In a school, the church building is 300m due east of the assembly hall. a classroom is 200m on a bearing of 123 from the assembly hall. how far is the classroom to the church?

The surface area that can be painted with one complete rotation of the roller is 226.19 inches².

Surface area is defined as the total amount of area that covers the surface or outside of a three-dimensional figure.

A paint roller is in the shape of a cylinder. To determine the surface area that can be painted with one complete rotation of the roller, solve for the surface area of a cylinder without the circular bases.

SA = 2πrh

where SA = surface area

r = radius of the base = 3 inches

h = height of the cylinder = width = 12 inches

Plug in the values and solve for the surface area.

SA = 2πrh

SA = 2π(3 inches)(12 inches)

SA = 226.19 inches²

Hence, the surface area that can be painted with one complete rotation of the roller is 226.19 inches².

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Expected real interest rate before change in money supply: 7% (11% nominal interest rate - 4% expected inflation)

Actual real interest rate before change in money supply: 7% (11% nominal interest rate - 4% actual inflation)

Expected real interest rate after increase in money supply: 5% (11% nominal interest rate - 6% expected inflation)

Actual real interest rate after increase in money supply: 5% (11% nominal interest rate - 6% actual inflation)

The unanticipated change in inflation arbitrarily benefits borrowers. When inflation increases unexpectedly, borrowers effectively pay back their loans with money that has less purchasing power than expected at the time of borrowing.

According to the Fisher effect, as expectations adjust to the new, higher inflation rate, the nominal interest rate will increase to compensate for the increase in expected inflation. This implies that the nominal interest rate on car loans will rise to offset the higher inflation rate and maintain the expected real interest rate.

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Answer:

x=3

Step-by-step explanation:

f(x)=2x+6

f(x)=12

Hence:

2x+6=12

2x+6-6=12-6

2x=6

x=6/2

x=3

The given function, after applying the series of transformations, results in the following equation:

y = -3 * f(3(x + 1)) - 2 * f(2(x - 2)) - 2 - 3 * f(x + 1) + 3 - 3 * |f(x + 2)| - 1 * |f(x)| / 2 - 3

The series of transformations can be summarized as follows:

(1) Compress horizontally by a factor of 3 and translate left 1 unit: f(3(x + 1)).

(2) Compress horizontally by a factor of 2 and translate right 2 units: f(2(x - 2)).

(3) Translate left 2 units and translate down 2 units: f(x + 1) - 2.

(4) Translate right 1 unit and translate up 3 units: -3 * f(x + 2) + 3.

(5) Expand vertically by a factor of 3 and reflect across the x-axis: -3 * |f(x + 2)|.

(6) Translate left 2 units and translate down 3 units: -3 * |f(x + 2)| - 1.

(7) Reflect across the x-axis and translate left 1 unit: -1 * |f(x)| / 2.

(8) Compress vertically by a factor of 2 and translate down 3 units: -1 * |f(x)| / 2 - 3.

The resulting equation combines all these transformations to describe the final function.

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Answer:

11.4

Step-by-step explanation:

Since this triangle is a right triangle, we can solve using SOHCAHTOA.

Our angle is 25 degrees and the given hypotenuse length is 27. So, the best trigonometry equation to use would be sine, since it includes the hypotenuse and the opposite side, which is the r length that we are looking for.

Through SOHCAHTOA, sin 25° = \(\frac{opp}{hyp}\)

sin 25° = \(\frac{r}{27}\)

r = 27 (sin 25°)

Using a calculator, 27 (sin 25°) ≈ 11.4

Step 1:

Write the parent coordinates

(4 , 6)

Step 2

The point can bo on the positive y-axis or on the negative y-axis.

New coordinates

( 4 + 5, 6 + 5)

= (9 , 11)

Or

( 4 - 5, 6 - 5)

= (-1 , 1)

Final answer

Smaller y-value = 1

Larger y-value = 11

6c^2=4,\:v^3 so yeah that is it

The lengths of the sides of triangle PQR are: PQ = 3, QR = 3√5, RP = 6.

In order to find the lengths of the sides of the triangle pqr with p(5, 1, 4), q(3, 3, 3), r(3, −3, 0), we can use the distance formula.

The distance formula for finding the distance between two points (x1, y1, z1) and (x2, y2, z2) in a 3-dimensional space is given by:

\($$d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2+(z_2-z_1)^2}$$\)

The length of the side PQ is:

\($$\begin{aligned} PQ&=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2+(z_2-z_1)^2} \\ &=\sqrt{(3-5)^2+(3-1)^2+(3-4)^2} \\ &=\sqrt{4+4+1} \\ &=\sqrt{9} \\ &=3 \end{aligned}$$\)

The length of the side QR is:

\($$\begin{aligned} QR&=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2+(z_2-z_1)^2} \\ &=\sqrt{(3-3)^2+(3-(-3))^2+(3-0)^2} \\ &=\sqrt{36+9} \\ &=\sqrt{45} \\ &=3\sqrt{5} \end{aligned}$$\)

The length of the side RP is:

\($$\begin{aligned} RP&=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2+(z_2-z_1)^2} \\ &=\sqrt{(3-5)^2+(-3-1)^2+(0-4)^2} \\ &=\sqrt{4+16+16} \\ &=\sqrt{36} \\ &=6 \end{aligned}$$\)

Therefore, the lengths of the sides of triangle PQR are: PQ = 3, QR = 3√5, RP = 6.

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Answer:

v=2

Step-by-step explanation:

Answer: 4/10 of those people have cats because 3/5 multiplied by 2/3 is 4/10.

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let's evaluate :

\(\\ \sf\longmapsto (c-7)(c+5)\)

\(\\ \sf\longmapsto c(c+5)-7(c+5)\)

\(\\ \sf\longmapsto c^2+5c-7c-35\)

\(\\ \sf\longmapsto c^2-2c-35\)

Answer:

Step-by-step explanation:

They are similar by angle-angle similarity.

The probability of getting a total value of $50 is 1/6.

There are three possible outcomes for Ben's prize: $5, $10, or $20.

There are two possible outcomes for Jamie's prize: $30 or $40.

Therefore, there are 3 x 2 = 6 total possible outcomes for the combined value of their prizes.

To find the probability that the total value of their prizes is exactly $50, we need to find the number of outcomes that result in a total value of $50, and divide that by the total number of possible outcomes.

The only way to get a total value of exactly $50 is that Ben wins $20 and Jamie wins $30. This is only one combination out of 6 possible combinations. So the probability of getting a total value of $50 is 1/6 or approximately 0.166.

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Maya has created a probability sample in which she uses random chance to select participants and can calculate the likelihood that a participant will be selected. A probability sample is a form of random sampling in which every member of a population has an equal chance of being selected. The process of random selection in a probability sample is a fundamental principle of statistical analysis. The probability sample can be used to make estimates about the whole population, provided that the sample size is sufficient and the random selection process is unbiased.


Probability sampling is a method of selecting a sample from a population in which every member of the population has an equal chance of being selected. Probability sampling is a more reliable way of selecting a sample because it eliminates the possibility of bias in the selection process. Probability samples are often used in research studies, surveys, and other types of data collection.

There are several types of probability sampling methods. One of the most common is simple random sampling, which involves selecting individuals at random from the population. Another type is stratified random sampling, which involves dividing the population into strata and then selecting individuals from each stratum at random. Cluster sampling is another type of probability sampling in which the population is divided into clusters, and then a random sample of clusters is selected for the study.


Maya has created a probability sample in which she uses random chance to select participants and can calculate the likelihood that a participant will be selected. Probability sampling is a reliable way of selecting a sample because it eliminates the possibility of bias in the selection process.

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The final cost of the item after a 35% discount and 9.8% sales tax is $53.54.

