A $1,400 loan has a simple annual interest rate of 4%. How much simple
interest is paid on the loan for 1 year?
A
$56.00
B
$67.20
C $560.00
D $672.00

The difference of the Fareinheit Temperature and 32 can be represented mathematically as:

Five ninth times the difference of the fahrenheit temperature, F, and 32 will be expressed mathematically as:

The above relationship equals the Celcius Temperature:

The final mathematical expression is:

To determine the length of BE, we can use the concept of the triangle's side lengths and apply the Triangle Inequality Theorem.

According to the Triangle Inequality Theorem, the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. In this case, we can apply it to triangle ABC, where AC is the longest side.

Given the lengths AE = 3, DE = 5, and CE = 2, we can conclude that AC > AE and AC > CE.

Now, let's focus on triangle ABE. Since AC is the longest side, we can conclude that AB + BE > AE.

Substituting the known values, we have:

AB + BE > 3

Rearranging the inequality, we get:

BE > 3 - AB

To find the length of BE, we need to determine the value of AB. Unfortunately, the length of AB is not provided in the given information. Therefore, without knowing the value of AB, we cannot determine the exact length of BE.

In conclusion, without additional information or the length of AB, we cannot calculate the exact length of BE.

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Answer:

I am pretty sure that it is 4.

Step-by-step explanation: Got it right on edge2020

Answer:

4

Step-by-step explanation:

i took on edge

(a) Parametrize the curve as r(t) = (t, 4 â€" t2), -1 ≤ t ≤ 2. Then we have F(r(t)) = (2t â€" (4-t2), t2) = (2t + t2 - 4, t2). Thus, F(r(t)) · r'(t) = (2t + t2 - 4, t2) · (1, â€"2t) = 2t - t3 - 4t2. The line integral is given by:

∫CF.dr = ∫2-1 (2t - t3 - 4t2) dt = [t2 - t4/4 - (4/3)t3]2-1 = -21/12.

(b) Parametrize the curve as r(t) = (3 cos t, 3 sin t), 0 ≤ t ≤ 2π. Then we have F(r(t)) = (18 sin2 t, 3 cos t + 3 sin t), so F(r(t)) · r'(t) = (18 sin2 t, 3 cos t + 3 sin t) · (-3 sin t, 3 cos t) = -54 sin3 t + 27 cos t sin t. The line integral is given by:

∫CF.dr = ∫2π0 (-54 sin3 t + 27 cos t sin t) dt = 0.

(c) Parametrize the curve as r(t) = (3 + t, 2t, 4 – 3t), 0 ≤ t ≤ 1. Then we have F(r(t)) = (3 + t, 2t(4 – 3t), 5), so F(r(t)) · r'(t) = (3 + t, 2t(4 – 3t), 5) · (1, 2, –3) = 4t – 6. The line integral is given by:

∫CF.dr = ∫10 (4t – 6) dt = 2.

(d) Parametrize the curve as r(t) = (3 + 2t, –2t, t3), 0 ≤ t ≤ 1. Then we have F(r(t)) = (t3, 1 – (3 + 2t), (–2t)2) = (t3, –2t – 2, 4t2), so F(r(t)) · r'(t) = (t3, –2t – 2, 4t2) · (2, –2, 3t2) = 2t3 – 4t – 24t4. The line integral is given by:

∫CF.dr = ∫1 2t3 – 4t – 24t4 dt = 0.

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Answer:

6x

Step-by-step explanation:

7x-x = x ( 7-1) = 6x

Answer:

6 x

Step-by-step explanation:

Subtract  x  from  7 x .

Answer:

It's -2, not -12 and the other is -21

Step-by-step explanation:

7*-3=-21

21/-12=-2

Answer: John is now 18 years old

Step-by-step explanation:

Let, John's age is now x years.

5 years ago, he was (x - 5) years old

In 8 years, he will be (x + 8) years old

By the given condition,

x - 5 = 1/2 (x + 8)

⇒ 2 (x - 5) = x + 8

⇒ 2x - 10 = x + 8

⇒ 2x - x = 8 + 10

⇒ x = 18

Answer:

Step-by-step explanation:

ΔLMN = ΔOPR ----- (given)

NM / NL = RP / RO

19 / 34 = 60 / RO

RO = 60 × 34 ÷ 19

RO = 107.36

Answer:

75

Step-by-step explanation:

I'm not sure l am strugging with this topic too

The amount of interest for the year was 3,770 cents, and the regular price of the electric drill that Pamela bought before the discount was 21,927 cents

Interest = P x R x T.

Where:

P = Principal amount (the beginning balance).

R = Interest rate

T = Number of time periods

In this case, we are given that;

Principal amount (P) = $580

Interest rate (R) = 6,5 %

Time = 1 year

Hence, The amount of the interest = 6,5% of $580

                                                     = 0.065 × $580

                                                     = $37.7

1 dollar = 100 cents

Hence, $37.7 = 37.7 × 100 cents equal to 3,770 cents

P = (1 – d) x

Where,

P = Price after discount

D = discount rate

X = regular price

In this case, we are given that:

P = $32.89

D = 85% = 0,85

Hence, the regular price:

P = (1 – D) x

32.89 = (1 – 0.85) X

32.89 = 0.15X

X = 32.89/0.15

X= 219.27

1 dollar = 100 cents

Hence, $219.27 = 219.27 × 100 cents equal to 21,927 cents

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Answer:

-1/2 (x + 1)

Step-by-step explanation:

y2 - y1 / x2 - x1

5 - 6 / 1 - (-1)

-1/2

y - 6 = -1/2 (x + 1)

Answer:

16 Miles/Hours

Step-by-step explanation:

Average speed is the total distance covered divided by the total time

In that case we have a distance of 4 miles

Time is 15 minutes and in order to convert from minutes to hours we divide by 60 and it becomes 0.25 hours

So 4/0.25 is 16 Miles/Hours

The probability that a randomly chosen toaster will have a total resistance of 345-355 ohms is approximately 0.7996, or 79.96%.

To find the probability that a randomly selected toaster will have a total resistance of 345 to 355 ohms, we need to know the distribution of total resistance and parameters such as mean and standard deviation.

Expecting that the dispersion of add up to resistance takes after a typical conveyance with cruel μ and standard deviation σ, ready to utilize the standard ordinary dispersion to calculate the likelihood that the entire resistance will be between 345 and 355 ohms.

 First, we need to normalize the 345 and 355 values ​​with the following formula:

z = (x - μ) / σ

where x=desired value, μ = mean, σ = standard deviation, and z =corresponding z-score.

For x = 345 ohms:

z1 = (345 - μ) / σ

For x = 355 ohms:

z2 = (355 - μ) / σ

Next, we need to find the area under the standard normal distribution curve between z-scores z1 and z2. This represents the probability that the total resistance will be between 345 and 355 ohms.

You can find this range using a standard regular table or calculator. For example, using the standard normal table, we can find the region between z1 and z2 like this:

P(345 ≤ x ≤ 355) = P(z1 ≤ z ≤ z2) = Φ(z2) - Φ(z1)

where Φ(z) is the standard cumulative normal distribution function (CDF), the probability that a standard normal random variable is less than or equal to z.

For example, if z1 = -1.5 and z2 = 1.5, then

P(345 ≤ x ≤ 355) = P(z1 ≤ z ≤ z2) = Φ(1.5) - Φ(-1.5) = 0.8664 - 0.0668 ≈ 0.7996

Therefore, the probability that a randomly chosen toaster will have a total resistance of 345-355 ohms is approximately 0.7996, or 79.96% (assuming the distribution of total resistance follows a normal distribution with a known mean and standard deviation).

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Answer:

49,744.8 so round up to 49,745

Step-by-step explanation:

Jupiter is 5,751.51 times more massive than Mercury.

The analysis of mathematical representations is algebra, and the handling of those symbols is logic.

The mass of the planet Jupiter is given below.

1,898,000,000,000,000,000,000,000,000 kg.

The scientific notation is:- 2 x 10²⁷ kg.

The mass of the planet Mercury is given below.

330,000,000,000,000,000,000,000 kg.

The scientific notation is:- 3.30 x 10²³ kg.

Divide the mass of the planet Jupiter by the mass of the planet Mercury. Then we have

Jupiter / Mercury =  2 x 10²⁷  / 3.30 x 10²³

Jupiter / Mercury = 5,751.51

Your question was incomplete, but the complete question was given below.

The most massive planet in the solar system, Jupiter, has a mass of about 1,898,000,000,000,000,000,000,000,000 kg.

The least massive planet is Mercury, which has a mass of about 330,000,000,000,000,000,000,000 kg.

Use your estimates to find out how many times more massive Jupiter is than Mercury. Express your answer in standard form (without using a power of 10).

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The approximate probability of exactly two people in a group of seven having a birthday on April 15 is (C) \(7.4 x 10^-^6\)

To calculate the probability of exactly two people in a group of seven having a birthday on April 15, we can use the binomial distribution formula:

\(P(X = k) = C(n, k) * p^k * (1 - p)^(^n^-^k^)\)

Where:

So, plugging in the values, we get:

\(P(X = 2) = C(7, 2) * (1/365)^2 * (1 - 1/365)^(7 - 2)\)

\(= 21 * (1/365)^2 * (364/365)^5\)

\(= 2.38 x 10^-5\)

The probability of exactly two people in a group of seven having a birthday on April 15 can be calculated using the binomial distribution formula.

