Stanley runs, swims, and bikes every day. During these workouts, he runs at 9 mph, bikes at 16 mph, and swims at 2.5 mph. Yesterday, he ran for half an hour longer than he swam, and his biking time was twice his running time. How long did Stanley run, swim, and bike yesterday if the total distance he covered was 64 miles?

(a

If Stanley swam for t hours yesterday, what was his running time?

The center of the hyperbola given as (y + 3)²/9 − (x − 2)²/2 = 1 is (2, -3)

From the question, the equation of the hyperbola is given as

(y + 3)²/9 − (x − 2)²/2 = 1

As a general representation, a hyperbola is represented as

(y - k)²/a² − (x − h)²/b² = 1

From the above general representation, the coordinates of the center of the hyperbola is

Center = (h, k)

By comparing the equations (y - k)²/a² − (x − h)²/b² = 1 and (y + 3)²/9 − (x − 2)²/2 = 1, we  have the following representstion

(h, k) = (2, -3)

This means that

Center = (2, -3)

Hence, the center is (2, -3)

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Answer:

(2,-3) See question 10

Step-by-step explanation:

Answer:

can't answer the first two questions as figure is not mentioned in picture

3. -3

4. 6

5. 3/4

6. -3

7. 5

8. 3

Step-by-step explanation:

Answer:

7/6 feet

Step-by-step explanation:

The board is 3 and 1/2 feet long, so it is 3+(1/2) feet long.

3 + 1/2 = ?

3/1 + 1/2 = ?

6/2 + 1/2 = ?

(6 + 1)/2 = ?

= 7/2

3 + 1/2 = 7/2

In other words, the board is 7/2 feet long.

Now we have to divide by 3 since Andrea is cutting the board in three pieces.

So:

(7/2)/3       or        (7/2) ÷ 3       or        [tex]\frac{\frac{7}{2}}{3}[/tex]        or     (7/2) × (1/3)

= 7/(2×3)

= 7/6

So we found that each piece (after cutting the board into three pieces) is 7/6 feet long.

We will have the following:

When we solve for x we will have

So, x is equal or grater than -5.

Answer:Answer: number 2 is correct

The 80th percentile for the number of hours spent studying each day is 7.07 hours.

A data set with a normal distribution has the majority of its values clustered in the middle of the range, while the remainder taper off symmetrically toward either extreme. The term "standard deviation" refers to the degree of dispersion of the data from the mean. Data are grouped around the mean when the standard deviation is low, and are dispersed when the standard deviation is high.

The percentage of scores below a given value is shown by percentiles. They provide information about how a score compares to other scores.

Given Data :

Mean time (u) = 6.4 hour

Standard Deviation = 0.80 hour

It is given that the probability distribution is normal.

The formula for the z-score is z =( x- mean)/standard deviation

For the 80th percentile,  the z value from the z table is 0.842.

We have,

0.842 = (x - 6.4)/0.8

0.842*0.8 = x - 6.4

0.6736 =x - 6.4

x = 0.6736 + 6.4

x = 7.0736

x = 7.07

Hence, the 80th percentile for the number of hours spent studying each day is 7.07 hours.

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The sampling distribution for is normal (or approximately normal) and give its mean and standard deviation is  the mean is $28520 and its standard deviation is $762.5.

The notion of mean is crucial in both mathematics and statistics. The mean is the average or most frequent value among a set of numbers. It is a statistical measure used to determine the median and mode of a probability distribution's central tendency. It's also known as an expected value. Sum of all observations divided by the total observations equals the mean. The term "standard deviation" refers to the degree of dispersion of the data from the mean. Data are grouped around the mean when the standard deviation is low, and are more dispersed when the standard deviation is high.  

Given information :

Mean annual income = $28540

Standard Deviation = $5000

Given sample size is n = 43

Sample size doesn't affect the mean, hence the mean remains the same

New mean = $28540

New standard Deviation = Standard Deviation / n^1/2 = 5000/ (43)^1/2

New standard Deviation = 5000/6.5574 = $762.5

Hence, The mean is $28520 and its standard deviation is $762.5

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Explanation:

Take any two whole numbers you want. Multiplying them together always result in some (other) whole number.

Examples:

In other words,

(whole number)*(whole number) = whole number

This is why we consider the set closed under multiplication.

Compound interest: $8,765.58

The area of the figure given below is 56.6 units² .

