Write in slope-intercept form an equation of the line that passes through the given points.
(6,8),(3,−9)

Answer:

Step-by-step explanation:

It s 55555555

Answer:

18x^2-45x

Step-by-step explanation:

-9x (5-2x)

=-9x X 5-(-9x) X 2x

=-9 X 5x+9 X 2xx

=18x^2-45x

I hope this helps!

-6.75 is a rational number since it can be expressed as a fraction of two integers. It's also a real number, but it's not a natural, whole, integer, or irrational number.

The number -6.75 is a Rational Number. Here's why:

A Natural Number is a number that is a positive integer, which would not include -6.75 because it is negative. A Whole Number is a number without fractional components, so -6.75 isn't a whole number as it has a fractional part. An Integer is a whole number that can be positive, negative, or zero, but does not include fractions or decimals, therefore, -6.75 isn't an integer. A Rational Number is a number that can be expressed as a fraction of two integers, and since -6.75 can be written as -675/100, it falls into this category. Since all rational numbers are included in the Real Number set, -6.75 is also a real number. However, an Irrational Number cannot be expressed as a ratio of two integers, which means that -6.75 isn't irrational.

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Answer:

Using the empirical rule, the probability of a zebra living less than 32.2 years is about [tex] \\ P(z<3) = P(x<32.2) = 0.9985[/tex] or about 99.85%.

Step-by-step explanation:

Roughly speaking, the empirical rule tells us that, in a normal distribution, the distance of one standard deviation from the mean, above and below it, contains approximately 68% of the observations of the normally distributed data; two standard deviations from the mean, above and below it, 95% of the data, and, finally, the distance of three standard deviations from the mean, above and below it, contains 99.7% of the data, approximately.

To estimate probabilities with this rule, we need to use, at least, two concepts: the standard normal distribution and the z-scores. A standard normal distribution is a normal distribution with mean = 0 and standard deviation = 1. It represents standardized data. This standardized data are those coming from a normal distribution and commonly called raw data. The way to standardized them is using the z-scores:

[tex] \\ z = \frac{x - \mu}{\sigma}[/tex] [1]

Where

x represents raw data. In this case, x = 32.2 years.

[tex] \\ \mu[/tex] is the population mean. In this case, [tex] \\ \mu = 20.5[/tex] years.

[tex] \\ \sigma[/tex] is the population standard deviation. In this case, [tex] \\ \sigma = 3.9[/tex] years.

Then, using [1], we "transform" the raw score into a z-score (a standardized value) and then use this to find the corresponding probability using the standard normal distribution (or the cumulative standard normal distribution to be more precise), available in any Statistics book or on the Internet.

However, applying the empirical rule, we can estimate those probabilities faster but in an approximate way.

Let us take the corresponding z-score:

[tex] \\ z = \frac{x - \mu}{\sigma}[/tex]

[tex] \\ z = \frac{32.2 - 20.5}{3.9}[/tex]

[tex] \\ z = \frac{11.7}{3.9}[/tex]

[tex] \\ z = 3[/tex]

That is, the value z = 3 tells us the raw score 32.2 years is three standard deviations from the mean. In other words, 99.7% of the values are between z = -3 and z = 3. However, we are asked for P(z<3). The remaining area is below z = -3 and above z = 3. Since the normal distribution is symmetrical, we have to divide the remaining area by 2. That is, (1 - 0.997)/2 = 0.003/2 = 0.0015.

The area below z = -3 is, therefore, 0.0015, as well as above z = 3 or P(z<-3) = P(z>3) = 0.0015. The only area that not correspond to P(z<3) is P(z>3). As a result, we need to add the area below z = -3 (0.0015) to the value of 0.997 to finally have P(z<3).

Then

[tex] \\ P(z<3) = P(x<32.2) = 0.997 + P(z<-3)[/tex]

[tex] \\ P(z<3) = P(x<32.2) = 0.997 + 0.0015[/tex]

[tex] \\ P(z<3) = P(x<32.2) = 0.9985[/tex]

Thus, using the empirical rule, the probability of a zebra living less than 32.2 years is about [tex] \\ P(z<3) = P(x<32.2) = 0.9985[/tex].

In the graph below, we have a representation of the area below z = 3 or P(z<3) = P(x<32.2) is, approximately, 0.9985 or 99.85%.

Notice that using the cumulative standard normal table, as explained before, we have that P(z<3) = 0.99865.

Answer: 68, if the question asks between 16.6 and 24.4 years. 99.85, if the question asks for less.

Step-by-step explanation:

Answer:

16 ft

Step-by-step explanation:

Hi there,

The formula for the area of a rectangle is A = b*h.

So, let's start out by plugging in what we know.

