6 Jessica runs for 15 minutes at an average speed of 6 miles per hour.
She then runs for 40 minutes at an average speed of 9 miles per hour.
It takes Amy 45 minutes to run the same total distance that Jessica runs.
Work out Amy's average speed.
Give your answer in miles
per hour.

Answer:

y = -1/2x - 7

Step-by-step explanation:

First, let's get the line in slope-intercept form. This is of the form y = mx + b. This helpful because we will be able to tell what the slope is, which is important because the parallel line will have the same slope. To do this, we need to isolate y. Subtract x from both sides. This gives us [tex]2y = 8-x[/tex]. Now divide both sides by 2 to completely isolate y. This gives us [tex]y = (8-x)/2[/tex], or [tex]y = -x/2 + 4[/tex]. From this we can tell that the slope is -1/2, because that is the coefficient of x.

This is the same slope we need for the parallel line! Let's put the line in slope-intercept form. We have our slope(-1/2), so we need to solve for b, which is the y-intercept. To do this, we will plug in the point on the graph to the equation for x an y. This gives us [tex]-6 = -1/2*-2 + b[/tex], or [tex]-6 = 1 + b[/tex]. Subtracting 1 from both sides tells us that which tells us b = -7. This is the y-intercept! Now we can plug this and the slope into our equation to get our answer: y = -1/2x - 6

I hope this helps!

The probability that the card is a king and a black card is 1/26.

There are 4 kings in a deck of 52 playing cards, and half of the cards are black, so there is a 1/13 probability that a randomly drawn card is a king, and a 1/2 probability that it is black.

To find the probability that a card is both a king and black, you can use the formula for the probability of the intersection of two events: P(A and B) = P(A) * P(B | A), where P(A) is the probability of event A occurring, and P(B | A) is the probability of event B occurring given that event A has already occurred.

Using this formula, the probability of drawing a king and a black card is:

P(King and Black) = P(King) * P(Black | King)

= (1/13) * (1/2)

= 1/26

So the probability of drawing a king and a black card is 1/26, or about 3.8%.

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The monthly payment is given as 11.95 0f the loan amount.

A percentage is a value that indicates 100th part of any quantity.

A percentage can be converted into a fraction or a decimal by dividing it by 100.

The given problem can be solved by the loan formula as follows,

The expression for the loan formula is given as,

PM = A(r(1 + r)ⁿ)/((1 + r)ⁿ- 1)

Where A is the loan amount, r is the rate of interest and n is the time interval.

The corresponding values of r and n as per the question are 6% = 0.06 and 12 respectively.

Substitute these values in the above expression to get,

PM = A(0.06(1 + 0.06)ⁿ)/((1 + 0.06)ⁿ- 1)

     = 0.119A

Which can be written in the form of percentage as,

PM = 0.119 × 100% of A

      = 11.9% of A

Hence, the per month payment of the loan will be 11.9% of the loan amount.

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The required algebraic expression when the that  total cost is $142.05.

That is $125.80 for Watermelon that weighs 185 lbs and $16.25 for 5 lbs of tomatoes.

=>Total cost = 3.25t +.68w

Given: Tomatoes cost $3.25 per lb while watermelons cost $.68 per lb.

Let w = weights of the tomatoes and watermelons.

The algebraic expression would be:

3.25t +.68w = Total cost

For 5 pounds of tomatoes and 185 lb of watermelon:

68(185) + 3.25(5)

=$125.80 + $16.25

= $142.05

The concept of algebraic expressions is the use of letters or alphabets to represent numbers without providing their precise values. We learned how to express an unknown value using letters like x, y, and z in the fundamentals of algebra. Here, we refer to these letters as variables.

Variables and constants can both be used in an algebraic expression. A coefficient is any value that is added before a variable and then multiplied by it.

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The break even point is x = 4  for cost C = 24x + 80 and Revenue R = 44x.

Cost is the amount of money spent by a business to produce or provide goods or services. It excludes the profit margin markup. Cost is the sum of money spent on making a thing or product, as seen from the seller's perspective.

Cost is defined as the total of real input costs and imputed costs associated with owner-supplied inputs.

The entire money derived from the sale of products or services pertaining to a business's core operations is referred to as revenue. Because it appears at the top of the income statement, revenue, which is also known as gross sales, is sometimes referred to as the "top line." A company's overall profits or profit are referred to as income, or net income.

The break-even threshold is reached when overall costs and total revenues are equal, leaving your small firm with no net benefit or loss. In other words, you've achieved the point in manufacturing when the income from a product matches the cost of manufacture.

At break even point cost equals revenue,

Therefore,

Cost = Revenue

⇒ 24x +80 = 44x

⇒ 20x = 80

⇒ x = 4.

The break even point is x = 4 .

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Answer:

  (b)  60.2°

Step-by-step explanation:

You want the measure of angle W if angles W and X are complementary and X = 29.8°.

Complementary angles total 90°:

  X + W = 90° . . . . . . . . . complementary relation

  29.8° +W = 90° . . . . . . use given value

  W = 90° -29.8° . . . . . . subtract 29.8°

  W = 60.2°

You should spend 30 minutes on machine 1 and 10 minutes on machine 2.

Given,

In the question:

You have 40 minute to exercise at the gym, and you want to burn a total of 300 hundred calorie using both machine.

Now, According to the question;

300 calories in 40 minutes can be set up as a ratio to find out how many calories per hour or calories per minute you are trying for:

300 calories /40 minutes = x calories/60 minutes for calories per hour (you are aiming for 450 calories burned per hour)

300 calories / 40 minutes = 7.5 calories per minute if you want to look at it that way instead.

One version of this problem that I found online completes the setup this way:

This allows us to set up a system of equations. The first equation will be for calories burned:

8x + 6y = 300

x is minutes on the 8 calorie per minute machine; y is minutes on the 6 calories per minute machine.

A second equation simply shows that the total minutes add up to 40:

x + y = 40

Now you can use substitution, elimination, or linear combinations to solve the system. I'll use substitution to rewrite the second equation:

x = 40 - y....(1)

Now substituting into the first equation:

8(40 - y) + 6y = 300

320 - 8y + 6y = 300

2y = 20

y = 10

Put the value of y in eq.(1)

Then, x gives the 30

Hence, You should spend 30 minutes on machine 1 and 10 minutes on machine 2.

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The transformation that is results in the given function is a horizontal shrink of scale factor 1/4.

Remember that for a function f(x), we define a horizontal shrink of scale factor k as:

g(x) = f(x*1/k)

Here we know that:

f(x) =x^2

g(x)= f(4x) = (4x)^2

Then this is equivalent to an horizontal shrink of scale factor of 1/4

Then the scale factor is k = 1/4, and the correct option is A.

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To convert the fraction 2 8/10 to a decimal, divide the numerator (8) by the denominator (10):

Then, add the integer part (2) to the result:

Therefore, the decimal representation of 2 8/10 is 2.8.

Answer:

x= -6/5

Step-by-step explanation:

[tex]\dfrac{1}{3} x=-\dfrac{2}{5}[/tex]

Multiply both sides by 3:

[tex]3\times(\dfrac{1}{3} x)=3\times(-\dfrac{2}{5} )[/tex]

[tex]\fbox{x = -$\dfrac{6}{5} $}[/tex]

The amount of carbon dioxide does a person exhale each minute is, 0.625 x 10^-2 kilogram.

What is kilogram?

With the unit symbol kg, the kilogram serves as the International System of Units' unit of mass. The term "kilo" is frequently used in colloquial speech and is a unit of measurement that is widely used in science, engineering, and commerce worldwide. It denotes "a thousand grams."

Given:

A person exhales about 1.25 x 10^-5 kilogram of carbon dioxide in 2 x 10^-2 minute.

We have to find the amount of kilograms of carbon dioxide does a person exhale each minute.

The amount of carbon dioxide for each minute is,

[tex]\frac{1.25*10^_^5}{2*10^-^2} =\frac{1.25}{2}*10^-^5^+^3 = 0.625*10^-^2[/tex]

Hence, the amount of carbon dioxide does a person exhale each minute is, 0.625 x 10^-2 kilogram.

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Answer:

Step-by-step explanation:

248miles ÷ 4hrs = 62mph

62mph × 6 hrs = 372miles

Mr. Chung will have driven 372 miles in 6 hours

Answer: Mr. Chung will have driven 372 miles in 6 hours

Step-by-step explanation:

Answer:

Step-by-step explanation:

1. 2310/35805 -> 3/10

2. 480/720 -> 2/3

3. 120/600 -> 1/5

4. 315/1680 -> 3/16

5. 126/840 -> 3/20

6. 1848/252​ -> 22/3

$592 is the minimum cost in dollars for a fair to be included in the highest 3% of domestic airfares. Using the concept of probability -

Probability is a mathematical discipline that concerns with numerical figures of how probable an occurrence is to occur or how probably a statement is to be true. A number between 0 and 1 is the probability of an occurrence, where, broadly speaking, 0 denotes the event's impossibility and 1 denotes its certainty.

