A recent survey was conducted to compare the cost of solar energy to the cost of gas or electric energy. Results of the survey revealed that the distribution of the amount of the monthly utility bill of a 3-bedroom house using gas or electric energy had a mean of $91 and a standard deviation of $8. If the distribution can be considered mound-shaped and symmetric, what percentage of homes will have a monthly utility bill of more than $83?

An equation to represent the total amount she has saved each month is 350x + 1200.

We have to write an equation to represent the total amount she has saved each month.

Brynn has $1,200 in her savings account and plans to save an additional $350 each month in order to purchase a car.

To write an expression we have to read the statement very carefully and also write the expression after reading the statement.

Let she save the money in x months.

If she save $350 each month, then the total saving in x months = 350x

She has $1200 in saving account. Now the expression is

= 350x + 1200

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Answer: ∠LKM=56° and ∠MKN=89°

Step-by-step explanation:

Notice that ∠LKM and ∠MKN make up ∠LKN. That means ∠LKM and ∠MKN combines equals 145°.

2x+10+4x-3=145               [combing like terms]

6x+7=145                           [subtract both sides by 7]

6x=138                              [divide both sides by 6]

x=23

We are almost done. We still need to plug it in to find the angle values.

∠LKM

2x+10                                 [plug in x=23]

2(23)+10                             [multiply]

46+10                                 [add]

56

∠LKM=56°

------------------------------------------------------------------------------------------------------------

∠MKN

4x-3                                   [plug in x=23]

4(23)-3                                [multiply]

92-3                                    [subtract]

89

∠MKN=89°

Therefore, ∠LKM=56° and ∠MKN=89°.

An algebraic expression which represents this word description "The quotient of nine and the sum of a number and one" is: D. 9 over x+1.

In Mathematics, a quotient can be defined as a mathematical expression that is simply used to represent the division of a number by another number.

In order to translate this word problem into algebraic equation, we would assign a variable to the unknown number and then translate the word problem into algebraic equation as follows:

Let the variable n represent the unknown number.

Translating the word problem into an algebraic equation, we have the following;

Quotient = 9/(x + 1)

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Complete Question:

Which algebraic expression represents this word description?

The quotient of nine and the sum of a number and one

A. x+1 over 9 B. 9/x +1 C. x/9 +1 D. 9 over x+1

If BC=6x-2 and DE=2x+2, then the length of BC is 16.

DE is a midsegment of the triangle.

As we know that;

A midsegment is a line segment that joins two of the midpoints of a triangle's sides.

The midsegment linking the midpoints of two sides of a triangle is parallel to the third side of the triangle, and its length is half that of the third side, according to the midsegment theorem.

So according to Midpoint Theorem

DE = BC/2

Now putting the value

2x+2 = (6x-2)/2

Multiply by 2 on both side, we get

4x + 4 = 6x-2

Add 2 on both side, we get

6x = 4x + 6

Subtract 4x on both side, we get

2x = 6

Divide by 2 on both side, we get

x = 3

Now putting the value of x in BC=6x-2

BC = 6(3) - 2

BC = 18 - 2

BC = 16

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Answer:

answer - x = − 12/7

The sketch a normal curve is attached below and in Normal Curve with mean of 50 and a Standard Deviation of 2.

The term normally curve in math is defined as a normal distribution is proper term for a Probability bell curve.

While we looking into the question we know that here from the Right of Normal standard curve we have to draw 3 vertical lines. And these lines would count up by 2 for each standard deviation 52, 54,56.

And then we have to plot from the Left of Normal standard curve, and then draw 3 vertical lines. And those lines would count up by 2 for each standard deviation 48,46,44.

Thus Normal standard curve extends indefinitely in both directions, and by approaching on the other hand it never touching the horizontal axis as it does so.

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The area of the shaded region of the circle is  1836.9 km².

Both circles have the same centre. The circumference of the inner circle is 100.48 kilometres. The circumference of a circle is the perimeter of the circle.

