the school carnival is coming up and jenny and sarah plan to sell cupcakes. since the school carnival is a fundraiser, jenny and sarah's parents make a donation to their cupcake booth to get them started. jenny starts with a $5 donation and sells her cupcakes for $3 each. sarah starts with a $10 donation and sells her cupcakes for $2 each. how many cupcakes do jenny and sarah have to sell for their profits to be equal?

Answer:

The value of r is 12.

Step-by-step explanation:

Since DM = 25, and DG + GM = DG, we can use this information to compose the equation:

r + 2 + 2r - 13 = 25

Combine like terms by adding r and 2r, and subtracting 2 and 13.

3r - 11 = 25

Add 11 to both sides.

3r = 36

Divide both sides by 3.

r = 12

Answer:

1. A

2. C

3. B

Step-by-step explanation:

1. we can create an equation y = 48x + 96

if we plug in 1 we get 144

2. we can create an equation y = 10x to represent how much battery you will lose every hour

if we plug in 5 to x, we get y = 50

so we get the plot point: (5, 50)

3. process of elimination

Answer:

i think the c answer is 5

Step-by-step explanation:

if the vertex is at the origin, and the focus point horizontally to the right-side 1/8 units away from the vertex, well, that means is a horizontal parabola with a "p" value of +1/8, so

\(\textit{horizontal parabola vertex form with focus point distance} \\\\ 4p(x- h)=(y- k)^2 \qquad \begin{cases} \stackrel{vertex}{(h,k)}\qquad \stackrel{focus~point}{(h+p,k)}\qquad \stackrel{directrix}{x=h-p}\\\\ p=\textit{distance from vertex to }\\ \qquad \textit{ focus or directrix}\\\\ \stackrel{p~is~negative}{op ens~\supset}\qquad \stackrel{p~is~positive}{op ens~\subset} \end{cases} \\\\[-0.35em] ~\dotfill\)

\(\begin{cases} h=0\\ k=0\\ p=\frac{1}{8} \end{cases}\implies 4(\frac{1}{8})(~~x-0~~) = (~~y-0~~)^2\implies \cfrac{1}{2}x=y^2\implies \boxed{x=2y^2}\)

Answer:

xy = 3

d/dt(xy) = d/dt(3)

ydx/dt + xdy/dt = 0

y = 3/x so substitute 3/5 for y, 5 for x, and 5 for dy/dt; and solve for dx/dt.

3/5(dx/dt) + 5(5) = 0

3/5(dx/dt) = -25

dx/dt = -125/3

Step-by-step explanation:

this should be able to help you :)

Answer: whichever one is easiest to get by itself.

Step-by-step explanation:

As the value of n increases and the probability of success remains the same, the distribution of the binomial random variable will become more focused across the expected value, that is equal to n times the probability of success.

Which means that the variance of the distribution also increases proportionally with n, even as the same old deviation increases with the rectangular root of n.

Moreover, as n becomes larger, the distribution will become more symmetric and procedures a regular distribution, because of the relevant restrict Theorem. which means the binomial distribution can be approximated by way of a normal distribution with the equal mean and variance, whilst n is satisfactorily huge.

Commonly, as n increases, the binomial distribution will become extra precise and closer to the theoretical expected value, making it a beneficial device for modeling real-world phenomena and making predictions based on opportunity.

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The probability that exactly 6 are white and 2 are red is equals to 7/15 and the probability that at least 6 of the balls are white is equals to the 8/15.

The probability of a series of dependent of events may be found by finding the probability of each event and combining all the probabilities together. We have a urn which contains total 10 balls.

Number of white balls in urn, W = 7

Number of red balls in urn, R = 3

Now, a sample of 8 balls is selected randomly without replacement. We have to determine the probability that exactly 6 are white and 2 are red.

The number of ways selecting 8 balls among 10 = ¹⁰C₈ = 10!/8!2! = 45

The number of ways selecting 6 white balls among 7 = ⁷C₆ = 7!/6! = 7

The number of ways selecting 2 red balls among 3 = ³C₂ = 3!/2! = 3

Total number of ways selecting exactly 6 white and 2 red balls = 7×3 = 21

So, probability that exactly 6 are white and 2 are red,

= favorable outcomes/total outcomes

= 21/45

= 7/15

b) ‘At least 6 white balls’ selected in 8 balls means 6 white balls and 2 red, or, 7 white balls and 1 red.