The given problem is related to percentage discounts and sales tax and can be solved using the following steps:

Step 1: Firstly, we need to determine the discount amount, which is 35% of the original price. Let's calculate it. Discount = 35% of the original price = 0.35 x $75 = $26.25

Step 2: Now, we will calculate the new price after the discount by subtracting the discount amount from the original price.New Price = Original Price - Discount AmountNew Price = $75 - $26.25 = $48.75

Step 3: Next, we need to calculate the amount of sales tax. Sales Tax = 9.8% of New Price Sales Tax = 0.098 x $48.75 = $4.79

Step 4: Finally, we will calculate the final cost of the item by adding the new price and the sales tax.

Final Cost = New Price + Sales Tax Final Cost = $48.75 + $4.79 = $53.54

Therefore, the final cost of the item after a 35% discount and 9.8% sales tax is $53.54.I hope this helps!

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Answer:5%

Step-by-step explanation:

The Food and Drug Administration should put a stronger warning label on packages of ibuprofen.

To determine whether this proportion of 23 out of 440 users suffered from side effects, it is significant that a hypothesis test can be conducted.

The null hypothesis would be that the proportion of arthritis patients who suffer side effects when using ibuprofen is less than or equal to 3%, while the alternative hypothesis would be that the proportion is greater than 3%.

Using a one-tailed z-test with a significance level of 1%, the calculated z-score is 2.32. This falls in the rejection region, meaning that the null hypothesis can be rejected in favor of the alternative hypothesis.

Therefore, it can be concluded that more than 3% of arthritis patients suffer side effects when using ibuprofen to relieve the pain. As a result, the Food and Drug Administration should put a stronger warning label on packages of ibuprofen.

It is important for patients to be aware of the potential side effects and risks associated with this medication.

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Answer:

$200

Step-by-step explanation:

Given :

Cost of blender + import duty = $240

Import duty = 20% of cost price

Let :

Cost of blender = x

Import duty = 20% of x = 0.2x

Therefore,

x + 0.2x = $240

1.2x = 240

x = 240 / 1.2

x = $200

Cost of blender = $200

Step-by-step explanation:

steps are in the image above

Answer:

Its most likely in Smavile

Step-by-step explanation:

S - Smavile

F - Fancyville

\(p_{s} = 150+ 0.041*2800 \\p_{s} = 150 + 114.8 = 264.8\\\\p_{f} = 250 + 0.198*2800\\p_{f} = 250 + 554.5 = 804.5\)

264.8 * 1000 (its in thousands of dollars) = 264,800

Answer:

r² = (9 - 4)² + (6 - 4)² = 5² + 2² = 25 + 4 = 29

So the equation of this circle is

(x - 4)² + (y - 4)² = 29

Answer:

67.466%

Step-by-step explanation:

No. of people aged below 14 years old= 60,094

No. of people aged between 15 and 64 years old= 212,468

No. of people aged above 65 years old= 42,362

Age Dependency Ratio= No. of people aged between 15 and 64 years old

                                          /Total People

                                       = \(\frac{212,468}{60,094+212,468+42,362}\) × 100

                                       = \(\frac{212,468}{314,924}\) × 100

                                       = 67.466%

∴ the Age Dependency Ratio is 67.466%.

It will take approximately 39.532 days for $9500 to earn $800 at an annual interest rate of 8.25%.

To find the number of days it will take for $9500 to earn $800 at an annual interest rate of 8.25%, we need to use the formula for simple interest:

Interest = Principal * Rate * Time

In this case, we are given the interest ($800), the principal ($9500), and the annual interest rate (8.25%). We need to solve for time.

Let's denote the time in years as "t". Since we're looking for the number of days, we'll convert the time to a fraction of a year by dividing by 365 (assuming a standard 365-day year).

$800 = $9500 * 0.0825 * (t / 365)

Simplifying the equation:

800 = 9500 * 0.0825 * (t / 365)

Divide both sides by (9500 * 0.0825):

800 / (9500 * 0.0825) = t / 365

Simplify the left side:

800 / (9500 * 0.0825) ≈ 0.1083

Now, solve for t by multiplying both sides by 365:

0.1083 * 365 ≈ t

t ≈ 39.532

Therefore, it will take approximately 39.532 days for $9500 to earn $800 at an annual interest rate of 8.25%.

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Cal must earn at least $130 on his next paycheck in order to reach his goal of at least $131 average weekly income.

To determine the lowest amount on Cal's next paycheck that he must earn in order to reach his goal of at least $131 average weekly income, we need to consider the current total income and the number of weeks.

Cal's first two weekly paychecks were $128 and $135, so his current total income is $128 + $135 = $263.

To calculate the lowest amount on his next paycheck, we can set up an equation:

(263 + x) / 3 ≥ 131

Here, x represents the amount of Cal's next paycheck.

Simplifying the equation:

263 + x ≥ 131 * 3

263 + x ≥ 393

x ≥ 393 - 263

x ≥ 130

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Answer:

\(x(3 + y)\)

Step-by-step explanation:

Hi there!

\(3x + xy\)

The two terms in this expression are 3x and xy. In both these terms, x is present. Therefore, we can factor x out:

\(x(3 + y)\)

We cannot factor this further.

I hope this helps!

Answer:

x(3+y)

Step-by-step explanation:

Hope this helps you

Answer:

1/17

Step-by-step explanation:

You're on the right track so far!

(2³ + 3²) ⁻¹

= (8 + 9) ⁻¹

= (17) ⁻¹

= 1/17 (Remember, (a)⁻ⁿ = 1 / aⁿ)

Hi there!! (✿◕‿◕)

⭐⭐⭐⭐⭐⭐⭐⭐⭐⭐⭐⭐⭐⭐⭐⭐⭐⭐⭐⭐⭐⭐

A = 2   B = 3

(a^b + b^a)^-1

(2^3 + 3^2)^-1

1/7 or 0.058824

Hope this helped!!  ٩(◕‿◕｡)۶

The property that is not true for the normal distribution among the given options is: "The mean, median, and mode are all equal."

The normal distribution is characterized by several key properties. It has a bell shape, meaning it is symmetric around its mean. The tails of the distribution asymptotically approach the horizontal axis, which means they gradually decrease in height as they extend toward positive and negative infinity. The area underneath the curve and to the right of the mean is equal to 0.5, not 1. This is because the total area under the curve represents the probability of all possible outcomes and must sum up to 1. Lastly, the mean, median, and mode of the normal distribution are all equal to each other, making them measures of central tendency that coincide.

Therefore, the property that does not hold for the normal distribution is that the area underneath the curve and to the right of the mean is 1, as it is actually 0.5.

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Answer:

D) \(-\sqrt[3]{x-1}\)

Step-by-step explanation:

-the function is the cube root

-the cube root of zero is zero

- the graph is at 0 when x = 1, thus "x-1" must be part of answer

- the cube root of -8 is -2, at -8 the graph is +2. so the function is negated

\(-\sqrt[3]{x-1}\)

In this simulation, we are assuming that 40% of community college students never use tutoring services. We are interested in calculating the proportion of students who do not use tutoring services in random samples taken from this population.

To simulate this, we can use a random number generator to select samples from the population. For each sample, we count the number of students who do not use tutoring services and calculate the proportion.

Here are the steps to conduct this simulation:

1. Determine the sample size you want to use. Let's say you want to use a sample size of 100 students.

2. Use a random number generator to select 100 students from the population. Assign a value of 0 to those who do not use tutoring services and 1 to those who do.

3. Count the number of students with a value of 0 (who do not use tutoring services) in the sample.

4. Calculate the proportion of students who do not use tutoring services by dividing the count from step 3 by the sample size. Multiply the result by 100 to express it as a percentage.

5. Repeat steps 2-4 for a large number of samples, such as 1000 samples.

6. Finally, calculate the average proportion of students who do not use tutoring services across all the samples.

By conducting this simulation, we can estimate the proportion of students who do not use tutoring services based on the assumption that 40% of the population falls into this category.

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