240 = 15h

Now, solve for h by dividing both sides by 15

h = 16

So, the height of the rectangle is 16 ft

Hope this helps! Stay safe!

- Emily

Answer:

x=4± 5sqrt(2)

Step-by-step explanation:

x^2 – 8x – 34 = 0

To complete the square Add 34 to each side

x^2 -8x -34+34=0+ 34

Take the coefficient of x, and divide by 2

-8/2 =-4

Then square it and add it to each side

(-4)^2 =16

x^2 – 8x +16 = 34+16

x^2 – 8x +16 = 50

We replace the left side with (x + the coefficient of x/2)^2

(x -4)^2=50

Take the square root of each side

sqrt((x -4)^2)=±sqrt(50)

x-4 = ±sqrt(25*2)

x-4 = ±sqrt(25)*sqrt(2)

x-4 = ±5sqrt(2)

Add 4 to each side

x=4± 5sqrt(2)

Answer:

4 + 5sqrt(2), 4 - 5sqrt(2)

Step-by-step explanation:

x² - 8x - 34 = 0

x = [-(-8) +/- sqrt((-8)² - 4(1)(-34))]/2

x = (8 +/- sqrt200)/2

x = 4 +/- 5sqrt(2)

Answer:

9

Step-by-step explanation:

just replace the x with 2 and solve

4(2)+1

8+1

= 9

Answer:

1.  The mean hemoglobin level in men is not equal to the mean hemoglobin level in women and

2. There is more hemoglobin in the average man than in the woman

Step-by-step explanation:

The confidence interval is from

-1.76 g/dl < μ₁ - μ₂ < -1.62 g/dl

Here we note that the range in the confidence interval for the difference between the two means lie in the negative part of the number line which is indicative of that μ₁ - μ₂ ≠ 0  or μ₁ ≠ μ₂

That is the statistic of the confidence interval implies that the mean hemoglobin level in men is not equal to the mean hemoglobin level in women and

That there is more hemoglobin in the average man than in the woman.

Answer:

$5 (5) - ($7+$9)=m

$25 - $16 =m

Step-by-step explanation:

$5 (5) - (7+9)=m

$25 - 16 =m

The equation to represent how much money Grace has left is:

m = $25 - $7 - $9

m = $25 − $16

m = $9

Grace earns $5 for each dog walk.

She walks the dog 5 times in one week, so she earns 5 walks * $5/per walk = $25.

She spends $7 on a book and $9 on a building set, so she spends a total of $7 + $9 = $16.

To find out how much money Grace has left, m, we subtract her total spending from her earnings.

So, the equation to represent how much money Grace has left is:

m = $25 − $16

m = $9

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Answer:

Length of pipe to Chesterville is 8.376 miles and

Length of pipe to Denton is 5.46 miles

Step-by-step explanation:

Here we have

The distance of Chesterville from the river is 3 miles, while the distance of Denton from the river is 5 miles

The bank of the river is 10 miles long

Therefore, we have

If x is the distance from the point directly opposite to Chesterville to the location of the water works, the equation is;

Cost to Chesterville = [tex]3000\times \sqrt{x^2 + 3^2}[/tex]

Cost to Denton = [tex]7000\times \sqrt{(10-x)^2 + 5^2}[/tex]

Total cost is then;

[tex]7000\times \sqrt{(10-x)^2 + 5^2} + 3000\times \sqrt{x^2 + 3^2}[/tex]

We differentiate the above equation and equate it to zero to get the minimum cost as

[tex]\frac{\mathrm{d} (7000\times \sqrt{(10-x)^2 + 5^2} + 3000\times \sqrt{x^2 + 3^2})}{\mathrm{d} x}[/tex] = 0

[tex]7000\frac{2x-20}{2\sqrt{x^2-20x+125} } +3000\frac{2x}{2\sqrt{x^2+9} } = 0[/tex]

[tex]3500\frac{2x-20}{\sqrt{x^2-20x+125} } = -1500\frac{2x}{\sqrt{x^2+9} }[/tex]

[tex]3500\frac{\sqrt{x^2+9}}{\sqrt{x^2-20x+125} } = -1500\frac{2x}{2x-20 }[/tex]

[tex]x^4-20x^3+10.54x^2-22.05x+110.25 =0[/tex]

Solving the quartic equation we get

x = 7.82 miles

Therefore the length of is given as

Length of pipe to Chesterville  [tex]\sqrt{7.82^{2} +3^2 } = 8.376 \, miles[/tex]

Length of pipe to Denton = [tex]\sqrt{(10-7.82)^2 + 5^2} = 5.46 \, miles[/tex].

Answer:

True

I hope this helps :)

Answer:

True

Step-by-step explanation:

True because there are only negative numbers in the calculation. Zero pairs are formed when a positive and a negative number are added

Answer:

$169

Step-by-step explanation:

Sara must pay the entry fee, and then a fee of 18$/month. if she is a member for 8 months the total paid must be

[tex]25 + 18*8 = 169[/tex]

Answer:

$169

Step-by-step explanation:

25+18m=$

m represents the months she participates for

25+18(8)=$

25+144=$

169=$

She pays $169 to be in a fruit club. Wow.

Answer:

The answer to your question is x = -2, y = 5 and z = 7

Step-by-step explanation:

Data

first number = x

second number = y

third number = z

Process

1.- Write equations to solve this problem

                 x + y + z = 10           Equation l

                 2y - x = 12                Equation ll

                  x - y + 2z = 7           Equation lll

2.- Solve equation ll for x

                x = 2y - 12

3.- Substitute the previous equation in equation l and lll

               (2y - 12) + y + z = 10                     (2y - 12) - y + 2z = 7

                2y - 12 + y + z = 10                       2y - 12 - y + 2z = 7

                3y + z = 10 + 12                             y + 2z = 19

                3y + z = 22

4.- Solve for y and z

                     -2(3y + z = 22)

                          y + 2z = 19

                    -6y - 2z = -44

                       y + 2z = 19

                   -5y   + 0 = -25

                      y = -25/-5

                      y = 5

-Find z

                       5 + 2z = 19

                             2z = 19 - 5

                             2z = 14

                               z = 14/2

                               z = 7

5.- Find x

                  x + 5 + 7 = 10

                  x = 10 - 5 - 7

                 x = -2

Listed in order from smallest to largest: -2, 5, 7.

Let's denote the three numbers as follows:

- First number: x

- Second number: y

- Third number: z

We have three equations based on the given information:

1. x + y + z = 10

2. 2y - x = 12

3. x - y + 2z = 7

We can solve this system of equations to find the values of x, y, and z.

From equation 2, we can isolate x:

x = 2y - 12

Now substitute the value of x in equations 1 and 3:

1. (2y - 12) + y + z = 10

3y + z = 22

3. (2y - 12) - y + 2z = 7

y + 2z = 19

Now we have a system of two equations with two variables (y and z):

1. 3y + z = 22

2. y + 2z = 19

Let's solve for one of the variables in terms of the other. From equation 2, we can isolate y:

y = 19 - 2z

Now substitute this value of y into equation 1:

3(19 - 2z) + z = 22

57 - 6z + z = 22

-5z = -35

z = 7

Substitute the value of z back into the equation for y:

y = 19 - 2(7)

y = 5

Now that we have values for y and z, we can substitute them back into the equation for x:

x = 2y - 12

x = 2(5) - 12

x = 10 - 12

x = -2

So, the numbers are:

First number: -2

Second number: 5

Third number: 7

Listed in order from smallest to largest: -2, 5, 7.

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Answer:

56.

Step-by-step explanation:

That is the number of permutations of 2 from 8

= 8P2

= 8!/(8-2)!

= 8!/6!

= 8 * 7

= 56.

Answer:57

Step-by-step explanation:

12

13

14

15

16

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18

21

23

24

25

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27

28

31

32

34

35

36

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41

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Answer:

If there are eleven apples to be shared between 3 boys and two bananas to be shared between 3 girls, find the difference between them.

Step-by-step explanation:

So there are 11 apples to be shared between 3 boys, which is represented mathematically as 11/3

And 2 bananas to be shared between 3 girls, which can be represented mathematically as 2/3, find the difference.

The difference between them would be 11/3 - 2/3

Solving this problem, they both have the same denominator, so we subtract the numerators directly.

11/3 - 2/3 = 9/3

Which is equals to 3.

So the difference between both of them is 3.

Answer: There are lots of common polar curves that are bounded therefore a polar curve is not always bounded all the time. A polar curve is required to have an unbounded function (right side of r = f(Θ)) to be an unbounded polar. An example of an unbounded curve would be r = Θ for 0 ≤ Θ.

Answer:

There are lots of common polar curves that are bounded therefore a polar curve is not always bounded all the time. A polar curve is required to have an unbounded function (right side of r = f(Θ)) to be an unbounded polar.

Step-by-step explanation:

its correct on EDGE2022

Given:

The area of the given sphere = 36π in²

To find the volume of the given sphere.

We need to find the radius first.

Formula

where, r be the radius of the sphere.

Now,

According to the problem,

[tex]4\pi r^{2} = 36\pi[/tex]

or,[tex]4r^{2} = 36\\[/tex] [ Eliminating π from both the side]

or, [tex]r^{2} = \frac{36}{4}[/tex]

or, [tex]r = \sqrt{9}[/tex]

or, [tex]r = 3[/tex]

So,

The radius of the sphere is 3 inches

Therefore,

The volume of the sphere is

[tex]V = \frac{4}{3} \pi (3)^{3}[/tex]

or, [tex]V = 36\pi[/tex]

Hence,

The volume of the sphere is 36π cube inches.

