suppose babies born in a large hospital have a mean weight of 3316 grams, and a standard deviation of 324 grams. if 83 babies are sampled at random from the hospital, what is the probability that the mean weight of the sample babies would differ from the population mean by less than 54 grams? round your answer to four decimal places.

Considering the situation with the parallel lines being cut by the two transversal lines, the measures of the angles are given as follows:

12. m<14 = 66º (option C).

13. m<12 = 86º (option D).

Angles 4 and 15 are alternate exterior angles, as they are on different sides of the same transversal line, hence they are congruent, that is:

m<15 = 114º.

Angles 14 and 15 are consecutive interior angles, meaning that they are supplementary, hence the measure of angle 14 is calculated as follows:

m<14 + m<15 = 180º

m<14 + 114º = 180º

m<14 = 66º.

Angles 5 and 10 are alternate interior angles, as they are on the opposite internal sides of the same transversal line, hence they are congruent and the measure of angle 10 is given as follows:

m<10 = 86º.

Angles 10 and 12 are equivalent angles, as they are on the same position, just relative to different transversal lines, hence they are also congruent, and the measure of angle 12 is given as follows:

m<12 = 86º.

The diagram with these lines is given by the image at the end of the answer.

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The unknown angles are as follows:

An angle bisector in geometry is the ray, line, or segment which divides a given angle into two equal parts.

In other words, a line that splits an angle into two equal angles.

Therefore, a bisector of an angle 120 degrees bisect the angle into 60 degrees.

Hence, FH bisect ∠EFG into the angles m∠EFH  and  m∠GFH .

Therefore,  m∠GFH  and m∠EFH are congruent.

m∠EFG = 119°

Hence,

m∠EFH = m∠GFH

Therefore,

m∠EFH  = 119 / 2

Hence,

m∠EFH  = 59.5°

m∠GFH  = 59.5°

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Answer:

Step-by-step explanation:

The reasonable price of the car after 4 years will be $8618.

What is regression analysis?

Regression analysis is a group of statistical procedures used in statistical modelling to determine the associations between a dependent variable and one or more independent variables.

Given that a dealership tracks the correlation between the age of its used cars and asking price for a car. The regression line is y = 12,338 – 930x, where x is the age of the car, in years.

The price of the car after 4 years will be calculated as follows:-

y = 12338 - 930x

y = 12338 - ( 930 x 4 )

y = 12338 - 3720

y = $8618

Therefore, the reasonable price of the car after 4 years will be $8618.

Answer:

B - For every one year in age, the price is predicted to decrease by $930

C- If the Car is new, the car is predicted to cost $12,338.

Step-by-step explanation:

correct on edge 2022

Answer:

3.24 years

Step-by-step explanation:

2 = e^it          Decimal interest = i    T = years     2 = double

T = 3.24 years   For ANY deposit amount to double

Based on the fact that Aster Inc. paid salaries to its employees, the effect on the balance sheet and the income statement is A. Assets ↓ Expenses ↑.

When the salaries were paid by Aster Inc. to its employees, the effect was that the assets decreased. This is because cash was used to pay the salaries and cash is an asset.

Expenses will increase because when there is a payment of expenses to employees, it is recorded as a debit to the relevant asset account so this is an increase that will decrease income.

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Answer: bean

Step-by-step explanation:

bean chd china bean poopies beans

26 = (110 - x)/2

52 = 110 - x

x = 110 - 52

x = 58°

Question 6 asks us to determine the period of the function.

Looking at the height of the blade tip, it varies in a sinusoidal manner.

Thus, the period is the distance between successive same heights on the table.

The function takes 360 degrees to return to its same value. At angle zero, the height was 150ft and it was still 150 ft at 360 degrees.

Thus the period is 360 degrees.

-6x-11=19/+11 <=>

<=> -6x=30/:(-6) <=>

<=> x=-5

The height of a the given shape which has a volume of 7/8, length of 5/8, width of 7/9 is 9/5

Volume = Length × width × height

7/8 = 5/8 × 7/9 × x

7/8 = 35/72x

x = 7/8 ÷ 35/72

= 7/8 × 72/35

= 9/5

So therefore, the height of the given shape is 9/5

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Step-by-step explanation:

E = (-8, 2)

reflected across the y axis means that there is kind of a mirror along the y-axis.

and when you look into that mirror, you see point D as point E all the way on the other side of the mirror, at the same distance from the mirror as point D is. and point E has the same "height" (y) as point D.

since the other side of the mirror represents the negative numbers, the same distance to the mirror means the same amount of negative units away from the mirror for E, as we have positive units away from the mirror for D.

The answer is A x^2-3x-1+1/x-1

The expression is x²-3x-1+ 1/ (x-1).

The mathematical procedure for splitting big numbers into several smaller groups or sections is known as long division. The dividend is the number we split into smaller groups, while the divisor is the number by which we divide. A difficulty can be solved by breaking it down into manageable parts.

The mathematical procedure for splitting big numbers into smaller groups or pieces is known as long division. A difficulty can be solved by breaking it down into manageable parts. Dividends, divisors, quotients, and remainders all exist in long divisions. When solving an issue involving long division, the dividend—a high number—is divided by the divisor, a smaller number. The extra amount that cannot be divided yields the quotient, which is known as the residual.

Given:

x cubed minus 4 times x squared plus 2 times x plus 2 in the numerator and x minus 1 in the denominator=x³ - 4x² + 2x + 2 / x-1

Now, performing the long division method we have

= [tex]x^2+\frac{-3x^2+2x+2}{x-1}[/tex]

= [tex]= [x^2-3x+\frac{-x+2}{x-1}[/tex]

= [tex]= (x^2-3x-1)+ 1/ (x-1)[/tex]

Hence, the simplified division is x²-3x-1+ 1/ (x-1)

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The location of point P such that the ratio AP / PB = 2 / 3 is (1, - 2).

In this question we have the location of two endpoints of a line segment, point A (3, 0) and point B (- 2, - 5). About the line segment, we are asked to find the coordinates of a point P such that the following ratio is met:

AP / PB = 2 / 3

3 · AP = 2 · PB

3 · [P(x, y) - A(x, y)] = 2 · [B(x, y) - P(x, y)]

3 · P(x, y) - 3 · A(x, y) = 2 · B(x, y) - 2 · P(x, y)

5 · P(x, y) = 3 · A(x, y) + 2 · B(x, y)

P(x, y) = (3 / 5) · A(x, y) + (2 / 5) · B(x, y)

P(x, y) = (3 / 5) · (3, 0) + (2 / 5) · (- 2, - 5)

P(x, y) = (9 / 5, 0) + (- 4 / 5, - 10 / 5)

P(x, y) = (9 / 5, 0) + (- 4 / 5, - 2)

P(x, y) = (1, - 2)

The location of point P is (1, - 2).

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Answer:

3(2×4)=(3×4)2

%%%%%%%%

The correct answer is [b] ΔHGF and ΔABC.

In geometry, the two figures or objects are said to be congruent if their shapes and sizes match, or if one is the mirror image of the other.

In geometry, the two figures or objects are said to be congruent if their shapes and sizes match, or if one is the mirror image of the other.

Formally speaking, two sets of points are said to be congruent if—and only if—they can be changed into the one another by an isometry, which is a combination of rigid motions like translation, rotation, and reflection. This indicates that either object may be precisely aligned with the other object by moving and reflecting it, but not by resizing it. So if we can cut out and then perfectly match up two separate plane figures on a piece of paper, they are congruent. The paper may be turned over.

Triangles with two pairs of congruent sides and an included congruent angle are said to be congruent by ASA.

According to the graph, sides TU, FG, and BC are congruent, as well as sides TV, HG, and AB. Additionally, it shows that angles G and B are congruent as well as angles U, F, and C. Triangle TUV is eliminated because ASA cannot find another triangle that is equivalent to angle U of triangle TUV using the information provided.

The only triangles left are FGH and ABC. These triangles are congruent by ASA since it is clear that angles G and B are included angles.

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Answer: 9 square inches

Step-by-step explanation:

The distance run by Amy per minute is 0.132 miles.

Given,

The distance run by Amy = 7 miles

Time taken by Amy to cover this distance = 53 minutes

We have to find the distance covered by Amy in one minute.

So,

Distance covered by Amy per minute = x

Then,

7 / 53 = x / 1

7 × 1 = x × 53

Here,

x = 7/53

Then,

x = 0.132

That is,

The distance run by Amy per minute is 0.132 miles.

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The probability that the mean age of a sample of 36 vehicles is between 98 and 100 months is 15.71%.

For the given question;

The data for the vehicles registered in the united states is given as-

The formula for the z score is-

z = (x - μ)/(σ/√n)

Put the values.

√n = √36 = 6

For x = 98 months

z = (98 - 96)/(15/6)

z = 0.8

p(z < 0.8) = 0.7881

For x = 100 months

z = (100 - 96)/(15/6)

z = 1.6

p(z < 1.6) = 0.9452

P(0.8<x<1.6) = 0.9452 - 0.7881

P(0.8<x<1.6) = 0.1571

Thus, the probability that the mean age of a sample of 36 vehicles is between 98 and 100 months is 15.71%.

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For this following function by evaluating f(5)-f(4) we get -19.

What is evaluate?

Finding the value of an algebraic expression when a given number is used to replace a variable is known as evaluating the expression. When evaluating an expression, we change the variable in the expression to the given number and then use the order of operations to simplify the expression.

Sol- f(5)-f(4)

f(5)-f(4)= (-2.5^2-5+3)-(-2.4^2-4+3)

Calculate the power

(-2×25-5+3)-(-2×4^2-4+3)

Calculate the product or quotient

(-50-5+3)-(-2×16-4+3)

Calculate the sum

-52-(-32-4+3)

=-52-(-33)

determine the sign

=-52+33

By calculating the sum of difference we are get

-19.

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Transformations that maps ∆ABC to ∆A''B''C'' is [tex]A^{''}(8,-2)\\B^{''}(5,-2)\\C^{''}(7,0)[/tex]

A coordinate plane is a two-dimensional surface made up of two number lines. It is produced when a horizontal line crosses the origin, which is the location where the X-axes and Y-axes meet. The numbers on a coordinate grid are used to find points. Using a coordinate plane, you may graph points, lines, and many other things. It functions as a map and gives precise driving instructions between two spots.

Reflection about x - axes (x,y)→(x,-y)

Reflection about y - axes (x,-y)→(-x,-y)

combined reflection is reflection about origin.

[tex]A^{'}(5,-3) \\B^{'}(2,-3)\\[/tex]

[tex]C^{'}(4,-1)[/tex]

Shift upward by 1 unit and on right hand side by 3 units

(x,y)→(x+3;y+1)

=[tex]A^{''}(8,-2)\\B^{''}(5,-2)\\C^{''}(7,0)[/tex]

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In case whereby You launch a toy rocket from a height of 5 feet with the  height h, in feet of the rocket t seconds after taking off is given by the formula h = -3t2 + 14t + 5, then the value of t will be 4.67 secs.

The giving equation is h = -3t2 + 14t + 5

where the height h is been given as 5 feet, then we can substitute the value of the height they the expression can be simplified as

5 =  -3t^2 + 14t + 5

Then this equation can be re arranged as :

-3t^2 + 14t + 5 - 5=0

This can as well be expressed as

-3t^2 + 14t = 0

t(-3t + 14)= 0

Then t= 0 and -3t + 14=0

t=14/3 = 4.67 secs

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The expression 8.61 x 10-1 in standard form is 0.861

The expression is given as

8.61 x 10-1

Rewrite the equation properly as follows

So, we have the following expression

8.61 x 10^-1

Express 10^-1 as 1/10

So, we have the following expression

8.61 x 1/10

Evaluate the products

So, we have the following expression

8.61/10

Evaluate the quotient

So, we have the following expression

0.861

Hence, the expression is 0.861

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The monomial in standard form is 6x¹¹y¹⁸.

The given expression is

[tex](-3xy^{2})^{3} .(-\frac{2}{3}x^{2} y^{3} )^{4}[/tex]

We to write the expression as a monomial in standard form

Monomial is an expression having a single term. It can be represented as kxⁿ, where k is any integer often known as the coefficient, x represents the variable/s in the given expression and n denotes the power.

In the expression

[tex](-3xy^{2})^{3} .(-\frac{2}{3}x^{2} y^{3} )^{4}[/tex]

we first need to multiply the powers

using the formula

(mn)ˣ = mˣnˣ

[tex](-3xy^{2})^{3} .(-\frac{2}{3}x^{2} y^{3} )^{4}\\(-3x^3y^{2.3}) .(-\frac{2}{3}x^{2.4} y^{3.4} )\\(-3x^3y^{6}) .(-\frac{2}{3}x^{8} y^{12} )\\[/tex]

Now, we need to multiply both the terms

The following formula is used

xᵃ . xᵇ = xᵃ+ᵇ

[tex](-3x^3y^{6}) .(-\frac{2}{3}x^{8} y^{12} )\\\\-3(-\frac{2}{3})x^{3+8} y^{6+12} \\\\6x^{11}y^{18}[/tex]

Therefore the monomial in standard form is 6x¹¹y¹⁸.

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Step-by-step explanation:

Answer:

Step-by-step explanation:

variable expenses sum is 6,100

fixed expenses sum is 18,942  

Answer:

135

Step-by-step explanation:

two interior angles of a triangle equal to the exterior of the angle that is neither of the interior angles

so in this case

p + t = 135

a. 11 year growth factor = 1 + (26/100) = 1.26

   1-year growth factor = (1.26)^1/11 = 1.0210

   Therefore,

    1-year growth percent = 1.0210 - 1 = 0.0210 %

     Answer: 2.10

b. 13-year decay factor = 1 - (39/100) = 0.61

   1-year decay factor = (0.61)1/13 = 0.9631

    Therefore,

    13-year decay factor = 1 - 0.9631 = 0.03686 = 3.68%

     Answer: 3.68

c. 5-year growth factor = 3

   1-year growth factor = (3) ^1/5 = 1.245

   Therefore,

   1-year growth factor = 1.2457 - 1 = 0.2457 = 2.45%

   Answer:2.45

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Answer: [tex]\frac{\sqrt{x}^3 }{3}[/tex]

Step-by-step explanation:

Step 1: Insert f(x) in for the x in g(x). This will give you [tex]\sqrt{x^3}[/tex]

Step 2: Insert [tex]\sqrt{x^3}[/tex] into the x in h(x) giving you [tex]\frac{\sqrt{x}^3 }{3}[/tex]

Jade give away 3/4 fraction of the cake.

The three responses that can show a number of friends Wes could divide his tokens among evenly include:

25 tokens each for 2 friends.

5 tokens each for 5 friends.

10 tokens for 5 friends.

From the information, Wes wants to treat his friends to some arcade games. He has 50 game tokens.

It should be noted that this information simply wants you to illustrate the factors of 50.

Therefore, the factors are 2, 5, 10, 25 and 50.

Therefore, 25 for 2 friends will be 50. Same with 5 for 10 friends. In this case, it should be noted that 25 × 2 = 50 and 5 × 10 = 50. This gives the original value and shows how he can divide the game tokens equally.

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Answer:

The answer is

[tex] {(5y - 9)}^{2} [/tex]

Step-by-step explanation:

factor

[tex] {(25y }^{2} - 90y + 81)[/tex]

get the GCF of 25,-90,81=1

get the square root of leading terms

[tex] \sqrt{25 {y }^{2} } = 5y \: and \: \sqrt{81} = 9[/tex]

the final answer is

[tex] {(5y -9) }^{2} [/tex]