400 invested at 4​% compounded after a period of 2 years

Answer:

√33 ≈ 5.7

Step-by-step explanation:

The length of the bottom diagonal is given by pythagoras, let's call it d:

\(d =\sqrt{5^2+2^2}\)

Then, the length of the diagonal through the box is also given by pythagoras as:

\(\sqrt{d^2 + 2^2}\)

In total, that is:

\(\sqrt{5^2 + 2^2 + 2^2} = \sqrt{33} \approx 5.7\)

a. About 50% of the students scored less than 78.

b. Approximately 68% of the students scored between 75 and 78.

c. Approximately 95% of the students scored between 72 and 81.

d. Approximately 99.7% of the students scored between 69 and 75.

a) The normal curve is symmetrical, meaning that the area to the left of the mean is equal to the area to the right of the mean. Since the mean score is 78, 50% of the students scored above 78 and 50% scored below 78.

b) To apply the Empirical Rule, we will assume that 68% of the data falls within one standard deviation of the mean, which in this case is 3 points. So, 68% of the students scored between 75 and 81.

c) The percentage of students who scored between 72 and 81 can be found by subtracting the area to the left of 72 from the area to the left of 81. Using the Empirical Rule, we know that 95% of the observations are within two standard deviations of the mean, so the area between 72 and 81 is equal to 95%.

d) The percentage of students who scored between 69 and 75 can be found by subtracting the area to the left of 69 from the area to the left of 75. Using the Empirical Rule, we know that 99.7% of the observations are within three standard deviations of the mean, so the area between 69 and 75 is equal to approximately 99.7%.

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Answer:

(a) The probability that X is at most 30 is 0.9726.

(b) The probability that X is less than 30 is 0.9554.

(c) The probability that X is between 15 and 25 (inclusive) is 0.7406.

Step-by-step explanation:

We are given that 11% of all steel shafts produced by a certain process are nonconforming but can be reworked. A random sample of 200 shafts is taken.

Let X = the number among these that are nonconforming and can be reworked

The above situation can be represented through binomial distribution such that X ~ Binom(n = 200, p = 0.11).

Here the probability of success is 11% that this much % of all steel shafts produced by a certain process are nonconforming but can be reworked.

Now, here to calculate the probability we will use normal approximation because the sample size if very large(i.e. greater than 30).

So, the new mean of X, \(\mu\) = \(n \times p\) = \(200 \times 0.11\) = 22

and the new standard deviation of X, \(\sigma\) = \(\sqrt{n \times p \times (1-p)}\)

                                                                  = \(\sqrt{200 \times 0.11 \times (1-0.11)}\)

                                                                  = 4.42

So, X ~ Normal(\(\mu =22, \sigma^{2} = 4.42^{2}\))

(a) The probability that X is at most 30 is given by = P(X < 30.5)  {using continuity correction}

        P(X < 30.5) = P( \(\frac{X-\mu}{\sigma}\) < \(\frac{30.5-22}{4.42}\) ) = P(Z < 1.92) = 0.9726

The above probability is calculated by looking at the value of x = 1.92 in the z table which has an area of 0.9726.

(b) The probability that X is less than 30 is given by = P(X \(\leq\) 29.5)    {using continuity correction}

        P(X \(\leq\) 29.5) = P( \(\frac{X-\mu}{\sigma}\) \(\leq\) \(\frac{29.5-22}{4.42}\) ) = P(Z \(\leq\) 1.70) = 0.9554

The above probability is calculated by looking at the value of x = 1.70 in the z table which has an area of 0.9554.

(c) The probability that X is between 15 and 25 (inclusive) is given by = P(15 \(\leq\) X \(\leq\) 25) = P(X < 25.5) - P(X \(\leq\) 14.5)   {using continuity correction}

       P(X < 25.5) = P( \(\frac{X-\mu}{\sigma}\) < \(\frac{25.5-22}{4.42}\) ) = P(Z < 0.79) = 0.7852

       P(X \(\leq\) 14.5) = P( \(\frac{X-\mu}{\sigma}\) \(\leq\) \(\frac{14.5-22}{4.42}\) ) = P(Z \(\leq\) -1.70) = 1 - P(Z < 1.70)

                                                          = 1 - 0.9554 = 0.0446

The above probability is calculated by looking at the value of x = 0.79 and x = 1.70 in the z table which has an area of 0.7852 and 0.9554.

Therefore, P(15 \(\leq\) X \(\leq\) 25) = 0.7852 - 0.0446 = 0.7406.

Answer:

36km hr

Step-by-step explanation:

The mean of the sampling distribution is given as follows:

37.827 millimeters.

The mean of the sampling distribution is obtained using the Central Limit Theorem.

The mean of the sampling distribution is the same as the population mean, hence it is given as follows:

37.827 millimeters.

(on the problem, we are given the population mean).

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Answer:

21873600

Step-by-step explanation:

brainlest

Answer:

You can buy exactly 4 fish.

I hope I'm right.

Approximately 3.6.

Hope this helps

Answer:

384 cm

Step-by-step explanation:

Perimeter is the sum of all external sides. (do not mix this up with area. Perimeter is the easy one) :)

There are 4 external sides.

Top = bottom = 132 cm

Left = Right = 60 cm

Add all 4 sides:

2(132) + 2(60)

264 + 120 = 384 cm

Half the deck is red so you have. 1/2 chance of picking red each time.

Picking red both times would be 1/2 x 1/2 = 1/4

The answer is 1/4

The  probability of drawing a red card, placing it back in the deck, and drawing another red card is 0.25 or \(\bold{\frac{1}{4}}\).

Given to us:

Eric is randomly drawing cards from a deck of 52.

Also,  Eric first draws a red card, places it back in the deck, meaning this is case of probability with replacement (outcomes are returned back to the sample space again).

So, the both the events are independent of each other, therefore the probability for second event will be same as the first, as the sample size and the desired outcome are same.

Probability for first event

                  \(=\dfrac{Desired\ outcome}{Total\ number\ of\ samples}\\\\=\dfrac{26}{52} \\\\=\dfrac{1}{2} = 0.5\)

The probability of drawing a red card, placing it back in the deck, and drawing another red card

= Probability for first event x Probability for second event

= 0.5 x 0.5

= 0.25

Hence, the  probability of drawing a red card, placing it back in the deck, and drawing another red card is 0.25 or \(\bold{\frac{1}{4}}\).

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Hyperbolic tan x is verified to equal to  

To verify the identity using the definitions of the hyperbolic functions, we start with the definition of hyperbolic tangent:

tanh x = sinh x / coxh x =  (e^x - e^-x) / (e^x + e^-x)

We can simplify this expression by multiplying the numerator and denominator by e^x:

tanh x = (e^x - e^-x) / (e^x + e^-x) * (e^x / e^x)

tanh x = (e^2x - 1) / (e^2x + 1)

We can see that this expression is equivalent to the given identity

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Answer:

The answer to this question is B

Step-by-step explanation:

Answer:

x = 6

Step-by-step explanation:

First, we need to cross multiply on both sides, which gives us:

9 * (5x - 6) = 27 * (2 + x)

45x - 54 = 54 + 27x

Now, we want to isolate x on either side.

We can substract 54 from both sides:

(45x - 54 = 54 + 27x) - 54

45x - 108 = 27x

We then subtract 45 from both sides:

(45x - 108 = 27x) - 45

-108 = -18x

Finally, we divide both sides by -18:

(-108 = -18x) / -18

6 = x

Answer:

a = 300

\(5 \sqrt{12} = \sqrt{25} \sqrt{12} = \sqrt{25 \times 12} = \sqrt{300} \)

Answer:

\(x + 59 + x + 51 = 180 - 84 \\ 2x + 110 = 96 \\ 2x = - 14 \\ x = - 7\)

Answer:

0 more lol

Step-by-step explanation:

The length of EB is approximately 14.6 units when rounded to the nearest tenth.

To find the length of EB, we can use the property of similar triangles in this diagram. By looking at triangle DFE and triangle CFB, we can see that they are similar triangles.

Using the similarity ratio, we can set up the proportion:

DF / CF = DE / EB

Plugging in the given values, we have:

13.1 / 10.9 = 17.5 / EB

To find EB, we can cross-multiply and solve for EB:

13.1 * EB = 10.9 * 17.5

EB = (10.9 * 17.5) / 13.1

EB ≈ 14.6

Therefore, the length of EB is approximately 14.6 units when rounded to the nearest tenth.

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Answer:

Its an function

Step-by-step explanation:

Since there is one value of y for every value of x

x

Answer: They resold them for $30 more than the original price.

Answer: 37.5%

Step-by-step explanation:

$80 - $50 = $30,

$30/$80 = 0.375 > 37.5%

Answer: 566.55 US dollars

Step-by-step explanation: i think, please give 5 stars

Answer:

\(\mathbf{V = \dfrac{16}{3}}\)

Step-by-step explanation:

From the information given:

A = (4,0,0)   B = (0,4,0)    C = (0,0,1)   D = (4,4,1)

\(\overline{ AB}\) = (0,4,0) - (4,0,0) = (-4, 4, 0)

\(\overline{ BC} =\) (0,0,1) - (0,4,0) = (0, -4, 1)

\(\overline{ CD}\) = (4,4,1) - (0,0,1) = (4, 4, 0)

The Volume of the tetrahedron \(V = \dfrac{1}{6} \bigg| AB \times BC \times CD \bigg|\)

The Volume of the tetrahedron \(V = \dfrac{1}{6} \left\begin{vmatrix}-4,&4&0\\0,&-4&1\\4&4&0\end{vmatrix}\right\)

\(V = \dfrac{1}{6}\bigg [ -4(-4 *0 - 1*4) -4(0*0-1*4) +0(0*4--4*4) \bigg ]\)

\(V = \dfrac{1}{6}\bigg [ -4(0 - 4) -4(0-4) +0(0+16) \bigg ]\)

\(V = \dfrac{1}{6}\bigg [ 16 + 16 +0 \bigg ]\)

\(V = \dfrac{1}{6}\bigg [ 32 \bigg ]\)

\(\mathbf{V = \dfrac{16}{3}}\)

The predicted likelihood that Nestor will win at least six of the upcoming races is therefore 90.1%, which is closest to the correct response of -1%.

The likelihood or chance that a specific occurrence or outcome will occur is quantified by probability. It is represented by a number between 0 and 1, with 0 denoting an impossibility and 1 denoting a certainty. For instance, there are two equally likely outcomes (heads or tails), but only one of them is heads, hence the probability of flipping a fair coin and obtaining heads is 0.5 or 50%. By dividing the number of favorable outcomes by the total number of possible outcomes, one can calculate probability.

given

We can see that Nestor won a medal in 6 out of the 10 trials by counting the number of victories.

We can use the binomial distribution with parameters n=10 (number of trials) and p=0.79 to calculate the likelihood that this will occur (probability of success).

The following calculation can be used to determine the likelihood of at least 6 successes in 10 trials:

P(X>=6) = 1 - P(X<=5)

Using a calculator for the binomial distribution, we obtain:

P(X>=6) = 90.1%

The predicted likelihood that Nestor will win at least six of the upcoming races is therefore 90.1%, which is closest to the correct response of -1%.

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Answer: 39/2 or 19 1/2

Step-by-step explanation:

Convert a mixed number 2 1/6 to a improper fraction:

2 1/6 = 2 1/6 = 2 · 6 + 1/6 = 12 + 1/6 = 13/6

To find a new numerator:

1. Multiply the whole number 2 by the denominator 6. Whole number 2 equally 2 * 6/6 = 12/6

2. Add the answer from previous step 12 to the numerator 1. New numerator is 12 + 1 = 13

3. Write a previous answer (new numerator 13) over the denominator 6.

Two and one sixth is thirteen sixths

Multiply: 9 * 13/6 = 9 · 13/1 · 6 = 117/6 = 39 · 3/2 · 3 = 39/2

Multiply both numerators and denominators. Result fraction keep to lowest possible denominator GCD(117, 6) = 3. In the following intermediate step, cancel by a common factor of 3 gives 39/2.

In other words - nine multiplied by thirteen sixths is thirty-nine halves.

Answer:

Yes it is rational

Step-by-step explanation:

The square root of 900 is a rational number if 900 is a perfect square. It is an irrational number if it is not a perfect square. Since 900 is a perfect square, it is rational number.

The equation of the line q that is perpendicular to line p is  y = - 3 / 5 x - 9.

The equation of a line can be represented in slope intercept form as follows:

y = mx + b

where

Therefore, p has an equation of y = 5 / 3 x - 4 Line q includes the point (-10,-3) and is perpendicular to line p.  The equation of line q can be found as follows:

The product of the slope of perpendicular lines is equals to negative one.

Therefore, let's find the slope of line q.

m₁m₂ = -1

5 / 3m₂ = - 1

m₂ = - 3 / 5

Hence, the equation of line q is y = - 3 / 5x + b.

Let's find the y-intercept using (-10, -3)

-3 = - 3 / 5(-10) + b

-3 = 6 + b

-3  - 6 = b

b = -9

Therefore, the equation of line q is y = - 3 / 5 x - 9

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The appropriate hypotheses for this test are: H0: There is no difference in the distribution of responses. Ha: There is a difference in the distribution of responses.

The chosen hypotheses are based on the objective of the investigation, which is to determine if there is convincing evidence that the distribution of responses about eating the potato salad differs between employees who are sick and those who are not sick.

The null hypothesis (H0) assumes that there is no difference in the distribution of responses about eating the potato salad between the sick and non-sick employees. This means that the proportion of employees who ate the potato salad would be the same in both groups, and any observed difference in the distribution of responses is due to random chance or factors unrelated to being sick or not sick.

On the other hand, the alternative hypothesis (Ha) proposes that there is a difference in the distribution of responses about eating the potato salad between the sick and non-sick employees. This suggests that the proportion of employees who ate the potato salad would be significantly different in the two groups, indicating a possible association between consuming the potato salad and getting sick.

By formulating these hypotheses, the investigation aims to evaluate whether the data provides convincing evidence to reject the null hypothesis in favor of the alternative hypothesis, indicating a meaningful relationship between eating the potato salad and falling sick.

Therefore, the correct answer is:

H0: There is no difference in the distribution of responses about eating the potato salad among those who are and are not sick.

Ha: There is a difference in the distribution of responses about eating the potato salad among those who are and are not sick.

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Answer: Total expenses if 3 widgets are produced is $11,018.00

Step-by-step explanation: The variable cost per unit is given by the coefficient of q in the expense function. In this case, the variable cost is $6.00 per widget. To find the variable costs to produce 2 widgets, we simply multiply the variable cost per unit by the number of units produced: Variable costs for 2 widgets = 2 x $6.00 = $12.00 Therefore, the variable costs to produce 2 widgets is $12.00. To find the variable costs to produce q widgets, we simply multiply the variable cost per unit by the number of units produced: Variable costs for q widgets = q x $6.00 = $6q Therefore, the variable costs to produce q widgets is $6q. To find the total expenses if 3 widgets are produced, we can use the expense function and substitute q = 3:E = 6.00 q + 11,000

E = 6.00 (3) + 11,000

E = 18.00 + 11,000

E = 11,018.00 Therefore, the total expenses if 3 widgets are produced is $11,018.00.

Answer:

The percentage of 18 people out of 50 is 36 %

Step-by-step explanation:

The percentage refers to the per hundred or hundredths and is ended with the symbol %.  By dividing two amounts, ratios and percentages are both used to compare the two amounts.

so,

Therefore the percentage of 18 people out of 50 people is 36 %.

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