all real zeros of the function f(x) = x^3+x^2-22x-40

The range would be the most appropriate measure of spread in this case because it takes into account the extreme values of $300 and $1,300 and provides a clear measure of the difference between them.

To measure the amount of money college students spend on rent per month, the most appropriate measure of spread would be the range. The range is the simplest measure of spread and is calculated by subtracting the lowest value from the highest value in a data set. In this case, the range would be $1,300 - $300 = $1,000.

The median would not be the best choice in this scenario because it only represents the middle value in a data set. It does not take into account extreme values like the $1,300 rent expense.

Standard deviation would not be the most appropriate measure of spread in this case because it calculates the average deviation of each data point from the mean. However, it may not accurately represent the spread when extreme values like the $1,300 rent expense are present.

The interquartile range (IQR) would not be the best choice either because it measures the spread of the middle 50% of the data set. It does not consider extreme values and would not accurately represent the range of rent expenses in this scenario.

In summary, the range would be the most appropriate measure of spread in this case because it takes into account the extreme values of $300 and $1,300 and provides a clear measure of the difference between them.

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Answer:

x = 20/3

you will need 20/3 of the 60% solution

Step-by-step explanation:

0.25(40) + 0.60x = 0.30(x + 40)

10 + 0.60x = 0.30x + 12

0.30x = 2

Not sure if it's right

Therefore, the standard deviation for the number of people with the genetic mutation in groups of 500 is approximately 6.726.

To find the standard deviation for the number of people with the genetic mutation in groups of 500, we can use the binomial distribution formula.

Given:

Probability of having the genetic mutation (p) = 0.09

Sample size (n) = 500

The standard deviation (σ) of a binomial distribution is calculated using the formula:

σ = √(n * p * (1 - p))

Substituting the given values:

σ = √(500 * 0.09 * (1 - 0.09))

Calculating the standard deviation:

σ ≈ 6.726 (rounded to three decimal places)

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Answer:

236

Step-by-step explanation:

we are to solve for f(g(2)

that means, solve for g(2) first, then place it in f

g(2) = x^3 + 1

= 2^3+1

= 8+1 = 9

f(g(2) = f(9) since g(2) = 9

f(9)= 3x^2-7

3*9^2-7

3*81-7

243-7

236

Answer:

236 is the answer

Step-by-step explanation:

Answer:

AAA and SSA are not real theorems

Step-by-step explanation:

Side Side Angle is not a valid theorem because the unknown side could be located in two different places which would not prove the triangles congruent.

Angle Angle Angle is also not a valid theorem because all the angles might have congruent measures but that doesn't mean the sides will have the same measures therefore AAA cannot prove triangles congruent.

The rest are valid congruence theorems.

The process capability index for the process is 0.1754.

The first sided specification limit will be:

= (Upper specification limit - mean)/(3 × standard deviation)

= (23.1 - 22.9)/(3 × 0.19)

= 0.2/0.57

= 0.3508

The second sided specification limit will be:

= (22.9 - 22.8)/(3 × 0.19)

= 0.1/0.57

= 0.1754

The process capability index for the process is 0.1754 wine it's the lower value.

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Answer:

the volume is 288 squared cm

Step-by-step explanation:

Answer:

It isn't a function

Step-by-step explanation:

2 and 4 both have 2 x values, and on a graph, a function cannot have more than 1 x value.

Answer:

This hurt my head

Step-by-step explanation:

The height of the flagpole is 22.64 feet when the flag pole is 16 ft away.

Triangles with the same shape but different sizes are said to be similar triangles. Squares with any side length and all equilateral triangles are examples of related objects. In other words, if two triangles are similar, their corresponding sides are proportionately equal and their corresponding angles are congruent.

Properties:

Despite having the same shape, both could have different sizes.

There are no matching angles that are not equal.

Similar equivalent side ratios exist.

The given figure forms two similar triangles.

According to the rule of similar triangles. the ratio of length of the segments of the similar triangles are equal.

Height of Jeremy is68 inches = 5.66 feet.

Thus,

8/24 = 5.66/x

Using cross multiplication we have:

6x = 5.66(24)

x = 22.64

Hence, the height of the flagpole is 22.64 feet.

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The complete question is:

Answer:

7

Step-by-step explanation:

Changing LHS as

Comparing LHS and RHS

Answer:

It is safe

Step-by-step explanation:

Using trigonometry :

Cosθ = adjacent / hypotenus

Hypotenus = length of ladder = 12 feets

Adjacent = distance between ladder and wall = 3 feets

Cosθ = 3 /12

Cosθ = 0.25

θ = cos^-1(0.25)

θ = 75.522°

To be safe ladder must be between (70 - 85)°

Sijce ladder is at an elevation of 75.22° ; then it is safe.

