List three different combinations of coins, each with a value of 30% of a dollar ​

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Work Shown:

M = number of miles

L = cost to rent a luxury car = 1.15M + 16.40

E = cost to rent an economy car = 0.80M+10.95

C = difference in price

C = L - E

C = (1.15M + 16.40) - (0.80M+10.95)

C = 1.15M + 16.40 - 0.80M-10.95

C = 0.35M + 5.45

Don't forget to distribute the negative to each term in the second parenthesis.

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Optional Section:

Let's say you drove M = 100 miles as an example.

The luxury car would cost L = 1.15M+16.40 = 1.15*100+16.40 = 131.40 dollars to rent.

The economy car would cost E = 0.80M+10.95 = 0.80*100+10.95 = 90.95 dollars to rent.

The difference in rental costs is L-E = 131.40-90.95 = 40.45 dollars.

Or you could say C = 0.35M+5.45 = 0.35*100+5.45 = 40.45

This means you pay $40.45 more if you go for a luxury car instead of an economy car.

A Polynomial function satisfies the requirement of having zeros at -2, 3/4, and 3i, and its coefficients are all integers.

To construct a polynomial function with integral coefficients and zeros at -2, 3/4, and 3i, we can use the concept of complex conjugate roots. The polynomial function will have a least degree, meaning we aim to find the simplest polynomial that satisfies the given conditions. Here is the summary of the answer:

The polynomial function with integral coefficients and zeros at -2, 3/4, and 3i can be constructed using complex conjugate roots.

Now let's delve into the explanation. To begin, we consider the zeros provided: -2, 3/4, and 3i. Since we want the coefficients to be integral, we know that the complex conjugate of 3i will also be a zero, namely -3i.

To form the polynomial function, we use the fact that if a polynomial has a complex zero, its conjugate must also be a zero. Therefore, we can pair the complex zeros 3i and -3i, resulting in the factors (x - 3i) and (x + 3i). Similarly, we have (x + 2) as a factor for the zero -2, and (4x - 3) as a factor for the zero 3/4.

Multiplying these factors together, we obtain the polynomial function with the least degree that satisfies the given conditions. The resulting polynomial with integral coefficients is:

P(x) = (x - 3i)(x + 3i)(x + 2)(4x - 3)

This polynomial function satisfies the requirement of having zeros at -2, 3/4, and 3i, and its coefficients are all integers.

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Answer:

Answer is d=9t.

Step-by-Step:

4.5/.5=9

6.75/.75=9

13.5/1.5=9

Answer:

He will owe $24 interest at the end of the year.

Step-by-step explanation:

Formula for finding Simple Interest:

S.I = PRINCIPAL × RATE × TIME/100

S.I = 200 × 12 × 1/100

S.I = $24

$24 is the Simple Interest.

The general solution of the system is: x = x (free parameter), y = (7/2)x, and z = -(3/2)x. This represents the set of all solutions to the system of equations.

To find the general solution of the system represented by the augmented matrix, we can perform row operations to bring the matrix to its reduced row-echelon form (RREF). The RREF will reveal the solution of the system.

Let's work through the row operations step by step:

Row 2 = Row 2 - 2 × Row 1

Row 3 = Row 3 - 4 × Row 1

The new augmented matrix after the first row operation:

[ 2 -7 3 0 ]

[ 0 0 0 0 ]

[ 0 0 0 0 ]

Next, divide Row 1 by 2:

Row 1 = Row 1 / 2

The updated augmented matrix:

[ 1 -7/2 3/2 0 ]

[ 0 0 0 0 ]

[ 0 0 0 0 ]

Now, we can see that the second and third rows consist of all zeros. This indicates that the system has infinitely many solutions.

To express the general solution, we can assign a parameter to one of the variables (let's choose x):

x = Free parameter

Then, we can express the other variables in terms of x:

y = (7/2)x

z = - (3/2)x

Therefore, the general solution of the system is:

x = x (free parameter)

y = (7/2)x

z = -(3/2)x

This represents the set of all solutions to the system of equations. By assigning different values to the parameter x, we can obtain infinitely many solutions.

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Answer:

30.144 or 3.14 if rounded.

Step-by-step explanation:

First you need to find the area of the table top

a = \(\pi r^{2}\)

a = (3.14) (\(.8^{2}\))    The radius is the half of the diameter 1.6/2 = .8

a = 3.14(.64)

a = 2.0096

The area is 2.0096 \(m^{2}\)

the cost will be

2.0096 x 15 = 30.144 rupees

Doe you round rupees to the nearest hundredths' place?  I am not sure. Rounded the number would be 30.14

Answer:

the answer is c im in college so

Step-by-step explanation:

if u help me i help u :)

Answer:

1. 4x+3x were added together because they are like terms

2. We subtracted 5 from both sides of the equation

3. We divide both sides of the equation by seven

Step-by-step explanation:

I hope this is what you were looking for... Good luck!

\( \frac{1}{6} \)

There are 6 sides in a cube and each side has a different number so you're chance of getting a 3 is 1/6.

The probability that z lies between -2.41 and 0 is approximately 0.9911.

To find the probability that a standard normal variable, z, falls within a specific range, we can use the standard normal distribution table or a statistical calculator.

In this case, we want to find the probability that z lies between -2.41 and 0. By referencing the standard normal distribution table or using a calculator, we can determine the area under the curve corresponding to this range. The resulting value represents the probability of z falling within that range.

Approximately 0.9911 is the probability that z lies between -2.41 and 0 when rounded to four decimal places. This means that there is a high likelihood (approximately 99.11%) that a randomly chosen value of z from a standard normal distribution falls within this range.

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The dimensions of the poster to be taken so that the least amount of poster is used are 17 by 34.

What is area of rectangle?

Area of rectangle = length x breadth

The dimensions of any rectangular figure can be found using this formula.

According to the given question:

Let x and y be the dimensions of the poster

The area of the poster, A= x*y

Margin at both up and bottom is 2 inches, at the right and left is 1 inch

(x-4)(y-2)= 450

Let us make y subject of the formula

(y-2) = 450/(x-4)

y = [450/(x-4)] + 2

If we substitute into the area A equation we have

A= x { [ 450/(x-4)] + 2}

A= 2x + (450x)/(x - 4)

If we differentiate we have

A'(x)= [2 + 450(x-4) + 450x ]/ (x-4)²

=[ 2(x-4)² + 450(x -4) + 450x ] / (x-4)²

=[ 2(x² - 8x +16) + 450(x-4) + 450x ] /(x-4)²

If we simplify this we have

=[ 2x² -16x +32 + 450x - 450x - 1800]/ (x-4)²

=( 2x² -16x - 1800) / (x-4)²

At A'(x)= 0

= ( x² - 8x - 1800) / (x-4)² =0

If we divide through by 2 we have

x² - 8x - 900= 0

X= 34 or -26 then we choose the positive one, then x= 34

Then from area of the poster

A= (x-4)(y-2)= 450

Substitute 34 as value of x

(34-4)(y-2)= 450

30(y-2)= 450

30y - 60 = 450

30y = 510

y = 17

Hence dimensions of the poster is 17 by 34.

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Answer: 67

Step-by-step explanation:

yeah lol

Answer:

15.60 for the t-shirts

48.80 for the jumpers

So 64.40 in total

The integral: S1 0 (-x³ - 2x² - x + 3)dx is -1/12

An integral is a mathematical operation that calculates the area under a curve or the value of a function at a specific point. It is denoted by the symbol ∫ and is used in calculus to find the total amount of change over an interval.

To evaluate the integral:

\($ \int_0^1 (-x^3 - 2x^2 - x + 3)dx $\)

We can integrate each term of the polynomial separately using the power rule of integration, which states that:

\($ \int x^n dx = \frac{x^{n+1}}{n+1} + C $\)

where C is the constant of integration.

So, we have:

\($ \int_0^1 (-x^3 - 2x^2 - x + 3)dx = \left[-\frac{x^4}{4} - \frac{2x^3}{3} - \frac{x^2}{2} + 3x\right]_0^1 $\)

Now we can substitute the upper limit of integration (1) into the expression, and then subtract the result of substituting the lower limit of integration (0):

\($ \left[-\frac{1^4}{4} - \frac{2(1^3)}{3} - \frac{1^2}{2} + 3(1)\right] - \left[-\frac{0^4}{4} - \frac{2(0^3)}{3} - \frac{0^2}{2} + 3(0)\right] $\)

Simplifying:

\($ = \left[-\frac{1}{4} - \frac{2}{3} - \frac{1}{2} + 3\right] - \left[0\right] $\)

\($ = -\frac{1}{12} $\)

Therefore,

\($ \int_0^1 (-x^3 - 2x^2 - x + 3)dx = -\frac{1}{12} $\)

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Answer:

D.

Step-by-step explanation:

They would charge a flat fee of $1000, and $200 per room

The volume of a stack of 9 books is 1368.75 cubic inches.

To find the volume of a stack of 9 books, we first need to find the height of the stack. Since each book is 3/4 inch thick, the height of the stack is 9 times 3/4 inch, which is 6 3/4 inches.

Now we need to find the area of the base of the rectangular prism formed by the stack of books. Since each book has an area of 22 1/2 square inches, the total area of the base of the stack is 9 times 22 1/2 square inches, which is 202 1/2 square inches.

Therefore, the volume of the stack of 9 books is:

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The term for placing concertina wire on top of a pre-existing fence is called "topping" or "topping with concertina wire."