Mean – 385 per ticket

Standard Deviation - 110

Now,

P (Z > x ) = 0.03

Value of z to the cumulative probability of 0.03 from the normal distribution table is 1.88

P(x - u / (standard deviation) > x - 385/110) = 0.03

That is, (x - 385/110) = 1.88

Therefore, x = 1.88 ×( 110+385)

= 591.91 or $592

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You see from the graph that when x = 0, y = 2 so the y-intercept is ( 0 , 2).

you are given points (-5 , 6) and (5 , -2). Find slope:

slope = change in y / change in x

slope = (6 - (-2)) / (-5 - 5)

slope = (6 +2) / (-5 - 5)

slope = 8/-10

slope = -4/5

slope-intercept form: y = mx + b where m = slope and b = y intercept.

y = -4/5x + 2

Answer:

25% increase

Step-by-step explanation:

120 thousand cars were manufactured in a country in the year 2004-O5. The production of cars increased to 150 thousand in 2005-06. Find the percentage increase in the manufacture of cars.

(150 - 120) / 120 = 0.25

0.25 = 25% increase

Answer:

A y = -3x + 1

Step-by-step explanation:

y = mx + b  When need to know the m (slope) and the b (y-intercept

The b is where the line crosses the y axis.  It crosses the y axis at 1.  The slope tells us the steepness of the line.  

If you start at the point (0,1) and move three units down and I unit to the right, you will be back on the line.  The slope is -3/1 which simplifies to -3

Answer:

d

Step-by-step explanation:

its 3 to the right and top and its not a negative number so we don't go left

Answer:

Graph A

Step-by-step explanation:

The equation indicates the line has a positive slope and a y-intercept of 0.  The only graph that corresponds to those conditions is Graph A.

Particular solution of the differential equation that satisfies the initial condition f'(s) = 10s - 4s³ , f(3) = 5 is f(s) =  5s² - s⁴ + 41.

We determine the particular solution to the differential equation. We do this by integrating the given differential equation and then applying the given initial condition. The power rule should be used for the given expression.

[tex]\int\ {x^{a} } \, dx[/tex] = [tex]\frac{x^{a+1} }{a+1} }[/tex]

we have given that,

f'(s) = 10s - 4s³

f(s) = ∫ f'(s)ds

     = ∫(10s - 4s³)ds

    = [tex]\frac{10s^{2} }{2} - \frac{4s^{2} }{4}+ C[/tex]

f(s) = 5s² - s⁴ + C

Now we will apply the initial condition,

f(3) = 5

⇒5(3)² - (3)⁴ + C =5

             -36 + C = 5

                       C =41

Therefore the solution is expressed as,

f(s) = 5s² - s⁴ + 41

This is the particular solution.

Given question is incomplete. Complete question is given as:

find the particular solution of the differential equation that satisfies the initial condition(s). f '(s) = 10s - 4s³, f(3) = 5.

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Answer: The product of two consecutive negative integers is 600. What is the value of the lesser integer?

Step-by-step explanation:

EDGE2021

The equation of the line that passes through point (-1, 3) and parallel to line y = 3x + 2 is

As a parallel line part of the qualities include that the slopes of the lines  are equal  

The equation of line is y = 3x + 2

The slope intercept form of the form as

y = mx + c

where

m = slope

c = intercept

x = input variables

y = output variables

Line has slope, m = 3, a new parallel line of slope 3 passing through point  (-1, 3)

(y - y₁) = m  (x - x₁)

y - 3 = 3 (x - -1)

y = 3x + 1 + 3

y = 3x +  4

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The equivalent value of the [x] that satisfy the given statement is 18.

Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis of the given problem.

Given is the statement -

the quotient of a number and three increased by 10 is 16

The given mathematical statement is -

the quotient of a number and three increased by 10 is 16

Assume the number to be [x]. Then, we can write -

(x/3) + 10 = 16

x/3 = 16 - 10

x/3 = 6

x = 6 x 3

x = 18

Therefore, the quotient of 18 and three increased by 10 is 16.

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Answer: $336.77

Step-by-step explanation:

So, the fencing is technically the perimeter, so we have to find the perimeter of the semicircle.

Perimeter of a semicircle = 2(pi)(r)/2

So, divide 26 by 2 to get the radius, which is 13.

(We will use 3.14 for pi)

Then fill in the variables 2 x (3.14) x (13) / 2

So, when you multiply all the numbers you will get 81.64/2.

81.64/2 = 40.82 ft.

Now that you have found how much feet the fencing will be, multiply it by the cost.

40.82 x 8.25 = 336.765.

Round your final answer by the nearest hundredth which is 336.77.

Answer: $336.77

Answer: A

Step-by-step explanation: Because when your weighing a box there can sometimes be decimals in the weight

9,000,000,000 is the best estimate of the number of bottles sold this year and last year

A number system is defined as a system of writing to express numbers.

