Ben starts walking along a path at 2 mi/h. One and a half hours after Ben leaves, his sister Amanda begins jogging along the same path at 7 mi/h. How long (in hours) will it be before Amanda catches up to Ben?

Answer:

#8 - 52°, #9 - 29°

Step-by-step explanation:

8. The two angles added together are a straight line, so they sum up to 180 degrees.

x + (2x + 24°) = 3x + 24° = 180°

3x + 24° = 180°

3x = 156°

x = 52°

9. Similar to #8. "Supplementary" means they add up to 180° (whether they are actually next to each other or not).

So,     4x + (2x + 6°) = 180°

                 6x + 6° = 180°

                     6x = 174°

                        x = 29°

Hope this helps. Get some rest. Zzzzz  :)

Answer:

The rule for reflecting over the X axis is to negate the value of the y-coordinate of each point, but leave the x-value the same.

Step-by-step explanation:

For example, when point P with coordinates (5,4) is reflecting across the X axis and mapped onto point P', the coordinates of P' are (5,-4).

Answer:

[tex]P(X = x) = \frac{2^{3-x}}{27}[/tex]

Step-by-step explanation:

Given

[tex]Black = 4[/tex]

[tex]Green = 2[/tex]

[tex]r = 3[/tex] --- selected balls (with replacement)

Required

Determine the probability distribution for the green balls.

Let x be a [tex]random\ variable[/tex] such that:

[tex]x = 0, 1, 2, 3[/tex]

Because it is a selection with replacement

The probability of a green ball being drawn is always:

[tex]P(G) = \frac{Green}{Total}[/tex]

[tex]P(G) = \frac{2}{6}[/tex]

[tex]P(G) = \frac{1}{3}[/tex]

The probability of a black ball being drawn is always:

[tex]P(B) = \frac{Black}{Total}[/tex]

[tex]P(B) = \frac{4}{6}[/tex]

[tex]P(B) = \frac{2}{3}[/tex]

So, the probability distribution of green is:

[tex]P(X = x) = (P(B))^{3-x} * (P(G))^x[/tex]

[tex]P(X = x) = (\frac{2}{3})^{3-x} * (\frac{1}{3})^x[/tex]

Apply law of indices

[tex]P(X = x) = \frac{2^{3-x}}{3^{3-x}} * \frac{1^x}{3^x}[/tex]

[tex]P(X = x) = \frac{2^{3-x}*1^x}{3^{3-x}*3^x}[/tex]

[tex]P(X = x) = \frac{2^{3-x}*1}{3^{3-x+x}}[/tex]

[tex]P(X = x) = \frac{2^{3-x}*1}{3^3}[/tex]

[tex]P(X = x) = \frac{2^{3-x}}{27}[/tex]

Answer:

0.73 = 73% probability that an attendee sits in on the information technology session or the social media session.

Step-by-step explanation:

What is the probability that an attendee sits in on the information technology session or the social media session?

They cant be in both sections simultaneously, so this probability is the sum of each probability.

0.11 = 11% probability that an attendee sits in on the information technology session

0.62 = 62% probability that an attendee sits in on the social media session

0.11 + 0.62 = 0.73

0.73 = 73% probability that an attendee sits in on the information technology session or the social media session.

Answer:

14x+2

Step-by-step explanation:

3x+11x = 14x then +2 is left over so it's 14x+2

Answer:

Step-by-step explanation:

Multiply each term of the first polynomial with   the second polynomial. Then combine the like terms.

(3a² + 5a - 2)* (5a² -3a + 4)

= 3a² *(5a² -3a + 4)  + 5a*(5a² -3a + 4)  - 2*(5a² -3a + 4)

=3a²*5a² - 3a*3a² + 4*3a² +  5a*5a² - 3a*5a  + 4*5a + 5a²*(-2) - 3a*(-2) + 4*(-2)

=15a⁴ - 9a³  + 12a² + 25a³ - 15a² + 20a - 10a² + 6a - 8

= 15a⁴ - 9a³ + 25a³   + 12a² - 15a² - 10a²   + 20a +6a - 8

= 15a⁴ + 16a³  - 13a² +26a  - 8

Answer:

Well, 2 quarters are 2 coins. But, if you are asking the value of 2 quarters, then your answer will be, 50.

Step-by-step explanation:

So, 1 quarter = 25 cents. So that means that, 25 x 2 or 25 + 25 = 50. So, your answer will be 50. Hope that helps! :)

Answer:50

Step-by-step explanation:if a quarter equals 25cents and you have 2 quarters,you have to add .25+25 that equals 50 this is a simple way to do it.

Answer:

Step-by-step explanation:

s(20/100)=40

20s=4000

s=200

So there are a total of 200 students.

Answer:

There are 200 middle school students

Step-by-step explanation:

The equation for this question can be: 40 is 20% of what. This can be simplified to 40 = 0.2x and then to get x by itself you divide 40 by 0.2 which is 200.

Answer:Yes, your answers are correct.

The volume of a cone is given by V = 1/3πr²h.  Since the diameter of the first cone is 4, the radius is 2; therefore the volume is

V = 1/3π(2²)(8) = 32π/3

We divide the volume of the sink, 2000π/3, by the volume of the cone:

2000π/3 ÷ 32π/3 = 2000π/3 × 3/32π = 6000π/96π = 62.5 ≈ 63.