Topping is a common security measure used to enhance the deterrent value and effectiveness of a fence by adding a layer of concertina wire or barbed wire on its top.

The concertina wire consists of sharp, barbed or razor wire coils that are attached to the fence at regular intervals.

This additional layer of security helps to prevent unauthorized entry or climbing over the fence, providing an additional physical barrier and discouraging potential intruders.

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The area of the backyard is 1000 square feet.

The square footage of the yard, you need to multiply the length and width of the yard.

So, the square footage of the yard would be: 50 ft (length) x 20 ft (width) = 1000 square feet

To calculate the area of the backyard, we need to use the formula for the area of a rectangle, which is:

Area = length x width

In this case, the length of the backyard is given as 50 feet, and the width is given as 20 feet.

So, we can substitute these values into the formula:

Area = 50 ft x 20 ft

Multiplying 50 by 20, we get:

Area = 1000 square feet

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Answer:

32 dollars

Step-by-step explanation:

Her total os unknown. ? - 5 = 27. 27 + 5 = 32. 32 = ?

Answer:

B-2

Step-by-step explanation:

It is B, because On the first month, Armando has 12 and Daniel has 8, now on the 2nd month Armando has 9 because he gives away 3 each month and Daniel now has 9 because he adds one each month, so all in all, they have the same exact number of pencils on the 2nd month

After 5 months is when Armando and Daniel had the same number of pencils.

Answer:

1286 more feet

Step-by-step explanation:

For a result to be considered significant, the chances of its occurring as a result of random error are often less than 5 percent.

A coincidental discrepancy between the observed and true values of anything is known as a random error (e.g., a researcher misreading a weighing scale records an incorrect measurement).

It's not always a mistake when there is random error; rather, it happens when measurements are made. Even when you measure the same item repeatedly, there will always be some variation in your results because to changes in the environment, the instrument, or your own perceptions.

Your measurements are equally likely to be greater or lower than the genuine values due to random error, which has unexpected effects.

According to the given data,

For a result to be considered significant, the chances of its occurring as a result of random error are often less than 5 percent.

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Answer:

q = 4.9

m∠R = 27.1°

m∠S = 136.9°

Step-by-step explanation:

To solve the triangle we will use the cosine rule and the sine rule

In the given triangle

∵ q is the opposite side of ∠Q

∵ s is the opposite side of ∠S

∵ r is the opposite side of ∠R

∵ m∠Q = 16°

∵ r = 8 and s = 12

→ By using the cosine rule to find q

∴ q² = r² + s² - 2 r s cos∠Q

→ Substitute the values of r, s, and ∠Q in the rule above

∵ q² = (8)² + (12)² - 2(8)(12)cos(16°)

∴ q² = 23.43775438

→ Take √ for both sides

∴ q = 4.841255455

→ Round it to the nearest tenth

∴ q = 4.9

→ To find angles R and S we will use the sine rule

∵ \(\frac{r}{sin(R)}\) =\(\frac{q}{sin(Q)}\) = \(\frac{s}{sin(S)}\)

→ Use the first two ratios to find m∠R

∵ \(\frac{8}{sin(R)}\) = \(\frac{4.841255455}{sin(16)}\)

→ By using cross multiplication

∴ 4.841255455 × sin(R) = 8 × sin(16)

→ Divide both sides by 4.841255455

∴ sin(R) = 0.4554807874

→ Use \(sin^{-1}\) to find m∠R

∵ m∠R =  \(sin^{-1}\) (0.4554807874)

∴ m∠R = 27.0958732

→ Round it to the nearest tenth

∴ m∠R = 27.1°

∵ The sum of the measures of the angle in a triangle is 180°

∴ m∠S + m∠Q + m∠R = 180°

→ Substitute the values of m∠Q and m∠R

∵ m∠S + 16° + 27.1° = 180°

∴ m∠S + 43.1 = 180

→ Subtract 43.1 from both sides

∴ m∠S = 136.9°

n - 2.5 represent the Cost Price after a discount of 2.50

Given parameters,

Modeling of the total cost = 35 + 3(n - 2.5)

The general format of models like this is as follows;

Price + quantity (cost after coupon)

Coupon literally is a code that are used to obtain a discount on the current purchase

By comparison;

Price = 35 (i.e. current dress price).

Quantity = n (i.e. the number of shirts bought)

Lastly, cost after coupon = n - 2.5

It is stated that she applies a coupon on each T shirt

This can be interpreted to: removing a total discount of $2.50 from the three t-shirt.

By removing, the expression is given as negative $2.5

Hence,

n - 2.5 represent the total cost on each T shirt after coupon is applied

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Answer:

I think it is 0.51? (I am complety off aren't I/)

Step-by-step explanation:

Find the surface area of a Cuboid of length, breadth, and height equal to 12 cm, 8 cm and 5 cm respectively.

