An angle measures 14.2° more than the measure of its supplementary angle. What is the measure of each angle?

Answer: 60

Step-by-step explanation: If you subtract then you will continue to get 60

In this question, measure of angle 4 is c. 60 degree. It has been calculated using properties of parallel lines.

It can be seen that in this question l and m are parallel lines and there is a transverse passing through it. We know through the properties of parallel lines that sum of ∠2 and ∠4 is 180° as they are consecutive interior angles and consecutive interior angles are supplementary meaning their sum is 180.

∠2 + ∠4 = 180° (consecutive interior angles)

120° + ∠4 = 180°

∠4 = 180 - 120

= 60°

Parallel lines are straight lines that never meet, no matter how far they are extended. Many pairs of angles are generated when two parallel lines are intersected by another line known as a transversal.

Some angles are congruent (equal), whereas others are supplementary (different).  Consecutive interior angles, also known as co-interior angles, develop on the inside of the transversal and are additional.

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From the given circles HJ is common external tangent.

From the given circles A and B,

1) EF is diameter.

2) EGf is semicircle.

3) G is point of tangency

4) HJ is common external tangent

5) CDK is semicircle

6) BF is radius

7) A is center.

8) KF is common external tangent

9) CD is segment

10) GK is chord

11) CK is minor arc

Therefore, from the given circles HJ is common external tangent.

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The height of the tree stump is approximately 32.5 inches. Where its radius as 22 in and its volume as 49265 cubic inches.

The volume of a right cylinder is calculated as follows:

V = πr²h

where V denotes volume, r denotes radius, and h denotes height.

We are provided the radius and volume of the tree stump in this scenario. We may plug these values into the algorithm to find the height:

49265 = π(22²)h

Simplifying the right-hand side, we get:

49265 = 484πh

Dividing both sides by 484π, we get:

h = 49265 / (484π)

h = 49265 / (484 * 3.14)

h = 49265/ 1519.76

h = 32.416

h ≈ 32.5

Therefore, the height of the tree stump is approximately 32.5 inches.

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Answer:

perimeter = 12.72 cm

Step-by-step explanation:

an equilateral triangle has 3 congruent sides

the perimeter is the sum of the 3 sides , that is

perimeter = 4.24 + 4.24 + 4.24 = 12.72 cm

Answer:

9th term = 524288

Step-by-step explanation:

An equation we can use to find the nth term in a geometric sequence is:

[tex]a_{n}=a_{1}(r)^(^n^-^1^)[/tex], where

Step 1:  We're already given that a1 = 8 and that n = 9 (since we want to find the 9th term).  However, we need to find the common ratio by dividing two consecutive terms with the successive term being divided by the preceding term.  We can divide 32 by 8 to find r, the common ratio:

r = 32/8

r = 4

Thus, the common ratio of the sequence is 4

Step 2:  In order to find the 9th term of the sequence, we can plug in 8 for a1, 4 for r, and 9 for n and simplify:

[tex]a_{n}=8(4)^(^9^-^1^)\\a_{n}=8(4)^8\\a_{n}=8(65536) \\a_{n}=524288[/tex]

Thus, the 9th term of the geometric sequence is 524288.

(5, 55) is the range of the given curve.

The given graph is similar to a quadratic graph. The range of a function is defined as the values of the function that lies along the y-coordinate.

From the given graph, the range will lie between the initial point on the graph top the vertex.

The initial point is (0, 5) while the vertex is (1, 55). The equivalent y-coordinate values will form the values for the range.

Hence the range of the given graph is (5, 55)

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The scale factor from triangle D to triangle D' is 4

From the question, we have the following parameters that can be used in our computation:

The triangles

From the triangles, we have the following parameters

Using the above as a guide, we have the following:

Scale factor of the dilation = Corresponding side length of D' / Side length of D

So, we have

Scale factor of the dilation = 32/8

Evaluate

Scale factor of the dilation = 4

Hence, the scale factor of the dilation is 4

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The arithmetic operations used to make the number 24 is  (7 - 5) × (7 - 5) = 24

To make the number 24 using the digits 5, 5, 7, and 7, you can use the following arithmetic operations:

(7 - 5) × (7 - 5) = 24

In this case, we subtract 5 from 7 to get 2, and then multiply the result by itself to get 24.

7-5=2.

Subtract the second 5 from the remaining 7: 7-5=2.

Multiply 2 and 2: 2x2=24.

Number 24 was created using 5, 5, 7, and 7.

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Answer:

The y-intercept is -3

Written as a point it is (0, -3)

Step-by-step explanation:

To find the y-intercept, let x = 0

(and to find x-intercepts, let y = 0)

So let's let x = 0

f(x) = x^2 + 2x - 3

y = x^2 + 2x - 3

y = 0^2 + 2(0) - 3

y = -3

This means the y-intercept is -3. The graph crosses the y-axis at -3. This is the point (0, -3).

