3(2x - 1) =
1
2
(4x - 2) + 2

Answer:

Juan got 18.50 miles per gallon.

Step-by-step explanation:

We are given the following in the question:

Odometer in the beginning of trip = 1460.3 miles

Odometer at the end of trip = 1830.2

Gallons of gas used for trip = 20 gallons

Distance of trip =

= Odometer at the end of trip - Odometer in the beginning of trip

[tex]=1830.2-1460.3\\=369.9\text{ miles}[/tex]

Thus, the trip was of 369.9 miles.

Miles per gallon =

[tex]=\dfrac{\text{Distance cover in trip}}{\text{Gallons of gas used}}\\\\=\dfrac{369.9}{20}\\\\=18.495\approx 18.50\text{ miles per gallon}[/tex]

Thus, Juan got 18.50 miles per gallon.

The angle -30 degrees is not a correct answer because it falls outside of the given interval [0, 360 degrees). The correct answer is theta = 210 degrees, which satisfies the equation sine theta = -1/2 over the interval. In the fourth quadrant, the angle whose sine is -1/2 should be in the third quadrant to satisfy the inequality sine theta <= 0.

In solving the equation Σ theta = -1/2, the student is looking for the values of theta that satisfy the equation over the interval [0, 360 degrees). The value -30 degrees is not a correct answer because it falls outside of the given interval. To find the correct answer, we need to determine the values of theta that make sine of theta equal to -1/2.

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Answer:

-2

Step-by-step explanation:

Using the slope theorem:

[tex]m=\frac{y_{1}-y_{0}}{x_{1}-x_{0}}[/tex]

[tex]\frac{6-2}{1-3} = \frac{4}{-2} =-2[/tex]

The slope of a line passing through two points can be calculated using a formula. In this case, the slope of a line passing through (1, 0.1) and (7, 26.8) is found to be 4.45.

The slope of a line passing through two points (x₁, y₁) and the (x₂, y₂) can be calculated using the formula:

m = (y₂ - y₁) / (x₂ - x₁)

Plugging in the values of the points (1, 0.1) and (7, 26.8) into the formula, we get:

m = (26.8 - 0.1) / (7 - 1) = 26.7 / 6 = 4.45

Therefore, the slope of the line passing through the points (1, 0.1) and (7, 26.8) is 4.45.

Answer:

0.0100925147183

Step-by-step explanation:

Answer:

48/4,756= 0.010

Step-by-step explanation:

Answer:

6.1

Step-by-step explanation:

Answer:

14

Step-by-step explanation:

she had 22 in all take away 8 then you get 14.

take away 8 because they came from another tree

Answer:

14 peaches

Step-by-step explanation:

10-8=2+12=14

Answer:

34601 liters

Step-by-step explanation:

Given:

Ben is filling his cylinder shaped pool up to 80% of its capacity.

His pool is 6 feet deep and has a diameter of 18 feet.

Question asked:

How much water will he put in the pool?

Solution:

First of all we will find volume of cylinder:

Diameter = 18 feet

Radius, r = [tex]\frac{Diameter}{2} =\frac{18}{2} =9\ feet[/tex]

Height, h = 6 feet

As we know:

[tex]Volume\ of \ cylinder=\pi r^{2} h[/tex]

                                 [tex]=\frac{22}{7} \times(9)^{2} \times 6\\ \\=\frac{22}{7} \times81 \times 6\\ \\ =\frac{10692}{7} \\ \\ =1527.42\ cubic\ feet[/tex]

Now, as given that pool is being filled up to 80%, we have to find quantity of water he will put in the pool:-

Quantity of water filled = 80% of the volume of the pool

                                      [tex]=\frac{80}{100} \times1527.42\\ \\ =1221.93\ cubic feet[/tex]

Now, convert it into liters.

1 cubic feet = 28.31 liters

1221.93 cubic feet = 28.31 [tex]\times[/tex] 1221.93 =  34,601.20 liters

Therefore, he will put about 34601 liters water in the pool.

Answer:

Therefore the required probability is [tex]\frac{30}{351}[/tex].

Step-by-step explanation:

Two events are dependents event if the occurrence of one of them has effect on the probability of the other.

If A and B are dependents,

then,

P(AB)=P(A)P(B).

Given that,

There are 27 chocolates in a box.

Number of nuts chocolates = 4

Number of caramel chocolates = 8

Number of solid chocolates= 15.

The probability of that a solid candy is drawn is

[tex]=\frac{\textrm{Number of solid chocolate}}{\textrm{Total number of chocolate}}[/tex]

[tex]=\frac{15}{27}[/tex].

After selecting a solid chocolate, the number of chocolate is= (27-1)=26.

The probability that a nut candy is drawn is

[tex]=\frac{\textrm{Number of nut chocolate}}{\textrm{Total number of chocolate}}[/tex]

[tex]=\frac{4}{26}[/tex]

[tex]=\frac{2}{13}[/tex]

Therefore the required probability is

[tex]=\frac{15}{27}\times\frac{2}{13}[/tex]

[tex]=\frac{30}{351}[/tex]

The probability that a randomly selected day of the year is in December or January is [tex]\( \frac{62}{365} \)[/tex].

To find the probability that a randomly selected day of the year is in December or January, we need to consider the total number of days in December and January and divide it by the total number of days in a year.

December has 31 days.

January also has 31 days.

A non-leap year has 365 days, and a leap year has 366 days.

Assuming we're considering a non-leap year for simplicity, the total number of days in a year is 365.

Now, let's calculate the probability:

Probability = [tex]\frac{\text{Number of days in December} \ + \ \text{Number of days in January}}{\text{Total number of days in a year}}[/tex]

Probability = [tex]\frac{31 + 31}{365}[/tex]

Probability = [tex]\frac{62}{365}[/tex]

Now, we can simplify this fraction if needed, but to keep it in the most accurate form, we can leave it as [tex]\( \frac{62}{365}[/tex].

1. I just bought a kite at the department store for $5.95. The owner of the store bought it from a wholesaler for $3.10. Which price is retail price?

Answer: The $5.95 is retail price because that's what I paid for it at the store

2. What percentage of the retail price is the wholesale price in #1?

 3.10 / 5.95 = 0.52100 = 52.1%

3. If the sandals cost $58.00 wholesale and $105.00 retail, what is the markup in dollars?

markup = 105 - 58 =  $47

4.The markup in #3 is what percent of the retail?

47/105 = 0.44761904761904764 = 44.8%

5.What percent of the wholesale in #3 is the markup?

47/58 = 0.8103 = 81.0%

6. A dozen eggs are purchased from the farmer at $1.05 per dozen. They are then sold to the consumer for $1.45. What percent of the retail is the markup.

(145-105)/145 = 0.2758620 = 27.6%

Answer:

uh what he said (:

Step-by-step explanation:

Answer:

The correct option is option C.

The width of the rectangular playground is  [tex]-8+8\sqrt5[/tex] ft.

Step-by-step explanation:

Area of rectangular plot is = length × wide.

Given that,

The ratio of longer length to the width of the rectangular playground is

(1+√5): 2

Let the length and width of the rectangular playground be (1+√5)x and 2x.

But the length of the longer side of the rectangular playground is = 16 feet.

According to the problem,

(1+√5)x= 16

[tex]\Rightarrow x= \frac{16}{1+\sqrt5}[/tex]

[tex]\Rightarrow x= \frac{16(1-\sqrt 5)}{(1+\sqrt5)(1-\sqrt 5)}[/tex]             [ rationalize]

[tex]\Rightarrow x= \frac{16(1-\sqrt 5)}{(1)^2-(\sqrt5)^2}[/tex]                 [ (a+b)(a-b)=a²-b²]

[tex]\Rightarrow x= \frac{16(1-\sqrt 5)}{1-5}[/tex]

[tex]\Rightarrow x= \frac{16(1-\sqrt 5)}{-4}[/tex]

[tex]\Rightarrow x=-4(1-\sqrt 5)}[/tex]

[tex]\Rightarrow x=-4+4\sqrt 5[/tex]

Then the width of the playground is = 2x

                                                            [tex]=2(-4+4\sqrt5)[/tex] ft

                                                            [tex]=-8+8\sqrt5[/tex] ft

Answer:

18 days

Step-by-step explanation:

Each cat eats 1/4 of the thin in a day, so between the two cats they eat:

 of the tin in one day.

if the two cats eat 1/2 of the tin in one day, this means that in 2 days they eat a whole tin of cat food.

we can represent this as follows

days     tins of cat food

 2                 1

and because she has 9 tins of cat food, and x represents the quantity of days:

days     tins of cat food

 2                 1

 x                 9

thus, we must multiply cross quantities from the table and divide by the remaining amount:

x = 2*9/1 = 18

the 9 tins of cat food will last 18 days

pls mark me brainliest

Answer:

[tex]60.2 + 124.6 = 184.8 \: calories[/tex]

The total number of calories in this breakfast is 184.8 calories if there are 86 calories in 100g of banana and there are 89 calories in 100g of yogurt.

Fraction number consists of two parts, one is the top of the fraction number which is called the numerator and the second is the bottom of the fraction number which is called the denominator.

There are 86 calories in 100g of banana.

In 1 g = 0.86 calories

In 70 g

= 0.86×70 = 60.2 calories

There are 89 calories in 100g of yogurt.

