The table below shows a proportional relationship between x and y
What is the constant of proportionality for the relationship between x and y

a. The chart is prepared below.

b. At the end of 4 years, Ross still owes his parents $1,576.92.

To solve this problem, we need to calculate the balance of Ross's loan at the end of each year.

The balance for each year can be calculated by subtracting the yearly payment from the balance at the beginning of the year and adding the interest earned for the year.

The interest for each year is calculated by multiplying the balance at the beginning of the year by the annual interest rate of 3.2%.

Here are the steps for calculating the balance for each year:

Year 1:

Beginning balance = $2,500.00

Interest for the year = $2,500.00 x 0.032 = $80.00

Ending balance = $2,500.00 + $80.00 - $300.00 = $2,280.00

Year 2:

Beginning balance = $2,280.00

Interest for the year = $2,280.00 x 0.032 = $72.96

Ending balance = $2,280.00 + $72.96 - $300.00 = $2,052.96

Year 3:

Beginning balance = $2,052.96

Interest for the year = $2,052.96 x 0.032 = $65.76

Ending balance = $2,052.96 + $65.76 - $300.00 = $1,818.72

Year 4:

Beginning balance = $1,818.72

Interest for the year = $1,818.72 x 0.032 = $58.20

Ending balance = $1,818.72 + $58.20 - $300.00 = $1,576.92

Here's a table that shows the details:

Year ,principal ,Interest rate, interest, Payment ,annual owing

1 $2,500.00 $80.00 $300.00              $2,280.00

2 $2,280.00 $72.96 $300.00              $2,052.96

3 $2,052.96 $65.76 $300.00               $1,818.72

4 $1,818.72         $58.20  $300.00       $1,576.92

b. At the end of 4 years, Ross still owes his parents $1,576.92.

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Quadrilateral is a family of plane shapes that have four straight sides. Thus the sum of their internal angles is \(360^{o}\). Examples include rectangle, square, rhombus, trapezium, and kite.

A kite is a plane shape that has its adjacent sides to have equal measures.

The given diagram in the question is a kite that has its specific properties compared to other quadrilaterals.

Thus, the required proof is stated below:

Given: ΔCAV and ΔCEV

Prove that: ΔCAV ≅ ΔCEV

Then,

CE ≅ CA (length of side property of a kite)

EV ≅ AV (length of side property of a kite)

<ACV ≅ <ECV (bisected property of a given angle)

<AVC ≅ <EVC (bisected property of a given angle)

CV is a common side to ΔCAV and ΔCEV

Therefore it can be deduced that;

ΔCAV ≅ ΔCEV (Angle-Angle-Side congruent theorem)

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Answer:

a.1 1 2 3

2'4'5'10 that is ig

The proportional relationship is given by the equation y = 2.5x

An equation is an expression that shows the relationship between two or more numbers and variables using mathematical operations. An equation can be linear, quadratic, cubic and so on, depending on the degree of the variable.

Proportional relationships are relationships in which the ratio of their variable are equivalent.

It is given by:

y = kx; where k is the constant of proportionality

Let y represent the pound of garbage and x represent the number of seagulls.

4 seagulls are 10 pounds of garbage. Hence:

10 = 4k

k = 2.5

y = 2.5x

The relationship is given by y = 2.5x

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5 ÷ 1/2 => 5 x 2/1 => 10/1 => 10

Answer:

10

Step-by-step explanation:

In the pic, it shows ten half squares.  

The probability that each bill is a $1 bill is given as follows:

1/16.

A probability is calculated as the division of the desired number of outcomes by the total number of outcomes.

The bills are replaced, hence we consider that for each trial, there is a 1/4 probability of selecting a $1 bill, as one out of the four bills are of $1.

Hence the probability that each bill is a $1 bill is obtained as follows:

p = 1/4 x 1/4

p = 1/16.

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Because the graph only intercepts the x-axis only once, the equation has only one solution. The correct option is the second one.

Here we want to see, based on a graph, how many solutions does the cubic equation:

x³ + 6x² + 12x +8 = 0

The graph of the function:

g(x) = x³ + 6x² + 12x +8

Can be seen below, the number of real solutions that the equation:

x³ + 6x² + 12x +8 = 0

has, will depend on how many times the graph intercepts the x-axis.

We can see that there is only one intercept, so there is one real solution.

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Step-by-step explanation:

total number of students are :4x 3 = 12

Fraction that's boys are : 3÷12

9514 1404 393

Answer:

  15.9 m

Step-by-step explanation:

The radius (18 m) and the slant height form one leg and the hypotenuse of the right triangle that has the cone height as the other leg. The Pythagorean theorem tells you the height (h) is ...

  18² + h² = 24²

  h = √(576 -324) = √252

  h ≈ 15.9 . . . . . meters

The height of the cone is about 15.9 meters.

The expression |-4| has a value of 4 when evaluated

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

|-4|

The above expression is an absolute expression

So, the solution is the positive value of the expression in bracket

Evaluate the expressions in the brackets

So, we have the following representation

|-4| = 4

Hence, the expression has a value of 4

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Answer:

Triangle x = 30. Pentagon x = 50

Step-by-step explanation:

For the triangle,

Find the angle which is beside x in the triangle,

let's name that angle y, so 55 + 55 + y = 180 ( we find 55 by subtracting both angles 125 from 180)

110 + y = 180

Y = 180 - 110

y = 70

Now that we have find Y, we can easily find x by subtracting 70 from 180 which would be, 70 + X = 180

x = 180 - 70

x = 30

For the pentagon,

Again find the angle which is beside x in the pentagon,

let's name that y again, 90 + 120( by subtracting 60 from 180) + 110( by subtracting 70 from 180)  + 90 + y = 540

210 + 200 + y = 540

410 + y = 540

y = 540 - 410

y = 130

Now that we have find y, we can easily find x by subtracting 130 from 180 which would be, 130 + x = 180

x = 180 - 130

x = 50

Hope this helps!

Answer:

\( \frac{x {y}^{2} }{ - 8} \\ x = 7 \\ y = 1 \\ then \\ \frac{7 \times {1}^{2} }{ - 8} = \frac{7}{ - 8} = \frac{ - 7}{8} \\ thank \: you\)

Answer:

A. y = 600x, the jet travels 12,000 miles in 20 hours

Explanation:

\(\sf slope: \dfrac{y_2 - y_1}{x_2- x_1} \ \ where \ (x_1 , \ y_1), ( x_2 , \ y_2) \ are \ points\)

Take two points: (2, 1200), (4, 2400)

\(\sf slope : \dfrac{2400-1200}{4-2 } = 600\)

Equation:

y - 1200 = 600(x - 2)

y - 1200 = 600x - 1200

y = 600x

Miles the Jet travels at 20 hours:

Miles the Jet travels at 22 hours:

Answer:

y = 600x, the jet travels 12,000 miles in 20 hours

Step-by-step explanation:

Slope-intercept form of a linear equation:

\(y = mx + b\)

where:

To find the slope, define two points on the line and use the slope formula to find the slope:

\(\implies \textsf{slope}\:(m)=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{1200-0}{2-0}=600\)

From inspection of the graph, the y-intercept (where the line crosses the y-axis) is at (0, 0).  Therefore, the equation of the line is:

y = 600x

y is defined as the distance (in miles).  Therefore, to find the number of hours it takes for the jet to travel 12,000 miles, substitute y = 12000 into the found equation and solve for x:

\(\sf \implies 600x=12000\)

\(\sf \implies x=\dfrac{12000}{600}\)

\(\sf \implies x=\dfrac{120}{6}\)

\(\implies \sf x=20\)

Therefore, it takes the jet 20 hours to travel 12,000 miles.

The Distance will be  5.

The distance between two points is the length of the line segment connecting the two points on the plane. The formula for finding the distance between two points is usually d=√((x2 – x1)² + (y2 – y1)²). This formula is used to find the distance between any two points on the coordinate or x-y plane.

Let point (7,5) be A and point (4,9) be B

Distance formula =

Ab  = √(x1- x2) ² + (y1 -y2) ²

Then Distance AB will be

Ab  = √(7-4) ² + (5 -9) ²

= √ 3² + 4²

= √ 9 + 16

= 5

Hence the distance  will be 5.

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The points \((7,5)\)  \((4,9)\) are separated by a distance of \(5\) units.

The distance between the two points is given by the length of the segment between them.

The Distance Formula is a helpful tool for figuring out how far apart two points are when they are arbitrarily represented on a coordinate plane as points A\((x_{1},y_{1})\) and B\((x_{2},y_{2})\).

The Pythagorean Theorem is essentially the source of the Distance Formula. Calculating the right triangle's hypotenuse's length is the fundamental purpose of the distance formula.

Use the distance formula to get the distance between two places.

\(d = \sqrt{ (x_{2} - x_{1})^{2} +(y_{2} - y_{1})^{2} }\)

In the posted query,

\((x_{1},y_{1})=(7,5)\\\\(x_{2},y_{2})=(4,9)\)

Distance formula,

\(d = \sqrt{ (x_{2} - x_{1})^{2} +(y_{2} - y_{1})^{2} }\)

\(d = \sqrt{ (4-7)^{2} +(9-5)^{2} }\)

\(d = \sqrt{ (-3)^{2} +(4)^{2} }\)

\(d = \sqrt{ 9+16 }\)

\(d = \sqrt{ 25 }\)

\(d = 5\)

Therefore, the points \((7,5)\)  \((4,9)\) are at a distance of \(5\) units.

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Answer:

14

Step-by-step explanation: divide..

Answer:

14 points per game

Step-by-step explanation:

42/3 = 14

Answer:

Step-by-step explanation:

-32, -102, 38, -10, 35, 27, 0, -19​

Ascending:

-102, -32, -19​, -10, 0, 27, 35, 38

Descending:

38, 35, 27, 0, -10, -19, -32, -102

The range of the function is {1,-1,10} for function f(x)=2x³−3x .

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

In a function what can go into a function is called the Domain. What may possibly come out of a function is called the Codomain. What actually comes out of a function is called the Range.

The given function is f(x)=2x³−3x

The domain is {-1,1,2}

Now f(-1)=2(-1)³-3(-1)

=-2+3=1

f(1)=2(1)³-3(1)=2-3=-1

f(2)=2(2)³-3(2)=16-6=10

Hence, the range of the function is {1,-1,10} for  f(x)=2x³−3x .

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Answer:

8(x+3)

Step-by-step explanation:

thats the answer

Answer:

the expression is 8×(x+3)

Answer:

Will has b+83 buttons

Step-by-step explanation:

Roy -> 83 buttons

Will -> b more buttons than Roy

      -> b + 83

Answer:

will= b+83

Step-by-step explanation:

Roy has 83

will has b more than Roy

therefore, will= b+83

Answer:

4x² + 22x - 12

Step-by-step explanation:

A = bh/2

A = (4x - 2)(2x + 12)/2

A = (8x² + 48x - 4x - 24)/2

A = (8x² + 44x - 24)/2

A = 4x² + 22x - 12

Based on the information we can infer that the pool cover costs: $1568.25

To find the price of the pool cover we must take into account the pool area. In this case, being an irregular polygon, we must divide it into regular polygons to find its area.

According to the above, the pool area is 697 square meters. So the value of the cover would be:

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Answer:

Irving earned about $363.00 during the week.

Step-by-step explanation:

Irving’s time-and-a-half pay rate an hour =$485.54

The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.

Given:

Payment for one hour =  $8.95

So, paid for 40 hours

=40*$8.95

= $358.00

Now for -a-half overtime

=$8.95*1.5

= $13.425

Now, for extra 9.5 hours

=$13.425*9.5

=$127.5375

Hence,  Irving’s time-and-a-half pay rate an hour

=127.5375+358.00

=$485.54

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Answer:

Manual painter, expected waiting time = 0.085

Automatic painter expected waiting time = 0.031

Step-by-step explanation:

See attachment

Answer:

195 yd

Step-by-step explanation:

Break the shape into pieces:

-Triangle

-Rectangle

-Square

Then solve for each shape:

Triangle- 12·(6+4+7)= 204/2 =102

Rectangle- 3·19= 57

Square- 6·6= 36

Then add:

102+57+36= 195

Hope this helps! :)

Answer:

there are many answers. The simplest one is x=1 y=3

Step-by-step explanation:

Answer:

12.5 minutes

Step-by-step explanation:

52.5÷4.2=12.5 minutes

Answer:

12.5 minutes

Step-by-step explanation:

in a minute 4.2 liters of water come out and we have to find in how much time does 52.5 liters of water come out, since we have the value of water per minute we divide the amount of water by water per minute 52.5 divided by 4.2 equals 12.5, which gives us the answer. Hope this helps

Answer:

b. Normal data is never one of the inference assumptions.

Step-by-step explanation:

A categorical data specifies among two or more groups, which one each observation belongs to, and one or more explanatory variables that can be used to predict this membership.

So, there are two propositions in statistical inference for categorical data

1. That each data in a cell is independent of the others.

2. That samples are randomly drawn.

Thus, there is no room for normality.

       The equation representing the relationship between Electricity and  Gas used, and your Bill is:

      T  =  0.25 * k + 0.97 * t

        Make a plan:

We need to find the equation that represents the relationship between the total monthly bill (T), The Kilowatt Hours of Electricity used (k), and the Terms of Gas used (t).

T  =  0.25  *  k  +  0.97  *  t

1 - Write the Equation for the cost of Electricity:

        0.25 * k

2 - Write the Equation for the Cost of Gas:

       0.97 * t

3 - Combine the Equations to Represent the total Monthly Bill (T):

       T  =  0.25 * k + 0.97 * t

Hence,  The equation representing the relationship between Electricity and  Gas used, and your Bill is:

       T  =  0.25 * k + 0.97 * t

I hope that helps!

Using linear functions, it is found that 4 movies would cause the two plans to have an equal monthly cost.

A linear function is modeled by:

y = mx + b

In which:

For the functions in this problem, we have that:

Hence the cost functions are given as follows:

The costs will be the same when:

C1(x) = C2(x).

Hence:

22 + x = 14 + 3x

2x = 8

x = 4.

4 movies would cause the two plans to have an equal monthly cost.

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