Runner A had a minor accident and is now 0.25 miles behind Runner B.


Runner B is currently has a speed of 7 miles per hour.


Runner A attempts to catch up runner B by running 8.5 miles per hour.


How long will it take Runner A to catch up to Runner B?

Answer:

x = 3

Step-by-step explanation:

Using the triangle similarity theorem

x/x+3 = x+3/12

Cross multiply

12x = (x+3)(x+3)

12x = x²+3x+3x+9

12x =  x²+6x+9

x²+6x+9-12x = 0

x²-6x+9 = 0

Factorize

x²-3x-3x+9 = 0

x(x-3)-3(x-3) = 0

x - 3 = 0

x = 3 twice

Hence the value of x is 3

Answer:

Add maybe

Step-by-step explanation:

add the 500+400+200 try that hope it helps have a great day

Answer:

19) Domain: - ∞ < x < ∞                    20) Domain:  - ∞ < x < ∞

Range: - ∞ < y < ∞                                  Range: - ∞ < y < ∞

Increases throughout                            Decreases throughout

Step-by-step explanation:

Given the parent function " y = ∛x" we know that the first graph should have a vertical shift down 2 units, and a horizontal shift 4 units to the right. There is no vertical stretch since there is no coefficient. (Check first graph)

Domain: - ∞ < x < ∞

Range: - ∞ < y < ∞

Increases throughout

______________________________

For the second graph there should be a vertical shift down three units, a horizontal shift 1 unit to the left, and a vertical stretch by a factor of - 1. (Check second graph)

Domain: - ∞ < x < ∞

Range: - ∞ < y < ∞

Decreases throughout

=============================================================

Work Shown:

Refer to the diagram below. The short leg (opposite the 30 degree angle) is equal to 1 unit, the long leg is equal to sqrt(3) units, and the hypotenuse is 2 units long.

For the reference angle 60 degrees, the opposite leg is sqrt(3) units and the adjacent leg is 1 unit

tan(angle) = opposite/adjacent

tan(60) = sqrt(3)/1

tan(60) = sqrt(3)

Answer: tan 60° = √3

Step-by-step explanation: a p e x (screenshot proof)

Answer:

The cup will be filled 6 times.

Step-by-step explanation:

If her measuring cup only holds 1/4 cups then we need to find how many 1/4 cups are in 3/4 cups:

(1/4) + (1/4) + (1/4) = 3/4

3/4 = 3/4

The measuring cup will have to be filled 3 times for 1 loaf.

If she has 2 loaves that means that she has to fill her 1/4 measuring cup 6 times (because 2 * 3 = 6)

Hope this helps!!

- Kay :)

Answer:

x² +5x - 36

= x² - 4x + 9x - 36

= x(x - 4) +9(x - 4)

= (x - 4) (x+9)

so x = 4, - 9

Answer:

(5,-6) is a solution

Step-by-step explanation:

Given

[tex]6x + 3y = 12[/tex]

[tex]4x + y = 14[/tex]

Required

Tell whether (5,-6) is a solution

In (5,-6): x = 5 and y = -6.

Substitute these values in the given equations

[tex]6x + 3y = 12[/tex] becomes

[tex]6 * 5 + 3 * -6 = 12[/tex]

[tex]30-18 = 12[/tex]

[tex]12 = 12[/tex]

[tex]4x + y = 14[/tex] becomes

[tex]4 * 5 - 6 = 14[/tex]

[tex]20 - 6 = 14[/tex]

[tex]14 = 14[/tex]

Because both solutions are true, then (5,-6) is a solution

Answer:

0.3636363636363636

Step-by-step explanation:

Its a repeating decimal because 4 cannot  be divided by 11

There ya' go :]

Answer:

angle a is 110

angle B is 110

angle C is 70

Answer:

The eighth term of the geometric sequence 3, 12, 48 ... is 49,152. You just multiply every number by 4 :)

So, the required 8th term is 49152.

The Geometric series formula or the geometric sequence formula gives the sum of a finite geometric sequence.

