Savannah recorded the grade-level and instrument of everyone in the middle school School of Rock below.
Seventh Grade Students
Instrument # of Students
Guitar 5
Bass 12
Drums 14
Keyboard 4
Eighth Grade Students
Instrument # of Students
Guitar 12
Bass 5
Drums 10
Keyboard 8

Based on these results, express the probability that a student chosen at random will play the drums as a percent to the nearest whole number.

The 90% confidence interval for the proportion of district residents in favor of starting the school day 15 minutes later is (0.392, 0.548). The true proportion is estimated to lie within this interval with 90% confidence.

To calculate the 90% confidence interval for the true proportion of district residents who are in favor of starting the school day 15 minutes later, we can use the following formula:

CI = p ± z*(√(p*(1-p)/n))

where:

CI: confidence interval

p: proportion of residents in favor of starting the day later

z: z- score based on the confidence level (90% in this case)

n: sample size

First, we need to calculate the sample proportion:

p = 94/200 = 0.47

Next, we need to find the z- score corresponding to the 90% confidence level. Since we want a two-tailed test, we need to find the z- score that cuts off 5% of the area in each tail of the standard normal distribution. Using a z-table, we find that the z- score is 1.645.

Substituting the values into the formula, we get:

CI = 0.47 ± 1.645*(√(0.47*(1-0.47)/200))

Simplifying this expression gives:

CI = 0.47 ± 0.078

Therefore, the 90% confidence interval for the true proportion of district residents who are in favor of starting the school day 15 minutes later is (0.392, 0.548). We can be 90% confident that the true proportion lies within this interval.

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The capacity of Supercut in customers per hour is 18.

The capacity of Supercut is the total number of customers served by three stylists in an hour, considering the average time it takes each stylist to serve one customer. This capacity calculation helps Supercut in keeping up with demand and avoiding long waiting periods, which could discourage clients.

The given data: Supercut salon has three stylists. The average time each stylist takes to serve one customer is 10 minutes. According to the data provided, it takes 10 minutes for each stylist to serve one customer, and there are three stylists. So, in 1 hour (60 minutes), each stylist will have the capacity to serve six clients.

Supercut's total capacity in an hour is calculated by adding up the capacity of each stylist. Therefore, the capacity of Supercut is: Capacity of Supercut = Capacity of each stylist * Number of Stylists= 6 customers * 3 stylists= 18 customers. Therefore, the capacity of the Supercut salon in customers per hour is 18.

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Answer:

\(m\angle ABC=60\textdegree\)

Step-by-step explanation:

\(m\angle ABC=360-90-90-m\angle AOC\\=180-120\\=60\textdegree\)

Answer:

173

Step-by-step explanation:

Answer:

173

Step-by-step explanation:

Answer:545

Step-by-step explanation: subtract 738-193 and get your answer

The sampling technique used in this scenario is Random sampling

The correct answer is an option (a)

We know that the random sampling is nothing but a method of choosing a sample of observations from a population to make assumptions about the population. It is also called as a porbability sampling.

It  allows for the randomization of sample selection.

There are four random sampling methods –

simple random sampling,

systematic sampling,

stratified sampling,

and cluster sampling.

In random sampling, the randomized selection of a small segment of individuals or members from a whole population.

Here, the soda bottle company  have equipment that can pull every tenth bottle from the assembly line without causing a backup on the line.

Therefore,  the sampling technique used: Random

The correct answer is an option (a)

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The complete question is:

Select the sampling technique used:

A soda bottling company needs to test the quality of the bottles they produce. They have equipment that can pull every tenth bottle from the assembly line without causing a backup on the line.

a) Random

b) Stratified

c) Cluster

d) Systematic

e) Convenience

To determine after what period of lighting hours we would expect 65.54% of the lamps to fail, we can use the concept of the standard normal distribution.

Given:

Average life of lamps (μ) = 10,000 hours

Standard deviation of lamps (σ) = 500 hours

We need to find the x value (number of lighting hours) at which 65.54% of the lamps would have failed.

First, we need to convert the desired percentile to a z-score. The z-score represents the number of standard deviations from the mean.

