50 points find x
Please help

Using the Central Limit Theorem, it is found that Jackson has 8 guinea pigs.

It states that the sampling distribution of sample means of size n has standard error [tex]s = \frac{\sigma}{\sqrt{n}}[/tex], in which [tex]\sigma[/tex] is the standard deviation of the population.

In this problem, we have that [tex]s = 0.2227, \sigma = 0.63[/tex], hence we solve for n to find the number of guinea pigs that he has.

[tex]s = \frac{\sigma}{\sqrt{n}}[/tex]

[tex]0.2227 = \frac{0.63}{\sqrt{n}}[/tex]

[tex]0.2227\sqrt{n} = 0.63[/tex]

[tex]\sqrt{n} = \frac{0.63}{0.2227}[/tex]

[tex](\sqrt{n})^2 = \left(\frac{0.63}{0.2227}\right)^2[/tex]

[tex]n = 8[/tex]

Jackson has 8 guinea pigs.

More can be learned about the Central Limit Theorem at https://brainly.com/question/24663213

Applying the product rule gives

[tex]\displaystyle \frac{d}{dx}\int_1^{x^2}\frac{2t}{1+t^2}\,dt \times \int_1^{\ln(x)}\frac{dt}{(1+t)^2} + \int_1^{x^2}\frac{2t}{1+t^2}\,dt \times \frac{d}{dx}\int_1^{\ln(x)}\frac{dt}{(1+t)^2}[/tex]

Use the fundamental theorem of calculus to compute the remaining derivatives.

[tex]\displaystyle \frac{4x^3}{1+x^4} \int_1^{\ln(x)}\frac{dt}{(1+t)^2} + \frac{1}{x(1+\ln(x))^2}\int_1^{x^2}\frac{2t}{1+t^2}\,dt[/tex]

The remaining integrals are

[tex]\displaystyle \int_1^{\ln(x)}\frac{dt}{(1+t)^2} = -\frac1{1+t}\bigg|_1^{\ln(x)} = \frac12-\frac1{1+\ln(x)}[/tex]

[tex]\displaystyle \int_1^{x^2}\frac{2t}{1+t^2}\,dt=\int_1^{x^2}\frac{d(1+t^2)}{1+t^2}=\ln|1+t^2|\bigg|_1^{x^2}=\ln(1+x^4)-\ln(2) = \ln\left(\frac{1+x^4}2\right)[/tex]

and so the overall derivative is

[tex]\displaystyle \frac{4x^3}{1+x^4} \left(\frac12-\frac1{1+\ln(x)}\right) + \frac{1}{x(1+\ln(x))^2} \ln\left(\frac{1+x^4}2\right)[/tex]

which could be simplified further.

Answer:

[tex]m=-3[/tex]

Step-by-step explanation:

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

Substitute and calculate

                   [tex]x_1=7[/tex]  

                   [tex]x_2=11[/tex]

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

                    [tex]y_1=6[/tex]

                    [tex]y_2=-6[/tex]

Substitute

[tex]m=\frac{-6-6}{11-7}[/tex]

Calculate the sum or difference

[tex]m=\frac{-12}{4}[/tex]

Cross out the common factor
[tex]m=-3[/tex]

I hope this helps you

:)

Hello.

Let's use the slope formula in order to find the slope:

[tex]\bf{\displaystyle\frac{y_2-y_1}{x_2-_x_1}[/tex]

Where

y₂ = the y-coordinate of the second point (-6)

y₁=the y-coordinate of the first point (6)

x₂=the x-coordinate of the second point (11)

x₁=the x-coordinate of the first point (7)

Plug in the values:

[tex]\bf{\displaystyle\frac{-6-6}{11-7} =\frac{-12}{4} =-3[/tex]

Therefore, m (the slope) is equal to -3.

I hope it helps.

Have an outstanding day. :)

[tex]\boxed{imperturbability}[/tex]

Answer:

(-0.481 , -0.144)

Step-by-step explanation:

Confidence Interval for difference is proportion formula is given as:

p1 - p2 ± z ×√[p1(1 - p1)/n1 +p2 (1 - p2)/n2]

For p1

Of the 96 people surveyed in the eastern half of a country, 42 said they fly to visit family members for the winter holidays.

n1 = 96 people

p1 = x/n

x = 42 people

p1 = 42/96

= 0.4375

1 - p1 = 0.5625

For p2

Of the 108 people surveyed in the western half of the country, 81 said they fly to visit family members for the winter holidays.

n2 = 108 people

p2 = x/n

x = 81 people

p2 = 81/108

= 0.75

1 - p2 = 0.25

99% confidence interval = 2.576

p1 - p2 ± z ×√[p1(1 - p1)/n1 +p2 (1 - p2)/n2]

