Can someone help me with these problems 5-8 I would appreciate it

Answer:

a. It will take approximately 40 months

b. The total amount Paul has to pay is approximately $8,000

c. The amount Paul pays each month is approximately $316.59

d. The amount Paul has to pay is approximately $7,598.16

e. Lower monthly payment

f. Lower total payment amount (amount to be paid)

Step-by-step explanation:

a. The loan amount, PV = $7,000

The annual interest rate, r = 8%

Option 1; The amount of equal monthly payment to repay the loan = $200

Option 2; The number of equal monthly payment to repay the loan = 24

The formula for the present value of an annuity is given as follows;

\(PMT = \dfrac{\dfrac{r}{12} \times PV}{1 - \left (1 + \dfrac{r}{12} \right)^{-n}}\)

Where;

PMT = The monthly payment

n = The number of months

Where PMT = $200, we have;

\(200 = \dfrac{\dfrac{0.08}{12} \times 7,000}{1 - \left (1 + \dfrac{0.08}{12} \right)^{-n}}\)

\(1 - \dfrac{\dfrac{0.08}{12} \times 7,000}{200} = \left (1 + \dfrac{0.08}{12} \right)^{-n}\)

\(1 - \dfrac{7}{30} = \dfrac{23}{30} = \left ( \dfrac{151}{150} \right)^{-n}\)

\(-n = \dfrac{ ln \left(\dfrac{23}{30} \right)}{ln\left(\dfrac{151}{150} \right) } \approx -39.988\)

∴ The number of months it will take for Paul to repay the loan, n ≈ 39.988 ≈ 40 months

b. The total amount Paul has to pay, A = PMT × n

Therefore, b plugging in the values of PMT, and 'n', we get;

A ≈ $200 × 40 = $8,000

c. Using option 2, we have;

n = 24

Therefore;

\(PMT = \dfrac{\dfrac{0.08}{12} \times 7,000}{1 - \left (1 + \dfrac{0.08}{12} \right)^{-24}} \approx 316.59\)

The monthly payment, PMT ≈ $316.59

d. The total amount Paul has to pay using option 2, A ≈ 316.59 × 24 = 7,598.16

The total amount Paul has to pay using option 2, A ≈ $7,598.16

e. A reason why Paul might choose option 1 is that option 1 offers lower monthly payment

f. A reason why Paul may choose option 2 is that option 2 offers a lower total amount that he has to pay.

A) It will take 48 months for Paul to repay the loan.

B) Paul will have to pay $ 9,523.42.  

C) Paul should pay $ 340.20 per month.

D) Paul will have to pay $ 8164.80.

E) Paul might choose option 1 because his monthly payments would be lower and, therefore, more accessible.

F) Paul might choose option 2 because his total payout would be much less than option 1.

Since Paul wants to buy a car, and he needs to take out a loan for $ 7000, and the car salesman offers him a loan with an interest rate of 8%, compounded annually, and Paul considers two options to repay the loan (Option 1: Pay $ 200 each month, until the loan is fully repaid, and Option 2: Make 24 equal monthly payments), for:

The following calculations must be performed:

A) 7000 x 1.08 ^ 4 = 9,523.42

200 x 12 x 4 = 9600

Therefore, it will take 48 months for Paul to repay the loan.

B) Paul will have to pay $ 9,523.42.

C) 7000 x 1.08 ^ 2 = 8,164.80

8,164.80 / 24 = 340.20

Therefore, Paul should pay $ 340.20 per month.

D) Paul will have to pay $ 8164.80.

E) Paul might choose option 1 because his monthly payments would be lower and, therefore, more accessible.

F) Paul might choose option 2 because his total payout would be much less than option 1.

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Answer: The answer is most likely 0.3

Step-by-step explanation:

The difference between the theoretical and experimental probabilities of getting heads is 0.3.

This question is solved using the concepts of theoretical and experimental probabilities.

----------------------------

Theoretical probability:

A fair coin means that it is equally as likely to be heads or tails, so 0.5 theoretical probability of getting heads.

----------------------------

Experimental probability:

Out of 10 trials, 2 resulted in heads, so 2/10 = 0.2 experimental probability of  getting heads.

----------------------------

Difference:

0.5 - 0.2 = 0.3

The difference between the theoretical and experimental probabilities of getting heads is 0.3.

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Therefore, the complex number [2 (cos 10° + i sin 10°)]º in standard notation is simply 2.

DeMoivre's theorem states that for any complex number z = r(cos θ + i sin θ), its nth power can be written as:

\(z^n = r^n (cos n\theta + i sin n\theta)\)

In this case, we have the complex number [2 (cos 10° + i sin 10°)]º and we want to express it in standard notation.

Using DeMoivre's theorem, we can raise the complex number to the power of 0:

[2 (cos 10° + i sin 10°)]º = 2º (cos 0° + i sin 0°)

Since cos 0° = 1 and sin 0° = 0, the expression simplifies to:

[2 (cos 10° + i sin 10°)]º = 2 (1 + i * 0) = 2

Therefore, the complex number [2 (cos 10° + i sin 10°)]º in standard notation is simply 2.

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Answer:

Deserea ate more

Step-by-step explanation:

One dozen equals 12

Carla ate 1/4 of it

1/4×12/1=3

Carla ate 3 cookies

Deserea ate 1/2

1/2×12/1=6

Deserea ate 6

6 is greater than 3 so Deserea ate more

The height of the chimney is 357 feet according to mentioned dimensions of the chimney and observer.

The ratio of base and height according to angled of elevation will be -

tan theta = perpendicular ÷ base. The same will be for chimney. Hence, equating the ratio of both to find the height of chimney.

The formula will be -

Perpendicular ÷ base of observer = perpendicular ÷ base of chimney

6/4 = height/238

Rewriting the equation according to height of chimney

Height = (6 × 238)/4

Performing multiplication on Right Hand Side of the equation

Height = 1428/4

Performing division on Right Hand Side of the equation

Height = 357

Thus, chimney is 357 feet tall.

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Answer:

The slope also increases

Step-by-step explanation:

The slope of a function is the ratio of change in y to change in x. For an exponential function f(x) = e^x, the slope of the function is equal to the function, i.e slope = e^x.

For a function represented by \(y=2^x\), this is an exponential function representing growth, the slope of  \(y=2^x\) is also  \(2^x\), therefore as the value of x increases, the value of the slope also increases.

At x = 1, slope = 2^1 = 2, At x = 4, slope = 2^4 = 16.

The probability of getting either a diamond or a Jack when drawing a single card from a deck of 52 cards is 4/13.

Determine the number of favorable outcomes (diamonds or Jacks) and the total number of possible outcomes (all cards in the deck).

There are 13 diamonds in a deck, and there are also 4 Jacks (one Jack for each suit). However, we need to subtract one Jack from the count because it is already counted as a diamond (the Jack of diamonds). So, the number of favorable outcomes is 13 (diamonds) + 4 (Jacks) - 1 (Jack of diamonds) = 16.

Total number of possible outcomes:

In a standard deck of 52 cards, there are 52 possible outcomes.

The probability of getting either a diamond or a Jack is given by the ratio of favorable outcomes to total possible outcomes:

Probability = Number of favorable outcomes / Total number of possible outcomes

Probability = 16 / 52

Probability = 4 / 13

Therefore, the probability is 4/13.

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\(\large{\green}\fcolorbox{purple}{pink}{\bf{\underline{\red{\color{red}Answer}}}}\)

6x + 20

Step-by-step explanation:

Perimeter of rectangle

Length = 2x + 7

Breadth/width = x + 3

We know that

\( \mathfrak {perimeter \: of \: rectangle =2(length + breadth) }\)

Now we will substitute the values of length and breadth

\( \sf \longmapsto perimeter = 2 \{(2x + 7) + (x + 3) \} \\ \\ \\ \sf \longmapsto perimeter = 2 \{3x + 10 \} \\ \\ \\ \sf \longmapsto perimeter = 6x + 20\)

Answer:

I would say B

Step-by-step explanation:

Only because if you were to take the money from the negative side and subtract it from the positive side you would get $87,025.

That would be my answer.

The probability that a randomly selected carton has a puncture or a smashed corner is 0.076, or 7.6%.

What is probability?

Probability is a measure of the likelihood of an event occurring. It is a number between 0 and 1, where 0 means the event is impossible and 1 means the event is certain to happen.

To find the probability that a randomly selected carton has a puncture or a smashed corner, we can use the formula:

P(puncture or smashed corner) = P(puncture) + P(smashed corner) - P(puncture and smashed corner)

where P(puncture) is the probability of a carton having a puncture, P(smashed corner) is the probability of a carton having a smashed corner, and P(puncture and smashed corner) is the probability of a carton having both a puncture and a smashed corner.

Substituting the given probabilities into the formula, we get:

P(puncture or smashed corner) = 0.03 + 0.06 - 0.014

P(puncture or smashed corner) = 0.076

Therefore, the probability that a randomly selected carton has a puncture or a smashed corner is 0.076, or 7.6%.

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To represent the fraction 6 in terms of 2, we can divide both the numerator and denominator by 2 to simplify the fraction. This gives us: 6/2 = 3/1.

In this fraction, the numerator is 3, representing the colored pieces that show the parts of the whole, and the denominator is 1, representing the total number of equal parts that make up the whole. So, the equivalent fraction sentence is: 6/2 = 3/1. This means that when we divide 6 by 2, we get a result of 3, which is equivalent to the fraction 3/1.

The fraction 3/1 indicates that the whole is divided into three equal parts, and we are considering one of those parts. Therefore, the completed equivalent fraction sentence is 6/2 = 3/1.

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Answer:

C =34.54 cm

Step-by-step explanation:

The circumference is the diameter times pi

C = pi *d

C = 3.14 * 11

C =34.54 cm

Answer:

Option C is the right option.

Solution,

Diameter=11 cm

Radius=11/2=5.5 cm

Circumference=?

Now,

\(circumference = 2\pi \: r \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 2 \times 3.14 \times 5.5 \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 34.54 \: cm\)

hope this helps..

Good luck on your assignment..

ok the answer is b

Step-by-step explanation:

Answer:

1a. first 7×9=63 Then substracting 16 we get 47 and 2-47= -45

Answer:

a.  - 77

b. 4

c. 5x-14

d. 14

Step-by-step explanation:

a. 2-(7*9)-16

=> 2-63-16

=>(-61) - 16

=> -77

b.64 / 4+(3*4)

=> 64 /  4+12

=> 64 / 16

=> 4

c. 3x+2(x-7)

=> 3x+2x - 14

=> 5x-14

d. 5 + 6^2/ 4

=> 5+ 36/4

=> 5+9

=> 14

Answer:

The probability of observing a sample mean of x = 52 or greater from a sample size of 25 is 0.0000026

Step-by-step explanation:

Mean = \(\mu = 45\)

Population standard deviation =\(\sigma = 6\)

Sample size = n =25

Sample mean = \(\bar{x} = 52\)

We are supposed to find  the probability of observing a sample mean of x = 52 or greater from a sample size of 25 i.e.\(P(x\geq 52)\)

\(Z=\frac{x-\mu}{\frac{\sigma}{\sqrt{n}}}\\Z=\frac{52-45}{\frac{6}{\sqrt{25}}}\)

Z=5.83

P(Z<52)=0.9999974

\(P(Z\geq 52)=1-P(z<52)=1-0.9999974=0.0000026\)

Hence  the probability of observing a sample mean of x = 52 or greater from a sample size of 25 is 0.0000026

Answer:

the probability of observing a sample mean of x = 52 or greater from a sample size of 25 is 0.0000026

Step-by-step explanation:

Answer:

Step-by-step explanation:

Let us suppose that length of Triangle is equal to x.

that is

Length = x

Than

width = x - 10

perimeter of Rectangle is

2(length) + 2(width) = 36

2x + 2(x-10) = 36

2x +2x - 20 = 36

4x -20 = 36

4x = 36 +20

4x = 56

x = 56/4

x = 14

so Length of Rectangle is 14 inches

and

width = x - 10

width = 14 - 10

width = 4

Answer: 2\(4\sqrt{x} 4\)

Step-by-step explanation:

Answer:

-3 is the coefficient of x here

Step-by-step explanation:

The first thing to do here is to open the brackets.

(x-5)(x + 2) = x(x + 2)-5(x + 2)

x^2 + 2x -5x -10

x^2 -3x -10

When we say the coefficient of x, we mean the value by which x only is multiplied by in the equation. That would be -3

This must not be confused with the coefficient of x^2 which is entirely different from the coefficient of x

The double integral of f(x, y) over D is ∫∫D f(x, y) dxdy = 2π/3.

What is intergration?

Integration is a fundamental concept in calculus that involves finding the integral of a function. It is the reverse process of differentiation and is used to compute areas, accumulate quantities, and solve various mathematical problems.

To evaluate the double integral ∫∫D f(x, y) dxdy over the region D, we need to determine the limits of integration.

The region D is defined by the condition \(x^2 + y^2\) ≤ 16, which represents a disk of radius 4 centered at the origin.

In polar coordinates, we can express x and y in terms of r and θ as follows:

x = r cos(θ)

y = r sin(θ)

The limits of integration for r and θ will correspond to the region D.

For r, we have 0 ≤ r ≤ 4, as the radius of the disk is 4.

For θ, we need to determine the range of angles that cover the entire disk. Since the disk is symmetric about the origin, we can choose any range of angles that covers a full circle. A suitable range is 0 ≤ θ ≤ 2π, which represents one complete revolution.

Now, we can set up the double integral:

∫∫D f(x, y) dxdy = ∫∫D √(16 - \(x^2 - y^2\)) dxdy

Converting to polar coordinates:

∫∫D √(16 - \(r^2\)) r dr dθ

Using the limits of integration:

∫₀²π ∫₀⁴ √(16 - \(r^2\)) r dr dθ

The inner integral with respect to r can be evaluated using substitution. Let u = 16 - \(r^2\), then du = -2r dr. The limits of integration become u(0) = 16 and u(4) = 0. The integral becomes:

∫₀²π ∫₁⁰ √u (-du/2) dθ

Simplifying:

-1/2 ∫₀²π ∫₁⁰ √u du dθ

The inner integral with respect to u is a standard integral:

-1/2 ∫₀²π [2/3 \(u^{(3/2)\)]₁⁰ dθ

Applying the limits of integration:

-1/2 ∫₀²π [2/3 \((0)^{(3/2)\) - 2/3 \((1)^{(3/2)\)] dθ

Simplifying further:

-1/2 ∫₀²π [-2/3] dθ

Integrating with respect to θ:

-1/2 [-2/3 θ]₀²π

Applying the limits of integration:

-1/2 [-2/3 (2π) - (-2/3 (0))]

Simplifying:

-1/2 [-4π/3]

Final result:

2π/3

Therefore, the double integral of f(x, y) over D is ∫∫D f(x, y) dxdy = 2π/3.

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Answer:

\(=4y\)

Step-by-step explanation:

\(y-\left(-3y\right)\\\mathrm{Apply\:rule}\:-\left(-a\right)=a\\=y+3y\\\mathrm{Add\:similar\:elements:}\:y+3y=4y\\=4y\)

Answer:

\( = 4y\)

Step-by-step explanation:

\(y - ( - 3y)\)

we know that,

\(( - ) \times ( - ) = ( + )\)

so,

\(y - ( - 3y) \\ y + 3y \\ = 4y\)

hope this helps

brainliest appreciated

good luck! have a nice day!

Answer:

100620261

i used my brain

Answer:

100620261

Step-by-step explanation:100620261

The simplified radical expression by rationalizing the denominator is, \(\frac{-6}{\sqrt{5y}}\times\frac{\sqrt{5y}}{\sqrt{5y}}\) = \(\frac{-6\sqrt{5y}}{5y}$$\) = $\frac{-6\sqrt{5y}}{5y}$.

To simplify the radical expression by rationalizing the denominator, multiply both numerator and denominator by the conjugate of the denominator.

The given radical expression is \($\frac{-6}{\sqrt{5y}}$\).

Rationalizing the denominator

To rationalize the denominator, we multiply both the numerator and denominator by the conjugate of the denominator, \($\sqrt{5y}$\)

Note that multiplying the conjugate of the denominator is like squaring a binomial:

This simplifies to:

(-6√(5y))/(√(5y) * √(5y))

The denominator simplifies to:

√(5y) * √(5y) = √(5y)^2 = 5y

So, the expression becomes:

(-6√(5y))/(5y)

Therefore, the simplified expression, after rationalizing the denominator, is (-6√(5y))/(5y).

\($(a-b)(a+b)=a^2-b^2$\)

This is what we will do to rationalize the denominator in this problem.

We will multiply the numerator and denominator by the conjugate of the denominator, which is \($\sqrt{5y}$\).

Multiplying both the numerator and denominator by \($\sqrt{5y}$\), we get \(\frac{-6}{\sqrt{5y}}\times\frac{\sqrt{5y}}{\sqrt{5y}}\) = \(\frac{-6\sqrt{5y}}{5y}$$\)

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Answer:

Step-by-step explanation:

7.6 is greater

Answer:

Not sure what you're asking here

Step-by-step explanation:

no cheating thanks <3