A nutrition laboratory tested 25 "reduced sodium" hotdogs of a certain brand, finding that the mean sodium content is 310 mg with a standard deviation of 36 mg.
Construct a 95% confidence interval for the mean sodium content of this brand of hot dog and interpret a 95% level of confidence. Show all work

Answer:

[tex] {(x - 3)}^{2} + {(y + 5)}^{2} = {5}^{2} [/tex]

Step-by-step explanation:

First find the radius

Which is the distance between the 2 points.

Radius =5

The answer in the standad form is above.

The equation of the circle in Standard Form is (x - 3)² + (y + 5)² = 25

The standard equation of a circle is given as:

(x - a)² + (y - b)² = r²

where (a, b) is the center of the circle and r is the radius of the circle.

Given the center as (3, -5) hence the radius of the circle is the distance between (3, -5) and (-1, -8). Hence:

[tex]Radius=\sqrt{(-8-(-5))^2+(-1-3)^2} \\\\Radius=5\ units\\[/tex]

hence:

(x - 3)² + (y - (-5))² = 5²

(x - 3)² + (y + 5)² = 25

The equation of the circle in Standard Form is (x - 3)² + (y + 5)² = 25

Find out more at: https://brainly.com/question/13658927

The shape has 11 sides.

Using the angle formula for polygons:

The sum of all the interior angles is:

11-2 x 180 = 9 x 180 = 1,620 degrees.

For one angle divide the total by number of sides:

1620 / 11 = 147.27 which rounds to 147.2

The answer is D.

Answer:

45 mins

Step-by-step explanation:

Answer:

(-2,-2); minimum

Step-by-step explanation:

From the graph, the vertex is (-2, -2) and since there are no y values that go less than the y value of the vertex, it is a minimum.

Answer:

Begin with a line segment on the paper and fold the paper so that the segment's endpoints lie on top of each other

Answer:

66 2/3 %

Step-by-step explanation:

First find the students not in the 8th grade

24 - 8 = 16

16 students are not in the 8th grade

Take the fraction of the students not in the 8th grade over the total

16/24 = 2/3

Change to a decimal

.66666666666

Multiply by 100 to change to a percent

66.666666%

66 2/3 %

Answer:

66.67% of students are not in eighth grade

Step-by-step explanation:

8/24=1/3

1/3=0.33333333333

1-0.33333333333=0.66666666667

0.66666666667=66.67%

Answer:

6.5

Step-by-step explanation:

The sum of all angles in a triangle are 180 degrees.

=> 10x -10 + 8x + 10x + 8 = 180

=> 28x -2 = 180

=> 28x = 182

=> x = 6.5

So, Angle A = 10 x 6.5 -10 = 65 - 10 = 55 degrees

     Angle B = 8 x 6.5 = 52 degrees

     Angle C = 10 x 6.5 + 8 = 65 + 8 = 73 degrees.

55 + 52 + 73 = 55 + 125 = 180 degrees

Answer:

10

Step-by-step explanation:

2x + 5 = 8x

Subtract 2x from each side

2x-2x + 5 = 8x-2x

5 = 6x

We want 12x so multiply each side by 2

2*5 = 6x*2

10 = 12x

Answer:

B. 10

Step-by-step explanation:

To find 12x, you first need to find the value of x using the first equation:

[tex]2x+5=8x[/tex]

You need to get the variables (x) on the same side of the equation in order to simplify them. To do this, use reverse operations. Subtract 2x from both sides to keep the equation balanced:

[tex]2x-2x+5=8x-2x\\\\5=6x[/tex]

Now isolate the variable (x) by dividing both sides of the equation by 6 (using reverse operations):

[tex]\frac{5}{6}=\frac{6x}{6} \\\\\frac{5}{6}=x[/tex]

Now insert the given value of x into 12x:

[tex]12(\frac{5}{6})[/tex]

Simplify:

[tex]12*\frac{5}{6} \\\\\frac{12}{1}*\frac{5}{6}\\\\\frac{60}{6}=10[/tex]

12x equals 10.

:Done

Answer:

610805 pounds

Step-by-step explanation:

The volume of grain in the silo will be calculated as equal to the volume of the cylinder formed by the silo

Height of the silo [tex]l[/tex] = 30 ft

radius of the silo r = 12 ft

volume of a cylinder = [tex]\pi r^{2} l[/tex]

substituting, we have

V = 3.142 x [tex]12^{2}[/tex] x 30 = 13573.44 cubic feet

We know that density ρ = weight/volume

density of the grains in the silo = 45 pound/cubic feet

therefore,

weight of grains = density x volume

weight of grains = 45 x 13573.44 = 610804.8 ≅ 610805 pounds

Answer:

Step-by-step explanation:

A probability density function (pdf) is used for continuous random variables. That is why p is between 0 and 1 (the two extremes - 0 and 1 - exclusive).

X = 100pth percentile of W

Y = 100(1-p)th percentile of W

Expressing Y as a function of X;

Y = 100(1-p)th = 100th - 100pth

Recall that 100pth is same as X, so substitute;

Y = 100th - X

where 100th = hundredth percentile of W and X = 100pth percentile of W  

Answer:

The correct option is (B).

Step-by-step explanation:

It is provided that, in a game of roulette the  wheel consists of slots numbered​ 00, 0,​ 1, 2,​ ..., 33.

The sample space of an experiment, is the set of all the possible outcomes of the random trials.

There are a total of 35 slots on the roulette wheel where the ball can land.

So, there are a total of 35 outcomes for one rotation of the wheel.

Then the sample space consists of all the 35 outcomes, i.e.

S = {00, 0, 1, 2, 3, ..., 33}

Thus, the correct option is (B).

Answer:

  b.  $11,820

Step-by-step explanation:

The 'rule of 72' tells you the doubling time of this account is about ...

  (72 years)/(4.25) = 16.9 years

So, in 18 years, the amount will be slightly more than double the present value. That is, the present value is slightly less than half the future amount.

  $25,000/2 = $12,500

The closest answer choice is ...

  $11,820

__

The present value of that future amount is ...

  PV = FV×(1 +r)^-t = $25,000×1.0425^-18 ≈ $11,818.73

The present value is about $11,820.

Answer:

B

Step-by-step explanation:

Answer:

x = 5

Step-by-step explanation:

Angle Bisector Theorem: When a ray bisects an angle, we get 2 congruent smaller angles

Step 1: Set equation equal to each other (Angle Bisector Theorem)

5x + 3 = 7x - 7

Step 2: Subtract 5x on both sides

3 = 2x - 7

Step 3: Isolate x term (Add 7 to both sides)

10 = 2x

Step 4: Isolate x (Divide both sides by 2)

x = 5

Answer:

0.1575.

Step-by-step explanation:

Here, as they are independent, we multiply the probabilities:

P( A and B) = 0.35*0.45

= 0.1575.

The probability that both events will occur simultaneously is 0.1575.

Given that, the events A and B are independent with P( A) = 0.35 and P( B) = 0.45.

Two events are independent if the occurrence of one event does not affect the chances of the occurrence of the other event. The mathematical formulation of the independence of events A and B is the probability of the occurrence of both A and B being equal to the product of the probabilities of A and B (i.e., P(A and B).

Since, the events A and B are independent

We have P(A and B)

= P(A) × P(B)

= 0.35 × 0.45

= 0.1575

Hence, the probability that both events will occur simultaneously is 0.1575.

Learn more about the independent probability here:

https://brainly.com/question/27987662.

#SPJ5

Answer:

Hey there!

Richard has 480 dollars.

Giving 1/4 of the money to his brother would mean giving 120 dollars to his brother.

Richard has 480-120, or 360 dollars left.

Giving 1/3 of the money left would be giving 120 dollars to his sister.

His sister and brother both got 120 dollars from Richard.

Hope this helps, and let me know if you need more help. :)

━━━━━━━☆☆━━━━━━━

▹ Answer

18x⁴ + 36x³ - 9x²

▹ Step-by-Step Explanation

9x²(4x + 2x² - 1)

36x³ + 18x⁴ - 9x²

18x⁴ + 36x³ - 9x²

Hope this helps!

CloutAnswers ❁

━━━━━━━☆☆━━━━━━━

Answer:

Step-by-step explanation:

Given the log function [tex](y-1)log_{10}(4) = log_{10} 16\\ \\[/tex] to get the value of y, the following steps must be carried out;

[tex](y-1)log_{10}(4) = log_{10} 16\\\\(y-1)log_{10}(2^2) = log_{10} 2^4\\\\ (y-1)2log_{10}(2) = 4log_{10} 2\\ \\DIvide\ both\ sides\ by \ log_{10}2\\\\\frac{2(y-1)log_{10}2 }{log_{10}2} = \frac{4log_{10}2}{log_{10}2} \\\\2(y-1) = 4\\\\[/tex]

Open the bracket

[tex]2y-2(1) = 4\\\\2y -2 = 4\\\\add \ 2 \ to \ both \ sides\\\\2y-2+2 = 4+2\\\\2y = 6\\\\Divide \ both \ sides\ by \ 2\\\\2y/2 = 6/2\\\\y = 3[/tex]

Hence the value of y is 3

Answer:

Balance at the age of 20 will be $1455966.46

Step-by-step explanation:

Formula to calculate the final amount is,

[tex]A=P(1+\frac{r}{n})^{nt}[/tex]

Where A = Final amount

P = Principal amount or amount invested

A = Final amount

r = Rate of interest

n = Number of compounding in a year

If Jason invested $200 in an account for 4 years with rate of interest 223%.

P = $200

r = 223%

n = 365

t = 4 years

A = [tex]200(1+\frac{2.23}{365})^{(4\times 365)}[/tex]

A = [tex]200(1.0061096)^{1460}[/tex]

A = $1455966.46

Therefore, balance amount in Jason's account at the age of 20 will be $1455966.46.

Answer:

8 (19) or  8 (18 +1)

Step-by-step explanation:

Distributive property means to distribute.

HCF of 144 and 8.

=> 8 is the HCF of 144 and 8

8 (18 + 1)

=> 8 (19)

Answer:

Term is something that is being added together. Factor is something that is being multiplied together. Coefficient is a number that is being multiplied by the variable. 2x+6x+14. The 2x, 6x, and 14 are terms because they are being added together.

Step-by-step explanation:

Answer:

depth 5 8.3 ft, length 5 24.9 ft, width 5 16.8 ft

Answer:

Step-by-step explanation:

6x³ - 4x² - 16x

To factorize the expression first factor out the GCF out

The GCF in the expression is 2x

That's

2x( 3x² - 2x - 8)

Next Factorize the terms in the bracket

To factorize write - 2x as a difference

that's

2x( 3x² + 4x - 6x - 8)

Factor out x from the expression

2x [ x( 3x + 4) - 6x - 8 ]

Next factor out - 2 from the expression

2x [ x ( 3x + 4) - 2( 3x + 4) ]

Factor out 3x + 4 from the expression

We have the final answer as

Hope this helps you

==================================================

Explanation:

When we reflect any point (x,y) over the line y = x, the x and y coordinates swap. So for instance, we have K = (5, -9) turn into K ' = (-9, 5).

Consider a point like (1,2). We can move it down 1 unit to have it land on the line y = x, then we can move it one unit to the right to move it to (2,1). These two translations effectively move the original point to its reflected location. The distance from (1,2) to y = x, is the same as the distance from (2,1) to y = x. Furthermore, the line connecting (1,2) to (2,1) is perpendicular to y = x.

Answer:

The question is incomplete, below is a possible match for the complete question:

You make $85,000 per year and your company matches 50 cents for every dollar you deposit into your 401k plan, up to 8% of your salary. Complete parts (a) through (c) below.

(a) If you contribute $200 every month to your 401k, what will your company contribute each month?

The company will contribute $ (Type an integer or a decimal rounded to two decimal places as needed.)

(b) If you contribute $830 every month to your 401k, what will your company contribute each month?

The company will contribute $ (Type an integer or a decimal rounded to two decimal places as needed.)

(c) What is the maximum amount of money the company will contribute to your 401k each year?

The maximum amount that the company will contribute each year is $

(Type an integer or a decimal rounded to two decimal places as needed.)

Answer:

a.) The company will contribute $100

b.) The company will contribute $415

c.) maximum amount the company will be willing to contribute = $6,800 per year

Step-by-step explanation:

First, let us calculate the maximum amount the company will be willing to pay into the 401k plan yearly:

Annual salary = $85,000

Monthly salary = $7083.3333

maximum amount = 8% = 8/100 = 0.08 of salary

maximum amount = 0.08 × 7083.3333 = $566.67

a.) If you contribute $200 every month.

Since $200 is less than the maximum amount that the company will be willing to contribute, let us calculate how much the company is willing to contribute:

Company matches 50 cents for every dollar you deposit

1 dollar deposited = 50 cents from company

but 1 cent = $0.01

∴ 50 cents = 0.01 × 50 = $0.5

$1 deposited = $0.5 from company

∴ $200 deposited = 0.5 × 200 = $100 contributed by company

Therefore, if you contribute $200 every month, your company will contribute $100 each month.

from this example, we can see that the company is willing to contribute half of every amount you deposit every month ($100 = half of $200), hence, subsequently, we will use this for calculations.

b.) If you contribute $830 every month, the company will be willing to contribute half this amount, which is:

half of $830 = 830 ÷ 2 = $415

Therefore, if you contribute $830 per month, your company will contribute $415 per month.

c.) The maximum amount the company will be willing to contribute each year = 8% of salary per year

= [tex]= \frac{8}{100}\times 85,000 \\ =0.08\ \times\ 85,000 = \$6,800[/tex]

Therefore, the company will be willing to contribute $6,800 per year.

Answer:

I found the answer on Yahoo

Step-by-step explanation:

P[rains in spain] = 1/9

P[hurricane in hartford & rain in spain] = 0.03*1/9 = A

P[hurricane in hartford & no rain in spain] = 0.02*8/9

P[hurricane in hartford] = 0.03*1/9 + 0.02*8/9 = 0.19/9 = B

P[rain in spain | hurricane in hartford] = A/B = 3/19 <---------

Answer/Step-by-step explanation:

[tex] (4 + 5) + 2 = 4 + (5 + 2) [/tex] => any combination of numbers were formed or grouped when adding. The associative property of addition was applied.

[tex] 2(2x + 4) = 4x + 8 [/tex] => the sum of two terms (addend) are multiplied by by a number separately (I.e., a(b + c) = a(b) + a(c) = ab + ac). The property applied is distributive property.

[tex] (7x * x) * 3 = 7 * (x * 3) [/tex] => the numbers were grouped in any combination to arrive at same result when multiplying. Associative property of multiplication was applied.

[tex] (8 * x * 2) = (x * 8 * 2) [/tex] => the numbers where ordered in any manner to arrive at same result when multiplying. Cummutative property of multiplication was applied.

[tex] (7 + 3) + 1 = (1 + (7 + 3) [/tex] => the order in which the nnumbers in the were arranged doesn't matter, as same result is arrive at. This is Cummutative property of addition.

Answer:

[tex]\huge\boxed{2x + y - 6 = 0}[/tex]

Step-by-step explanation:

2x + y = 6

Subtracting both sides by 6

2x + y - 6 = 0

Comparing it with the general form of equation [tex]\sf Ax+By +C = 0[/tex] , we get:

A = 2, B = 1 and C = -6.

So, the equation is in proper general form.

Answer:

[tex]\boxed{2x+y-6=0}[/tex]

Step-by-step explanation:

[tex]\sf The \ general \ form \ for \ the \ equation \ of \ a \ line \ is \ given \ as \ Ax+By+C=0.[/tex]

[tex]2x+y=6[/tex]

[tex]\sf Subtract \ 6 \ from \ both \ sides.[/tex]

[tex]2x+y-6=6-6[/tex]

[tex]2x+y-6=0[/tex]

[tex]\sf A=2 \ \ \ B = 1 \ \ \ C=-6[/tex]

[tex]\sf The \ equation \ is \ in \ general \ form.[/tex]

[tex]\sf Graph \ equation:[/tex]

Answer:

D  y= x+1

Step-by-step explanation:

The line has a positive slope since it goes up from left to right

We can eliminate A and B

3 is a fairly steep slope for line C

Lets check with point x=7

y = 3*7 +2 = 21+2 = 23

Way too steep

Lets check 2

y = 3*2+2 = 6+2 = 8

Still above the points

Checking D

y = x+1

x=7

y = 7+1 =8  A little high

x=2

y = 2+1 =3  A little low    but much better than C

Answer:

[tex]\huge \boxed{y=x+1}[/tex]

Step-by-step explanation:

Using a graph,

we can see the line y=x+1 is best fit for the data.

Answer:

[tex](\frac{4}{3},-\frac{10}{3})[/tex]

Step-by-step explanation:

If the extreme ends of a line segment AC are A[tex](x_1,y_1)[/tex] and C[tex](x_2,y_2)[/tex].

If a point B(x, y) divides the segment in the ratio of m : n

Then the coordinates of the point B are,

x = [tex]\frac{mx_2+nx_1}{m+n}[/tex]

y = [tex]\frac{my_2+ny_1}{m+n}[/tex]

If the ends of AC are A(-2, 5) and C(2, -5) and a point B divides it in the ratio of m : n = 5 : 1

Therefore, coordinates of this point will be,

x = [tex]\frac{5\times (2)+1(-2)}{5+1}[/tex]

  = [tex]\frac{10-2}{5+1}[/tex]

  = [tex]\frac{8}{6}[/tex]

  = [tex]\frac{4}{3}[/tex]

y = [tex]\frac{5\times (-5)+1(5)}{5+1}[/tex]

  = [tex]\frac{-25+5}{6}[/tex]

  = [tex]-\frac{20}{6}[/tex]

  = [tex]-\frac{10}{3}[/tex]

Therefore, coordinates of the point B are [tex](\frac{4}{3},-\frac{10}{3})[/tex].

Answer:

  C)  549 km²

Step-by-step explanation:

The area of the regular pentagon is given by ...

  A = (1/2)Pa

where P represents the perimeter, and 'a' represents the apothem (6.2 km). Of course, the perimeter is 5 times the side length.

The lateral area is the product of the perimeter and the height:

  LA = Ph

Using these formulas, and recognizing the total area includes two (2) pentagons, we have ...

  total area = (LA) +2(A) = Ph +2(1/2)Pa = P(h +a)

  = (45 km)(6 km +6.2 km) = 549 km^2