9. The price of one gallon of heating oil is $2.689.Which is this number rounded
to the nearest penny?

A $2.68
B $2.69
C $2.70
D $3.00

Answer:

Georgia earns $8.35 per hour

Step-by-step explanation:

$125.25 / 15 hours = $8.35

$167.00 / 20 hours = $8.35

You can also find how much Georgia makes an hour by:

15 hours + 20 hours = $125.25 + $167.00

OR...

15x + 20x = $125.25 +$167.00

35x = $292.25

x = $292.25 / 35

x = $8.35 earned per hour

Applying the exterior angle theorem, the value of x in the given triangle is: x = 6.

The exterior angle theorem states the relationship between the two remote angles in a triangle and the angle measure of the external angle formed by an extended side outside the triangle.

According to the exterior angle theorem:

The measure of the exterior angle = sum of the measures of the two remote angles in a triangle.

Given the following:

Measure of angle YWX = (2x + 12)°

Measure of angle WXY = (2x + 5)°

Measure of angle XYZ = (7x - 1)°

Therefore:

m∠XYZ = m∠YWX + m∠WXY [exterior angle theorem]

Substitute

(7x - 1)° = (2x + 12)° + (2x + 5)°

Solve for x

7x - 1 = 2x + 12 + 2x + 5

Combine like terms

7x - 1 = 4x + 17

7x - 1 + 1 = 4x + 17 + 1 [addition property of equality]

7x = 4x + 18

7x - 4x = 4x + 18 - 4x [subtraction property of equality]

3x = 18

3x/3 = 18/3 [division property of equality]

x = 6

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Answer:

900in goes in 25 yd

3960ft goes in 0.75 mi

360in goes in 30 ft

10yd goes in 30 ft

75ft goes in 25 yd

1320yd goes in 0.75 mi

Step-by-step explanation:

[tex]\frac{1yd}{36in} =900in[/tex]

900 · 1 = 900
900/36 = 25 yd

______________

[tex]\frac{1mi}{5280ft} =3690ft[/tex]

3690 · 1 = 3690
3690/5280 = 0.75 mi

______________

[tex]\frac{1ft}{12in} =360in[/tex]

360 · 1 = 360
360/12 = 30 ft

______________

[tex]\frac{3ft}{1yd} =10yd[/tex]

3 · 10 = 30
30/1 = 30 ft

______________

[tex]\frac{1yd}{3ft} =75ft[/tex]

75 · 1 = 75
75/3 = 25 yd

______________

[tex]\frac{3ft}{1yd} =1320yd[/tex]

3 · 1320 = 3960
3960/1 = 3960ft

[tex]\frac{1mi}{5280ft} =3960ft[/tex]

3960 · 1 = 3960
3960/5280 = 0.75 mi

______________

hope this helps!

Answer:

I am not sure if you're accustomed to using a z-score and table of probabilities or technology, so I will answer using both!

a) Since you're choosing one person from the population, you will use the mean and standard deviation from the population.  z= (210.9-197.5)/8.6 = 1.56 Using a table of normal probabilities,

P(x>210.9)= 1-P(z<1.56)= 1- 0.9406=0.0594

Using technology: normalcdf(210.9, 1E99, 197.5, 8.6)=0.0596

b) Since you're calculating the population for a sample to occur, you need to get a mean of the sampling distribution and standard deviation of the sampling distribution.

Meanpop=Meansampling dist.=197.5

St. Devsampling dist.= Stdpopulation/√n = 8.6/√15 = 2.22

Using technology, P(X>196.20)= normalcdf( 196.20, 1E99, 197.5, 2.22) = 0.7209

c) You only have to worry about the sample size in a sampling distribution if you either do not know the shape of the distribution of the population or if the distribution of the population is not normally distributed. Since this population is normally distributed (as stated in the given information), then your sample size does not have to be greater than 30.

Step-by-step explanation:

The anticipated value of the dividend in:

Year 1  is $45.86

Year 2 is  $49.07.

Year 3 is $52.50.

Year 4 is $56.18.