In the question ,

a figure is given

where there is one rectangle and two semicircles .

the length of the rectangle is given as 11 units

and the breadth of the rectangle is = 4 units

we know that the area of the rectangle is = length × breadth

on substituting the values ,

we get

area = 11 × 4

area = 44 units²

the radius of the semicircle = 2 units

the are of the semi circle = (1/2)*π*r²

since there are two semicircle , the area of the two semi circle will be

= 2 * (1/2)πr²

= π*r²

On substituting , the value of radius = 2 ,

we get the area is = 3.14*(2)² = 12.56       using π = 3.14

so the area of the complex figure is = 44 + 12.56 = 56.56

≈ 56.6

Therefore , The area of the figure given below is 56.6 units²  .

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We need to know how to read a graph inorder to solve the problem. At the end of 6 weeks, Lorena will have more money, she will have $8 more than Benita.

We know that Lorena started with $40 and she added $8 every week. We need to find out the final amount she has at the end of 6 weeks. For Benita, we can see from the graph that she started with $50, since the graph starts from $50, and if we observe the amount after every week we can see that she adds $5 every week to the savings. We can directly say from the graph that the final amount Benita has after 6 weeks is $80.

amount Lorena has after 6 weeks = 40+ (6x8)=40+48=$88

Therefore we can see that Lorena will have more money after 6 weeks and she has $8 more than Benita.

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x = 12° and y = 7° are the value of linear angles.

What is linear pair of angles?

8x° = 96°

x = 96/8

x = 12°

8x° = 11y + 19

8 * 12° = 11y + 19

96 = 11y + 19

11y = 96 - 19

11y =    77

y = 77/11

y = 7°

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The equation of the line is found as y = -x/2 + 9/2.

For the given question;

The equation of the perpendicular line is given as;

y = 2x - 7

Compare the equation with the standard form of slope intercept.

y = mx + c

m = slope and c is the y intercept.

m1 = 2

Now, the line is perpendicular, thus the relation between both slopes is;

m1 × m2 = -1

m2 = -1/2

The passing coordinates of the line is (1. 4).

Find the equation using formula.

y - y1 = m2(x - x1)

y - 4 = (-1/2) (x - 1)

Simplifying,

y = -x/2 + 9/2

Thus, the equation of the line is found as y = -x/2 + 9/2.

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The rate at which the volume of the cone is changing is -5235.98 inches³/s when the radius of the circular cone is 50 inches and the height is 10 inches.

The formula for the circular cone can be given as;

V = 1/3 πr²h

Now we take the derivative with respect to time as follows;

V = 1/3 πr²h

dV/dt = 1/3π d/dt(r²h)

dV/dt = 1/3π [2r(dr/dt) × h + r²(dh/dt)]

Now we substitute the values in this equation as follows;

dV/dt = 1/3π [2 × 50 × 5 × 10 + (50²) (-4)]

dV/dt = 1/3π [ 5000 - 10000]

dV/dt = 1/3π [-5000]

dV/dt = -5235.98

Hence the negative sign indicates that the volume is decreasing over time and the rate of change is calculated to be -5235.98 inches³/s.

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Answer:

y=[tex]\frac{3}{2}[/tex]x - [tex]\frac{5}{2}[/tex]

Step-by-step explanation:

To get slope intercept form (y=mx+b), simplify and solve for y.

y+1=[tex]\frac{3}{2}[/tex](x-1)

Simplify

y+1=[tex]\frac{3}{2}[/tex]x - [tex]\frac{3}{2}[/tex]

Solve for y

y=[tex]\frac{3}{2}[/tex]x - [tex]\frac{5}{2}[/tex]

Answer:

14.7 times bigger is (1.176 x 10¹) than (8 × 10-¹) if the numbers are  (1.176 x 10¹) than (8 × 10-¹).

Step-by-step explanation:

Answer:

22

Step-by-step explanation:

To compare numbers this way, we divide.

(1.76 × 10^1) / (8 × 10^-1) =

= 1.76/8 × 10^1 / 10^-1

= 0.22 × 10^(1 - (-1))

= 0.22 × 10^2

= 22

The answer for the equation:

7x+31 = 8x -1/3(27x+3) is x=-4

The approximate air distance from La Sarre to Lebel-sur-Quevillon is 167.71 km.

To determine the air distance from La Sarre to Lebel-sur-Quevillon, analyze the path she has traveled.

