Help and explain why

Answer:

d

Step-by-step explanation:

the answer is d because we learned about this everyday

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

Explanation:

Check out the diagram below to see what's going on.

Use the pythagorean theorem to find b

\(a^2 + b^2 = c^2\\\\b = \sqrt{c^2 - a^2}\\\\b = \sqrt{9^2 - (8.2)^2}\\\\b = \sqrt{81 - 67.24}\\\\b = \sqrt{13.76}\\\\b \approx 3.709 447\\\\b \approx 3.7\\\\\)

The length is roughly 3.7 feet.

Answer:

Step-by-step explanation:

\(log_{10}(2000xy)-(log_{10}x})(log_{10}y)=4\\\\log_{10}(2000(xy))-log_{10}(xy)=4\\\\log_{10}(2000)+log_{10}(xy)-log_{10}(xy)=4\\\\log_{10}(2(1000)=4\\\\log_{10}2+log_{10}(1000)=4\\\\log_{10}2+log_{10}(10^3)=4\\\\log_{10}2+3log_{10}(10)=4\\\\log_{10}2\approx0.3\\\\Hence,\\\\log_{10}2+3\neq 4\)

\(log_{10}(2yz)-(log_{10}y)(log_{10}z)=1\\\\log_{10}(2(yz))-log_{10}(yz)=1\\\\log_{10}2+log_{10}(yz)-log_{10}(yz)=1\\\\log_{10}2\neq 1\)

\(log_{10}(zx)-(log_{10}z)(log_{10}x)=0\\\\log_{10}(zx)-log_{10}(zx)=0\\\\0\equiv0\)

Answer:

the correct answer is option ( B )

The probability of drawing a white marble if we draw marbles out 25 times with replacement is 1/5.

We know that there are 5 marbles in the bag which are:

White, yellow, pink, blue, and red.

We also know that there is an equal probability of getting a marble.

Probability formula: P(E) = Favourable events/Total events

So, the probability of drawing white marble:

P(E) = Favourable events/Total events

P(E) = 5/25

P(E) = 1/5

Therefore, the probability of drawing a white marble if we draw marbles out 25 times with replacement is 1/5.

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The mean displacement of the dart throws is calculated to be 3.149 cm. The error, standard deviation, and uncertainty are determined as 4.588 cm, 5.469 cm, and 1.341 cm respectively. The measurement is imprecise due to the large standard deviation and uncertainty.

To calculate the mean displacement, error, standard deviation, and uncertainty, we use the given list of 15 numbers. We sum up the values and divide by the number of measurements to obtain the mean, which is 3.149 cm. The error is calculated by taking the absolute difference between the largest and smallest values, resulting in 4.588 cm. The standard deviation measures the spread of the data points around the mean and is found to be 5.469 cm. The uncertainty is calculated as the standard deviation divided by the square root of the number of measurements, resulting in 1.341 cm.
The measurement is considered imprecise due to the large standard deviation and uncertainty. The data points are widely spread around the mean, indicating inconsistency and variability in the dart throws. However, without a known target value or true value, it is not possible to determine the accuracy of the measurement.
To improve precision and accuracy, several steps can be taken. Firstly, increasing the number of measurements would help in reducing the uncertainty and providing a more reliable estimate of the mean. Additionally, ensuring a consistent throwing technique, such as maintaining the same distance, posture, and throwing force, would help reduce variability in the measurements. Calibration of the measuring device and checking for any systematic errors would also contribute to improving accuracy. Finally, identifying and minimizing any sources of error, such as air drafts or unstable target setup, would lead to more precise and accurate measurements.
By implementing these improvements, a new set of measurements can be obtained. The mean, error, standard deviation, and uncertainty can then be recalculated to assess the impact of the changes on the precision and accuracy of the measurements.

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Answer:

-1=(5+x)/6

mulitply both sides by 6

-6=5+x

subtract both sides by 5

-11=x

The equation of the line would be y = (-3/4)x + 5.

What is the slope-point form of the line?

For the line having slope "m" and the point (x1, y1) the equation of the line passing through the point (x1, y1) having slope 'm' would be

                      y - y1 = m(x - x1)

The given equation is \(y=-\frac{3}{4}x-17\)

The required line is parallel to the given line.

and we know that the slopes of the parallel lines are equal so the slope of the required line would be m = -3/4

And the required line passes through (8, -1)

so by using slope - point form of the line,

      y - (-1) = (-3/4)(x - 8)

      y + 1 = (-3/4)x - (-3/4)8

       y + 1 = (-3/4)x + 24/4

       y = (-3/4)x + (12/2 - 1)

       y = (-3/4)x + 5

Hence, the equation of the line would be y = (-3/4)x + 5.

