Paolo purchased a shirt at store A. He paid $19.50 for the shirt. Raoul purchased the same shirt at store B for $22.35.

How much money did Paolo save by purchasing the shirt at store A instead of at store B?

The solution to the equation of the polynomial function x³-5x+5 = 2x²-5  is (c) –2.24, 2, 2.24.

A polynomial is an expression consisting of indeterminates and coefficients, that involves only the operations of addition, subtraction, multiplication, and non-negative integer exponentiation of variables.

Here, The function is given as:

         x³-5x+5 = 2x²-5

Split the function.

So, we have:

   y = x³-5x+5

   y = 2x²-5

Using a graphing calculator, we have the x coordinate at the point o intersection of both equations to be

x = –2.24, 2, 2.24

Hence, the solution to the equation is (c) –2.24, 2, 2.24

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Answer:

We can write the equation of a line parallel to a given line if we know a point on the line and an equation of the given line. y=2x+3 . Parallel lines have the same slope. The slope of the line with equation y=2x+3 is 2 .

Step-by-step explanation:

There are 9,999 natural numbers that have no more than 4 digits.

To determine the number of natural numbers that have no more than 4 digits, we consider the range of numbers from 1 to 9,999.

The natural numbers with no more than 4 digits include all numbers from 1 to 9 (which form the single-digit numbers), all numbers from 10 to 99 (which form the two-digit numbers), all numbers from 100 to 999 (which form the three-digit numbers), and all numbers from 1,000 to 9,999 (which form the four-digit numbers).

To calculate the total count, we can add the number of single-digit numbers, two-digit numbers, three-digit numbers, and four-digit numbers:

Single-digit numbers: 9 (from 1 to 9)

Two-digit numbers: 90 (from 10 to 99)

Three-digit numbers: 900 (from 100 to 999)

Four-digit numbers: 9,000 (from 1,000 to 9,999)

Adding these counts together:

9 + 90 + 900 + 9,000 = 9,999

Therefore, there are 9,999 natural numbers that have no more than 4 digits.

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Considering the information about trees, The value of a is 5500

The value of r is calculated to be 0.92

In 1 October 2030 the number is 2022

A mathematical function called an exponential function is employed frequently in everyday life. It is mostly used to compute investments, model populations, determine exponential decay or exponential growth, and so on.

Exponential function is a type of function of the form: f(x) = a(b)^x. It is made up of  3 main parts

a = the starting or initial value

b = the base function

x = the exponents

Considering the given problem,  N = ar^t

the starting, a = 5500

the base, r =

the exponents = t

Solving for the base

N = ar^t

5500 = ar^t in 2018 t = 0

a = 5500

in 2019, t = 1

N = ar^t

5060 = 5500 * r

r = 5060/5500

r = 0.92

From 2018 to 2030 = 12 years, hence t = 12

N = 5500 * 0.92^12

N = 2,022.165132

N = 2022

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A graph representation of the problem is shown in the image attached. The graph shows the seven seniors and the open positions posted by the university.

Each node in the graph represents a senior or a position. An edge connects a senior and a position if the senior has applied for that position. For instance, B has applied for positions c and e, so there are edges between node B and nodes c and e.

Similarly, there are edges between each senior and the positions they have applied for. The graph is bipartite since there are two sets of nodes, seniors and positions, and all edges connect a senior to a position (and vice versa). It is not possible to hire all seven students for the position they like since there are only four reporter positions available, but three students (F, J, and L) have applied for the reporter position. Therefore, at least one of these students will not be able to get the position they like.

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Answer: A) 6

Step-by-step explanation:

The ratio can be found by looking at the last column. If there are 60 pies and 70 items total, then the amount of pies would be 10.

This would make the ratio 6:1, or 6 pies for every 1 cake.

This can be confirmed by looking at the second column. If you treat the numbers like a fraction 42/7, you would once again get 6/1, as 42 divided by 7 is 6.

The new cost of the fertilizer after applying the coupon is $20.39 (excluding sales tax).

Part A:

To determine which fertilizer would be cheaper for Daija to purchase, we need to calculate the cost per square foot for each fertilizer.

Super Lawn fertilizer costs $18.49 and covers 6,000 square feet. Cost per square foot for Super Lawn fertilizer = $18.49 / 6,000 = $0.00308 per square foot.

Quick Fertilizer costs $23.99 and covers 8,000 square feet. Cost per square foot for Quick Fertilizer = $23.99 / 8,000 = $0.00299 per square foot.