Answer:

Step-by-step explanation:

Amount loaned = $10,000

Interest rate = 3%

Duration = 6 years

10,000 / 100 x 3/1 × 6

= 300 × 6

= 1800 + 10,000

Total Amount to pay

= $11,800

Answer:

60 ft, 120 ft, 182 ft

Step-by-step explanation:

Hi there,

To find the perimiter of a polygon, you need to add of all of the sides.

So, let's do that:

x + 2x + 3x+2

Since we are given the perimeter, we make what we just did above, equal to the perimeter

x + 2x + 3x +2 = 362

Combine lke terms...

6x + 2 = 362

Subtract 2 from both sides to start to isolate the variable...

6x = 360

Divide both sides by 6 to isolate x...

x = 60

But we're not done yet...

The length of the first side is 60 ft, the length of the second side is 2*60 which is 120 ft, and the length of the third side is 3*60 + 2 which is 182 ft.

Let's check...

Does 60 + 120 + 182 = 362?

362 = 362

Our answers are right

Hope this helps! Stay safe!

- Emily

Answer:

She has 2 pieces left

Step-by-step explanation:

Answer:

30% not likely

Step-by-step explanation:

We have 10 marbles

The probability must equal 100%

10% red

60% yellow

----------------

70 %

That leaves 30% for orange

Orange is 30%

This is less than 50% so it is not likely to occur

Answer:

30%

not likely

Step-by-step explanation:

P(orange) = 100 - 10 - 60

= 30%

Less likely or not likely

Answer:

4 i did the quizzzzzzzzzzzzzzzzzzzzzzzzz

Step-by-step explanation:

Answer:

-2

or

A.

Step-by-step explanation:

on edge 2020

To find the lateral surface area of a cylinder with a radius of 30.8 cm and a height of 20.5 cm, use the formula 2πrh. The calculation gives a result of approximately 3981.86 square centimeters.

The question asks for the closest measurement to the lateral surface area of a cylinder with a radius of 30.8 centimeters and a height of 20.5 centimeters. To find the lateral surface area of the cylinder, we use the formula: Lateral Surface Area = 2πrh, where 'r' is the radius, and 'h' is the height of the cylinder. Substituting the given values,

we get Lateral Surface Area = 2 × 3.14 × 30.8 cm × 20.5 cm.

Calculating this, we find:

Lateral Surface Area = 3981.864 square centimeters. Therefore, the closest measurement to the lateral surface area of the cylinder is 3981.86 square centimeters.

Answer:

2

Step-by-step explanation:

your welcome

Answer:

2:2,4,6,8,10,12,14,16

4:4,8,12,16

8:8,16

the LCM is 16

Answer:

B. 4/5

Step-by-step explanation:

8/10 simplified is 4/5 so the other person is still correct.

But if there's a fraction that could be simplified, then the simplified answer would be the best answer you're looking for.

Answer:

Initial value is at t = 0

Y-intercept is the initial value

Answer:

E

Step-by-step explanation:

-18x + 21 > -15

-18x > -36

x < 2

20x - 13》17

20x》40

x》2

Or is union

Union of x < 2 and x》2 is all real numbers

Answer:

  11

Step-by-step explanation:

Let e represent the number of students with blue eyes. Then the number of students with blond hair is 2e. The total number of students is ...

  3 + e + 2e -6 = 30

We subtracted 6 because the expressions e and 2e cause the 6 students with both blond hair and blue eyes to be counted twice.

  3e = 33 . . . . add 3 and simplify

  e = 11

11 students have blue eyes.

In the given problem, using the logical reasoning to deduce from the given facts, it can be determined that there are 10 students in Mrs. Taylor's class that have blue eyes.

To find out how many students in Mrs. Taylor's kindergarten class have blue eyes, we need to use the information given in the problem and make a series of logical deductions.

First, we know that there are twice as many students with blond hair as with blue eyes. Let's say the number of students with blue eyes is x. This implies that the number of students with blond hair is 2x.

We also know that there are 6 students with both blond hair and blue eyes. So, those students are included in both of our previous counts. Therefore, we need to subtract 6 from each count to get the number of students with only one of those attributes.

So far, this gives us x - 6 students with only blue eyes and 2x - 6 students with only blond hair. We know that there are 3 students with neither attribute, so the total number of students is (x - 6) + (2x - 6) + 6 (students with both attributes) + 3 (students with neither attribute) = 30.

Adding these together gives us 3x = 30, so x = 30/3 = 10. Therefore, there are 10 students with blue eyes.

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