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The business cycle is a recurring pattern of economic expansion and contraction that occurs in economies over time. Each business cycle typically consists of four phases: expansion, peak, contraction, and trough.

The peak is the highest point of economic activity within a business cycle. It marks the end of the expansion phase and the beginning of the contraction phase. During this phase, economic indicators, such as GDP, employment, and consumer spending, reach their highest levels.

The peak is indeed a part of the business cycle. It represents the phase of maximum economic activity and is characterized by various indicators reaching their highest points. This phase is followed by the contraction phase, where economic activity slows down. Therefore, the peak is a crucial element in understanding and analyzing business cycles.

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The percentage change from 6 to 27 is approximately 350.00%.

To calculate the percentage change, we can use the following formula:

Percentage Change = ((New Value - Old Value) / Old Value) * 100

Given:

Old Value (X) = 6

New Value = 27

Using the formula, we have:

Percentage Change = ((27 - 6) / 6) * 100

Calculating this expression, we find:

Percentage Change ≈ 350.00

Rounding the percentage change to two decimal places, we have:

Percentage Change ≈ 350.00%

Therefore, the percentage change from 6 to 27 is approximately 350.00%.

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The percentage change from 6 to 27 is approximately 350.00%.

To calculate the percentage change, we can use the following formula:

Percentage Change = ((New Value - Old Value) / Old Value) * 100

We have:

Old Value (X) = 6

New Value = 27

Using the formula, we have:

Percentage Change = ((27 - 6) / 6) * 100

Calculating this expression, we find:

Percentage Change ≈ 350.00

Rounding the percentage change to two decimal places, we have:

Percentage Change ≈ 350.00%

Therefore, the percentage change from 6 to 27 is approximately 350.00%.

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Answer:

You mean thousandths?

It’s 1.891

Step-by-step explanation:

The thousandths place is the 3rd digit to the right of the decimal. 5-4=1

Answer:

1.891

Step-by-step explanation:

Look to picture for further explanation

Hope this helps :)  

Solution :-

Here we have been given with two equations :

¤ From Equation No.1 :

>> x = -5y

¤ In Equation No.2 :

Substituting the value of x which we got above as -5y here.

>> 3y + 2(-5y) = -21

>> 3y + 2 × (-5y) = -21

>> 3y - 10y = -21

>> -7y = -21

>> 7y = 21

>> y = 21 / 7

>> y = 3

¤ Finding out value of x :

>> x = -5y

>> x = -5(3)

>> x = -15

The z-values for the given situations are approximate:

a. The area to the left of z is 0.1827. z = -0.90

b. The area between −z and z is 0.9830. z = 2.17

c. The area between −z and z is 0.2148. z = 0.85

d. The area to the left of z is 0.9997. z = 3.49

e. The area to the right of z is 0.6847. z= -0.48

a. For an area of 0.1827 to the left of z, the corresponding z-value can be found using a standard normal distribution table or a statistical calculator. The z-value is approximately -0.90.

b. To find the z-value for an area between -z and z equal to 0.9830, we need to find the value that corresponds to (1 - 0.9830)/2 = 0.0085 in the upper tail of the standard normal distribution. Using the table or calculator, the z-value is approximately 2.17.

c. Similarly, for an area between -z and z equal to 0.2148, we find the value that corresponds to (1 - 0.2148)/2 = 0.3926 in the upper tail. The z-value is approximately 0.85.

d. For an area of 0.9997 to the left of z, we find the value that corresponds to 0.9997 in the upper tail. The z-value is approximately 3.49.

e. To find the z-value for an area to the right of z equal to 0.6847, we find the value that corresponds to 1 - 0.6847 = 0.3153 in the upper tail. The z-value is approximately -0.48.

In summary, the z-values for the given situations are approximate:

a. -0.90

b. 2.17

c. 0.85

d. 3.49

e. -0.48

These values can be used to determine the corresponding percentiles or probabilities for the standard normal distribution. The values are typically found using standard normal distribution tables or statistical calculators that provide the cumulative probability distribution function (CDF) for the standard normal distribution.

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9514 1404 393

Answer:

  more than half are being used

Step-by-step explanation:

Perhaps easiest to understand is the most straightforward: figure the total number of seats and the number of seats being used. Check to see if that is more than half.

The 1 first-class carriage has usage of ...

  (3/8)(64 seats) = 24 seats.

The 6 standard carriages have usage of ...

  (7/13)(6 · 78 seats) = 252 seats.

The total number of seats used is ...

  24 + 252 = 276 . . . . seats used

__

The total number of seats on the train is ...

  1·64 +6·78 = 532 . . . . seats on the train

Half of the seats on the train will be ...

  532/2 = 266 seats . . . . half the seats

The 276 used seats are more than half of the total number. More than half the seats are being used.

_____

Alternate solution

Another way to look at this is to compare utilization to 1/2 in each carriage class.

  In first class 1/2 -3/8 = 1/8 of 64 seats = 8 seats fewer than 1/2 the seats are being used.

  In standard class, 7/13 -1/2 = 14/26 -13/26 = 1/26 of 78 seats = 3 seats more than 1/2 the seats are being used. There are 6 standard class carriages, so 6·3 = 18 more than half the seats in the standard-class carriages are being used.

This number is 10 more than the 8 under-utilized seats in first class, so more than half the train seats are being used.

Using the information provided, it appears that your neighbor will not save money by picking up the soil himself as its total cost is $103.86 as opposed to cost of delivery $30.

Here is a detailed breakdown of the calculations and assumptions made:

The area of the yard is estimated to be around 7,200 sq.ft. Assuming a 4 inch layer of topsoil, this requires 4 cubic yards (1 cubic yard = 27 cubic feet).

The cost of the soil delivery is $30 per truckload (up to 18 cubic yards). So the delivery cost for 4 cubic yards of soil would be $30.

The cost of topsoil per cubic yard is $18. Thus, the total cost of the topsoil is $72.

The weight of topsoil is 2000 pounds per cubic yard, so the total weight of the soil is 8,000 pounds (4 cubic yards x 2000 pounds).

The pickup truck's payload capacity is 1800 pounds, so the truck can only transport 1/4 of the total weight of the soil (1800/8000 = 0.225). Thus, it would require 4 trips to transport the soil, and the total trip distance is 36 miles (9 miles x 4 trips).

The truck gets 17 miles per gallon, so it would require 2.1 gallons of gas for each trip (36 miles/17 mpg = 2.12). The total amount of gas needed for the 4 trips is 8.4 gallons (2.1 gallons x 4 trips). The cost of gas per gallon is assumed to be $3.79, so the total cost of gas for the 4 trips is $31.86.

Thus, the total cost of picking up the soil himself is $31.86 + $72 = $103.86. This is higher than the cost of delivery which is only $30, so it would be better to pay for delivery.

To conclude, your neighbor will not save money by picking up the soil himself, and it is recommended that he pays for delivery.

Note: The question is incomplete. The complete question probably is: He has decided to remove all the old sod (grass), bring in a new 4 inch layer of topsoil, install new in-ground sprinklers, and reseed the lawn. He seems to think that he'll be able to save money by hauling loads of topsoil from the store himself in his pickup truck, rather than paying for delivery, but I don't think he's right. You're going to help us settle this. Here is (most of) the information you asked for:

Using this information, figure out whether my neighbor will save money by picking up the soil himself. Use the results of your calculations to guide your decision: would you recommend that my neighbor pick up the soil himself, or pay for delivery? Detail all your assumptions and calculations, and clearly write out your final conclusions.

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The term that is not possible in the domain of a sequence is:

-5

The domain of a function is the set that contains all possible input values for the function. For a sequence, the domain is the set that contains all the indexed of the terms, starting at 0 and going until the nth term.

For example, suppose we have the following sequence: 3, 5, 7, ...

From what was explained above, which also can be visualized with the example, an index term of a sequence cannot be negative, hence the term that is not possible in the domain of a sequence is:

-5.

Which is the only negative number of the options.

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There are 15 positive integers that can be expressed as a product of two or more of the prime numbers 5, 7, 11, and 13 if no one product is to include the same prime factor more than once.The prime numbers are:5, 7, 11, 13Product of two of the prime numbers are:35, 55, 65, 77, 85, 91, 115, 143, 165, 385

Product of three of the prime numbers is:385 Product of all the prime numbers is: 5005There are 15 positive integers that can be expressed as a product of two or more of the prime numbers 5, 7, 11, and 13 if no one product is to include the same prime factor more than once. Prime numbers are numbers that are only divisible by 1 and itself. 5, 7, 11, and 13 are prime numbers.

The question is asking to find the number of positive integers that can be expressed as a product of two or more of these prime numbers without including the same prime factor more than once. The products of two prime numbers are: 5 x 7 = 35, 5 x 11 = 55, 5 x 13 = 65, 7 x 11 = 77, 7 x 13 = 91, 11 x 13 = 143. There are six of these products. The products of three prime numbers is 5 x 7 x 11 = 385. There is only one of this product. There are fifteen possible positive integers that can be expressed as a product of two or more of the prime numbers 5, 7, 11, and 13 if no one product is to include the same prime factor more than once.

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The probability of receiving exactly 6 purchase orders in 5 minutes is 0.104, or about 10.4%.

The mean of the Poisson distribution is λ, which represents the average number of events in a given time period. In this case, the company receives an average of 0.8 purchase orders per minute, so the mean number of purchase orders in 5 minutes would be:

λ = (0.8 orders/min) x (5 min) = 4 orders

Thus, the Poisson distribution for the number of purchase orders in 5 minutes has a mean of 4. To calculate the probability of receiving 6 purchase orders in 5 minutes, we use the Poisson probability formula:

\(P(X = 6) = (e^(-λ) * λ^6) / 6!\)

where X is the random variable representing the number of purchase orders in 5 minutes.

Plugging in the values, we get:

\(P(X = 6) = (e^(-4) * 4^6) / 6! = 0.104\)

Therefore, the probability of receiving exactly 6 purchase orders in 5 minutes is 0.104, or about 10.4%.

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The lengths that could be the length of the third side are any values less than 12 feet, the value of 12 feet itself, and any values greater than 2 feet.

To determine which lengths could be the third side of the triangle, we can use the triangle inequality theorem. According to the theorem, the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

Given that the lengths of the two sides are 5 feet and 7 feet, we can evaluate the following possibilities for the length of the third side:

The third side is less than the sum of the two given sides: If the third side is less than 5 + 7 = 12 feet, it can be a valid length.

The third side is equal to the sum of the two given sides: If the third side is equal to 5 + 7 = 12 feet, it can be a valid length, forming a degenerate triangle.

The third side is greater than the difference between the lengths of the two given sides: If the third side is greater than |5 - 7| = 2 feet, it can be a valid length.

Based on these conditions, the possible lengths for the third side are:

Less than 12 feet

Equal to 12 feet

Greater than 2 feet

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The sample size for estimate the proportion of families in a certain area that are living below the poverty level is equals to the 318.75.

The standard error is a statistic term that is the standard deviation of its sampling distribution or an estimate of that standard deviation. In case of sample mean, it is called the standard error of the mean. Formula of standard mean is

\( SE =\sqrt{ \frac{\hat p (1 - \hat p)}{n}} \)

where, n--> sample size

We have a simple random sample for estimate the proportion of families,

Sample proportion = 0.15

Standard error = 0.02

We have to determine the sample size for the standard error of the estimate is .02.

Here, SE = 0.02, \hat p = 0.15

Using the standard score formula,

\( 0.02 =\sqrt{ \frac{0.15 (1 - 0.15)}{n}} \)

Squaring both sides

\( 0.02² = \frac{0.15 ×0.85 }{n} \)

\( 0.0004 = \frac{0.1275 }{n} \)

=> n = 318.75

Hence, required value is 318.75.

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Kelsey is traveling at a speed of 14 mph, while Julia is traveling at a speed of 23 mph.

Let's denote the speed of Kelsey as x mph. Since Julia travels 9 mph faster than Kelsey, her speed can be expressed as (x + 9) mph. In 7 hours, the total distance covered by both Kelsey and Julia is 259 miles.

Using the formula distance = speed × time, we can write the following equation for Kelsey:

Distance traveled by Kelsey = Kelsey's speed × time

= x mph × 7 hours

= 7x miles

Similarly, for Julia:

Distance traveled by Julia = Julia's speed × time

= (x + 9) mph × 7 hours

= 7(x + 9) miles

According to the problem, the total distance covered is 259 miles, so we can set up the equation:

Distance traveled by Kelsey + Distance traveled by Julia = Total distance

7x + 7(x + 9) = 259

Simplifying the equation:

7x + 7x + 63 = 259

14x = 196

x = 14

Therefore, Kelsey's speed is 14 mph, and Julia's speed is (14 + 9) mph = 23 mph.

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To translate triangle A to B, left 3, down 2 and to translate triangle B to A, up 2, right 3

There are two triangles in the graph

Consider the triangle on top as triangle A and the triangle on bottom as triangle B

The translation is the process of the changing the coordinates of the given shapes in the graph. The shape and size will be same only the coordinates will vary

Consider the triangle A

If we want triangle A to translate to triangle B

First translate 3 units to left and translate 2 units down

Now consider the triangle B

If we want to translate triangle B to triangle B

First translate 2 units up and translate 3 units right

Hence, to translate triangle A to B, left 3, down 2 and to translate triangle B to A, up 2, right 3

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So the base of the ladder is moving away from the wall at a rate of 3/4 feet per minute when the top of the ladder is 4 feet from the ground.

We can use the Pythagorean Theorem to relate the ladder's length to the distance it is from the wall. Let's call the distance from the wall "x", and the length of the ladder "y". Then:

x^2 + y^2 = 5^2

We can take the derivative with respect to time of both sides of this equation, using implicit differentiation:

2x(dx/dt) + 2y(dy/dt) = 0

Now we can plug in the values we know and solve for the rate at which the base of the ladder is moving away from the wall (which is the same as the rate at which x is increasing):

x = sqrt(5^2 - 4^2) = 3

y = 4

dx/dt = 1 (given)

dy/dt = ?

Plugging in these values, we get:

2(3)(1) + 2(4)(dy/dt) = 0

Simplifying:

6 + 8(dy/dt) = 0

Solving for dy/dt:

dy/dt = -6/8 = -3/4

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The null hypothesis for this test is that the mean ECLSE test score for the university is equal to 1200. The alternative hypothesis is that the mean is not equal to 1200.

To perform the test, you will need to calculate the t-statistic and the p-value. The t-statistic is calculated by:

t = (sample mean - hypothesized mean) / (sample standard deviation/sqrt (sample size))

In this case, the sample mean is 1180, the hypothesized mean is 1200, the sample standard deviation is 100, and the sample size is 100. Plugging these values into the equation gives:

t = (1180 - 1200) / (100 / sqrt(100)) = -20 / 10 = -2

Next, you will need to calculate the p-value. The p-value is the probability of observing a t-statistic as extreme as the one calculated, given that the null hypothesis is true.

To calculate the p-value, you will need to use a t-distribution table or a software package to find the t-critical value for a one-tailed test with 99 degrees of freedom (since you have a sample size of 100) and a significance level of 0.05. The t-critical value is the value that defines the rejection region for the test. If the t-statistic falls in the rejection region, you can reject the null hypothesis.

If the p-value is less than the significance level of 0.05, you can reject the null hypothesis and conclude that the mean ECLSE test score for the university is not equal to 1200 at the 95% significance level. If the p-value is greater than or equal to 0.05, you cannot reject the null hypothesis and cannot conclude that the mean is different from 1200.

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Probability helps us to know the chances of an event occurring. The probability that any given customer will buy coffee is 2/5. The correct option is A.

Probability helps us to know the chances of an event occurring. The sum of all the probabilities of an event is always equal to 1. The formula for probability is given as,

\(\rm Probability=\dfrac{Desired\ Outcomes}{Total\ Number\ of\ outcomes\ possible}\)

Given that sells black tea, green tea, herbal tea, hot coffee, and iced coffee. Also, An equal number of her customers like each of these drinks. Therefore, the probability that any given customer will buy coffee is,

Probability = Number of coffee available / Total number of coffee

                  = 2/5

Hence, the probability that any given customer will buy coffee is 2/5.

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Answer:

4.1148

Step-by-step explanation:

Answer:

5 : 7

Step-by-step explanation:

groom's side: 40

bride's side: 56

ratio groom to bride = 40/56 = 20/28 = 10/14 = 5/7

Answer: 5 : 7

The correct answer is option D. No, because the sample sizes are not large enough to assume the distribution of the difference in sample means is approximately normal.Researchers investigated whether there is a difference between two headache medications, R and S.

Researchers measured the mean times required to obtain relief from a headache for patients taking one of the medications. From a random sample of 75 people with chronic headaches, 38 were randomly assigned to medication R and the remaining 37 were assigned to medication S. The time, in minutes, until each person experienced relief from a headache was recorded. The sample mean times were calculated for each medication.To construct a confidence interval, we require that some conditions are satisfied. The assumptions that should be met for inference with a confidence interval for the difference in population means are as follows:The data is independent;The data in each group should be roughly normally distributed;Both groups have the same variance, and each group should have a large enough sample size so that the central limit theorem (CLT) holds. The CLT holds for the difference in the sample means since both samples are taken from a population that is normally distributed. We can also assume that the sample size is large enough to use the t-distribution since each sample has more than 30 observations. As a result, all of the conditions have been met. As a result, we may employ a t-distribution to make inferences about the population difference between the two headache medications.

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