Comparing the cost per square foot, we can see that Quick Fertilizer is cheaper. Therefore, Daija should purchase Quick Fertilizer to fertilize her entire lawn.

Part B:

Daija has a 15% off coupon on the cheaper fertilizer, which is Quick Fertilizer. To calculate the new cost of the fertilizer after applying the coupon, we need to subtract 15% of the original cost from the original cost.

Original cost of Quick Fertilizer = $23.99

15% of $23.99 = $23.99 * 0.15 = $3.599

New cost of Quick Fertilizer = $23.99 - $3.599 = $20.391

Rounded to the nearest cent, the new cost of the fertilizer after applying the coupon is $20.39 (excluding sales tax).

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Answer:

(0.7465 , 0.8429 )

Step-by-step explanation:

Confidence Level - "P" values  

90% 1.645

Confidence Interval - "P" values  

(0.7465 , 0.8429 )  

Answer:

-5 turns into 5 and the y is probably 1, so 5+9 is equal to 14.

Step-by-step explanation:

The relation R is symmetric and antisymmetric, but not reflexive or transitive.

Let's examine each property of the relation R separately:

Reflexive: A relation R is reflexive if every element in the set is related to itself. In this case, we have (x, x-1) or (x-1, x) for any integer x. Therefore, the relation is not reflexive since x is not related to itself.

Symmetric: A relation R is symmetric if for any pair of elements x and y in the set, (x,y) being in R implies that (y,x) is also in R. In this case, we have (x, y-1) or (y, x-1) for any integers x and y. It is clear that if (x, y-1) is in R, then (y, x-1) is also in R, and vice versa. Therefore, the relation is symmetric.

Antisymmetric: A relation R is antisymmetric if for any distinct elements x and y in the set, if (x,y) is in R, then (y,x) cannot also be in R. In this case, if we have (x, y-1) and (y, x-1), then x = y-1 and y = x-1. This implies that x = y, which contradicts our assumption that x and y are distinct. Therefore, the relation is antisymmetric.

Transitive: A relation R is transitive if for any elements x, y, and z in the set, if (x,y) and (y,z) are in R, then (x,z) is also in R. In this case, we have (x, y-1) and (y, z-1) for any integers x, y, and z. If we add these two relations, we get (x, z-2).

However, this does not satisfy the original relation, which requires that (x, z-1) be in R. Therefore, the relation is not transitive.

In summary, the relation R is symmetric and antisymmetric, but not reflexive or transitive.

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Answer:

Step-by-step explanation:

\(s = \frac{1}{2} (u + v)t \\ s = \frac{1}{2} (6 + 20)5 \\ s = \frac{1}{2} \times 26 \times 5 \\ s = 13 \times 5 \\ s = 65 \\ \)

Answer:

The polls were open for 9 hours on election day.

Step-by-step explanation:

10167 - 6504 = 3663

3663 / 407 = 9

The results obtained using the algebraic approach and the matrix approach should be the same. Both methods are mathematically equivalent and provide the most probable values of A and B that minimize the sum of squared weighted residuals.

To solve the system of equations using the weighted least squares method, we need to minimize the sum of the squared weighted residuals. Let's solve the problem using both the algebraic approach and matrices.

Algebraic Approach:

We have the following equations:

A + 2B = 10.50 + V1 ... (1)

2A - 3B = 5.55 + V2 ... (2)

2A - B = -10.50 + V3 ... (3)

To minimize the sum of squared weighted residuals, we square each equation and multiply them by their respective weights:

\(2^2 * (A + 2B - 10.50 - V1)^2\)

\(3^2 * (2A - 3B - 5.55 - V2)^2\\1^2 * (2A - B + 10.50 + V3)^2\)

Expanding and simplifying these equations, we get:

\(4(A^2 + 4B^2 + 10.50^2 + V1^2 + 2AB - 21A - 42B + 21V1)\\9(4A^2 + 9B^2 + 5.55^2 + V2^2 + 12AB - 33A + 16.65B - 11.1V2)\\(A^2 + B^2 + 10.50^2 + V3^2 + 2AB + 21A - 21B + 21V3)\\\)

Now, let's sum up these equations:

\(4(A^2 + 4B^2 + 10.50^2 + V1^2 + 2AB - 21A - 42B + 21V1) +\\9(4A^2 + 9B^2 + 5.55^2 + V2^2 + 12AB - 33A + 16.65B - 11.1V2) +\\(A^2 + B^2 + 10.50^2 + V3^2 + 2AB + 21A - 21B + 21V3)\int\limits^a_b {x} \, dx\)

Simplifying further, we obtain:

\(14A^2 + 31B^2 + 1113 + 14V1^2 + 33V2^2 + 14V3^2 + 14AB - 231A - 246B + 21V1 - 11.1V2 + 21V3 = 0\)

Now, we have a single equation with two unknowns, A and B. We can use various methods, such as substitution or elimination, to solve for A and B. Once the values of A and B are determined, we can substitute them back into the original equations to find the most probable values of A and B.

Matrix Approach:

We can rewrite the system of equations in matrix form as follows:

| 1 2 | | A | | 10.50 + V1 |

| 2 -3 | | B | = | 5.55 + V2 |

| 2 -1 | | -10.50 + V3 |

Let's denote the coefficient matrix as X, the variable matrix as Y, and the constant matrix as Z. Then the equation becomes:

X * Y = Z

To solve for Y, we can multiply both sides of the equation by the inverse of X:

X^(-1) * (X * Y) = X^(-1) * Z

Y = X^(-1) * Z

By calculating the inverse of X and multiplying it by Z, we can find the values of A and B.

Comparing Results:

The results obtained using the algebraic approach and the matrix approach should be the same. Both methods are mathematically equivalent and provide the most probable values of A and B that minimize the sum of squared weighted residuals.

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Answer:b

Step-by-step explanation:

just took the quiz

Given:

After 4 minutes of reading, Aaron was on page 14 of his book.

After 8 minutes he was on page 20.

To find:

The equation that models the page number, y in terms of minutes x.

Step-by-step explanation:

Let  y be the page number after x minutes of reading.

After 4 minutes of reading, Aaron was on page 14 of his book. So, the line must be passes through (4,14).

After 8 minutes he was on page 20. So, the line must be passes through (8,20).

The equation of line which passes through two points is

\(y-y_1=\dfrac{y_2-y_1}{x_2-x_1}(x-x_1)\)

The required line passes through (4,14) and (8,20), so the equation is

\(y-14=\dfrac{20-14}{8-4}(x-4)\)

\(y-14=\dfrac{6}{4}(x-4)\)

\(y-14=1.5(x-4)\)

\(y-14=1.5x-6\)

Add 14 on both sides.

\(y-14+14=1.5x-6+14\)

\(y=1.5x+8\)

Therefore, the correct option is B.

The value of b is 3.

The value of c is 1/8.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

Example:

2x + 5 = 9 is an equation.

We have,

Two equations given are:

b = 24c ____(1)

(1/4)b + 4c = 5/4 _____(2)

Putting (1) in (2) we get,

(1/4)24c + 4c = 5/4

6c + 4c = 5/4

10c = 5/4

c = 5/40

c = 1/8

Putting c = 1/8 in (1) we get,

b = 24/8

b = 3

Thus,

b = 3.

c = 1/8.

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Step-by-step explanation:

x + y = 18 We have at least 4 quarters

0.25x + 0.1y = 3.6

If we graph both equations, the point of intersection will give us our answer.

In this case, the lines intersect at the point (12, 6) which means I have 12 quarters and 6 dimes. This solution is correct as it also satisfies the condition of having at least 4 quarters.

(got this from another website, maybe it's wrong..

Wishing you the best!! )

If the quadrilateral is a trapezoid , then the value of x is = (b) 5 .

We know that the Midsegment of a trapezoid is parallel to each of the base and it's length is one half the sum of the lengths of the bases.

From the figure , we can observe that ⇒ side lengths are  21 units, 27 units , and the sides are parallel to each other.

From the given diagram of the trapezoid , the below expression is true:

that means : ⇒ 5x-1 = (21 + 27)/2  ;

⇒ 2(5x - 1) = 21 + 27 ;

⇒ 10x = 48 + 2 ;

⇒ 10x = 50

On Divide both sides by 10 ;

we have ;

⇒ x = 50/10  ;

⇒ x = 5  .

Therefore , for the quadrilateral the value of x is = 5 .

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The given question is incomplete , the complete question is

The quadrilateral in the below figure is a trapezoid. What is the value of x ?