Step-by-step explanation:

The first step is to find the radius of the circle, which is half the diameter:

r = 5.6/2 = 2.8 inThe area of the entire circle is:

A = πr² = 3.14 x 2.8² = 24.616 in²To find the area of the sector, we need to multiply the area of the whole circle by the fraction of the circle represented by the central angle. Since the central angle is 130° out of 360° (a full circle), the fraction of the circle represented by the sector is:

130/360 = 13/36Therefore, the area of the sector is:

A = (13/36) x 24.616 = 8.912 in²Rounding to the nearest hundredth, we get:

A ≈ 8.91 in²Therefore, the area of the sector is approximately 8.91 in².

Answer: [tex]cosx =- \sqrt{ 1 - sin^2x}[/tex]

Step-by-step explanation:

Generally speaking; [tex]cos^2x + sin^2x = 1[/tex]

rearranging this gives us all sorts of cool things.

for now, we will use: [tex]cosx = \sqrt{ 1 - sin^2x}[/tex]

This however, is general.

In the third quadrant, cosine is negative. So cosx in QIII will be:

[tex]cosx =- \sqrt{ 1 - sin^2x}[/tex]

and thats the answer :)

Probability = # of desired options / # of total options

Our desired option is blue and there are 9 blue marbles in the bag.

There are 32 total marbles (options) in the bag.

P(blue) = 9 / 32 = 0.28125 = 28.125%

Hope this helps!

To find the best prediction of the cost of the groceries nine years after the beginning of the study, we need to use the given data to find the values of a and b in the function C=a(b)x. So, the best prediction of the cost of the groceries nine years after the beginning of the study is $53.34.

To do this, we can use the first data point where x = 0:
30 = a(b)^0

This simplifies to:  

30 = a
So, we know that a = 30.

Next, we can use any other data point to solve for b. Let's use the second data point where x = 1:
32.10 = 30(b)^1

This simplifies to:
32.10 = 30b
b = 1.07
Now we can use the function C = 30(1.07)^x to find the best prediction of the cost of the groceries nine years after the beginning of the study:
C = 30(1.07)^9
C ≈ $53.34

Therefore, the best prediction of the cost of the groceries nine years after the beginning of the study is $53.34.

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The graph of the modulus function is plotted

Given data ,

Let the modulus function be represented as A

Now , the value of A is

| x | + 1 < 3

On simplifying the inequality , we get

Subtracting 1 on both sides , we get

| x | < 2

When x is positive or zero: In this case, the absolute value of x is equal to x itself. Therefore, we have x < 2

When x is negative: In this case, the absolute value of x is equal to -x. Therefore, we have -x < 2

Hence , the graph of function is plotted

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The total volume of the composite figure is 64 in³.

Volume of a rectangular prism

The volume of a rectangular prism, V = lwh where

l = length,

w = width and

h = height

Volume of horizontal rectangular prism

Since horizontal rectangular prism has a length of eight inches, a width of two inches, and a height of two inches. So,

l = 8 in,

w = 2 in and

h = 2 in.

So, its volume V' = lwh

= 8 in × 2 in × 2in

= 32in³

Volume of vertical rectangular prism,

Since the vertical rectangular prism connected at the right end of the other prism has a length of two inches, a width of two inches, and a height of eight inches. So,

l = 2 in,

w = 2 in and

h = 8 in.

So, its volume V" = lwh

= 2 in × 2in × 8 in

= 32 in³

Volume of composite figure

The volume of the composite figure V"' = V' + V"

= 32 in³ + 32 in³

= 64 in³

So, the total volume of the composite figure is 64 in³.

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This value is quite close to the doubling time approximation of 18 years that is often used for populations growing at a rate of 4% per year.

The given rate of growth = 4.1%

We know that,

The doubling time is the amount of time required for a population to double in size or value.

It is used to calculate population growth, inflation, resource extraction, commodities consumption, compound interest, the volume of malignant tumors, and a variety of other things that tend to develop over time. When the relative growth rate is constant (rather than the absolute growth rate), the amount grows exponentially and has a constant doubling time or period, which may be determined simply from the growth rate.