The sequence will be of the form [tex]\{a, ar, ar^2, ar^3, ..\}[/tex]

And the formula for the nth term is [tex]t_n=ar^{n-1}[/tex]

The given series is,

3, 12, 48, ....

First term=3

The common ratio is,

[tex]\frac{12}{3}=4\\ \frac{48}{12}=4[/tex]

So, the given series is geometric series so the 8th term by the above formula is,

[tex]t_8=3\times (4)^{8-1}\\t_8=49152[/tex]

Learn more about the topic Geometric Series:

https://brainly.com/question/26042879

Answer:

linear and increasing

Step-by-step explanation:

uwu

Answer:

See Explanation

Step-by-step explanation:

Required

Prove that Dexter is wrong

To prove that Dexter is wrong, we use the following numbers.

[tex]Number = 4[/tex]

The factors are:

[tex]Factor = 1,2\ and\ 4[/tex]

3 factors

Using a greater number:

[tex]Number = 5[/tex]

The factors are:

[tex]Factor = 1\ and\ 5[/tex]

2 factors

From the above analysis:

4 has 3 factors and 5 has 2 factors; which shows that 5 has fewer factors

This shows that Dexter is wrong

Answer:

The probability that each player will receive three picture cards = 0.0324

Step-by-step explanation:

As given,

A deck of 52 cards contains 12 picture cards

Remaining card = 52 - 12 = 40

So,

Total number of ways in which 12 picture card is distributed = [tex]\frac{12!}{3! 3! 3! 3!}[/tex]

Now,

The Total number of ways in which Remaining cards are distributed = [tex]\frac{40!}{10! 10! 10! 10!}[/tex]

So,

Total number of ways of getting 3 picture card and remaining card = [tex]\frac{12!}{3! 3! 3! 3!}[/tex]× [tex]\frac{40!}{10! 10! 10! 10!}[/tex]

= [tex]\frac{12! 40!}{(3!)^{4} (10!)^{4} }[/tex]

Now,

Total number of ways to distribute 52 cards so that each people get 13 card = [tex]\frac{52!}{13! 13! 13! 13!} = \frac{52!}{ (13!)^{4} }[/tex]

∴ The probability = [tex]\frac{\frac{12! 40!}{(3!)^{4} (10!)^{4} }}{\frac{52!}{(13!)^{4} }}[/tex]

                            = [tex]\frac{12! 40!}{(3!)^{4} (10!)^{4} }[/tex]×[tex]\frac{(13!)^{4} }{ 52! }[/tex]

                           = [tex]\frac{12! 40!}{(3!)^{4} (10!)^{4} }[/tex]×[tex]\frac{(13.12.11.10!)^{4} }{ 52.51.50.49.48.47.46.45.44.43.42.41.40! }[/tex]

                           = [tex]\frac{12!}{(3!)^{4} }[/tex]×[tex]\frac{(13.12.11)^{4} }{ 52.51.50.49.48.47.46.45.44.43.42.41}[/tex]

                           = [tex]\frac{479,001,600}{(6)^{4} }[/tex]×[tex]\frac{(1716)^{4} }{ 52.51.50.49.48.47.46.45.44.43.42.41}[/tex]

                           = 0.0324

∴ we get

The probability that each player will receive three picture cards = 0.0324

Each of these limits correspond to the derivative of some function f(x) at a point x = a.

Recall the limit definition of a function f(x) :

f '(x) = lim [h → 0] ( f(x + h) - f(x) ) / h

Then if x = a, we get

f '(a) = lim [h → 0] ( f(a + h) - f(a) ) / h

From here, it's easy to identify what each function and point should be:

(a) f (a + h) = (1 + h)¹ʹ³   →   f(x) = x ¹ʹ³ and a = 1

(that's a 1/3 in the exponent)

(b) f (a + h) = cos(π + h)   →   f(x) = cos(x) and a = π

(c) f (a + h) = 5 (4 + h)⁵   →   f(x) = 5x ⁵ and a = 4

(d) f (a + h) = exp(4h) = exp(4 (0 + h))   →   f(x) = exp(4x) and a = 0

(where exp(x) = eˣ )