To find the z-score corresponding to a percentile of 65.54%, we subtract it from 100% to get the cumulative area to the left:

Percentile = 100% - 65.54% = 34.46%

Using the standard normal distribution table or a statistical calculator, we find that the z-score associated with a cumulative area of 34.46% is approximately -0.385.

Now, we can use the z-score formula to find the corresponding x value:

z = (x - μ) / σ

-0.385 = (x - 10,000) / 500

Solving for x, we get:

x = -0.385 * 500 + 10,000

x ≈ 9812.5

Therefore, after approximately 9812.5 hours of lighting, we would expect 65.54% of the lamps to have failed.

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Answer:

B. 50 students in her school

Step-by-step explanation:

Every other answer is at a seperate place designed to help someone in a specific field, besides the school.

The number of kilowatt-hours consumed in a week by the 850-Watt window air conditioner that is left on all day is approximately 14.28 kW-hrs.

To calculate the number of kilowatt-hours (kW-hrs) consumed by the air conditioner in a week, we need to consider the power rating of the air conditioner (850 Watts) and the duration it is left on each day.

Power of the air conditioner = 850 Watts

Duration of usage per day = 24 hours (left on all day)

Number of days in a week = 7 days

To calculate the energy consumption, we can use the formula:

Energy (kW-hrs) = Power (kW) * Time (hours)

First, let's convert the power from Watts to kilowatts by dividing it by 1000:

Power (kW) = 850 Watts / 1000 = 0.85 kW

Now we can calculate the energy consumption in a week:

Energy (kW-hrs) = Power (kW) * Time (hours)

Energy (kW-hrs) = 0.85 kW * 24 hours/day * 7 days

Energy (kW-hrs) = 14.28 kW-hrs

Therefore, the number of kilowatt-hours consumed in a week by the 850-Watt window air conditioner that is left on all day is approximately 14.28 kW-hrs.

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The number of dimes Hailey has is 29 dimes.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

Example:

2x + 4 = 8 is an equation.

We have,

Number of dimes = x

Number of quarters = y

Now,

1 dime = $0.10

1 quarter = $0.25

We can make two equations.

x + y = 65 ____(1)

x = 65 - y _____(2)

0.10x + 0.25y = 11.90 ______(3)

Now,

Substituting (2) in (3).

0.10 (65 - y) + 0.25y = 11.90

6.5 - 0.10y + 0.25y = 11.90

6.5 + 0.15y = 11.90

0.15y = 11.90 - 6.5

0.15y = 5.4

y = 36

And,

x = 65 - y

x = 65 - 36

x = 29

Thus,

Hailey has 29 dimes.

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Answer:

When the truck is full: \(g_{mf} = \frac{m}{8}\)

When the truck is empty: \(g_{me} = \frac{m}{9.6}\)

Step-by-step explanation:

When the truck is full for every eight miles traveled by the vehicle, there is a cost of one gallon of fuel, therefore for every mile the cost is one eight of a gallon, with this information we can create the following expression:

\(g_{mf} = \frac{m}{8}\)

Where m is the number of miles traveled by the truck.

When the vehicle is empty, it's performance improves by 20 %, which means that for the same amount of fuel it'll travel a distance 120% of the previous one. Therefore we need to multiply 1.2 on the denominator of the last expression:

\(g_{me} = \frac{m}{8*1.2}\\\\g_{me} = \frac{m}{9.6}\)

The expression represents the amount of gasoline used (g) is,

When the truck is full (mf) is represented as \(m_f = \dfrac{m}{8}\),

And when the truck is empty (me) is represented as,  \(m_e = \dfrac{m}{9.6}\)

Given that,

A long-distance delivery truck averages 8 miles per gallon when the truck is full.

The miles per gallon improve by 20% when the truck is empty.

We have to determine,

Which expression represents the amount of gasoline used (g) in terms of the number of miles driven when full (mf) and the number of miles driven when empty (me).

According to the question,

The amount of gasoline used (g) in terms of the number of miles driven when full (mf),

And The distance delivery truck averages 8 miles per gallon when the truck is full.

The amount of gasoline when the truck is full is represented as,

\(m_f = \dfrac{m}{8}\)

Then,

The miles per gallon improve by 20% when the truck is empty.

The number of miles driven when empty is represented as,

\(m_e = \dfrac{m}{8 + 8 \times 0.20}\\\\m_e = \dfrac{m}{8+ 1.6}\\\\m_e = \dfrac{m}{9.6}\)

Hence, The expression represents the amount of gasoline used (g) is,

When the truck is full (mf) is represented as \(m_f = \dfrac{m}{8}\),

And when the truck is empty (me) is represented as,  \(m_e = \dfrac{m}{9.6}\).

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Answer:

x = -4

y = -4

Step-by-step explanation:

Since y = x, we can say:

x = 2x + 4

-x = 4

x = -4

And now we can substitute -4 in for x, in the equation y = x

y = -4

Hope this helps!

Answer:

(-4,-4)

Step-by-step explanation:

set 2x + 4 and x equal to each other since they both equal 'y'

2x+4 = x

subtract 2x from each side to get:

4 = -x

divide by -1 so the variable becomes positive

-4 = x

if x=-4 and y=x then y=-4 also (you can check this by graphing each equation)

The statement "a student given four quarters is more likely to have spent the money than a student given a $1 bill" is incorrect.

In terms of value, four quarters and a $1 bill are equivalent, as they both amount to $1. Therefore, the likelihood of spending the money would be the same for both scenarios.

The decision to spend or keep the money is dependent on the individual's personal choices, financial situation, and needs. It cannot be determined solely based on the denominations of the currency given.

Hence, it would be inaccurate to conclude that a student given four quarters is more likely to have spent the money compared to a student given a $1 bill.

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Assume, Steve walks at a constant pace, he will be in his house after 5 hours

Given the Parameters :

The distance walked in 1 hour = 15 miles - 12 miles = 3 miles

Recall :

Steve's speed = 3 miles ÷ 1 hour = 3mi/hr

Time taken to reach his destination :

Time taken = distance / speed

Time = (15 ÷ 3) = 5 hours

Therefore, It will take Steve 5 hours to reach his destination.

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Answer:

Wheres the polygon ?

Step-by-step explanation:

Step-by-step explanation:

1. 5+2+3=5+(2+3) 2. 9a is equivalent to 11a-2a 3. 7a + 04 - 2a is equivalent to 7a + -2a + 4 4. 8a-(8a-8) is equivalent or = to 8.

The decibel level of the sound from the leaf blower is approximately 104 dB.

The decibel level of a sound is measured in logarithmic units and is defined as the ratio of the sound's intensity to a reference intensity that is just barely audible to the human ear.

The decibel level (dB) of a sound is given by the equation 10 log(I/I_0), where I is the intensity of the sound being measured and I_0 is the reference intensity.

For this problem, the intensity of the sound from the leaf blower is given as 28 × 10^-2 W/m².

The reference intensity is generally taken to be 1 × 10^-12 W/m².

Substituting these values into the formula, we get: 10 log(28 × 10^-2 / (1 × 10^-12)) = 10 log(28 × 10^10) = 10 (10.447) ≈ 104.47

Therefore, the decibel level of the sound from the leaf blower is approximately 104 dB.

Decibel (dB) is a unit used to measure the intensity or level of sound, as well as the ratio of power or amplitude of a signal. It is a logarithmic unit that compares the measured quantity to a reference level. The decibel scale is logarithmic because the human perception of sound intensity is not linear. A change of 1 dB is considered the smallest perceptible difference in sound level, while a change of 10 dB is perceived as approximately a doubling or halving of loudness.

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Answer:

Rajiv bought 23,382 balls.

Step-by-step explanation:

Given that Rajiv bought 1325 packs of red balls, 1238 packs of yellow balls and 1334 packs of green balls, and there were 6 balls in each pack, to determine how many balls did Rajiv buy the following calculation must be performed:

(1,325 + 1,238 + 1,334) x 6 = X

3.897 x 6 = X

23.382 = X

Therefore, Rajiv bought 23,382 balls.

The maximum value attained by the sum of the expression is 169 when N is the two-digit number 98.

Let N be a two-digit number with digits a and b. Then, the sum of N and the product of its digits is N + ab, and the sum of N's digits is a + b. Therefore, the expression we want to maximize is:

Substituting N = 10a + b, we get:

To maximize this expression, we want to maximize a and b. Since a and b are digits, they must be between 1 and 9. If we set a = 9 and b = 8, we get:

Therefore, the maximum value attained by the expression is 169 when N is the two-digit number 98.

