In an A-Frame house, the roof extends to the ground level. If each side of the roof meets the ground at a 62° angle, what will be the measure of the angle where the two sides of the roof meet?

(x+5)² + (y+2)² = 4

(x - x0)² + (y - y0)² = r²

with circle center point (x0 ; y0) and r for circle radius

so you have to place the point (- 5 ; - 2) and graph the circle with r = 2

Answer:

Equilateral and acute

Explanation:

Equilateral triangles refer to triangles where all side lengths are equal. Acute triangles are triangles where all angles are acute (less than \(90^{\circ}\)). Since each side length of the triangle is \(4cm\), the triangle is an equilateral triangle. Due to the property of equilateral triangles where each angle is equivalent to \(60^{\circ}\), we can conclude that this triangle is equilateral and acute.

Hope this helps :)

The percentile of 6.2 in the given dataset is 30%. This means that 30% of the values in the dataset are lower than or equal to 6.2.

To determine the percentile of 6.2 in the given dataset, we need to calculate the percentage of values in the dataset that are lower than or equal to 6.2.

First, we arrange the dataset in ascending order: 4.2, 4.6, 5.1, 6.2, 6.3, 6.6, 6.7, 6.8, 7.1, 7.2.

Next, we count the number of values that are lower than or equal to 6.2. In this case, there are three values: 4.2, 4.6, and 5.1.

The next step is to calculate the percentage. We divide the count (3) by the total number of values in the dataset (10) and multiply by 100.

(3/10) * 100 = 0.3 * 100 = 30%

Percentiles are used to understand the relative position of a particular value within a dataset. In this case, 6.2 is higher than 30% of the values in the dataset and lower than the remaining 70%.

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Answer:

the last one

Step-by-step explanation:

there is no rhythm

Recall that Two events A and B are mutually exclusive if they cannot happen at the same time.

Hence, the probability that both of them will occur at the same time is zero. That is,

The required probabilty is 0.

Answer:

492 seconds.

Step-by-step explanation:

Every minute is 60 seconds.

Over here, 8minutes,12seconds has a value of minute in it.

Since we're dealing with seconds, we convert the 8 minutes into seconds and add it to the 12 seconds to get the overall value.

If 1 minute=60seconds

8 minutes=x

x=60×8=480 seconds

=> 480+12= 492 seconds.

Hope it helps

There are 492 seconds are there in 8 minutes 12 seconds ​

Arithmetic operations can also be specified by subtracting, dividing, and multiplying built-in functions.

The operator that performs the arithmetic operation is called the arithmetic operator.

Operators which let do a basic mathematical calculation

+ Addition operation: Adds values on either side of the operator.

For example 4 + 2 = 6

- Subtraction operation: Subtracts the right-hand operand from the left-hand operand.

for example 4 -2 = 2

* Multiplication operation: Multiplies values on either side of the operator

For example 4*2 = 8

/ Division operation: Divides left-hand operand by right-hand operand

For example 4/2 = 2

One minute has 60 seconds in there.

To determine that 8 minutes and 12 seconds have a value of a minute in it.

We convert the 8 minutes into seconds since we're functioning with seconds and add that to the 12 seconds to get the total value.

Let n numbers of seconds are there in 8 minutes

Since, 1 minute = 60 seconds

8 minutes = n

⇒ n = 60×8

⇒ n = 480 seconds

⇒ 480+12 = 492 seconds.

Hence, there are 492 seconds are there in 8 minutes 12 seconds. ​

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Answer:

The 85% confidence interval for the true mean number of reproductions per hour for the virus is between 10.1 and 10.3.

Step-by-step explanation:

We have that to find our \(\alpha\) level, that is the subtraction of 1 by the confidence interval divided by 2. So:

\(\alpha = \frac{1-0.85}{2} = 0.075\)

Now, we have to find z in the Ztable as such z has a pvalue of \(1-\alpha\).

So it is z with a pvalue of \(1-0.075= 0.925\), so \(z = 1.44\)

Now, find the margin of error M as such

\(M = z*\frac{\sigma}{\sqrt{n}}\)

In which \(\sigma\) is the standard deviation of the population and n is the size of the sample.

\(M = 1.44*\frac{2.4}{\sqrt{907}} = 0.1\)

The lower end of the interval is the sample mean subtracted by M. So it is 10.2 - 0.1 = 10.1 reproductions per hour.

The upper end of the interval is the sample mean added to M. So it is 10.2 + 0.1 = 10.3 reproductions per hour.

The 85% confidence interval for the true mean number of reproductions per hour for the virus is between 10.1 and 10.3.

Answer:

Step-by-step explanation:

The text is a statistics problem that asks to find the probability of a certain range of values in a normal distribution. A normal distribution is a bell-shaped curve that shows how data values are spread around the mean. The mean is the average of all the data values, and the standard deviation is a measure of how much the data values vary from the mean. To solve this problem, we can use the following steps:

Convert the given range of values to standard scores or z-scores. A z-score tells us how many standard deviations a value is away from the mean. To find the z-score, we use the formula: z=σx−μ​

where x is the value, μ is the mean, and σ is the standard deviation. For example, to find the z-score for 33.5 psi, we plug in the values: z=233.5−35​=−0.75

This means that 33.5 psi is 0.75 standard deviations below the mean. Similarly, to find the z-score for 36 psi, we plug in the values: z=236−35​=0.5

This means that 36 psi is 0.5 standard deviations above the mean.

Use a z-table to find the area under the curve for each z-score. A z-table is a table that shows the probability of getting a z-score less than or equal to a given value. For example, to find the area under the curve for -0.75, we look up the row for -0.7 and the column for 0.05 in the z-table and get 0.2266. This means that there is a 22.66% chance of getting a z-score less than or equal to -0.75. Similarly, to find the area under the curve for 0.5, we look up the row for 0.5 and the column for 0 in the z-table and get 0.6915. This means that there is a 69.15% chance of getting a z-score less than or equal to 0.5.

Subtract the smaller area from the larger area to find the area between the two z-scores. This area represents the probability of getting a value between 33.5 and 36 psi in the normal distribution. For example, to find the area between -0.75 and 0.5, we subtract: 0.6915−0.2266=0.4649

This means that there is a 46.49% chance of getting a value between 33.5 and 36 psi in the normal distribution.

Multiply the area by 100 to convert it to a percentage and write it with the appropriate units: The percentage of tires that are inflated to a pressure between 33.5 and 36 psi is 0.4649×100=46.49%

Answer:

v = -4

Step-by-step explanation:

2v + 7 = 3

Subtract 7 on both sides

2v = -4

Divided by 2 both sides

v = -4

The area of the square with a side length of 3.1 meters is 9.61 square meters.

To find the area of a square, we need to multiply the length of one side by itself. In this case, the square has a side length of 3.1 m.

Area of a square = side length × side length

Substituting the given side length into the formula:

Area = 3.1 m × 3.1 m

To perform the calculation:

Area = 9.61 m²

It's worth noting that when calculating the area, we are working with squared units. In this case, the side length is in meters, so the area is expressed in square meters (m²). The area represents the amount of space enclosed within the square.

Remember, to find the area of any square, you simply need to multiply the length of one side by itself.

The area of the square with a side length of 3.1 meters is 9.61 square meters.

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Answer:

The probability that his bill will be less than $50 a month or more than $150 for a single month is 0.3728 = 37.28%.

Step-by-step explanation:

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean \(\mu\) and standard deviation \(\sigma\), the z-score of a measure X is given by:

\(Z = \frac{X - \mu}{\sigma}\)

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

A salesman who uses his car extensively finds that his gasoline bills average $125.32 per month with a standard deviation of $49.51.

This means that \(\mu = 125.32, \sigma = 49.51\)

Less than 50:

p-value of Z when X = 50. So

\(Z = \frac{X - \mu}{\sigma}\)

\(Z = \frac{50 - 125.32}{49.51}\)

\(Z = -1.52\)

\(Z = -1.52\) has a p-value of 0.0643

More than 150

1 subtracted by the p-value of Z when X = 150. So

\(Z = \frac{X - \mu}{\sigma}\)

\(Z = \frac{150 - 125.32}{49.51}\)

\(Z = 0.5\)

\(Z = 0.5\) has a p-value of 0.6915

1 - 0.6915 = 0.3085

The probability that his bill will be less than $50 a month or more than $150 for a single month is:

0.0643 + 0.3085 = 0.3728

The probability that his bill will be less than $50 a month or more than $150 for a single month is 0.3728 = 37.28%.

Answer: 11

Step-by-step explanation:

F(1) = 3(1) + 8

F(1) = 3 + 8

F(1) = 11

You just substitute the x in for 1 and solve from there.

Answer:

C is the answer i think

Step-by-step explanation:

Answer:

10/14 or 0.71428571428 or 71.428571428571%

Step-by-step explanation:

Answer:

1 1/4 miles

Step-by-step explanation:

3/4 + 2/4 (1/2 = 2/4) = 5/4 = 1 1/4

The approximate 90% confidence interval for this situation is given as follows:

(70244, 70632).

The bounds of the confidence interval are given by the rule presented as follows:

\(\overline{x} \pm z\frac{\sigma}{\sqrt{n}}\)

In which:

From the z-table, the critical value for a 95% confidence interval is given as follows:

z = 1.645.

The parameters are given as follows:

\(\overline{x} = 70438, \sigma = 645.3, n = 30\)

The lower bound of the interval is given as follows:

\(70438 - 1.645 \times \frac{645.3}{\sqrt{30}} = 70244\)

The upper bound of the interval is given as follows:

\(70438 + 1.645 \times \frac{645.3}{\sqrt{30}} = 70632\)

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You would expect to find the middle 98% of most averages for the lengths of pregnancies in the sample between approximately 264.0 days and 274.1 days.

To find the range in which you would expect to find the middle 98% of most pregnancies, you can use the concept of z-scores and the standard normal distribution.

For the given data:

Mean (μ) = 269 days

Standard deviation (σ) = 17 days

To find the range, we need to find the z-scores corresponding to the 1% and 99% percentiles. Since the normal distribution is symmetric, we can find the z-scores by subtracting and adding the respective values from the mean.

To find the z-score for the 1% percentile (lower bound):

z1 = Φ^(-1)(0.01)

Similarly, to find the z-score for the 99% percentile (upper bound):

z2 = Φ^(-1)(0.99)

Now, we can calculate the z-scores:

z1 = Φ^(-1)(0.01) ≈ -2.33

z2 = Φ^(-1)(0.99) ≈ 2.33

To find the corresponding values in terms of days, we multiply the z-scores by the standard deviation and add/subtract them from the mean:

lower bound = μ + (z1 * σ) = 269 + (-2.33 * 17) ≈ 229.4 days

upper bound = μ + (z2 * σ) = 269 + (2.33 * 17) ≈ 308.6 days

Therefore, you would expect to find the middle 98% of most pregnancies between approximately 229.4 days and 308.6 days.

Now, let's consider drawing samples of size 58 from this population. The mean and standard deviation of the sample means can be calculated as follows:

Mean of sample means (μ') = μ = 269 days

Standard deviation of sample means (σ') = σ / sqrt(n) = 17 / sqrt(58) ≈ 2.229

To find the range in which you would expect to find the middle 98% of most averages for the lengths of pregnancies in the sample, we repeat the previous steps using the mean of the sample means (μ') and the standard deviation of the sample means (σ').

Now, calculate the z-scores:

z1 = Φ^(-1)(0.01) ≈ -2.33

z2 = Φ^(-1)(0.99) ≈ 2.33

Multiply the z-scores by the standard deviation of the sample means and add/subtract them from the mean of the sample means:

lower bound = μ' + (z1 * σ') = 269 + (-2.33 * 2.229) ≈ 264.0 days

upper bound = μ' + (z2 * σ') = 269 + (2.33 * 2.229) ≈ 274.1 days

Therefore, you would expect to find the middle 98% of most averages for the lengths of pregnancies in the sample between approximately 264.0 days and 274.1 days.

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We are given the radius of the scoop and asked to find the volume of ice cream in one scoop. By using the formula for the volume of a sphere and substituting the given radius, we can calculate the volume. The final answer is approximately 33.49 cubic inches.

a) The problem asks for the volume of ice cream in one scoop.

b) The given fact is that the radius of the scoop is 2 inches.

c) The formula to be used is the volume of a sphere, which is given by V = (4/3)πr³, where V is the volume and r is the radius.

d) Number Sentence:

  - Given: Radius (r) = 2 inches

  - Formula: V = (4/3)πr³

  - Substituting the value: V = (4/3)π(2)³

  - Simplifying: V = (4/3)π(8)

  - Evaluating: V = (4/3)(3.14)(8)

  - Multiplying: V = 33.49333333 (approx.)

e) Final answer: The volume of ice cream in one scoop is approximately 33.49 cubic inches.

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The sampling method used by the restaurant manager allows for efficient data collection and a representative sample, it may introduce bias and lacks randomization.

Based on the information provided, we can identify the following statements that are true about the sampling method used by the restaurant manager to evaluate customer satisfaction with the new smoothie:

1. The manager uses systematic sampling: The manager surveys every other customer who orders the new smoothie. This systematic approach involves selecting every second customer, providing a consistent and organized sampling method.

2. The sample is representative: By surveying every other customer who orders the new smoothie, the manager ensures that the sample includes a variety of customers, reflecting the customer population as a whole.

3. The sample size may be smaller than the total customer base: Since the manager surveys every other customer, the sample size may be smaller compared to surveying every customer. This allows for efficient data collection and analysis.

4.The sampling method may introduce bias: The manager may inadvertently introduce bias by only surveying every other customer. Customers who are skipped in the survey may have different preferences or opinions, leading to a potential bias in the results.

5. The sampling method lacks randomization: Randomization is not employed in this sampling method, as the manager systematically selects customers. This could potentially introduce bias or exclude certain types of customers from the sample.

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A sample of 100 is sufficiently large, the random variable has a sampling distribution that has a mean of 3.2 inches, a sampling distribution that is approximately Normal by the central limit theorem and a sampling distribution that has a standard deviation of 3 inches.

We know that the number of column inches of classified advertisements appearing on Mondays in a certain daily newspaper has mean 320 inches and standard deviation 30 inches and the results for 100 consecutive Mondays can be regarded as a simple random sample and let denote the mean number of column inches of classified advertisements in the sample. With this we can say that a sample of 100 is sufficiently large, the random variable has a sampling distribution that has a mean of 3.2 inches, a sampling distribution that is approximately Normal by the central limit theorem and a sampling distribution that has a standard deviation of 3 inches.

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Answer:

In ten year you will be 10 years older than you are now and so will your brother. The 6 years difference will remain if no one dies.

Step-by-step explanation:

You are z years old

Your brother is 6 years younger than z years; z - 6 years

In 10 years time, you will be z + 10 years

Your brother will be z - 6 years + 10 years = z + 4 years

OR

In 10 years time, you will be z + 10 years

You brother is still 6 years younger than you, so is z + 10 years - 6 years = z + 4 years

Answer:

62.1

Step-by-step explanation:

PEMDAS!

9.1 * 3 = 27.3

8.7 * 4 = 34.8

27.3 + 34.8 = 62.1

The three vertices will give us the dilated figure.

First we find the slope of the line that would pass through the point of dilation, (-3, 0), and each vertex.