Total number of ways selecting at least 6 of the balls are white,

= ⁷C₆ × ³C₂ + ⁷C₇ ³C₁

= 21 + 7!/7! × 3!/2! = 21 + 3 = 24

Probability that at least 6 of the balls are white = 24/45 = 8/15

Hence, required probability is 8/15.

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Answer

your answer is not shown but the correct answer based on the top is going to be −

7.6x + 6.393

please check to ensure that you wrote the problem correctly as well as your answers.

Step-by-step explanation:

By applying the concept of central and extreme scores, it can be concluded that a score of x = 85 would be considered a central score in population 1, and an extreme score in populations 2 dan 3.

A central score is a score that is near the middle of the distribution, while an extreme score is a score that is far out in the tail of the distribution.

In order to determine whether a score of x = 85 is a central score or an extreme score for each of the following populations, we need to look at the distribution of scores in each population.

Overall, whether a score of x = 85 is considered a central score or an extreme score depends on the distribution of scores in the population. If the scores are evenly distributed and x = 85 is near the middle of the distribution, it would be considered a central score. However, if the scores are clustered around a different value and x = 85 is far out in the tail of the distribution, it would be considered an extreme score.

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Randy needs 8 loads.

To find the answer on the question we have to follow the method of multiplication and division .

A washing machine can hold \(\frac{3}{4}\) kg of laundry in each load.

\(\frac{3}{4}\) kg of laundry is equal to 1 load.

\(\frac{3}{4}\) kg of laundry =  1 load

1 kg of laundry  =  \(\frac{1 * 4}{3}\) load ( following the method of division )

1 kg of laundry = \(\frac{4}{3}\) load

Randy has 6kg of laundry.

So, 1kg of laundry i.e \(\frac{4}{3}\) load is to be multiplied by 6.

6kg of laundry = \(\frac{4 * 6}{3}\) load ( following the method of multiplication)

                         = 8 loads

Hence, Randy needs 8 loads.

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The solution is A, which is $13.50 as a two-day bike rental normally costs $7 each day multiplied by two days for a total of $14.

The term "amount" designates a sum or number, typically expressed in terms of monetary value or a tangible good. It can also be used to describe the whole amount of anything, such as the total time that is spent on a work or the total amount of rain that falls in a specific location. "Amount" is frequently used synonymously with "amount" or "total."

given

A two-day bike rental normally costs $7 each day multiplied by two days for a total of $14.

Joanna paid $7/2 ($3.50) on Friday thanks to a voucher she utilised to pay half the price.

The normal Saturday bike rental fee should be "x." Then, according to the issue, Joanna paid $4 less than double what renting a bike normally costs during the workweek. As a result, she spent $10 on Saturday (2($7) - $4).

As a result, she spent the following sum overall to rent the bike:

$3.50 + $10 = $13.50

The solution is A, which is $13.50 as a two-day bike rental normally costs $7 each day multiplied by two days for a total of $14.

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Answer:

Step-by-step explanation:

x is greater than or equal to 1. (see work below for steps to solve)

You can check this answer by plugging 1 back into the equation.

5+4(1) = 5+4 = 9

(1) = 8 = 9

since both sides are equal when x=1, this is true.

Step-by-step explanation:

Average speed (S) = 200 m/s

Time taken (t) = 2 .5 hours = 2.5 *60*60 = 9000 sec

Now distance travelled (d) = ?

We know

The distance travelled by a body per unit time is

speed so

S = d / t

200 = d / 9000

d = 9000 * 200

d = 1800000 meters.

The plane flies 1800000 meters.

Answer:

A. P=11*3 = 33 ft

   A= 21*3 = 63 ft^3

B. P = 9*3 = 27 ft

   A = 15*3 = 45 ft^3

C. P = 20*3 = 60 ft

   A = 24*3 = 72 ft^3

D. P = 13*3 = 39 ft

   A = 25*3 = 75 ft^3

Step-by-step explanation:

The longest poster that can fit in the box must have dimensions of 10 inches (height) by 20 inches (length) by 12 inches (width).

To find the longest poster that can fit in the box, we need to determine the longest dimension of the box itself. Since the box is 10 inches high, the longest poster that can fit in the box must have a height of no more than 10 inches.

