Rewrite the function by completing the square.
h(x) = 4x2 + 4x + 1

Answer:

Step-by-step explanation:

Answer:

The probability that the sample mean will be between 82.5 and 86 years is 0.8351.

Step-by-step explanation:

According to the Central Limit Theorem if an unknown population is selected with mean μ and standard deviation σ and appropriately huge random samples (n > 30) are selected from this population with replacement, then the distribution of the sample means will be approximately normally.  

Then, the mean of the sample means is given by,

[tex]\mu_{\bar x}=\mu\\[/tex]

And the standard deviation of the sample means is given by,

[tex]\sigma_{\bar x}=\frac{\sigma}{\sqrt{n}}[/tex]

The information provided is:

[tex]\mu=85\\\sigma=6\\n=36[/tex]

As the sample size is large enough the Central Limit Theorem can be used to approximate the sampling distribution of sample mean life expectancy (M) in the United States.

Compute the probability that the sample mean will be between 82.5 and 86 years as follows:

[tex]P(82.5<\bar X<86)=P(\frac{82.5-85}{6/\sqrt{36}}<\frac{\bar X-\mu_{\bar x}}{\sigma_{\bar x}}<\frac{86-85}{6/\sqrt{36}})\\\\=P(-2.5<Z<1)\\\\=P(Z<1)-P(Z<-2.5)\\\\=0.84134-0.00621\\\\=0.83513\\\\\approx 0.8351[/tex]

Thus, the probability that the sample mean will be between 82.5 and 86 years is 0.8351.

The probability that the sample mean will be between 82.5 and 86 years is 0.8351.

Standard deviation σ = 6

Sample size n =36

The central limit theorem (CLT) states that the distribution of sample means approximates a normal distribution as the sample size gets larger, regardless of the population's distribution.

Since the sample size is significant i.e. large, so the given scenario can be treated as normally distributed as per the central limit theorem.

So, the standard deviation of sample means =  σ/√n

The probability that the sample mean will be between 82.5 and 86 years:

[tex]P(82.5 < X < 86) = P(\frac{82.5-85}{\frac{6}{\sqrt{36} } } < Z < \frac{86-85}{\frac{6}{\sqrt{36} } } )[/tex]

[tex]P(-2.5 < Z < 1)=P(Z < 1)-P(Z < 2.5)[/tex]

[tex]P(-2.5 < Z < 1) =0.8413-0.0062=0.8351[/tex]

Therefore, the probability that the sample mean will be between 82.5 and 86 years is 0.8351.

To get more about the central limit theorem visit:

https://brainly.com/question/18403552

Answer:

C

Step-by-step explanation:

We are given a line that contains the two points (-3, 3) and (-1, -1) and we want to determine the slope of the line.

To find the slope of a line given any two points, we can consider using the slope formula:

[tex]\displaystyle m=\frac{y_2-y_1}{x_2-x_1}[/tex]

Where (x₁, y₁) and (x₂, y₂) are the two points.

We have the two points (-3, 3) and (-1, -1).

So, let (-3, 3) be (x₁, y₁) and let (-1, -1) be (x₂, y₂).

Substitute and evaluate:

[tex]\displaystyle\begin{aligned} m&=\frac{(-1)-(3)}{(-1)-(-3)}\\ \\ &= \frac{-1 -3 }{-1 + 3} \\ \\ &= \frac{-4}{2} \\ \\ &= -2\end{aligned}[/tex]

So, the slope of the line is -2.

In conclusion, our answer is C.

Answer:

m=-2

Step-by-step explanation:

Its just -2 I cant explain sorry

Answer:

y = 4x - 1

Step-by-step explanation:

Equation y = 4x - 1 matches the function described in the table.

Answer:

b=-2(3x-xa-a)/a

Step-by-step explanation:

2x(3-a)=a(2-b)

6x-2xa=2a-ab

b=-2(3x-xa-a)/a

You can simplified to top because im a little lazy, sorry

Answer:

4 would be $55.00 and 8 would be $75.00

Answer:

4/9

Step-by-step explanation:

20+16= 36 total shapes. 16/36 simplifys to 4/9.

The simplest ratio of triangles to total shapes is 4:7.

Given that the number of squares=20 and the number of triangles=15.

The total number of shapes=20+15=35.

We need to find the simplest ratio of triangles to total shapes.

The quantitative relation between two amounts shows the number of times one value contains or is contained within the other.

Now, triangles: total shape=20:35

=4:7

Therefore, the simplest ratio of triangles to total shapes is 4:7.

To learn more about the ratios visit:

https://brainly.com/question/13419413.

#SPJ2

Answer:

400 ft²

Step-by-step explanation:

The maximum area of a rectangle results from it being a square. The rectangle (or square) must have 4 equal sides in order to maximize area. But in this case, one side is a wall. That means that the remaining three sides will be = 60 / 3 = 20 feet long. You formed an square that is 20 ft x 20 ft = 400 ft²

Answer:

4 - 5y - 2y + 16

like terms

20 - 7y

Answer:

4-5y)-(2y-16)=0

Step-by-step explanation:We add all the numbers together, and all the variables

(-5y+4)-(2y-16)=0

We get rid of parentheses

-5y-2y+4+16=0

We add all the numbers together, and all the variables

-7y+20=0

We move all terms containing y to the left, all other terms to the right

-7y=-20

y=-20/-7

y=2+6/7

Answer:

i cant see the graph if there was a graph with it it would really help lol

Step-by-step explanation:

Answer:

Don't Be mean Online. Be a buddy, Not a Bully

Step-by-step explanation:

Answer:

7:00

Step-by-step explanation:

0.5x^4+10.5 or 12.5 simplified is correct answer. Remove any grouping symbol such as brackets and parentheses by multiplying factors.

Use the exponent rule to remove grouping if the terms are containing exponents.

Combine the like terms by addition or subtraction.

Combine the constants.

Answer:

Step-by-step explanation:

the conversion for farenheit to celsius is to subtract 32 and multiply by 5/9.

-40-32 is -72. multiply that by 5/9 and that is -40

50-32 is 18. multiply that by 5/9 and you get 10. so no she's wrong

Answer:

hey hows ur day

Step-by-step explanation:

mins good

Answer:

Ok, so slope is basically the steepness of the line, and intercept is when it crosses the x or y axis.

Step-by-step explanation:

To identify the slope, find two points on the line, then use this equation to find the slope: [tex]\frac{y2 - y1}{x2 - x1}[/tex], where x1 and y1 are the coordinates of the first point on the line, and x2 and y2 are the coordinates of the second point on the line. y2 - y1 is called the rise, and x2 - x1 is called the run. Then, to find the intercept (commonly the y-intercept), you must find the point at which the line crosses the axis. This is the easiest part because you just need to find a point on the axis. When you need to find the y-intercept, look for where the line crosses the x-axis, and when you need to find the x-intercept, look for where the line crosses the y-axis.

Answer:

x=NaN your welcome hehe

Answer:

i do not know i will try .

Answer:

The amount of right-handed players is 53

Hope this Helps :)

Answer:

62

because 14 is twice more than 8

so 24 * 2 = 48

and 48 + 14 = 62

most likely 62

Step-by-step explanation:

‎

Answer:

1) 5/4 or 1 1/4

2) 9/16

Step-by-step explanation:

3/4+1/2: you multiply 1/2 by 2 to get a common denominator then get 2/4, 3+2=5, 5/4 or 1 1/4

1/3+11/48: you multiply 1/3 by 16 to get common denominator & get 16/48, 16+11= 27/48, divide by 3 & get simplest form of 9/16

Answer:

3/4+1/2= 1 5/8  and 1/3+11/48 is not a mixed number 9/16

Step-by-step explanation:

Answer:

She typed 32 words in her letter

Step-by-step explanation:

Assume that the letter has x words

∵ She typed x words in her letter

∵ She misspelled 8 words

∵ She misspelled 25% of the words she typed

∴ She misspelled 25% of x

→ That means 8 is equivalent to 25% of x

∴ 25% of x = 8

∴ 25% × x = 8

→ Change 25% to decimal by divide it by 100

∵ 25% = 25 ÷ 100 = 0.25

∴ 0.25 × x = 8

∴ 0.25x = 8

→ Divide both sides by 0.25

∵ [tex]\frac{0.25x}{0.25}[/tex] = [tex]\frac{8}{0.25}[/tex]

∴ x = 32

∵ x represents the number of words that she typed in the letter

∴ She typed 32 words in her letter

Answer:

x=11, y=1 or (11, 1)

Step-by-step explanation:

I used substitution to solve this. Basically wherever there's an x, I would fill it in as 12-y.

2(12-y)+3y=29

24+2y+3y=29

24+5y=29

subtract 24 from both sides

5y=5

divide by 5

y=1

Now substitute y back in to get x.

x=12-1

x=11

You can also graph this into desmos, and wherever they intercept, that's your answer.  I hope this helps!

Answer:

At least 401 chosen guests

Step-by-step explanation:

Represent those with same birth day with Same

So:

[tex]P(Same) > \frac{2}{3}[/tex]

Represent number of people with n

There are 365 days in a year and 364 days out of these days is not your birthday.

So, there the probability that n people do not share your birthday is [tex](\frac{364}{365})^n[/tex]

i.e.

[tex]P(none) = (\frac{364}{365})^n[/tex]

Solving further, we have that:

[tex]P(same) + P(none) = 1[/tex]

[tex]P(same) + (\frac{364}{365})^n = 1[/tex]

[tex]P(same) = 1 - (\frac{364}{365})^n[/tex]

We're calculating the probability that [tex]P(Same) > \frac{2}{3}[/tex].

So, we have:

[tex]1 - (\frac{364}{365})^n > \frac{2}{3}[/tex]

Collect Like Terms

[tex]1 - \frac{2}{3}> (\frac{364}{365})^n[/tex]

[tex]\frac{3-2}{3}> (\frac{364}{365})^n[/tex]

[tex]\frac{1}{3}> (\frac{364}{365})^n[/tex]

[tex]3^{-1} > (\frac{364}{365})^n[/tex]

Take natural logarithm (ln) of both sides

[tex]ln(3^{-1}) > ln((\frac{364}{365})^n)[/tex]

[tex]-ln\ 3 > n\ ln\ (\frac{364}{365})[/tex]

Apply laws of logarithm

[tex]-ln\ 3 > n\ (ln(364) - ln(365))[/tex]

Multiply through by -1

[tex]ln\ 3 < n\ (ln(365) - ln(364))[/tex]

Solve for n

[tex]\frac{ln\ 3}{(ln(365) - ln(364))} < n[/tex]

Reorder

[tex]n > \frac{ln\ 3}{(ln(365) - ln(364))}[/tex]

[tex]n > \frac{1.09861228867}{(5.89989735358 - 5.89715386764)}[/tex]

[tex]n> \frac{1.09861228867}{0.00274348594}[/tex]

[tex]n > 400.443928891[/tex]

[tex]n > 400[/tex] (approximated)

This implies that n = 401, 402, 403 .....

i.e

[tex]n \geq 401[/tex]

So, at least 401 people has to be invited

Answer:

12.9x-9

Step-by-step explanation:

5.3x-9+7.6x

5.3x+7.6x = 12.9x

=12.9x-9

Answer:

It is 2/15

Step-by-step explanation:

[tex]\frac{3}{19\frac{7}{2} } =\frac{3}{\frac{45}{2} }\\=\frac{2}{15}[/tex]

Dont know if this helps but here you go :)

Answer:

answer big no l

x=-6

y=10

Step-by-step explanation:

answer of 4

x 30

Answer:

Step-by-step explanation:

1) 5x + 4 + 3x - 8 = 180 ( co - interior angles )

8x - 4 = 180

8x = 184

x = 184 / 8

x = 23°

y = 3x - 8 ( vertically opposite angles )

y = 3 × 23 - 8

= 69 - 8

= 61°

4) 5 x + 7 = 2x + 97 ( vertically opposite angles )

5x - 2x = 97 - 7

3x = 90

x = 90 / 3

x = 30°

Hope this helps

plz mark as brainliest!!!!!