The formula that can be used to determine the value of the dividend is:

Value = dividend paid last year x (1 + growth rate^number of years)  / (required return - growth rate)

D1 = ($6 x 1.07) / (20% - 7%) = $45.86

D2 = ($6 x 1.07²) / (20% - 7%) = $49.07

D3 = ($6 x 1.07³) / (20% - 7%) = $52.50

D4 = ($6 x 1.07^4) / (20% - 7%) = $56.18

An exponential function can represent growth or decay, and the function that has a growth factor of 5 is f(x) =2(5^x)

An exponential function is represented as:

f(x) = ab^x

Where b represents the growth factor

From the list of options, we have:

f(x) = 2(5^x) and f(x) = 0.5(2^x)

This means that:

b = 5 for f(x) = 2(5^x)

And b = 0.2 for f(x) = 0.5(2^x)

Hence, the function that has a growth factor of 5 is f(x) =2(5^x)

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Answer:

A.

f(x) = 2(5x)

Step-by-step explanation:

The middle 95% of customers have to wait for 18 to 34 minutes at the resturant.

The empirical rule states that for a normal distribution. 68% of the values are within one standard deviation from the mean, 95% of the values are within two standard deviation from the mean and 99.7% of the values are within three standard deviation from the mean

Given a mean of 26 minutes and a standard deviation of 4 minutes. Hence:

95% are within 2 standard deviations = 26 ± 2(4) = (18, 34)

The middle 95% of customers have to wait for 18 to 34 minutes at the resturant.

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Answer: 50V

Step-by-step explanation:

Use Ohm's Law, which states that the voltage is proprtional to the current. The proprtionality constant is the resistance:

[tex]V=IR[/tex]

We are given the resistance in Ohms, and the current in Amps. Therefore:

[tex]V=(2.5)(20)=50V[/tex]

Answer :-

The value of all the steel sheet is $2080

Solving steps:-

⇢ A=2(wl+hl+hw)

Where,

⇢ A = 2((5)(6)+(2)(6)+(2)(5))

⇢ A = 2(52)

⇢ A = 104

We multiply 104 by $20

⇢ 104 × 20

⇢ 2080

Therefore,the sheet steel will cost $2080 in total

Hopes this helps,

Have a wonderful day ,:-)

Answer:

A = 4x² + 3x - 1

Step-by-step explanation:

Area of trapezoid = (a + b)(h)/2

A = [((5x - 4) + (3x + 2)) · (x + 1)] ÷ 2

A = [(8x - 2) · (x + 1)] ÷ 2

A = (8x² + 8x - 2x - 2) ÷ 2

A = 4x² + 4x - x - 1

A = 4x² + 3x - 1

Hope this helps and God bless!

To setup an equation for the area of the figure:

  ⇒ must know the formula for the area of a trapezoid

        [tex]\frac{1}{2}*(base1+base2)*height[/tex]

Now's lets set up the equation:        

[tex]Area =\frac{1}{2}(5x-4+3x+2)(x+1) =\frac{1}{2}(8x-2)(x+1)=\frac{1}{2}*(8x^2+8x-2x-2)\\Area = \frac{1}{2} *(8x^2+6x-2)\\Area = 4x^2+3x-1[/tex]

Thus the equation is [tex]4x^2+3x-1[/tex]

Answer: [tex]4x^2+3x-1[/tex]

Hope that helps!

Answer:

9

Step-by-step explanation:

The explanation is in the picture

[tex]\cos 32^{\circ} = \dfrac{14.7}a\\\\\implies a=\dfrac{14.7}{\cos 32^{\circ}}\\\\\implies a=17.33[/tex]

A. x = -9

__________

D. x = 3

__________

The number of months it would take the bunny farm to triple in size is 5.3 months.

The formula that can be used to determine the number of months it would take Mrs. Galicia's bunnies to triple in size is:

Number of years =  (In FV / PV) / r

IN(3) / 0.2075 = 5.3 months

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Answer:

A beaver burrows 10 holes every 5 minutes. How many holes will it burrow if the time is increased to 25 minutes? Answer it will burrow 50 holes in 25 minutes

hope this helps

Step-by-step explanation:

Answer:

50 holes

Step-by-step explanation:

5 minutes = 10 holes

25/5 = 5

10 x 5 = 50

Answer:

A, B, C, or D.

Step-by-step explanation:

Answer:

No

Step-by-step explanation:

for the sides to form a triangle then the sum of any 2 must be greater than the third.

[tex]\frac{3}{8}[/tex] , 1 [tex]\frac{1}{6}[/tex] , [tex]\frac{3}{4}[/tex] ( change 1 [tex]\frac{1}{6}[/tex] into an imprioper fraction )

[tex]\frac{3}{8}[/tex] , [tex]\frac{7}{6}[/tex] , [tex]\frac{3}{4}[/tex]

rewrite each fraction with a denominator of 24 ( the LCM of 8,6,4 )

This will allow the fractions to be compared more easily.

[tex]\frac{9}{24}[/tex] , [tex]\frac{28}{24}[/tex] , [tex]\frac{18}{24}[/tex]

[tex]\frac{9}{24}[/tex] + [tex]\frac{28}{24}[/tex] = [tex]\frac{37}{24}[/tex] > [tex]\frac{18}{24}[/tex]

[tex]\frac{28}{24}[/tex] + [tex]\frac{18}{24}[/tex] = [tex]\frac{46}{24}[/tex] > [tex]\frac{9}{24}[/tex]

[tex]\frac{9}{24}[/tex] + [tex]\frac{18}{24}[/tex] = [tex]\frac{27}{24}[/tex] < [tex]\frac{28}{24}[/tex]

the condition is not met for the 3 sides , so they do not form a triangle.

Answer:

A

Step-by-step explanation:

Answer:

162 units^2

Step-by-step explanation:

add all of the areas of the sides

2 ( 3 x 7) + 2 ( 3 x 6) + 2 ( 6 x 7 ) = 162 units^2

Answer:

EI = 30

GH = 30

RS = 10

Step-by-step explanation:

Given:  PQRST ~ HGFEI

From inspection of the diagram, the corresponding sides are:

RS ~ FE

ST ~ EI

TP ~ IH

QP ~ GH

QR ~ GF

The only pair of sides that both have side lengths are QR and FG.  Therefore, we can use these to work out the scale factor of dilation.

QR = 8   and   GF = 20

⇒ GF/QR = 20/8 = 2.5

Therefore, HGFEI is an enlargement of PQRST by a scale factor of 2.5

If ST = 12,

⇒ EI = 12 x 2.5 = 30

If QP = 12,

⇒ GH = 12 x 2.5 = 30

If EF = 25,

⇒ RS = 25 / 2.5 = 10

If IH = 15,

⇒ TP = 15 / 2.5 = 6

Answer:

See below ~

Step-by-step explanation:

As they are similar, find the scale factor.

Finding EI

Finding GH

Finding RS

Answer:

Step-by-step explanation:

The 'odds' is

The 'odds against' is

Answer:

"Odds for" - Number of successes : Number of failures

Number of success = 2, 3, 7 or 10

Number of failures = 1, 4, 5, 6, 8, 9, 11, 12

⇒ odds for stopping on 2, 3, 7 or 10 = 4/8 = 1/2

"Odds against" - Number of failures : Number of successes

Number of success = 1, 2, 3, 4

Number of failures = 5, 6, 7, 8, 9, 10, 11, 12

⇒ odds against stopping on 1, 2, 3 or 4 = 8/4 = 2

Answer:

The answer is C.

Step-by-step explanation:

This is because that shape only has the top and bottom lines which are parallel. The sides are not vertical and leaning outwards, which are not parallel. Leaving that shape to only have one pair of parallel sides.

Answer:

C.

Step-by-step explanation:

A & B both have 2 pairs of parallel lines, so they're not a choice. D has three sides, making it a triangle. Meaning it has no pairs of parallel lines. That leaves us with C. The reason why C is the answer is because, we can see that both top and bottom lines are parallel to each other. However, the left and right lines are not.

I hope this helped!

Answer:

111°

Step-by-step explanation:

Answer: d. (-8,-5)

1nonly(((((((((((:<3

Step-by-step explanation:

this trapezoid has 3 parts

rectangle, 2 triangles

area of rectangle = 8.7*9.8 = 85.26 m^2

area of first right triangle = .5*b*h = .5*7.3*9.8 = 35.28 m^2

area of 2nd right triangle = .5*7.6*9.8 = 37.24 m^2

total area = 156.78 m^2

Answer:

2,750 meters

Step-by-step explanation:

1000 meters = 1 kilometer

M = 2.75 km (M = variable for unknown amount of meters)

Cross multiply: 1000 * 2.75 km = 1 * M

2.75 km * 1000 m = 2750 meters

Answer:95139 units^2

Step-by-step explanation:

(31*31)*99 = 95139

So the answer should be 95139 units ^2

Answer:

m∠x = 47°

Step-by-step explanation:

The given shape is a triangle.

Sum of interior angles of the triangle is 180,

x + 102 + 31 = 180

x + 133 = 180

x = 180 - 133

m∠x = 47°

Answer:

c).3

Step-by-step explanation:

let the number be x

5x-3=x+9

collect like terms

5x-x=9+3

4x= 12

divide both sides by 4

x=3

the number is 3

Answer:

90,000 (ninty thousand)

Step-by-step explanation:

hope this helps:)

Answer:

The number that is in the ten thousands is 9, whose value is 90,000

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I hope help you :)

Kind regards, Antonio.