Answer:

There are 2 solutions to square root x = 9

They are 3, and -3

Step-by-step explanation:

The square root of x=9 has 2 solutions,

The square root means, for a given number, (in our case 9) what number times itself equals the given number,

Or, squaring (i.e multiplying with itself) what number would give the given number,

so, we have to find the solutions to \(\sqrt{9}\)

since we know that,

\((3)(3) = 9\\and,\\(-3)(-3) = 9\)

hence if we square either 3 or -3, we get 9

Hence the solutions are 3, and -3

Answer:

y= -x^2

vertex:  (0, 0)

a= -1

domain:  (-∞, ∞)

range:  (-∞, 0]

axis of symmetry:  y-axis (x = 0)

increasing on:  (-∞, 0)

decreasing on:  (0, ∞)

y= (x-2)^2-3

vertex: (2, -3)

a = 1

vertical shift:  shift of 3 units downwards from the origin

horizontal shift:  2 units to the right

width: 1

reflected? nope

y= (x-1)^2-2  

vertex:  (1, -2)

a= 1

domain: all real numbers

range:   y ≥ -2

axis of symmetry:  x = 1

increasing on:   (-∞, 1]

decreasing on:   [1, ∞)

y = (x+1)^2+2

vertex:  (-1, 2)

a = 0

vertical shift:  2 units upwards from the origin

horizontal shift:  1 unit to the left

width:  infinite

reflected? no

Answer:

Total number of peanuts =n

He shared with 5 people = 6 people

Each person had at least 18

n/6>=18

Step-by-step explanation:

When question like this is given , the English is very important. He shares with his friends is different from he shares among his friends. Then also, at least means greater than or equal to.

Answer:

18 ≤ n ÷ 6

Step-by-step explanation:

My text book says Isaac has a bag of n peanuts. He shares the peanuts with 5 of his friends. Each person gets at least 18 peanuts. The inequality 18 ≤ n ÷ 6 represents this situation. Graph the solution of this inequality

The given logarithm expression is:

This can be re-written as:

(a) The mean of Z in case (a) is -60 and the variance is 400.

(b) The mean of Z in case (b) is 280 and the variance is 3600.

(c) The mean of Z in case (c) is 60 and the variance is 65.

(d) The mean of Z in case (d) is -20 and the variance is 65.

(e) The mean of Z in case (e) is 80 and the variance is 505.

To find the mean and variance of the random variable Z for each case, we can use the properties of means and variances.

(a) Z = 40 - 5X

Mean of Z:

E(Z) = E(40 - 5X) = 40 - 5E(X) = 40 - 5 * 20 = 40 - 100 = -60

Variance of Z:

Var(Z) = Var(40 - 5X) = Var(-5X) = (-5)² * Var(X) = 25 * Var(X) = 25 * (4)² = 25 * 16 = 400

Therefore, the mean of Z in case (a) is -60 and the variance is 400.

(b) Z = 15X - 20

Mean of Z:

E(Z) = E(15X - 20) = 15E(X) - 20 = 15 * 20 - 20 = 300 - 20 = 280

Variance of Z:

Var(Z) = Var(15X - 20) = Var(15X) = (15)² * Var(X) = 225 * Var(X) = 225 * (4)² = 225 * 16 = 3600

Therefore, the mean of Z in case (b) is 280 and the variance is 3600.

(c) Z = X + Y

Mean of Z:

E(Z) = E(X + Y) = E(X) + E(Y) = 20 + 40 = 60

Variance of Z:

Var(Z) = Var(X + Y) = Var(X) + Var(Y) = (4)² + (7)² = 16 + 49 = 65

Therefore, the mean of Z in case (c) is 60 and the variance is 65.

(d) Z = X - Y

Mean of Z:

E(Z) = E(X - Y) = E(X) - E(Y) = 20 - 40 = -20

Variance of Z:

Var(Z) = Var(X - Y) = Var(X) + Var(Y) = (4)² + (7)² = 16 + 49 = 65

Therefore, the mean of Z in case (d) is -20 and the variance is 65.

(e) Z = -2X + 3Y

Mean of Z:

E(Z) = E(-2X + 3Y) = -2E(X) + 3E(Y) = -2 * 20 + 3 * 40 = -40 + 120 = 80

Variance of Z:

Var(Z) = Var(-2X + 3Y) = (-2)² * Var(X) + (3)² * Var(Y) = 4 * 16 + 9 * 49 = 64 + 441 = 505

Therefore, the mean of Z in case (e) is 80 and the variance is 505.

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In ΔRST, the measure of ∠T=90°, the measure of ∠R=29°, and ST = 6.7 feet. Find the length of TR to the nearest tenth of a foot.

We will draw the rectangle triangle:

We can use the trigonometry property where the sine of an angle (∠R) is equal to the ratio between the opposite side (ST) and the hypotenuse (RS).

Also, the cosine of ∠R is equal to the ratio between the adyacent side (RT) and the hypotenuse (RS).

We can express this as:

The length of TR is 12 feet.

Answer:

C

Step-by-step explanation:

The interquartile range (IQR) is found as the 20.24. The correct option is (d) 20.24.

Given that X N(300, 15), find the Interquartile Range (IQR).

The given distribution is normal with mean μ = 300 and standard deviation σ = 15.

We need to calculate the interquartile range (IQR).IQR is defined as the difference between the third quartile (Q3) and the first quartile (Q1).

The first quartile (Q1) is the value below which 25% of the data fall and the third quartile (Q3) is the value below which 75% of the data fall.

We can find these values using the standard normal distribution table.

For the first quartile,

z1 = invNorm(0.25)

= -0.67449

Q1 = μ + σ × z1

= 300 + 15 × (-0.67449)

= 289.88

≈ 289.89

For the third quartile,

z3 = invNorm(0.75)

= 0.67449

Q3 = μ + σ × z3

= 300 + 15 × 0.67449

= 310.12

Therefore, the interquartile range (IQR)

= Q3 – Q1

= 310.12 – 289.89

= 20.23

≈ 20.24

Hence, the correct option is (d) 20.24.

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The given fraction (x^2-25)/(x^2-x-20) expressed in simplest form is (x+5)/(x+4). (Option C)

A fraction is in simplest form if the numerator and denominator have no common factors other than 1. In order to solve the given fraction, the numerator and denominator must be factorized, and the common factor will be canceled out.

Factoring x^2 – 25 using the difference of squares formula that states that a^2 – b^2 = (a + b)(a - b)

x^2 – 25 = x^2 – 5^2 = (x + 5)(x – 5)

Factoring x^2 – x – 20,

x^2 – x – 20 = x^2 + 4x – 5x – 20 = x(x + 4) -5(x + 4) = (x + 4)(x – 5)

Hence, factor (x – 5) is there in both numerator and denominator, it is canceled out. Hence the fraction in the simplest form is:

(x + 5)(x – 5)/ (x + 4)(x – 5) = (x + 5)/(x + 4)

Note: The question is incomplete.  The complete question probably is:  What fraction represents(x^2-25)/(x^2-x-20) expressed in simplest form. A) 5/4 B) (x-5)/(x-4) C) (x+5)/(x+4) D)25/(x+20)

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The expected number of cards Percy turns over before stopping = 3.78≈3

Probability refers to the chance of occurrence of an event E.

Let E be an event and P(E) be the probability of E occurring.

Then, P(E) = \(\frac{Number Of Favourable Outcomes Of E}{Total Number Of Outcomes}\)

Now, given a 52-card deck; cards are turned over till a spade comes up.

Then, the number of cards turned over is the sum of all card over 'kth' card, having probability \(P_{k}\), where, the card 'k' comes up if no previous card was a spade.

=> \(P_{k}=\frac{\binom{39}{k}}{\binom{52}{k}} = \frac{39!(52-k)!}{52!(39-k)!}\)

\(\sum^{39}_{k=0} (P_{k})=\frac{39!}{52!} \sum^{39}_{k=0}(\frac{(52-k)!}{(39-k)!}=\frac{53}{14} = \frac{52+1}{13+1}=3.78\)

Hence, after 3.78≈3 cards, Percy will stop turning the cards.

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To prove that if a person buys at least 400 cups of coffee in a year, then there is at least one day in which the person has bought at least two cups of coffee, we can use the Pigeonhole Principle.

There are 365 days in a year, and if a person buys at least 400 cups of coffee, there are more cups of coffee than days. By the Pigeonhole Principle, there must be at least one day where the person buys at least two cups of coffee.

The average of three real numbers is greater than or equal to at least one of the numbers. This is true because the average of the three numbers is the sum of the numbers divided by three. If all the numbers are equal, then the average is equal to each number. If at least one number is greater than the other two, the average will be greater than or equal to the smallest number.

To show that the cube root of 2 is irrational, we can use proof by contradiction. Assume that the cube root of 2 is rational, meaning it can be expressed as a fraction a/b where a and b are integers with no common factors. Then (a/b)^3 = 2. This implies a^3 = 2b^3. Since a^3 is even (because it is equal to 2 times an integer), we know that a must be even based on the given fact. Let a = 2c, then (2c)^3 = 2b^3. This simplifies to 8c^3 = 2b^3, or b^3 = 4c^3. Now, b^3 is also even, meaning b is even. However, this contradicts our assumption that a and b have no common factors, as both are divisible by 2. Thus, our assumption that the cube root of 2 is rational must be false, and the cube root of 2 is indeed irrational.

Regarding the statement "there is no smallest integer," we can prove this by considering any integer n. Since integers include negative numbers, we can find a smaller integer by subtracting 1 from n, resulting in n - 1. This process can be repeated indefinitely, showing that there is no smallest integer.

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Answer:

x= 0.333 if this help well there

Answer:

Step-by-step explanation:

Given triangle HIJ with:

Find the value of x first, solving the following equation:

Find the angle measure of I and J:

Find the measure of angle H:

Answer:

$3066.58

Step-by-step explanation:

$2893 x 1.06= $3066.58

Hope this helps!