Given,

Current year consumers purchased 7,234,267,990 bottles of water

Last year consumers purchased 2,000,900,999 bottles of water.

We need to find the best estimate of the number of bottles sold current year and last year.

The best estimate means rounding up to the nearest whole number.

The estimate of the bottles sold this year and last year from the above value is:

= 7,000,000,000 + 2,000,000,000

= 9,000,000,000

Hence, 9,000,000,000 is the best estimate of the number of bottles sold this year and last year

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Answer:

g(x) = |x-4| + 3

The graph f(x) of  y = 1/2 f(x).

The graph demonstrates that regardless of its value, y is always positive. From the question figure, the following conclusions can be made.

Whenever x is 0, y also equals 0.

If x is 1, then y is 2.

when x is two, y is four.

Y is two when x is -1.

If x is -2, then y is 4.

It implies that the modulus function (|x|) is a function of f(x).

Here is a definition of the modulus function:

g(x)

g(x) = |x| = {x,i∫x≥0

               {-x,i∫x<0

As we can see, it is twice as large as |x|, therefore the graph in the question figure

y = f(x) = 2|x |{ -2 ≤ x ≤2}

Therefore, we must create a graph y = 1/2 f(x)

y = |x | {-2 ≤ x ≤ 2}

Please see the graphic in the attachment for the graph of  y = 1/2 f(x).

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Step-by-step explanation:

[tex]5 \sin(4(x - \frac{1}{2} ) ) - 3[/tex]

Period is b/2pi

Which is

[tex] \frac{4}{2\pi} [/tex]

[tex] \frac{2}{\pi} [/tex]

Correct representations of the inequality -3(2x - 5) 5 are - 6x + 15 10 - 5x (2 – x)

An inequality in mathematics is a relation that compares two numbers or other mathematical expressions in an unequal way. [1]

The majority of the time, size comparisons between two numbers on the number line are made. Different types of inequalities are represented by a variety of notations, including:

The symbol a b indicates that an is smaller than b.

When a > b is used, it indicates that an is bigger than b.

A is not equivalent to b in any scenario. Since an is strictly less than or strictly greater than b, these relationships are known as stringent inequalities[1]. Equivalence is not considered.

There are two form of inequality relations that are not strict, in contrast to strict inequalities:

The indication of an or b denotes that.

According to our question-

The fourth response is shown by an open circle at 5, and a bold line that begins at 5 and points to the right (attached figure)

Detailed explanation

The difference is 5 (-3(2x - 5)). (2 - x)

First, make each side simpler.

∵ -3(2x - 5) = -3(2x) + -3(-5) (-5)

Recall that (+)=(-)

∴ -3(2x - 5) = - 6x + 15

∵ 5(2 - x) = 5(2) + 5(-x) (-x)

Recall that (+)(-) = (-)

∴ 5(2 - x) = 10 - 5x

∴ - 6x + 15 < 10 - 5x

Take 15 away from both sides.

∴ - 6x < -5 - 5x

5 times on both sides

∴ - x < - 5

Because the coefficient of x is negate, you must change the inequality's sign when you divide both sides by it.

The x coefficient is -1.

∴ Add -1 to both sides.

∴ x > 5

The appropriate answers are:

- 6x + 15 < 10 - 5x

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The values of x and y are -49/4 and -15/8 respectively for the given set of equations -2x + 4y = 17 and 3x - 10y = -3.

An equation is a combination of different variables, in which two mathematical expressions are equal to each other.

The given pair of equations,

-2x + 4y = 17      (1)

3x - 10y = -3      (2)

Multiply equation (1) with 3 and equation (2) with 2  

-6x + 12y = 51         (3)

6x - 20y = -6          (4)

Add equation (3) and (4),

- 8y = 15

y = -15/8

Substitute the value of  y in equation (1)

-2x + 4 (-15/8) = 17

-2x - 15/2 = 17

-2x = 49/2

x = - 49/4

The values of x and y for the given equations are -49/4 and -15/8 respectively.

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For the given equation the value of x and y will be 15/4 and 17/8 respectively

An equation is a statement that two expressions, which include variables and/or numbers, are equal. In essence, equations are questions, and efforts to systematically find solutions to these questions have been the driving forces behind the creation of mathematics.

It is given that, the equations are,

-2x+4y=17 -------(1)

3x-10y= -3

The value of x from equation 1 is,

-2x+4y=17

x=(17-4y)/2 -------(2)

Substitute the value of x in equation 2,

3x-10y=-3

3(17-4y)/2-10y= -3

y=17/8

The value of x is obtained as,

x=15/4

Thus, for the given equation the value of x and y will be 15/4 and 17/8 respectively

The question is incomplete the complete question is"solve the linear equation -2x+4y=17, 3x-10y=-3

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