Which ordered pair is a solution to this equation?
2x + 3y = 16
A. (3, 2)

B. (7, 2)

C. (5, 2)

D. (11, 1)

Answer: the factored form of 3x+24y is 3(x+8y) 3(x+8y)

Answer:

y=-x+6

Step-by-step explanation:

make it into y=mx+b form

x+y=6

-x      -x

y=-x+6

Answer:

y=-x+6

Step-by-step explanation:

slope intercept form means y=mx+b

y is y

m is the slope (in this one I don't have a picture, so I didn't put slope)

x turns into -x (because to get x to the other side, you have to subtract x from both sides)

b is the y intercept (in this case 6)

The probability to get a sample average of 51 or more customers if the manager had not offered the discount is 1.36%

We can use the formula for the standard error of the mean to calculate the standard deviation of the sample means. The standard error of the mean is given by:

standard error of the mean = standard deviation / √(sample size)

In this case, the standard error of the mean is:

standard error of the mean = 10 / √(6) = 4.08

To find the probability of observing a sample mean of 51 or more customers, we need to standardize the sample mean using the standard error of the mean. This gives us the z-score, which we can use to look up the probability in a standard normal distribution table.

The z-score is given by:

z-score = (sample mean - population mean) / standard error of the mean

In this case, the population mean is 42, and the sample mean is 51. Therefore, the z-score is:

z-score = (51 - 42) / 4.08 = 2.21

Using Table 1 (or a calculator or statistical software), we can find that the probability of observing a z-score of 2.21 or higher is approximately 0.0136 or 1.36%.

This means that if the manager had not offered the discount, there would be a 1.36% chance of observing a sample mean of 51 or more customers.

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Complete Question:

A small hair salon in Denver, Colorado, averages about 42 customers on weekdays with a standard deviation of 10. It is safe to assume that the underlying distribution is normal. In an attempt to increase the number of weekday customers, the manager offers a $4 discount on 6 consecutive weekdays. She reports that her strategy has worked since the sample mean of customers during this 6-weekday period jumps to 51. Use Table 1.

What is the probability to get a sample average of 51 or more customers if the manager had not offered the discount?

Answer:

64 Ounces

Step-by-step explanation:

64 Ounces of hot dogs

Answer:

64 oz

Step-by-step explanation:

1 lb = 16 oz

4 × 1 lb = 4 × 16 oz = 64 oz

Answer:

fncscscsdcsdcsadcsddcscsdcs

Step-by-step explanationso you do nine 9 x9

ok

Dimensions = 5 ft x 7 ft

Brick = 4 in x 12 in

1.- Convert ft to in

1 ft -------------------- 12 in

5 ft ------------------- x

x = (5 x 12) / 1

x = 60 in

1 ft -------------------- 12 in

7 ft -------------------- x

x = (7 x 12) / 1

x = 84 in

2.- Calculate the area of the wall

Area = 60 x 84

= 5040 in^2

3.- Calculate the area of a brick

Area = 4 x 12 = 48 in^2

4.- Divide the area of the wall by the area of the brick

Number of bricks = 5040 / 48

= 105

There will be 105 brick on the wall.

Answer:

It is a linear.

Step-by-step explanation:

Because after factor the function you will get f(x)= 5x, and the linear function is y=ax.

The correct answer is c. 12.5% of the original amount of the isotope will remain after 6,000 years.

In the first cycle (2,000 years), half of the original amount would remain. In the second cycle (another 2,000 years), half of that remaining amount would remain, which is one quarter of the original amount. In the third cycle (another 2,000 years), half of that remaining amount would remain, which is one eighth of the original amount. Therefore, after three cycles (6,000 years), only one eighth or 12.5% of the original amount would remain.
Your answer is based on the half-life of the isotope, which is 2,000 years. After each half-life period, the remaining amount of the isotope will be reduced by 50%.

In this scenario, 6,000 years have passed, which is equal to three half-life cycles (6,000 / 2,000 = 3). To find the percentage of the original amount that remains after these three cycles, you can simply apply the half-life reduction for each cycle. After the first half-life (2,000 years), 50% remains. After the second half-life (4,000 years), 50% of the remaining 50% remains, which is 25%. Finally, after the third half-life (6,000 years), 50% of the remaining 25% remains, which is 12.5%.

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The value of  Fourier coefficient Coy is -4 * 0 = 0 after using signal propertry .

Given periodic signal is a(t) with period To = 2 and Co = 3.

The transformation of x(t) gives y(t) where:y(t)=-4x(t-2)-2 Find the Fourier coefficient Coy.

The Fourier series expansion of the signal y(t) is given by:-

\($$y(t)=\sum_{n=-\infty}^{\infty} C_{n} e^{j n \omega_{0} t}$$\) (1)where Cn is the Fourier coefficient.

ω0 is the fundamental angular frequency of the periodic signal and is given by:

\($$\omega_{0}=\frac{2 \pi}{T_{0}}$$\)

Here, the fundamental period T0 is given as 2 seconds, so the fundamental angular frequency ω0 is:

\($$\omega_{0}=\frac{2 \pi}{2}= \pi$$\)

The Fourier series coefficients can be obtained by multiplying both sides of Eq. (1) by e−j n ω0 t and integrating over one period of the signal.

The Fourier coefficients of the periodic signal a(t) are given as:

\($$C_{n}=\frac{1}{T_{0}} \int_{-T_{0} / 2}^{T_{0} / 2} a(t) e^{-j n \omega_{0} t} d t$$(2)\)

Given that y(t)=-4x(t-2)-2,

we can write:

\($$y(t)=-4x(t-2)-2$$$$= -4 \sum_{n=-\infty}^{\infty} C_{n} e^{j n \omega_{0}(t-2)} -2$$$$= -4 \sum_{n=-\infty}^{\infty} C_{n} e^{j n \omega_{0} t} e^{-j 2n \pi} -2$$\)

Comparing the above equation with Eq. (1), we have:

\($$C_{n}=-4e^{-j 2n \pi}= -4(cos(2n \pi) - j sin(2n \pi))=-4$$\)

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Answer:

A

Step-by-step explanation:

Answer:

21

Step-by-step explanation:

Since the girls have the same age, let their age be x.
Then, their average is

\(\frac{x+x}{2} = \frac{2x}{2} = x\)

Let \(S_{i}\) denote the age of 'i' girls.
Then, \(S_{8} = S_{6} + x + x - eq(1)\)

Also, we have,

\(\frac{S_{8}}{8} =15 - eq(2)\)

\(\frac{S_{6}}{6} =13 - eq(3)\)

Then eq(2):

(from eq(1) and eq(3))

\(\frac{S_{6} + 2x}{8} =15\\\\\frac{13*6 + 2x}{8} = 15\\\\78+2x = 120\\\\2x = 120-78\\\\x = 21\)

The average of the other two girls with equal age​ is 21

The expected utility of Marlee with the ticket from Fony is 28.

The utility function of Marlee is given by u(x) = x+k. Here, k equals 100 if Marlee gets to go to the concert and equals 0 otherwise.

Marlee has $100 to buy tickets to the Fleet Foxes concert in Atlanta. She found two different websites selling tickets, Fony Front Seats and Best Tickets. If she buys a $20 ticket from Fony, there is a 60% chance that the ticket is fake, but she won't know until she gets to the concert.

If she buys a $60 ticket from Best Tickets, the ticket is certainly real. The seat placements for both tickets are identical and it costs $10 in gas to get to the concert.

Marlee's utility function is given as u(x) = x+k, where k equals 100 if Marlee gets to go to the concert and equals 0 otherwise. Her goal is to maximize her utility function.

Marlee is facing a trade-off between the cost of the ticket and the probability of getting a real ticket.

If she buys a $20 ticket from Fony, there is a 60% chance that the ticket is fake, but she won't know until she gets to the concert. Thus, there is a 40% chance that the ticket is real.

So, the expected utility of Marlee with the ticket from Fony is given by,

0.6u(0)+0.4u(100-20-10)=0.6(0)+(0.4)(70)=28

Therefore, the expected utility of Marlee with the ticket from Fony is 28. This indicates that Marlee will not be able to go to the concert if she buys the ticket from Fony Front Seats.

If she buys a $60 ticket from Best Tickets, the ticket is certainly real. Therefore, the expected utility of Marlee with the ticket from Best Tickets is,

u(100-60-10)=u(30)=30+100=130

Therefore, the expected utility of Marlee with the ticket from Best Tickets is 130.

This indicates that Marlee should buy the ticket from Best Tickets to get the maximum utility.

Therefore, Marlee should buy her ticket from Best Tickets because she will receive the maximum utility if she buys the ticket from Best Tickets.

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Answer:

B

Step-by-step explanation:

Answer:

B. \(\frac{x^2}{3^2} +\frac{y^3}{2^2} =1\)

Step-by-step explanation:

The amount that one family paid is 25 pound

Here two families had dinner and bill was 100 pound

They used the coupon on which they got 50% off

To find the percentage we have to use percentage formula:

\(=\frac{Value}{Total \ Value} *100\)

\(=\frac{50}{100} *100\)

\(= 50 \ Pounds\)

The remaining bill was 50 pound

Now this amount is divided between the 2 families

\(=\frac{50}{2}\)

\(= 25 \ pound\)

So one family has to pay 25 pounds

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Answer: check explanation for the solution

Step-by-step explanation:

A business that offers services to people by providing many amusement and fun with gate fees

The algebraic equations to be used is the general linear equation

Y = MX + C

Where

Y = total income or money realised

M = rate or price rate

X = number of goods or services

C = flat rate or gate fees

The business can also operate differently by using exponential equation

A = P(1 + R%)^t

Where

A = profit

P = capital

R = rate

t = time

Answer:

Step-by-step explanation:

b/7<23

Answer:

Step-by-step explanation:

he would have to pay 60 dollars but I don't really understand your question

Answer:

$20/3  or $6.67

Step-by-step explanation:

the question is incomplete the full question is Jon buys 3 shirts for 20 find his rate and the answer is above

Answer:

  10.97 seconds

Step-by-step explanation:

You want to know when a rocket will hit the ground if its height is given by y = -16x² +170x +61, where x is seconds after launch.

The formula for the solutions of a quadratic equation is ...

  \(\text{for }ax^2+bx+c=0\\\\x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}\)

When we apply this to the equation y=0, we have ...

  \(x=\dfrac{-170\pm\sqrt{170^2-4(-16)(61)}}{2(-16)}=\dfrac{170\pm\sqrt{32804}}{32}\\\\x\approx 10.97\quad\text{seconds}\)

The rocket will hit the ground after about 10.97 seconds.

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Lines l and m are parallel; line l will map onto line m with a 90° rotation; line l can map onto line m with a vertical line of reflection.

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The distance between Bert and Ernie is 8.8 miles.

What is law of cosine?

According to a trigonometry rule, the square of a side in a plane triangle is equal to the total of the squares of the other sides minus twice that amount, along with the cosine of the angle that separates them.

Here using law of cosine we can find the distance between Bert and Ernie. Then,

\(a^2=b^2+c^2-2ab cos(A)\)

Here a = BC , b = 5 mi , c = 6.5 mi and A = 100° then,

=> \(BC^2 = 5^2+6.5^2-2\times5\times6.5\times cos (100\textdegree)\)

=> \(BC ^2= 25+42.25-65\times(0.1736)\)

=> \(BC^2= 78.534\)

=> BC = 8.8 miles.

Hence the distance between Bert and Ernie is 8.8 miles.

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The equation obtained for Kim will be t = x/2

Equation obtained for Jake will be t = (x - 6)/1.5

As for the problem, Kim and Jake are competing in the big race. And the values of their speed are given below.

Kim moves at a 2-meter-per-second running pace.

Jake moves at a 1.5 meter per second running pace (3 meters per 2 seconds)

Jake gets 6 meters ahead of Kim.

To get equations for the same case to both persons we should get it as,

Let x be the complete race distance and t be either Kim's or Jake's total race time.

Time = Speed/Distance

Kim's time equation is t = x/ 2.

The time equation that Jake uses is t = (x - 6)/1.5.

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There are 608400 plates are possible.

If the first is A, we have 26 possibilities:

AA, AB, AC,AD,AE ...................................... AW, AX, AY, AZ.

If the first is B, we have 26 possibilities:

BA, BB, BC, BD, BE .........................................BW, BX,BY,BZ

And so on for every letter of the alphabet.

There are 26 choices for the first letter and 26 choices for the second letter. The number of different combinations of 2 letters is:

26×26=676

The same applies for the three digits.

There are 9 choices for the first as first digit cannot be 0

10 for the second,

10 for the third

9×10×10=900

So for a license plate which has 2 letters and 3 digits, there are:

676 × 900 = 608400 possibilities

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To answer this question we will use the following property of logarithms:

Dividing the given equation by 4 we get:

Simplifying the above result we get:

Applying the natural logarithm we get:

Applying the property of logarithms we get:

Therefore:

Answer: Option D.

Answer:

39

Step-by-step explanation:

I don't exactly know how to explain it.

I followed the formula

a^2+b^2= c^2

The number of collections of 50 coins that can be chosen from this pile is: C(125, 25) = 177,100,565,136,000
This is a very large number, which shows that there are many possible collections of 50 coins that can be chosen from the pile.

If the pile contains only 25 quarters but at least 50 of each other kind of coin, then the total number of coins in the pile must be at least 50 + 50 + 50 = 150. Let's assume that there are 150 coins in the pile, including the 25 quarters.
To choose a collection of 50 coins from this pile, we need to exclude the 25 quarters and choose 25 coins from the remaining 125 coins. We can do this in C(125, 25) ways, which is the number of combinations of 25 items chosen from a set of 125 items.
Therefore, the number of collections of 50 coins that can be chosen from this pile is:
C(125, 25) = 177,100,565,136,000

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There are 351 possible collections of 50 coins that can be chosen, considering the given conditions.

To find the number of collections of 50 coins that can be chosen, we will consider the given conditions:
The pile contains only 25 quarters.

There are at least 50 of each other kind of coin (pennies, nickels, and dimes).
Now, let's break this down step by step:
Determine the minimum number of coins from each kind required to make a collection of 50 coins.
- 25 quarters (as it's the maximum available)
- The remaining 25 coins must be a combination of pennies, nickels, and dimes.
Find the different combinations of pennies, nickels, and dimes that can be chosen to make a collection of 50 coins.
- We need 25 more coins, so we can divide them into three groups:
 a) Pennies (P)
 b) Nickels (N)
 c) Dimes (D)
Calculate the combinations for the remaining 25 coins.
- Using the formula for combinations with repetitions: C(n+r-1, r) = C(n-1, r-1)
 Where n is the number of types of coins (3) and r is the number of remaining coins (25)
- C(3+25-1, 25) = C(27, 25) = 27! / (25! * 2!) = 351.

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Answer:

The number of packages of gift wrap and greeting cards sold is 181 and 44 respectively

Step-by-step explanation:

The computation of the number of packages of gift wrap and greeting cards sold is as follows:

Let us assume the number of packages of gift wrap be x

And, for greeting cards be y

The equation are as follows

x + y = 225 ..................(1)

We can write as

y = 225 - x

4x + 10y = $1,164 ............(2)

Now put the y value in the equation 2

4x + 10 (225 - x) = $1,164

4x + $2,250 - 10x = $1,164

-6x = $1,164 - $2,250

-6x = -$1,086

x = 181

And, y = 225 - 181

= 44

The area enclosed by the parametric curve and the y-axis is 0.7542 square units.

The parametric curve is defined by \(\(x = t^2 - 2t\)\) and \(\(y = \sqrt{t}\)\).

Now, let's calculate the area enclosed by the curve and the y-axis:

\(\[ \text{Area} = \int_{0}^{c} |y| \, dt \]\)

Here,  \(\(c\)\)  is the upper bound of the domain, which is the value of \(\(t\)\) where the curve intersects the y-axis.

At the y-axis, the x-coordinate is 0, so we set \(\(x = 0\)\) in the equation for the parametric curve:

\(\[ x = 0\\ t^2 - 2t = 0\]\)

Solving for t:

\(\[ t^2 - 2t = 0 \\ t(t - 2) = 0 \]\)

So, t=0, or t=2. Since we are considering the domain where  \(\(t \geq 0\)\), the upper bound of the domain c is \(\(t = 2\)\).

Now, we'll integrate the absolute value of y with respect to t from 0 to 2:

\(\[ \text{Area} = \int_{0}^{2} |\sqrt{t}| (2t-t)\, dt \]\)

Since \(\(y = \sqrt{t}\)\) is positive in the given domain, the absolute value is not necessary, and we can simplify the integral:

\(\[ \text{Area} = \int_{0}^{2} \sqrt{t} (2t-t)\, dt \]\)

Now, integrate:

\(\[ \text{Area} = [\frac{4}{5}t^{5/2} -\frac{4}{3}t^{3/2} \Big|_{0}^{2} \]\\\)

\(\[ \text{Area} = [\frac{4\times\4\sqrt{2}}{5} -\frac{4\times\2\sqrt{2}}{3}] -0\)

\(\[ \text{Area} = \frac{8\sqrt{2}}{15}\)

\(\[ \text{Area} =0.7542 \ sq\ units\)

So, the area enclosed by the parametric curve and the y-axis is 0.7542 square units.

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The complete question is as follows:

Find the area enclosed by the given parametric curve and the y-axis. x = t² − 2t, y = √(t)

Answer:

  Miguel, because Andy is incorrect.

Step-by-step explanation:

The Angle Sum Theorem tells you the sum of angles in a triangle is 180°. If two of the angles are 45°, the third must be 180° -45° -45° = 90°. The third angle cannot be less than 90°.

__

Miguel is correct to disagree with Andy.