The table shows the gallons of fuel remaining after a car

travels a certain distance in miles

Distance

(miles)

Fuel Remaining

(gallons)

The change in fuel remaining from one row to the next

in the table is gallon(s)

The change in distance from one row to the next in the

table is

mile(s)

The slope of the line that runs through the points given

in the table is

The slope indicates a

13. 50

13. 46

13. 42

3

13. 38

13. 34

5

13. 30

a)  The maximum mortgage amount they could afford to borrow from the bank, if all the other conditions were the same =  $369,181.93.

b)  The total amount that would be paid to the lender over 25 years = $540000

To find the maximum mortgage amount they could afford to borrow if they could only pay $1800.

Here, future value = 0

number of periods = 25 years

                                = 25 × 12 months per year

                                = 300

payment amount = -1800 dollars

interest rate = 4.25% per year

                    = 0.3542% per month

the maximum mortgage amount they could afford = $369,181.93.

And the total payments would be equal to 300 × 1800 = 540000

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The complete question is:

Aya and Harumi would like to buy a house and their dream house costs $500,000. They have $50,000 saved up for a down payment but would still need to take out a mortgage loan for the remaining $450,000 and they're not sure whether they could afford the monthly loan payments. The bank has offered them an interest rate of 4.25%, compounded monthly.

What if Aya and Harumi could only afford a monthly payment of $2,000?

What would be the maximum mortgage amount they could afford to borrow from the bank if all the other conditions were the same?

What is the total amount that would be paid to the lender over 25 years?

A triangle has sides of 7, 24, and 25 cm. The length of the hypotenuse is equal to 25 cm if the triangle is a right triangle.

The triangle's sides are 7 cm, 24 cm, and 25 cm, as is obvious.

49, 576, and 625 are the results of squaring the lengths of the side of the.

49 + 576 = 625\s(7)2 + (24)2 = (25)2

As a result, the aforementioned equation satisfies Pythagoras's theorem. As a result, it is a right-angled triangle.

the hypotenuse is 25 cm long.

Angles of 16.26 degrees and 73.74 degrees are suitable.

Yes, since 72+242=252 (sum of squares on smaller two sides equals square on largest side).

The triangle's sides are 7 cm, 24 cm, and 25 cm, as is obvious. 49, 576, and 625 are the results of squaring the lengths of the side of the. As a result, the aforementioned equation satisfies Pythagoras's theorem. As a result, it is a right-angled triangle.

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Vertices are at (-7, 5) and (-1, 5) and foci are at (-9, 5) and (1, 5) of the hyperbola with equation quantity x plus 4 squared divided by 9 minus the quantity of y plus 3 squared divided by 16.

As per the given data the given equation is:

[tex]\\$$\frac{ (x+4)^2}{9} - \frac{(y-5)^2 }{16}=1$$[/tex]

The standard form for the equation of a hyperbola with center (h, k) is [tex]\frac{(x-h)^{2} }{a^{2} } - \frac{(y-k)^2}{b^{2} } =1[/tex]

Your hyperbola opens left/right, because it is of form x - y.

Comparing terms, we find that

h = -4, k = 5, a = 3, y = 4

In the general equation, the coordinates of the vertices are at [tex]$(h \pm a, k)$[/tex].

Thus, the vertices of your hyperbola are at (-7,5) and (-1,5).

The foci are at a distance c from the center, with coordinates [tex]$(\mathrm{h} \pm \mathrm{c}, \mathrm{k})$[/tex], where [tex]$c^2=a^2+b^2$[/tex]

[tex]c^2=9+16=25$[/tex], so c = 5.

The coordinates of the foci are (-9, 5) and (-1, 5).

The Figure below shows the graph of the hyperbola with its vertices and foci.(attached at the end of solution)

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Answer:

I)3^4 x 3^7=3^4+7(b/c the base is similar)

3^4 x 3^7=3^11

Ii) first 3^4=3x3x3x3=81

3^7=2187

then 81 x 2187=177147

Answer:

21x

Step-by-step explanation:

5x+14=19x

3x-5=-2x

-2x-19x=21x

Answer:

Step-by-step explanation:

The total cost of the items before tax was $1.50 * 4 = $<<1.54=6>>6.

The sales tax was $6 * 8.25% = $<<68.25*.01=0.495>>0.495.

So the total price was $6 + $0.495 = $<<6+0.495=6.495>>6.495.

The distribution has the greatest spread is

The term standard deviation refers to a measurement of the data's dispersion or spread from the mean.

A low standard deviation implies that the data are grouped around the mean, whereas a large standard deviation shows that the data are more dispersed or spread out.

In the given problem the distribution that has a higher value of standard deviation is the one that has the highest spread spread

This is distribution 3 with a standard deviation of 7.2

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The correct answer is A representative, random sample of individuals are questioned regarding their attitudes or behaviours. (Option B)
A) "Individuals are carefully observed in their natural environments" is a description of participant observation, which is a type of qualitative research method. In this method, researchers observe and interact with individuals in their natural environments in order to understand their behaviours and attitudes in context. This method is often used in fields such as anthropology, sociology, and psychology.

B) "A representative, random sample of individuals are questioned regarding their attitudes or behaviours" describes a survey, which is a quantitative research method. Surveys are used to gather information from a representative sample of individuals in order to make inferences about a larger population. Surveys can be conducted in various ways, such as through phone calls, mail or online and can be used to study the attitudes, behaviours, and characteristics of a population.

C) "An individual is studied in great depth" is a description of a case study, which is a qualitative research method. In this method, a researcher closely examines an individual or a small group of individuals in order to gain a detailed understanding of their experiences, behaviours, and attitudes. Case studies are often used in fields such as psychology, sociology, and anthropology.

D) "An investigator determines the extent to which two variables influence each other" is a description of a correlation study, which is a quantitative research method. In this method, the researcher examines the relationship between two or more variables. The researcher measures the values of the variables for a sample of individuals, and then uses statistical methods to determine the degree of association between the variables, and if there is a causal relationship or not.

Thus, The correct answer is A representative, random sample of individuals are questioned regarding their attitudes or behaviours. (Option B)

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The ratio of blue shirts to red shirts is 2:5, so for every five red shirts, there are two blue shirts.

Ratio is a mathematical term used to compare two different values. It is a way of expressing one quantity in relation to another. Ratios can be written as fractions, decimals, or percentages. Ratios are used in many different areas, such as finance, economics, science, and engineering. Ratios are also used to compare the size, speed, or cost of different items. Ratios can be used to compare parts of a whole, or to compare different items within a group.

Since there are 100 red shirts in the store, there are 40 blue shirts in the store (100 / 5 x 2 = 40).

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The numerical coefficient of xy in the given expression 6xy is 6.

In mathematical terms, a coefficient is a numerical value that is multiplied by a variable in an algebraic expression. The coefficient is the number that appears in front of the variable.

For example, in the expression 3x, the coefficient is 3. In the expression 2[tex]y^2[/tex], the coefficient is 2. In the expression -5[tex]z^3[/tex], the coefficient is -5.

In the case of a constant term in an expression, the coefficient is the constant term itself.

For example, in the expression 3x + 4, the coefficient of x is 3 and the coefficient of the constant term 4 is 4.

Here, in the expression 6xy, the numerical coefficient of xy is 6.

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The angle K for the Isosceles trapezoid is a supplementary angle to the angle J and the measure of angle K = 152°

This is a trapezoid in which the base angles are equal and therefore the left and right side lengths are also equal. The opposite angles are supplementary which implies they sum up to 180°.

angle J and angle M are base angles for the Isosceles trapezoid and are equal, so:

23x + 5 = 13x + 15

23x - 13x = 15 - 5 {collect like terms}

10x = 10 {divide through by 10}

x = 1

angle J = 23(1) + 5 = 28°

Angle K and angle J are supplementary so:

K = 180 - 28

K = 152°

Therefore, the measure of the angle K for the Isosceles trapezoid JKLM is equal to 152°

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The number of seeds produced from a single seed when it is sown and harvested is referred to as the seed multiplication ratio.

A seed is an undeveloped plant embryo and food reserve that is encased in a protective outer covering in botany. More broadly, "seed" refers to anything that can be sown, which could include seed and husk or tuber.

Seeds are the result of a ripened ovule being fertilised by sperm from pollen, resulting in a zygote. The embryo within a seed develops from the zygote, forming a seed coat around the ovule and growing to a certain size within the mother plant before growth stops.

The formation of the seed is a step in the reproduction process of seed plants (spermatophytes). Other plants, such as ferns, mosses, and liverworts, do not have seeds and must reproduce through water-based means.

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The probability of the intersection of the two diagonals chosen lying inside the nonagon is 2/3.

What is the probability?

Probability is a measure of the likelihood of an event occurring. It is a number between 0 and 1, with 0 representing an impossible event and 1 representing a certain event.

In this problem, the event of interest is the intersection of the two diagonals lying inside the nonagon. A nonagon is a 9-sided polygon, so there are 9 total corners, each of which can be one end of a diagonal. Therefore, there are 9 choose 2 = 36 total ways to choose two diagonals.

To find the number of favorable outcomes, we need to find the number of ways to choose two diagonals such that their intersection is inside the nonagon. To do this, we can notice that the diagonals that have an intersection inside the nonagon are the diagonals that connect non-adjacent corners of the nonagon. There are 8 non-adjacent corners, so there are 8 choose 2 = 28 ways to choose two non-adjacent corners.

So the probability of the intersection of the two diagonals lying inside the nonagon is:

P(intersection inside nonagon) = favorable outcomes / total outcomes = 28/36 = 2/3

Hence, the probability of the intersection of the two diagonals chosen lying inside the nonagon is 2/3.

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The probability of the intersection of the two diagonals chosen lying inside the nonagon is 2/3.

What is the probability?

Probability is a measure of the likelihood of an event occurring. It is a number between 0 and 1, with 0 representing an impossible event and 1 representing a certain event.

In this problem, the event of interest is the intersection of the two diagonals lying inside the nonagon. A nonagon is a 9-sided polygon, so there are 9 total corners, each of which can be one end of a diagonal. Therefore, there are 9 choose 2 = 36 total ways to choose two diagonals.

To find the number of favorable outcomes, we need to find the number of ways to choose two diagonals such that their intersection is inside the nonagon. To do this, we can notice that the diagonals that have an intersection inside the nonagon are the diagonals that connect non-adjacent corners of the nonagon. There are 8 non-adjacent corners, so there are 8 choose 2 = 28 ways to choose two non-adjacent corners.

So the probability of the intersection of the two diagonals lying inside the nonagon is:

P(intersection inside nonagon) = favorable outcomes / total outcomes = 28/36 = 2/3

Hence, the probability of the intersection of the two diagonals chosen lying inside the nonagon is 2/3.

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There are 3 terms in expression 7[tex]x^{2}[/tex]-5x+5.

Monomials, binomials, trinomials, and polynomials are all examples of algebraic expressions in mathematics. Algebraic expressions are those that are modeled utilizing unknowable constants, coefficients, and variables. A variable can have any value because it is not fixed, unlike a constant, which has a definite value. Monomials, binomials, trinomials, and polynomials are examples of algebraic expressions that are created by combining variables and constants using arithmetic operations. Terms are the components of algebraic expressions that are separated by addition or subtraction. The type of expression—monomial, binomial, trinomial, or polynomial—depends on the number of terms.

An algebraic expression with three terms is called a trinomial.

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3y + 2 = 2y - 5x

3y - 2y = -5x -2

y = -5x - 2

If the ratio of cars to truck in Main Street Auto Leasing  Company is 9 to 4 and in the airport Auto Leasing Company is 5 to 3 , then the Main Street Auto Leasing Company has more number of cars .

The Ratio of cars to truck in Main Street Auto Leasing Company is = 9:4 ;

the ratio of cars to truck in Airport Auto Leasing Company is = 5:3 ;

the number of trucks in each Leasing Company is = 24 trucks ;

Case (i)  : Main Street Auto Leasing Company  ;

Since the ratio is = 9:4 ,

So , the number of cars is = 9x   and

the number of trucks = 4x ;

That means , [tex]4x = 24[/tex] ;

[tex]x = 6[/tex] ;

the number of cars in Main Street company is = [tex]9 \times 6[/tex] = 54 cars .

Case (ii) : Airport Auto Leasing Company ;

the ratio is = 5:3 ;

So , the number of cars is = 5x   and

the number of trucks = 3x ;

That means , [tex]3x = 24[/tex] ;

[tex]x = 8[/tex] ;

the number of cars in Airport Auto company is = [tex]5 \times 8[/tex] = 40 cars .

Therefore , the Main Street Auto Leasing Company has more  number of Cars .

The given question is incomplete , the complete question is

Main Street Auto Leasing has a ratio of cars to trucks that is 9 to 4. Airport Auto Leasing has a ratio of cars to trucks that is 5 to 3. If each leasing center has 24 trucks, which auto leasing company has more cars ?

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The lengths of each diagonal are given as follows:

As the lengths are different, the polygon TUVW is not a rectangle.

The diagonal length is obtained using the formula for the distance between two points, presented as follows:

[tex]D = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

In which [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] are the coordinates of each point.

The first diagonal is TV, and the length is given as follows:

[tex]TV = \sqrt{(9 - (-5))^2 + (6 - 0)^2} = \sqrt{232}[/tex]

The second diagonal is WU, and the distance is given as follows:

[tex]WU = \sqrt{(-3 - 7)^2 + (-9 - 3)^2} = \sqrt{244}[/tex]

A rectangle has diagonals of equal length, hence the polygon for this problem is not a rectangle.

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The number of nickels that Sonji has as per the given equation is 63.

We are given the information that Sonji has 21 dimes (which means that d=21). We can use the equation to find the number of nickels n.

0.10d + 0.05n = 5.25

0.10(21) + 0.05n = 5.25

2.10 + 0.05n = 5.25

0.05n = 3.15

n = 3.15 / 0.05

n = 315 / 5

n = 63

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Corresponding angle pairs - (1,5) , (2,6) , (3,7) and (4,8)

Ratios express the relationship between two or more quantities, they can be expressed in different forms such as 6:12, 42:12 and 3:1, 10:10, 100:10, and 10:1, 24:36 and 2:3.

1. 6 Weeks to 12 days:

2. 10 decimeters to 10 centimetres:

3. 4 days to 36 hours:

4. 4 months to 8 weeks:

5. 30 seconds to 6 minutes:

6. 24 girls to 16 boys:

7. 12 mangoes to 36 fruits:

8. 2 years to 36 months:

9. 45 points to 9 games:

10. 468 students for 9 classrooms:

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Answer:

3x³ is a polynomial of degree

The degree of the polynomial 3x³ is 3

Answer:

55555555546776546567

When an algorithm necessitates extensive sharing of instantaneous results, parallelism slows it down. Because there are multiple independent parallel processes and the right number of threads, parallelism will speed up an algorithm.

The ones with data dependencies are the most challenging. It will be exceedingly challenging, for instance, if you are dealing with a vector and the input for the computation at point n depends on the output at position n-1.

When this occurs, you must comprehend what the original algorithm is doing and take an alternative approach. For the aforementioned case, it might be a difficulty with digital signal processing including a feedback-containing digital filter. These are challenging to parallelize, but that is not the sole solution. Instead, you might use the filter and signal's fast Fourier transforms, multiply them, and then perform the inverse transform. All of these operations can be partially parallelized.

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The value of tan 3° is 0.0524.

tangent is the trigonometric ratio.

we can find out the value of tangent by taking perpendicular of the triangle divided by base of the triangle.

tan Q = perpendicular of the triangle  /base of the triangle.

sine theta divided by cos theta gives the value of tan theta.

tan Q = sin Q/ cos Q.

some formula of the tan Q are as follows,

1- tan Q = sin Q/cos Q

2- tan Q= 1 /cot Q

3-tan^2 Q =sec^2 Q -1

4- tan(90 - Q)=cot Q

5- tan (Q+π) = tan Q

6- tan (π-Q) = -tan Q

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The linear equation that passes through these two points is:

y = -4x

A general linear equation can be written as:

y = a*x + b

Where a is the slope and b is the y-intercept.

If we know that the line passes through two known points (x₁, y₁) and (x₂, y₂), then we can write the slope as:

a = (y₂ - y₁)/(x₂ - x₁)

Here we know the two points (-2, 8) and (5, -20), so the slope is:

a = (-20 - 8)/(5 + 2) = -28/7 = -4

So the line is:

y = -4*x + b

To find the value of b, we can replace the values of the point (-2, 8), so we will get:

8 = -4*(-2) + b

Now we can solve this for b.

8 = -4*(-2) + b

8 = 4*2 + b

8 = 8 + b

8 - 8 = b

0 = b

Then the linear equation is:

y = -4*x

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Answer:fixed cost=10

Independent variable=months paid

Dependent=hours on support

month=x,h=hour,10x+35h=total cost

97.50=10+35h

87.50=35h

h=2.5 hours

Step-by-step explanation:

showed work

The one-to-one function is obtained as f(x) = 4x + 1 which is a linear function.

A function y = f(x) is defined as a one to one relation between sets X and Y. The set X is called the domain while Y is called the range of f(x).

A function can either have one-to-one or many-to-one mapping.

One-to-one mapping implies unique element in the domain for each element in the range while for many-to-one mapping there are many elements in the domain for one element in the range.

The given functions are y = [2x] , y = x² and f(x) = 4x + 1 respectively.

They can be examined one by one as follows,

(a) y = [2x]

It is a greatest integer function.

At x = 1.1, y = [2 × 1.1] = [2.2] = 2

And, for x = 1.2, y = [2 × 1.2] = [2.4] = 2

It implies for different values of x, the function has same value.

Thus, it is not one-to-one function.

(b)  y = x²

Find values of the function at two different x as,

x = -2, f(x) = (-2)² = 4

And, for x = 2, f(x) = 2² = 4.

It implies for different values of x, the function has same value.

Thus, it is not one-to-one function.

(c) f(x) = 4x + 1

It is a equation of a straight line.

Which implies it has different values for different values of x.

Thus, it is a  one-to-one function.

Hence, out of the given functions only f(x) = 4x + 1 is one-to-one.

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The function domain is X≥5  Or in interval notation [5, ∞)

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Answer: It looks like you are trying to find the value of the function h(x) = √ (x-3) - 2.

To find the value of this function for a given value of x, you need to substitute the value of x into the function definition and simplify the expression.

For example, if you want to find the value of h(x) for x = 5, you would substitute 5 for x in the function definition and simplify the expression to get:

h(5) = √(5-3) - 2

= √2 - 2

= 1.4 - 2

= -0.6

Therefore, the value of h(x) for x = 5 is -0.6.

You can follow this same process to find the value of h(x) for any other value of x. Just be sure to substitute the correct value of x into the function definition and simplify the expression to find the final result.

Step-by-step explanation:

Answer:

g[f(x)]

Step-by-step explanation:

Given functions:

[tex]f(x)=x-3[/tex]

[tex]g(x)=\sqrt{x}-2[/tex]

Composite functions are when the output of one function is used as the input of another.

Therefore, to create √(x-3)-2, substitute the function f(x) in place of the x in function g(x):

[tex]\begin{aligned}\implies g[f(x)]&=\sqrt{f(x)}-2\\&=\sqrt{x-3}-2\end{aligned}[/tex]