Now, we need to consider the other two dimensions of the box. The box is 20 inches long and 12 inches wide, so the longest poster that can fit in the box must have a length of no more than 20 inches and a width of no more than 12 inches.

As for why we can only fit one maximum-length poster in the box but we can fit multiple 22-inch posters in the same box, it's because the length and width of the box are larger than the length and width of the 22-inch poster.

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Answer:

Here’s the answer! Best of luck.

Step-by-step explanation:

The functions and their transformations are

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

f(x) = 2(x + 1)² - 3

A translation down by 5 units is represented as

f(x) - 5

So, we have

f(x) - 5 = 2(x + 1)² - 3 - 5

f(x) - 5 = 2(x + 1)² - 8

Rewrite as

h(x) = 2(x + 1)² - 8

A translation left by 5 units is represented as

f(x + 5)

So, we have

f(x + 5) = 2(x + 1 + 5)² - 3

f(x + 5) = 2(x + 6)² - 3

Rewrite as

k(x) = 2(x + 6)² - 3

A translation right by 5 units is represented as

f(x - 5)

So, we have

f(x - 5) = 2(x + 1 - 5)² - 3

f(x - 5) = 2(x - 4)² - 3

Rewrite as

g(x) = 2(x - 4)² - 3

A translation up by 5 units is represented as

f(x) + 5

So, we have

f(x) + 5 = 2(x + 1)² - 3 + 5

f(x) + 5 = 2(x + 1)² + 2

Rewrite as

j(x) = 2(x + 1)² + 2

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Answer:

0.25

Step-by-step explanation:

Answer:

V = πr²h

To determine the volume of a cylinder you have to multiply the area of the base by the height of the cylinder.

Step-by-step explanation:

The base of a cylinder is a circle. So we must find the area of the circle first. (Which is πr²)

Then we multiply the height by the area of the circle.

V = π·r²·h

This can be used in different ways as well,

if we don't know the radius but know everything else we could use the formula:

\(r=\sqrt{\frac{V}{\pi*h} }\) (r = √(V/πh))

If we don't know the height we use this formula:

(h = V/(πr²))

Answer: 9.7 seconds

Step-by-step explanation:

\(16t^2 =1503\\\\t^2 =1503/16\\\\t=\sqrt{1503/16} \text{ } (t > 0)\\\\t \approx 9.7\)

Answer:

3

Step-by-step explanation:

Total 108 chips were in the both bags.

A ratio or value that may be stated as a fraction of 100 is called a percentage. And it is represented by the symbol '%'.

10% of chips in the first bag is 6.

To find the total chips in the first bag:

6 = 10 x total number of chips in the first bag / 100

total number of chips in the first bag = 600/10

total number of chips in the first bag  = 60

25% of chips in the second bag is 12.

To find the total chips in the second bag:

12 = 25x total number of chips in the second bag / 100

total number of chips in the second bag = 1200/25

total number of chips in the second bag  = 48

Now, total chips in the both bags = 60 + 48 = 108

Therefore, total 108 chips were in the both bags.

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Answer:

x = 9

Step-by-step explanation:

To solve these problems, you first set up an equation representing the information given.

6x = x² - 27

This turns into a quadratic equation which you need to factor out.

0 = x² - 6x - 27

You want to choose two numbers that multiply to -27, and add up to -6

0 = (x - 9)(x + 3)

If you're unfamiliar with factoring, you take the opposite sign of the number in the parentheses because it's a shortcut when setting it equal to 0.

x = 9, -3

Since it asks for the positive solution only, the answer is x = 9.

I hope this helps!

Answer:

D. 57

Step-by-step explanation

\(f(x)=5x^3 - 3x - 7 \\ \\ f'(x) = 5 \times 3 {x}^{2} - 3 \times 1 - 0 \\ \\ f'(x) = 15 {x}^{2} - 3 \\ \\ plug \: x = - 2 \\ f'( - 2) = 15 {( - 2)}^{2} - 3 \\ \\ f'( - 2) = 15 \times 4 - 3 \\ \\f'( - 2) = 60 - 3 \\ \\f'( - 2) = 57 \\ \\\)

P EQUALS NEGATIVE NINE(9)

a) Relation of recurrence for the number of bacteria remaining after n hours is   \(a_{n} = a_{n-1} + 2a_{n-1} - a_{n-2} = 3a_{n-1}-a_{n-2}\)

b) the solution to this recurrence relationship is \(a_{n} = (50 + 30\sqrt{5}) [(3 + \sqrt{5}) / 2]^{n} - (30\sqrt{5} - 50) [(3 - \sqrt{5}) / 2]^{n}\)

c) There will be more than a million microorganisms after 7 hours.

A recurrence relation is an equation that states that some combination of the previous terms and the nth term in a series of numbers equals 1.

a) a₀ = 100, a₁ = 300 Every hour the bacteria - bacteria before two hours, and every hour the bacteria + 2(existing bacteria). Consequently, the corresponding recurrence relationship is \(a_{n} = a_{n-1} + 2a_{n-1} - a_{n-2} = 3a_{n-1}-a_{n-2}\)  where n is an hour reference.

(b) The associated difference equation is

r² - 3r + 1 = 0

⇒ r = [3 ± (√9 - 4)] / 2 = (3 ± √5) / 2

hence, the answer is \(a_{n} = a[(3 + \sqrt{5}) / 2] ^{n} + b [(3 - \sqrt{5}) / 2] ^{n}\)

Using n = 0 as the initial condition, we have a₀ = 100 = a + b → (1)

putting n = 1,

⇒ √5 (a - b) = 300 → (2)

(1) ⇒ √5 (a + b) = 100√5

By combining these relationships, we have

a = [(300 + 100√5) / 2√5] = 50 + 30√5

therefore, b = 50 - 30√5

Consequently, the answer to the equation is \(a_{n} = (50 + 30\sqrt{5}) [(3 + \sqrt{5}) / 2]^{n} - (30\sqrt{5} - 50) [(3 - \sqrt{5}) / 2]^{n}\)

c) if there are more than one million bacteria, i.e.

\(a_{n} = (50 + 30\sqrt{5}) [(3 + \sqrt{5}) / 2]^{n} - (30\sqrt{5} - 50) [(3 - \sqrt{5}) / 2]^{n} > 1,000,000\)

⇒ log (50 + 30√5) + n {log (3 + √5)} - log2} - log {30√5 - 50} - n {log (3 - √5) - log2} > log 1,000,000

⇒ 2.06849 + n {0.719 - 0.3010} - 1.2325 - n {-0.41797} > 6

⇒ 0.835975n > 5.16401

⇒ n > (5.16401 / 0.83975)

Therefore, n > 6.177, or after 7 hours, there will be more than 1 million bacteria.

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Answer:

Area of the shape = 62.135 (units^2)

Step-by-step explanation:

To start, divide the shape into simpler parts.

A triangle (4 by 6)

A Rectangle (6 by 6)

A half Circle (Radius of 3) - take the height (6) and divide it by 2 (= 3)

First get the area of the Triangle. Base x Height / 2

    4 x 6 = 24; 24 / 2 = 12;

         Area of the Triangle is 12

Second get the area of the Rectangle. Length x Width

    6 x 6 = 36

         Area of the Rectangle is 36

Third get the area of the circle Pie x Radius ^2 (squared)

   3.14 x (3 ^2) = 28.27

         Now take the area of the whole circle and divide it by 2 to get the      half circle

              28.27 / 2 = 14.135; Area of the half Circle is 14.135

Add up all the areas to get the total for your shape.

    12 + 36 + 14.135 = 62.135

Answer:

The answer you're looking for is 1470.

Step-by-step explanation:

The method I used was PEMDAS

Since there was no parenthesis, I simplified the exponents.

2.130 x 10³ - 6.6 x 10² = ?
2.130 x 1000 - 6.6 x 100 = ?

After that, I multiplied all terms next to each other.

2.130 x 1000 - 6.6 x 100 = ?
2130 - 660 = ?

The final step I did was to subtract the two final terms and ended up with 1470 as my final answer.

1470 = ?

I hope this was helpful!

Answer:

(-4, -7).

Step-by-step explanation:

The graph of y= |x + 4| (absolute values) is V shaped with the vertex at (-4, 0) . y = -| x + 4| inverts the graph about the x axis, the vertex remaining at (-4, 0).

The - 7 moves the graph 7 units down

So the vertex point is (-4, -7).

The equation is a parabola with the coefficient of term squared x negative, so the range is from - infinity to the y-value of the vertex.

We need to find the y-value of the vertex:

So, the Range of the function is (-infinity, 3]