= 0.4375 - 0.75 ± 2.576 ×√[0.4375(1 -0.4375)/96 +0.75 (1 - 0.75)/108]

= -0.3125 ± 2.576 × √0.4375× 0.5625/96 + 0.75 × 0.25 /108

= -0.3125 ± 2.576 × √0.0025634766 + 0.0017361111

= -0.3125 ± 2.576 × √0.0042995877

= -0.3125 ±2.576 × 0.0655712414

= -0.3125 ± 0.1689115178464

Confidence Interval

-0.3125 - 0.1689115178464

= -0.4814115178

Approximately to 3 decimal places = -0.481

= -0.3125 + 0.1689115178464

= -0.1435884822

Approximately to 3 decimal places = -0.144

Therefore, the 99% confidence interval for difference in proportion = (-0.481 , -0.144)

Answer:

y=-11

Step-by-step explanation:

Answer:

y = -11

Step-by-step explanation:

y – 3(2y – 7) = 76

y - 6y + 21 = 76

-5y + 21 = 76

-5y = 55

y = -11

Answer:

T2, –4(x, y)

Step-by-step explanation:

Pre image has taken place ⇒ 2 units Horizontally right and 4 unit vertically down to obtain vertices of Image.

Hence, Answer = T2, –4(x, y)

~Lenvy~

Answer: T2, –4(x, y)

Step-by-step explanation:

right on edge 2023

Hey there!

The magnitude of 218 will always be 218 because the absolute value of a positive number is always itself. The magnitude of -218 will be 218 as well because the absolute value of a negative number is the positive version of the number without the negative sign. You are essentially dropping or ignoring the negative sign.

Therefore, the magnitude of an account of -218 Dollars is 218 dollars

Answer:

they have the same slope

Step-by-step explanation:

because if they are parallel they have the same slope

Answer:

Therefore If you exchange $522 for euros, then we will get 

Step-by-step explanation:

mark me brainliest!!

Answer:

412.38Є

Step-by-step explanation:

The answer is simple, since 1$ = 0.79Є, multiply 0.79 by 522, or the other way around, if you want.

0.79*522

=412.38Є

Hope it helped.

Answer:

Step-by-step explanation:

LCD: 90

10: 10, 20, 30, 40, 50, 60, 70, 80, 90

45: 45, 90

9/90 and 34/90

Answer:

[tex]\displaystyle h(x) = x-\frac{13}{2}[/tex]

Step-by-step explanation:

We are given that:

[tex]\displaystyle g(x) = \int_{-1}^x f(t)\, dt[/tex]

And we want to write the equation for the tangent to the graph of g at x = 4.

First, determine g(4):

[tex]\displaystyle \begin{aligned} g(4) & = \int_{-1}^{(4)} f(t)\, dt \end{aligned}[/tex]

This is equivalent to the area of f from -1 to 4:

[tex]\displaystyle \begin{aligned} g(4) & = \frac{1}{2}(2)(3) + \frac{1}{2}(2)(-3)+\frac{1}{2}(-3+(-2))(1) \\ \\ & = \frac{1}{2}(6-6-5) \\ \\ & = -\frac{5}{2}\end{aligned}[/tex]

Note that areas under the x-axis are negative.

Find g'(4):

[tex]\displaystyle \begin{aligned} g'(x) = \frac{d}{dx}\left[ \int_{-1}^x f(t)\, dt\right]\end{aligned}[/tex]

By the Fundamental Theorem of Calculus:
[tex]\displaystyle \begin{aligned} g'(x) & = f'(x) \\ \\ g'(4) & = f'(4) \\ \\ & =1 \end{aligned}[/tex]

Note f is a line for 3 < x < 6 with a slope of 1.

Therefore:
[tex]\displaystyle \begin{aligned} h(x) -g(x_1) & = g'(x_1)(x-x_1) \\ \\ h(x) - \left(-\frac{5}{2}\right) & = (1)(x-(4)) \\ \\ h(x)& = (x-4) - \frac{5}{2} \\ \\ & = x - \frac{13}{2}\end{aligned}[/tex]

In conclusion, the equation of the tangent line is:
[tex]\displaystyle h(x) = x-\frac{13}{2}[/tex]

Answer:

A function that gives the work required in foot-lbs to lift the bucket up x feet from the ground is [tex]W=16(50-x)+(19-\frac{x}{5})(8.3)x[/tex] and  the work to get the bucket to the top of the cliff is 3726 foot-lbs

Step-by-step explanation:

Work done to lift the rope by distance x feet:

[tex]W_1=32(\frac{50-x}{2})[/tex]