The diameter of the second conical cup is 8, so the radius is 4.  The volume then is:

V = 1/3π(4²)(8) = 128π/3

Dividing the volume of the sink, 2000π/3, by 128π/3:

2000π/3 ÷ 128π/3 = 2000π/3 × 3/128π = 6000π/384π = 15.625 ≈ 16

Step-by-step explanation:

Answer:

7 x (8 ÷ 5)

hhhhhhhhhhhhhhhhhhhhhhhhhhh

Answer:

Volume = 27 cubic units

Step-by-step explanation:

First, the formula of volume is l x h x w.

Second, the l, h, and w, are all 3, so to get your answer you do 3 x 3 x 3 which equals 27.

Hope this helps!

Answer:

13.825, 13, -13 25/40

Answer:

13.825, 13, and -13 25/40

Step-by-step explanation:

Hope this helps :)

The situation can be modeled by a geometric sequence with an initial term of 284. The student population will be 104% of the prior year, so the common ratio is 1.04.

Let \displaystyle PP be the student population and \displaystyle nn be the number of years after 2013. Using the explicit formula for a geometric sequence we get

{P}_{n} =284\cdot {1.04}^{n}P

n

=284⋅1.04

n

We can find the number of years since 2013 by subtracting.

\displaystyle 2020 - 2013=72020−2013=7

We are looking for the population after 7 years. We can substitute 7 for \displaystyle nn to estimate the population in 2020.

\displaystyle {P}_{7}=284\cdot {1.04}^{7}\approx 374P

7

=284⋅1.04

7

≈374

The student population will be about 374 in 2020.

Answer:

3/8

Step-by-step explanation:

3/8 of 16 is 6

1/4 of 16 is 4

6+4 = 10

16-10 = 6

3/8 of 16 = 6

Answer:

23+62−36

2(3+32−18)

Step-by-step explanation:

Answer:

I think the answer is 1,370 , not sure .

∠ O ≈ 42.7°

Step-by-step explanation:

Using the cosine ratio in the right triangle

cos O =  =  =  , thus

∠ O =  (  ) ≈ 42.7° ( to the nearest tenth )

Can I have brainliest

Answer:

( 2 , 2 )

Step-by-step explanation:

Solve the eqaution :

3x +2y=10

4x-y=6

Solve the eqaution for y :

3x + 2y = 10

y = -6 + 4x

Substitute for y : 3x + 2 ( -6 + 4x ) = 10

x = 10

Substitute for the value of x : x = 2

Substitute the given value of x into the eqaution

y = -6 + 4x : y = -6 + 4 × 2

Solve the eqaution: y = -6 + 4 × 2

solve the eqaution for y : y = 2

y = 2 A possible solution : the ordered solution pair is

( 2 , 2 )

Answer:

-2/11

Step-by-step explanation:

Answer:

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Answer:

Ratio of the area of MIKE to TEAM = 9 : 1

Step-by-step explanation:

Ratio of similar shapes = square of the ratio of their corresponding sides

Since TEAM ~ MIKE, therefore the ratio of their areas = square of the height of MIKE : square of the height of TEAM

Ratio = 33² : 11²

Ratio = 1089 : 121

Ratio = 9 : 1

Answer:

f=-15

Step-by-step explanation:

Let's solve your equation step-by-step.

f /3 +22=17

Step 1: Simplify both sides of the equation.

1 /3 f+22=17

Step 2: Subtract 22 from both sides.

1/ 3 f+22−22=17−22

1/3f=-5

Step 3: Multiply both sides by 3.

3*(1/3f)=(3)*(-5)

f=−15

Answer:

f=−15

The value of the variable f for the given expression is f=-15.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that the expression is f/3+22=17. The value of f will be calculated as:-

f /3 +22=17

Step 1: Simplify both sides of the equation.

1 /3 f+22=17

Step 2: Subtract 22 from both sides.

1/ 3 f+22−22=17−22

1/3f=-5

Step 3: Multiply both sides by 3.

3*(1/3f)=(3)*(-5)

f=−15

Hence, the value of f will be -15.

To know more about an expression follow

https://brainly.com/question/25968875

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Answer:

13 I think

Step-by-step explanation:

So basically all i did was double what the gate had. 5=15 3=13 I dont know if that makes lol

Answer:

0.6 ;

0.7

Reaukt in B will give a better estimate because it has a larger sample size (120) than the result on A ,with sample size (30)

Step-by-step explanation:

Probability of hitting the target using Tuesday's result :

P(hitting the target):

Probability = required outcome / Total possible outcomes

Required outcome = number of hits = 18

Total possible outcomes = number of throws =. 30

Hence, Probability of hitting the target using Tuesday's result : 18 / 30 = 0.6

B.)

Probability of hitting the target using Total result:

Required outcome = number of hits = 84

Total possible outcomes = number of throws =. 120

= 84 / 120

= 0.7

Answer:

1.6 or 2?

Step-by-step explanation:

5-3 =2

1/3 - 7/9 LCD

3/9 - 7/9 =-4/9

2-4/9 = 1 5/9

16/3-34/9 LCD

1 5/9 = 1.5555555555 rounded is 1.6 or 2? Not sure if decimals count.