When she drove east and drove another north, the total path she ave traveled is similar to the sides of a right triangle, where the distance from the start and end point is the hypotenuse. (see photo attached)

Using Pythagorean theorem, solve the distance from La Sarre to Lebel-sur-Quevillon.

c² = a² + b²

where a = 150 km and b = 75 km

distance² = 150² + 75²

distance² = 22500 + 5625

distance² = 28125

distance = 167.71 km

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The proportion of these banks that had an interest rate less than 2.5 percent is 0.724.

For a normally distributed set of data, given the mean and standard deviation, the probability can be determined by solving the z-score and using the z-table.

First, solve for the z-score using the formula below.

z-score = (x – μ) / σ

where x = individual data value = 2.5

μ = mean = 2.28

σ = standard deviation = 0.37

z-score = (2.5 - 2.28) / 0.37

z-score = 0.22 / 0.37

z-score = 0.5946

To get the proportion, find the probability that corresponds to the z-score in the z-table. (see attached images)

z-score = 0.5946

By interpolating the values,

probability = 0.724

proportion = 0.724

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Answer:

1. 39, 46

2. 180

Step-by-step explanation:

1. count up by 7

2. not sure..

The length of the rectangular pegboard is 80 inches

A rectangle is a polygon with four sides in which two opposite sides are parallel and equal

Since Vince is cutting a rectangular piece of pegboard to use in his garage for organization. The width of the pegboard is 8 inches less than half the length. The perimeter of the pegboard is 224 inches.

Let

Since the width of the pegboard is 8 inches less than half the length, we have that

W = L/2 - 8

Also, since the pegboard is a rectangle, its perimeter, P = 2(L + W)

Now, its perimeter P = 224 inches.

So, 2(L + W) = 224

L + W = 112

Now, substituting the width, W into the equation, we have

L + W = 112

L + L/2 - 8 = 112

L + L/2 = 112 + 8

L + L/2 = 120

3L/2 = 120

L = 120 × 2/3

L = 240/3

L = 80 inches

So, the length of the pegboard is 80 inches

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Explanation

From the given question

We are given the formula to compute the amount that a sum of $8000 compounded quarterly will yield after time t at a rate of 2.8%

The formula is given by

Part A

part B

the amount in the account after 7 years will be

The amount that will be in the account after 7 years will be $9725.57

Part C

APY is given by

In our case we have

Hence, we will have the APY as

Hence, the APY is 2.829%

The number is 234.

Step-by-step explanation:

Let the 3 digits be H , T and U so the number is HTU.

H + T + U = 9

T = 0.5H + 0.5U

U = 2H

So  from the last 2 equations

T = 0.5H + 0.5(2H)

T = 0.5H + H

T = 1.5H

So substituting for T and H is the first equation:

H + 1.5H + 2H = 9

4.5H = 9

H = 2.

So T = 1.5*H = 1.5 *2 = 3.

Mathematics → Solid Figures → Volume

The volume of a cylinder is:

In this question,

r = 2 ft (4/2 =2)

h = 5 ft

Then, the volume of the cylinder is (Vc):

Using π = 3:

The volume of a rectangular prism (Vr) is:

In this question:

l = 9 ft

w = 5 ft

h = 5 ft

Then, the volume of the rectangular prism is:

The volume of the object (V) is the sum of the volumes:

Answer: 285 ft³.

⇒For perpendicular lines when their gradients are multiplied they have to give -1, in this case we are given a line with gradient [tex]\frac{1}{2}[/tex] meaning the gradient of the line perpendicular to it will be -2 since

[tex]-2*\frac{1}{2} =-1[/tex]  this means that the gradient of the new line will be -2

⇒Now we have a point and  gradient.

⇒And we know that the general equation for a straight line is y=mx+c

[tex]3=-2(0)+c\\3=c\\c=3[/tex]

The equation of the line perpendicular to the given one is

y=-2x+3

GOODLUCK!!

Given data:

The given amount of equipment purchased by the Sandra is A=$1,200.

To solve an inequation for x you have to follow the same procedure you follow when solving equations, with exception that when you multiply/divide by a negative number the direction of the inequality gets inverted.

So to solve the given inequelity for x, you have to pass "+49" to the other side of the expression. To do so, subtract it from both sides of the expression:

The result of the inequality is x > -21

The cost of the total bill for the friends is $154.665.

This implies a levy that's paid to the government by individuals and firms.

From the information, the.group of friends’ dinner bill before tax is $122.75, sales tax rate is 8% and they want to leave an 18% tip after tax.

The total bill will be:

= Cost of food + Tax + Tip

= $122.75 + (8% × $122.75) + (18% × $122.75)

= $122.75 + $9.82 + $22.095

= $154.665

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