\( \bullet \) Length (l) of a Cuboid is 12 cm.

\( \bullet \) Breadth (b) of a Cuboid is 8 cm.

\( \bullet \) Height (h) of a Cuboid is 5 cm.

The surface area of a Cuboid.

We know,

Formula of surface area of a Cuboid is 2(lb + bh + lh) sq units.

So, Surface area of a Cuboid = 2(12×8 + 8×5 + 12×5) sq cm.

= 2(96 + 40 + 60) sq cm.

= 2 × 196

= 392 sq cm

The nth term of the sequence whose integers are between 1 -7 such that there is the permission of repetition but no two consecutive digits must be even is 1.254 × 10¹¹

Consecutive numbers are those numbers that succeed each other in increasing order from least to greatest. The numbers that are given:

Now, suppose a (n) denotes the number of n-digit positive integers as stated in the question, thereby using:

Then, the number of n can be computed as n!

= (7!) × (6!) × (5!) × (4!) × (3!) × (2!) × (1!)

= 1.254 × 10¹¹

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The nth term of the series of integers is between 1 -7 such that there is the permission of repetition but no two consecutive digits must be even is 1.254 × 10¹¹

Consecutive numbers are those numbers that succeed by each other in increasing order from lowest to greatest such are 1, 2, 3, 4, 5, 6, or 7.

Now, suppose n represents the number of n-digit positive integers.

1, 2, 3, 4, 5, 6, or 7 with the permission of repetition no two consecutive digits are even.

Then, the number of n can be calculated as n!

= (7!) × (6!) × (5!) × (4!) × (3!) × (2!) × (1!)

= 1.254 × 10¹¹

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1.1.1 Short-term investment: An example of a short-term investment is investing in a 3-month Treasury bill. These are government-issued debt securities with a maturity of less than one year, providing a relatively low-risk investment option with a fixed interest rate.

1.1.2 Medium-term investment: A medium-term investment example is investing in a corporate bond with a maturity of 5 years. Corporate bonds offer a higher yield compared to government bonds, making them suitable for investors with a moderate risk appetite seeking stable income over a longer time horizon.

1.1.3 Long-term investment: An example of a long-term investment is investing in a diversified stock portfolio. Stocks represent ownership in a company and have the potential for higher returns over an extended period, although they also involve higher risk.

1.1.4 Fixed income: An example of a fixed income investment is purchasing a 10-year government bond. These bonds pay a fixed interest rate over the bond's duration, providing a predictable stream of income for the investor.

1.1.5 Fixed expense: A fixed expense example is paying a monthly mortgage payment. The mortgage payment remains constant throughout the loan term, typically spanning several years, and includes both the principal repayment and the interest charged by the lender.

1.1.1 Short-term investment: A short-term investment option is the 3-month Treasury bill. Treasury bills are considered low-risk investments issued by the government, and they offer a fixed interest rate that is determined through an auction process. Investors can purchase Treasury bills directly from the government or through a broker.

1.1.2 Medium-term investment: A medium-term investment example is investing in a corporate bond with a 5-year maturity. Corporate bonds are issued by companies to raise funds, and they pay a fixed interest rate to bondholders over the bond's duration. The bond's yield and risk profile depend on the creditworthiness of the issuing company.

1.1.3 Long-term investment: An example of a long-term investment is investing in a diversified stock portfolio. A diversified portfolio consists of a mix of stocks from different sectors and regions, spreading the risk across multiple companies. The goal is to achieve long-term capital appreciation and potentially earn dividends from the stocks held in the portfolio.

1.1.4 Fixed income: An example of a fixed income investment is purchasing a 10-year government bond. Government bonds are issued by national governments to finance their operations. The bond's interest rate is fixed at the time of issuance, and the investor receives periodic interest payments until the bond reaches maturity, at which point the principal amount is returned.

1.1.5 Fixed expense: A fixed expense example is paying a monthly mortgage payment. When purchasing a property with a mortgage loan, the borrower agrees to make fixed monthly payments that include both the principal repayment and the interest charged by the lender. The monthly payment amount remains constant throughout the mortgage term, typically ranging from 15 to 30 years.

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It is correct to say that any point on the perpendicular bisector of a segment is equidistant from the endpoints of the segment.

Any point on the perpendicular bisector of a segment is equidistant from the endpoints of the segment. What is a perpendicular bisector? A perpendicular bisector is a line that intersects a line segment and forms a 90-degree angle. It divides the line segment into two equal halves.Each point on the perpendicular bisector of a line segment is equidistant from the endpoints of the segment. This means that the distance from any point on the line to one endpoint of the segment is the same as the distance to the other endpoint of the segment.

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