(a) 4

(b) 5

(c) 48

(d) 25

Answer:

12%

Step-by-step explanation:

Read a book = 16%

Listen to music = 28%

We can read the question in different ways:

1.  The simple difference between the two is 12%

2.  Out of the sample, the two groups include:

    15 chose books

    35 chose music

    Within this sample of 50 teenagers,

           (15/50) or 30% chose books, and

            (35/50) or 70% chose music

             That makes a difference of 40%

I would chose the first interpretation, 12%  [Especially since 40% is not an option.]

Answer:

Solution given:

A triangle PQR is right angled at R, with hypotenuse{h}PQ=80cm

and

base[b]PR=60cm.

perpendicular [P]= QR

by using Pythagoras law

h²=p²+b²

80²=QR²+60²

QR²=80²-60²

QR=\(\sqrt{2800}\)

QR=20\(\sqrt{7}\)=52.9=53cm

QR=53cm.

The equation that shows the total response of the system under the initial conditions of xo = 0.1 m and to 10 m/s is:

x(t) = (-1/5) * cos(30t) + 0.1 * cos(20t) + 0.5 * sin(20t).

The equation that describes the motion of the system is given by:

m * x''(t) + k * x(t) = F(t),

where:

m is the mass

x(t) is the displacement of the mass from the equilibrium position

x''(t) is the second derivative of x(t) with respect to time

k is the spring constant

F(t) is the external force.

Given that k = 4000 N/m, m = 10 kg, and F(t) = 400 cos(30t) N, we can substitute these values into the differential equation:

10 * x''(t) + 4000 * x(t) = 400 cos(30t).

Using the method of undetermined coefficients, we assume the solution has the form:

x(t) = A * cos(30t) + B * sin(30t) + C

where A, B, and C are constants to be determined.

Taking the derivatives, we have:

x''(t) = -900 A * cos(30t) - 900 B * sin(30t),

Substituting these into the differential equation, we get:

-9000 A * cos(30t) - 9000 B * sin(30t) + 4000 (A * cos(30t) + B * sin(30t) + C) = 400 cos(30t).

Equating the coefficients of cos(30t), sin(30t), and the constant terms separately, we get the following equations:

-9000 A + 4000 A = 400,

-9000 B + 4000 B = 0,

4000 C = 0.

Solving these equations, we find A = -1/5, B = 0, and C = 0.

Thus, the particular solution to the differential equation is:

x_p(t) = (-1/5) * cos(30t).

Now, we need to find the general solution to the homogeneous equation:

10 * x''(t) + 4000 * x(t) = 0.

The characteristic equation is:

10 * r² + 4000 = 0,

r² = -400,

which has complex roots r₁ = 20i and r₂ = -20i.

The general solution to the homogeneous equation is:

x_h(t) = A * cos(20t) + B * sin(20t),

where A and B are constants to be determined.

To find the values of A and B, we apply the initial conditions:

x(0) = x₀ = 0.1 m,

x'(0) = v₀ = 10 m/s.

Substituting t = 0 into the general solution and its derivative, we get:

x_h(0) = A = x₀ = 0.1,

x_h'(0) = 20B = v₀ = 10,

B = 0.5.

Therefore, the general solution to the differential equation is:

x_h(t) = 0.1 * cos(20t) + 0.5 * sin(20t).

Finally, the total response of the system is the sum of the particular and homogeneous solutions:

x(t) = x_p(t) + x_h(t),

x(t) = (-1/5) * cos(30t) + 0.1 * cos(20t) + 0.5 * sin(20t).

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ANSWER

Solutions: x = -6, x = 2i, and x = -2i

EXPLANATION

To solve this equation, first, we have to raise both sides of the equation to the exponent 3,

Now, we have to expand the binomial cubed using the cube of a binomial rule,

So we have,

So the equation is,

Subtract 8x from both sides of the equation, and also add 16 to both sides,

So, we have to find the zeros of this equation.

First, assuming at least one root is an integer, write the possible values. Since the constant is 24, the possible roots are factors of 24:

Now, let's test these values in the equation,

*Note: I have not tested all the possible values in this answer to make the explanation shorter.

Now, we know that x = -6 is a zero, so (x + 6) is a factor. To find the quadratic factor, we can divide the 3rd-degree polynomial by the factor (x + 6):

The zeros of the resulting factor are not real,

Hence, the solutions of this equation are x = -6, x = 2i, and x = -2i.

