Restate the problem in a way that can be easily translated into an equation.
It took Dani 5 minutes longer to run the course than it did Candice.

A. Dani’s rate is slower than Candice’s rate.

B. Dani’s time is greater than Candice’s time.

C. Dani’s time equals Candice’s time plus 5

C. Candice’s time equals Dani’s time plus 5 minutes.

I am a little confused by the wording on the question. It says "within the circle" but the image is of 2 squares.

I am just going to answer it as if the question said "probability that a randomly selected point within the square falls in the red shaded square."

So red square area = 3 x 3 = 9.

The area of the bigger square = 4x4 = 16.

The prob of landing in that red square = 9/16 = 0.5625 or approx 56%.

Answer:

  81, 89, 91

Step-by-step explanation:

You want to know Aura's three exam scores if their average was 87, the second was 8 point higher than the first, and the third was 2 points higher than the second.

Let x represent the first exam score. Then x+8 and x+10 will be the other two scores. Their average is ...

  (x +(x +8) +(x +10))/3 = 87

  x +6 = 87 . . . . . . . . simplify

  x = 81 . . . . . . . . subtract 6

  x +8 = 89

  x +10 = 91

Aura's three exam scores were 81, 89, and 91.

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The probability of both getting a heart card and a red heart card is 1/4.

Given that there is a deck of 52-cards, we need to find the probability of getting a heart cards,

Probability shows how likely an event will happen.

P(E) = n(E) /n(S).

n(E) = Number of favorable outcomes of E.

n(S) = total number of possible outcomes of E.

No. of heart cards = 13

n(E) = 13

P (getting a card of heart) = no. of favorable outcomes/total no. of possible outcomes of E

= 13/52

= 1/4

Since heart card is red that means there are 13 heart cards which is red in color.

So, the probability of getting a red heart card = 13/52 = 1/4

Hence the probability of both getting a heart card and a red heart card is 1/4.

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The linear equation will be y = - 25x + 500. And the graph is given below.

Given that:

Slope, m = -25 mL/s

Y-intercept, c = 500 mL

The linear equation is given as,

y = mx + c

Where m is the slope of the line and c is the y-intercept of the line.

Let 'x' be the number of seconds and 'y' be the remaining amount. Then the equation is given as,

y = - 25x + 500

The diagram is given below.

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The area of the trapezoid is 57.75m²

The area of the trapezoid is given by the equation below:

A = (a+b)*h/2

where, a = length of smaller parallel line, b = length of larger parallel line & h = height of the trapezium.

The given values are a= 8.5m, b = 8.5+2+2=12.5m & h = 5.5m

Substituting the given values in the equation above to get the area.

Area = (8.5+12.5)*5.5/2

Area = 57.75m²

Hence, the area of the given trapezoid is 57.75m².

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Answer:

B. Triangle A and B

Step-by-step explanation:

Answer: C

Step-by-step explanation: Okay it is very simple. Slope Formula= Y2-Y1/X2-X1

So -4-6/-7-3= -10/-10= 1

Option C

Given (3,6) (-7,-4)
X1=3
Y1=6

X2=-7

Y2=-4

Answer:

A. one solution

Step-by-step explanation:

The only solution was negative one half

The monthly property tax bill will be $2,670.42.

To determine the property tax, we need to first find the assessed value of the condominium:

Next, we need to find the property tax rate:

Mill rate = 81.85%o = 0.8185

To find the annual property tax, we multiply the assessed value by the mill rate:

Finally, to find the monthly property tax, we divide the annual property tax by 12:

Therefore, the monthly property tax bill will be $2,670.42.

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Answer: 3x-3

Step-by-step explanation: Let's express "a number" by the variable x.

The symbol for "three times a number" is 3x.

"The difference between a number of times three and three" can be expressed mathematically as:

"3x - 3".

