Aaron had $22 to spend on 4 beakers for his science class. After buying them, Aaron had $2 left. How much did each of the beakers cost?

To evaluate the given integral, the most helpful substitution is x = 15 sec θ. The rewritten integral will be dx = 15 sec θ tan θ dθ / (225 + 225 sec² θ)².

In trigonometric substitution, we choose a substitution that simplifies the integral by transforming it into a form that can be easily evaluated using trigonometric identities. In this case, the most helpful substitution is x = 15 sec θ.

To rewrite the integral, we need to express dx in terms of θ. Since x = 15 sec θ, we can differentiate both sides with respect to θ to find dx. The derivative of sec θ is sec θ tan θ, so we have dx = 15 sec θ tan θ dθ.

Substituting this expression for dx and rewriting (225 + x²)² in terms of θ, we obtain:

∫(x² dx) / (225 + x²)² = ∫[(15 sec θ)² (15 sec θ tan θ dθ)] / (225 + (15 sec θ)²)².

Simplifying further, we get:

∫(225 sec² θ tan θ dθ) / (225 + 225 sec² θ)².

This is the rewritten form of the integral using the substitution x = 15 sec θ.

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Answer:

slope = - \(\frac{3}{2}\)

Step-by-step explanation:

calculate the slope m using the slope formula

m = \(\frac{y_{2}-y_{1} }{x_{2}-x_{1} }\)

with (x₁, y₁ ) = (2, 1 ) and (x₂, y₂ ) = (8, - 8 ) ← 2 ordered pairs from the table

note that any 2 ordered pairs may be used to calculate m

m = \(\frac{-8-1}{8-2}\) = \(\frac{-9}{6}\) = - \(\frac{3}{2}\)

Answer:

12

Step-by-step explanation:

5^2 + b^2 = 13^2

25 + b^2 = 169

169-25= 144

take the square root of 144

answer: 12

Solution:

Starting point = (4, -12)

Length = units

Along the y axis, the endpoints could be

(4, -7) and (4, -17)

Along the x- axis, the endpoints could be

(9, -12) and (-1, -12).

The answer is (4, -7), (4, -17), (9, -12), (-1, -12).

The average power output of a bike rider at a speed of 20 miles per hour is 556 W

Given, Riding a bike burns 100 Calories per mile. Speed of riding a bike is 20 miles per hour. Power is a measure of the rate at which work is done over time.

Therefore, the formula for average power is given by,

P = W/t

Where, P is power, W is work and t is time.

Now, We know that riding a bike burns 100 Calories per mile, but we have to find out the work done.

So, work done = 100 Calories × distance traveled= 100 × 1.609 × 1000 = 160900 J

Time taken = distance/speed= 1.609/20 = 0.08045 hours

Putting values in the formula of power, we get,

P = W/t= 160900/0.08045= 1999999.9 J/hour

Converting hour to seconds,1 hour = 3600 seconds1 J/s = 1 watt1 J/hour = 1 / 3600 watt

Therefore, power = 1999999.9 / 3600= 555.5556 watts (approx)

Therefore, the average power output of a bike rider at a speed of 20 miles per hour is 556 W (approx). Answer: 556

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Answer:

it’s D, I just

Took the quiz

Answer:

Correct answer is C.

Step-by-step explanation.

The explicit formula for h(n) is, -65-10n

Given that:

h(1)=-75

h(n)=h(n-1)-10  {.....[1] }

Put n=2 in [1] we have;

h(2)=h(1)-10=-75-10=-85

Similarly for n=3

h(3)=h(3)-10=-85-10=-95 { and so on... }

The series we get;

-75,-85,-95,....

This is an arithmetic sequence series with common difference(d) =-10

Since,

-85-(-75)=-85+75=-10 {, }

-95-(-85)=-95+85=-10 and so on

First term(a) =-75

the Explicit formula for arithmetic sequence is given by:

a_{1}=a+(n-1) d

where a is the first term,

d is the common difference and

n is the number of terms.

