eighty-one
is to nine Forty-nine is to​

This statement in the article is wrong because $2.69 is not the mean price ($2.81)

The prices from 5 gas stations surveyed are given as:

$2.79, $2.99, $2.69, $2.89, and $2.69.

There are no outliers in the dataset

So, the dataset can be summarized by the mean

The mean is

Mean = Sum/Count

So, we have

Mean = ($2.79+ $2.99+ $2.69+ $2.89+$2.69)/5

Evaluate

Mean = 2.81

The article quoted $2.69 as the typical price

This statement in the article is wrong because $2.69 is not the mean price ($2.81)

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Answer:

Step-by-step explanation:

Year 1: $850 * 0.91 = $773.50

Year 2: $773.50 * 0.91 = $704.69

Year 3: $704.69 * 0.91 = $641.95

...

Year 34: (continue the pattern)

We can continue this calculation for each year, but to save time, we can use an exponential decay formula:

Remaining Amount = Initial Amount * (1 - rate)^years

Substituting the values:

Remaining Amount = $850 * (1 - 0.09)^34

Calculating this expression:

Remaining Amount ≈ $850 * (0.91)^34 ≈ $255.88

After 34 years, approximately $255.88 will be left with Sally.

If the nex day, the biologist retums to the lake and takes a sample of 7 fish. Of those fish, 2 of them have tags. The estimated number of fish in the lake is 35 fish.

Let x represent the estimated number of fish in the lake

Hence,

x /10 = 7/2

Cross multiply

2x = 10 × 7

2x = 70

Divide both side by 2x

x =70/2

x = 35 fish

Therefore 35 is the number of fish.

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The dimensions of the rectangle are 4 ft by 5 ft.

Given that the length of a rectangle is 3 ft less than twice the width, and the area of the rectangle is 44 sq.ft. We have to find the dimensions of the rectangle. Let's consider the width of the rectangle as x ft.Length of the rectangle = (2x - 3) ftArea of the rectangle = Length x Width44 = (2x - 3) x x44 = 2x^2 - 3x44 = x (2x - 3)2x^2 - 3x - 44 = 0To solve for x, we will factorize the equation by splitting the middle term.2x^2 - 8x + 5x - 20 = 0Factorize2x(x - 4) + 5(x - 4) = 0(x - 4) (2x + 5) = 0x = 4 ft (since the width of a rectangle can't be negative)or 2x = -5This gives us an invalid value, so x = 4 ftNow that we have the width of the rectangle, we can calculate the length as follows:Length of the rectangle = (2x - 3) ftLength of the rectangle = (2 * 4) - 3Length of the rectangle = 8 - 3Length of the rectangle = 5 ft.

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Step-by-step explanation:

a)\( \sf \: Factor 6x2−3x \\ \sf {6x}^{2} −3x \\ \sf \: =3x(2x−1) \\ \sf \: Answer:3x(2x−1) \\ \)

b)Let's factor x²+3x−28

⇒x²+3x−28

⇒x² - 4x + 7x - 28

⇒(x² - 4x) + (7x - 28)

⇒x( x - 4) + 7(x - 4)

⇒(x -4) (x + 7)

Answer:

(x−4)(x+7)

Answer:

in a span of 30 years, the family would pay $40,410 in rent.

Step-by-step explanation:

you simply multiply $1,347 by 30!

(comment any questions)

Step-by-step explanation:

I’m assuming that you’re asking about quadratic equations, but suffice it to say that the method may even work for polynomials of higher degrees.

Let’s take an example. You have x^2+6x+8.

First, multiply the term in x^2 with the constant; in this case we get 8x^2.Next, break the value in x into two numbers, such that when you add them, the value becomes that of the middle term and when you multiply them, the value becomes that which you have just calculated.

Step 1:

x^2 * 8= 8x^2

Step 2:

(break the middle term)

x^2+4x+2x+8 (notice how 4x when added to 2x gives 6x but when multiplied, gives 8x^2)

Step 3:

(separate the common terms)

x(x+4)+2(x+4)

(x+2)(x+4)

Answer:

Hope the picture will help you.........................

Answer:

  C.  16 and 8

Step-by-step explanation:

You want the number of apples in each of two boxes if halving the number in the first box and adding 4 to the second box changes the total from 24 to 20.

We can write equations for this scenario as ...

  x + y = 24

  (x/2) +(y +4) = 20

Subtracting the second equation from the first gives ...