Answer:

\(x=-\frac{41}{6}\)

Step-by-step explanation:

Pay attention to the two tick marks. This indicates that those sides are congruent to each other and so will the angles on the bottom and top. Therefore, we can set up the equation \(137+2(-3x+1)=180\) and solve for x:

\(137+2(-3x+1)=180\)

\(137+(-6x+2)=180\)

\(137-6x+2=180\)

\(139-6x=180\)

\(-6x=41\)

\(x=-\frac{41}{6}\)

Juliet was charged $18 for driving 120 miles.

Given,

The rent of car per day = $80

The charge for per miles driven = $0.15

Juliet was charged a total of $98 for the rental and mileage.

We have to find the total miles of driving;

Here,

Charge for miles driven = Total charge - Rent of car for a day

Charge for miles driven = 98 - 80

Charge for miles driven = $18

Now,

Total miles driven = Charge for miles driven / Charge for one mile

Total miles driven = 18/0.15

Total miles driven = 120

That is,

Juliet was charged $18 for 120 miles of driving.

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The problem involves setting up an amortization schedule for a $19,000 loan to be repaid in equal installments at the end of each of the next 3 years.

The interest rate is 8% compounded annually. The task is to determine the percentage of the payment that represents interest and principal for each year and explain why these percentages change over time.

To set up an amortization schedule, we need to calculate the equal installment payment for each year. The loan amount of $19,000 is divided by 3 years to determine the annual payment. In this case, the annual payment would be $6,333.33.

In the first year, the interest portion of the payment is calculated based on the outstanding loan balance, which is $19,000. The interest is 8% of $19,000, which is $1,520. The principal portion of the payment is the difference between the annual payment and the interest, which is $6,333.33 - $1,520 = $4,813.33.

For the second year, the interest portion is calculated based on the remaining loan balance after the first year's payment. The interest is 8% of the remaining balance, which is $19,000 - $4,813.33 = $14,186.67. The principal portion is the difference between the annual payment and the interest, which is $6,333.33 - $14,186.67 = -$7,853.34. Since the principal portion is negative, it means the loan will be fully paid off in the second year.

In the third year, there is no outstanding loan balance, so both the interest and principal portions of the payment will be zero.

The percentages of interest and principal change over time because the interest is calculated based on the remaining loan balance, which decreases with each payment. As the loan balance decreases, the interest portion becomes smaller, and the principal portion becomes larger. Therefore, the interest percentage decreases, while the principal percentage increases over the repayment period.

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Answer:

D) x=60

The choose

Step-by-step explanation:

360 =70+70+50+50+2x

360=240+2x

360-240=2x

120=2x

x=120/2

x=60

Answer:

No solution

Step-by-step explanation:

In one sweep, the area covered by the sprinkler is 77.19 sq ft (approx). The area of the lawn, to the nearest square foot, that receives water from this sprinkler is 616 sq ft (approx).

We know that a rotating sprinkler can reach up to 14 feet through a 300-degree angle. Area covered by the sprinkler in one sweep = area of the sector whose radius = 14 feet and angle = 300°Area of sector = (θ / 360) × πr²Where θ = 300°, r = 14 ftArea of sector = (300/360)× π(14)²= 77.19 sq ft (approx) Therefore, the area covered by the sprinkler in one sweep is 77.19 sq ft (approx).

We need to find the total area of the lawn that receives water from this sprinkler. The sprinkler rotates 360 degrees, so it will cover a full circle whose radius is 14 feet. Area of a circle = πr²= π(14)²= 615.752 sq ft (approx) Therefore, the area of the lawn, to the nearest square foot, that receives water from this sprinkler is 616 sq ft (approx).

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Answer:

X1=0

Y1=-3

X2=4

Y2=1

Slope=(y2-y1)/(x2-x1)

Slope=(1-(-3))/(4-0)

Slope=4/4

Slope=1

Step-by-step explanation:

The ratio of Mary's share to Katherine's share to Alex's share is 5:4:1, which means Mary pays 5/10 of the bill, Katherine pays 4/10 of the bill, and Alex pays 1/10 of the bill.

To find the ratio, we can write their contribution as a fraction of the total parts and then solve the fractions then they'll have the same denominator.

So, Mary's share is 5/10, Katherine's share is 4/10, and Alex's share is 1/10.

To convert this as a ratio, we write 5:4:1, where each number represents the number of parts each person pays, and the colon separates each person's contribution.

Therefore, the ratio of Mary's share to Katherine's share to Alex's share is 5:4:1

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