What method can be used to write the equation of a line in slope-intercept form given two points?
A. Find the slope using the formula m = StartFraction y 2 minus y 1 Over x 2 minus x 1 EndFraction, and then substitute one point and the slope into the equation y = m x + b to find the y-intercept.
B. Find the slope using the formula m = StartFraction x 2 minus x 1 Over y 2 minus y 1 EndFraction, and then substitute one point and the slope into the equation y = m x + b to find the y-intercept.
C. Find the y-intercept using the formula m = StartFraction y 2 minus y 1 Over x 2 minus x 1 EndFraction, and then substitute one point and the y-intercept into the equation y = m x + b to find the slope.
D. Find the y-intercept using the formula m = StartFraction x 2 minus x 1 Over y 2 minus y 1 EndFraction, and then substitute one point and the y-intercept into the equation y = m x + b to find the slope.

Answer:

13

Step-by-step explanation:

Organizing the numbers

8 10 11 12 14 15 15 16

The median are both 12 and 14 but to get one median you add the two numbers 12 + 14 which equals 26. 26 divided by 2 numbers  equals 13

After applying a 10% coupon and 12.75% sales tax, the total cost for one night at the Great Wolf Lodge is approximately $252.67.

To find the total cost for one night at the Great Wolf Lodge including a 10% discount and 12.75% sales tax, we first need to calculate the amount of the discount. Since the discount is 10% off, you would multiply the original cost of $249 by 0.10 to get $24.9. Then subtract this from the original cost to find the discounted cost: $249 - $24.9 = $224.1. Next, apply the 12.75% sales tax to the discounted cost. Multiply $224.1 by 0.1275 to get $28.5725. Add this to the discounted cost: $224.1 + $28.5725 = $252.6725. So, including the discount and sales tax, the total cost for one night would be approximately $252.67.

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To find the total cost for one night, calculate the discount, subtract it from the original price, calculate the sales tax, and add it to the discounted price.

To find the total cost for one night at the Great Wolf Lodge, you need to calculate the discount from the coupon and add the sales tax to the discounted room rate.

The total cost for one night at the Great Wolf Lodge, after applying the 10% discount and including the 12.75% sales tax, is $252.68.

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Answer:

D. Kailey is not correct:  [tex]89.12 \times 10^5[/tex] is not written in scientific notation.

Step-by-step explanation:

We have been given that Kailey wrote 8,912,000 in scientific notation as [tex]89.12 \times 10^5[/tex]. We are asked to choose the statement that best describes Kailey's work.    

We know that to convert a number into scientific notation, we write the given number as product of two numbers. One factor is a number between 1 and 10, while the 2nd factor is power of 10.  

Upon looking at [tex]89.12 \times 10^5[/tex] , we can see that 1st factor is 89.10, which is greater than 10. This means that Kailey did not write 8,912,000 in scientific notation.

Therefore, option D is correct choice.

Answer:

d

Step-by-step explanation:

Step-by-step explanation:

undefined

Answer:

C) Undefined

Step-by-step explanation:

When the slope on a graph is straight there is no slope so therefore it is undefined.

Answer:

there are three x-intercepts

Step-by-step explanation:

-5, -1, 9 are all the x-intercepts that appear on the graph.

Answer: 3

Step-by-step explanation:

egde

Answer:

The new function is [tex]y=\frac{1}{x-5}+3[/tex] , where x ≠ 5

Step-by-step explanation:

The reciprocal parent function is [tex]f(x)=\frac{1}{x}[/tex] , where x ≠ 0

The translation of f(x) to the right h units is f(x - h)

The translation of f(x) up k units is f(x) + k

The translation of f(x) to the right h units and up k units is f(x - h) + k

∵ The equation of the reciprocal parent function is  [tex]y=\frac{1}{x}[/tex]

∵ The function is translated 5 units right

∴ h = 5

- That means 5 is subtracted from x ⇒ (x - 5)

∵ The function is  translated 3 units up

∴ k = 3

- That means y added by 3

∴ [tex]y=\frac{1}{x-5}+3[/tex]

The new function is  [tex]y=\frac{1}{x-5}+3[/tex] , where x ≠ 5

Answer:

0.123

Step-by-step explanation:

Use the random variable E - S, which will follow a normal distribution with a mean of 70 - 60 = 10 and SD = \sqrt{5^2+7^}

P(E - S < 0) = 0.123

The probability that a randomly selected standard model tire will get more mileage than a randomly selected extended life tire is 0.123.

Normally distributed data is the distribution of probability which is symmetric about the mean.

The mean of the data is the average value of the given data. The standard deviation of the data is the half of the difference of the highest value and mean of the data set.

A company advertises two car tire models. The number of thousands of miles that the standard model tires last has a mean and standard deviation,

[tex]\mu_S= 60[/tex]

[tex]\sigma_S = 5[/tex]

The number of miles that the extended life tires last has a mean and standard deviation,

[tex]\mu_E = 70[/tex]

[tex]\sigma_E = 7[/tex]

Use the E-S random variable rule,

[tex]E=\mu_E-\mu_s\\E=70-60\\E=10[/tex]

Similarly, the value of S,

[tex]E=\sqrt{\sigma^2_E+\sigma^2_s}\\S=\sqrt{7^2+5^2}\\S=\sqrt{49+25}\\S=\sqrt{74}\\S=8.60[/tex]

For this E-S value, the value of probability from the table of normal distribution, we get as 0.123.