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Answer: y=8

Step-by-step explanation:

Since DF is bisected, it means but in half. This means DU and UF are equal in length. We can set them equal to each other to find y.

2y=16          [divide both sides by 2]

y=8

Answer:

y=8

Step-by-step explanation:

when a triangle is bisected opposite sides become equal

Both sides are the same

2y=16 divide both sides by 2

y=8

Answer:

0.1%

Step-by-step explanation:

138 into a percent=1.38%

156 into a percent=1.56%

175 into a percent=1.75%

1.38-1.56=0.18

1.56-1.75=0.19

0.19-0.18= 0.1%

The increase in volunteers from year 1 to year 2 is 13.04 % and the increase from year 1 to year 3 is 26.81 %.

The percentage can be defined as a relative value that represents the hundredth part of any quantity.

Given that the number of volunteers in a program during year 1, year 2 and year 3 are 138, 156 and 175 respectively.

The percentage of increase in volunteers from year 1 to year 2 is given below.

Volunteers (%) = \(\dfrac {156-138}{138} \times 100\)

Volunteers (%) = 13.04%

The percentage of increase in volunteers from year 1 to year 3 is given below.

Volunteers (%) = \(\dfrac {175-138}{138} \times 100\)

Volunteers (%) = 26.81 %

Hence we can conclude the increase in volunteers from year 1 to year 2 is 13.04 % and the increase from year 1 to year 3 is 26.81 %.

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Answer:

4+12v or 12v+4

Step-by-step explanation:

you distribute (multiply 2 with 2 and 6v)

To write the equation of a circle, we typically use the general form of the equation:

(x - h)^2 + (y - k)^2 = r^2

Where (h, k) represents the center of the circle, and r represents the radius.

In this case, the center of the circle is translated 13 units left and 6 units up from the origin (0, 0), so the new center coordinates are (-13, 6). The diameter of the circle is given as d = 22, which means the radius is half of the diameter, so r = 22 / 2 = 11.

Substituting the values into the equation, we have:

(x - (-13))^2 + (y - 6)^2 = 11^2

Simplifying further:

(x + 13)^2 + (y - 6)^2 = 121

Therefore, the equation of the circle with a diameter of 22 and a center translated 13 units left and 6 units up from the origin is (x + 13)^2 + (y - 6)^2 = 121.

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Answer:

9 goes in the blank

Step-by-step explanation:

Since 21 divided by 7 is 3 then you would have to multiply 3 to the numerator to get the equivalent. Hope this helped :)

Answer:

9/21

Step-by-step explanation:

multiply the numerator and denominator by 3 and you will get 9/21

According to the given scenario, Kyle will not be able to make his monthly payment by the first of the month. He does expect to be able to make it by the 9th of the month. Hence, to avoid any inconvenience or further delay, Kyle needs to notify the bank to let them know that his payment is going to be eight days late.

The answer to this question is option B. Notify the bank to let them know that his payment is going to be eight days late. It is important for Kyle to notify the bank of his inability to make the payment by the first of the month. By informing the bank, Kyle ensures that his payment is recorded as late instead of missed, and he may also be able to avoid any late payment fees associated with the loan.

He also needs to inform the bank about the expected date of payment.  This will help to keep the bank informed of the situation and will prevent any negative impact on his credit score. So, it's very important to keep in touch with the bank about any financial changes that affect the payment of loans.  Therefore, the answer to the given question is option B. Notify the bank to let them know that his payment is going to be eight days late.

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Answer:

down 8 units

Step-by-step explanation:

going from +6 to -2 goes down 8 units

Answer:

Step-by-step explanation:

f(x) + n - shift the graph n units up

f(x) - n - shift the graph n units down

f(x + n) - shift the graph n units to the left

f(x - n) - shift the graph n units to the right

==============================================

We have y = 3/7x + 6. It has been changed to y = 3/7x - 2.

y = 3/7x + 6 → f(x) = 3/7x + 6

f(x) - 8 = (3/7x + 6) - 8 = 3/7x + 6 - 8 = 3/7x - 2