The value of coefficient of x³ is,

⇒ 2

The value of degree of the expression is,

⇒ 3

The value of constant term is,

⇒ 22

The polynomial is the expression of third degree.

Given that;

Expression is,

⇒ 2x³ - x² + 8x + 22

Now, We get;

There are 4 terms in the expression,

And, The value of coefficient of x³ is,

⇒ 2

The value of degree of the expression is,

⇒ 3

The value of constant term is,

⇒ 22

And, The polynomial is the expression of third degree.

Thus, The value of coefficient of x³ is,

⇒ 2

The value of degree of the expression is,

⇒ 3

The value of constant term is,

⇒ 22

The polynomial is the expression of third degree.

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Answer:

60

Step-by-step explanation:

To find the volume of this object, find The volume of the cuboid as a whole (ignore the hole as if it's not there) and then remove the volume of the hole (cuboid) from it.

Volume of whole solid = 9 × 6 × 5/4 = 67.5 ft³

For the invisible solid (hole part), you already have width and height, you can find the length too. Length = 9 - (2+3) = 9 - 5 = 4 ft

Volume of invisible solid = 5/4 × 4 × 5/2 = 12.5 ft³

Required volume = 67.5 - 12.5 = 55 ft³

After considering the given data we conclude that the experimental probability of next menu slipping under Britney's apartment door will be from a Chinese restaurant is 0.1 or 10%.

The experimental probability  refers to a specified event that is classified on the basis of count that projects the event which has taken place during the experiment and the total number of times the experiment was conducted.
For the given case, the total of 20 menus from different restaurants  were slipped under Britney's apartment door.
In which , 2 were from Chinese restaurants. Then, the experimental probability of the next menu being slipped under Britney's door would come from a Chinese restaurant is
2/20
= 0.1 or 10%.
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The complete question is
Restaurants often slip takeout menus under Britney's apartment door. Britney counted how many menus there were from each type of restaurant.
A) Chinese 2
B) Japanese 9
C) Mediterranean 1
D) Thai 2
E) Italian 6
1) What is the experimental probability that the next menu slipped under Britney's door will be from a Chinese restaurant?

Answer:

ΑΠSШЕЯ®

Step-by-step explanation:

The probability that all three students prefer to take some of their courses fully online can be found by multiplying the probabilities of each event together. Since each student has a 68% chance of preferring fully online courses, the probability that the first student prefers fully online courses is 0.68, the probability that the second student prefers fully online courses given that the first student does is also 0.68, and the probability that the third student prefers fully online courses given that the first two students do is also 0.68. Therefore, the probability that all three students prefer to take some of their courses fully online is 0.68 x 0.68 x 0.68 = 0.314. The probability is approximately 0.314 or 31.4%.

The solution is : Sebastian swam 40laps in one hour in average.

Here, we have,

Sebastian swam 45minutes per day.

If she swam 5days a week, this is equivalent to Sebastian swimming 60days in 12weeks.

If Sebastian swam 45minutes in a day, she must have swam for (45×60)minutes in 60days which is equivalent to 2700minutes

Converting 2700minutes to hours;

60minutes = 1hour

2700minutes = x

x = 2700/60

x = 45hours

Since sebastian swam 1800laps in that 12weeks in 45hours, her average rate lap per hour can be calculated thus;

1800laps = 45hours

X laps = 1hour

30 × X = 1800

X = 1800/45

X = 40laps

This shows that Sebastian swam 40laps in one hour in average.

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Answer:

Step-by-step explanation:

Let us say that the number is x

Now , According to the question ,

let us start by considering the L.H.S first i.e. three times a number increased by 12 i.e. 3^x+12  -------(1)

Now , consider R.H.S i.e. Five times the same number decreased by 18 i.e.

5^x-18-------------(2)

Now we are given that both the numbers are equal so here we equate eqn (1) and eqn (2)

⇒ 3x + 12 = 5x - 18

⇒ 12 +18 = 5x - 3x

⇒ 30 = 2x

⇒ 2x = 30

⇒ x = 30/2

⇒ x = 15

∴ Hence 15 is the required number

Option - B is correct that is the measure of angles A is 31° when ∠A and ∠B are complementary angles.

