At Cheng's Bike Rentals, it costs $36 to rent a bike for 9 hours.
How many hours of bike use does a customer get per dollar?

To test the claim that the mean difference between the prices of the two models is $10, we can use a t-test for dependent samples.

To test the claim that the mean difference between the prices of the two models is $10, we can use a t-test for dependent samples.

Answer:

Shirt: $20

Trouser: $40

Step-by-step explanation:

5x + 3y = 220

6x + 2y = 200

3x + y = 100

y = 100 - 3x

5x + 3(100 - 3x) = 220

5x + 300 - 9x = 220

4x = 80

x = 20

y = 100 - 3(20)

y = 40

The cost of a shirt is $20 and the cost of pair of a jeans is $40.

Given that, five shirts and 3 pairs of jeans cost $220. Six shirts and 2 pairs of jeans cost $200.

We need to find the cost of one shirt and the cost of pair of jeans.

A linear equation is an equation in which the highest power of the variable is always 1.

A linear equation in two variables is of the form Ax + By + C = 0, in which A, B, and C are real numbers and x and y are the two variables, each with a degree of 1. If we consider two such linear equations, they are called simultaneous linear equations.

Let the cost of a shirt be x and the cost of pair of jeans be y.

Now, five shirts and 3 pairs of jeans cost $220.

That is, 5x+3y=220------(1)

Six shirts and 2 pairs of jeans cost $200.

6x+2y=200------(2)

Multiplying the equation (1) with 2, we get 10x+6y=440------(3)

Multiplying the equation (2) with 3, we get 18x+6y=600------(4)

Now, equation (4)-(3) is 8x=160

⇒x=$20

Substitute x=20 in equation (1), we get 5(20)+3y=220

⇒y=$40

Therefore, the cost of a shirt is $20 and the cost of pair of a jeans is $40.

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Answer:

Hey Tamia,

          the answer is 0.4969564

Please rate me as brainiest as the answer explanation is in attached picture, which will clear every step.

Thanks

Step-by-step explanation:

To estimate the integral within an error rate, use the power series expansion of sin(x) to construct an equivalent series for sin(x²). Add terms until the error is less than  [tex]10^{-5}[/tex]. Integrate each term from 0 to 0.5.

To estimate the value of the integral ∫ from 0 to 0.5 sin(x²) dx with an error of magnitude less than 10^-5, we can use a power series expansion of sin(x). The power series expansion is given as sin(x) = x - x³/3! + x⁵/5! - x⁷/7! + .... Now since we are interested in sin(x²), we just replace x in the above series with x²: sin(x²) = x² - (x²)³/3! + (x²)⁵/5! - (x²)⁷/7! + .... This series can be truncated at any term, and the remaining terms would represent the error in your approximation. We keep adding terms until we reach an error less than [tex]10^{-5}[/tex]. Finally, integrate term by term from 0 to 0.5 to get the approximate value of the original integral.

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Answer:

$6000

Step-by-step explanation:

so she made 72000 in a year, a year as 12 months so to find the monthly rate we just need to divide 72000 by 12 which gives 6000

Answer:

The Correct answer is 6000

Step-by-step explanation:

All you do is divide all the months in a year by how much she got paid to find salary.

Answer:

    [tex]\frac{31}{50}[/tex]

Step-by-step explanation:

percentage of graduates with loan = 62%

total sample = 50

Number of student in the sample with student loan

  = (percentage of graduates with loan) x  (total sample)

  = 62% x 50

  = 31

Proportion of student in the sample with student loan = [tex]\frac{31}{50}[/tex]

Answer:

1) 0.700

2) 0.730

3) 0.030

4) 0.959

Step-by-step explanation:

1) proportion of support for the ban with at least one child =

     [tex]\frac{no of support atleast 1 child}{Total no of atleast 1 child\\}[/tex]

   = [tex]\frac{1739}{2485}[/tex]

   = 0.700

2)  proportion of support for the ban with no child =

    = [tex]\frac{no of support with no child}{Total of no child}[/tex]

    = [tex]\frac{3089}{4231}[/tex]

    = 0.730

3) Difference in proportion of supporters for the ban between those with atleast one child and those with no child

    =  0.700 - 0.730

    = -0.03

4) Relative risk = [tex]\frac{proportion with atleast on child}{proportion with no child}[/tex]

    = [tex]\frac{0.700}{0.730}[/tex]  = 0.959

To solve 24+36 using mental math, break it down into simpler steps. First, add 20 + 30 = 50. Then, add 4 + 6 = 10. Finally, combine 50 + 10 to get 60.

To solve the equation 24+36 using mental math, you can break it down into simpler steps. First, add the tens together: 20 + 30 = 50. Then add the remaining units: 4 + 6 = 10. Finally, combine these results: 50 + 10 = 60. Therefore, 24 + 36 equals 60 when using mental math strategies.

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Answer:

see the explanation

Step-by-step explanation:

we know that

The equation of a exponential growth function is given by

[tex]f(x)=a(b^x)[/tex]

where

a is the initial value or y-intercept

b is the factor growth (b>0)

In this problem

a=1

so

[tex]f(x)=b^x[/tex]

we know that

The graph of the function has no x-intercept

Remember that the x-intercept of a function is the value of x when the value of the function is equal to zero

That means ----> The output of the function can NEVER be equal to zero

Verify

For f(x)=0

[tex]0=b^x[/tex]

Apply log both sides

[tex]log(0)=xlog(b)[/tex]

Remember that

log 0 is undefined. It's not a real number, because you can never get zero by raising anything to the power of anything else.

Final answer:

Exponential functions with a positive base can never output zero due to their growth pattern.

Explanation:

Exponential functions of the form f(x) = b^x, where b is greater than 0, never output zero.

To verify this, consider that any positive number raised to any power will never result in zero, as it will approach zero but never reach it. For example, 2^x will grow rapidly but never touch zero. This property holds true for all exponential functions with a positive base.

Correction

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Answer:

Amounts invested in each bank:

GCB=$1,713,33    

Barclays=$3,426.66

ADB=$1,363.33

Step-by-step explanation:

-Given that ADB pays 2% pa, GCB pays 4% and Barclays pays 5%

-From the information provided, the amount invested in each of the 3 banks can be expressed as:

-Let X be the Amount invested in GCB:

[tex]GCB=X\\\\Barclays=2X\\\\ADB=2X-X-350=X-350[/tex]

-Since the total interest earned on all 3 accounts after 1 year is $250, we can equate and solve for X as below:

[tex]I=Prt\\\\I_{GCB}=X\times 0.05\times1= 0.05X\\\\I_{Barclays}=2X\times 0.04\times 1=0.08X\\\\I_{ADB}=(X-350)\times 0.02\times 1=0.02X-7\\\\I=I_{GCB}+I_{ADB}+I_{Barclays}\\\\250=0.05X+0.08X+(0.02X-7)\\\\250=0.15X-7\\\\0.15X=257\\\\X=1713.33\\\\GCB=\$1713.33\\Barclays=2X=\$3426.66\\ADB=X-350=\$1363.33[/tex]

Hence, the amounts invested in each bank is GCB=$1,713,33    ,   Barclays=$3,426.66 and ADB=$1,363.33

Answer:

Amounts invested in each bank:

GCB=$1,713,33    

Barclays=$3,426.66

ADB=$1,363.33

Step-by-step explanation:

Answer:

2 yards 5 inches=77 inches

9 feet= 3 yards

2 feet 8 inches= 32 inches

1 yard 1 foot= 48 inches

hope this helps!

