I'd be happy to help you calculate these percentages! Here are the solutions:

- 100% of 30 = 30

- 40% of 60 = 0.4 x 60 = 24

- 20% of 80 = 0.2 x 80 = 16

- 40% of 50 = 0.4 x 50 = 20

- 80% of 20 = 0.8 x 20 = 16

- 50% of 30 = 0.5 x 30 = 15

- 60% of 80 = 0.6 x 80 = 48

- 60% of 10 = 0.6 x 10 = 6

- 90% of 70 = 0.9 x 70 = 63

I hope that helps! Let me know if you have any other questions.

The range of the function y=e⁴ˣ is y>0

The range of the function y=e⁴ˣ is the same as the range of any exponential function:

y > 0

The function can take on any positive value, but will never be 0 or negative.

It has a horizontal asymptote of y=0.

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Answer:

To find the formula for (g∘f)(x), we need to first evaluate g(f(x)):

g(f(x)) = g(x+3) = (3(x+3)+5)/3 = (3x+14)/3

So, (g∘f)(x) = (3x+14)/3

To find the domain for (g∘f)(x), we need to consider any restrictions on x that would make the function undefined. The only possible restriction is if the denominator of (3x+14)/3 is zero, which occurs when 3x+14=0. Solving for x, we get x=-14/3. Therefore, the domain of (g∘f)(x) is all real numbers except -14/3, or (-∞, -14/3) U (-14/3, ∞).

Therefore, the answer is (B) 5 hours. We can start by finding out how long it takes Kylie to fill one 2-ounce container. we can get by forming equation .

what is equation ?

In mathematics, an equation is a statement that two expressions are equal. An equation can contain variables, constants, and mathematical operations like addition, subtraction, multiplication, division, exponents, and roots.

In the given question,

We can start by finding out how long it takes Kylie to fill one 2-ounce container. To do this, we can set up a proportion:

75 containers / 50 minutes = 1 container / x minutes

Solving for x, we get:

x = (50 minutes) / (75/1) = 0.67 minutes per container

Now we can use this information to find how long it will take Kylie to fill 450 containers:

450 containers × 0.67 minutes per container = 301.5 minutes

So it will take Kylie 301.5 minutes to make the slime and fill up 450 containers. We can convert this to hours by dividing by 60:

301.5 minutes / 60 minutes per hour = 5.025 hours

Rounding to the nearest hour, we get 5 hours.

Therefore, the answer is (B) 5 hours.

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The answers are A = 46% and B = 20%.

Given that, a table of data, each cell in the table shows the number of cars in that category.

A) The probability that the car's total repair cost is less than $10000 =

86 / (86+35+67) x 100 = 86/188 x 100 = 46%

B) The probability that the car's purchase was more than $40,000 =

40 / (40+86+71) x 100 = 40/197 x 100 = 20%

Hence, the answers are A = 46% and B = 20%.

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Answer: x=102900 feet.

Step-by-step explanation:

The horizontal line extending from the airplane is parallel to the ground. Therefore, the angle of elevation (the angle opposite to the side measuring 20,000 ft) is also 11°. In addition, the angle opposite to x is 90-11=79°. Then, you can use the law of sines to solve for x.

[tex]\frac{sin11}{20000} =\frac{sin79}{x}[/tex]

Solve for x. x=102891. Rounded, 102900.

Or, you can use the tan function. [tex]tan11=\frac{20000}{x}[/tex]

Solve for x. Rounded, x=102900.

Answer: long term

Step-by-step explanation: I got it right on the test

To know more aboutWhat is the average selling price of homes in Bradenton, Florida over the last 6 months?

The average selling price is a statistical measure that represents the total sum of all selling prices divided by the number of items being sold. It provides a useful indication of the typical or central value of a dataset.

According to the given information:

Fom the given information we can frame a question -

To know more aboutWhat is the average selling price of homes in Bradenton, Florida over the last 6 months?

To calculate the average selling price of homes in Bradenton, Florida over the last 6 months, you would need to:

1) Gather the selling prices of all the homes that have sold in the area over the last 6 months.

2) Add up all of the selling prices to get a total sum.

3) Divide the total sum by the number of homes that have sold to get the average selling price.

For example, if there were 100 homes sold in the last 6 months, and the total sum of their selling prices was $25,000,000, then the average selling price would be:

Average Selling Price = Total Sum / Number of Homes Sold

Average Selling Price = $25,000,000 / 100

Average Selling Price = $250,000

Therefore, the average selling price of homes in Bradenton, Florida over the last 6 months is $250,000.

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For the given data we've Number of class = 5, minimal value = 67900, Maximum value = 321550, Class range = 50730. The histogram, frequency polygon, and accretive frequency polygon are as shown.

In a graphic representation of data called a histogram, a set of nonstop numerical data is distributed in a given way. Each cube's area is related to the frequency of data values being within a given interval or caddy. It consists of a sequence of blocks or bars. The y- axis displays the frequency or count of values that fall inside each interval, while thex-axis displays the range of values that are divided up into intervals or lockers. Large data sets can be visually summarised using histograms, which can also be used to spot patterns and trends as well as outliers or unanticipated figures.

For the given data we have

Number of class = 5

minimal value = 67900

Maximum value = 321550

Class range = Range/ Number of class

= 321550- 67900/ 5

= 50730

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The complete question is:

Caleb earned an interest of $27.50 on $500 for 1 year at a rate of 5.5% per year.

Explanation:

The interest earned by Caleb on $500 for 1 year at a rate of 5.5% per year can be calculated using the simple interest formula:

I = P * r * t

where I is the interest earned, P is the principal (starting amount), r is the annual interest rate as a decimal, and t is the time period in years.

Plugging in the given values, we get:

I = 500 * 0.055 * 1

I = 27.50

Therefore, Caleb earned an interest of $27.50 on $500 for 1 year at a rate of 5.5% per year.

If one flyer is  3.0 × 10⁻³ inches thick, the stack of 1.25 × 10³ flyers has a thickness of 3.75 inches.

To find the thickness of a stack of flyers, we need to multiply the thickness of a single flyer by the number of flyers in the stack. In this case, the thickness of a single flyer is given as 3.0 × 10⁻³ inches, and the number of flyers in the stack is 1.25 × 10³.

So, the thickness of the stack can be calculated as:

Thickness of stack = Thickness of a single flyer x Number of flyers in the stack

Thickness of stack = 3.0 × 10⁻³ inches x 1.25 × 10³

Thickness of stack = (3.0 x 1.25) × (10⁻³ × 10³) inches

Thickness of stack = 3.75 inches

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The coordinates of the vertices of the triangle A''B''C'' after the two successive dilations are (3 times the x-coordinate and 3 times the y-coordinate of the original triangle's vertices).

To find the coordinates of the vertices of the dilated triangle A''B''C'' after two successive dilations, first with a scale factor of 4 and then with a scale factor of 3/4.

Firstly, Apply the first dilation with a scale factor of 4 to the original triangle ABC, with a center of dilation at the origin. This can be done by multiplying each coordinate of the original triangle by 4.

The coordinates of the dilated triangle A'B'C' after the first dilation would be;

A' = (4 × x-coordinate of A, 4 × y-coordinate of A)

B' = (4 × x-coordinate of B, 4 × y-coordinate of B)

C' = (4 × x-coordinate of C, 4 × y-coordinate of C)

Now, we apply the second dilation with a scale factor of 3/4 to the dilated triangle A'B'C', again with a center of dilation at the origin. This can be done by multiplying each coordinate of A'B'C' by 3/4.