Answer:

y = 0.8x

Step-by-step explanation:

y = x-0.2x

y=x(1-0.2)

y=x(0.8)

hence y = 0.8x

Answer:

2×=64

2×/2=64/2

×=32.....x is solved

Answer:

x=32

Step-by-step explanation:

when divided by 2, 64 is equal to 32

Answer:

[tex]600, 900, 1350[/tex]

Step-by-step explanation:

Given

[tex]a = 400[/tex] -- initial subscribers

[tex]b = 1.5[/tex] -- growth factor

Required

Determine the number of subscribers in the next three months

To do this, we make use of:

[tex]y = ab^x[/tex]

In this case:

x is the number of months

y is the number of subscribers

So:

when x = 1;

[tex]y = ab^x[/tex]

[tex]y = 400 * 1.5^1[/tex]

[tex]y = 400 * 1.5[/tex]

[tex]y = 600[/tex]

when x = 2

[tex]y = 400 * 1.5^2[/tex]

[tex]y = 400 * 2.25[/tex]

[tex]y = 900[/tex]

when x= 3

[tex]y = 400 * 1.5^3[/tex]

[tex]y = 400 * 3.375[/tex]

[tex]y = 1350[/tex]

So, the next three number of subscribers is:

[tex]600, 900, 1350[/tex]

Answer:

Beck actually caught 45 fish

Step-by-step explanation:

System of Equations

We call the following variables:

x = number of fish Ally caught

y = number of fish Beck caught

They caught a total of 75 fish, thus:

x + y = 75      [1]

If Ally had caught twice as much fish as she actually did, and Beck had caught three times as many fish as he actually did, then Ally would have caught 75 fewer fish than Beck, thus:

3y = 2x + 75      [2]

From [1]:

x = 75 - y      [3]

Substituting in [2]:

3y = 2(75 - y) + 75

Operating:

3y = 150 - 2y + 75

Simplifying:

5y = 225

Dividing by 5:

y = 45

Beck actually caught 45 fish

Answer:

Beck caught 45 fish

Step-by-step explanation:

a = number of fish Ally caught

b = number of fish Beck caught

They caught a total of 75 fish, so we have:

b + a = 75  

From the facts in our question we know Ally would have caught 75 fewer fish than Beck.

3b = 2a + 75  

a = 75 - b

3b = 2(75 - b) + 75

3b = 150 - 2b + 75

5b = 225

5b ÷ 5 = 225 ÷ 5

b = 45

Beck caught 45 fish.

Answer:

[tex]3.52 \times 10^{-9} = 3.52 \times 10^{-7}\%[/tex] probability that all the 15 students selected are girls

Step-by-step explanation:

The selection is from a sample without replacement, so we use the hypergeometric distribution to solve this question.

Hypergeometric distribution:

The probability of x sucesses is given by the following formula:

[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}[/tex]

In which:

x is the number of sucesses.

N is the size of the population.

n is the size of the sample.

k is the total number of desired outcomes.

Combinations formula:

[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

All girls from the first group:

20 students, so [tex]N = 20[/tex]

10 girls, so [tex]k = 10[/tex]

5 students will be selected, so [tex]n = 5[/tex]

We want all of them to be girls, so we find P(X = 5).

[tex]P_1 = P(X = 5) = h(5,20,5,10) = \frac{C_{10,5}*C_{10,5}}{C_{20,5}} = 0.0163[/tex]

All girls from the second group:

20 students, so [tex]N = 20[/tex]

5 girls, so [tex]k = 5[/tex]

5 students will be selected, so [tex]n = 5[/tex]

We want all of them to be girls, so we find P(X = 5).