From (-3, 0) to (5, 4), the slope would be

m = (4-0)/(5--3) = 4/8

Since the scale factor is 1/2, this means each part of the slope would be multiplied by this scale factor:

(4(1/2))/(8(1/2)) = 2/4

This means from our point of dilation we count up 2 and over 4; this puts the new point at (-3+4, 0+2) = (1, 2).

From (-3, 0) to (3, 8) the slope is

m = (8-0)/(3--3) = 8/6

Multiplying the rise and run by 1/2, we have

(8(1/2))/(6(1/2)) = 4/3

This means the dilated point would be up 4 and over 3 from (-3, 0), putting it at (-3+3, 0+4) = (0, 4).

From (-3, 0) to (-5, 4), the slope is

m = (4-0)/(-5--3) = 4/-2.

Multiplying the rise and run by 1/2, we have

(4(1/2))/(-2(1/2)) = 2/-1

This means the dilated point would be up 2 and over -1 from (-3, 0), putting it at (-3+-1, 0+2) = (-4, 2).

These three vertices give us the dilated figure.

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Answer:

The bill is $1837.5

Step-by-step explanation:

Given

\(B = Bills\)

\(T = Temperature\)

\(B\ \alpha\ \frac{1}{T}\) --- The variation

T = 35; when B = 210

Required

Find B when T = 40

\(B\ \alpha\ \frac{1}{T}\)

Express as an equation

\(B = \frac{k}{T}\)

Make k the subject

\(k = BT\)

T = 35; when B = 210

\(k = 35 * 210\)

\(k = 7350\)

When T = 40, we have:

\(k = BT\)

\(7350 = B * 40\)

Make B the subject

\(B = \frac{7350}{4}\)

\(B = 1837.5\)

Answer:

6

Step-by-step explanation:

this question is basically asking you to find the HCF of 30 and 36

step 1 : draw prime factor tree diagrams and write the numbers out as the product if their prime factors

step 2: multiply the prime factors they have in common

30 = 2 x 3 x 5

36 = 2 x 2 x 3 x 3

HCF = 2 x 3 = 6

Answer: 6 rows of lemon trees and 6 rows of lime trees.  

Steps: All you need to do is to find the highest common factor of 30 and 36, which is 6.  

30 divided by 6 is 5 and 36 divided by 6 is 6.  So uncle john can plant 5 lemon trees and 6 lime trees each row. That would make 6 rows of lemon trees and 6 rows of lime trees.

Brainliest pls if it is correct!

The triple integral using the spherical coordinates is 16 π .

Given :

Use spherical coordinates. Evaluate( x^2 + y^2 + z^2 )^1/2 dv, where B is the ball with center the origin and radius 3.

we know that ,

= ∫∫∫ ( x^2 + y^2 + z^2 )^1/2 dv

= ∫∫∫ x . x^2 .sin Φ dΦ dθ dx

where lower limits and upper limits are ( 0 , 2 ) , ( 0 , 2 π ) , ( 0 , π ) .

= ∫ x^3 . dx ∫ dθ ∫ sin Φ dΦ

= 2^4 / 4 * 2 π * 2

= 4 * 2 π * 2

= 8 π * 2

= 16 π

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The surface area of the pyramid is given by -

\($A = lw\;+l\sqrt{(\frac{w}{2})^{2} +h^{2} } +w\sqrt{(\frac{l}{2})^{2} +h^{2} }\).

The pyramid is not given. So, we will discuss some important points regarding the pyramids along with its surface area.

The surface area of the pyramid is given by -

\($A = lw\;+l\sqrt{(\frac{w}{2})^{2} +h^{2} } +w\sqrt{(\frac{l}{2})^{2} +h^{2} }\)

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Answer:

2 89/100

Step-by-step explanation:

its 289/100 as an improper fraction

Keep in mind that 0.89 means 89/100.

Now apply the whole number 2.

We get 2_(89/100).