1g = 0.89 calories

In 140g yogurt:

= 140×0.89

= 124.6 calories

Total calories = 60.2 + 124.6 = 184.8 calories

Thus, the total number of calories in this breakfast is 184.8 calories if there are 86 calories in 100g of banana and there are 89 calories in 100g of yogurt.

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Answer:

10.6 ft

Step-by-step explanation:

The complete question is:

The area of the triangle is 35 square feet. Use a quadratic equation to find the length of the base. Round your answer to the nearest tenth.Base=x+4 Height=x

SOLUTION:

As you know, Area of triangle 'A' = 1/2 x b x h

Where,

Base 'b' = x+4

Area 'A' = 35 ft²

Height 'h'= x

35 = (1/2)(x+4)x

35 =(x² + 4x)/2

2 * 35 =x² + 4x

70 = x² + 4x

x² + 4x - 70=0

Formula for the quadratic equation is

x = [- b ± √(b² - 4ac)]/2a

Where,

a=1,  b= 4,   c=-70

Plugging in the values.

x = [- 4 ± √4² - (4 × 1 × - 70)] / (2 × 1 )

x = [- 4 ± √(16  + 280)]/2

x = [- 4 ± √296]/2

x = (- 4 + 17.2)/2 or x = (- 4 - 17.2)/2

x = 13.2/2 or x = - 21.2/2

As, we choose to ignore negative value of 'x'

Therefore, x = 13.2/2 = 6.6

And, Length of the base will be:

x + 4 = 6.6 + 4 => 10.6 ft

The base is approximately 10.6 feet when rounded to the nearest tenth.

We know the area of the triangle is 35 square feet, the base is x + 4, and the height is x.

The formula for the area of a triangle is:

Area = 1/2 × base × height

1. Substitute the given values into the formula:

35 = 1/2 × (x + 4) × x

2. To simplify, multiply both sides by 2 to eliminate the fraction:

70 = (x + 4) × x

3. Expand the equation:

70 = [tex]x^{2}[/tex] + 4x

4. Rearrange into a standard quadratic form:

[tex]x^{2}[/tex] + 4x - 70 = 0

5. To solve this quadratic equation, we can use the quadratic formula:

x = (-b ± √([tex]b^{2}[/tex] - 4ac)) / 2a

6. Here, a = 1, b = 4, and c = -70. Plug these values into the formula:

x = (-4 ± √([tex]4^{2}[/tex] - 4(1)(-70))) / 2(1)

x = (-4 ± √(16 + 280)) / 2

x = (-4 ± √296) / 2

x = (-4 ± 17.2) / 2

7. This gives us two potential solutions:

x = (-4 + 17.2) / 2 ≈ 6.6

x = (-4 - 17.2) / 2 ≈ -10.6 (This solution is not valid since the height cannot be negative)

8. So, the height (x) is 6.6 feet. Therefore, the length of the base is:

Base = x + 4 ≈ 6.6 + 4 = 10.6 feet.

Question- The area of the triangle is 35 square ft. Use a quadratic equation to find the length of the base. Round your answer to the nearest tenth. Base = x + 4, Height = x.

Answer:3 * (n + 4) = 93

3n + 12 = 93

Subtract 12 to both sides:

3n = 81

Divide 3 to both sides:

n = 27

Step-by-step explanation:

Final answer:

The smaller number is 15.

Explanation:

To find the smaller number, let's assign variables to the two numbers. Let's call the larger number 'x' and the smaller number 'y'. According to the given information, we have two equations:

x + y = 39

2x + 3y = 93

To solve this system of equations, we can use the method of substitution.

Rearrange the first equation to get x = 39 - y.

Substitute this expression for x into the second equation:

2(39 - y) + 3y = 93

Now, simplify and solve for y:

78 - 2y + 3y = 93

y = 15

Therefore, the smaller number is 15.

Answer:

90^30/43046721

Step-by-step explanation:

Answer:

the answer is 5b^3+8

Step-by-step explanation:

To subtract (5b^3 +9b+4)−(9b−4) in standard form, distribute the negative sign, combine like terms, and simplify the expression.

To subtract (5b^3 +9b+4)−(9b−4) in standard form, we need to remove the parentheses and combine like terms. Distribute the negative sign to both terms in the second parentheses, which changes the sign of each term inside.

This gives us 5b^3 + 9b + 4 - 9b + 4.

Combining like terms, we have 5b^3 + 4b + 8.

