a researcher wants to know how the residents of a town feel about constructing a new road through the town

The standard deviation of the distribution = 1.5°F

Given that the distribution of daily high temperature is approximately normal.

Population mean, [tex]\mu[/tex] = 86°F

Also approximately 95% of all daily high temperatures are between 83°F and 89°F.

So here [tex]X_1[/tex] = 83°F and [tex]X_2[/tex] = 89°F

We have the z - statistic ,

             [tex]z=\frac{x-\mu}{\sigma}[/tex]

where [tex]\sigma[/tex] is the Standard deviation.

For 95% probability, the z-value for normal distribution is 1.96.

As we consider the positive z-value, take X =  [tex]X_2[/tex] =  89°F

So,   [tex]z=\frac{x-\mu}{\sigma}[/tex]

⇒  [tex]\sigma = \frac{x-\mu}{z} = \frac{89-86}{1.96} =1.53[/tex] ≈ 1.5°F

So the standard deviation of the distribution = 1.5°F

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The solution to the system of equations is:

e = 0.109

g = 0.183

Defining the variables:

g = cost of the unit of gas.

e = cost of the unit of electricity.

Then the system of equations is:

150*g + 520*e = 84.20

210*g + 405*e = 82.35

Now we want to solve this.

To do so, we need to isolate one of the variables in one of the equations. Let's isolate g in the first one:

g = (84.20 - 520*e)/150

Now we replace that in the other equation so we get:

210*(84.20 - 520*e)/150 + 405*e = 82.35

Now we can solve this for e:

210*(84.20 - 520*e)/150 + 405*e = 82.35

(210/150)*(84.20 - 520*e) + 405*e = 82.35

117.6 - 728*e + 405*e = 82.35

117.6  - 323*e = 82.35

e = (117.6  - 82.35)/323 = 0.109

Then:

g = (84.20 - 520*0.109)/150 = 0.183

Then we can conclude that:

e = 0.109

g = 0.183

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Answer:

[tex](f + g)( \times ) = { \times }^{4} [/tex]

3 1/2 subtracted from 4 7/8 is equal to 3/8.

A fraction is a quantity that is not a non-integer. A fraction usually has a numerator and a denominator. The numerator is the number above. While the denominator is the number below. An example of a fraction is 1/2.

A mixed number is a number that has a whole number and a proper fraction. A proper fraction is a fraction is which the numerator is less than the denominator. An example of a mixed number is 3 1/2.

Subtraction is the mathematical operation that is used to determine the difference of two or more numbers. The sign used to represent subtraction is -.

[tex]3\frac{1}{2} - 4\frac{7}{8}[/tex]

[tex]-1\frac{4 - 7}{8}[/tex]

[tex]-1\frac{-3}{8}[/tex] = 3/8.

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Answer:

- 1 makes the equation true

Step-by-step explanation:

2s - 10 = - 12 ( isolate the term in s by adding 10 to both sides )

2s = - 2 ( divide both sides by 2 )

s = - 1

The integer ion in the solution set will make the equation true is -1. The correct option is a.

Zero, a positive natural number, or a negative integer denoted by a minus sign are all examples of integers. The inverse additives of the equivalent positive numbers are the negative numbers.

An integer, pronounced "IN-tuh-jer," is a whole number that can be positive, negative, or zero and is not a fraction. Any positive or negative number without fractions or decimal places is known as an integer, often known as a "round number" or "whole number."

Given equation is

2s - 10 = - 12 ( isolate the term in s by adding 10 to both sides )

2s = - 2 ( divide both sides by 2 )

s = - 1

Therefore, the correct option is a, −1.

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Answer:

9

Step-by-step explanation:

a quotient is the result of dividing one number by the other, so we know 8 is being divided by 2

8÷2 is 4

five more just means adding 5

so we are left with 4+5 which =9

Ratios which are not equivalent to 3: 5 are 13: 15, 7:9, 5:3.

As given in the question,

Mo is sorting number cards with ratios

Ratio = 3 : 5

Equivalent ratio to 3 : 5

13 : 15 cannot be reduced.

13 : 15 not equivalent to 3:5

30:50 = (3 ×10) : (5×10)

          = 3:5

7:9  cannot be reduced . It is not equivalent to 3:5

3x:5x = 3:5

5:3 reciprocal of 3:5 .It is not equivalent to 3:5.

Therefore, ratios which are not equivalent to 3: 5 are 13: 15, 7:9, 5:3.

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1-  if the main coefficient isn't always 1, divide each facets by way of the coefficient so that the resulting equation has a leading coefficient of 1.

2- write the equation within the form ax²+ bx = c

3- write the left aspect of the equation because the rectangular of a binomial and simplify the proper side if possible.

4- add the rectangular of half of the coefficient of the linear time period to both aspects of the equation.

5- practice the rectangular root property for equation and solve as usual.

What do you mean by quadratic?

Quadratics can be defined as a polynomial equation of a second degree, which means that it incorporates a minimum of one time period that is squared. it's also referred to as quadratic equations. the general shape of the quadratic equation is: ax² + bx + c = 0.

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Answer:

A. 25h+30=80

B.25(2)+30=80

Answer:

200 km/hr

Step-by-step explanation:

We can find the speed by dividing the distance by the time taken for the trip.

[tex]\sf \boxed{Speed = \dfrac{distance }{time}}[/tex]

 [tex]\sf r = \dfrac{300}{t}[/tex]

In the above equation, substitute t = 1.5 hours and find the train's rate.

[tex]\sf r = \dfrac{300}{1.5}\\\\= \dfrac{300*10}{1.5*10}\\\\= \dfrac{3000}{15}\\\\r = 200 \ kilometers \ per \ hour[/tex]

Answer: are there any options?

Step-by-step explanation:

Answer:

3/4 or 0.75

Step-by-step explanation:

8-4x=2x

-4x-2x=-8

-6x=-8

x=-6/-8

=3/4 or 0.75

So far, he has ridden 70% of the bike course.

Percentage, which was adapted from the Latin word "per centum", which means "by the hundred", is a fraction or a ratio in which the value of whole is always 100. It is represented by the symbol "%".

The formula to get the percentage is:

Percentage = (Value / Total Value) × 100

If the total value of the bike course is 40 miles and the value which the percentage we are looking for is 28 miles, evaluating the equation:

Percentage = (Value / Total Value) × 100

Percentage = (28 / 40) × 100

Percentage = (0.7) × 100

Percentage = 70

Therefore, he has ridden 70% of the bike course so far.

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Answer:

x = -2

Step-by-step explanation:

5x - 5 = 9x + 3

- 5 = 4x + 3

- 8 = 4x

- 8/4 = 4x/4

x = -2

Answer:

£27400

Step-by-step explanation:

The original salary of x.

The raise was 7.5% = 7.5/100 = 0.075 of the salary.

The original salary plus the raise is x + 0.075x = 1.075x.

The new salary is £29455.

Therefore,

1.075x = £29455

Divide both sides by 1.075.

x = £27400

Answer: £27400

The value of the expression when x = 7 is 70

Algebraic expressions are expressions made up of variables, terms, coefficients, factors and constants.

They are also made up of mathematical operations such as addition, multiplication, division, subtraction, etc.

Given the expression;

2x^2- 5x - 3

To determine the the value, we substitute the value of x a 7 into the expression, we have;

2(7)² - 5(7) - 3

expand the bracket

2(49) - 25 - 3

98 - 25 - 3

Find the difference

70

Thus, the value of the expression when x = 7 is 70

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The square root of - 10 is not a real number but a complex number, an irrational number.

Numbers can be classified in real numbers and complex numbers. Real numbers are classified in natural numbers (i.e. 1, 4, 5), whole numbers (i.e. 0, 1, 4, 5), integers (i.e. - 4, -1, 0, 5, 6) and rational numbers (i.e. 5 / 7, 0, - 13 / 3) and part of the irrational numbers (i.e. √3, π) and the rest of irrational numbers are complex numbers (i.e. i 4, - 4 + i 5).

In consequence, the square root of - 10 is not a real number but a complex number, an irrational number.

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Answer:

8 + 3x < 2 + x the answer would be x<-3

2x + 23 ≤ 11 the answer would be [tex]x\leq -6[/tex]

1)  8 + 3x < 2

To solve this, you first want to subtract 8 from both sides to isolate 3x on one side.

This gives you 3x < 2 - 8, which can be simplified to 3x < -6.

After you have this, you want to get x on its own. To do this, divide both sides of the inequality by 3 to get x < -6

2)  2x + 23 [tex]\leq[/tex] 11

For this one, we use the same steps. First, subtract 23 from both sides to isolate 2x, giving us 2x [tex]\leq[/tex] 11 - 23, which we simplify down to 2x [tex]\leq[/tex] -12.

From here, we divide both sides of the inequality by 2 to get x on its own. This gives us x [tex]\leq[/tex] -6

Answer:

answer of the first one

x+1>3 equal to x>2 by subtracting 1 from each side

so x>2 equal ]2,infinity[

answer of the second

-4<x<2 so the quantity of x is all the numbers from -4 to 2 but when it be greater than or smaller than without saying or equal we put the brackets opened so the result is ]-4,2[

but i can,t understand 3 and 4

Answer: [tex]-1 \frac{19}{24}[/tex]

Step-by-step explanation:

5/6 + (−2 5/8)=

5/6 + (−2 - 5/8)=

5/6 −2 - 5/8=

(5/6 −2 - 5/8)*24/24=      ==> 24 is the LCM of 6 and 8

[tex]\frac{(5*24/6 -2*24-5*24/8)}{24}[/tex]=

[tex]\frac{(120/6 -48-120/8)}{24}[/tex]=

[tex]\frac{(20-48-15)}{24}[/tex]=

(-28-15)/24=

-43/24 =

(-24-19)/24=

-24/24 -19/24=

-(24/24 +19/24)=[tex]-1 \frac{19}{24}[/tex]

The required equation would be t  = (nRT + 5ab)/M which is the result of the equation for t.

The equation is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are equal.

The equation is given as

Mt - 5ab = nRT

We have to determine the result of solving this equation for t

⇒ Mt - 5ab = nRT

⇒ Mt  = nRT + 5ab

⇒ t  = (nRT + 5ab)/M

Therefore, the required equation would be t  = (nRT + 5ab)/M which is the result of the equation for t.

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Answer:

-3n+12

Step-by-step explanation:

Term to term rule:

9-6=3

6-3=3

3-0=3

term to term rule is -3

-3 x n + 9 - (-3)

-3n + 12

Answer:

Denominator: The value in a fraction that appears below the fractional bar and indicates the total number of equal parts.

In a fraction, the value that appears above the horizontal line is referred to as the numerator. It represents the number of pieces removed from the whole. The denominator of a fraction is the numerical value that comes before the vinculum.

A mixed number is a representation of both a whole number and a legal fraction. In most cases, it denotes a number that falls between any two whole numbers.

An integer that totally or partially divides another integer is known as a divisor.

In a division equation, a divisor is represented by the formula

Dividend ÷ Divisor = Quotient.

The correct option is (a).

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Greetings from Brasil...

Let Ca be the function for Plan A and Cb the function for Plan B.

According to the problem statement, we can conclude that:

where C is the cost and n is the number of videos

Cost that the user will pay for having watched n videos

Ca = cost of Plan A

Cb = cost of Plan B

Is there any point (n) that Ca will be equal to Cb??? Let's equate the functions to check if there is a common point and if there is, what would it be.

Ca = Cb

3n + 8 = 5n

2n = 8

n = 4

In n = 4 we have a condition for the cost that does not matter Ca or Cb.

I will present 2 ways to solve:

1 - building the graph of the functions and observing the points where the Y axis (cost axis) its smaller

2 - assigning 2 points - below n = 4 and above n = 4 - to observe the cost behavior

1 - see attachment

2 - let's choose the points n = 1 and n = 10 (as already said, n=4 does not matter Ca or Cb - meeting point / intersection point)

n = 1

Ca(1) = 3.1 + 8 = 11

Cb(1) = 5.1 = 5

Ca > Cb, then Cb better to the user

n = 10

Ca(10) = 3.10 + 8 = 38

Cb(10) = 5.10 = 50

Ca < Cb, then Ca better to the user

We can come to the following conclusion:

0 < n < 4 → better use Plan B (in this interval the cost to the user will be lower with Plan B)

n = 4 → It doesn't matter to use Plan A or Plan B.

n > 4 → better use Plan A (for n above 4 the cost to the user will be lower with Plan A)

The height of this cone is 3( 1 +  [tex]\frac{l}{r}[/tex] ). Which have the same volume and surface area.

Given that

The value of the surface area (in square centimeters) of the cone is equal to the value of the volume (in cubic centimeters) of the cone.

The formula for the surface area S of a right cone is S=πr2+πrl, where r is the radius of the base and l is the slant height.

To find

The height of the cone.?

So, according to the question

We have,

The surface area of the cone = The volume of the cone.

We know that

The surface area of the cone,

  S = πr²+πrl

And,

The volume of the cone,

 V = [tex]\frac{1}{3} \pi r^2h[/tex]

So, from question

The surface area of the cone = The volume of the cone

  S = V              

Now, put the all values,

 πr²+πrl =  [tex]\frac{1}{3} \pi r^2h[/tex]

πr(r+ l)  =  [tex]\frac{1}{3} \pi r^2h[/tex]

 (r+l) =  [tex]\frac{1}{3}[/tex] × [tex]\frac{\pi r^2h}{\pi r}[/tex]

 (r+l) =  [tex]\frac{1}{3}[/tex] × rh

 [tex]\frac{3(r+l)}{r}[/tex] = h

  h = 3( [tex]\frac{r}{r} + \frac{l}{r}[/tex] )

   h = 3( 1 +  [tex]\frac{l}{r}[/tex] )

So the height of this cone is 3( 1 +  [tex]\frac{l}{r}[/tex] ).

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Using the common factors, the expression can be rewritten as follows:

The expression can be represented as follow using common factor.

1 / 4 x³y + 3 / 4 xy²

Using the common factors,

The common factors of 1 / 4 x³y  and  3 / 4 xy² is 1 / 4 xy.

Therefore,

1 / 4 x³y + 3 / 4 xy² = 1 / 4 xy (x² + 3y)

Therefore, rewriting 1 / 4 x³y + 3 / 4 xy² using the common factors is 1 / 4 xy (x² + 3y).

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