Work done to lift the bucket by distance x feet:

[tex]W_2=(19-\frac{x}{5})(8.3)x[/tex]

On reaching top 7 gallons of water spilled out so , on going up by x feet [tex]\frac{7x}{35}=\frac{x}{5}[/tex] gallons of water spilled out.

a function that gives the work required in foot-lbs to lift the bucket up x feet from the ground:

[tex]W=16(50-x)+(19-\frac{x}{5})(8.3)x[/tex]

Now the work to get the bucket to the top of the cliff i.e. x =35

[tex]W=16(50-35)+(19-\frac{35}{5})(8.3)(35)[/tex]

W=3726

Hence, a function that gives the work required in foot-lbs to lift the bucket up x feet from the ground is [tex]W=16(50-x)+(19-\frac{x}{5})(8.3)x[/tex] and  the work to get the bucket to the top of the cliff is 3726 foot-lbs

Answer:

Two possible equations:

Point-slope form is [tex]y-1=-\frac{2}{3} (x+3)[/tex]

Slope-Intercept form is [tex]y=-\frac{2}{3}x+-1[/tex]

Step-by-step explanation:

So to start we need to know what makes a line parallel. In an equation we know that for lines to be parallel they must have the same slope([tex]m[/tex]).

Then, we  need to know the slope-intercept form of an equation. The point slope form is [tex]y-y1=m(x-x1)[/tex] where [tex]m[/tex] is the slope of the line and [tex]y1[/tex] and [tex]x1[/tex] represent the point on the graph. This is the equation we'll use for the line.

So now that we understand what we need to find, we need to find the slope of the existing line. To do this we use the equation [tex]m=\frac{y2-y1}{x2-x1}[/tex]. We can plug in the points (-2,3) and (1,1) on the graph to get [tex]m=\frac{1-3}{1+2}[/tex]. When we simplify this we get [tex]m=-\frac{2}{3}[/tex] so we know our slope is [tex]-\frac{2}{3}[/tex]. Lastly, all we need to do is plug the slope and the new point into our point slope equation to get [tex]y-1=-\frac{2}{3} (x+3)[/tex].

If you needed to go further and put this into slope-intercept form, you could solve the equation for y to get [tex]y=-\frac{2}{3}x+-1[/tex]

Answer:

i know this but do not lol

Step-by-step explanation:

Answer:

did u mean to put (9,5) and (21,1) in there twice? but if so ur answer is m= -1/3

TRY USING SYMBOLAB I USE ALL THE TIME

Answer : Life Insurance

Explanation : Have A Good Day

◊ YusuCr ◊

The optional deduction for money to be taken out of an employee's paycheck is life insurance.

Option C is the correct answer.

An employee's paycheck is a document issued by an employer that lists the amount of money an employee has earned during a certain pay period and the amount of money that has been withheld for taxes, insurance, and other deductions.

It also includes the net amount of money that the employee is entitled to receive after all deductions have been made.

We have,

Life insurance is an optional deduction for money to be taken out of an employee's paycheck.

The other options listed (Federal income tax, Medicare, and Social Security) are typically mandatory deductions required by law.

Thus,

The optional deduction for money to be taken out of an employee's paycheck is life insurance.

Learn mroe about employee's paychecks here:

https://brainly.com/question/2819285

#SPJ7

the time is only 9:30 and fine in it lol

Answer:

68

Step-by-step explanation:

bidmas rule

8×8=64

64+68

Answer: $79.12

Step-by-step explanation:

We have to find total amount that was paid for dinner

5 people each order was worth $12.80

Therefore, total bill = 12.80*5

= $64

Tax: 7.5%

Therefore, the bill after tax was:

[tex]=64(\frac{100+7.5}{100})\\= 64(1.075)\\[/tex]

Bill with tax = $68.8

Gratuity = 15.0% of bill with tax

Therefore, gratuity = 0.15 * 68.8

= $10.32

Ended up paying in total = Gratuity + Bill with tax

= $68.8 + $10.32

= $79.12

Fifty-pound bag of valencia rice has 3.2 * 10⁵ grains more than fifty pound bag of basmati rice

An equation is an expression that shows the relationship between two or more numbers and variables.

A fifty pound bag of basmati rice has 1.1 * 10³ grains in each ounce of 8 * 10² ounce and fifty pound bag of valencia rice has 1.2 * 10⁶ grains

Difference in number of grains = 1.2 * 10⁶ grains - (1.1 * 10³ grains * 8 * 10² ounce) = 3.2 * 10⁵ grains

Fifty-pound bag of valencia rice has 3.2 * 10⁵ grains more than fifty pound bag of basmati rice

Find out more on equation at: https://brainly.com/question/2972832

Answer:

Mixed fraction:    -15  1/8

Improper fraction:   121/8

The maximum length of the rectangular front is the highest length of the rectangular front, and the value is 128.1 feet

Let the dimension of the rectangular front be x and y.

Such that:

y = 2x

So, the area of the rectangular front is:

A = xy

[tex]A = 2x^2[/tex]

The surface area of the pyramid roof is:

A = 4bh

Where:

b = base =25

h = height =18

So, we have:

[tex]A = 4* 25 * 18[/tex]

[tex]A = 1800[/tex]

The total surface area of the figure is:

[tex]T = 1800 +2x^2[/tex]

The range of the cost of material is: $25 per square foot to $50 per square foot.

So, the maximum cost is:

[tex]50 * (1800 +2x^2) = 500000[/tex]

Divide both sides by 50

[tex]1800 +2x^2 = 10000[/tex]

Subtract 1800 from both sides

[tex]2x^2 = 8200[/tex]

Divide both sides by 2

[tex]x^2 = 4100[/tex]

Take the square root of both sides

x = 64.03

Recall that:

y = 2x

So, we have:

y = 2 * 64.03

y = 128.06

Approximate

y = 128.1

Hence, the maximum possible length of the rectangular front of the building is 128.1 feet

Read more about maximum area at:

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Answer: 82

Step-by-step explanation:

Answer:

[tex]\large\boxed{\sf sin(A)=0.5}[/tex]

Step-by-step explanation:

A right angled triangle is given to us and we would like to find out the value of sin(A) .

From the triangle we can see that the measure of angle BAC is 30° . Therefore ,

[tex]\longrightarrow A = 30^o[/tex]

On using sin both sides ,

[tex]\longrightarrow sin(A) = sin30^o[/tex]

As we know that the value of sin30° = 1/2. So;

[tex]\longrightarrow sin(A)=\dfrac{1}{2} [/tex]

Simplify by converting it into decimal ,

[tex]\longrightarrow \underline{\underline{sin(A) = 0.5}} [/tex]

Hence option B is correct .

And we are done!

Answer:

(x)t(xt1)t(xt2)=1266

Step-by-step explanation:

here here we will use the algebra to find three consecutive integers whose sum is 1266 we start by assigning x to the first integer since there are consecutive it means that the second number will be x plus 1 and the third will be x plus 2 they shall all add up to 1 2 6 6 therefore you can write the equation as a following

Answer:

11:15

Step-by-step explanation:

Answer:

[tex]4x^3-16x^2+19x-6[/tex]

Step-by-step explanation:

P(x)=a(x-r1)(x-r2)(x-r3)

This is a third degree polynomial of leading coefficient a, where r1, r2 and r3 are the roots.

So just replace it with the values you are asked for :

[tex]4\left(x-\frac{3}{2}\right)\left(x-\frac{1}{2}\right)\left(x-2\right)\\[/tex]

Then expand and you will find the answer : [tex]4x^3-16x^2+19x-6\\[/tex]

The equation of pressure is given by:

[tex]p = \frac{f}{s} [/tex]

where p is the pressure.

f is the applied force.

s is the surface area to which the force is applied.

I will start off by calculating the surface area of the table top given by:

[tex]s = l \times w = 1.8 \times 1.2 = 2.16[/tex]

s=2.16 m²

We know that f=400 N, that is given.

[tex]p = \frac{400 \: n}{2.16 \: m {}^{2} } [/tex]

Plug this on your calculator (excluding the units lol)

[tex]p = 185.185 \frac{n}{m {}^{2} } [/tex]

[tex]p = 185 \frac{n}{m {}^{2} } [/tex]

Answer:

3.7

Step-by-step explanation:

You have to divide

Answer:

i do not know tbh .

Step-by-step explanation:

Answer:

  75°, 112°, 125°, 113°, 89°, 98°, 90°, 130°

Step-by-step explanation:

The marked angle pairs are one of ...

1) vertical angles (congruent): ? = 75°

2) linear pair (supplementary): ? = 180° -68° = 112°

3) consecutive interior (supplementary): ? = 180° -55° = 125°

4) alternate interior (congruent): ? = 113°

5) corresponding (congruent): ? = 89°

6) alternate exterior (congruent): ? = 98°

7) alternate interior (congruent): ? = 90°

8) alternate interior (congruent): ? = 130°

_____

Additional comment

For parallel lines in general, all of the obtuse angles are congruent, and all of the acute angles are congruent. All of the obtuse angles are supplementary to the acute angles. (In (7), all angles are right angles, so all are congruent.) These facts can help you with problems like this one.

Learning the language (names/relationships) of these angles will be helpful to you in the future.