Nolan bought 7 packs of
Starbursts, x. He had a
total of 98 individual
Starbursts, y Determine
the constant of
proportionality and write
a linear equation to
represent the
relationship

The total value of the loan with the quarterly compounded interest

is $117599.

Borrowers are required to pay interest on interest in addition to principal since compound interest accrues and is added to the accrued interest from prior periods.

We know the formula for compound interest is,

A = P(1 + r/100)ⁿ.

Where, A = amount, P = principle, r = rate, and n = time in years.

The formula for compound interest compounded quarterly is,

A = P(1 + (r/4)/100)⁴ⁿ.

\(A = 50000(1 + 6.15/100)^{4\times\frac{43}{12}}\).

\(A = 5000(1 + 0.0615)^{14.33}\).

\(A = 5000(1.0615)^{14.33}\).

\(A = 5000\times2.352\).

A = $117,599.

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The equation of line passes through the point (0, 7) will be;

⇒ y  = 1/2x + 7

What is Equation of line?

The equation of line in point-slope form passing through the points

(x₁ , y₁) and (x₂, y₂) with slope m is defined as;

⇒ y - y₁ = m (x - x₁)

Where, m = (y₂ - y₁) / (x₂ - x₁)

Given that;

The point on the line are (0, 7).

And, The perpendicular line is,

⇒ y = -1/2x + 5

Now,

Since, The equation of line passes through the point (0, 7).

So, We need to find the slope of the line.

Since, The product of slope of the perpendicular lines is - 1.

Hence, Slope of the perpendicular line is,

y = -1/2x + 5

m₁ = dy/dx = - 1/2

m₁ = - 1/2

So, The slope of the line,

m₂ = - (- 1/2)

    = 1 / 2

Thus, The equation of line with slope 1/2 is,

⇒ y - 7 = 1/2 (x - 0)

⇒ y - 7 = 1/2 x

⇒ y  = 1/2x + 7

Therefore, The equation of line passes through the point (0, 7) will be;

⇒ y  = 1/2x + 7

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Answer:

Step-by-step explanation:

Step 1: Add straight-time hourly wages for all hours worked and bonus to determine total straight-time compensation.

($12 hourly rate x 50 hours worked) + $100 bonus =  $700

Step 2: Divide total straight-time compensation by total hours worked to determine regular rate of pay.

$700 straight-time pay divided by 50 hours worked =  $14

Step 3: Multiply regular rate of pay by .5 and then multiply by total overtime hours.

$14 regular rate of pay x .5 x 10 overtime hours =  $70

Since the straight-time earnings have already been calculated for all hours worked (see Step 1), the employee is entitled to an additional 10 hours of overtime pay, calculated at one-half the regular rate of pay.

Step 4: Calculate total compensation.

$70 overtime pay + $700 straight-time pay =  $770

State Law: Your state law may require a different formula. California, for example, requires a different methodology for calculating overtime when an employee receives a flat sum bonus.

Note: If the nondiscretionary bonus is earned over a single workweek, as is the case above, the bonus is added to the employee's regular earnings for that workweek when determining the regular rate of pay. However, if the bonus is earned over a series of workweeks, the prorated bonus must be included in the regular rate of pay in all overtime weeks covered by the bonus period.

Example #3: Multiple Rates of Pay

A non-exempt employee works for the same employer in two different jobs. In one workweek, the employee works 10 hours for $10 per hour and 40 hours for $20 per hour. When there are two or more rates of pay, the regular rate for that workweek is the weighted average. To calculate overtime:

Step 1: Calculate total straight-time pay.

($10 hourly rate x 10 hours) + ($20 hourly rate X 40 hours) =  $900

Step 2: Divide total straight-time compensation by total hours worked to determine regular rate of pay.

$900 straight-time pay divided by 50 hours worked =  $18

Step 3: Calculate overtime premium pay.

$18 regular rate of pay x .5 x 10 overtime hours =  $90

Since the straight-time earnings have already been calculated (see Step 1), the additional amount to be calculated is one-half the regular rate of pay.

Step 4: Calculate total compensation for week.

$900 straight-time pay + $90 overtime pay =  $990

Answer: The correct question is "Segments AB and BC are both tangent to the circle shown above. What is the value of x"

The value of x is also 5 units , by tangent rule.

Step-by-step explanation:

The Two Tangent Theorem:

The two tangent theorem states that if we draw two lines from the same point which lies outside a circle, such that both lines are tangent to the circle, then their lengths are the same.

We will now prove that theorem.

Problem

AB and AC are tangent to circle O. Show that AB=AC

Proof of the Two Tangent Theorem

(1) AB is tangent to Circle O     //Given

(2) ∠ABO=90°                          //tangent line is perpendicular to circle

(3) AC is tangent to Circle O     //Given

(4) ∠ACO=90°                          //tangent line  is perpendicular to circle

(5) AO=AO                              //common side (reflexive property)

(6) OC=OB=r                           //radii of a circle are all equal

(7) △ABO≅△ACO                 //Hypotenuse-leg  

(8) AB=AC                 // Corresponding sides in congruent triangles (CPCTC)

Therefore,  segment AB = BC = 5 units

Answer:

Value of x is 5

Step-by-step explanation:

Have a great day

After subtracting the given two distances, It can be obtained that the mall is five and a half kilometers further than the grocery store from the house.

If there are three points \(A, B, C\) and the distance between \(A\) and \(B\) is \(d_1\)  and the distance between \(A\) and \(C\) is \(d_2\). Also, \(d_2 > d_1\). Then the distance between \(B\) and \(C\) can be obtained by subtraction \(d=d_2-d_1\).

Given that the distance from the house to the grocery store is five and one-quarter kilometers i.e., \(d_1=5.25\) km and the distance from the house to the mall is ten and three-quarter kilometers i.e., \(d_2=10.75\) km.

So, the distance from the grocery store to the mall is \(d=d_2-d_1=10.75-5.25=5.5\) km.

Therefore, after subtracting the given two distances, we can conclude that the mall is five and a half kilometers further than the grocery store from the house.

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The given code is in c++ .

#include<iostream>

using namespace std;

int main( ){

     int s ;

     cout<< "Enter sound in decibel "<<endl;

     cin>> s;

     if( s > 40 ){

           cout<< "Too loud "<<endl;

     }

     else{

           cout<< "Correct Volume"<<endl;

     }

     return 0;

}

//Hence, this is the required solution.

The sets A and B are not equal, but they are equivalent.

We have,

The concept used is set notation and comparison.

a)

The sets A and B are equivalent because they contain the same elements, which are real numbers (x) that satisfy the given conditions.

b)

Sets A and B are not equal because the condition in Set A includes endpoints 97 and 102, while the condition in Set B excludes endpoints 96 and 103.

Therefore, the sets have different boundaries and elements.

Thus,

The sets A and B are not equal, but they are equivalent.

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The amount of your tax refund is $1,414

To find the tax refund, we need to subtract the amount of federal taxes owed after deductions from the amount of federal taxes already paid.

Tax refund = Federal taxes paid - Federal taxes owed after deductions

Tax refund = $12,042 - $10,628

Tax refund = $1,414

Rounding to the nearest cent, the tax refund is $1,414.00.

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Answer:

40 students are in the class :)

Step-by-step explanation:

35%=14

1%=14/35=0.4

0.4*100=40=100%

Requirement [a] CORRECT

Requirement Year 1 Year 2

Total Liabilities $15,650 $20,880

Total Stockholder's Equity $31,300 $29,000

Ratio (Liabilities/Equity) 0.50 0.72

Additional information:

The ratio of liabilities to stockholders' equity increased from 0.50 in Year 1 to 0.72 in Year 2.

This indicates an increase in risk for creditors from Year 1 to Year 2.

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Answer:

b) 28

c) 52

Step-by-step explanation:

f(2) = -2³ + 7(2)² - 2(2) + 12

= -8 + 28 - 4 + 12

= 28

f(-2) = -(-2)³ + 7(-2)² - 2(-2) + 12

= 8 + 28 + 4 + 12

= 52

9514 1404 393

Answer:

  60°

Step-by-step explanation:

The sum of angles in a quadrilateral is 360°. The interior angle adjacent to x will have measure 180°-x. So, the equation can be written ...

  100° +50° +90° +(180° -x°) = 360°

  420° -x° = 360° . . . . simplify

  x = 420 -360 . . . . . . divide by °, add x-360

  x = 60

Answer:

7/6=2/7/6

7/6=2

7/6=27/6

7/6=2

7/6

The matrix formed by performing the row operation 4R₁ + R₂ — R₂ on M will have R₁ = [1 0 3] and R₂ = [ -1 2 10]

Row operations are a set of operations that can be performed on the rows of a matrix in order to transform it into a row equivalent matrix, which has the same solution set as the original matrix.

performing the row operation 4R₁ + R₂ — R₂ on M, we have;

4(1) + (-5) = -1 {row 2 column 1}

4(0) + 2 = 2 {row 2 column 2}

4(3) + (-2) = 10 {row 2 column 3}

Therefore, the matrix formed by performing the row operation 4R₁ + R₂ — R₂ on M will have R₁ = [1 0 3] and R₂ = [ -1 2 10]

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The mean from a Histogram, table, and dot plot, it is not possible to determine the mean directly from a stem-and-leaf plot.

Out of the given options, the display of data for which it is not possible to find the mean is the stem-and-leaf plot.

A histogram displays data in the form of bars, where the height of each bar represents the frequency of data within a specific range. From a histogram, it is possible to calculate the mean by summing up the products of each value with its corresponding frequency and dividing it by the total number of data points.

A table presents data in a structured format, typically with rows and columns, allowing for easy calculation of the mean. By adding up all the values and dividing by the total number of values, the mean can be obtained from a table.

A stem-and-leaf plot organizes data by splitting each value into a stem (the first digit or digits) and a leaf (the last digit). While a stem-and-leaf plot provides a visual representation of the data, it does not directly provide the frequency or count of each value. Hence, it is not possible to determine the mean directly from a stem-and-leaf plot without additional information.

A dot plot represents data using dots along a number line, with each dot representing an occurrence of a value. Similar to a histogram and table, a dot plot allows for the calculation of the mean by summing up the values and dividing by the total number of data points.

In summary, while it is possible to find the mean from a histogram, table, and dot plot, it is not possible to determine the mean directly from a stem-and-leaf plot.

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Answer:

3:25

Step-by-step explanation:

The photo shows how it's solved.

Answer: 3:25

Step-by-step explanation:

Step 1) Convert the decimal number to a fraction by making 0.12 the numerator and 1 the denominator

0.12 = 0.12/1

Step 2) Multiply the numerator and denominator by 100 to eliminate the decimal point.
0.12 x 100

------------ = 12/100
1 x 100

Step 3) Simplify the fraction in the previous step by dividing the numerator and the denominator by the greatest common factor (GCF) of 12 and 100. (The GCF of 12 and 100 is 4.)

12 ÷ 4

---------  = 3/25  

100 ÷ 4

Step 4) Convert the fraction in the previous step to a ratio by replacing the divider line with a colon like this:  

3  

25   =  3:25

Answer:

Yes its a function!!

Answer:

Yes

Step-by-step explanation:

y = -3x² + 10

10 - y = 3x²

as you see in the picture below

there are unique values of y for every value of x

so it is a function

Answer:

about 2.666 times

Step-by-step explanation:

you know that 80 days have past and it only takes 30 days for the population to double. if you do 80/30 you get 2.666 meaning that the population would of been 2.666 times greater.

The population be than after 30 days about 2.666 times greater.

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

Given; A population of insects can double in 30 days.

After 80 days, We need to find that how many times greater will the population be than after 30 days

We know that 80 days have past and it only takes 30 days for the population to double.

if we do 80/30 = 2.666 meaning that the population would of been 2.666 times greater.

Therefore, The population be than after 30 days about 2.666 times greater.

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Answer:

To calculate 2 3/4 of 500 grams, follow these steps:

1. Convert the mixed number to an improper fraction:

2 3/4 = (2 x 4 + 3)/4 = 11/4

2. Multiply the improper fraction by 500:

11/4 x 500 = (11 x 500)/4 = 2,750/4

3. Simplify the fraction by dividing the numerator and denominator by their greatest common factor, which is 2:

2,750/4 = (2 x 1,375)/(2 x 2) = 1,375/2

Therefore, 2 3/4 of 500 grams is equal to 1,375/2 grams or 687.5 grams.

Step-by-step explanation:

a. Length of GK = \(\sqrt{34}\)  and Length of adjacent to GK = \(\sqrt{34}\)

b. Slope of GK = \(\frac{5}{3}\) and Slope of adjacent to RS =  \(-\frac{3}{5}\)

c. The parallelogram GHJK is Square.

A quadrilateral with two sets of parallel sides is referred to as a parallelogram. As a result, a parallelogram's opposite sides are parallel and congruent in length, and its opposite angles are similarly congruent.

Given in figure GHJK, the vertices are G(-3, 6), H(2, 3), J(-1, -2), K(-6, 1)

a. Length of line = \(\sqrt{({x_{2}-x_{1})^{2} } + ({y_{2}-y_{1})^{2}}\)

for points G(-3, 6) and K(-6, 1)

Length of GK = \(\sqrt{(-6+3)^{2} + (1-6)^{2} }\) = \(\sqrt{34}\)

Length of GK = \(\sqrt{34}\)

Length of adjacent side (GH, KJ) to GK =  \(\sqrt{(2+3)^{2} + (3-6)^{2} }\) = \(\sqrt{34}\)

Length of adjacent to GK = \(\sqrt{34}\)

b. \(Slope = \frac{(y_{2} -y_{1})}{(x_{2} -x_{1})}\)

Slope of GK = \(\frac{(1 - 6)}{(-6 + 3)}\) = \(\frac{5}{3}\)

Slope of GK = \(\frac{5}{3}\)

Slope of adjacent side to GK = \(\frac{3-6}{2+3}\) = \(-\frac{3}{5}\)

Slope of adjacent to RS =  \(-\frac{3}{5}\)

c. All sides are equals to \(\sqrt{34}\)

So, length of diagonal GJ = \(\sqrt{({-3+1))^{2} } + ({6+2})^{2}} = \sqrt{68}\)

and length of diagonal HK = \(\sqrt{({2+6))^{2} } + ({3-1})^{2}} = \sqrt{68}\)

All sides and diagonals are equal then parallelogram GHJK is Square.

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The temperature at the bottom of the mountain is 50.9 °C.

Let's work through the given information step by step to find the temperature at the bottom of the mountain.

The temperature in the hotel is 21 °C.

The temperature in the hotel is 26.7 °C warmer than at the top of the mountain.

Let's denote the temperature at the top of the mountain as T_top.

So, the temperature in the hotel can be expressed as T_top + 26.7 °C.

The temperature at the top of the mountain is 3.2 °C colder than at the bottom of the mountain.

Let's denote the temperature at the bottom of the mountain as T_bottom.

So, the temperature at the top of the mountain can be expressed as T_bottom - 3.2 °C.

Now, let's combine the information we have:

T_top + 26.7 °C = T_bottom - 3.2 °C

To find the temperature at the bottom of the mountain (T_bottom), we need to isolate it on one side of the equation. Let's do the calculations:

T_bottom = T_top + 26.7 °C + 3.2 °C

T_bottom = T_top + 29.9 °C

Since we know that the temperature in the hotel is 21 °C, we can substitute T_top with 21 °C:

T_bottom = 21 °C + 29.9 °C

T_bottom = 50.9 °C

Therefore, the temperature at the bottom of the mountain is 50.9 °C.

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To solve the savings plan balance, we have to calculate the interest for 19 months. The formula for calculating interest for compound interest is given below:$$A = P \left(1 + \frac{r}{n} \right)^{nt}$$where A is the amount, P is the principal, r is the rate of interest, t is the time period and n is the number of times interest compounded in a year.

The given interest rate is 11% per annum, which will be converted into monthly rate and then used in the above formula. Therefore, the monthly rate is $r = \frac{11\%}{12} = 0.0091667$.

The monthly payment is $PMT = $250. We need to find out the amount after 19 months. Therefore, we will use the formula of annuity.

$$A = PMT \frac{(1+r)^t - 1}{r}$$where t is the number of months of the plan and PMT is the monthly payment. Putting all the values in the above equation, we get:

$$A = 250 \times \frac{(1 + 0.0091667)^{19} - 1}{0.0091667}$$$$\Rightarrow

A = 250 \times \frac{1.0091667^{19} - 1}{0.0091667}$$$$\Rightarrow

A =250 \times 14.398$$$$\Rightarrow A = 3599.99$$

Therefore, the savings plan balance after 19 months with an APR of 11% and monthly payments of $250 is $3599.99 (approx).

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Step-by-step explanation:

75 = 3 x 5 x 5    in prime factorization

Answer:

Step-by-step explanation:

3x5x5

Answer:

x to the 3rd power

Step-by-step explanation:

x+x to the 2nd power = x to the 3rd power

Step-by-step explanation:

The area is the sum of three figures

A = 1*1 + 1*x + x²

   = x² + x + 1

The perimeter is the sum of border segments

P = x*4 + 1*4

  = 4x + 4

The most general solution to the associated homogeneous differential equation is y=x/2-1/4

C=0

dy/dx+2y=x

Use the formula:

\(\int\ \,xe^(2x)dx=e^(2x)\)((x/2−1/4).

We know that a linear differential equation is written in the standard form:

y' + a(x)y = f(x)

we get that: a(x)=2 and f(x)=x.

We know that the integrating factor is defined by the formula:

u(x)=\(e^{\int\ \, a(x) dx}\)

⇒ u(x)=\(e^{∫ 2 dx}\)= \(e^{2x}\)

The general solution of the differential equation is in the form:

y=\frac{ ∫ u(x) f(x) dx +C}{u(x)}

⇒ y=\frac{\(e^{2x}\)· x dx  + 0}\({e^{2x}}\)

y=\frac{\(e^{2x}\) (x/2-1/4)\(}{e^{2x}\)

y=x/2-1/4

Hence, the most general solution to the associated homogeneous differential equation is y=x/2-1/4.

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The ratio of the length of a tile in the model to the length of an actual tile is 1/8.

The ratio of the area of a tile in the model to the area of an actual tile is 1/64.

From the information, it should be noted that in the model, each tile has length 1/3in and width 1/4 in and the actual tiles have length 1/4 ft and width 3/16ft .

The ratio of the length of a tile in the model to the length of an actual tile will be:

= 1/4 ÷ 2

= 1/4 × 1/2

= 1/8

The ratio of the area of a tile in the model to the area of an actual tile is (1/4 × 1/6) / (2 × 4/3)

= 1/64

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Step-by-step explanation:

Since is it parallel to the given line, we can directly take the slope from the given equation.

m = -2 according to the given equation.

Next, use the point (-4,-5) to write the point-slope form first.

y-(-5) = -2(x-(-4))

Then use basic algebra to put it into slope-intercept form, which is y = mx + b.

y + 5 = -2x - 8

y = -2x - 13

Answer:

The \(66\)th term is \(363\).

Step-by-step explanation:

To find the \(n\)th term, the formula is \(7n - 99\). Since we want to find the \(66\)th term, we can plug \(n\) for \(66\). So our expression is now \(7 \cdot 66 - 99 =\) \(66\)th term. Solving this we have

\(462 - 99 = 66\text{th term}\\363 = 66\text{th term}\\\). Therefore, the \(66\)th term is \(\boxed{363}\).

Answer:

a₆₆ = 363

Step-by-step explanation:

the nth term of an arithmetic sequence is

\(a_{n}\) = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

here a₁ = - 92 and d = a₂ - a₁ = - 85 - (- 92) = - 85 + 92 = 7 , then

a₆₆ = - 92 + (65 × 7)

      = - 92 + 455

     = 363

Answer:

I want to stand on my own three feet

Step-by-step explanation:

The GCD of 5! and 7! is 2^3 * 3^1 * 5^1 = 120.

the greatest common divisor of 5! and 7! is 120.

To find the greatest common divisor (GCD) of 5! and 7!, we need to factorize both numbers and identify the common factors.

First, let's calculate the values of 5! and 7!:

5! = 5 * 4 * 3 * 2 * 1 = 120

7! = 7 * 6 * 5 * 4 * 3 * 2 * 1 = 5,040

Now, let's factorize both numbers:

Factorizing 120:

120 = 2^3 * 3 * 5

Factorizing 5,040:

5,040 = 2^4 * 3^2 * 5 * 7

To find the GCD, we need to consider the common factors raised to the lowest power. In this case, the common factors are 2, 3, and 5. The lowest power for 2 is 3 (from 120), the lowest power for 3 is 1 (from 120), and the lowest power for 5 is 1 (from both numbers).

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