Finding Angle Measures When Parallel Lines Are Cut By a Transversal

Answer:

The amount of cholesterol in 11 ounces of lobster is 220 mg

Step-by-step explanation:

The amount of cholesterol in 11 ounces of lobster can be calculated as follows

The first step is to convert all units of measure from ounce to mg

1 gram = 0.0352 ounce

Divide both sides by 0.0352 to get the value of 1 ounce

[tex]\frac{1}{0.0352}[/tex] gram = [tex]\frac{0.0352}{0.0352}[/tex] ounce

28.35 gram = 1 ounce

Since 1 gram equals 1000 milligrams, then multiply the left side by 1000 and change the unit of measure to milligram

28.35 [tex]\times[/tex] 1000 mg = 1 ounce

28350 mg = 1 ounce

Convert 3.6 ounces to milligrams

3.6 ounces = 3.6 [tex]\times[/tex] 28350 mg

3.6 ounces = 102060 mg

Convert 11 ounces to milligrams

11 ounces = 11 [tex]\times[/tex] 28350 mg

11 ounces = 311850 mg

Since there are 72 mg of cholesterol in a 3.6 ounces serving of lobster, then the ratio equation to follow is

[tex]\frac{72}{102060}=\frac{x}{311850}[/tex]

Where x is the amount of cholesterol in 11 ounces of lobster

Multiply both sides by 311850 to isolate x

[tex]\frac{72}{102060}\times 311850=\frac{x}{311850}\times 311850[/tex]

[tex]\frac{22453200}{102060} =x[/tex]

Simplify the left side of the equation

220 = x

Since the value of x is 220, then the amount of cholesterol in  11 ounces of lobster is 220 mg

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Answer:

n = 8

Step-by-step explanation:

to solve this equation you must first isolate the variable

that is n

so first

add 2n to both sides to get rid of n on one of the sides

-4n + 2n + 14 = -2 - 2n + 2n

-2n + 14 = -2

now subtract 14 to both sides to isolate n

-2n + 14 - 14 = -2 - 14

-2n = -16

now divide everything by -2 to isolate n completely

(-2n)/(-2) = (-16)/(-2)

n = 8

that is your answer

Answer:

[tex]\boxed{\sf n=8}[/tex]

Step-by-step explanation:

[tex]\sf -4n+14=-2-2n[/tex]

Subtract 14 from both sides:-

[tex]\sf -4n+14-14=-2-2n-14[/tex]

Simplify:-

[tex]\sf -4n=-2n-16[/tex]

Add 2n to both sides:-

[tex]\sf -4n+2n=-2n-16+2n[/tex]

Simplify:-

[tex]\sf -2n=-16[/tex]

Divide both sides by -2:-

[tex]\sf \cfrac{-2n}{-2}=\cfrac{-16}{-2}[/tex]

Simplify:-

[tex]\sf n=8[/tex]

____________________

Hope this helps!

Have a great day!

Area of the base 'B' of a given rectangular prism is equal to 12 ft².

As given in the question,

For the given rectangular prism ,

Shape of the base is rectangle,

Length of the base of a rectangular prism = 4 ft

Width of the base of a rectangular prism = 3ft

Area of the base of a rectangular prism is given by

= ( length of the base ) × ( Width of the base)

Substitute the value of length and width of the base of the rectangular prism we get,

= ( 4 × 3 ) ft²

= 12 ft²

Therefore, area of the base 'B' of given rectangular prism is equal to 12 ft².

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Answer:

Step-by-step explanation:

By the use of the law of conservation of mass, the mass of the aluminum chloride is  267 g.

We know that a chemical reaction occurs when there is the combination of two or more substances such that a new substances is formed. We have to put down the reaction equation in this case and we have;

[tex]4Al(s) + 3ZnCl_{2} (aq) ---- > 2Al_{2} Cl_{3}(aq) +3 Zn(s)[/tex]

Using the law of the combination of mass, the total mass of the reactants must be equal to the total mass of the products; Let the mass of the aluminum chloride formed be x

54 + 409.2 = 196.2 + x

x = (54 + 409.2) - 196.2

x = 267 g

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Reciprocal functions have a general form of:

Let's see which of the given functions follow same form:

All the other functions are either linear or quadratic functions.

answer

microstates

Step by step explanation

Answer:1/9 or decimal form it’s ≅ 0.111111

Answer:

156

Step-by-step explanation:

36*3=108

8*-6=-48

108-(-48)=156

The solution of the expression 36(3) - 8(-6) will be 156.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that the expression is 36(3) - 8(-6). the expression will be solved as below,

E = 36(3) - 8(-6)

E = 108 - ( -48 )

E = 108 + 48

E = 156

Hence, the solution will be 156.

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Answer:

13

Step-by-step explanation:

This is a special right triangle with side lengths 5-12-13 respectively.

If we can't remember the lengths we can use the following formula to calculate the lentgh of hypotenuse:

[tex] {a}^{2} + {b}^{2} = {c}^{2} [/tex]

the sum of square measure of both legs is equal to the square measure of hypotenuse

[tex] {5}^{2} + {12}^{2} = {c}^{2} [/tex]

25 + 144 = c^2

169 = c^2 find the root of both sides

13 = c, hypotenuse.

Answer:yesno

Step-by-step explanation:

yes

Using linear equation model, the change per week in the amount in the account is 20 dollars per week.

The starting amount of the money in the account is 350 dollars.

Omar is putting money into a checking account. y represent the total amount of money in the account (In dollars). x represent the number of weeks Omar has added money.

x and y are related with the equation y = 350 + 20x

The equation can be modelled to a linear equation.

Therefore,

y = mx + b

where

Therefore,  according to the equation, the change per week  in the amount if money is in the account is 20 dollars per week.  The slope is the rate of change.

The starting money amount of money in the account is the y-intercept of the equation which is 350 dollars

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Answer:

- 5/2 (z + 2)

Step-by-step explanation:

Distribute

- 7/2 z - 2 + z - 3

Subtract the numbers

- 7/2 z - 5 + z

Combine like terms

- 5/2 z - 5

Common factor

- 5/2 (z + 2)

The 95% Confidence Interval for the mean number of defects per screen for all screens produced by this manufacturer is (1.447646, 2.352354)

Given Data:

3, 5, 0, 3, 5, 2, 5, 1, 0, 0, 0, 4, 2, 1, 0, 5, 1, 0, 1, 1, 0, 2, 0, 2, 1, 0, 2, 4, 4, 3, 2,

2, 3, 2, 1, 2, 1, 1, 4, 1, 1, 6, 0, 3, 1, 0, 2, 2, 1, 3

We calculate sample mean and standard deviation from given data.

Sample Mean, a = 2 (2) _ 95

-50

= 1.9

Sample Variance, $2 _ _(2 -x)2 _130.5

= 2.663265

n - 1

49

Sample std dev, s = V82 = v2.663265 ~ 1.631951

95% CI for u using Normal dist

Sample Mean = T = 1.9

Since sample size is large, sample standard deviation can be taken as an approx-

Limation of population standard deviation.

Population Standard deviation = o ~ 1.631951

Sample Size = n = 50

Significance level = 0 = 1- Confidence = 1 - 0.95 = 0.05

The Critical Value = za/2 = 20.025 = 1.96 (From z table)

Critical Values , 1za/2 = 41.96

Margin of Error = E = za/2 X -= 1.96 x 1.631951

0.452354

V50

Margin of Error, E = 0.

Limits of 95% confidence interval are given by:

Lower limit = I - E = 1.9 -0.452354 ~ 1.447646 ~ 1.448

Upper limit = I + E = 1.9 + 0.452354 ~ 2.352354 ~ 2.352

95% confidence interval is: T + E = 1.9 4 0.452354

= (1.447646, 2.352354)

95% CI using normal dist: (1.448 ) < < (2.352)

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Answer:

26

Step-by-step explanation:

Supplemental means that the two angles together equal 180

124 + 2x + 4 = 180  Combine like terms

128 + 2x = 180  Subtract 128 from both sides of the equation

2x = 52  Divide both sides by 2

x = 26

Choices made by consumer leads to financial irresponsibility are as follow:

As given in the question,

Choices made by consumer leads to financial irresponsibility are as follow:

When a person is spending money just on emotional feeling and buying large gifts for children which is beyond the budget. Due to this habits a person may have to take debt.

When a person is not saving enough money for the time of emergency, it can be a medical emergency then it is financial  irresponsible behavior.

When you are not making any budget and spending money ,it might possible at the end of the month or some time you have to face financial crises.

Don't compare yourself with anyone, this might lead you to take loan or debts which lead your life in facing financial trouble.

Therefore, choices made by consumer leads to financial irresponsibility are as follow:

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Situations a and c can represent a proportional relationship. Options a and c are correct.

It is defined as the relationship between two quantities as one quantity increases the other quantity also increases and vice versa.

The following situations are found to represent proportionality using the concept of proportionality:

A) The total amount a babysitter makes who earns $10 an hour for babysitting r hours.

C) The total amount Andrew saves when he saves $24 a week for w weeks.

Thus, situations a and c can represent a proportional relationship. Options a and c are correct.

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The third congruent side is not included the side of angles thus it will be congruent by the AAS rule thus option (B) is correct.

If two figures are exactly the same in sense of their length side all things then they will be congruent.

In other meaning, if you can copy a figure then that copy and the original figure will be congruent.

As per the given two triangles,

The two angles are congruent.

The sides which are congruent in both triangles are not the common side of angles or not included in the side of angles thus it will be AAS congruency.

Hence "The third congruent side is not included the side of angles thus it will be congruent by the AAS rule".

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Part a:  The side of the square is found as 6 cm.

Part b: The side length of the square is found as 10 cm.

For the given dimensions for the question,

Part a: Area of square is same as area of rectangle.

Rectangle area = Length x breath

Rectangle area =  18 x 2

Rectangle area =  32 sq. cm

Now,

Area of square = Rectangle area

Area of square = side²

36 =  side²

side = √36

side = 6 cm.

Thus, the side of the square is found as 6 cm.

Part b: Side length of square.

Rectangle perimeter =  square perimeter

Rectangle perimeter =  2(length + width)

Rectangle perimeter =  2(18 + 2)

Rectangle perimeter =  40

square perimeter = 4 side

40 = 4 side

side = 40/4 = 10 cm.

Thus, the side length of the square is found as 10 cm.

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Explanation:

We can do cross multiplying through ratios:

310 feet / 10 secs = x feet / 12 secs

10x = 310 * 12

10x = 3720

x = 372 feet

OR

Divide 310 feet and 10 secs to get 31 feet in 1 sec

Multiply 31 ft and 1 sec to get 372 ft in 12 secs

No, this solution is not valid because of wrong concept and wrong calculations as he solved  [tex]\frac{10^{-7} }{10^{-2} }[/tex]  as [tex]10^{-7 + (-2)}[/tex]  but it should be solved as [tex]10^{-7-(-2)}[/tex] .

These exponents can be split since they all share the same base, x. You divide them by the highest exponent in the numerator (the numerator) and the lowest exponent in the denominator (the bottom exponent).

So according to it,

As they have same the base i.e. 10, we will subtract their power which would be like  [tex]10^{-7-(-2)}[/tex]  = [tex]10^{-5}[/tex] not the [tex]10^{-9}[/tex].

Hence, the solution is not valid due to the wrong concept and wrong calculations.

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It is nonlinear because linear functions, which correspond to option D on the provided graph, grow or shrink at the same rate.

On the coordinate plane, a straight line can be represented by a linear function. In the coordinate plane, for instance, the linear function denoted by the equation y = 3x - 2 is a straight line. The graph of a linear function is a straight line. The form of a linear function is depicted below. a + bx = y = f (x). One independent variable and one dependent variable make up a linear function. X and Y are the independent and dependent variables, respectively.

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Answer: y=9/7

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

The required expression is

(4/3)π(7)³

What is volume?

In three-dimensional space, volume is the area occupied by an object within its borders. Another name for it is an object's capacity.

We are given to select the correct expression that gives the volume of a sphere with a radius of 7 units.

We know that,

the VOLUME of a sphere with radius 'r' units is given by

V=(4/3)πr³

Here, the radius of the given sphere is

r = 7 units.

Therefore, the volume of the sphere will be

V=(4/3)π(7)³

Thus, the required expression is

(4/3)π(7)³

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Answer:

Where the angle bisectors cross

Where the perpendicular bisectors cross

Answer:

-4/-5

Step-by-step explanation:

Gotchu bro

Answer:

4/5 or 0.8

Step-by-step explanation:

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