Mrs smith the soup kitchens chef estimates that they will serve 40 000 people soup. If they give each person 1 cup of soup over 2 weeks , if the month has 5 weeks. Is Mrs smith estimations correct

Answer: The first 3 options

Step-by-step explanation:

You have to make sure that the given variable would be able to equal -5. The  \(\geq\) sign in the second and third answer show that the variable could be equivalent to -5.

Answer:

g > -7, f ≤ -5 and g ≥ -5

Step-by-step explanation:

the < and > symbols mean less than and greater than respectively, but not including. Therefore -5 cannot be a valid solution if the range is (for example) g > -5. However, ≤ and ≥ mean less/greater than or equal to, so -5 would be a valid solution for g ≥ -5 (for example).

There are between 14.24 million and 19.86 million teens in the U.S. who, according to estimates, will value helping others highly as adults.

a. Since the margin of error is 13.3%, we can construct a 95% confidence interval as follows:

Point estimate = 81%

Margin of error = 13.3%

Lower limit = 81% - 13.3% = 67.7%

Upper limit = 81% + 13.3% = 94.3%

Therefore, the interval that is likely to contain the exact percentage of all U.S. teenagers who think that helping others who are in need will be very important to them as adults are between 67.7% and 94.3%.

b. To estimate the number of teenagers in the U.S. who think helping others will be very important to them as adults, we can use the point estimate of 81%.

Number of teenagers who think helping others will be very important = 81% of 21.05 million

= 0.81 x 21.05 million

= 17.05 million

Using the margin of error, we can construct a range for our estimate:

Lower limit = 67.7% of 21.05 million = 14.24 million

Upper limit = 94.3% of 21.05 million = 19.86 million

Therefore, the estimate for the number of teenagers in the U.S. who think helping others will be very important to them as adults is between about 14.24 million and 19.86 million.

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to eliminate the variable y

we have steps are,

1) Divide the second equation by 2. then add the result to the first equation

or

2) Multiply the first equation by 2. then add the result to the second equation

or

3) Multiply the first equation by 4 and the second equation by 6, then subtract the resulting equations.

so the answer is the first three options.

Answer:

$2,854.2

Step-by-step explanation:

For Sebastian

It took Sebastian 10 years to repay a loan of $30,000, paying $296.66 per month.

1 year = 12 months

10 years = x

Cross Multiply

x = 10 × 12 = 120 months

He pays $296.66 monthly

Hence, the total amount he paid in 10 years =

$296.66 × 120

= $35,599.2

The loan he took was $30,000.

Hence, the interest Sebastian paid on his loan = $35,599.2 - $30,000

= $5,599.2

For Jana

Jana paid off a loan for the same

amount at the same interest rate in 5 years by paying $545.75 per month.

1 year = 12 months

5 years = x

Cross Multiply

x = 10 × 5 = 60 months

He pays $545.75 monthly

Hence, the total amount he paid in 5 years =

$545.75 × 60

= $32,745

The loan she took was $30,000.

Hence, the interest Sebastian paid on his loan = $32,745 - $30,000

= $2,745

How much more did Sebastian pay in interest than Jana?

This is calculated as:

The interest Sebastian paid - The Interest Jana paid

= $5,599.2 - $2,745

= $2,854.2

Therefore, Sebastian paid $2,854.2 more than Jana

Answer:

2

Step-by-step explanation:

Answer:

the answer is 2

Step-by-step explanation:

3+5=8

8÷4=2

Answer:

x = 3/2y

y = 2/3x

Step-by-step explanation:

x = 3/2y

Swap sides so that all variable terms are on the left hand side

2x + 15 = 3y + 15

Subtract 15 from both sides

2x = 3y + 15 - 15

Subtract 15 from 15 to get 0

2x = 3y

Divide both sides by 2

2x/2= 3y/2

Dividing by 2 undoes the multiplication by 2

X = 3y/2

Y = 2/3x

Subtract 15 from both sides

3y = 2x + 15 - 15

Subtract 15 from 15 to get 0

3y = 2x

Divide both sides by 3

3/3y = 2/3x

Dividing by 3 undoes the multiplication by 3

y = 2/3x

The price elasticity of the supply is 0.43.

The relationship between the percentage change in a product's quantity demanded and the percentage change in price is known as price elasticity of demand. It helps economists comprehend how supply and demand shift in response to changes in a product's price.

Price Elasticity of Demand =\(\frac{Percentage Change in Quantity}{Percentage Change in Price }\)=\(\frac{\Delta Q}{\Delta P}\)

Further, the equation for price elasticity of demand can be elaborated into

Percentage change in quantity=ΔQ=\(\frac{(q_{2}-q_{1})}{(q_{2}+q_{1})}}\)

Percentage change in quantity=ΔP=\(\frac{(p_{2}-p_{1})}{(p_{2}+p_{1})}}\)

Where, \(q_{1}\)= Initial quantity, \(q_{2}\)= Final quantity,\(p_{1}\)= Initial price and \(p_{2}\) = Final price

Here,  \(q_{1}\)=10000,\(q_{2}\)=5000

Percentage change in quantity=ΔQ

=\(\frac{10000-5000}{10000+5000}\)

=\(\frac{5000}{15000}\)

=0.333

Here,  \(p_{1}\)=20 and \(p_{2}\)=15

Percentage change in quantity=ΔP

= \(\frac{20-15}{20+15}\)

=\(\frac{5}{35}\)

=0.143

Price Elasticity of Demand

=\(\frac{Percentage Change in Quantity}{Percentage Change in Price }\)

=\(\frac{0.333}{0.143}\)

=2.33

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Answer:

Step-by-step explanation:

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5x - 8 = x + 27

4x = 35

x = 35/4

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0

Answer: 2n^2. let me know if you need the explanation :).

Step-by-step explanation:

Answer:

Step-by-step explanation:

no solution

Answer:

Three consecutive multiples are 110,121 and 132 which has the sum of 363. 33C = 363; C = 33, By substituting C = 33 in numbers 11C, 11(C – 1) and 11(C + 1) we get values 110, 121, 132.

The inverse Fourier transform of F₂(jw) is given by f₂(t) = δ(t - 1/4) + δ(t + 1/4).

(a) To find the inverse Fourier transform of F₁(jw) = 1/(3+w) + 1/(4-jw), we can use the linearity property of the Fourier transform.

The inverse Fourier transform of F₁(jw) can be calculated by taking the inverse Fourier transforms of each term separately.

Let's denote the inverse Fourier transform of F₁(jw) as f₁(t).

Inverse Fourier transform of 1/(3+w):

Using the table of Fourier transforms,

F⁻¹{1/(3+w)} = e^(-3t) u(t)

Inverse Fourier transform of 1/(4-jw):

Using the table of Fourier transforms, we have:

F⁻¹{1/(4-jw)} = e^(4t) u(-t)

Now, applying the linearity property of the inverse Fourier transform, we get:

f₁(t) = F⁻¹{F₁(jw)}

      = F⁻¹{1/(3+w)} + F⁻¹{1/(4-jw)}

      = e^(-3t) u(t) + e^(4t) u(-t)

Therefore, the inverse Fourier transform of F₁(jw) is given by f₁(t) = e^(-3t) u(t) + e^(4t) u(-t).

(b) To find the inverse Fourier transform of F₂(jw) = cos(4w + π/3), we can use the table of Fourier transforms and properties of the Fourier transform.

Using the table of Fourier transforms, we know that the inverse Fourier transform of cos(aw) is given by δ(t - 1/a) + δ(t + 1/a).

In this case, a = 4, so we have:

F⁻¹{cos(4w + π/3)} = δ(t - 1/4) + δ(t + 1/4)

Therefore, the inverse Fourier transform of F₂(jw) is given by f₂(t) = δ(t - 1/4) + δ(t + 1/4).

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The transformation from function f(x) to g(x) is a vertical shift of 4 units up.

The transformation from f(x) to g(x) is a vertical shift of 4 units up. This can be seen by comparing

f(x) = |x| to g(x) = |x| + 4

. In other words, the graph of g(x) is 4 units higher than that of f(x), and the x-intercepts of the two functions are 4 units apart.

The transformation from f(x) to g(x) is a vertical shift of 4 units up. This can be seen by comparing the equations of the two functions. The parent function, f(x), is defined as f(x) = |x|, and the transformed function, g(x), is defined as g(x) = |x| + 4. By adding 4 to the parent function, the graph of the transformed function is shifted up 4 units, which is the same as saying it is shifted 4 units in the positive y-direction. This can be seen in the graphs of the two functions, where the x-intercepts of the two functions are 4 units apart. The transformation from f(x) to g(x) is a vertical shift of 4 units up, and it is the same as the transformation of

y = f(x) to y = f(x) + 4.

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The equivalent expression of -6(b + 2) + 8 is -6b - 4

The expression is given as

-6(b + 2) + 8

Expand

-6b - 12 + 8

Evaluate the like terms

-6b - 4

Hence, the equivalent expression of -6(b + 2) + 8 is -6b - 4

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Answer:

The first option: -5/4x + 1/6.

Step-by-step explanation:

(3/4x - 2/3) - (-5/6 + 2x)

= (3/4x - 2/3) + 5/6 - 2x

= 3/4x - 2x - 2/3 + 5/6

= 3/4x - 8/4x - 4/6 + 5/6

= -5/4x + 1/6

So, the first option: -5/4x + 1/6.

Hope this helps!

By answering the presented question, we may conclude that P(990< X <1150) = normal distribution  P[(990-1000)/100 < Z < (1150-1000)/100] = P(-1.0 < Z < 1.5) = 0.7745

The normal distribution is an example of a continuous probability distribution, in which the majority of data points cluster at the middle of the range and the remaining ones drop symmetrically towards one of the extremes. The mean of the distribution is another term for the range's centre. According to the normal distribution, also known as the Gaussian distribution, which is symmetrical around the mean, data that are close to the mean are more frequent than data that are far from the mean. I'm utilising heuristics in normal distribution to obtain a student's SAT scores from a new exam prep course. The data exhibit a normal distribution with a mean (M) of 1150 and a standard deviation (SD) of 150.

Question 1:

a) P(Z<1.72) = 0.9582 (using standard normal distribution table or calculator)

b) P(Z>1.1) = 0.1357

c) P(1.1<Z<1.70) = 0.0808

Question 2:

a) P(X<1070) = P(Z<(1070-1000)/100) = P(Z<0.7) = 0.7580

b) P(990< X <1150) = P[(990-1000)/100 < Z < (1150-1000)/100] = P(-1.0 < Z < 1.5) = 0.7745

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Answer:

P=1538.461

Step-by-step explanation:

do it by the formula of

I=PRT, I=750 R=3.25% T=15

Answer: y = -3x - 4

Step-by-step explanation:

Slope intercept form would be y = mx + b. To get your equation to this form you would need to isolate for y as shown:

3x + y = -4

y = -3x - 4 <-- Here I subtracted both sides by 3x

Answer: the third choice

Step-by-step explanation:

A Markov chain model, also known as a Markov process or simply a Markov model, is a mathematical framework used to describe and analyze systems that evolve over time.

To create a Markov chain model for a rat wandering through the maze, we need to consider the different states the rat can be in and the probabilities of transitioning between these states.

In this maze, the rat can be in different rooms. Let's say there are three rooms: A, B, and the center room (C). The center room is an absorbing state, which means that once the rat enters this room, it will stay there and not move to any other room.

To create the Markov chain, we need to define the transition probabilities between the different rooms. Since the rat is equally likely to leave its current room through any of the doorways, the transition probabilities for each room will be 1/3.

Here is an example of the transition probabilities:

1. From room A:
  - Probability of transitioning to room B: 1/3
  - Probability of transitioning to the center room C: 1/3
  - Probability of staying in room A: 1/3

2. From room B:
  - Probability of transitioning to room A: 1/3
  - Probability of transitioning to the center room C: 1/3
  - Probability of staying in room B: 1/3

3. From the center room C:
  - Probability of staying in room C: 1

Once the transition probabilities are defined, we can represent the Markov chain using a transition matrix. In this case, the transition matrix will be a 3x3 matrix, where each row represents the current room and each column represents the next possible room. The values in the matrix will correspond to the transition probabilities.

Transition matrix:
```
| 1/3   1/3   1/3 |
| 1/3   1/3   1/3 |
|   0     0     1   |
```

Note that the last row of the matrix represents the absorbing state (center room C), where the probability of transitioning to any other room is 0, and the probability of staying in the center room is 1.

By using this Markov chain model, we can analyze the rat's behavior and calculate probabilities of different events, such as the number of periods it takes for the rat to reach the center room or the probability of the rat being in a specific room after a certain number of periods.

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Answer:

- 2x² - 6x + 6 = 0

Step-by-step explanation:

A quadratic equation in standard form is

ax² + bx + c = 0 ( a ≠ 0 )

Given

6 - 2x² = 6x ( subtract 6x from both sides and rearrange )

- 2x² - 6x + 6 = 0 ← in standard form

To find the point Q such that R is the midpoint of PQ, we can use the midpoint formula. The midpoint formula states that the coordinates of the midpoint M between two points A(x₁, y₁, z₁) and B(x₂, y₂, z₂) can be calculated as follows:

M = ((x₁ + x₂) / 2, (y₁ + y₂) / 2, (z₁ + z₂) / 2).

In this case, we have the point P(9, 7, 10) and the midpoint R(10, 2, 1). We want to find the coordinates of point Q, where R is the midpoint of PQ. Let's denote the coordinates of point Q as (x, y, z).

Using the midpoint formula, we can set up the following equations:

(x + 9) / 2 = 10,  

(y + 7) / 2 = 2,  

(z + 10) / 2 = 1.

Simplifying these equations, we get:

x + 9 = 20,  

y + 7 = 4,  

z + 10 = 2.

Solving for x, y, and z, we find:

x = 20 - 9 = 11,  

y = 4 - 7 = -3,  

z = 2 - 10 = -8.

Therefore, the point Q is Q(11, -3, -8).

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Answer:

3 hours 45 minutes

Step-by-step explanation:

Answer:

(25x * 4y * 2z) + (15x * 2y^3)

10xy(20z + 3y^2)

(if you want working, just comment [too much effort lol])

1.The total cost would be:50 cash registers x 450 AED per cash register = 22,500 AED

2.the cost of one new cash register at the end of 8 years would be approximately 661.39 AED.

3. the value of one old cash register after 8 years would be approximately 222.19 AED.

4.It is not possible to determine whether the money from selling the old cash registers is enough to pay for the new ones without knowing the selling price of the old cash registers.

5.It would take approximately 19 years for the value of the cash registers to reach 95 AED.

1. The company needs to buy at least 50 cash registers, each costing 450 AED. Therefore, the total cost would be:

50 cash registers x 450 AED per cash register = 22,500 AED

 2. The continuous compounding formula is A = \(Pe^(^r^t^)\), where A is the resulting amount, P is the initial amount, e is Euler's number, r is the annual interest rate, and t is the time in years. We can apply this formula here by setting P = 450 AED, r = 6%, t = 8 years and solving for A:

A = 450*e^(0.06*8) = 661.39 AED (rounded to two decimal places)

 3. The value of each old cash register decreases at a rate of 7.5% per year. We can use the formula for exponential decay, P = , where P is the resulting amount, P is the initial amount, e is Euler's number, r is the rate of change, and t is the time in years. Setting P to 450 AED, r to -7.5%, and t to 8 years, we can solve for the resulting value:

P = 450*e^(-0.075*8) = 222.19 AED (rounded to two decimal places)

 4. If the selling price is greater than the value of the old cash registers after 8 years (i.e., 222.19 AED), then the company would make a profit on each old cash register sold to help pay for the new ones; if the selling price is less than 222.19 AED, then the company would incur a loss on each old cash register sold.

 5. To find when the value of the cash register will be approximately 95 AED, we can use the formula from part (3).

95 = 450*e^(-0.075t)

Dividing both sides by 450 and taking the natural logarithm of both sides, we get:

ln(95/450) = -0.075t

Solving for t, we get:

t = -(1/0.075) * ln(95/450) ≈ 19.01 years

With a lifespan of only 8 years, it is not a realistic scenario for the cash registers to depreciate to such a low value. Therefore, it is important for the company to properly maintain and replace the cash registers on a regular cycle to ensure that their value remains close to the original purchase price.

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It looks like the boundaries of \(R\) are the lines \(y=\dfrac23x \) and \(y=3x\), as well as the hyperbolas \(xy=\frac23\) and \(xy=3\). Naturally, the domain of integration is the set

\(R = \left\{(x,y) ~:~ \dfrac{2x}3 \le y \le 3x \text{ and } \dfrac23 \le xy \le 3 \right\}\)

By substituting \(x=\frac uv\) and \(y=v\), so \(xy=u\), we have

\(\dfrac23 \le xy \le 3 \implies \dfrac23 \le u \le 3\)

and

\(\dfrac{2x}3 \le y \le 3x \implies \dfrac{2u}{3v} \le v \le \dfrac{3u}v \implies \dfrac{2u}3 \le v^2 \le 3u \implies \sqrt{\dfrac{2u}3} \le v \le \sqrt{3u}\)

so that

\(R = \left\{(u,v) ~:~ \dfrac23 \le u \le 3 \text{ and } \sqrt{\dfrac{2u}3 \le v \le \sqrt{3u}\right\}\)

Compute the Jacobian for this transformation and its determinant.

\(J = \begin{bmatrix}x_u & x_v \\ y_u & y_v\end{bmatrix} = \begin{bmatrix}\dfrac1v & -\dfrac u{v^2} \\\\ 0 & 1 \end{bmatrix} \implies \det(J) = \dfrac1v\)

Then the area element under this change of variables is

\(dA = dx\,dy = \dfrac{du\,dv}v\)

and the integral transforms to

\(\displaystyle \iint_R 9xy \, dA = \int_{2/3}^3 \int_{\sqrt{2u/3}}^{\sqrt{3u}} \frac{dv\,du}v\)

Now compute it.

\(\displaystyle \iint_R 9xy \, dA = \int_{2/3}^3 \ln|v|\bigg|_{v=\sqrt{2u/3}}^{v=\sqrt{3u}} \,du \\\\ ~~~~~~~~ = \int_{2/3}^3 \ln\left(\sqrt{3u}\right) - \ln\left(\sqrt{\frac{2u}3}\right) \, du \\\\ ~~~~~~~~ = \frac12 \int_{2/3}^3 \ln(3u) - \ln\left(\frac{2u}3\right) \, du \\\\ ~~~~~~~~ = \frac12 \int_{2/3}^3 \ln\left(\frac{3u}{\frac{2u}3}\right) \, du \\\\ ~~~~~~~~ = \frac12 \ln\left(\frac92\right) \int_{2/3}^3 du \\\\ ~~~~~~~~ = \frac12 \ln\left(\frac92\right) \left(3-\frac23\right) = \boxed{\frac76 \ln\left(\frac92\right)}\)

The relative fitness of red birds is 1, not 0.5.

To determine the relative fitness of each bird type, we need to compare the average number of offspring each type produces in the next generation.

For red birds, the average number of offspring is 10.

For orange birds, the average number of offspring is 8.

For yellow birds, the average number of offspring is 2.

To calculate the relative fitness of each bird type, we divide each average number of offspring by the highest average number of offspring (which is 10):

- Redbirds: 10/10 = 1
- Orange birds: 8/10 = 0.8
- Yellow birds: 2/10 = 0.2

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Answer:

7

Step-by-step explanation:

The middle 2 numbers are 6 and 8. Add them both up and divide them by 2. Gets you 7.