Devaughn's age is two times Sydney's age. The sum of their ages is 72 What is Sydney's age?

Answer:

[tex]A= 125*250=31250 ft^2[/tex]

Step-by-step explanation:

Let's define some notation first :

w= width , l = length , A= Area, P perimeter

For this case we want to maximize the Area given by this function:

A= l w   (1)

With the following restriction P=500 ft

We know that the perimeter on this case is given by:

[tex]P=2w +l[/tex]

Since they are using the creek as one side.

So then we have this:

[tex]500 =2w +l[/tex]   (2)

Now we can solve w in terms of l from eqaution (2) and we got:

[tex]w=\frac{500-l}{2}[/tex]   (3)

And we can replace this condition into equation (1) like this:

[tex]A= \frac{500-l}{2} l =250l - \frac{1}{2} l^2[/tex]

And we can maximize this function derivating respect to l and we got:

[tex]\frac{dA}{dl}= 250 -l=0[/tex]

And then we got that [tex]l=250[/tex]

And if we solve for w from equation (3) we got:

[tex]w=\frac{500-250}{2}=125[/tex]  

And then the dimensions would be:

[tex] l =250ft , w=125ft[/tex]

And the area would be:

[tex]A= 125*250=31250 ft^2[/tex]

To maximize the area of the corral, we can solve a mathematical optimization problem. By expressing the length in terms of the width, we can find the derivative of the area formula and set it to zero. Substituting the resulting value of the width into the area formula gives us the maximum area.

To find the maximum area of the corral, we need to determine the dimensions of the rectangle. Let's assume the length of the corral is L and the width is W.

Since one side of the corral is the creek, we only need to use fencing for the other three sides. This implies that 2W + L = 500 (since there are two widths and one length that need fencing).

To maximize the area, we can express L in terms of W using the formula L = 500 - 2W and substitute it into the area formula A = LW. Simplifying, we get A = W(500 - 2W). To find the maximum area, we can take the derivative of A with respect to W, set it equal to zero, and solve for W. The resulting value of W can be substituted back into the equation to find the corresponding value of L. The maximum area is obtained by multiplying these two dimensions together.

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The right answer is Option B.

Step-by-step explanation:

Given,

Purchase price of car with sales tax = $17300

DMV fees = 1.25%

Amount of DMV fees = 1.25% of purchase price

Amount of DMV fees = [tex]\frac{1.25}{100}*17300=\frac{21625}{100}[/tex]

Amount of DMV fees = $216.25

Total price = Purchase price + DMV fees

Total price = 17300 + 216.25

Total price = $17516.25

The total price of car with DMV fees is $17,516.25

The right answer is Option B.

Keywords: percentage, addition

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Final answer:

The total price of the car including DMV fees of 1.25% is (B) $17,516.25, which is found by adding the DMV fees of $216.25 to the purchase price of $17,300.

Explanation:

The question asks for the total price of a car including DMV fees, which are 1.25% of the purchase price of the car after sales tax.

To find the DMV fees, first convert the percentage to a decimal by dividing 1.25 by 100, which gives us 0.0125. Then multiply the purchase price after sales tax, $17,300, by 0.0125 to get the DMV fees.

The calculation is: $17,300 x 0.0125 = $216.25.

Finally, add the DMV fees to the purchase price to get the total price: $17,300 + $216.25 = $17,516.25. Therefore, the correct answer is B. $17,516.25.

Answer:

0 handshakes

Step-by-step explanation:

There are 8 women of different heights.

Let the eight women be A, B, C, D, E, F, G and H

Assume A is taller than B and A decides to shake hands with B, B will refuse because A is taller. If this happens across the eight women then there will be 0 hand shakes.

If this assumption is taken out, we have 7+6+5+4+3+2+1 = 28

Answer:

0

Step-by-step explanation:

There are 0 handshakes because if A is taller than B, then A will want to shake hands with B, but B will not participate because she is shorter.

Completed question: A bag of rare spice that weighs 3/5 pounds will be split equally among 15 people. How much spice will each person get?

Answer:

0.04 pounds

Step-by-step explanation:

The number of spice received by each person will be equal to the total number of spice divided by the number of people sharing it.

Amount of spice received per person = (3/5) /15

                                                     = 0.04 pounds

The cost of the phone contract will be C = 35 + 12m.

From the information given, the fixed line rental is £35 and the price of calls made is £12, therefore the monthly cost will be represented by:

C = 35 + (12 × m)

C = 35 + 12m

Therefore, the cost of the phone contract will be C = 35 + 12m where m represents the number of months.

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The cost of a monthly phone contract is made up of the fixed line rental and the price of the calls made. This can be represented with the formula: c = l + p, where c is the cost, l is line rental, and p is the price of calls. With a line rental of £35 and call price of £12, the total cost of the phone contract is £47.

In the scenario presented, the cost, c, of a monthly phone contract is constituted by the fixed line rental or l and the price or p of the calls made. This can be represented with the formula: c = l + p. We can substitute in the provided costs - a line rental of £35 and call price of £12 - into the equation to find the total cost of the phone contract. Thus, c = £35 + £12 = £47.

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Answer:

[tex]k=-\frac{2}{7}[/tex]

Step-by-step explanation:

The two equations given represent two straight lines in 2-D graph.

The two lines will not intersect if they are parallel.

Hence the two equations will not have solution if the lines are parallel and not coincident.

The condition for 2 lines given by the equations :

ax+by+c=0

dx+ey+f=0 to be parallel but not coincident is:

[tex]\frac{a}{d}=\frac{b}{e}\neq\frac{c}{f}[/tex]

here a=2  b=-3k  c=-1  d=4  e=k+2  f=-5

[tex]\frac{2}{4}=\frac{-3k}{k+2}\\k+2=-6k\\k=-\frac{2}{7}[/tex]

But also:

[tex]\frac{-3k}{k+2}\neq\frac{1}{5}[/tex]

Hence the value of k is -2/7.

Given:

$ 1.50 / gallon

1 gallon = 28 miles;

Solution:

$ 24.00 / $ 1.50 = 16 gallons

16 gallons x 28 miles = 448 miles

have a nice day:)

Answer:they would drive 448 miles if they spend $24 on gasoline

Step-by-step explanation:

The Morrison’s car uses one gallon of gasoline for every 28 miles. If gasoline costs $1.50 per gallon, then the cost of driving 28 miles would be $1.5.

Therefore, the number of miles can they drive if they spend $24 on gasoline would be

(28 × 24)/1.5 = 448 miles

Answer:

Kobe attended barber school for 9 hours each day.

Step-by-step explanation:

Total number of hours completed by Kobe in barber school = 612 hours

Total number of days Kobe attended the school for = 68 days

We are given that Kobe attended school for same number of hours each day.

So, in order to find the number of hours Kobe attended each day we will use unitary method.

In 68 days Kobe completed = 612 hours of school

So, in 1 day he will complete = [tex]\frac{612}{68}=9[/tex] hours

Thus, Kobe attended barber school for 9 hours each day.

Answer: it would take 3.1 months

Step-by-step explanation:

Let m represent the number of months that that it will take either of the runners to have the same amount of money in their accounts.

Let y represent the total amount that runner 1 saves for m months

Let z represent the total amount that runner 2 saves for m months

The first runner has $112 in savings, received a $45 gift from a friend, and will save $25 each month. This means that the total amount that he will save for m months would be

y = 112 + 45 + 25m

y = 157 + 25m

The second runner has $50 in savings and will save $60 each month. This means that the total amount that he will save for m months would be

z = 50 + 60m

To determine the number of months before the amount in the account of both runners becomes the same, we would equate y to z. It becomes

157 + 25m = 50 + 60m

157 - 50 = 60m - 25m

35m = 107

m = 107/35

m = 3.06

Answer:

y=0

Step-by-step explanation:

Answer:

y = [tex]\frac{9}{4}[/tex]

Step-by-step explanation:

The horizontal asymptote is the ratio of the coefficient of the highest degree term on the numerator and denominator, that is

9x² - 3x - 8 ← coefficient 9

4x² - 5x + 3 ← coefficient 4, thus

y = [tex]\frac{9}{4}[/tex] ← equation of horizontal asymptote

Answer:

The answer to your question is letter C

Step-by-step explanation:

Process

1.- Find two points of the line

   A ( 0, 1)

   B ( 1, -3)

2.- Find the slope of the line

    [tex]m = \frac{y2 - y1}{x2 - x1}[/tex]

    [tex]m = \frac{-3 - 1}{1 - 0}[/tex]

    [tex]m = \frac{-4}{1}[/tex]

           m = -4

3.- Find the equation of the line

            y - y1 = m (x - x1)

            y - 1 = -4( x - 0)

            y -1 = -4x

            y = -4x + 1

Answer:

800 people a year

Step-by-step explanation:

When there is an increment in an observed value, the increment implies that there is a growth or percentage increase in the observed value. The percentage increase in participation is 33%:

Given that:

[tex]Initial = 2400[/tex] --- last year

[tex]New= 3200[/tex] --- this year

The percentage increase is calculated as:

[tex]\%Increase = \frac{New - Initial}{Initial} \times 100\%[/tex]

So, we have:

[tex]\%Increase = \frac{3200 - 2400}{2400} \times 100\%[/tex]

[tex]\%Increase = \frac{800}{2400} \times 100\%[/tex]

[tex]\%Increase = 0.3333 \times 100\%[/tex]

[tex]\%Increase = 33.33 \%[/tex]

Approximate

[tex]\%Increase = 33 \%[/tex]

Hence, the percentage increase in participation from last year to this year is 33%

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Answer:

  B) shifts the line 4 units down

Step-by-step explanation:

The point (x, f(x)) is moved to the point (x, f(x)-4), one with a y-coordinate 4 units lower. The line is shifted down 4 units.

Answer:

B) shifts the line 4 units down.

Step-by-step explanation:

The constant negative number makes a vertical translation of the parent function in the -y direction. Slope keeps intact. So, the right answer is B.

Answer:

The coordinates of  A'(8,-5)

Step-by-step explanation:

we know that

When you reflect a point across the line y = x, the x-coordinate and y-coordinate change places

so

The rule of the reflection across the line y=x is

(x,y) -----> (y,x)

we have the point A(-5,8)

Applying the rule of the reflection across the line y=x

A(-5,8) ----> A'(8,-5)

see the attached figure to better understand the problem

Answer:

Step-by-step explanation:

Area Of Triangle And Rectangle

Given a triangle of base b and height h (perpendicular to b), the area can be computed by

[tex]\displaystyle A=\frac{bh}{2}[/tex]

A rectangle of the same dimensions has an area of

[tex]A=bh[/tex]

We have a triangle of base 3 cm and a height of 4 cm. Its area is

[tex]\displaystyle A=\frac{(3)(4)}{2}=6\ cm^2[/tex]

That triangle moves upward at 4 cm per second for 3 seconds. It means that the triangle 'sweeps' upwards three times its height forming a rectangle of base 3 cm and height 12 cm. The area of the swept area is

[tex]A=(3)(12)=36\ cm^2[/tex]

The triangle stays in the top of this rectangle, so its area is part of the total swept area:

Total swept area = 6 + 36 = [tex]42\ cm^2[/tex]

Answer:

Step-by-step explanation:

The total number of outcomes the two fair number cubes are thrown is 36. This can be seen by counting the outcomes shown on the table.

a) for a sum of 4, there are only 3 possible outcomes. They are 3,2 2,2 and 1,3

Therefore, the probability of getting a sum of 4 will be

3/36 = 1/12

b) for a sum of 5, there are only 4 possible outcomes. They are 4,1 3,2 2,3 and 1,4

Therefore, the probability of getting a sum of 4 will be

4/36 = 1/9

c)for a sum of 6, there are only 5 possible outcomes. They are 5,1 4,2 3,3 2,4 and 1,5

Therefore, the probability of getting a sum of 6 will be

5/36 = 5/36

The probability that the sum of the results of the throw is 4,5 or 6 would be

1/12 + 1/9 + 5/36 = (3 + 4 + 5)/36 = 12/36 = 1/3

Answer:

66 cups of fruit juice will be required .

Step-by-step explanation:

According to the question ,

90 Cups of fruit juice is required for making of 210 cups of punch .

So,

For making of one cup of punch ,

[tex]\frac{90}{210}[/tex] =  [tex]\frac{3}{7}[/tex] cups of fruit juice will be required ,

Thus,

For making of 154 cups of punch ,

Total number of cups of fruit juice required will be [tex]\frac{3}{7}[/tex]×154.

= 66 cups.

Thus a total of 66 cups of fruit juice will be required.

Answer:

see the explanation

Step-by-step explanation:

Remember that

[tex]1\ week=7\ days[/tex]

To convert weeks to days , multiply by 7

so

[tex]3\ weeks=3(7)=21\ days[/tex]

we know that

Each night Tim's Tacos sell 57 chicken tacos and 89 beef tacos

To find out how many of each type of taco sold after three weeks, multiply the number of taco sold daily by 21 (3 weeks)

Chicken tacos

[tex]57(21)= 1,197\ chicken\ tacos[/tex]

Beef tacos

[tex]89(21)= 1,869\ beef\ tacos[/tex]

Answer:the number of cupcakes that Sue purchased is 12

Step-by-step explanation:

Let x represent the number of cupcakes that Sue purchased at the bakery.

Let y represent the number of cookies that Sue purchased at the bakery.

She needs to serve 36 people. This means she would purchase a total of 36 people. Therefore,

x + y = 36

Cupcakes cost $2.50 each, cookies cost $1.00 each. She spends $54.00. This means that

2.5x + y = 54 - - - - - - - - - 1

Substituting x = 36 - y into equation 1, it becomes

2.5(36 - y) + y = 54

90 - 2.5y + y = 54

- 2.5y + y = 54 - 90

- 1.5y = - 36

y = - 36/ - 1.5

y = =24

x = 36 - y = 36 - 24 = 12

She purchased 24 cupcakes

If she needs to serve 36 people, then;

x + y = 36 ....................  1

if cupcakes cost $2.50 each, cookies cost $1.00 each while she spends $54.00, then;

2.5x + y = 54 ...................... 2

From equation 1, x = 36 - y

Substitute into equation 2;

2.5(36-y) + y = 54

90 - 2.5y + y = 54

-1.5y = - 36

y = 36/1.5

y = 24

Hence she purchased 24 cupcakes

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Answer:

As [tex]x \to -3^{+}, f(x) \to -\infty[/tex]

Step-by-step explanation:

Given:

From the graph, we can conclude that:

The function has vertical asymptotes at [tex]x=-3\ and\ x=2[/tex]

The function has horizontal asymptote at [tex]f(x)=0[/tex]

Vertical asymptotes are those values of 'x' for which the functions tends towards infinity. Horizontal asymptote is the value of the function as the 'x' value tends to infinity.

Now, as [tex]x \to -3^{+}[/tex] means the right hand limit of the function at [tex] x=-3[/tex]

From the graph, the right hand limit is the right side of the asymptote of the function at [tex] x = -3[/tex]. The right side shows that the function is tending towards negative infinity.

Therefore, As [tex]x \to -3^{+}, f(x) \to -\infty[/tex]

Answer:

10

Step-by-step explanation:

The individual scores in the data are represented by frequency denoted by f column. f column depicts that how many times the individual scores are occurring in the data set. Hence to calculate the amount of individual score in the data set we simply add all frequencies. n=sum of f=2+4+1+3=10. Hence there are 10 individual scores present in the entire data set.

The number of individual scores in the given frequency distribution set is 10, obtained by adding the frequencies together.

In the given question, it's the frequency distribution that is given with scores X: 5, 4, 3, and 2 with their respective frequencies f: 2, 4, 1, and 3. To find the total number of individual scores in the entire set, you simply sum up all the frequencies. So, 2+4+1+3 equals 10. So, the number of individual scores in the entire set is 10. Hence, the correct answer is c. N = 10.

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Answer:

Option 1 - [tex]\frac{At}{60}=g[/tex]

Step-by-step explanation:

Given : The goals against average (A) for a professional hockey goalie is determined using the formula [tex]A=60(\frac{g}{t} )[/tex]. In the formula, g represents the number of goals scored against the goalie and t represents the time played, in minutes.

To find : Which is an equivalent equation solved for g?

Solution :

Solve the formula in terms of g,

[tex]A=60(\frac{g}{t})[/tex]

Multiply both side by t,

[tex]At=60g[/tex]

Divide both side by 60,

[tex]\frac{At}{60}=\frac{60g}{60}[/tex]

[tex]\frac{At}{60}=g[/tex]

Therefore, option 1 is correct.

Answer:

a

Step-by-step explanation:

Answer:

A.True

Step-by-step explanation:

Multiple of 3 is given by

3,6,9,12,15,18,,,,

Let one number a=6

6 is a multiple of 3.

Another number =5

5 is not a multiple of 3.

Sum of 6 and 5=6+5=11

We know that

11 is not a multiple of 3.

Therefore, if one number is a multiple of 3 and the other is not , then the sum of these number is not a multiple of 3 is true.

Option A is true

Answer:

Repeaters.

Step-by-step explanation:

This is essential to effective communication because your EMS system must use Repeaters.

These are machines used to carry signals across a great distance. We may be in ambulances or put around an EMS network in different areas. The repeater receives and re transmits signals from lower power systems, such as mobile and handheld phones, to a higher power.

Final answer:

When using portable radios in an EMS system, waiting before speaking is necessary to prevent frequency interference with medical equipment like AEDs. This ensures effective communication and prevents disruptions with critical equipment operations.

Explanation:

When using a portable radio and instructed to push the "press to talk" button and wait one second before speaking, it is essential for effective communication because it ensures that the EMS system has time to establish a clear connection. This waiting period is crucial because communications or medical equipment may use similar radio frequencies. Interruptions and interference on these frequencies can arise from external devices, such as mobile phones operating at 1.9 GHz. Moreover, important medical devices, like automated external defibrillators (AEDs), which provide verbal instructions during cardiac emergencies, rely on these frequencies to function correctly without disruption. Therefore, allowing a small delay ensures that all emergency communication and equipment can operate without interference.

Additionally, speaking slowly and clearly is also vital to ensure that the message is conveyed accurately, especially in situations where there might be wi-fi delays or microphone malfunctions.

Answer: d. 112

Step-by-step explanation:

First Quartile is the median of the first half of ordered data (from  smallest to largest).

The given data : 118, 124, 108, 116, 99, 120, 148, 118, 119, 121, 45, 130, 118.

Arrange in Ascending order , we get

45,99, 108,116,118, 118, 118, 119,120, 121,124,130, 148

First half = 45,99, 108,116,118, 118

No. of elements = 6

First Quartile = Median of first half = Mean of middlemost terms

=[tex]\dfrac{108+116}{2}=\dfrac{224}{2}=112[/tex]

Hence, the First quartile = 112

Correct answer = d. 112

Answer: d) 0.238

Step-by-step explanation:

We would assume binomial distribution for the number of men sampled. The formula for binomial distribution is expressed as

P(x =r) = nCr × q^(n - r) × p^r

Where

p represents the probability of success.

q represents the probability of failure.

n represents the number of samples.

From the information given,

n = 10

p = 65% = 65/100 = 0.65

q = 1 - p = 1 - 0.65 = 0.35

The probability that exactly six of them will consider themselves knowledgeable fans is expressed as P(x = 6). It becomes

P(x =6) = 10C6 × 0.35^(10 - 6) × 0.65^6

P(x =6) = 10C6 × 0.35^4 × 0.65^6

P(x =6) = 0.238

Final answer:

Option d) 0.238

Explanation:

To find the probability that exactly six out of 10 men consider themselves knowledgeable football fans, we can use the binomial probability formula:

P(X=k) = C(n, k) * p^k * (1-p)^(n-k)

Where:

Using the formula, we get:

P(X=6) = C(10, 6) * 0.65^6 * (1-0.65)^4

Calculating C(10, 6) which is 210, and then raising 0.65 to the power of 6 and (1-0.65) to the power of 4, simplifies to:

P(X=6) = 210 * 0.1160290625 * 0.1502625 = 0.238

After rounding to three decimal places, we get:

P(X=6) = 0.238

Therefore, the correct answer is (d) 0.238.

Answer:

  6500

Step-by-step explanation:

In 24 hours, there are 12 times 2 hours, so the bacteria count will increase by 500 twelve times. That is, the increase after 24 hours will be ...

  12 × 500 = 6000 . . . bacteria

Since the starting number was 500, the total will be ...

  500 + 6000 = 6500 . . . . bacteria after 24 hours

_____

If you like, you can compute the rate of change as 500 bacteria / (2 hours) = 250 bacteria/hour. Then the equation for the number is ...

  bacteria = 500 + 250h . . . . . where h is the number of hours.

Filling in h=24, we get

  bacteria = 500 + 250(24) = 500 +6000 = 6500 . . . . after 24 hours

Answer:

[tex]P(x < 535.8) = 0.64[/tex]

[tex]P_{64} = 535.8[/tex]

Step-by-step explanation:

We are given the following information in the question:

Mean, μ = 500

Standard Deviation, σ = 100

We are given that the distribution of SAT score is a bell shaped distribution that is a normal distribution.

Formula:

[tex]z_{score} = \displaystyle\frac{x-\mu}{\sigma}[/tex]

We have to find the value of x such that the probability is 0.64

P(X<x) = 0.64

[tex]P( X < x) = P( z < \displaystyle\frac{x - 500}{10})=0.64[/tex]  

Calculation the value from standard normal z table, we have,  [tex]p(z<0.358) = 0.64[/tex]

[tex]\displaystyle\frac{x - 500}{100} = 0.358\\x = 535.8[/tex]

[tex]P(x < 535.8) = 0.64[/tex]

[tex]P_{64} = 535.8[/tex]

Tyrell's math score is 554.

To find Tyrell's math score, we need to use the z-score formula. The z-score formula is given as z = (x - μ)/σ. In this case, we want to find x, so we rearrange the formula to solve for x: x = zσ + μ. Given that Tyrell's score is in the 64th percentile, we can use the z-score table to find the corresponding z-score. The z-score for the 64th percentile is approximately 0.355. Plugging this into the formula, we get: x = 0.355(100) + 500 = 53.55 + 500 = 553.55. Rounding to the nearest whole number, Tyrell's math score is 554.

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Answer:

To convert larger units to smaller units, multiply. When the units are smaller, you need more of them to express the same measure. To convert smaller units to larger units, divide. When the units are larger, you need fewer of them to express the same measure.

Multiply to convert larger units to smaller units.

Divide to convert smaller units to larger units.

When the units are smaller, you need more of them to express the same measure.

When the units are larger, you need fewer of them to express the same measure.

Answer:

To convert between units, you're usually given one measure and asked to convert to another measure.

Step-by-step explanation:

Going to smaller units means going to bigger numbers so you multiply and going to bigger units means going to small. or in other words if you need to convert from a larger unit to a smaller unit Multiply. and if you need to convert from a smaller unit into a larger unit Divide. When converting customary units of measure from a larger unit to a smaller unit, multiply the the larger unit by its smaller equivalent unit.

Answer:

Minimum number of weeks = 4

Step-by-step explanation:

Charles earns $5 each week .Also he makes $15 each week by mowing his neighbours lawn.

Thus , in total , he earns a total of $20 each week.

We have to find the minimum number of weeks needed to make $75 .

Number of weeks required = [tex]\frac{money required}{money made per week}[/tex]

                                   = [tex]\frac{75}{20}[/tex]

                                    =3.75

Since the number of weeks, W, is an integer, choose the next highest integer.

Hence the minimum number of weeks required = 4