The coordinates of the dilated triangle A''B''C'' after the second dilation would be;

A'' = ((3/4) × x-coordinate of A', (3/4) × y-coordinate of A')

B'' = ((3/4) × x-coordinate of B', (3/4) × y-coordinate of B')

C'' = ((3/4) × x-coordinate of C', (3/4) × y-coordinate of C')

Plugging in the values of A', B', C' obtained from the first dilation, we get;

A'' = ((3/4) × 4 × x-coordinate of A, (3/4) × 4 × y-coordinate of A)

B'' = ((3/4) × 4 × x-coordinate of B, (3/4) × 4 × y-coordinate of B)

C'' = ((3/4) × 4 × x-coordinate of C, (3/4) × 4 × y-coordinate of C)

Simplifying further, we get;

A'' = (3 × x-coordinate of A, 3 × y-coordinate of A)

B'' = (3 × x-coordinate of B, 3 × y-coordinate of B)

C'' = (3 × x-coordinate of C, 3 × y-coordinate of C)

Therefore, the  coordinates of the vertices of the triangle A''B''C'' after the two successive dilations are (3 times the x-coordinate and 3 times the y-coordinate.

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Answer:

A) (1, 0)

Step-by-step explanation:

The point (0, 0) lies on the x-axis and y-axis, so any point that lies on either axis will be collinear to it. Therefore, the answer is A) (1, 0).

Hope this helps!

Answer:

is a measure of the average absolute distance between each data value and the mean of a data set.

It will take 2.48 hours for the number of bacteria to reach 3500.

In order to find number of hours to take for the number of bacteria to reach 3500, we can set the function equal to 3500 and solve for h.

The function given is P(h) = 2800e^(0.09h). So, plugging the values of 3500, we will get:

3500 = 2800e^(0.09h)

Dividing both sides by 2800, we get:

e^(0.09h) = 3500/2800

Taking the natural logarithm of both sides, we get:

0.09h = ln(3500/2800)

h = (ln(3500/2800))/0.09

h = 0.22314355131/0.09

h = 2.47937279233

h = 2.48 hours

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Answer:

8[tex]\frac{29}{40}[/tex]

Step-by-step explanation:

The least common multiply is 40

[tex]\frac{4}{5}[/tex] x [tex]\frac{8}{8}[/tex] = [tex]\frac{32}{40}[/tex]

2 [tex]\frac{3}{10}[/tex] x [tex]\frac{4}{4}[/tex] = 2 [tex]\frac{12}{40}[/tex]

5 [tex]\frac{5}{8}[/tex] x [tex]\frac{5}{5}[/tex] = 5 [tex]\frac{25}{40}[/tex]

Now that we have a common denominator, add these numbers together

[tex]\frac{32}{40}[/tex] + 2 [tex]\frac{12}{40}[/tex] + 5 [tex]\frac{25}{40}[/tex]

7 [tex]\frac{69}{40}[/tex]

7 + [tex]\frac{40}{40}[/tex] + [tex]\frac{29}{40}[/tex]  I broke up [tex]\frac{69}{40}[/tex] because I know that [tex]\frac{40}{40}[/tex] equals 1

8 [tex]\frac{29}{40}[/tex]

Helping in the name of Jesus.

The correct answer is to increase from left to right. The correct option is B.

To complete the table for the function [tex]y = 3^x - 3[/tex],

x y

-3 1/27

-2 1/3

-1 0

0 2

1 6

2 18

3 54

To graph the function, we can plot the points from the completed table on a coordinate plane and connect them with a smooth curve.

The graph of the function [tex]y = 3^x - 3[/tex]  looks like an exponential function that increases from left to right, passing through the point (0, 2) on the y-axis. The graph is concave up and approaches the x-axis but never touches it.

Therefore, the correct answer is to increase from left to right. The correct option is B.

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1) consumers are willing to buy more of a good at a lower price than at a higher price  Option B

2) All of these

3) All of these

An economic theory known as the law of demand states that, all other things being equal, if a good or service's price rises, consumers will demand fewer units of it, and vice versa.

Price and quantity demanded are inversely related, to put it another way. This is a fundamental concept in economics and plays a key role in shaping market behavior and pricing strategies.

The price system is a way of adjusting the balance between the forces of supply and demand. A key advantage of the corporate form of business organization is the ability to raise significant amounts of financial capital.

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The value of N in the algebraic equation is 600.

An algebraic equation is when two expressions are set equal to each other, and at least one variable is included.

If to 15% of 20% of 5N we add 30% of 50% of 2N we get 270. We have:

(15/100 * 20/100 * 5N)  + (30/100 * 50/100 * 2N) = 270

0.15N + 0.3N = 270

0.45N = 270

N = 270/0.45

N = 600

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Question in English

If to 15% of 20% of 5N we add 30% of 50% of 2N we get 270. Calculate N.

Answer:

965.22%

Step-by-step explanation:

To write 9.6522 as a percentage, we can multiply it by 100 and add the percent symbol (%):

9.6522 * 100% = 965.22%

Therefore, 9.6522 is equal to 965.22% as a percentage.

Hope this helps!

Answer:

Step-by-step explanation:

41.67 is the answer brainlist and verifed  answer

Answer:

a) $299.60

b) $337.05

c) Nicole would pay more at the store

Step-by-step explanation:

a) 10% of $749 = $74.90

60% = ($74.90 x 6) = $449.40

$749 - $449.40 = $299.60

b) 10% = $74.90

50% = $374.50

$749 - $374.50 = $374.50

10% of $374.50 = $37.45

$374.50 - $37.45 = $337.05

The y-intercept of the function is -1. (option a).

In mathematics, a function is a rule that assigns each input (or argument) of a set, to a unique output (or value) of another set. In this case, the function f(x) is given by f(x)=−1(2/3)^x.

To find the y-intercept of a function, we need to evaluate the function at x=0. This is because the y-intercept is the point at which the graph of the function intersects the y-axis, and the y-axis is where x=0.

To find the y-intercept of the function f(x)=−1(2/3)ˣ, we need to evaluate the function at x=0. This gives us:

f(0) = -1(2/3)⁰

f(0) = -1(1)

f(0) = -1

This means that the graph of the function intersects the y-axis at the point (0,-1).

Hence the correct option is (a).

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x = 12 times square root 2 (45 45 90 triangle)

y = 6 times square root 2 (30 60 90 triangle)

Answer:

  y = -x +3

Step-by-step explanation:

You want the slope-intercept equation of the line with the same intercept as -3y = -9 +3x, and the same slope as -2x -2y = -8.

The slope-intercept form of the equation of a line is ...

  y = mx +b . . . . . where m is the slope, and b is the y-intercept

For the given equations, we can put them in this form to find the desired parameters.

  -3y = -9 +3x

  y = -x +3 . . . . . . . . . . divide both sides by -3

We observe that the y-intercept is +3, which we will need for our answer.

The slope-intercept form of the second equation is ...

  -2x -2y = -8

  x + y = 4 . . . . . . . . . . divide by -2

  y = -x +4 . . . . . . . . . . subtract x

We observe that the slope (coefficient of x) is -1, which we will need for our answer.

We want the equation of the line with slope -1 and y-intercept 3. It is ...

  y = -x +3 . . . . . . . . . . same as the equation of the first line

__

Additional comment

The slope-intercept equation (green) is plotted using dots, so that you can see it is coincident with the line described by the first equation (red). Parallel lines have the same slope, so our desired line must be parallel to the blue line. (It is.)

When abraham was born his parents put 2000 into an account that yielded 1.2%, Abram will receive $2,213.10 on his 16th birthday.

To calculate how much Abram will receive on his 16th birthday, we need to use the compound interest formula:

A = [tex]P(1 + r/n)^{(nt)[/tex]

Where:

A = the amount Abram will receive

P = the principal amount (initial investment) = $2,000

r = the annual interest rate = 1.2% = 0.012

n = the number of times the interest is compounded per year = 2 (semi-annually)

t = the number of years = 16/2 = 8 (since interest is compounded twice a year)

Plugging in the values, we get:

A = $2,000(1 + 0.012/2)¹⁶

A = $2,000(1.006)¹⁶

A = $2,000(1.10655)

A = $2,213.10

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Complete question is:

When Abram was born, his parents put $2,000 into an account that yielded 1.2% interest, compounded semi-annually. When he turns age 16, his parents will give him the money to buy a car. How much will Abram receive on his 16th birthday?