[tex]P(E - S < 0)=0.123[/tex]

Thus, the probability that a randomly selected standard model tire will get more mileage than a randomly selected extended life tire is 0.123.

Learn more about the normally distributed data here;

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Answer:

adult 10

child 4

Step-by-step explanation:

for example,we buy x tickets for adults,y tickets for children.

so we can know x+y=14,9x+5y=110

5(x+y)=70

110-70=40

40/(9-5)=10,this is for adults

the rest are for child

Answer:9×10=90+15=105+5=110

Step-by-step explanation:

Answer:

Step-by-step explanation:

The 20% discount amounted to ...

  0.20 × $42.00 = $8.40

so the price before tax was ...

  $42.00 -8.40 = $33.60

The tax amount is 3% of this value, so is ...

  0.03 × $33.60 = $1.008 ≈ $1.01

So the total price paid for the shirt was ...

  $33.60 +1.01 = $34.61

Randy paid $34.61 for the shirt after discount and tax.

___

Alternate solution

You can realize that the 20% discount means that Randy will pay 80% of the original price of the shirt. Similarly, the 3% added tax means Randy will finally pay 103% of the discounted price. Then the total price Randy pays is ...

  $42.00×0.80×1.03 = $34.608 ≈ $34.61

Answer:

the correct answer is...

Step-by-step explanation:

4x+9

Answer:

  434,470 gallons

Step-by-step explanation:

The exponential equation for the volume v remaining after t hours can be written as ...

  v(t) = (initial amount)×(decay factor)^(t/(decay time))

  v(t) = 500,000×(1 -10%)^(t/3)

Then after 4 hours, the remaining volume is ...

  v(4) = 500,000×(0.90^(4/3)) ≈ 434,470 . . . . gallons

_____

Comment on the form of the equation

The decay factor is related to the decay rate by ...

  decay factor = 1 - (decay rate)

and the decay time is the time applicable to that decay rate. Here, the rate is 10% every 3 hours, so the decay time is 3 hours for a decay rate of 10%.

Answer:

24 possible outcomes

Step-by-step explanation:

Combination has to do with selection. For example, if r object is selected from a pool of n objects, the number if possible ways can be expressed according to the combination formula:

nCr = n!/(n-r)!r!

Applying this in question, if each student receives one of 4 calculator models and one of 3 types of ruler, the number of ways this can be done is:

4C1 × 3C1

4C1 = 4!/(4-1)!1! {If a student gets one calculator)

4C1 = 4×3×2/3×2

4C1 = 4ways

3C1 = 3!/(3-2)!1! {If a student gets a ruler}

3C1 = 3×2/1

3C1 = 6ways

Total number of possible outcomes if a student gets one ruler and one calculator will be 4×6 = 24ways

Answer:

Yes, an isosceles triangle is always 45 45 90 so its TRUE!!

Answer:

[tex]\huge \boxed{\mathrm{True}}[/tex]

Step-by-step explanation:

An isosceles right triangle is always 45 45 90 triangle.

An isosceles right triangle has a right angle or 90 degrees angle.

An isosceles right triangle has two angles equal in size.

If one angle is a right angle, then the other two will be 45 45.

Sphere

The radius of the sphere is the only unknown variable need to find the volume of a sphere.

Step-by-step explanation:

Sphere is a geometrical three dimensional round figure with every point on its surface equidistant from its center. It is a three dimensional representation of a circle. A line which connects from the center to the surface is called radius of the sphere.The diameter of the sphere is the longest straight line which passes through the center of the sphere.

The volume of sphere is given by:

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

where V is the volume of the sphere

r is the radius of the sphere

[tex]\pi = \frac{22}{7}[/tex]  = 3.14

Hence the only unknown variable to find the volume of a sphere is the radius.

Answer: 1.33333333333

Step-by-step explanation: 8x1=8

8/6=1.33333333333

Answer: The area of the notebook that the sticker covers is 128 cm^2

Step-by-step explanation:

The equation for the area of a rectangle should be:

[tex]A=bh[/tex]

-The height of the stickers measures 16 cm:

[tex]height = 16cm[/tex]

-So, if the base is half as long as the height, you divide it by 2:

[tex]base=\frac{16}{2}=8cm[/tex]

-Then, you substitute it:

[tex]A=16[/tex] · [tex]8[/tex]

-Result:

[tex]128cm^2[/tex]

Answer:

1/2 + 8 is equivalent to 1/2 - (-8)

0.5 - (-8) is ALSO equivalent to 1/2 - (-8)

0.5 + 8 is another equation that is equivalent to 1/2 - (-8)

Step-by-step explanation:

Step-by-step explanation:

0.5-(-8) is equal to it

Answer:A. 1/4 - 3/4

Step-by-step explanation:For future students

Answer:x= -54.7

Step-by-step explanation:

-66.5-66.5= -133+ 78.3= -54.7

Answer:

The slope is 3/2

Step-by-step explanation:

6-3=3      4-2=2    3/2

The 7 in the tenth place is equal to 7 times the value on the right

Answer: [tex]x=5[/tex]

Divide both sides by 7

[tex]7x/7=35/7\\x=5[/tex]

Answer:

[tex]7x = 35 \\ \frac{7x}{7} = \frac{35}{7} \\ x = 5[/tex]

hope this helps you...

the probability that the ball will have a letter that is lower case or earlier in the alphabet than d (or D) is 0.557

Step-by-step explanation:

Here  we have ,A bag contains 52 balls lettered from a to z and A to Z (i.e. uppercase or lowercase letters). One ball is withdrawn. We need to find What is the probability that the ball will have a letter that is lower case or earlier in the alphabet than d (or D)? Let's find out:

There are 26 lowercase letters and 26 uppercase letters  ! According to question we need to choose a ball which is either a lowercase ( i.e. from 26 letters ) or earlier in the alphabet than d ( or D ) which is A or B or , C  .

Probability = (Favorable outcome)/(Total outcome)

Favorable outcome = 26+3=29

Total Outcome = 52

So ,

⇒ [tex]Probability = \frac{29}{52}[/tex]

⇒ [tex]Probability = 0.557[/tex]

Therefore ,  the probability that the ball will have a letter that is lower case or earlier in the alphabet than d (or D) is 0.557

Final answer:

To calculate the probability of drawing a ball that is lower case or earlier in the alphabet than 'd', we count the number of qualifying balls (29) and divide by the total number (52), resulting in a probability of 29/52.

Explanation:

The student's question is about calculating the probability of drawing a ball from a bag that either contains a lower case letter or a letter that comes earlier in the alphabet than the letter 'd'. Given that the bag contains 52 balls, with each letter of the alphabet represented in both upper and lower case, we can calculate the probability by counting the number of balls that satisfy the condition and dividing by the total number of balls.

There are 3 letters in the alphabet before 'd' (‘a’, ‘b’, and ‘c’) and each comes in two forms (upper and lower case), so there are 3 * 2 = 6 balls that meet the 'earlier in the alphabet than d' criterion. Since there are 26 letters in the alphabet and each has a lower case form, there are 26 balls that are lower case.

To avoid double-counting the lower case balls ‘a’, ‘b’, and ‘c’, we subtract those 3 balls from the 26 lower case balls, resulting in 23. Adding these 23 to the 6 balls already counted, we have a total of 29 balls that satisfy either condition. The probability is therefore 29/52.

Answer:

  x^2 + y^2 -2x +y -71 = 0

Step-by-step explanation:

The center of the circle is the midpoint of the diameter, so is ...

  ((-3, -8) +(5, 7))/2 = (-3+5, -8+7)/2 = (1, -1/2)

The square of the radius of the circle can be found from the Pythagorean theorem. The x- and y- differences between an end point and the center are the legs of a right triangle with r as the hypotenuse.

  r^2 = (5 -1)^2 +(7 -(-1/2))^2 = 4^2 +7.5^2 = 16 +56.25

  r^2 = 72.25

__

The standard form equation of the circle with center (h, k) and radius r is ...

  (x -h)^2 +(y -k)^2 = r^2

  (x -1)^2 +(y -(-1/2))^2 = 72.25

Eliminating parentheses, we have ...

  x^2 -2x +1 +y^2 +y +0.25 = 72.25

Subtracting the right-side constant and rearranging to descending powers, we find the general form of the equation to be ...

  x^2 + y^2 -2x +y -71 = 0

_____

Comment on the work

Of course, you know that ...

  (a -b)^2 = a^2 -2ab +b^2

This helps you simplify the squares of binomials.

Answer:

20

Step-by-step explanation:

12+x=0.8(x+20)

Divide both sides by 0.8:

15+1.25x=x+20

Subtract x from both sides:

0.25x+15=20

Subtract 15 from both sides:

0.25x=5

Multiply both sides by 4:

x=20. Hope this helps!

Answer:

x = 20

Step-by-step explanation:

12 + x = 0.80(x + 20)

Distribute the 0.80 on the right side.

12 + x = 0.8x + 16

Subtract 0.8x from both sides.

12 + 0.2x = 16

Subtract 12 from both sides.

0.2x = 4

Divide both sides by 0.2.

x = 20

Answer:

TA = 6 units

GT = 10 units

Step-by-step explanation:

Angle G is common to both triangles, so that's a congruent angle.

Since RT is parallel to EA,

Angle R = Angle E

And

Angle T = Angle A

When two triangles have the same distribution of angles, they are similar (by AAA).

Therefore GRT and GEA are similar

GE/GR = GA/GT

8/5 = 16/(16-x)

16-x = 16 × 5/8

16 - x = 10

x = 16 - 10

x = 6

GT = 16 - x = 16 - 6 = 10

Answer:

it is 2

Step-by-step explanation: