x^3 - x^2 + 5x – 5 = 0

Answer: I would suppose 2.

Mean: X = 67.4133 (rounded to four decimal places)

Standard Deviation: s ≈ 2.4484 (rounded to four decimal places)

Variance: s^2 ≈ 5.9952 (rounded to four decimal places)

To calculate the mean, we need to sum up all the heights and divide by the total number of observations.

Adding up the heights given in the sample, we get a sum of 1002.2. Since there are 15 heights, we divide the sum by 15 to get the mean: X = 1002.2 / 15 ≈ 67.4133.

To calculate the standard deviation, we can use technology or software such as Excel or statistical calculators.

The standard deviation measures the dispersion or spread of the data points around the mean. Using the sample data, the standard deviation is approximately 2.4484.

To calculate the variance, we square the standard deviation. In this case, s^2 ≈ (2.4484)^2 ≈ 5.9952.

The variance represents the average squared deviation from the mean. It is useful for understanding the spread of the data and is often used in further statistical calculations.

Therefore, for the given sample of student heights, the mean is approximately 67.4133, the standard deviation is approximately 2.4484, and the variance is approximately 5.9952.

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The Triangle inequality theorem of a triangle says that the sum of any of the two sides of a triangle is always greater than the third side. The length of QS can lie between 3 < QS < 13.

The Triangle inequality theorem of a triangle says that the sum of any of the two sides of a triangle is always greater than the third side.

Suppose a, b and c are the three sides of a triangle. Thus according to this theorem,

As per the given law of triangle inequality, the sum of the two sides of the triangle is greater than the third side.

x + 8 > 5

x > -3

x + 5 > 8

x > 3

8 + 5 > x

13 > x

Hence, the length of QS can lie between 3 < QS < 13.

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Answer:

The coordinates of point P along the segment AB is (-1, 6).

Step-by-step explanation:

It is known that ratio of AP to PB is:

\(\frac{AP}{PB} = \frac{2}{3}\)

Or vectorially speaking:

\(\overrightarrow{AP} = \frac{2}{3}\overrightarrow{PB}\)

The vector that represents the segment AB is:

\(\overrightarrow{AB} = \vec B -\vec A\)

If \(\vec A = (-7,4)\) and \(\vec B = (8,9)\), then:

\(\overrightarrow{AB} = (8,9)-(-7,4)\)

\(\overrightarrow {AB} = (8+7,9-4)\)

\(\overrightarrow{AB} = (15,5)\)

But \(\overrightarrow{AB} = \overrightarrow{AP} + \overrightarrow{PB}\), then:

\(\overrightarrow{AB} = \frac{2}{3}\overrightarrow{PB} +\overrightarrow{PB}\)

\(\overrightarrow{AB} = \frac{5}{3}\overrightarrow{PB}\)

\(\overrightarrow{PB} = \frac{3}{5}\overrightarrow{AB}\)

\(\overrightarrow{PB} = \frac{3}{5}(15,5)\)

\(\overrightarrow{PB} = \left(9, 3\right)\)

The location of \(\vec P\) is derived of this formula:

\(\overrightarrow{PB} = \vec B - \vec P\)

\(\vec P = \vec B - \overrightarrow{PB}\)

If \(\vec B = (8,9)\) and \(\overrightarrow{PB} = \left(9, 3\right)\), then:

\(\vec P = (8,9) - (9,3)\)

\(\vec P = (8-9,9-3)\)

\(\vec P = (-1, 6)\)

The coordinates of point P along the segment AB is (-1, 6).

A function assigns the value of each element of one set to the other specific element of another set. The zeroes of the functions are -2, 1, and 3.

A function assigns the value of each element of one set to the other specific element of another set.

Given f(x) = (x - 1)(x + 2)(x − 3), therefore, the zeroes of the functions are -2, 1, and 3. The end behavior of the function is that if x approaches ∞ then f(x) approaches ∞, while if x approaches -∞ then f(x) approaches -∞, as can be observed from the given graph.

Hence, the zeroes of the functions are -2, 1, and 3.

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Answer:

−1, 2, −3; continues downward to the left and upward to the right

Step-by-step explanation:

For the Random variables, X and Y where both are nonnegative for all points in a sample space S. The expected value of Z ( random variable) is, E(Z) = E(X) + E(Y).

We have X and Y are random variables and that X and Y are non-negative for all points in a sample space S. Let us consider X be another random variable defined as Z(s) = max( X(s), Y(s))

for all elements s belongs to S. We have to show that E( Z) = E(X) + E(Y)

Now, for simple way of representation let

Max ( X(s),Y(s)) = Max(X,Y)

We know that Max(X,Y) = [(X+Y) + |X-Y|]

So, Z = Max(X,Y) = [(X+Y) + |X-Y|]

Taking expectations E(Z) = E(Max(X,Y)

= E{[(X+Y) + |X-Y|]}

\(E(Z)= \frac{1}{2} [E(X+Y) + E|X-Y|] = [E(X) + E(Y) + E|X-Y|] \\ \) (Since E(X + Y) = E(X)+ E(Y))

\(E(Z) = \frac{1}{2}[E(X)+ E(Y) + E|X| + E|-Y|]\\ \)

\(= \frac{1}{2} [E(X) + E(Y) + E(X) + E(Y)]\) (Since X and Y are non negative so E|X| = E(X) and E(-Y)=E(Y) )

=> E(Z) = E(X)+ E(Y)

Hence, required results occurred.

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The mean height of the hexagon is 21.33 in.

To find the length of the sides of a regular hexagon with a perimeter of 372 inches, you must divide the perimeter by 6. This gives you a result of 62 inches for the length of each side. The other steps are:

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Answer: b=2/5

Step-by-step explanation:

Step 1: Cross-multiply.

2b−1/2 = b−1/6

(2b−1)*(6)=(b−1)*(2)

12b−6=2b−2

Step 2: Subtract 2b from both sides.

12b−6−2b=2b−2−2b

10b−6=−2

Step 3: Add 6 to both sides.

10b−6+6=−2+6

10b=4

Step 4: Divide both sides by 10.

10b/10 = 4/10

b = 2/5

a) the revenue after two years is approximately $3.23 million

b) after 5.39 years, the revenue will decline to $2.7 million.

(a) We need to find the revenue in the present year and the revenue after two years of decline during a recession. The given equation is: R = 4e⁻⁰.¹²t (where t is the time measured in years)

Hence, put t = 0 (as we want the revenue of the present year)

R = 4e⁻⁰= 4 x 1 = 4 million dollars

Hence, the revenue in the present year is $4 million.

Now, put t = 2 (as we want the revenue after two years)R = 4e⁻⁰.¹² x 2= 4e⁻⁰.²⁴= 3.23 (approx)

Therefore, the revenue after two years is $3.23 million (approx).

(b) We need to find after how many years, the revenue will decline to $2.7 million. The given equation is: R = 4e⁻⁰.¹²t (where t is the time measured in years)

Now, equate the given revenue to $2.7 million 2.7 = 4e⁻⁰.¹²t 0.675 = e⁻⁰.¹²tln 0.675 = -0.12 tln e= -0.12 t

Therefore, t = ln 0.675 / (-0.12) t = 5.39 (approx)

Therefore, after 5.39 years, the revenue will decline to $2.7 million.

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Answer:

42

Step-by-step explanation:

bases : 4+8= 12 .   12/2 = 6

height = 7

7•6 = 42

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The heaviest 8% of fruits weigh more than 539.56 grams.

The standard normal distribution can be used to determine that the heaviest 8% of fruits weigh more than the upper tail of the normal distribution.

Since the standard normal distribution has a mean of 0 and a standard deviation of 1, we can use the following formula to translate the weight of the fruit into a standard normal score:

z = (x - mean) / standard deviation

Where x is the fruit's weight, the mean is its average weight of 503 grams, and the standard deviation is 17 grams.

Finding the z-score for the right-tail area of 0.08 for the heaviest 8% of fruits will need consulting a conventional normal table or using a tool that can calculate the cumulative distribution function (CDF).

For instance, if we utilize the common normal table, we discover that the z-score for 0.08 is roughly 1.28.

Next, we apply the following formula to return the z-score to the fruit's weight:

x = (z * standard deviation) + mean

Plugging in the values, we get:

x = (1.28 * 17) + 503 = 539.56 grams

So the heaviest 8% of fruits weigh more than 539.56 grams.

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Answer:

Please see the attached picture for full solution.

Answer:

sorry i donk knows this question

The statement "As long as N is significantly less than K, logistic growth is indistinguishable from exponential" is false. If dN/dt > 0, then N increases.

The statement "As long as N is significantly less than K, logistic growth is indistinguishable from exponential" is false. Logistic growth takes into account the carrying capacity of the environment, represented by K, which limits the growth of a population as it approaches this limit. In contrast, exponential growth assumes an unlimited supply of resources and no constraints on population growth. Therefore, as N approaches K, logistic growth begins to level off, while exponential growth continues to increase indefinitely.
If dN/dt > 0, then N increases. This means that the population size is growing at a positive rate. If dN/dt is equal to zero, then N remains stable, indicating that the population size is not changing. Finally, if dN/dt is negative, then N decreases, indicating that the population size is shrinking. Therefore, the correct answer to this question is "increases."

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Answer: Perimeter of given square:40,Area of given square:100

Perimeter of Dilated square:200

Area of Dilated square: 2500

Step-by-step explanation:

The value of the time premium is $100.

According to the statement

we have to find the time premium from the given information.

So, For this purpose, the given information is:

a strike price of $25 when the option price is $2 and the underlying common stock sells for $24

And

Time premium is the amount by which an option price exceeds its intrinsic value. The value of an option beyond its current exercise value representing the option holder's control until expiration, the risk of the underlying asset, and the risk less return.

So, From the given information and the formula

The value of the time premium is $100.

So, The value of the time premium is $100.

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Answer:

15/8

Step-by-step explanation:

17/8=15/8

17+15=32

The answer is 8/17.

Cosine, or cos, is the adjacent line/ the hypotenuse

In this case, the hypotenuse is 17 since it is the longest side in this right triangle. The adjacent line is 8 since it is adjacent, or touching, to the Angle A. 15 is the tangent that is facing opposite from Angle A.

If we plug in the given numbers correctly, the answer should be 8/17.

We need to check if y=8 and x = -1 are perpendicular or parallel.

The line y=8, is a straight line for which the y-values within it are equal to 8, therefore it is parallel to the x-axis.

The line x=-1, is a straight line for which all the values have the same value of x, which is -1, therefore it is parallel to the y-axis.

The lines are, therefore, perpendicular.

The expected repair cost is $39.60 calculated by using the function repair cost C = 3Y2 + Y + 2.

The probability of selecting a defective item is 0.10, so the probability of selecting Y defective items out of 4 is given by the binomial distribution: P(Y) = (4 choose Y) * (0.10)^Y * (0.90)^(4-Y).

The expected value of Y is E(Y) = ΣY * P(Y) = 0(0.6561) + 1(0.2916) + 2(0.0486) + 3(0.0036) + 4(0.0001) = 0.6.

Plug E(Y) into the repair cost equation to find the expected repair cost: C = 3(0.6)^2 + 0.6 + 2 = $39.60.

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Answer:

I believe that the answer is B

Step-by-step explanation:

If you look at the problem there is a pattern , y always has 10x as much than x

Answer:

144

Step-by-step explanation:

Answer:

x=t-p

Step-by-step explanation:

just move p to the other side and since it crosses the equals sign so you have to change it from positive to negative

Answer:

x=t-p

Step-by-step explanation:

To make x the subject of the formula, you’d have to take p to the other side. And when (+p) crosses over to the other side, it changes to (-p) because of the equality sign.

Answer:

you correct answer should be 17

By counting the combinations, we will see that there are 10 combinations such that the sum gives a Fibonacci number.

We have two number cubes with 6 outcomes each, such that we have a total of 36 combined outcomes.

For each dice, the outcomes are:

{1, 2, 3, 5, 8, 13}

Now, let's count the combinations that also give a Fibonacci number (these are given by adding two consecutive numbers in the sequence).

I will list each possible red outcome, then the blue outcomes that would give a Fibonacci term, and then we can count the number of combinations.

Adding the numbers of combinations, we have:

C = 1 + 2 + 2 + 2 + 2 + 1 = 10

There are 10 combinations that give a Fubbonaci number.

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Answer:

The median for Week 2 is more than the median for Week 1.

Step-by-step explanation: Remeber that Range of a set is the difference of the largest number and smallest number.

Median is the middle number of a set. If we have 20 numbers, the middle numbers will be the average of the 10th and 11th number. If we have 21 numbers, it would be the 11th number.

Mean is Σ\(\frac{x+x_{2} +x_{3} .....+x_{n} }{n}\) , n is the number of terms in a set. This  expression means add up all the terms in the set, and divide by the number of terms in a set.

We have a dot plot . Number of dots represent frequency, and the number is our quanititive data. so our following set for Week 1 is

{62,68,68,68,69,70,70,72,72,72,75,75,76,78,78,80,80,80,89,89}

Let find its Range, Median, and Mean.

Range is 27.

Median is 73.5

Mean is 74.55

For the second data set, the following set is

{62,68,68,68,69,70,70,72,72,72,75,75,76,78,78,80,80,80,85, 86,86,86, 88,88,88,88,89,89,89,89}.

Range is 27

Median is 79

Mean is 78.8

So according to both sets, W1 and W2 have the same range, but W2 have a higher mean and median.

So the answer is The median for Week 2 is more than the median for Week 1.

Answer:

4 and 8

Step-by-step explanation:

(a)

f(0) for x = 0 , that is the interval x < 5, thus

f(0) = x + 4 = 0 + 4 = 4

(b)

f(6) for x = 6 , that is the interval 5 ≤ x < 7, thus

f(6) = 8

Answer:

HL

Step-by-step explanation:

The HL Therom only proves right triangles are congruent and since both triangles are right triangles, HL can work here.