The first used 20 gal of fuel and the second used 25 gal. The 2 drove 1450 miles and the sum of their fuel efficiencies was 65 miles per gal. What we’re each car fuel efficiency?

Log base 19 of 53.875 is approximately 0.97212 when converted to base 10.

To convert log base 19 of 53.875 to base 10, we can use the formula:

log base b of x = log base a of x / log base a of b

where a: current base and b: desired base.

So, in this case, we want to convert log base 19 of 53.875 to base 10. We can use the formula above with a = 19 and b = 10:

[tex]log base 10 of 53.875 = log base 19 of 53.875 / log base 19 of 10[/tex]

Log base 19 of 10 is equal to 1/log base 10 of 19, since the logarithm of 10 to any base is equal to 1. Using a calculator, we can determine that the log base 10 of 19 is roughly 1.278753.

Substituting:

log base 10 of 53.875 = log base 19 of 53.875 / 1.278753

To find the value of log base 19 of 53.875, we can use a calculator to evaluate log base 19 of 53.875, which is approximately 1.244036.

Substitute to equation:

log base 10 of 53.875 = 1.244036 / 1.278753

Simplify to get:

log base 10 of 53.875 = 0.97212

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Answer:

A) 2 to 7

Step-by-step explanation:

Step 1: Determine How Many Child Tickets Were Sold

The question is asking about the ratio of the number of child tickets sold to the number of total tickets sold, but we can't find that unless we know how many child tickets were sold, so let's figure that out first.

We are given that 175 tickets were sold. Of those 175 tickets, 125 were adult tickets, and the rest were child tickets. This means that the number of total tickets sold was equal to the sum of the number of child and adult tickets sold. Therefore, there were 175 - 125 = 50 child tickets sold.

Step 2: Determine the Ratio of Child Tickets to Total Tickets

We now know that 50 out of the 175 total tickets sold were child tickets, so we can find the ratio of the two values. Remember that a ratio just represents the relation between numbers, so we can write the current ratio of child tickets to total tickets as 50 to 175. However, since ratios can be written as fractions, we quickly see that this ratio can be simplified.

In fraction form, this ratio is [tex]\frac{50}{175}[/tex]. Simplifying this fraction by dividing both the numerator and denominator by their greatest common factor, which is 25 in this case, gives us [tex]\frac{2}{7}[/tex], so the final ratio is 2 to 7.

Answer:

y = 4x^2

Step-by-step explanation:

To find a quadratic function of the form y = ax^2 that passes through the point (-2,16), we need to substitute the coordinates of the point into the equation and solve for the coefficient a.

Substituting x=-2 and y=16 into the equation, we get:

16 = a(-2)^2

16 = 4a

a = 4

Therefore, the quadratic function of the form y = ax^2 that passes through the point (-2,16) is:

y = 4x^2

By answering the presented question, we may conclude that Therefore the pattern is that these three fractions are all equal and reflect the same proportion of a whole, which is half.

In mathematics, a fraction is a number that represents a component of a whole or a ratio between two things. It is shown as a top number (numerator) split by a horizontal line, also known as a vinculum, over a bottom number (denominator). For example, the fraction 3/4 indicates three-quarters of a whole split into four equal pieces. A fraction can be expressed using proper fractions, improper fractions, or mixed integers. A appropriate fraction is one with a numerator smaller than the denominator, such as 2/5.

The provided fractions 1/2, 2/4, and 4/8 have the pattern of being comparable fractions.

This indicates that even though they are worded differently, they reflect the same percentage or quantity of a total. Each fraction, in particular, represents half of the whole.

To see that these fractions are comparable, divide the numerator and denominator by the same number. For example, 2/4 may be simplified by dividing both the numerator and denominator by 2, yielding 1/2. Similarly, we may simplify 4/8 by dividing the numerator and denominator by 4, yielding 1/2.

Therefore the pattern is that these three fractions are all equal and reflect the same proportion of a whole, which is half.

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Joe made about $72 from selling comic books last week.

To determine how much money Joe made from selling comic books, we need to find the percentage of $720 that corresponds to comic book sales.

According to the graph, comic book sales account for 10% of Joe's total sales.

To calculate this, we can multiply the total sales ($720) by the percentage of comic book sales (10% or 0.1):

$720 x 0.1 = $72

Therefore, Joe made about $72 from selling comic books last week.

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Joe’s Convenience Store took in $720 last week. According to Example Graph #1, about how much money did he make from selling comic books?

From the content of the graph

The amount of money Joe made is given below:

Selling comic books 10%

Selling costumes 25%

Selling hardware 40%

Selling miscellaneous 20%

It is obvious that he cannot read an entire page in one minute, meaning D (2/3) is literally the only possible answer.

Answer:

Step-by-step explanation:

first give me a high five

Answer:

First one worked for 20 hours, second one worked for 5 hours.

Step-by-step explanation:

50 times 5 : 250

45 times 20 :900

250+900 = 1150

Answer:

Step-by-step explanation:

0.35 = 35/100

100.00 = 100

100×(35/100) = 35

0.5 = 5/10 = 1/2

150.50 = 1505/10

(1505/10)×(1/2) = 75,25

35+75.25 = 110.25

Answer: Ten liter, or one tenth of a hectoliter (2.6418 gallons liquid measure or 1.135 pecks dry measure): abbrev.dal.

A.Factorizing the polynomial is  (8x + 1/2)².

B.The polynomial 64x² + 8x + 1/4 is not prime.

Factorization is the process of expressing a mathematical expression, such as a number or a polynomial, as a product of its factors or simpler components.

To factorize 64x² + 8x + 1/4, we can use the factoring formula for a quadratic trinomial:

a² + 2ab + b² = (a + b)²

In this case, we have 64x² + 8x + 1/4, so we can rewrite it as:

(8x)² + 2(8x)(1/2) + (1/2)²

Notice that the first and last terms are perfect squares, so we can apply the factoring formula to get:

(8x + 1/2)²

Therefore, the factorization of 64x² + 8x + 1/4 is:

64x² + 8x + 1/4 = (8x + 1/2)²

The polynomial 64x² + 8x + 1/4 is not prime.

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Answer:

R5.98

Step-by-step explanation:

R3.60×66÷100= R2.38 (66% of R3.60)

R3.60+R2.38= R5.98

how to find 66%

R5.98-R3.60

=R2.38÷R3.60

=R0.66×100

=66%

By answering the presented question, we may conclude that As a result, variable P(A) = 0.667.

A variable is something that may be changed in the setting of a math concept or experiment. Variables are often represented by a single symbol. The characters x, y, and z are often used generic symbols for variables. Variables are characteristics that can be examined and have a large range of values. These include things like size, age, money, where you were born, academic status, and your kind of dwelling, to name a few. Variables may be divided into two main categories using both numerical and categorical methods.

To compute E[X], we must integrate the PDF X times over its support:

From x=1 to x=2, E[X] = x fX(x) dx

Because the PDF is only non-zero in the interval (1,2), we have:

[tex]E[X] = x(2x/3) dx between x=1.5 and x=2.E[X] = (2/3) x2 dx between x=1.5 and x=2.E[X] = (2/3) [(2^3)/3 - (1.5)^3]E[X] = (2/3) [8/3 - (27/8)]E[X] = 19/12As a result, E[X] = 1.583.[/tex]

P(A) is calculated by integrating the PDF across the area where X is higher than or equal to 1.5:

[tex]P(A) = fX(x) dx between x=1.5 and x=2.P(A) = (2x/3) dx between x=1.5 and x=2.P(A) = [(2/3)x^2] between x=1.5 and x=2P(A) = (2/3)(2^2 - 1.5^2)P(A) = 2/3As a result, P(A) = 0.667.[/tex]

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Complete question -

Consider a random variable X with PDF fX(x) = (2x/3, if 1 < x ≤ 2, 0, otherwise, and let A be the event {X ≥ 1.5}. Calculate E[X], P(A), and E[X | A].

Answer:

Step-by-step explanation:

We Know

A car last month was $250 this month its $330

What is the percent increase?

We Take

(330 ÷ 250) × 100 = 132%

Then We take

132 - 100 = 32%

So, 32% increase.

Answer:

15.36

Step-by-step explanation:

In this equation, we will be using tangent, which is opposite over adjacent. In this case, the "opposite" will be x, and the "adjacent" will be 12. "θ" means the degrees or measurements of the angle.

To find the missing side of the triangle, we will set up a function. The function is:

Tan (θ) = opposite/adjacent

After plugging in the numbers and variables it will be:

Tan(52) = x/12

Then, we would multiply the 12 to both sides.

12 Tan(52) = x

Then we can plug it into a calculator. We should get 15.3592. We would then round it to the nearest hundredth, which is 15.36.

The simplified expression is 28 - 4 using distributive property.

To simplify the expression (4 + )(7 – ), we can use the distributive property of multiplication over addition.

First, we have to multiply the 4 by both the terms inside parentheses:

(4 + )(7 – ) = (47) + (4- )

Next, we distribute negative sign to second term inside parentheses:

(47) + (4- ) = 28 - 4

The simplified expression = 28 - 4.

In other words, the phrase is the outcome of adding 4 to an unknown quantity, taking it out of 7 after that, and then taking the outcome of that subtraction out of 28. The operation's outcome is simplified to 24, which can be used in additional calculations or problem-solving.

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Answer:

They will collide at (2,28),(8,16)

Step-by-step explanation:

give me branliest

Answer:

-7\sqrt[3]{193}x^3\sqrt[3]{x}

Step-by-step explanation:

The number of CDs that need to be produced by the company in order to break even would be 685 CDs .

To break even, the revenue generated by selling the CDs must equal the total cost of producing them. Let's denote the number of CDs produced and sold as a.

Revenue = Price per CD × Number of CDs = 52a

Total Cost = Fixed Cost + Variable Cost × Number of CDs = 26000 + 14a

To break even, we set Revenue equal to Total Cost:

52a = 26000 + 14a

Now, we can solve for a:

52a - 14a = 26000

38a = 26000

a = 26000 / 38

a = 685 CDs

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Answer:

59

Step-by-step explanation:

The values of the quadratic equation; y = x² - 2·x - 1 can be used to complete the table and draw the graph as follows;

(a) x[tex]{}[/tex]       -2        -1           0          1           2          3           4

    y[tex]{}[/tex]       7         -1           2         -2          -1          2           7

(b) Please find attached the graph of the quadratic equation created with MS Excel

A graph of an equation is a visual representation of the rule of the equation that shows how the output value changes as the input values is varied.

The table of values in the question can be completed by substituting the x-values in the table into the equation; y = x² - 2·x - 1 as follows;

The values that complete the table are;

y when x = -1 is; y = (-1)² - 2 × (-1) - 1 = 2

y when x = 0 is; y = (0)² - 2 × (0) - 1 = -1

y when x = 3 is; y = (3)² - 2 × (3) - 1 = 2

y when x = 4 is; y = (4)² - 2 × (4) - 1 = 7

The completed table is therefore presented as follows;

x[tex]{}[/tex]  -2         -1          0          1           2          3             4

y [tex]{}[/tex]  7          -1         2          -2         -1          2             7

(b) The steps that can be used to draw the graph on the coordinate grid using MS Excel are as follows;

Please find attached the graph of the quadratic equation, y = x² - 2·x - 1, created with MS Excel

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Answer: -3x - 6y = -27 (Equation 1)

4x - 2y = -4 (Equation 2)

We can use the method of elimination, which involves adding or subtracting the equations to eliminate one of the variables.

In this case, we can start by multiplying Equation 2 by 3 to eliminate the y variable:

-3x - 6y = -27 (Equation 1)

12x - 6y = -12 (Equation 2 multiplied by 3)

Now we can add Equation 1 to Equation 2:

-3x - 6y = -27 (Equation 1)

12x - 6y = -12 (Equation 2 multiplied by 3)

9x = -39

Simplifying this expression, we get:

x = -39/9 = -13/3

Now we can substitute this value of x into either Equation 1 or Equation 2 to solve for y. Let's use Equation 1:

-3x - 6y = -27

-3(-13/3) - 6y = -27

13 + 6y = -27

6y = -40

y = -40/6 = -20/3

Therefore, the solution to the system of equations is x = -13/3 and y = -20/3, or (-13/3, -20/3) in coordinate form.

To check the solution, we can substitute the values of x and y into both equations:

-3(-13/3) - 6(-20/3) = -27

4(-13/3) - 2(-20/3) = -4

Simplifying both expressions, we get:

13 + 40 = 27 (which is true)

-52/3 + 40/3 = -4 (which is also true)

Therefore, the solution is correct.

Step-by-step explanation:

In the exponential decay, A) r = -0.0839 , B) r = -8.39% , C) Value=$11,800.

What is exponential decay?

The term "exponential decay" in mathematics refers to the process of a constant percentage rate reduction in an amount over time. It can be written as y=a(1-b)x, where x is the amount of time that has passed, an is the initial amount, b is the decay factor, and y is the final amount.

To find the annual rate of change between 1992 and 2006, we can use the formula:

r = [tex](V_2/V_1)^{1/n}-1[/tex]

where V1 is the initial value, V2 is the final value, and n is the number of years between the two values.

=>r = -0.0839

Therefore, the rate of change between 1992 and 2006 is -0.0839.

To express the rate of change in percentage form, we can multiply the result from part A by 100:

=>r = -0.0839 x 100

=> r = -8.39%

Therefore, the rate of change between 1992 and 2006 is a decrease of 8.39%.

To find the value of the car in the year 2009, we can assume that the value continues to drop at the same percentage rate as calculated in part A.

From 2006 to 2009, there are 3 years. So, using the formula for exponential decay, we have:

where V0 is the value in 2006, r is the rate of decrease, and n is the number of years between 2006 and 2009.

=>V = 11792.51

Therefore, the value of the car in the year 2009 would be approximately $11,800 (rounded to the nearest $50).

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After solving the question, we can say that diameter of the soap bubble =14.30 mm.

A sphere, like a ball, is a three-dimensional geometrical object that is completely spherical. It is a symmetrical form with all points on its surface being equidistant from the centre. The radius of a sphere is the distance from its centre to its surface. Spheres can be found in nature in the shape of planets, stars, and bubbles, and they are utilised in a variety of applications including sports equipment, ball bearings, and aesthetic things.

volume of a sphere

[tex]V = (4/3) * \pi * r^3\\ r = (3V / 4 \pi)^(1/3)\\ r = (3 * 1696.5 mm^3 / (4 * 3.14))^(1/3)\\ r = 7.15 mm[/tex]

d = 2r

d = 14.30 mm

diameter of the soap bubble =14.30 mm.

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The apprοximate cοst per square inch οf the cοοkie cake is $0.50.

A line segment cοnnecting twο pοints οn a circle's perimeter and passing thrοugh its center is said tο be the circle's diameter. It is the furthest pοint οn the circle that can be measured.

The equation A=[tex]\pi r^{2}[/tex],where r is the circle's radius, determines the area οf a prοcess. The radius οf the cοοkie cake is equal tο half οf its diameter, οr 6 inches, οr 3 inches. The cοοkie cake's surface area is as fοllοws:

  A  = [tex]\pi r^{2}[/tex]

       = 3.14 x [tex]3^{2}[/tex]

       = 28.26 square inches

We divide the tοtal cοst by the area tο determine the apprοximate cοst per square inch οf the cοοkie cake:

Cοst per square inch = $14.13 / 28.26

                                   = $0.50

As a result, the cοοkie cake cοsts abοut $0.50 per square inch.

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Therefore, the rate of the jet in still air is 708 mph and the rate of the Jetstream is 55 mph.

An equation is a mathematical statement that shows the equality between two expressions. It consists of two sides separated by an equal sign (=). The left-hand side of the equation contains one expression and the right-hand side contains another expression. An equation can contain variables, constants, and mathematical operations such as addition, subtraction, multiplication, and division.

Here,

Let's call the rate of the jet in still air "v" and the rate of the Jetstream "w". When the jet travels against the Jetstream, the effective speed of the jet is v-w, and when it travels with the jetstream, the effective speed is v+w.

We can set up two equations based on the given information:

1959 = 3(v - w)

2289 = 3(v + w)

Simplifying these equations, we get:

653 = v - w

763 = v + w

Now we can solve for v and w using elimination or substitution. Let's use elimination:

Add the two equations together:

653 + 763 = 2v

v = 708 mph

Substitute v back into either equation to solve for w:

763 = v + w

763 = 708 + w

w = 55 mph

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The value of y-intercept = -1 and The value of x-intercept = -4

The value of the vertexes is-

Horizontally vertex: y = -2

Virtically vertex: x = -5

For the y-intercept, you must look at where the graph intersects with the y-axis. In this case, the graph intersects at -1.

For the x-intercept, you must look at where the graph intersects with the x-axis. In this case, the graph intersects at -4.

The horizontal asymptote is a y value the graph approaches but does not pass or touch. In this case, the y value is -2.

The vertical asymptote is an x value the graph approaches but does not pass or touch. In this case, the x value is -5.

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The values of the segments A'B' and B'B for the similar triangle ∆ABC area 4 and 4 respectively.

The triangles ABC and A'B'C are similar, this implies that the length A'C of the smaller triangle is similar to the length AC of the larger triangle

so for the segment A'B;

3/9 = A'B'/12

A'B' = (3 × 12)/9 {cross multiplication}

A'B' = 4.

Also for the segment B'B;

3/9 = 2/(2 + B'B)

3(2 + B'B) = 2 × 9 {cross multiplication}

6 + 3B'B = 18

3B'B = 18 - 6

B'B = 12/3

B'B = 4

Therefore, the values of the segments A'B' and B'B for the similar triangle ∆ABC area 4 and 4 respectively.

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