Leila just put 14.11 gallons of fuel into her car. There were 1.9 gallons in the car to begin with. How much fuel is in Leila's car now?

The area of the triangle is 59.6[tex]m^2[/tex]

Now, According to the question:

The area of a triangle is defined as the total region that is enclosed by the three sides of any particular triangle. Basically, it is equal to half of the base times height, i.e. A = 1/2 × b × h.

In the question, Area unit is not mentioned.

But i take the unit in meter.

Now, We have the given data is:

In triangle HPK:

K = 8 m

P = 14.9 m

To find the area of triangle.

We know that :

Area of Triangle is  = 1/2 × b × h.

A  = 1/2 × 8 × 14.9

A = 59.6 [tex]m^2[/tex]

Hence, The area of the triangle is 59.6

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The angular speed is 8 rad/s and the angular position of point A  will be 8m/s².

The angular speed of the wheel at t=2s can be calculated using the equation ω=αt, where ω is the angular speed, α is the angular acceleration and t is the time. Substituting the given values, we get ω = 4 (2) = 8 rad/s.

The angular position of point A at t=2s can be calculated using the equation

θ = ωt + (1/2)αt².

Substituting the given values, we get

θ = 8 (2) + (1/2) (4) (2²) = 24 rad.

The total acceleration of point A at t=2s can be calculated using the equation a = rα, where a is the total acceleration, r is the radius of the wheel and α is the angular acceleration. Substituting the given values, we get a = 2 (4) = 8 m/s²

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We can conclude that (1-sinx)(1+cscx)=cscx-sinx is a true equation.

An equation is a mathematical expression containing symbols, constants, and/or numbers that combine to create an equation that states the equality of two mathematical expressions. Equations are used to describe relationships between different quantities and can be used to model real-world phenomena. Equations can also be used to solve problems and make predictions about a system.

To verify that this equation is true, we can use algebraic manipulation. First, we need to expand the left side of the equation. We can do this by multiplying (1-sinx) by (1+cscx). This gives us the equation (1-sinx)(1+cscx) = 1+cscx-sinx-sinxcscx.
Next, we need to simplify the right side of the equation. We can do this by combining the two terms with a minus sign. This gives us cscx-sinx.
Finally, we can compare the two equations. We see that both equations are equal, so the original equation is true.
Therefore, we can conclude that (1-sinx)(1+cscx)=cscx-sinx is a true equation.

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Answer:

36

Step-by-step explanation:

An arithmetic sequence is a sequence of numbers in which the difference between any two consecutive terms is constant. A geometric sequence is a sequence of numbers in which any two consecutive terms have a constant ratio.

Given that 8, 2x, 2y is an arithmetic sequence, we know that:

2x - 8 = 2y - 2x

x = y

Given that 2x, 2y, 36 is a geometric sequence, we know that:

(2y)/(2x) = 36/2y

y^2 = 36x

Now, we can use the first equation to substitute for y in the second equation, and get:

x^2 = 36x

x^2 - 36x = 0

x(x-36) = 0

So x = 0 or x = 36

However, x cannot be equal to zero because in that case the second term of the arithmetic sequence will be zero, and it will not be a valid solution. Therefore, x = 36.

So, y = x = 36.

Therefore, the values of x and y are 36.

The future value of the investment after 10 years is $14,158.54.

The future value refers to the value of an investment whose present value is compounded at an interest rate into the future.

We can compute the future value using an online finance calculator as below.

N (# of periods) = 10 years

I/Y (Interest per year) = 4%

PV (Present Value) = $9,565

PMT (Periodic Payment) = $0

Results:

Future Value (FV) = $14,158.54

Total Interest = $4,593.54

Thus, in 10 years, the initial investment of $9,565 at 4% a year will grow to $14,158.54.

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The word description "3 to the power of a + 4" should be written as 3^{a + 4}.

In Mathematics, an exponent is sometimes referred to as power and it can be defined as a mathematical operation that is used in conjunction with an algebraic expression to raise a quantity to the power of another and it is generally written as;

bⁿ

Where:

the variables b and n represent numerical values or an algebraic expression.

By applying the property of exponents based on the law of indices for powers, we have the following:

Expression = 3^{a + 4}.

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Complete Question:

What is 3 to the power of a+4?

An equation to represent the relationship is y=15x.

What is linear equation ?

Linear equation can be defined as the equation in which highest degree is one.

Given ,

The table represents a proportional relationship.

So we have to write an equation to represent the relationship

Given,

Time that is

x = {5,8,12 }

Distance that is

y = {75,120,180}

so here from the given table,

75 = 15*5

120 = 8*15

180 = 12*15

hence , it is in the form of y = 15x.

Therefore, An equation to represent the relationship is y=15x.

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This is consistent with the solutions for the equation x2 - 6x + 5 = 0 being x = 1 and x = 5.

An equation is a mathematical statement that expresses the equality of two expressions. It consists of one or more terms, each of which contains one or more variables. The terms are separated by an equal sign (=) and are usually written in a standard form known as an algebraic equation. Equations can be used to model and solve problems in a wide variety of fields, from physics and chemistry to economics and finance.

The graph of the quadratic equation is a parabola that opens upward and intersects the x-axis at two points. The x-intercepts occur when the equation is equal to zero, so the x-intercepts for the equation x2 - 6x + 5 = 0 are the solutions for x. These solutions are x = 1 and x = 5.

The graph of the quadratic equation also shows that the two solutions of the equation, x = 1 and x = 5, are the x-intercepts of the parabola. This means that when x equals 1 or 5, the equation is equal to zero, so the x-intercepts are the solutions of the equation. This is consistent with the solutions for the equation x2 - 6x + 5 = 0 being x = 1 and x = 5.

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The transformation that does not preserve congruence is translation

The term called transformation is defined as the process of changing the position of an object on an xy-plane.

Here we have know that the  transformation is applied to a figure to create a new figure.

And here we also know that the only transformation that does not preserve congruence is a translation 7 units down

So the transformation of figure and the reflection preserve the congruence since it only create a mirror image of the figure.

And the term called dilation also preserve congruence since it only enlarges the given figure.

Here we want to know that concept of translation a type of transformation that takes each point in a figure and slides it the same distance in the same direction.

Based on this definition we have conclude that the solution is translation.

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Answer:

sorry I want to help you but I can't sorry

Step-by-step explanation:

i don't know how to solve this

The slope of the line is 1/2 and the y-intercept is 4. Then the correct option is D.

A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.

The linear equation is given as,

y = mx + c

Where m is the slope of the line and c is the y-intercept of the line.

If you have a different linear equation such as y = (1/2) x + 4. Then the slope and y-intercept of the line are given as,

m = 1/2

y = 4

The slope of the line is 1/2 and the y-intercept is 4. Then the correct option is D.

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Answer: 0.3K IS THE DIFFERENCE

Step-by-step explanation:

HOPE IT HELPS =D

Answer:

3k

Step-by-step explanation:

1. Combine multiplied terms into a single fraction

2. Multiply all terms by the same value to eliminate fraction denominators

3. Cancel multiplied terms that are in the denominator

4. Multiply the numbers

The property descibed by the statement "whatever is done on one side of the equation must also be done on the other side of the equation” is (d) Property of Equality

From the question, we have the following parameters that can be used in our computation:

“whatever is done on one side of the equation must also be done on the other side of the equation”

This means that if x is added to the first side, it must be done on the other side

The property described above is (d)

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Ty works 22 hours in weekdays and 14 hours in weekends to earn at least $600 by working a total of 36 hours in a week.

In the question, we have to find how many hours he need work on the weekends.

Let he work x hours on weekdays.

Let he work y hours on weekends.

He works total 36 hours. So the required question is:

x + y = 36..................(1)

Ty earns $14 an hour working on weekdays. If he works x hours, then he earns total 14x.

Ty earns $21 an hour working on weekends. If he works y hours, then he earns total 21x.

He earns total $600.

So the required equation is:

14x + 21y = 600..................(2)

Multiply equation 1 by 21 and subtract by equation 2

21x + 21y - (14x + 21y) = 756 - 600

Simplify

7x = 156

Divide by 7 on both side, we get

x = 22.29

x = 22

Now put the value of x in equation 1, we get

22 + y = 36

Subtract 22 on both side, we get

y = 14

Hence, he works 22 hours in weekdays and 14 hours in weekends.

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The answer is The graph does not represent a one-to-one function because the y-values between 0 and 2 are paired with multiple x-values.​

What is the one-to-one function?

The one-to-one function is a special function that maps every element of the range to exactly one element of its domain i.e, the outputs never repeat. As an example, the function g(x) = x - 4 is a one-to-one function since it produces a different answer for every input.

To be a function, it has to pass the vertical line test, which means a vertical line drawn anywhere in the graph should cut the graph only once, not more.

To be a one-to-one function, it has to pass the vertical line test as well as the horizontal line test, which means that a horizontal line drawn anywhere in the graph should cut the graph only once, not more.

Of course, it passes the vertical line test, so it's a function.

Does it pass the horizontal line test? NO! As shown in the attached picture, the blue line (horizontal line) cuts the graph at 3 places.

We, therefore eliminate choices A and B.

We can eliminate choice C because nowhere is it requires a function to pass through the origin for it to be one-to-one.

Hence, the answer is The graph does not represent a one-to-one function because the y-values between 0 and 2 are paired with multiple x-values.​

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Answer:

D for Edge

Step-by-step explanation:

y

If 6x/(x²-3x) is subtracted from the sum of 3/(5x-15) and (x+3)/(x-3) , then the result is (12 - 5x)/(x - 3) .

The sum of the algebraic expressions 3/(5x-15) and (x+3)/(x-3)  are written as ; ⇒ 3/(5x-15) + (x+3)/(x-3) ;

taking 5 common from the denominator of the first term ,

we get ;

⇒ 3/5(x-3) + (x+3)/(x-3) ;

taking LCM as 5(x-3) and simplifying further ,

we have ;

⇒ 3/5(x-3) + (x+3)/(x-3) ;

⇒ [3 + 5(x+3)]/5(x-3)  ;

⇒ (5x + 18)/5(x-3)  .......equation(1)

Now 6x/(x²-3x) is subtracted from the equation(1)

⇒ (5x + 18)/5(x-3) - 6x/(x²-3x)  ;

⇒ (5x + 18)/5(x-3) - 6x/x(x-3)  ;

⇒ (5x + 18)/5(x-3) - 6/(x-3)  ;

taking LCM as as 5(x-3) and simplifying further ,

we have ;

⇒ (5x + 18 - 30)/5(x-3)  ;

⇒ (5x -12)/5(x-3)  ;

Therefore , the  final result is (5x -12)/5(x-3) .

The given question is incomplete , the complete question is

If 6x/(x²-3x) is subtracted from the sum of 3/(5x-15) and (x+3)/(x-3) .  What is the result ?

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Answer:

5

Step-by-step explanation:

1.5+5x

The derivative of a polynomial is the sum of the derivatives of its terms. The derivative of a constant term is 0. The derivative of ax n is nax n−1

5x1−1

Subtract 1 from 1.

5x 0

For any term t except 0, t 0 =1.

5×1

For any term t, t×1=t and 1t=t.

5

This is how i would solve it :))

Answer:

a. 1750; b. 900; c. sean 50%, Adrian = 850/3500= 24.3%, James =25.7%

Step-by-step explanation:

Sean got half = 3500/2 =1750

Adrian = 850

James = 3500-1750-850 =900

Answer:

y = -4/3x + 4

Step-by-step explanation:

4x+3y=12

3y = -4x + 12

y = -4/3x + 4

The length of an arc that has a measure of 190° is equal to 9 cm.

In Mathematics, if you want to calculate the length of an arc formed by a circle, you will divide the central angle that is subtended by the arc by 360 degrees and then multiply this fraction by the circumference of the circle.

Mathematically, the length of an arc formed by a circle is given by:

Length of an arc = 2πr × θ/360

Length of an arc = C × θ/360

Where:

Substituting the given points into the length of an arc formula, we have the following;

Length of an arc = 36 × 90/360

Length of an arc = 36 × 1/4

Length of an arc = 9 cm.

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Step-by-step explanation:

11.47 + 9.02

= 20.49 ...

[its takes so much time to solve and write here so plzzz =》]

The rate of change over 1 ≤ x ≤ 3 is -5.76 and  rate of change over 4 ≤ x ≤ 7 is -2.665.

A relation is a function if it has only One y-value for each x-value.

The general form of an exponential function is:

f(x) = 40(0.8)ˣ

where 40 is the initial value and 0.8 is the decay factor.

To get the average rate of change over an interval, compute the slope of the line that connects the endpoints of the interval (it's called the secant line). For an interval running from x₁ to x₂, the slope formula for a straight line is:

slope = (f(x₂)-f(x₁)) / (x₂-x₁)

where f(x₁) and f(x₂) are the values of your function at x₁ and x₂.

So for the interval 4 ≤ x ≤ 7

slope = average rate of change = (f(7)-f(4)) / (7-4)

=8.388-16.384/3

=-2.665

For the interval  1 ≤ x ≤ 3

Average rate of change =f(3)-f(1)/2

=20.48-32/2

=-5.76

Hence, the Rate of change over 1 ≤ x ≤ 3 is -5.76 and  rate of change over 4 ≤ x ≤ 7 is -2.665.

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Answer:

Step-by-step explanation: Hello! You know that there are 3 students who scored 55, 4 students who scored 60, 8 students who scored 65, 4 students who scored 70, 4 students who scored 75, 1 student who scored 80, 9 students who scored 85, and 5 students who scored 90.  To find the mean of a set of values, here is the formula:

a + b + c + d + e . . .

--------------------------

           2

Each variable should represent the score of a single student, so write each score for each individual student.

(55 + 55 + 55 + 60 + 60 + 60 + 60 + 65 + 65 + 65 + 65 + 65 + 65 + 65 + 65 + 70 + 70 + 70 + 70 + 75 + 75 + 75 + 75 + 80 + 85 + 85 + 85 + 85 + 85 + 85 + 85 + 85 + 85 + 90 + 90 + 90 + 90 + 90)/2

You could divide all of this by 2 or you could multiply the values and then add them:

((55 x 3) + (60 x 4) + (65 x 8) + (70 x 4) + (75 x 4) + 80 + (85 x 9) + (90 x 4))/2

Either way works, but the second way is probably faster.

--------------------------------------------------------------------------------------------------

How to find the answer:

55 x 3 = 165
60 x 4 = 240
65 x 8 = 520
70 x 4 = 280
80 = 80
85 x 9 = 765
90 x 4 = 360

Substitute this into the equation

(165 + 240 + 520 + 280 + 80 + 765 + 360)/2

(405 + 800 + 845 + 360)/2

(1205 + 1205)/2

2410/2

= 1205

The answer is 1205

Answer:

8 cups of flour

Step-by-step explanation:

If you want an equation it will be:

[tex]\frac{2}{8} * \frac{32}{1} = \frac{64}{8} = 8[/tex]

So Francessa used 8 cups of flour

The problem deals with the concept of simple random sampling and stratified random sampling techniques. Here, use these techniques to identify the correct statement for the given study.

a sampling technique that guarantees each population member or object has the same chance of being selected for the sample.

Stratified random sample: A stratified random sample is created by first separating the population's components into distinct, non-overlapping groups, or strata, and then randomly choosing a sample from each stratum in turn. A stratified SRS is a unique type of stratified sampling that chooses units from each stratum using SRS.

To forecast appraised value from different variables, such as size, age, number of bathrooms, etc., the real estate appraiser may utilize basic random or stratified random samples.

A real estate appraiser must get a random sample of single-family homes in the basic random sample approach in order to analyze or anticipate the necessary qualities.

He must create a basic random sample from each of the ten neighborhood districts that are specified as stratums in the stratified random sample method. He can research or extrapolate the necessary qualities from the sample that was generated. The population in this investigation is limited and recognizable. This makes it enumerative.

An appropriate approach is to create a stratified random sample by selecting a simple random sample from each of the 10 district neighborhoods or to construct a random sample of all single-family residences in the city.

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For the 5 GB and x GB over use of the data plan per month the total cost paid by Penelope is $160 and $(35 + 25x ).

Let 'x' represents the extra GB used by Penelope in his smart phone data plan.

Cost to used fixed 9 GB of data in a month is equal to $35

Extra charge per GB over the included amount for fixed 9 GB is $25

Equation represents the data plan relation is:

35 + 25x

When Penelope used 5 GB extra over the 9 GB data plan then ,

x = 5GB

Amount to be paid for extra 5 GB is

= 35 + 25( 5 )

= 35 + 125

= $ 160

Amount to be paid for extra 'x' GB is $(35 + 25x).

Therefore, the total cost for extra use of data plan per month is:

a. For 5 GB it is $160.

b. For x GB it is $(35 + 25x).

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The probability of obtaining heads on fourth trial is 1/2

In a random experiment of tossing a penny, let H be the event of obtaining head and T be the event of obtaining tail

As it is a fair penny, the probability of obtaining head=1/2

The outcomes of the trials are independent when a coin is tossed multiple times.

Probability of getting three heads ,

P(3H)=P(H∩H∩H)

=P(H)xP(H)xP(H)

=1/2x1/2x1/2

=1/8

We will use conditional probability to find the probability of obtaining head in the fourth trial, given that three heads are already obtained in three trials

P(H|3H)=P(H∩3H)/P(3H)=(1/8x1/2)/(1/8)=1/2

Thus, the required probability is 1/2

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The average rate of change of demand when the number of items demanded increases from 2 thousand units to 4 thousand units is 401.13 and if it increase from 1 thousand units to 5 thousand units is 201.13

What is Algebraic expression ?

Algebraic expression can be defined as the combination of variables and constants.

Given,

The expression, p(x) = 0.2 x^2 + 1.13x+5.2

where x is given in units of a thousand .

The average rate of change of demand when the number of items demanded increases from 2 thousand units to 4 thousand units.

p(x) = 0.2x^2 + 1.13x+5.2

p(2000 ) = 0.2 (2000*2000) + 1.13 (2000) + 5.2

= 800000 + 2260 + 5.2

= 802265.2

p(4000 ) = 0.2 (4000*4000 ) + 1.13 (4000) + 5.2

= 1600000 + 4520 + 5.2

= 1604525.2

p(2000) - p (4000) / 2000-4000  = 802265.2 - 1604525.2 /  -2000

= -8,02,260 / -2000

= 401.13

p (1000) = 0.2 (1000*1000) + 1.13 (1000) + 5.2

= 200000 + 1130 + 5.2

= 201135.2

p (5000 ) = 0.2 (5000*5000) + 1.13(5000) + 5.2

= 1000000 + 5650 + 5.2

= 1005655.2

p (1000) - p (5000) / 1000 - 5000  = 201135.2 - 1005655.2  / -4000

= 804520 / 4000

= 201.13

Hence, The average rate of change of demand when the number of items demanded increases from 2 thousand units to 4 thousand units is 401.13 and if it increase from 1 thousand units to 5 thousand units is 201.13.

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Answer:

Step-by-step explanation:I  D   K