We have to find the explicit formula for h(n);

h(n)=a+(n-1) d

Substitute the given values we have;

h(n)=-75+(n-1)(-10)

or

h(n)-75-10 n+10=-65-10 n

Therefore, the explicit formula for h(n) is, -65-10 n

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Answer:

10

Step-by-step explanation:

Your scale factor is 3/2, because when you compare AC and DF, the ration is 18/12, or 3/2. We can set up a proportion:

3/2=15/x

We cross multiplu

3x=30

x=10

So, the length of DE is 10 units.

Hope this helps!

Answer:5

Step-by-step explanation:

use the slope formula

18 7/10 liters of milk does he milk from both cows.

According to the question

Mr. benjamin milk 8 1/5 from the black cow and 10 1/2 liters of the brown cow

Milk from both cows

= 8 1/5 + 10 1/2

converting mixed fraction into proper fraction

8 1/5 = \(\frac{8 \times 5 +1}{5}\) = 41/5

10 1/2 = \(\frac{10 \times 2 +1}{2}\) = 21/2

= \(\frac{41}{5} +\frac{21}{2}\)

= \(\frac{2 \times 41+21 \times 5}{10}\)

= \(\frac{82+105}{10}\)

= \(\frac{187}{10}\)

converting fraction into mixed fraction

= \(\frac{180+7}{10}\)

= 18 7/10

Therefore,

18 7/10 liters of milk does he milk from both cows.

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Answer:

100 minutes / \(1 \frac{2}{3}\) hours

First, we need to do 40 ÷ 12 = 3 1/3

Next, multiply 3 1/3 by 30 = 100

So, it is 100 minutes. But wait! We can simply it...

100 minutes = 1 2/3 hours

You can always convert it into different time labels. I think this is the most popular.

25/8 or 3 1/8 I think.

Step-by-step explanation:

Multiply 5/8 by 5 and you get 25/8. Simplify it then you are done.

Answer:

H 3 and 1/8

Step-by-step explanation:

i did the math

Answer:

your mom

Step-by-step explanation:

dababy lets go

Answer:

Hello,

Step-by-step explanation:

A: roots are x=-1 and x=5 : x-intercepts are (-1,0) and (5,0) :TRUE

B: There are only 2 roots for quadratic function : FALSE

C: the function has a minimum for x=2 but the value of that minum is -9 : FALSE

D: (-oo,-9) :decrease ok, but (-x,oo) false: FALSE

E: TRUE (function is y=(x+1)(x-5)=x²-4x-5

F: minimum=-9 TRUE

G: TRUE (see graph jointed)

H: TRUE like F

I: FALSE

Answer:

55° because 2and 6 are corresponding angles (they are equal)

6 and 8 are vertically opposite angles (they are equal)

Step-by-step explanation:

hope this is helpful

The proportion of cases of disease X that are due to smoking among those who smoke is approximately 41%.

To determine the proportion of cases of disease X that are due to smoking among those who smoke, we can use the population attributable risk formula:

Population attributable risk (PAR)

= incidence in exposed (smokers) - incidence in unexposed (nonsmokers)

PAR = (56/1000) - (33/1000)

= 23/1000

The proportion of cases of disease X that are due to smoking among those who smoke can be calculated as:

Proportion of cases due to smoking = PAR / incidence in exposed (smokers)

Proportion of cases due to smoking

= (23/1000) / (56/1000)

= 23/56

≈ 0.41

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To determine the proportion of cases of disease X that are due to smoking among those who smoke, we can use the formula for attributable risk percent (ARP). ARP is calculated by subtracting the incidence rate among the unexposed group (nonsmokers) from the incidence rate among the exposed group (smokers), dividing that difference by the incidence rate among the exposed group, and then multiplying by 100.

In this case, the ARP for smokers would be: ((56/1,000) - (33/1,000)) / (56/1,000) * 100 = 41%

Therefore, 41% of cases of disease X among smokers can be attributed to smoking. This means that if all smokers were to quit smoking, 41% of disease X cases among them could potentially be prevented.
To calculate the proportion of cases of disease X due to smoking among those who smoke, we can use the formula for attributable risk (AR):

AR = (Incidence in smokers - Incidence in nonsmokers) / Incidence in smokers

First, identify the given data:
Incidence in smokers = 56/1,000
Incidence in nonsmokers = 33/1,000

Now, plug the data into the formula:
AR = (56/1,000 - 33/1,000) / (56/1,000)
AR = (23/1,000) / (56/1,000)

Next, cancel the common term (1,000) in the numerator and denominator:
AR = 23/56

Finally, convert the fraction to a percentage:
AR = (23/56) * 100 = 41.07%

Thus, the proportion of cases of disease X due to smoking among those who smoke is approximately 41%.

I got 7

7, it's the right answer

Answer:

1) 50, 2) 41.44, 3) 12, 4) 12.5%

Step-by-step explanation:

1) 50. 35 is 70% of 50

2) 41.44. 41.44 is 74% of 56

3) 12. 12 is 15% of 80

4) 12.5%. 9 is 12.5% of 72

Hopefully this helps :3 sorry if wrong :( plz mark brainiest if correct :D Your bootiful/handsome! Have a great day luv <3

-Bee~

a) The power of the test for this two sided alternative is 0.684

b) We need a sample size of at least 716 from each machine to detect the difference with a probability of at least 0.9 and a significance level of 0.05.

The power of the test, denoted by 1 - β, where β is the probability of failing to reject the null hypothesis when it is actually false, can be calculated using the non-central standard normal distribution.

Using the given values, we have n1 = n2 = 300, p1 = 0.05, p2 = 0.01, α = 0.05, and δ = 0.04. Substituting these values into the formula, we can compute the power of the test as follows:

1 - β = P( Z > Z0.025 - 0.04√(n) / √( p (1 - p) (1/n1 + 1/n2) ) ) + P( Z < -Z0.025 - 0.04√(n) / √( p (1 - p) (1/n1 + 1/n2) ) )

where Z0.025 is the upper 0.025 quantile of the standard normal distribution, which is approximately 1.96.

We can estimate the pooled sample proportion as:

p = (x1 + x2) / (n1 + n2) = (15 + 8) / (300 + 300) = 0.0433

Substituting the values, we have:

1 - β = P( Z > 1.96 - 0.04√(300) / √(0.0433(1 - 0.0433)(1/300 + 1/300))) + P( Z < -1.96 - 0.04√(300) / √(0.0433(1 - 0.0433)(1/300 + 1/300)))

Solving this equation using statistical software or a calculator, we obtain 1 - β = 0.684.

Therefore, with the given sample sizes, the power of the test for the two-sided alternative hypothesis H1: p1 ≠ p2 is 0.684 when the significance level is 0.05 and the effect size is 0.04.

Moving on to part (b) of the question, we need to determine the sample size needed to detect the difference with a probability of at least 0.9 and a significance level of 0.05..

Substituting the values, we have:

n = (Z0.025 + Z0.90)² * (0.0433 * 0.9567 / 0.04²) ≈ 715.27 or 716

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The Cpk (Process Capability Index) for this machine is 0.5 (rounded to 3 decimal places).

To calculate the Cpk (Process Capability Index), we need to consider the specification limits and the process variation.

The Cpk is given by the formula:

Cpk = min[(USL - μ) / (3σ), (μ - LSL) / (3σ)], Where:

USL = Upper Specification Limit

LSL = Lower Specification Limit

μ = Process mean

σ = Process standard deviation

In this case, the Upper Specification Limit (USL) is 2 + 0.004 = 2.004 inches, and the Lower Specification Limit (LSL) is 2 - 0.004 = 1.996 inches.