  (x +y) -(x/2 +y +4) = (24) -(20)

  x/2 -4 = 4 . . . . . . . . . simplify

  x = 2(8) = 16 . . . . . . . add 4, multiply by 2

  y = 24 -16 = 8

The two boxes initially contained 16 and 8 apples.

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The triangle for which angle a =30\degree, angle b=45\degree, and a=20, side a ≈ 20, side b ≈ 28.284, and side c ≈ 38.636

Two angles (a and b) and one side (a) are provided for us to solve the triangle. Let's call the side across from angle a side A, the side across from angle b side B, and the side across from the final angle (angle c) side C.

Here, it is given that,

angle a = 30 degrees

angle b = 45 degrees

side a = 20

angle c = 180 - (angle a + angle b)

angle c = 180 - (30 + 45)

angle c = 180 - 75

angle c = 105 degrees

We know that, a/sin(A) = b/sin(B) = c/sin(C)

a/sin(A) = b/sin(B) = c/sin(C)

20/sin(30) = b/sin(45) = c/sin(105)

b/sin(45) = 20/sin(30)

b = (sin(45) * 20) / sin(30)

b ≈ (0.7071 * 20) / 0.5

b ≈ 14.142 / 0.5

b ≈ 28.284

Now,

c/sin(105) = 20/sin(30)

c = (sin(105) * 20) / sin(30)

c ≈ (0.9659 * 20) / 0.5

c ≈ 19.318 / 0.5

c ≈ 38.636

Thus, side a ≈ 20, side b ≈ 28.284, and side c ≈ 38.636.

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Answer:x=-2,5, -\(i\sqrt{2}\), +\(i\sqrt{2}\)

Step-by-step explanation:

Answer: 192

Step-by-step explanation:

192

Answer:

6(32)

6x32

192

explanation:

The method is: Find the increase and find the ratio of the increase and the old price.

The percentage increase is 20%

A percentage is defined as the ratio that can be expressed as a fraction of 100.

The method below shows how you would calculate the % increase.

First step: Find the increase:

increase = 480 - 400 = $80

Second step: Find the ratio of the increase and the old price and multiply by 100 to express in percentage:

80/400 * 100 = 20%

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Answer:

no fred is not correct

Step-by-step explanation:

so u say

5/8×6/1

then u say 5×6=30

then u say 8×1=8

then u say 30÷8= 3.75

so yr answer is =3.75

hope u understand

Answer:

The correct answer is: u = 10,500. When the value of the alternative hypothesis is greater than that of the null hypothesis, the power of the test will be increased, so a value of u = 10,500 would yield the greatest power to reject the null hypothesis.

The number of pages in each section is 8 (1/8).

A fraction is a part of the whole represented by a/b, where a and b are any integers.

Given that, Mr. Stanford wrote 65 pages of a travel brochure, and he wants to divide it into 8 equal sections.

The number of pages in each section is given by:
65/8

= 8 (1/8)

Hence, the number of pages in each section is 8 (1/8).

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Remainder of question:

Find the probability distribution of x

Answer:

The random variable x is defined as: X = {0, 1, 2, 3, 4}

The probability distribution of X:

P(X = 0) = 0.656

P(X = 1) = 0.2916

P(X= 2) = 0.0486

P(X=3) = 0.0036

P(X = 4) = 0.0001

Step-by-step explanation:

Sample size, n = 4

Random variable, X = {0, 1, 2, 3, 4}

10% (0.1) of the homeowners are insured against earthquake, p = 0.1

Proportion of homeowners who are not insured against earthquake, q = 1 - 0.1

q = 0.9

Probability distribution of x,

\(P(X = r) = ^nC_r *p^r q^{n-r} \\\\P(X= 0) =(^4C_0 *p^1 q^4 )\\P(X=0) = (^4C_0 *0.1^0 0.9^4 ) = 0.656\\P(X= 1)= (^4C_1 *p^1 q^3 )\\P(X=1) = (^4C_1 *0.1^1 0.9^3 ) = 0.2916\\P(X= 2)=( ^4C_2 *p^2 q^2) \\P(X=2) = (^4C_2 *0.1^2 0.9^2 ) = 0.0486\\P(X= 3) = (^4C_3 *p^3 q^3) \\ P(X=3) = (^4C_3 *0.1^3 0.9^1 ) = 0.0036\\P(X= 4) = (^4C_4 *p^4 q^0 )\\ P(X=4) =(^4C_4 *0.1^4 0.9^0 ) = 0.0001\)

Answer:

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

Given system:

Add up the two equations to get same coefficient on both variables:

As we see none of the choices match the answer. It means either question or answer choices are inaccurate.

Answer:

C. (100)(1/6)

Step-by-step explanation:

This is based on the "number cube" being a regular 6-sided die. You have a 1 out of 6 chance of rolling a 4 each time you roll the die. So that chance times 100 rolls is your answer.

Answer:

b at most 199

Step-by-step explanation:so the total was 121 and there is a flat fee of 21.50 so you subtract that out and gat 99.5 since its .5 per mile its going to be divided giving 199 and that is the most she could have driven.

1064 x

19

________

20216 legos

Sharon has 20216 legos

Answer:

a. 0.8944 = 89.44% probability that the player functions for at least 8 hr

b. 0.9938 = 99.38% probability that the cassette player works for at most 11 hr

c. z* = 10.024 hr

Step-by-step explanation:

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean \(\mu\) and standard deviation \(\sigma\), the z-score of a measure X is given by:

\(Z = \frac{X - \mu}{\sigma}\)

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Mean value of 9 hr and a standard deviation of 0.8 hr

This means that \(\mu = 9, \sigma = 0.8\)

a. What is the probability that the player functions for at least 8 hr?

This is 1 subtracted by the pvalue of Z when X = 8. So

\(Z = \frac{X - \mu}{\sigma}\)

\(Z = \frac{8 - 9}{0.8}\)

\(Z = -1.25\)

\(Z = -1.25\) has a pvalue of 0.1056

1 - 0.1056 = 0.8944

0.8944 = 89.44% probability that the player functions for at least 8 hr.

b. What is the probability that the cassette player works for at most 11 hr?

This is the pvalue of Z when X = 11. So

\(Z = \frac{X - \mu}{\sigma}\)

\(Z = \frac{11 - 9}{0.8}\)

\(Z = 2.5\)

\(Z = 2.5\) has a pvalue of 0.9938

0.9938 = 99.38% probability that the cassette player works for at most 11 hr.

c. Find a number z* such that only 10% of all cassette players will function without battery replacement for more than z* hr.

This is the 90th percentile, which is X when Z has a pvalue of 0.9, that is, X when Z = 1.28.

\(Z = \frac{X - \mu}{\sigma}\)

\(1.28 = \frac{X - 9}{0.8}\)

\(X - 9 = 1.28*0.8\)

\(X = 10.024\)

So

z* = 10.024 hr

There is a possible translation of the form g(x) = f(x) + k for which the graph y=g(x) will have no x-intercepts.

A translation is a movement to a graph or figure in which only the position of the figure changes, either left, right, up or down, keeping the inclination, orientation and congruence.

The translations are represented as follows:

Hence, for the function to have no x-intercepts, the function must be shifted up as though the minimum value of the function is greater than zero.

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Answer:

- 8a²

Step-by-step explanation:

using the rule of exponents

\(\frac{a^{m} }{a^{n} }\) = \(a^{(m - n)}\)

given

\(\frac{80a^9}{-10a^7}\)

= \(\frac{80}{-10}\) × \(a^{(9-7)}\)

= - 8 × a²

= - 8a²

there is an error in step 2

8 should have multiplied with x and -1, but at the end the answer is the same so I guess it can be all corect or the error in step 2

Answer:

3x^2-1

Step-by-step explanation:

Answer:

f(x) = 3x – 1 and g(x) = x²

Putting the value of g(x) in f(x), we get

(fog)(x)= f{g(x)}= f(x²) = (3x²-1)

Answer (with explanation):

6 - 2 is an expression, where 6 - 2 = 4.

62 is a number (natural number), and of course, 62 = 62.

These two are very different, and the results of 4 and 62 are in great contrast as well.

Hope this helps! Thanks.

Answer:

7

Step-by-step explanation:

3RD MAN: 1

2ND MAN: 2

1ST MAN: 4

3rd Man = 1/2+1/2 = 1

2nd Man = 1+1 = 2

1st Man = 2*2 = 4

Hope it helps ~

Answer:

x=24

Step-by-step explanation:

i cant quite explain how i did it