Therefore, the area of the shaded portion can be calculated as follows:

Hence,

circumference of the inner circle = 2πr

100.48 = 2 × 3.14 × r

100.48 = 6.28 r

r = 100.48 / 6.28

r = 16 km

Therefore,

area of the inner circle = πr²

area of the inner circle = 3.14 × 16²

area of the inner circle = 803.84 km²

area of the outside circle = πr²

area of the outside circle = 3.14 × (16 + 13)²

area of the outside circle = 3.14 × 29²

area of the outside circle = 2640.74 km²

Therefore,

area of the shaded region =  2640.74  - 803.84

area of the shaded region =  1836.9 km²

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Answer:

10;37°

Step-by-step explanation:

Pythagoras theorem will be used to find the length of EF and the knowledge of complementary angles will be used to solve for angle D

Each numbered angle has a measurement of 109°, 109°, and 71°, respectively.

Two rays that come together at a vertex or node, also known as a common point, to produce an angle for any figure.

Angles are frequently expressed in degrees or radians.

Think about triangle

A triangle's internal angles add up to 180°.

URS, UVT, and URT add up to 180°.

35° + 36° + ∠1 = 180°

∠1 = 180° - (35° + 36°)

∠1 = 180° - 71°

∠1 = 109°

The angles 1 and 2 are now vertically opposed. This makes them equal.

∠2 = 109°.

For triangle NQO once more

∠2 + ∠3 + 35° = 180°

36° + ∠3 + 35° = 180°

∠3 = 180° - (35° + 36°)

∠3 = 180° - 109°

∠3 = 71°

As a result, 1, 2, and 3 are 109, 109, and 71 degrees, respectively.

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Answer: Given that 6log3 + 7 - 3loga = 0, we can start by isolating the variable a. To do this, we'll add 3loga to both sides:

6log3 + 7 = 3loga

Next, we'll divide both sides by 3:

2log3 + (7/3) = loga

Now we have loga on one side of the equation and a constant on the other. To find the possible values of a, we'll need to use the properties of logarithms.

We know that logb(x) = y is equivalent to b^y = x, so we can rewrite the equation as:

a = 3^(2log3 + (7/3))

To find the possible values of a, we'll need to evaluate the exponent on the right side of the equation. Since we don't know the value of log3, we can't find the exact value of a. However, we can say that the possible values of a are all the values that can be expressed as 3 raised to the power of (2log3 + (7/3))

Step-by-step explanation:

The measure of angle P is 82°.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

125° and (109° + ∠N) are alternate angles.

Alternate angles are equal.

125 = 109 + ∠N

∠N = 125 - 109

∠N = 16

Now,

The sum of the triangle ABC is 180.

∠P + ∠M + ∠N = 180

Sides opposite to equal angles are equal.

∠P = ∠M

2∠P + 16 = 180

2∠P = 180 - 16

2∠P = 164

∠P = 164/2

∠P = 82

Thus,

∠P is 82°.

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The number is decreased by 1%.

Now, According to the question:

Let the number be 100

Number is increased by 10% = 100+10% of 100

=100+10

=110

Now, the resultant number is reduced by 10% =110-10% of 110

=110-11

=99

The number obtained is 99

Decrease in value = 100 – 99 = 1

Percentage decrease = 1100 × 100=1%

Hence, the number is decreased by 1%.

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The Volume or liters required to fill a 12.0 - gal gas tank is 45.42 liters.

Gallon to liter conversion factors are:

[tex]1 \ Gallon = 3.785 \ Liter[/tex]

Assuming that the gallon measurement for the gas tank is 12.0 gal.

We now need to calculate the gas tank's liter capacity.

As, 1 gallon = 3.785 liter

[tex]So \ 12\ gallon = 12*3.785[/tex]

[tex]=45.42\ gallons.[/tex]

Therefore, 45.42 liters of liquid are needed to fill the gas tank.

Meaning of gasoline:

Petroleum is the source of gasoline, which is a mixture of flammable, volatile liquid hydrocarbons used as a fuel for internal combustion engines and as a solvent for oils and fats.

It is a by-product of the petroleum industry and is used as fuel for cars because it burns with a high degree of energy and mixes easily with air in a carburetor.

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The diameter of a bowling ball that rolls 96 cm down the lane each time it turns once is 16.58 cm

the term called diameter is known as the length of the line through the center that touches two points on the edge of the circle.

Here we know that the ball rolls 96 cm down the lane each time it turns once.

According to the formula of circumference, the total circumference is calculated by using the formula,

C = 2πr

Where the value of r is 96, then

=> c = 2 x π x 96

=> C = 192 x 3.14

=> C = 602.88

Here we have consider that the lane is 10000 cm in length , then the diameter is calculated as,

=> 10000/602.88

=> 16.58

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The rounding up of each of the 12 +2 11/14 5/7 mixed number to the nearest whole number then the estimatation of the sum  can be expressed  as  A.16.

The concept here is addition of the fractions and the digits, In mathematics, summation is the process of adding a series of different types of numbers, known as addends or summands, to produce their sum or total.

The rounding up to whole number can be done as :

12 = 12.0

2 11/14 = 39/14 = 2.786= 3.0

5/7  = 0.71=1.0

Then the sum = 12+3+1=16

Therefore, option A is correct.

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I stash my allowance, birthday cash or paycheck in a bank.

The facts about Banks include the following:

The  facts about Credit union include the following:

These are non profit organizations that exist to serve their members and offer some banking services.

They accepts deposits with a higher interest rate and give loan at a lower rate which is why my decision in where to put my money will be in a credit union due to the high interest rate.

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The final amount after a certain rate of decrease over a period of time can be calculated by Xₙ = X₀ (1-r)ⁿ. From calculations the sales after 6 weeks are 13286.025.

If the percent increase or decrease, period of time and initial amount are given, the final amount can be calculated using the equation Xₙ = X₀ (1±r)ⁿ. Here the percentage decrease is given. So the equation is

   Xₙ = X₀ (1-r)ⁿ

     Xₙ is the final amount

     X₀ is the initial amount

     r is the rate

    n is the period of time

Here percent is given as 10%. So the rate, r = 10/100 = 0.10

 Xₙ = X₀ (1-r)ⁿ

      = 25000× (1-0.10)⁶

       = 13286.025

So the sales after 6 weeks are 13286.025

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Option (c) is the correct option.

9/10 is rational and a real no. but not an integer.

What is a rational number?

A number with the form p/q, where p and q are integers and q is not equal to 0, is said to be rational.

What is an integer?

In the category of real numbers are irrational numbers, fractions, and rational numbers like positive and negative integers.

What is a real number?

Integers, which can be both negative and positive and include zero, are numbers without a decimal or fractional component.

Our objective is to find a number which is rational and a real number but not an integer.

√2 is not rational and not a real number.

-5 is rational and a real number but It is an integer.

9/10 is rational and a real number and also not an integer.

Hence, (c) is the correct option.

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The set builder notation for the given inequality is [tex]\left \{ {{b | b \geq 2\right \}[/tex].

The answer set of an inequality is expressed in mathematics using a set builder notation. For instance, the set builder notation is understood to mean the collection of all y, where y is bigger than 0.

Mathematical expressions with inequalities are those in which the two sides are not equal. Contrary to equations, we compare two values in inequality. Less than, larger than, or not equal to signs are used in place of the equal sign.

The given inequality is:

b + 2 ≥ 4

Subtract 2 on both sides of the equation:

b + 2 - 2 ≥ 4 -2

b ≥ 2

Hence, the set builder notation for the given equality is [tex]\left \{ {{b | b \geq 2\right \}[/tex].

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Answer:

Step-by-step explanation: 23.4

Here we are given a right angled triangle in which there are two unknown angles x and y . we need to find out the values of x and y. Firstly, as we know that the angle sum property of a triangle is 180° . So that,

[tex]\longrightarrow x + y +90^o = 180^o\\[/tex]

[tex]\longrightarrow x + y = 180^o -90^o = 90^o \dots \\[/tex]

[tex]\longrightarrow y = 90^o - x \dots (i) \\[/tex]

And we also have,

[tex]\longrightarrow 4x + 40 = y \\[/tex]

from equation (i) , we have ,

[tex]\longrightarrow 4x + 40 = 90 - x \\[/tex]

[tex]\longrightarrow 4x + x = 90 +40 \\[/tex]

[tex]\longrightarrow 5x = 130\\[/tex]

[tex]\longrightarrow x =\dfrac{130}{5}\\[/tex]

[tex]\longrightarrow \underline{\underline{x = 26^o}} \\[/tex]

substitute this value in equation (i) ,

[tex]\longrightarrow y = 90 - 26 \\[/tex]

[tex]\longrightarrow \underline{\underline{y = 64^o}} \\[/tex]

And we are done!

Answer:

10 1/2 lbs = 168 oz

Answer:

168

Step-by-step explanation:

i think

the solution of the given problem of coordinates comes out to be  the coordinate P = (7, 0.4).

A coordinate system is a technique used in geometry to precisely locate points or other topological objects on a continuum, such as Euclidean space, using one or more numbers or coordinates. A point or item on an a double plane is located using a pair of integers known as coordinates. The x and y positions are two integers that describe a point's location on a 2D plane.

David want to find the coordinate are a useful tool for segmenting lines into smaller units.

P's coordinate is P = (7, -0.4)

The criteria are as follows:

A = (8,0)

=> B = (3,-2) (3,-2)

m: n=1:4

Using P = mx2+nx1 my2+ny

m+n

m+n, line ratio is computed.

The result is:

P 1x3+4x8 /1x-2+4x0 = 1+4 / 7

=> P = 35, 2

=>P = (7, -0.4) (7, -0.4)

1+4

P therefore has the coordinate P = (7, 0.4).

Therefore , the solution of the given problem of coordinates comes out to be  the coordinate P = (7, 0.4).

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According to the information in the table, the value of C is 51.

To find the value of C we must calculate the constant, for that we have to perform the following operation:

In this case, we use the values of another column to identify the constant that applies to all the values in the table and the result is the following:

Additionally, to find the value of C we must perform the following operation:

According to the above, the value of C is 51.

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yup

Step-by-step explanation: the triplets of 15,8,7 make a right triangle

u can also add 8 squared and 7 squared and if it equals to 15 squared then it’s right

The number of next 14 students that will be expected to be adults education students would be = 7 adult education students.

An adult education student is the student that is undertaken by individuals that are mature men and women who take course for continuing education.

The first enrollment consist of the following;

Adult education student = 18

other = 18

Total for first enrollment = 18+18 = 36

If first 36 enrolled students = 18 adult students

second 14 enrolled students = X adults

Make X the subject of formula;

X adults = 14× 18/36

= 252/36

= 7

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By using the point-slope form, the equation of a line that passes through the point (11, 18) with slope 3 is equal to y - 18 = 3(x - 11).

Mathematically, the point-slope form of a straight line can be calculated by using this mathematical expression:

y - y₁ = m(x - x₁)

Where:

From the information provided above, we have the following slope and data points on the line:

At data point (11, 18), a linear equation of this line can be calculated in point-slope form as follows:

y - y₁ = m(x - x₁)

y - 18 = 3(x - 11)

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Answer:

a: 2250. b: 1200. c: 5:2.3:2.7  d: 23.3%

Step-by-step explanation:

Sian gets 1/2 so 4500/2 = 2250

Anesha = 1050

Joanna = 2250-1050 = 1200

Answer:

1,942,364

Step-by-step explanation:

   1 8 4 9 0 3 2

+        9 3 3 3 2

------------------------

   1 9 4 2 3 6 4

Joseph now has 1,942,364 apples.

No. of apples Joseph had in the beginning = 93332

No. of apples he gets more = 1849032

Total no. of apples he has now = 93332 + 1849032

= 1,942,364