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Answer:

Step-by-step explanation:

In an arithmetic sequence, the consecutive terms differ by a common difference, d. Therefore,

d = Term 2 - Term 1 = Term 3 - Term 2

In an geometric sequence, the consecutive terms differ by a common difference, r. Therefore,

r = Term 2 /Term 1 = Term 3 / Term 2

1) 128, 32, 8, 2, .. Is a geometric sequence

r = 32/128 = 1/4

2) 1, 3, 9, 27, .. Is a geometric sequence

r = 3/1 = 3

3) 5, 10, 15, 20, ...is an arithmetic sequence

d = 10 - 5 = 5

4) 20, 17, 14, 11, … is an arithmetic sequence

d = 17 - 20 = - 3

Answer: D. He made a mistake in his calculations when substituting the ordered pair into the equation 5x -2y =6 and simplifying.

Step-by-step explanation: I got the answer correct on a test. Hope this helps!

Answer:

true

Step-by-step explanation:

Answer:

True is the answer

Step-by-step explanation:

got it correct on my quiz

Answer:

8:20 am

Step-by-step explanation:

Final answer:

The area of the semicircle is 0.051 square meters.

Explanation:

The area of a semicircle can be found using the formula A = πr²/2, where r is the radius of the semicircle. In this case, the radius is given as 18 cm. So, substituting this value into the formula, we get A = 3.142 x (18 cm)²/2. Now, let's calculate the area step by step:

Convert the radius to meters: 18 cm = 0.18 m

Square the radius: (0.18 m)² = 0.0324 m²

Multiply by π and divide by 2: 0.0324 m² x 3.142 / 2 = 0.051 m²

Therefore, the area of the semicircle is 0.051 square meters.

Answer:

Ok so lets start with finding the equations or the steps:

so for a trapazoid  the formula is  A= A+B/2  SO the area is 6

Step-by-step explanation: For more info on how i did this just contact me or reply to this also inform it if its wrong Thanks! have a good day

Answer:

10

Step-by-step explanation:

The area of a triangle is given by the formula  [tex]\frac{(base)(height)}{2}[/tex].

The first triangle has 4 units in base and 2 in height, in the formula is

[tex]\frac{(4)(2)}{2}[/tex] = 4

The second triangle has 2 units in base and 2 in height, in the formula is

[tex]\frac{(2)(2)}{2}[/tex] = 2

The area of a square is given by the formula base x height = 2 x 2 = 4.

The sum of the areas is 10.

Answer:

See below.

Step-by-step explanation:

1. a and b are supplementary ( they add up to 180 degrees as they are on a straight line).

2,3 and 4 are complementary as in each case a + b = 90 degrees.

Answer:

Complementary angles are the angles which add up to 90°. example - 60° + 30° = 90° . Supplementary angles are those angles which add up to 180° . example - 110° + 70° = 180°.

Step-by-step explanation:

Answer:

95% Confidence interval for y

= (-9.804, -5.979)

Lower limit = -9.804

Upper limit = -5.979

Step-by-step explanation:

^y= 2.097x - 0.552

x = -3.5

Standard error = 0.976

Mathematically,

Confidence Interval = (Mean) ± (Margin of error)

Mean = 2.097x - 0.552 = (2.097×-3.5) - 0.552 = - 7.8915

(note that x=-3.5)

Margin of Error is the width of the confidence interval about the mean.

It is given mathematically as,

Margin of Error = (Critical value) × (standard Error of the mean)

Critical value for 95% confidence interval = 1.960

Standard Error of the mean = 0.976

95% Confidence Interval = (Mean) ± [(Critical value) × (standard Error of the mean)]

CI = -7.8915 ± (1.960 × 0.976)

CI = -7.8915 ± 1.91296

95% CI = (-9.80446, -5.97854)

95% Confidence interval for y

= (-9.804, -5.979)

Hope this Helps!!!

Answer:

8

Step-by-step explanation:

a = -4

r = 16/-4 = -4

Sn = a(r^n - 1)/(r - 1)

52428 = -4[(-4)^n - 1]/(-4-1)

(-4)^n - 1 = 65535

(-4)^n = 65536

Means n is even

(4)^n = 65536

nln(4) = ln(65536)

n = 8

Answer:

6(6)² + 0 = 6³

6(0) + 1 = 1³

6(1) + 2 = 8 = 2³

6(4) + 3 = 27 = 3³

6(10) + 4 = 64 = 4³

6(20) + 5 = 125 = 5³

Answer:

150.4

Step-by-step explanation:

Answer:

3 metres

Step-by-step explanation:

Work done = Force × displacement

60= 20×d

d= 60/20

d= 3 metres

Uisng the relationship between force, work and distance, the distance moved by the object would be 3 meters

Given the Parameters :

Recall :

Substituting the values into the formula :

60 = 20 × Distance

Distance = 60 / 20

Distance = 3

Therefore, the object moves a distance of 3 meters

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