f(x) = 3x + 5
g(x) = 4x² - 2
h(x)=x²-3x+1
Find f(x) - g(x) — h(x).

(i) The probability that the bulb that lang selects will last exactly 9950 hours is 0.3085.

(ii) The probability that the bulb that lang selects will last at most 9950 hours is 0.5

(iii) The probability that the bulb that lang selects will last at least 9950 hours is 0.6915.

(iv) The probability that the bulb that lang selects will last less than 9000 hours or more than 11,500 hours is 0.0668

(v) The probability that the bulb that lang selected will last between 9000 hours and 11,000 hours, inclusively is  0.6826.

(vi) The life length represents the 95th percentile is 11,645

The lifespan of the Lights of America light bulb is normally distributed, with a mean of 10,000 hours and a standard deviation of 1000 hours. This means that the majority of bulbs will last around 10,000 hours, but there will be some that last longer or shorter than this.

(i) To find the probability that the bulb selected by Lang will last exactly 9950 hours, we need to use the normal distribution formula. We know that the mean is 10,000 hours and the standard deviation is 1000 hours. Using these values, we can calculate the z-score (standardized value) for 9950 hours.

z = (9950 - 10000) / 1000 = -0.5

Using a standard normal distribution table or calculator, we can find the probability of a z-score of -0.5, which is 0.3085. Therefore, the probability that the bulb will last exactly 9950 hours is 0.3085.

(ii) To find the probability that the bulb will last at most 9950 hours, we need to find the area under the normal curve to the left of 9950 hours. We can use the z-score formula to calculate the z-score for 9950 hours as we did in part (i).

z = (9950 - 10000) / 1000 = -0.5

Using a standard normal distribution table or calculator, we can find the probability of a z-score of -0.5, which is 0.3085. However, since we want the probability of the bulb lasting at most 9950 hours, we need to add the area under the normal curve to the left of -0.5, which is 0.3085 + 0.1915 = 0.5. Therefore, the probability that the bulb will last at most 9950 hours is 0.5.

(iii) To find the probability that the bulb will last at least 9950 hours, we need to find the area under the normal curve to the right of 9950 hours. We can use the z-score formula to calculate the z-score for 9950 hours as we did in part (i).

z = (9950 - 10000) / 1000 = -0.5

Using a standard normal distribution table or calculator, we can find the probability of a z-score of -0.5, which is 0.3085. However, since we want the probability of the bulb lasting at least 9950 hours, we need to add the area under the normal curve to the right of -0.5, which is 1 - 0.3085 = 0.6915. Therefore, the probability that the bulb will last at least 9950 hours is 0.6915.

(iv) To find the probability that the bulb will last less than 9000 hours or more than 11,500 hours, we need to find the areas under the normal curve to the left of 9000 hours and to the right of 11,500 hours, and add them together. We can use the z-score formula to calculate the z-scores for 9000 hours and 11,500 hours.

For 11,500 hours: z = (11,500 - 10,000) / 1000 = 1.5

Then the corresponding probability from Z table is written as,

=> 0.0668

(v) To find the probability that the bulb will last between 9000 hours and 11,000 hours, inclusively, we need to find the area under the normal curve between the z-scores for 9000 hours and 11,000 hours. We can use the z-score formula to calculate the z-scores for 9000 hours and 11,000 hours.

For 9000 hours: z = (9000 - 10,000) / 1000 = -1

For 11,000 hours: z = (11,000 - 10,000) / 1000 = 1

Using a standard normal distribution table or calculator, we can find the probability of a z-score of -1 (for 9000 hours), which is 0.1587, and the probability of a z-score of 1 (for 11,000 hours), which is 0.8413. Subtracting the area under the normal curve to the left of -1 from the area under the normal curve to the left of 1, we get the probability of the bulb lasting between 9000 hours and 11,000 hours inclusively, which is 0.8413 - 0.1587 = 0.6826.

(vi) To find the lifelength that represents the 95th percentile, we need to find the z-score that corresponds to the 95th percentile of the normal distribution. We can use a standard normal distribution table or calculator to find this value, which is approximately 1.645.

Using the z-score formula, we can solve for the life length that corresponds to a z-score of 1.645:

1.645 = (x - 10,000) / 1000

Multiplying both sides by 1000 and adding 10,000, we get:

x = 11,645

Therefore, the life length that represents the 95th percentile is 11,645 hours, which means that only 5% of bulbs will last longer than this value.

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Answer:

Therefore, the simplified expression with the given values is √e^16.

Step-by-step explanation:

Given the values of the variables m = 4, n = -3, and p = -3, we can simplify the expression √e^(m + n^2 - p) as follows:

m + n^2 - p = 4 + (-3)^2 - (-3) = 4 + 9 + 3 = 16

So the expression becomes: √e^16 = √e^(m + n^2 - p) = √e^16

Therefore, the simplified expression with the given values is √e^16.

3.9979(depends on what place you need to round to

The equation is V=πr2h. First plug in what you know, 314=π5^2h. 5x5=25 and its multiplied with π. It would look like 314=25πh. Divide the 25π by both sides, leaving your h. Plug it into your calculator.

Check answer:

(I rounded the 4 to the nearest whole number) 4*25*π is approximately 314

Answer:

4 ft

---------------

Volume of cylinder formula:

Given:

Find h:

The difference between the investment below and one with the same principal at the same rate compounded yearly is $18123.29.

The Payback Period is the most straightforward metric to use when contrasting investment options. Simply defined, this is the minimal amount required for you to recoup your initial investment.

compound interest, which is referred to as

[tex]A = P(1+r/n)^n×t[/tex]

Where

A = amount at the end of t years

r = interest rate.

n = periodic interval

P = principal amount deposited

Considering  investment compounded annually

P = 7000

r = 3% = 3/100 = 0.03

n = 1

t = 17 years

[tex]A = 7000(1 + 0.03/1)^1× 12A = 7000(1.03)^12[/tex]

A = $9980.32

For the second investment,

n = 6

[tex]A = 7000(1 + 0.08/6)^6 × 12A = 7000(1 + 0.0133)^72A = 7000(1.0133)^72A = $18123.29[/tex]

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Answer:

y=-2 over 1x+18

Step-by-step explanation:

Answer:

66mm

Step-by-step explanation:

Mr. Steiner will need to pay $18774 in total and he paid $4774 more than the actual price of the car.

we know that the amount of money earned, in compound interest after t years is showed as, A(t) = P (1+[tex]\frac{r}{n}[/tex])ⁿ[tex]^{t}[/tex]

here, we know that A(t) is the amount of money after t years.

P is the initial sum of money, know as principal,

r is the interest rate as a decimal value,

n is the number of times that interest is compounded per year,

and

t is the time in years for which the money is invested or borrowed.

now here we know,

P = 14000, r = 0.049, n = 12, t = 6

when we have all values we can find,

A(t) = P(1+[tex]\frac{r}{n}[/tex])ⁿ[tex]^{t}[/tex]

A(6) = 14000 (1+[tex]\frac{0.049}{12}[/tex])¹²ˣ⁶

A(6) = 18774

therefore we know that Mr. Steiner needs to pay $18774 in total.

now,

18774 - 14000 = 4774

therefore we get to know that Mr. Steiner paid $4774 more than the actual price of the car.

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The length TE in the parallelogram is 11 units

From the question, we have the following parameters that can be used in our computation:

The parallelogram QRST

The diagonals of parallelogram are equal

Using the above as a guide, we have the following:

QE =SE

Substitute the known values in the above equation, so, we have the following representation

3x + 12 = x + 16

So, we have

2x = 4

Divide

x = 2

Recall that

TE = 6x - 1

So, we have

TE = 6 * 2 - 1

Evaluate

TE = 11

Hence, the lentth is 11 units

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The probability that the student is from other majors is 0.40, the probability that the student majors only math is 0.13, and the probability that the student does not major engineering is 0.73.

a) Probability of a student being from other majors = (150-90) / 150 = 0.40

b) Probability of a student majoring only math = (30 - 20) / 150 = 0.13

c) Probability of a student not majoring engineering = (150 - 40 - 20) / 150 = 0.73

Probability = Number of Favorable Outcomes / Total Number of Outcomes

For part a)

Number of Favorable Outcomes = 150-90 = 60

Total Number of Outcomes = 150

Therefore, Probability = 60 / 150 = 0.40

For part b)

Number of Favorable Outcomes = 30-20 = 10

Total Number of Outcomes = 150

Therefore, Probability = 10 / 150 = 0.13

For part c)

Number of Favorable Outcomes = 150-40-20 = 90

Total Number of Outcomes = 150

Therefore, Probability = 90 / 150 = 0.73

The probability that the student is from other majors is 0.40, the probability that the student majors only math is 0.13, and the probability that the student does not major engineering is 0.73.

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Doane's rule is used for choosing the number of histogram bins, not for determining the minimum sample size needed for a multiple regression analysis.

However, a commonly cited rule of thumb is that the sample size should be at least 10 times the number of predictors, so for a multiple regression dataset with 3 predictors, a minimum of 30 observations may be recommended.

Doane's rule is a guideline for choosing the number of histogram bins based on the sample size and skewness of the data. It suggests that the number of bins should be approximately equal to 1 + log2(N) + log2(1 + |g1|/SE(g1)), where N is the sample size and g1 is the sample skewness.

It is important to note that Doane's rule is used for determining the number of bins for a histogram, not for determining the minimum sample size needed for a multiple regression analysis.

That being said, in general, the minimum sample size needed for a multiple regression analysis depends on a variety of factors, including the number of predictors, the strength of the relationships between the predictors and the outcome variable, the desired statistical power, and the level of significance. There is no set minimum sample size that applies to all situations. However, a commonly cited rule of thumb is that the sample size should be at least 10 times the number of predictors, so for a multiple regression dataset with 3 predictors, a minimum of 30 observations may be recommended.

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Y = -0.0063e0.16x + 99.97 is the exponential regression equation for the data, where x is the time in minutes and y is the temperature of the soup.

Calculate the x and y means in step one.

X's average: (0 + 10) / 2 = 5.

(95 + 88.5) / 2 = 91.75 is the mean of y.

Calculate the variance and covariance in step two.

(-5 6.5) + (5 -2.5) = 32.5 is the covariance.

X's variation is (5 0).

2 + (10 − 0)2 = 125

Calculate the regression coefficients in step three.

x = -32.5 / 125 = -0.26 where a = Covariance / Variance of x

Mean of x = 91.75 (-0.26 5) = 99.97 where b = Mean of y a Mean of x

Step 4: Compose the equation for exponential regression.

y = -0.0063e^0.16x + 99.97

Y = -0.0063e0.16x + 99.97 is the exponential regression equation for the data, where x is the time in minutes and y is the temperature of the soup. We must first determine the means of x and y before we can solve the problem. By summing the first and last values of x and dividing by 2, the mean of x is 5 and the mean of y is 91.75. (calculated by adding the first and last y values and then dividing by 2).

Calculating the covariance and variance comes next. The difference between each x and the mean of x is multiplied with the difference between each y and the mean of y to determine the covariance. By squaring the difference between each x and the mean of x, the variance of x is determined. The regression coefficients a and b can be determined when the covariance and variance have been computed.

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According to the given figure Mrs Martinez data has greater variability than Mrs Jone's data.

The average may be calculated by dividing the total number of values by the sum of all the numbers. The arithmetic average of a group of two or more data variables is referred to as a mean. Typically, average is referred to as mean or arithmetic mean. The word "mean" is only a way of defining the sample's average.

By adding up each value individually and dividing the result by the total number of observations, the average is obtained. The "middle" value, for which half of such observations are greater and half are less, is used to compute the median.

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The product of 1/2 and 2/3 is equivalent to one third

Fractions are expressions written as a ratio of two integers. For instance a/b is a fraction

Given the expression below

1/2 of 2/3

This can also be written as;

1/2 of 2/3 = 1/2 of two thirds

Simplify

1/2 * 2/3 = 2/6

1/2 of 2/3 = 1/3

Hence the resulting value of the expression is one third

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plug in 20 = x for function f(x)

1.2(1.11)^20 = ?

Answer:

w = 25 / 4 feet wide.

Step-by-step explanation:

Let's call the width of the walkway "w."

The area of the rectangular pool is 13 * 27 = 351 ft^2.

The area of the walkway can be calculated by adding up the area of four rectangles, one around each side of the pool:

2 * (13 + w) * w + 2 * (27 + w) * w = 384

Expanding the equation:

2 * 13w + 2w^2 + 2 * 27w + 2w^2 = 384

Combining like terms:

2w^2 + 40w = 384

Solving for w^2:

2w^2 + 40w - 384 = 0

Using the quadratic formula:

w = (-40 ± √(40^2 - 4 * 2 * -384)) / (2 * 2)

Simplifying:

w = (-40 ± √(1600 + 3072)) / 4

w = (-40 ± √4272) / 4

w = (-40 ± 65) / 4

w = (25 / 4) or (-105 / 4)

Since w must be a positive value, w = 25 / 4 feet wide.

Answer:look it up frfr

Step-by-step explanation:

The equation is [tex]y=-87(x-1)^{2} (x-3)^{3}[/tex].

What is meant by zeroes of polynomials?

All the x-values that bring a polynomial, p(x), to zero are referred to as its zeros. They are intriguing to us for a variety of reasons, one of which is that they provide information on the graph's x-intercepts for the polynomial.

It is given that degree of the equation is 5. so the highest power is 5 and there will be 5 zeroes.

It is given that 2 zeroes at x=1 and 3 zeroes at x= 3.

So, the equation is [tex]y=a(x-1)^{2} (x-3)^{3}[/tex].

We will substitute x=2 and y= 87 in the above equation.

[tex]87=a(2-3)^{3} \\a=-87[/tex]

Therefore now the equation will be:

[tex]y=-87(x-1)^{2} (x-3)^{3}[/tex].

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The probability of both free throws is 0.7921, at least one free throw is 0.9889, missing both free throws is 0.0121.  58% of his free throws is a better strategy as it results in a higher probability of missing at least one free throw.

The probability of making one free throw is 0.89. Therefore, the probability of making both free throws is: 0.89 * 0.89 = 0.7921 (rounded to 2 decimals).

The probability of missing one free throw is 1 - 0.89 = 0.11. Therefore, the probability of making at least one free throw is: 1 - 0.11 * 0.11 = 0.9889 (rounded to 2 decimals).

The probability of missing one free throw is 0.11. Therefore, the probability of missing both free throws is: 0.11 * 0.11 = 0.0121 (rounded to 2 decimals).

For the worst free-throw shooter who makes 58% of his free throws:

The probability of making both free throws is: 0.58 * 0.58 = 0.3364 (rounded to 4 decimals).

The probability of making at least one free throw is: 1 - 0.42 * 0.42 = 0.8236 (rounded to 2 decimals).

The probability of missing both free throws is: 0.42 * 0.42 = 0.1764 (rounded to 4 decimals).

For the player who makes 89% of his free throws:

The probability of making both free throws is: 0.89 * 0.89 = 0.7921 (rounded to 4 decimals).

The probability of making at least one free throw is: 1 - 0.11 * 0.11 = 0.9889 (rounded to 2 decimals).

The probability of missing both free throws is: 0.11 * 0.11 = 0.0121 (rounded to 4 decimals).

Therefore, intentionally fouling the player who makes 58% of his free throws is a better strategy as it results in a higher probability of missing at least one free throw.

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Option C : The number of individual outcomes from flipping and rolling one time is 12.

A permutation is a selection of items from a set where the order of the items does matter. In this case, a permutation would be an ordered pair of a heads or tails outcome from flipping a coin followed by a 1, 2, 3, 4, 5, or 6 outcome from rolling a die.

The number of possible combinations is found by multiplying the number of possible outcomes for each event. In this case, there are two possible outcomes from flipping a coin (heads or tails) and six possible outcomes from rolling a die (1, 2, 3, 4, 5, or 6), so the number of combinations is:

2 (outcomes from coin flip) * 6 (outcomes from die roll) = 12

The number of permutations is equal to the number of combinations because the order of the items in each combination does not matter. So, there are 12 individual outcomes from flipping and rolling one time.

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a)

63 cans in 7 boxes.

b)

11 boxes are needed for 99 cans.

It is a rate of one of another quantity.

In 2 hours, a man can walk for 6 miles

In 1 hour, a man will walk for 3 miles.

We have,

36 cans in 4 boxes.

This means,

1 box = 36/4 cans

1 box = 9 cans

Multiply 7 on both sides.

7 box = 63 cans ______(1)

1 box = 9 cans

Multiply 11 on both sides.

11 box = 99 cans ______(2)

Now,

From (1) and (2)

a)

63 cans in 7 boxes.

b)

11 boxes are needed for 99 cans.

Thus,

63 cans in 7 boxes.

11 boxes are needed for 99 cans.

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Answer:

5

Step-by-step explanation:

  2 1/2

+ 2 1/2

1/2 and 1/2 makes a whole which is 1

so if you have 4 and and a whole which is 5

They can also be turned into decimals. 1/2 as a decimal is .5

so 2.5 plus 2.5 = 5

If the area of  a rectangle 1/3 square mile and length of the field is 2/5 mile then the width of the field is

What is Area of a Rectangle?

The quantity of unit squares that can fit inside a rectangle called its area. In other terms, the area of a rectangle is the area that it occupys. The flat surfaces of laptop monitors, blackboards, painting canvases, etc. are a few instances of rectangular shapes.

Given in the question,

Area of rectangle [tex]= \frac{1}{3} square mile[/tex]

The length of the field [tex]= \frac{2}{5} mile[/tex]

Let breadth be x.

As we know that,

Area of rectangle = [tex]length * breadth[/tex]

Now,

[tex]\frac{1}{3} = \frac{2}{5} *x[/tex]

[tex]x=\frac{1}{3} * \frac{5}{2}[/tex]

[tex]x=\frac{5}{6}[/tex]

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Answer: 54 degrees

Step-by-step explanation:

The angle will be half of that arc segment

Because angles 1 and 2 are adjacent, we will see that the measure of angle 2 is 77°.

Here we know that m∠1 = 103°, and we want to find the measure of angle 2, which is an angle adjacent to angle 1.

That means that if we add their measures, then we will get a plane angle, this means that:

m∠1 + m∠2 = 180°

Then we can write:

103° + m∠2 = 180°

m∠2 = 180° - 103° = 77°

That is the measure of angle 2.

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Answer: The theme park made a 46.8% profit on Thursday.

Step-by-step explanation:

Step 1: First, we need to calculate the total revenue from ticket sales:

627 tickets x £54.99 = £34,341.73

Step 2: Subtract the costs from the total revenue:

£34,341.73 - £18,273 = £16,068.73

Step 3: Calculate the percentage profit:

£16,068.73 / £34,341.73 x 100 = 46.8%

The theme park made a 46.8% profit on Thursday.

Rounding to the nearest minute, we get that the ships will be 100 nautical miles apart at 8 hours and 10 minutes after the first ship left the harbor.

What is Pythagorean theorem?

The Pythagorean theorem is a fundamental concept in geometry that relates to the three sides of a right-angled triangle. It states that the square of the length of the hypotenuse (the longest side of the triangle) is equal to the sum of the squares of the lengths of the other two sides. In mathematical terms, it can be expressed as:

                             [tex]a^2 + b^2 = c^2[/tex]

We can use the Pythagorean theorem to find the distance between the two ships at any given time:

d² = (20t)² + (15(t-4))²

Simplifying this equation, we get:

d² = 400t² + 225(t² - 8t + 16)

d² = 625t² - 1800t + 3600

d = √(625t²- 1800t + 3600)

We want to find the value of t when d = 100 nautical miles, so we can set up the following equation:

100 = √(625t² - 1800t + 3600)

Squaring both sides, we get:

10000 = 625t² - 1800t + 3600

Rearranging, we get:

625t² - 1800t - 6400 = 0

Using the quadratic formula, we get:

t = (1800 ± √(1800² + 46256400)) / (2*625)

t = (1800 ± 3900) / 1250

t = 3.84 or t = 8.16

So the time elapsed for the second ship is:

t2 = t + 4

t2 = 7.84 or t2 = 12.16

We can see that the only solution that works is when t = 8.16 and t2 = 12.16. At that time, the first ship will have sailed for 8.16 hours at 20 knots, or 163.2 nautical miles, and the second ship will have sailed for 8.16 - 4 = 4.16 hours at 15 knots, or 62.4 nautical miles. The distance between the two ships will be:

d = √((163.2)² + (62.4)²) = 174.9 nautical miles

Rounding to the nearest minute, we get that the ships will be 100 nautical miles apart at 8 hours and 10 minutes after the first ship left the harbor.

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The equivalent expression for  8b-4b is 4b.

In algebra, like terms are the terms that contain the same variable which is raised to the same power. In this only numerical coefficients may vary.

Given 8b-4b. b=5

We have to combine the like terms to get an equivalent expressions.

Like terms containing variables with same power.

When combining like terms, we have to add or subtract their coefficients.

Coefficients are the numbers which are placed with variable.

Then, 8b-4b=4b.

When b=5⇒4*5=20

Hence, the equivalent expression for  8b-4b is 4b.

Complete question:

Write an equivalent expression by combining the like terms 8b-4b. Find the value of expressions when b=5.

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Answer:

6 units

Step-by-step explanation:

Since the two angles are equal, this means that the triangle is isosceles. So x+4 = 3x-8. After solving, 2x = 12,  x = 6. So AC is 6 units.

Answer: 6 units

Step-by-step explanation:

Since this is an isosceles triangle lines AB and BC are congruent so

x + 4 = 3x - 8 ---- add 8 and subtract x on both sides

12 = 2x ---- divide by 2 to isolate the x

x = 6

The expected value of the sample mean amount of money spent on books is equal to the population mean, which is $400.

This is a property of the sampling distribution of the sample mean, which states that the mean of all possible sample means is equal to the population mean.

In other words, if we take all possible random samples of size 100 from the population of undergraduate students, and calculate the mean amount of money spent on books for each sample, then the average of all these sample means will be $400.

The expected value of the sample mean amount of money spent on books can be calculated using the formula:

E(X) = μ

where X is the sample mean, and μ is the population mean.

In this case, the population mean is given as $400. Therefore, the expected value of the sample mean amount of money spent on books is also $400.

However, we can also calculate the standard error of the mean (SE) to get a measure of the variability of the sample mean. The formula for SE is:

[tex]SE = σ / sqrt(n)[/tex]

where σ is the population standard deviation, and n is the sample size.

Substituting the values, we get:

[tex]SE = 80 / sqrt(100) = 8[/tex]

This property is true regardless of the sample size, as long as the sample is randomly selected and independent. However, as the sample size increases, the sampling distribution of the sample mean becomes more normal and the standard error of the mean decreases, making the sample mean a more precise estimate of the population mean.

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The answers are:

To calculate the interest and maturity value, we need to use the formula:

Interest = Principal x Rate x Time

Maturity Value = Principal + Interest

Where:

For the given information, we have:

Drum Set:

Principal = $900.00

Rate = 4% = 0.04

Time = 10/365 = 0.0274 years (assuming an exact interest calculation based on days)

Interest = $900.00 x 0.04 x 0.0274 = $0.98

Maturity Value = $900.00 + $0.98 = $900.98

Used Car:

Principal = $1,960.00

Rate = 6% = 0.06

Time = 9/365 = 0.0247 years (assuming an exact interest calculation based on days)

Interest = $1,960.00 x 0.06 x 0.0247 = $2.88

Maturity Value = $1,960.00 + $2.88 = $1,962.88

Used Dirt Bike:

Principal = $4,800.00

Rate = 4% = 0.04

Time = 10/365 = 0.0274 years (assuming an exact interest calculation based on days)

Interest = $4,800.00 x 0.04 x 0.0274 = $5.23

Maturity Value = $4,800.00 + $5.23 = $4,805.23

School Tuition for Twins:

Principal = $9,675.00

Rate = 6% = 0.06

Time = not specified

We don't have the time period for this investment, so we can't calculate the interest or maturity value without that information.

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