[tex]P_2 = P(X = 5) = h(5,20,5,5) = \frac{C_{5,5}*C_{15,5}}{C_{20,5}} = 0.00006[/tex]

All girls from the third group:

20 students, so [tex]N = 20[/tex]

8 girls, so [tex]k = 8[/tex]

5 students will be selected, so [tex]n = 5[/tex]

We want all of them to be girls, so we find P(X = 5).

[tex]P_3 = P(X = 5) = h(5,20,5,8) = \frac{C_{8,5}*C_{12,5}}{C_{20,5}} = 0.0036[/tex]

All 15 students are girls:

Groups are independent, so we multiply the probabilities:

[tex]P = P_1*P_2*P_3 = 0.0163*0.00006*0.0036 = 3.52 \times 10^{-9}[/tex]

[tex]3.52 \times 10^{-9} = 3.52 \times 10^{-7}\%[/tex] probability that all the 15 students selected are girls

Step-by-step explanation:

2. x =101

3. x= 120

4. x= 30

I am very confused in question no 1 and 5 th .

hope this will be helpful to you.

plz mark my answer as brainlist if you find it useful .

The volume of the rectangular prism is V = 936 cm³

The volume of the rectangle is given by the product of the length of the rectangle and the width of the rectangle and the height of the rectangle

Volume of Rectangle = Length x Width x Height

Volume of Rectangle = Area of Rectangle x Height

Given data ,

To find the volume of the figure, we need to calculate the volumes of the two rectangular prisms separately and then add them together.

The volume of a rectangular prism is given by the formula:

Volume = length x width x height

For the first prism:

Length = 12 centimeters

Width = 9 centimeters

Height = 2 centimeters

Volume of first prism = 12 cm x 9 cm x 2 cm = 216 centimeters³

For the second prism:

Length = 10 centimeters

Width = 9 centimeters

Height = 8 centimeters

Volume of second prism = 10 cm x 9 cm x 8 cm = 720 centimeters³

Now, we add the volumes of the two prisms together to get the total volume of the figure:

216 cubic centimeters + 720 cubic centimeters = 936 centimeters³

Hence , the rectangular prism has volume of 936 cm³

To learn more about volume of rectangle click :

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Answer:

A≈4536.46

Step-by-step explanation:

I hope this helps! ^^

☁️☁️☁️☁️☁️☁️☁️

Answer:

Radius 19

A ≈ 4536.46 .....ans

Answer:

Nominal data are used to label variables without any quantitative value. Common examples include male/female (albeit somewhat outdated), hair color, nationalities, names of people, and so on. In plain English: basically, they're labels (and nominal comes from "name" to help you remember). You have brown hair (or brown eyes).

Answer: C. 254

Step-by-step explanation: All engineers is the population so this is stats and the number that chose math no matter what kind of engineer is 254

Step-by-step explanation:

4 + 8 + 3 + 5 + 5 + 7 + 6 + 4 divided 8

42 divided 8

5,25

cmiiw!

Answer:

[tex]c = 14.9cm[/tex]

Step-by-step explanation:

Given

[tex]b = 10cm[/tex]

[tex]B = 12^{\circ}[/tex]

[tex]A = 150^{\circ}[/tex]

Required

Determine the length of c

First, we calculate C (the third angle of the triangle).

[tex]C = 180 - A - B[/tex]

[tex]C = 180 - 150 - 12[/tex]

[tex]C = 18^{\circ}[/tex]

Using Sine's law, we make use of:

[tex]\frac{sin\ B}{b} = \frac{sin C}{c}[/tex]

By substituting values, we have:

[tex]\frac{sin\ 12}{10} = \frac{sin 18}{c}[/tex]

Cross multiply

[tex]c* sin\ 12 = 10 * sin\ 18[/tex]

Make c the subject

[tex]c = \frac{10 * sin\ 18}{sin\ 12}[/tex]

[tex]c = \frac{10 * 0.3090}{0.2079}[/tex]

[tex]c = 14.9cm[/tex] approximated

Answer:

x=21

Step-by-step explanation:

x/x+14=9/15

15x=9x+126

6x=126

x=21

Answer:

(x+2)^2

Step-by-step explanation: