A researcher was interested in studying americans email habits. She suspected that americans spend less than 7 hours a week answering their email. The general social survey in 2004 included a question that asked about the number of hours that the respondent spend on email per week. They asked 617 respondents. The sample mean number of hours was 6. 01 and the sample standard deviation was 8. 96. Find the test statistic.

first off let's change the mixed fractions to improper fractions, and let's Hailey's account first.

\(\stackrel{mixed}{9\frac{1}{4}}\implies \cfrac{9\cdot 4+1}{4}\implies \stackrel{improper}{\cfrac{37}{4}} ~\hfill \stackrel{mixed}{8\frac{7}{8}}\implies \cfrac{8\cdot 8+7}{8}\implies \stackrel{improper}{\cfrac{71}{8}} \\\\[-0.35em] ~\dotfill\)

\(~~~~~~ \textit{Continuously Compounding Interest Earned Amount} \\\\ A=Pe^{rt}\qquad \begin{cases} A=\textit{accumulated amount}\dotfill &\stackrel{43000(2)}{\$86000}\\ P=\textit{original amount deposited}\dotfill & \$43000\\ r=rate\to \frac{71}{8}\%\to \frac{~~ \frac{71}{8}~~}{100}\dotfill &0.08875\\ t=years \end{cases} \\\\\\ 86000=43000e^{0.08875\cdot t}\implies \cfrac{86000}{43000}=e^{0.08875t}\implies 2=e^{0.08875t}\)

\(\ln(2)=\ln(e^{0.08875t})\implies \log_e(2)=\log_e(e^{0.08875t})\implies \ln(2)=0.08875t \\\\\\ \cfrac{\ln(2)}{0.08875}=t\implies 7.81\approx t\)

ok, now we know how long it takes for Hailey's money to double, how much money does Aiden have by then?

\(~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$43000\\ r=rate\to \frac{37}{4}\%\to \frac{~~ \frac{37}{4}~~}{100}\dotfill &0.0925\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{monthly, thus twelve} \end{array}\dotfill &12\\ t=years\dotfill &\frac{\ln(2)}{0.08875} \end{cases}\)

\(A=43000\left(1+\frac{0.0925}{12}\right)^{12\cdot \frac{\ln(2)}{0.08875}}\implies A=43000\left( \frac{4837}{4800} \right)^{\frac{12\ln(2)}{0.08875}}\implies \boxed{A\approx 88311}\)

notice, in Hailey's amount we used the logarithmic value for "t", just to avoid any rounding issues.

Answer:

y = -6x + 2

Step-by-step explanation:

Slope intercept form: y = mx + b

m is the slope

b is the y-intercept

The line pictured goes down 6 for each 1 it moves to the right, slope is rise over run, in this case, -6/1 or just -6

The y-intercept is the point that the function crosses the y-axis, in this case 2

Plug those in to get:

y = -6x + 2

Light bulbs is normally distributed with a variance of 625 and a mean lifetime of 520 hours, we need to calculate the cumulative probability up to 549 hours. The answer will be rounded to four decimal places.

Given a normally distributed lifetime with a mean of 520 hours and a variance of 625, we can determine the standard deviation (σ) by taking the square root of the variance, which gives us σ = √625 = 25.

To find the probability of a bulb lasting for at most 549 hours, we need to calculate the area under the normal distribution curve up to 549 hours. This can be done by evaluating the cumulative distribution function (CDF) of the normal distribution at the value 549, using the mean (520) and standard deviation (25).

The CDF will give us the probability that a bulb lasts up to a certain point. Rounding the result to four decimal places will provide the desired precision.

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The problem involves using normal distribution to find the probability of a given outcome. Using the Z-score, we can determine that the probability of a light bulb lasting for at most 549 hours is approximately 0.8770 or 87.70%

Given the mean (µ) of the lifetime of a bulb is 520 hours. Also, the variance (σ²) is given as 625. Thus, the standard deviation (σ) is the square root of the variance, which is 25.

To find the probability of a bulb lasting for at most 549 hours, we first calculate the Z score. The Z-score formula is given as follows: Z = (X - µ) / σ, where X is the number of hours, which is 549. So substitute the given values into the formula. Z = (549 - 520) / 25, the Z value is 1.16.

We then look up the Z-table to find the probability associated with this Z-score (1.16), which is approximately 0.8770. Therefore, the probability of a bulb lasting for at most 549 hours is approximately 0.8770 or 87.70%.

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Answer:

he faked too much

Step-by-step explanation:

Answer: she can run \(6\dfrac54\) mile sin 1 hour.

Step-by-step explanation:

Given : Distance run by Jasmine in \(\dfrac23\) of an hour = \(4\dfrac56\text{ miles}=\dfrac{24+5}{6}\text{ miles}\)

\(=\dfrac{29}{6}\) miles

Distance run by Jasmine in 1 hour = \(\dfrac{29}{6}\times\dfrac{3}{2}=\dfrac{29}{4}\) miles.

\(=6\dfrac{5}{4}\)   miles.

Hence, she can run \(6\dfrac54\) mile sin 1 hour.

Answer:

Each book cost $12.50 dollars.

Step-by-step explanation:

1,187.50 / 95 = 12.50

1. Total revenue formula: Rx = 10,000x^(3/2)/(2+√x). 2. Marginal revenue formula: MR(x) = R′(x). 3. MR(9) calculation.


To find the marginal revenue (MR) and evaluate MR(9), we first need to understand the total revenue formula and how to calculate the derivative of this formula.

1. Total revenue formula (Rx):
The total monthly revenue from the sale of x automobiles of a certain model is given by:
Rx = 10,000x^(3/2)/(2+√x)
2. Marginal revenue formula (MR):
The marginal revenue (MR) is calculated by taking the derivative of the total revenue formula, Rx.
3. MR(9) calculation:
To find MR(9), we substitute x = 9 into the derivative formula of Rx.

Now, let's calculate the MR(9) step by step:
Step 1: Find the derivative of Rx:
To find the derivative, we need to apply the power rule and chain rule.
The derivative of Rx with respect to x is given by:
R′(x) = (d/dx) [10,000x^(3/2)/(2+√x)]
Step 2: Simplify the derivative:
To simplify the derivative, we can use the quotient rule and the power rule.
R′(x) = [10,000 * ((2+√x) * (3/2) * x^(1/2)) - (10,000 * x^(3/2) * (1/2) * (√x))] / (2+√x)^2
Simplifying further:
R′(x) = [15,000x^(3/2) + 5,000x - 10,000x^(3/2)√x] / (2+√x)^2
Step 3: Calculate MR(9):
Substitute x = 9 into the derivative formula.
MR(9) = [15,000(9)^(3/2) + 5,000(9) - 10,000(9)^(3/2)√9] / (2+√9)^2
Simplifying:
MR(9) = [15,000(27) + 5,000(9) - 10,000(27)√9] / (2+3)^2
MR(9) = [405,000 + 45,000 - 270,000] / 25
MR(9) = 180,000 / 25
MR(9) = 7200
Therefore, MR(9) = 7200.

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Answer:

The answer is 57 and 46

Step-by-step explanation:

Answer:

a). $(725 - 22t)

b). $99

Step-by-step explanation:

Expense account of the school has balance after 't' weeks = $(450 - 70t)

And fundraising account has the balance = $(275 + 48t)

a). Total amount in both the accounts after 't' weeks

    = $(450 - 70t) + $(275 + 48t)

    = $(450 + 275) + $(-70t + 48t)

    = $(725 - 22t)

b). Total amount after 8 weeks

    = $(725 - 22×8)

    = $(275 - 176)

    = $99

The price index for a train ticket from Lanchester to London, using the base year 2000, can be calculated by dividing the price in each year by the price in the base year and multiplying by 100. The price index for 1995 is 50, for 1996 is 66.67, for 1997 is 83.33, and for 2000 (the base year) is 100.

To calculate the price index for a train ticket from Lanchester to London, we need to compare the prices in different years to a base year, which in this case is 2000. The formula for calculating the price index is (Price in Year / Price in Base Year) x 100.

For the year 1995, the price of the ticket is £30. Dividing this price by the price in the base year (2000), which is £60, gives us 0.5. Multiplying this by 100 gives a price index of 50.

For 1996, the ticket price is £40. Dividing by the base year price (£60) gives us 0.6667. Multiplying by 100 gives a price index of approximately 66.67.

Similarly, for 1997, the price index is 83.33, as the ticket price of £50 divided by the base year price (£60) gives us 0.8333 when multiplied by 100.

Lastly, for the base year 2000, the price index is 100, as it is the reference point and used as the denominator in the formula.

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The required result of the sliding filament model given below.

The mechanism by which muscles contract is described by the sliding filament model. Actin and myosin myofilaments move over one another as a result of a cycle of repeated occurrences, constricting the sarcomere and creating tension in the muscle.

The A band is the middle, darkly pigmented area of the sarcomere that runs the entire length of the thick filaments. The portion of the thin filaments that cross over the thick filaments is also included. The I band is formed by the remaining thin filaments within the sarcomere but not by any thick filaments. Each A band has a narrow region in the middle called the H zone, which is made up entirely of dense filaments.

Myosin heads pull the thin filaments in the direction of the M line during muscle contraction. Because of this, the thin filaments glide inward, allowing their ends to overlap and connect at the sarcomere's core. The I band and H zone become smaller as a result.

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Answer:

one solution

Step-by-step explanation:

just did the same edge

Answer:

one solution

Step-by-step explanation:

12y+24=12y+28

12+12=24

28-24=4

24÷4=6

Thank you

Answer:

  A, C, D, E

Step-by-step explanation:

You want to identify the expressions that have a value of 0 among these:

A product is zero if and only if one of the factors is zero. That is the case for the expressions ...

The sum of a number and its additive inverse is zero. Another way to say this is that the difference between a number and itself is zero. That is the case for the expressions ...

Applying the inscribed angle theorem, we have:

a. x = 55° b. x = 60°  c. x = 92°    d. x = 84°

These theorem states that:

Inscribed angle measure = 1/2(central angle) or measure of intercepted arc.

Intercepted arc measure = central angle measure.

Therefore, we have:

a. x = 180 - 35 - 90 [tangent theorem]

x = 55°

b. x = 1/2(120) [inscribed angle theorem]

x = 60°

c. x = 2(46) [inscribed angle theorem]

x = 92°

d. m(FE) = 2(42) = 84°

m(EB) = 180 - FE = 180 - 84

m(EB) = 96°

m(AB) = 180 - m(EB) = 180 - 96

m(AB) = 84°

x = m(AB) = 84° [central angle theorem]

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The value of angle x in decimal place is 57.8°.

A decimal number's digits are assigned a place value according to a chart that displays decimal place values. A digit in a number's place value is, as far as we are aware, its numerical value. The correct placement of each digit in a decimal number is therefore determined using decimal place value charts, just like with other place value diagrams. In this chart, the place values of the digits before and after the decimal point are shown.

Draw the altitude of the triangle

We know that

sinθ =  Opposite / Hypotenuse

sin 38° = y/11

y = 11 sin 38°

y = 6.77

sin(x) = y/8

sin(x) = 6.77/8

sin(x) = 0.84625

sin(x) = 57.8°

Thus, the value of angle x in decimal place is 57.8°.

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Answer:

D

Step-by-step explanation:

Using the law of radicals/ exponents

\(\sqrt{a^{3} }\) ⇔ \(a^{\frac{3}{2} }\)

Consider the right side

\(\sqrt{729}\) = \(\sqrt{9^{3} }\) = \(9^{\frac{3}{2} }\)

Thus

\(9^{x}\) = \(9^{\frac{3}{2} }\)

Since the bases on both sides are equal, equate the exponents, so

x = \(\frac{3}{2}\) → D

Answer:

it needs to be written step by step

Answer:

Q is the point (3, 4).

Step-by-step explanation:

The formulae for the coordinates of a point (h, k) which divides a line  joining the points (x1, y1) and (x2, y2) in the ratio m : n is:

h = (mx2 + nx1) / (m + n), k = (my2 + my1)/(m+n)

Now we have S = (x1, y1) = (-2, -6) and T = (x2, y2) = (5, 8) and

m = 5 and n = 2.

So here, for point Q:

h = (5*5) + 2*-2)/(2+5)

    = 21/7

     = 3.

k = (5*8 + (-6*2) / 7

   = 28/7

    = 4.

Answer:

\frac{170}{48}

Step-by-step explanation:

1\(\frac{1}{6}\) = \(\frac{7}{6}\)

2\(\frac{3}{8}\) = \(\frac{19}{8}\)

in order to add these fractions, we need the denominators to be same. We can multiply 6 and 8 to get 48.

In doing this, we need to multiply the numerators by the respective numbers also.

So, 7 (8) = 56 and 19 (6) = 114.

Add:

\(\frac{56}{48}\) + \(\frac{114}{48}\) = \(\frac{170}{48}\)

The translation of the function 2 | x | - 9 when translated 6 units up gives the function as 2 | x | - 3.

We are given a function:

2 | x | - 9.

A function from a set X to a set Y assigns to each element of X exactly one element of Y.

We are asked to translate the function 6 units up.

This means that we have to add 6 units to the function.

A function has been “translated” when it has been moved in a way that does not change its shape or rotate it in any way.

So, we get that:

f(x) = 2 | x | - 9 + 6

f(x) = 2 | x | - 3

Therefore, the translation of the function 2 | x | - 9 when translated 6 units up gives the function as 2 | x | - 3.

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Answer:

D. y = StartFraction 1,000 Over 1 + 19 e Superscript negative 0.6 t Baseline EndFraction

Step-by-step explanation:

edge 2020

Answer:

The coefficient of 6m is 6

Step-by-step explanation:

Blake needs to invest $50,300, to the nearest hundred dollars, for the value of the amount to reach $76,000 in 17 years.

In order to reach a value of $76,000 in 17 years, Blake needs to calculate the future value of his investment. To do this, he needs to take his initial investment amount, the interest rate, and the number of compounding periods. In this case, the initial investment amount is unknown, the interest rate is 5.7% compounded daily, and the number of compounding periods would be 17 years x 365 days, or 6205 days. Using the formula FV = PV(1 + r/n)^nt, Blake can calculate the future value of his investment. Plugging in the known values, we can calculate the initial investment amount to be $50,300, to the nearest hundred dollars. This means that Blake needs to invest $50,300 in an account paying an interest rate of 5.7% compounded daily, in order to have the account reach a value of $76,000 in 17 years.

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Answer:

  (8, 63)

Step-by-step explanation:

The ordered pair is a solution to the equation when substituting the values for x and y make the equation a true statement.

If we let x represent the first number of the ordered pair, it will be a solution when ...

  63 = 9x -9

  7 = x -1 . . . . . . . divide by 9

  8 = x . . . . . . . add 1

The blank gets filled with 8, so the ordered pair is (8, 63).

Answer:

40 I think, if I wrong sorry

Step-by-step explanation:

a) No, p1 = 20, p2 = 19.50 is not a Nash Equilibrium.

b) Yes, there is a Nash Equilibrium in which Firm 2 makes a positive profit.

c) Player 1 has infinitely many strategies.

d) Yes, p1 = 15, p2 = 15 is a Nash Equilibrium.

e) No, p1 = 21, p2 = 21 is not a Nash Equilibrium.

Nash Equilibrium is a state of a strategic game where no player has an incentive to deviate from his or her chosen strategy after considering the strategies of other players. A game has more than one Nash equilibrium if players are unable to agree on a cooperative strategy to play.

Finding Nash Equilibrium

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Option:-

a) f(x) = 4^x is applicable

b) f(x) ={ (1/4)^-x = 4^x }is applicable

c.) f(x) = (2/3)^x is not applicable

d.) f(x) = (2.3)^x is applicable

e.) f(x) = (.8)^x is not applicable

Options (a), (b) and (d) are exponential growth functions.

An exponential decay is in the form:

y = abˣ

where y, x are variables, a is the initial value of y and b is the multiplier which is less than 1.

By the Exponential decay form,

An exponential decay is in the form: y = abˣ

(a) f (x)=4ˣ is applicable as 4>1

(b) f (x)=(1/4)⁻ˣ is applicable as (1/4)-1=4>1

(c)  f (x)=(2/3)ˣ is not applicable because 2/3<1

d) f (x)= (2.3)ˣ is applicable as 2.3>1

e) f (x)=(.8)ˣ is not applicable, 0.8<1.

So options (a), (b) and (d) are applicable for exponential growth functions.

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