Formula for calculating the doubling time using logarithms is:

doubling time = ln(2) / (annual growth rate)

Since 41% = 0.041

doubling time = ln(2) / (0.041)

doubling time = 16.85 years

So the doubling time for South Sudan's population at this growth rate is approximately 16.85 years ≈ 18 years

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Note that the  the probability that both spins result in the same color is 0.28

Probability of getting ...


red on both spins = (1/5) x   (1/5) = 1/25

yellow on both spins = (1/5) x  (1/ 5) =  1/25

blue on both spins = (1/5) x  (1/5 =  1/25

pink on both spins = (2/5)x (2/5) =  4/25

So the total   probability of getting the same color in both spins is computed as        

= 1/25 + 1/25 +  1/25 +  4/25

= 7/25 or 0.28

So the correct asnwer is 0.28 or 7/25

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The cost of electricity consumption (excluding VAT) for a household using 196 kWh in a month is given by [tex]\( \text{Cost} = 196 \, \text{kWh} \times r \), where \( r \)[/tex]represents the rate per kilowatt-hour charged by the electricity provider.

To determine the cost of electricity consumption excluding VAT, we need to know the rate charged per kilowatt-hour (kWh) by the electricity provider. Let's denote this rate as [tex]\(r\)[/tex] (in currency per kWh).

The total cost of electricity consumption (excluding VAT) can be calculated by multiplying the electricity usage in kWh by the rate:

[tex]\[ \text{Cost} = \text{Usage} \times \text{Rate} \][/tex]

Given that the household uses 196 kWh in a month, the cost can be expressed as:

[tex]\[ \text{Cost} = 196 \, \text{kWh} \times r \][/tex]

Please note that we still need the specific rate per kWh from the electricity provider to calculate the actual cost.

The cost of electricity consumption (excluding VAT) for a household using 196 kWh in a month is given by [tex]\( \text{Cost} = 196 \, \text{kWh} \times r \), where \( r \)[/tex]represents the rate per kilowatt-hour charged by the electricity provider.

Note: The given question is incomplete. The complete question is:

If a household uses 196kWh of electricity in a month how much would they pay for their electricity consumption excluding VAT?

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Answer:

1.

The cost of the carpet is given in dollars per square foot.

First I calculated the number of square feet which is the area of the carpet.

Then I multiplied the area of the carpet in square feet by the unit cost of the carpet.

2.

$576

Step-by-step explanation:

A = LW

A = 12 ft × 12 ft

A = 144 ft²

Unit cost of carpet: $4/ft²

cost of carpet = unit cost × area of carpet

cost of carpet = $4/ft² × 144 ft² = $576

1.

The cost of the carpet is given in dollars per square foot.

First I calculated the number of square feet which is the area of the carpet.

Then I multiplied the area of the carpet in square feet by the unit cost of the carpet.

2.

$576

The area of a right triangle with a height of 8 yards and a base of 17 yards is 136 square yards.

The area of a right triangle with a height of 8 yards and a base of 17 yards can use the formula for the area of a triangle:

Area = (base x height) / 2

Substituting the given values into the formula get:

Area = (17 x 8) / 2

Area = 136 square yards

The area of the right triangle is 136 yd².

To understand why this formula works can visualize the right triangle as half of a rectangle.

The height of the triangle is one side of the rectangle and the base of the triangle is the adjacent side of the other half of the rectangle.

The area of the rectangle is the product of its height and base is twice the area of the right triangle.

The product of the height and base by 2 to get the area of the right triangle.

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Answer:

301.593 mm²

Step-by-step explanation:

surface area of cylinder = 2π r² + 2π r h

where r = radius and h = height

so we have surface area = 2π (4)² + 2π (4) (8)

= 32π + 64π

= 96π mm² (in exact form)

= 301.593 mm² (to one-thousandth of mm)

Step-by-step explanation:

To calculate the value of Elia's share in the business, we need to multiply the company's worth by the fraction representing Elia's ownership.

Here's the calculation:

(2/5) * $157,000 = $62,800

So, the value of Elia's share in the business is approximately $62,800.

Answer:

His share is 62800 dollars

Step-by-step explanation:

You would divide 157000 by 5 and then multiply your answer by 2.

The estimated circumference of the Moon's orbit around the Earth is approximately 1,579,896.8 kilometers.

The circumference of the Moon's orbit around the Earth can be estimated using the given distance of 251,400 kilometers.

The circumference of a circle is calculated using the formula:

Circumference = 2 × π × Radius

The Moon's orbit around the Earth can be considered as a circular path.

We can estimate the circumference by considering the given distance as the radius of the circle.

Circumference ≈ 2 × π × 251,400 kilometers

Using an approximate value of π as 3.14, we can calculate the estimated circumference:

Circumference ≈ 2 × 3.14 × 251,400 kilometers

Circumference ≈ 1,579,896.8 kilometers

The stated distance of 251,400 kilometres can be used to calculate the circumference of the Moon's orbit around the Earth.

In order to determine a circle's circumference, use the following formula:

Circumference equals two radii.

It is possible to think of the Moon's orbit around the Earth as a circle.

By using the specified distance as the circle's radius, we can calculate the circumference.

Approximately 251,400 km around.

We may determine the approximated circumference using an approximation of as 3.14:

= 2 × 3.14 × 251,400 kilometers around the earth.

1,579,896.8 km around the circumference

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Answer: its D because Jews (Hebrew: יְהוּדִים, ISO 259-2: Yehudim, Israeli pronunciation: [jehuˈdim]) or Jewish people are an ethnoreligious group,[10] nation or ethnos[11][12] originating from the ancient Israelites[13][14][15] and Hebrews[16][17][18] of historical Israel and Judah. Jewish ethnicity, nationhood, and religion are strongly interrelated,[19][20] as Judaism is the ethnic religion of the Jewish people, although its observance varies from strict to none.[21][22]

Jews originated as an ethnic and religious group in the Middle East during the second millennium BCE,[9] in a part of the Levant known as the Land of Israel.[23] The Merneptah Stele of ancient Egypt appears to confirm the existence of a people of Israel somewhere in Canaan as far back as the 13th century BCE (Late Bronze Age).[24][25] The Israelites, as an outgrowth of the Canaanite population,[26] consolidated their hold in the region with the emergence of the kingdoms of Israel and Judah. Some consider that these Canaan-sedentary Israelites melded with incoming nomadic groups known as the "Hebrews".[27] The experience of life in the Jewish diaspora, from the Babylonian captivity and exile (though few sources mention this period in detail[28]) to the Roman occupation and exile, and the historical relations between Jews and their homeland in the Levant thereafter became a major feature of Jewish history, identity, culture, and memory.[29]

In the following millennia, Jewish diaspora communities coalesced into three major ethnic subdivisions according to where their ancestors settled: the Ashkenazim (Central and Eastern Europe), the Sephardim (initially in the Iberian Peninsula), and the Mizrahim (Middle East and North Africa).[30][31] Prior to World War II, the global Jewish population reached a peak of 16.7 million,[32] representing around 0.7 percent of the world population at that time. During World War II, approximately 6 million Jews throughout Europe were systematically murdered by Nazi Germany during the Holocaust.[33][34] Since then, the population has slowly risen again, and as of 2018, was estimated to be at 14.6–17.8 million by the Berman Jewish DataBank,[1] comprising less than 0.2 percent of the total world population.[35][note 1] The modern State of Israel is the only country where Jews form a majority of the population.

Step-by-step explanation: Hitler + jew=bad

Answer: The expression showing the total number of gel pens ="8g"

Step-by-step explanation:

Number of bags with Zoe= 8

Number of gel pens with Zoe=g

According to the question, Zoe puts g gel pens in  each one of the 8 bags, which means that the total number of gel pens would be the sum of all pens present in all the 8 bags .

=(no of pens in one bag)x(no of bags)

=gx8

=8g

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Step-by-step explanation:

The formula for the nth term of an arithmetic sequence is:

a_n = a + (n - 1)d

where a is the first term, d is the common difference, and n is the term number.

Substituting a=1 and d=5, we get:

a_n = 1 + (n - 1)5

Simplifying this expression, we get:

a_n = 5n - 4

Therefore, the formula for the nth term of the arithmetic sequence with first term a=1 and common difference d=5 is a_n = 5n - 4.

Answer:

nth=3n+1. (B) nth=5n−13. Explanation: the nth term of an Ap is given by. nth=a+(n−1)d. (A). nth=4+(n−1)3. nth=4+3n−3.

The correct option is c. $300,000. In 2007, the FDIC’s insurance limit was $100,000 per person per bank. Kit had three separate $50,000 CDs at Bank R, a $60,000 checking account and a $140,000 money market account at Bank S, and an $80,000 savings account at Bank T.

How much of Kit’s money was FDIC insured?The amount of Kit’s money that was FDIC insured was c. $300,000.In 2007, the Federal Deposit Insurance Corporation (FDIC) insured deposit accounts up to $100,000 per person per bank, or up to $250,000 for certain retirement accounts.

This means that if the bank fails, the FDIC will provide insurance coverage up to the specified amount for the deposits.Based on the details given in the question, we need to calculate the amount of Kit’s money that was FDIC insured.Kit has the following accounts:

Three $50,000 CDs at Bank R.$60,000 checking account and a $140,000 money market account at Bank S.$80,000 savings account at Bank T.

So, the total amount of money that Kit has is:$50,000 + $50,000 + $50,000 + $60,000 + $140,000 + $80,000 = $430,000Therefore, the total amount of Kit’s money that was FDIC insured is:$100,000 (maximum amount insured per person per bank) × 3 banks = $300,000.So, the correct option is c. $300,000.

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Answer:

The answer is B) 280,000

Step-by-step explanation: