the table shows that the total cost of buying and running a small heater

175 yards long is the 15th hole if the map shows 17.5 inches.

hole = c yards

1.5 / 15 = 17.5 / c

1.5 c = 15 * 17.5

1.5 c = 262.5

c = 175 yards

A length unit equal to 36 inches, or 3 feet (see foot), in the United States Customary System, or 0.9144 metre in the International System of Units. A cloth yard is 37 inches long, and it was also the standard length for arrows.

The yard is an English unit of length that equals 3 feet or 36 inches in both the British imperial and US customary measurement systems. Since 1959, it has been standardized as 0.9144 meter by international agreement. One mile is equivalent to 1,760 yards. The survey yard in the United States is slightly longer.

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Answers:

E ' = (0, 1)

F ' = (0.5, 0.5)

G ' = (0, 0)

D ' = (-1, 0.75)

Notes: 0.5 = 1/2 and 0.75 = 3/4

================================================

Explanation:

Assuming the origin is the center of dilation, then we multiply each coordinate by the scale factor of 1/4 = 0.25

For instance, the point E(0,4) moves to E ' (0, 1) since

Do the same for the other points.

Answer:

Step-by-step explanation:

The 95% confidence interval estimate for the mean number of absences for clerical workers during the year is (8.132, 11.268).

It should be noted that the mean of your estimate plus and minus the range of that estimate constitutes a confidence interval. Within a specific level of confidence, this is the range of values you anticipate your estimate to fall within if you repeat the test. In statistics, confidence is another word for probability.

Given a = 0.05, Z(0.025) = 1.96 (from standard normal table).

The 95% confidence interval will be:

xbar +/- Z*s/vn

= 9.7 +/- 1.96*4/✓(25)

= (8.132, 11.268)

Therefore, the 95% confidence interval is (8.132, 11.268).

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Step-by-step explanation:

[tex]y = 3x + 10......eq3 \\ 2(3x + 10) = 6x + 20 \\ 6x + 20 = 6x + 20[/tex]

you can see that coming across that complication where the eqaution is balanced there is no solution for x and y fir those systems of equations.

Answer:

1/9

Step-by-step explanation:

When the quantities are proportional, you are able to find the constant of proportionality by y/x.  If you take each one of the y's listed and divide it by x, you will get 1/9.

For example 1 2/9 ÷11

1 2/9 is the same at 9/9 + 2/9 or 11/9

[tex]\frac{11}{9}[/tex] ÷ 11 is the same as [tex]\frac{11}{9}[/tex] ÷ [tex]\frac{11}{1}[/tex] To divide with fractions, you multiply by the reciprocal.

[tex]\frac{11}{9}[/tex] x [tex]\frac{1}{11}[/tex] The 11 can cancel out and we are left with [tex]\frac{1}{9}[/tex]

Answer: r = [tex]\frac{1}{9}[/tex]

Step-by-step explanation:

y = rx

finding r (substitute y and x):

5 = r x 45

5/45 = r

r = [tex]\frac{5}{45} = simplify = \frac{1}{9}[/tex]

checking:

rx = y

   [tex]\frac{1}{9}[/tex] x 11 = 1 [tex]\frac{2}{9}[/tex]

[tex]\frac{11}{9}[/tex] = 1 [tex]\frac{2}{9}[/tex]

convert mixed fraction into improper fraction

[tex]\frac{11}{9}[/tex] = [tex]\frac{11}{9}[/tex]

correct

Answer:

101

Step-by-step explanation:

Because if f(x) = [tex]x^{2}[/tex] + 1 and f(x) is f(10), this means that x = 10. If x = 10, then you can plug that into the equation, getting you [tex]10^{2}[/tex] + 1. [tex]10^{2}[/tex] is 100, plus 1 is 101.

Hope this helps!

Answer:

Step-by-step explanation:

You want to know the length of the sides of a 250 ft² square, and one with an area 50% larger. You also want to know the percentage change in side length.

The area of a square is given by the formula ...

  A = s²

Solving for the side length (s), we find ...

  s = √A

The side length of a square with 250 ft² area is ...

  s = √250 ft = 5√10 ft ≈ 15.81 ft . . . side length

The area of a square that has 50% more area is ...

  (250 ft²) × (1 +50%) = 375 ft²

The side length of that square is ...

  √375 ft = 5√15 ft ≈ 19.36 ft . . . side length

The percentage change can be found from ...

  percentage change = ((new value)/(old value) -1) × 100%

  = ((5√15)/(5√10) -1) × 100% = (√1.5 -1) × 100% ≈ 22.47%

The percentage increase in the length of one side is about 22.47%.

The number of points the borrower needs to buy down interest rate to 3.8% is 0.350 points

What is the desired annual percentage rate for the borrower?

The desired annual percentage rate(APR) for the borrower is 3.8% whereas the the loan officer offer is 4.15%, which means that the borrower needs to buy the interest rate from 4.15% to 3.8%

difference in interest rate=4.15%-3.8%

difference in interest rate=0.35%

We need to translate the reduction in interest rate of 0.35% to points , bearing in mind that the 1% is the same as 1 point

number of points required to buy down interest=1 point*0.35%

number of points required to buy down interest=0.350

In essence, the home loan borrower needs to buy down interest by 0.350 points in order to achieve the desired loan APR of 3.8%

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The Four-fifths is equal to ten-sixteenths of a number is x=32/25.

Given the statement is four-fifths is equal to ten-sixteenths of a number.

A mathematical statement is a meaningful component of words that can be  true or false. Simply, they are known as a statement.

Let us assume the given number be x.

According to the given statement,

Four fifths means 4/5.          ......(1)

And ten sixteenths means 10/16.

It is also given that ten sixteenths of a number means is (10/16)x.      .......(2)

Now, we will equate equation (1) and equation (2) according to the given statement is

4/5=(10/16)x

Further, we will cross multiply both sides, we get

4×16=10x×5

64=50x

Now, we will divide both sides by 50, we get

64/50=50x/50

64/50=x

32/25=x

Hence, the number for the given statement "Four fifths is equal to ten sixteenths of a number" is 32/25.

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Answer:

==========================

Identities we will use:

===========================

Given expression:

Factorize it by completing the square and setting the difference of squares:

The value of x based on the equation illustrated as 3x - 1 + 5 < 1 is x < 1.

It should be noted that an equation is simply used to show the relationship between the expression or variables.

From the information, 3x - 1 + 5 < 1.

Collect like terms

3x - 1 + 5 < 1.

3x < 1 + 1 - 5

3x < -3

Divide

3x / 3 < -3 / 3

x < 1

Therefore, the value of x based on the equation illustrated as 3x - 1 + 5 < 1 is x < 1.

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The radius of the spherical tank of capacity 750 gallons to the nearest hundredth is 2.88 ft.

How much s a gallon?

In both imperial and US customary units, the gallon is a unit of volume. The imperial gallon (imp gal), which is or was used in the United Kingdom, Ireland, Canada, Australia, New Zealand, and some Caribbean countries, is defined as 4.54609 liters; the US gallon (US gal), which is used in the US and some Latin American and Caribbean countries, is defined as 3.785411784 L[1] (231 cubic inches); and the US dry gallon ("usdrygal"), which is defined as 18 US bushel (exactly 4.40488377086 L).

Given data: 1 gallon ≈ 0.1337 ft³

Then, 750 gallons = 0.1337 x 750 ≈ 100.275 ft³

We know, Volume of sphere,  [tex]V=\frac{4}{3}\pi r^{3}[/tex]

then, r = [tex]\sqrt[3]{\frac{3}{4\pi }V }[/tex]

           = [tex]\sqrt[3]{\frac{3}{4\pi } 100.275}[/tex]

           = [tex]2.88 ft.[/tex]

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Answer:

3/5, 9/15 - some equivalent fractions for 6/10

Step-by-step explanation:

perimeter=s+s+s

p=x/2+x-5+x-2

13=x/2+x-5+x-2

26=x+x+x-10-4

26=3x-14

26+14=3x

3x/3=40/3

x=13.3cm

b.

x/2=6.65

x-5=8.3

x-2=11.3

longest side=11.3cm

Answer:

0.66

Step-by-step explanation:

Answer:1=a

             2=b

             3=c

Step-by-step explanation:

Answer:

14x+11

Step-by-step explanation:

Answer:

-13 13/35

Step-by-step explanation:

Answer:

The answer is C

Step-by-step explanation: Just took it

The equation of the line is y = - (2 / 5) · x - 2. (Correct choice: D)

Lines are represented by first grade polynomials of the form y = m · x + b, where m and b are the slope and the y-intercept of the line, and x and y are the independent and dependent variables, respectively.

We can find the values of the slope and the y-intercept by knowing the location of two distinct points on Cartesian plane. If we know that (x₁, y₁) = (- 5, 0) and (x₂, y₂) = (0, - 2), then the equation of the line is:

- 5 · m + b = 0               (1)

b = - 2                           (2)

The solution to the system of linear equations is (m, b) = (- 2 / 5, - 2). Lastly, the equation of the line is y = - (2 / 5) · x - 2. (Correct choice: D)

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Regarding the average rate of change of the function, it is found that:

a) 245 habitants per year between 1998 and 2001.

b) The average rate of change was of -328.5 habitants per year between 2002 and 2004.

c) The rate of population increase was greater between 1998 and 2001.

d) The rate of population decrease was greater between 2002 and 2004.

The average rate of change of a function is given by the change in the output divided by the change in the input. Hence, over an interval [a,b], the rate is given as follows:

[tex]r = \frac{f(b) - f(a)}{b - a}[/tex]

For item a, we have that:

Hence the rate is:

(1591 - 856)/3 = 245.

The average rate of change was of 245 habitants per year between 1998 and 2001.

For item b, we have that:

Hence the rate is:

(826 - 1483)/2 = -328.5.

The average rate of change was of -328.5 habitants per year between 2002 and 2004.

Hence:

c) The rate of population increase was greater between 1998 and 2001.

d) The rate of population decrease was greater between 2002 and 2004.

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Factors of the polynomial 2x² + 8x - 90 is Option (c) 2(x + 9)(x - 5).

Factorization is the method used to discover the factors of a given value or mathematical statement. A factor is an integer that is multiplied by another to create the original number. For instance, 2, 3, 6, 9, and 18 are the factors of 18. Likewise, in the case of polynomials, the factors are the polynomials that are multiplied to create the initial polynomial.

Given Equation: 2x² + 8x - 90

Step 1: Pull out like factors from the equation

 ⇒ 2x² + 8x - 90  =   2 • (x² + 4x - 45)

Step 2: Factorize by splitting the middle term of the equation (x² - 4x - 45)

   ⇒ x²+ 9x - 5x - 45

Step 3: Take Common factors from the two pairs of the equation

⇒ x(x + 9) - 5(x + 9)

Step 4: Rewrite the polynomial in factored form

  ⇒ 2(x + 9)(x - 5)

Therefore the factorization result is 2(x + 9)(x - 5).

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Thee number in which case has the value of the 8 ten times greater than than the value of the 8 in 8304 as required in the task content is; 83450.

It follows from the task content that the number which satisfies the condition that, the value of its 8 is ten times greater than the value of the 8 in 8304 is to be determined.

It follows from place value that the 8 in 8304 has a value of; 8 × 1000 = 8000.

Hence, an example of a number that is ten times greater is; 10 × 80,000.

Ultimately, an example of the required number as in the task content is; 83450 where it's 8 digit is ten times greater than that in 8304.

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Answer:

1 revolution is 360 degrees

1 hour = 60 minutes

360/60 = 6

so it rotates 6 degrees every minute

135/6 = 22.5 minutes

Answer:14 000

Step-by-step explanation:

Simple interest formula: A=P(1+in)

A= amount after interest is added

P= initial amount (10000)

i= interest rate (8%)

n= number of periods (5 years)

Now substitute what you have into the simple interest formula:

A=P(1+in)

A=10000(1+(8/100)(5))

A= 14 000

The reason why 8 is divided by 100 is that 8 is a percentage. Unless you have a percentage function on your calculator, I'd strongly encourage you to ALWAYS divide your percentages by 100.