The table representing the equivalent lengths in each case is-

3 yards : 2 yards 5 inches

77 inches : 9 feet

48 inches : 2 feet 8 inches

32 inches : 1 yard 1 foot

An expression in mathematics is a combination of terms both constant and variable. For example, we can write the expressions as -

2x + 3y + 5

2z + y

x + 3y

Given is to complete the table by matching the equivalent lengths for -

3 yards

77 inches

48 inches

32 inches

In one yard there are 36 inches. We can write the equivalent length in each case as -

3 yards : 2 yards 5 inches

77 inches : 9 feet

48 inches : 2 feet 8 inches

32 inches : 1 yard 1 foot

Therefore, the table representing the equivalent lengths in each case is-

3 yards : 2 yards 5 inches

77 inches : 9 feet

48 inches : 2 feet 8 inches

32 inches : 1 yard 1 foot

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Answer:

a) 231

The sample to estimate the population mean with 95 percent confidence and a margin of error of ±$2.00

n = 231

Step-by-step explanation:

Explanation:-

Given data the population standard deviation is known σ =$15.50

Given the margin of error ±$2.00

we know that  95 percent confidence interval of margin of error is determined by  

[tex]M.E = \frac{Z_{\alpha }S.D }{\sqrt{n} }[/tex]

cross multiplication √n we get ,

[tex]\sqrt{n} = \frac{Z_{\alpha }S.D }{M.E }[/tex]

squaring on both sides, we get

[tex](\sqrt{n} )^2 = (\frac{Z_{\alpha }S.D }{M.E })^2[/tex]

[tex]n = (\frac{Z_{\alpha }S.D }{M.E })^2[/tex]

the tabulated z- value = 1.96 at 95% of level of significance.

[tex]n = (\frac{1.96(15.50) }{2 })^2[/tex]

n = 230.7≅231

Conclusion:-

The sample to estimate the population mean with 95 percent confidence and a margin of error of ±$2.00

n = 231

The required sample size to estimate the mean dollars spent on pharmaceutical products with 95% confidence and ±$2.00 margin of error is 231.

To estimate the required sample size, we need to use the formula:

Sample size = (Z^2 * σ^2) / E^2

Where:

Plugging in the values into the formula gives us:

Sample size = (1.96^2 * 15.50^2) / 2^2 = 231.36

Rounding up to the nearest whole number, the required sample size is 231.

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Answer:

10 :/

Step-by-step explanation:

If you have 0 and I give you 10, then you have 10 because 0+10 is 10.

The given 95% confidence interval of (1.6, 7.0) for the difference between the average weekly study times (mu_1 - mu_2) means we are 95% confident that students planning to attend graduate school study between 1.6 to 7 hours more per week on average than those who do not.

The teaching assistant is comparing the average weekly study times between students intending to go to graduate school and those who are not with the use of data. The relevant statistical concept in this context is the confidence interval for the difference in population means.

The given 95% confidence interval for the difference between the average weekly study times (mu_1 - mu_2) is (1.6, 7.0). This interval was calculated from the provided data, and it provides a statistical estimation that, in this context, means we are 95% sure that students who plan to attend graduate school study between 1.6 to 7 hours more per week on average compared to those who do not plan to go to graduate school.

To interpret this, you can say that we are 95% confident that the true difference in average weekly study times between the two groups falls within this interval. As the entire interval is positive, we may infer that those planning for graduate school likely study more on average than their peers not planning for graduate school.

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Answer:

  0.2036

Step-by-step explanation:

u = arcsin(0.391) ≈ 23.016737°

tan(u/2) = tan(11.508368°)

tan(u/2) ≈ 0.2036

__

You can also use the trig identity ...

  tan(α/2) = sin(α)/(1+cos(α))

and you can find cos(u) as cos(arcsin(0.391)) ≈ 0.920391

or using the trig identity ...

  cos(α) = √(1 -sin²(α)) = √(1 -.152881) = √.847119

Then ...

  tan(u/2) = 0.391/(1 +√0.847119)

  tan(u/2) ≈ 0.2036

__

Comment on the solution

These problems are probably intended to have you think about and use the trig half-angle and double-angle formulas. Since you need a calculator anyway for the roots and the division, it makes a certain amount of sense to use it for inverse trig functions. Finding the angle and the appropriate function of it is a lot easier than messing with trig identities, IMO.

Answer:

the answer is C. 3(2k + 7)   i hope this helps!   :)

Step-by-step explanation:

trying to find 6k + 21

given 3(2k + 6)

distribute the 3 to both inside the parenthesis 6k + 18

given 3(k + 6)

distribute the 3 to both inside the parenthesis 3k + 18

given 3(2k + 7)

distribute the 3 again to both inside of the parenthesis 6k + 21

Answer:

C. 3(2k+7)

Step-by-step explanation:

you should mark me brainliest lol

Answer:

4.875 billion hours

Step-by-step explanation:

-Let X be the total time spent on taxes and 7.8 billion (80%) is time on paper work.

#We equate and cross multiply to get the total time on taxes:

[tex]0.8=7.8\\1=X\\\\\therefore X=\frac{1\times 7.8}{0.8}\\\\\\=9.75[/tex]

-let y be the 50% amount of time spent. we equate to find it in actual hours:

[tex]1=9.75\\0.5=y\\\\y=\frac{9.75\times 0.5}{1}\\\\=4.875[/tex]

Hence, 50% of the time is equivalent to 4.875 billion hours

Answer:

y= -2x +6

Step-by-step explanation:

Since we have a point, and the slope, we can use the point slope formula

[tex]y-y_{1} =m(x-x_{1} )[/tex]

m is the slope, y1 is the y coordinate of the point, and x1 is the x coordinate of the point

In this case, m is -2, y1 is 8, and x1 is -1, so we can substitute them in

y-8= -2(x--1)

Now, we need to solve for y

y-8=-2(x+1)

Distribute the -1

y-8= -2x-2

Add 8 to both sides

y= -2x +6

Answer:

0.3108 is the probability that the sample mean is between 7.8 and 8.2 minutes.    

Step-by-step explanation:

We are given the following information in the question:

Mean, μ = 8 minutes

Standard Deviation, σ = 2.5 minutes

Sample size, n = 25

We are given that the distribution of  time spent is a bell shaped distribution that is a normal distribution.

Formula:

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

Standard error due to sampling =

[tex]=\dfrac{\sigma}{\sqrt{n}} = \dfrac{2.5}{\sqrt{25}} = 0.5[/tex]

P(sample mean is between 7.8 and 8.2 minutes)

[tex]P(7.8 \leq x \leq 8.2)\\\\ = P(\displaystyle\frac{7.8 - 8}{0.5} \leq z \leq \displaystyle\frac{8.2-8}{0.5})\\\\ = P(-0.4 \leq z \leq 0.4})\\\\= P(z < 0.4) - P(z < -0.4)\\\\= 0.6554 -0.3446= 0.3108[/tex]

0.3108 is the probability that the sample mean is between 7.8 and 8.2 minutes.

Answer:

The solutions listed from the smallest to the greatest are:

x:  [tex]-\sqrt{2}[/tex]   [tex]-\sqrt{2}[/tex]  [tex]\sqrt{2}[/tex]  [tex]\sqrt{2}[/tex]

y:      -1         1     -1     1

Step-by-step explanation:

The slope of the tangent line at a point of the curve is:

[tex]m = \frac{\frac{dy}{dt} }{\frac{dx}{dt} }[/tex]

[tex]m = -\frac{\cos 2\theta}{\sin \theta}[/tex]

The tangent line is horizontal when [tex]m = 0[/tex]. Then:

[tex]\cos 2\theta = 0[/tex]

[tex]2\theta = \cos^{-1}0[/tex]

[tex]\theta = \frac{1}{2}\cdot \cos^{-1} 0[/tex]

[tex]\theta = \frac{1}{2}\cdot \left(\frac{\pi}{2}+i\cdot \pi \right)[/tex], for all [tex]i \in \mathbb{N}_{O}[/tex]

[tex]\theta = \frac{\pi}{4} + i\cdot \frac{\pi}{2}[/tex], for all [tex]i \in \mathbb{N}_{O}[/tex]

The first four solutions are:

x:   [tex]\sqrt{2}[/tex]   [tex]-\sqrt{2}[/tex]  [tex]-\sqrt{2}[/tex]  [tex]\sqrt{2}[/tex]

y:     1        -1        1     -1

The solutions listed from the smallest to the greatest are:

x:  [tex]-\sqrt{2}[/tex]   [tex]-\sqrt{2}[/tex]  [tex]\sqrt{2}[/tex]  [tex]\sqrt{2}[/tex]

y:      -1         1     -1     1

Using derivatives of the parametric curves and the solving a trigonometric equation, it is found that the points (x,y) are:

[tex]x = 2\cos{\left(\frac{k\pi}{4}\right)}, k = 1, 3, 5, \cdots[/tex]

[tex]y = \sin{\left(\frac{k\pi}{2}\right)}, k = 1, 3, 5, \cdots[/tex]

Given two parametric curves x(t) and y(t), the slope of the tangent line is given by:

[tex]m = \frac{dy}{dx} = \frac{\frac{dy}{dt}}{\frac{dx}{dt}}[/tex]

The tangent line is horizontal for:

[tex]\frac{dy}{dt} = 0, \frac{dx}{dt} \neq 0[/tex]

In this problem, since we are working with trigonometric functions sine and cosine, they will never be simultaneously 0, hence, the equation of interest is:

[tex]\frac{dy}{dt} = 0[/tex]

Then:

[tex]y(t) = \sin{2\theta}[/tex]

[tex]\frac{dy}{d\theta} = 2cos{2\theta}[/tex]

Hence:

[tex]2\cos{2\theta} = 0[/tex]

[tex]\cos{2\theta} = 0[/tex]

[tex]\cos{2\theta} = \cos{\left(\frac{k\pi}{2}\right)}, k = 1, 3, 5, \cdots[/tex]

[tex]2\theta = \frac{k\pi}{2}[/tex]

[tex]\theta = \frac{k\pi}{4}, k = 1, 3, 5, \cdots[/tex]

Hence, the points (x,y) are:

[tex]x = 2\cos{\left(\frac{k\pi}{4}\right)}, k = 1, 3, 5, \cdots[/tex]

[tex]y = \sin{\left(\frac{k\pi}{2}\right)}, k = 1, 3, 5, \cdots[/tex]

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Answer:

4x + 276

Step-by-step explanation:

Multiply 4 by 69 and x.

Answer:

35/36

Step-by-step explanation:

total outcome: 6 x 6 = 36

getting 12: 1/36

getting less than 12: 1 - 1/36 = 35/36

Answer:

35/36

Step-by-step explanation:

The sum can be between 2 and 12.

P(sum < 12) = 1 - P(sum = 12)

Sum = 12: (6,6)

P(sum < 12) = 1 - 1/36

35/36

Answer:

8% is the final answer.

Step-by-step explanation:

(2.4/29.99)x100

=0.08x100

=8%

Answer:

2900g

Step-by-step explanation:

1kg=1000g

2.9(1000)

=2900g

Answer:

B

Step-by-step explanation:

Take 2 points and use the slope formula

The 2 points: (0,0) and (5,4)

The slope formula is:

[tex]m=\frac{y_{2}-y_{1} }{x_{2} -x_{2} }[/tex]

We can say (0,0) is our first point, and (5,4) is our second, and substitute them in. y2 is 4, y1 is 0, x2 is 5, and x2 is 0.

[tex]m=\frac{4-0}{5-0}[/tex]

[tex]m=\frac{4}{5}[/tex]

So, the slope if 4/5, or choice B

Answer:

a) 0.6062

b) 0.9505

c) 0.679

Step-by-step explanation:

The customer service center in a large new york department store has determined tha the amount of time spent with a customer about a complaint is normally distributed, with a mean of 9.3 minutes and a standard deviation of 2.5 minutes. What is the probability that for a randomly chosen customer with a complaint, the amount of time spent resolving the complaint will be

(a) less than 10 minutes?

(b) longer than 5 minutes?

(c) between 8 and 15 minutes?

a) The Z score (z) is given by the equation:

[tex]z=\frac{x-\mu}{\sigma}[/tex],

Where:

μ is the mean = 9.3 minutes,

σ is the standard deviation = 2.6 minutes and x is the raw score

[tex]z=\frac{x-\mu}{\sigma}=\frac{10-9.3}{2.6}=0.27[/tex]

From the z tables, P(X < 10) = P(z < 0.27) = 0.6062 = 60.62%

b) The Z score (z) is given by the equation:

[tex]z=\frac{x-\mu}{\sigma}[/tex],

[tex]z=\frac{x-\mu}{\sigma}=\frac{5-9.3}{2.6}=-1.65[/tex]

From the z tables, P(X > 5) = P(z > -1.65) = 1 - P(z < -1.65) = 1 - 0.0495 =  0.9505 = 95.05%

c) For 8 minutes

[tex]z=\frac{x-\mu}{\sigma}=\frac{8-9.3}{2.6}=-0.5[/tex]

For 15 minutes

[tex]z=\frac{x-\mu}{\sigma}=\frac{15-9.3}{2.6}=2.19[/tex]

From the z tables, P(8< X < 15) = P(-0.5 < z < 2.19) = P(z < 2.19) - P(z< -0.5) = 0.9875 - 0.3085 = 0.679 = 67.9%

The question pertains to finding a probability concerning the time taken to resolve a customer's complaint. The time follows a normal distribution with a mean of 9.3 minutes and a standard deviation of 2.6 minutes. We need to calculate the Z-score with the required time, mean and standard deviation, which can then be referenced on a standard normal distribution table to find the probability.

The question is about finding the probability of the time spent with a customer in a Customer Service Center of a department store in New York, given that the time that is spent follows a normal distribution with a mean of 9.3 minutes, and a standard deviation of 2.6 minutes.

To calculate this, we'll use the standard normal distribution, Z-score, which standardizes the distribution. The Z-score is a measure of how many standard deviations an element is from the mean. It can be calculated by using the formula: Z = (X - μ) / σ

where X is the time about which we want to find the probability, μ is the mean, and σ is the standard deviation.

Unfortunately, the exact time (X) you want to find the probability for was not provided in your question. However, assuming X to be a given time, t, you substitute t, 9.3 (the mean), and 2.6 (the standard deviation) into the formula to get a Z-score. Then, by referencing the Z-score on a standard normal distribution table, you can find the probability for a complaint taking at an amount of time, t, to be resolved.

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Answer:

x = -6,1

Step-by-step explanation:

Isolate the variable by dividing each side by factors that don't contain the variable.

Answer:

Step-by-step explanation:

Given that Anna has a flush, this means that the three shared cards and the 2 cards with Anna has the same suit, therefore given this condition the probability that Brad also has a flush is computed here as:

= Probability that Brad has the same suit cards as those shared cards and Anna

= Probability that Brad selected 2 cards from the 8 cards remaining of that suit

= Number of ways to select 2 cards from the 8 cards of that same suit / Total ways to select 2 cards from the remaining 47 cards

 = 0.0259

Therefore 0.0259 is the required probability here.

the little calculation is shown in the picture attached

Answer:

A sample size of 400 was used in the study.

Step-by-step explanation:

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation(standard error) [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

In this problem, we have that:

[tex]\sigma = 860, s = 43[/tex]

We have to find n.

[tex]s = \frac{\sigma}{\sqrt{n}}[/tex]

[tex]43 = \frac{860}{\sqrt{n}}[/tex]

[tex]43\sqrt{n} = 860[/tex]

[tex]\sqrt{n} = \frac{860}{43}[/tex]

[tex]\sqrt{n} = 20[/tex]

[tex](\sqrt{n})^{2} = 20^{2}[/tex]

[tex]n = 400[/tex]

A sample size of 400 was used in the study.

Answer:

153.9380400259 in2

Step-by-step explanation:

Answer:

49 pi or 153.86

Step-by-step explanation:

The area of a circle can be found using

a=pi*r^2

We know the radius is 7 so we can substitute that in

a=pi*7^2

a=pi*49

The answer in terms of pi is 49pi units^2

For an exact answer, substitute 3.14 in for pi

a=pi*49

a=3.14*49

a=153.86

The area is also 153.86 units^2