Given that,

The part of your question is missing that is ∠A and ∠B are complementary angles with ∠A = (2x - 3)°  and ∠B = (3x + 8)°.

We have to measure the angle A.

We know that,

Complementary angles means sum of the angles is equal to 90°

That means,

∠A + ∠B = 90°

2x -3 + 3x + 8 = 90°

5x + 5 = 90°

5x = 90 - 5

5x = 85

x = [tex]\frac{85}{5}[/tex]

x = 17°

Now by substituting

∠A = 2x -3

∠A = 2(17) -3

∠A = 34 - 3

∠A = 31

Therefore, The measure of angles A is 31°.

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For the person to reach a retirement savings goal (future value) of $100,000 at age 55, they need to invest an additional $81 monthly.

Determining the additional monthly investment:

The additional monthly investment is computed as the difference between the expected monthly deposits and the intended monthly deposits.

The expected monthly deposits (periodic payments) are determined using an online finance calculator.

Current age = 21 years old

Retirement age = 55 years old

Investment period = 34 years (55 - 21)

N (of periods) = 408 months (34 years x 12)

I/Y (Interest per year) = 2.5%

Present Value = $0

FV (Future Value) = $100,000

Periodic Payments (PMT) = $155.75

Sum of all periodic payments = $63,546

Total Interest = $36,454

Intended monthly deposits = $75

Additional monthly deposits required = $80.75 ($155.75 - $75) = $81

Thus, the investor needs to invest an additional $81 to the $75 monthly deposits to reach a future value of $100,000 in 34 years, compounded at 2.5% monthly.

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The complete question =

A person is 21 years old and plans on retiring at age 55. This person is going to invest $75 each month into an IRA that is expected to earn 2.5% interest, compounded monthly. How much more money, rounded to the nearest dollar, is needed per month to reach a retirement savings goal of $100,000?

The two students that mix the same ratio of juice to water is given as follows:

A. Luca.

D. Micah.

The ratio between two amounts a and b is given as follows:

a to b.

Which is also the division of the two amounts.

Hence the ratio of juice to water for each person is given as follows:

Hence Luca and Micah used the same ratio, meaning that options A and D are correct.

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The volume inside the cube but outside of an inscribed sphere is 231.6 cubic inches

From the question, we have the following parameters that can be used in our computation:

Cube volume = 486

This means that the side length of the cube is

l³ = 486

So, we have

l = 7.86

This represents the diameter of the sphere

So, the sphere volume is

V = 4/3πr³

So, we have

V = 4/3 * 22/7 * (7.86/2)³

Evaluate

V = 254.36

So, the required volume is

Volume = 486 - 254.36

Evaluate

Volume = 231.64

Approximate

Volume = 231.6

Hence, the volume inside the cube but outside of an inscribed sphere is 231.6 cubic inches

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Step-by-step explanation:

you are sure ?

sqrt(105)

[tex] \sqrt{105} [/tex]

105 = 3×35 = 3×5×7

there is no factor that is a square number.

therefore, this cannot be further simplified.

it can be split into parts like

sqrt(3)×sqrt(5)×sqrt(7)

but I would not call that simplified.

we could use exponents :

sqrt(105) = 105^(1/2)

but that's about it.

Answer:

-7 < f(x) < 17

Step-by-step explanation:

f(x) = 3x + 2

The given domain is -3 < x < 5

If x = -3, f(x) = f(-3) = 3(-3) + 2 = -9 + 2 = -7

If x = 5, f(x) = f(5) = 3(5) + 2 = 15 + 2 = 17

The range of f(x) is the set of permissible values for f(x) for the given domain -3 < x < 5

Therefore range of f(x): -7 < f(x) < 17

Compound interest, also known as interest on principal and interest, is the practice of adding interest towards the principal amount of a loan or deposit.

The yearly interest rate is raised to the amount of compounded periods minus one, and the starting principal amount is multiplied by both of these factors. The resulting value is subsequently deducted from the loan's entire original amount.

P = $5,000 for the principle (initial investment)

Annual interest rate equals 0.03 (as a decimal)

t = the number of years (10).

Euler's number is e = 2.718281.

A = the sum at time t, or A = P·(e(rt))

[tex]\sf A = 5000(2.718281^{(0.03\times10)})[/tex]

[tex]\sf A = \$6,749.29[/tex]

After 10 years, you'll have $6,749.29 in your account.

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The factored form of the expression 816² - 25c² is 816 + 5c )( 816 - 5c).

Given the expression in the question:

816² - 25c²

To factor 816² - 25c², we the:

a² - b² = (a + b)(a - b)

Written as the product of two factors

Since both terms are perfect squares

a = 816

b = 5c

Hence, plugging into the formula:

a² - b² = (a + b)(a - b)

816² - 25c² = ( 816 + 5c )( 816 - 5c)

Therefore, the factored form is ( 816 + 5c )( 816 - 5c ).

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Using the hypergeometric distribution, it is found that there is a 0.19704% probability that the balls have the same number.

The balls are chosen without replacement, hence, the hypergeometric distribution is used.

Hypergeometric distribution:

P (X = x) = h (x, N, n, k)

              = [tex]\frac{C_{k, x} C_{n - k, n - k} }{C_{N, n} }[/tex]

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

The parameters are:

x is the number of successes.

N is the size of the population.

n is the size of the sample.

k is the total number of desired outcomes.

In this problem:

There are 3 balls, hence .

For each number, there are 3 balls, hence .

3 balls are selected, hence .

For each ball, the probability is P(X = 3). There are 8 balls, hence we have to find 8P(X = 3).

P (X = x) = h (x, N, n, k)

              = [tex]\frac{C_{k, x} C_{n - k, n - k} }{C_{N, n} }[/tex]

P (X = 3) = h (3, 30, 3, 3) = 0.0002463

0.0002463 x 8 = 0.0019704

0.0019704 = 0.19704% probability that the balls have the same number.

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The slope which shows  the cost per guest is $35 per guest

The given cost for 50 guests is $2150.

The cost for 75 guests is $3025.

It can also be represented as:

(Guest, Cost) =(50, $2150) & (75, $3025)

The slope can now be calculated as

Slope = (y₂ - y₁)/(x₂ - x₁)

Where

(x, y) = (50, $2150) & (75, $3025)

Substituting the given values in the equation as follows:

Slope = (3025 - 2150)/(75 - 50)

Slope = 35

Hence, the slope is $35 per guest.

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Answer:

Step-by-step explanation:

60 miles per hour.

If you were proving the theorem about the equality of the corresponding angles in this diagram, first you will prove d)That the angles are congruent.

Corresponding angles are generated when a line intersects two parallel lines, resulting in angles that are in the same location with regard to the lines. In this circumstance, all of the angles have measurements that are connected. These are the facts regarding the formed lines and angles.

The parallel lines do not cross. The transversal is the line that connects the parallel lines. Each parallel line has a straight angle, which means that the line measures 180 degrees.

The angles generated by the lines are either equal or supplementary, which indicates that the sum of two angles is 180 degrees. It is necessary that the corresponding angles are congruent angles hence we will check for them first.

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Part C is best represents the solution set to the system of inequalities .

Given that;

1st equation is,

⇒  y ≤ x + 1

And, 2nd equation is,

y + x ≤ –1

 y ≤ -x -1

Since, 1st equation represent Part C and Part D region.

And, 2nd equation represent Part B and Part C region.

Thus, Part C is common among those.

So, Part C is best represents the solution set to the system of inequalities .

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