Given that the process mean (μ) is 2.001 inches and the process standard deviation (σ) is 0.002 inch, we can substitute these values into the formula:

Cpk = min[(2.004 - 2.001) / (3 * 0.002), (2.001 - 1.996) / (3 * 0.002)]

Cpk = min[0.003 / 0.006, 0.005 / 0.006]

Cpk = min[0.5, 0.833]

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Answer:

π (pi) = 3.14

c = 2πr

Step-by-step explanation:

The value of pi is 3.14. It relates to the circumference and the diameter because inorder to solve for the circumferences you need pi. Which is in the formula.

The answer is option A. No, there is a good chance that 12 randomly selected adult male passengers will exceed the elevator capacity.

Probability that it is overloaded if 12 adult male passengers have a mean weight greater than 157 lb is 0.0229.Round to four decimal places as needed.Based on the calculations the elevator does not appear to be safe.The solution for the given problem is as follows:

Given that, the maximum capacity of the elevator is 1884 lb - 12 passengers.

We can write as below:

Maximum capacity per person=1884/12=157lb.

And, weights of males are normally distributed with a mean of 165 lb and a standard deviation of 32 lb.Thus, Z = (157-165) / (32 / √12) = -1.7321Then, P(Z > -1.7321) = 0.9586

Hence, the probability that it is overloaded if 12 adult male passengers have a mean weight greater than 157 lb is:P(Z > -1.7321) = 1 - P(Z < -1.7321) = 1 - 0.0229 = 0.9771 (rounded off to 4 decimal places).This probability is greater than 5% and therefore, the elevator does not appear to be safe.

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Answer:80 notebooks

Step-by-step explanation:

If n is the number of notebooks and t is the number of t shirts the 2 equations that can be made are this:

\(6n+12t=600\\n+t=90\)

You can solve this by,

\(t=n+90\\6n+12(90-n)=600\\6n-12n+1080=600\\-6n=-480\\n=80\\\\)So 80 notebooks.

Answer:

D. 80

Step-by-step explanation:

It is right i did it on the test

Answer:

45:40

27:24

Step-by-step explanation:

45:40 c=5

27:24 c=3

The statement showing a percent error greater than 100% is given as follows:

A) The estimated wait time for an amusement park ride is 12 minutes and the actual wait time is 5 minutes. The percent of error is 12-5 or 7; 7÷5=1.4, so the percent of error is 140%.

A percent error is calculated applying a proportion, as it is the absolute value of the difference between the actual amount and the estimated amount, divided by the actual amount.

Hence option A shows a percent error greater than 100%.

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Ken will run 3 laps and Hamid will run 4 laps in 80 and 60 seconds.

To find this, we first find the number of seconds that will have passed when they meet again.  We use the LCM, or least common multiple, for this.  First we find the prime factorization of each number:

LCM of 80 and 60 = 2X2X5X4X3

                             = 4X5X4X3

                             = 240

Now, divide the respective seconds from the total 240, we get

for Ken, 240÷ 80 = 3 laps

For Hamid, 240÷ 60 = 4 laps

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Answer:

  0.4 m = 40 cm

Step-by-step explanation:

You want the height of a model water tower with a volume of 0.1 liters that models a city water tower 40 m high with a volume of 100,000 liters.

The scale factor for volume is the cube of the scale factor for linear dimensions, such as height. Conversely, the scale factor for height is the cube root of the scale factor for volume.

This lets us write a proportion for the height of the model tower:

  \(\dfrac{h}{40\text{ m}}=\sqrt[3]{\dfrac{0.1\text{ L}}{100000\text{ L}}}\\\\h=(40\text{ m})\sqrt[3]{10^{-6}}=\boxed{0.40\text{ m}}\)

Logan should make his tower 0.4 meters, or 40 cm high.