The formula takes into account the number of trials, the probability of success in a single trial, and the number of successes desired.

In this case, we want to find the probability that exactly two people in a group of seven have a birthday on April 15, assuming that all days of the year are equally likely for a birthday.

Plugging in the values into the formula gives us an approximate probability of \(7.4 x 10^-^6\), which is the answer (C).

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Answer:

There are 42 dogs and 105 cats at the shelter. To find the number of rabbits, subtract these numbers from the total number of animals at the shelter. So there are 21 rabbits at the shelter.

Step-by-step explanation:

Because there are 168 animals at the shelter and \(\frac{1}{4}\) of the animals are dogs, you can infer that there are \(\frac{168}{4}\) or 42 dogs at the shelter. The question says that \(\frac{5}{6}\) of the remaining animals are cats, which you can get two things from this statement: #1, \(\frac{5}{6}\) of the remaining animals (not including dogs) are cats in the shelter. #2, \(\frac{1}{6}\) of the remaining animals (not including dogs) are rabbits in the shelter, since that is the remaining number of animals left that aren't cats or dogs. Using this, you can get the number of cats is the number of dogs subtracted by the total number of animals at the shelter and multiplied by \(\frac{5}{6}\), which would be  \(\frac{5}{6}\)(168 - 42) = \(\frac{5}{6}\)*126 = 5 * 21 = 105 cats at the animal shelter. Since the number of rabbits is \(\frac{1}{5}\) the number of cats in the shelter (\(\frac{5}{6}\) = \(\frac{1}{6}\) * 5), that means there are \(\frac{105}{5}\) or 21 rabbits at the animal shelter, and that we'd need to subtract the number of cats and dogs from the total number of animals at the shelter to find the number of rabbits.

Answer:

0.4

Step-by-step explanation:

The question is to find the problity of random events.

The total:17+8+14+16=55

8+14=22

p=22/55=2/5=0.4

The expression \(y[n] = \Sigma_{m=0}^\infty x[m]\delta[m + 3n]\) represents the output of a system when the input is x[n] and the impulse response is \(h[n] = \delta[n+3]\), which is an impulse shifted to the left by 3 units.

To simplify this expression, we can first consider the Dirac delta function \(\delta[m + 3n]\) in the expression. The Dirac delta function is zero for all values of m, except when m = -3n. Therefore, we can rewrite the expression as:

y[n] = x[-3n]             for n = 0, ±1, ±2, ...

y[n] = 0                 otherwise

However, the original expression has a summation from m = 0 to infinity, which means that it includes the term \(x[0]\delta[3n]\). But, since the Dirac delta function is zero for all values of n, except when n is zero and the argument of the Dirac delta function is also zero, which happens when m = 0, the expression becomes:

y[0] = x[0]u[0], where u[0] is the unit step function that is 1 for n ≥ 0

For all other values of n, the output y[n] is zero, because the Dirac delta function is zero for all values of m, except when m = -3n.

Therefore, we can simplify the expression \(y[n] = \Sigma_{m=0}^\infty x[m]\delta[m + 3n]\) as:

y[n] = x[0]u[0]         for n = 0

y[n] = 0                 otherwise

And we can rewrite this expression using the step function u[n] as:

y[n] = x[0]u[n]          for n ≥ 0

y[n] = 0                 for n < 0

So, the output of the system when the input is x[n] and the impulse response is  \(h[n] = \delta[n+3]\) the input signal x[n] multiplied by a delayed unit step function.

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Answer:

1,946

Step-by-step explanation:

251+175+1500+20=1,946

Answer:

$2.41

Step-by-step explanation:

There are 4 quarts in a gallon. If there are 3 gallons that means there is 12 quarts (3x4=12) You then take $28.92 and divide it by 12, which will give you 2.40833333 and on and on, you round that to $2.41. I hope that helps!

Answer:

Equation of the line (slope-intercept form):  y = 2/3x + 4

Step-by-step explanation:

We can find the equation in slope-intercept form, whose general form is

y = mx + b, where

y-intercept, b:  We see on the graph that the line intersects the y-axis at the point (0, 4).  Thus, the y-intercept (b in the slope-intercept equation) is 4.

Slope, m:  We can find the slope using the slope formula, which is

m = (y2 - y1) / (x2 - x1), where

We see from the line intersects the x-axis at (-6, 0).  Thus, we can allow (-6, 0) to be our (x1, y1) point and (0, 4) to be our (x2, y2) point:

m = (4 - 0) / (0 - (-6))

m = (4) / (0 + 6)

m = 4 / 6

m = 2/3

Since the slope of the line is 2/3 and the y-intercept is 4, the equation of the line is y = 2/3x + 4

Answer:

x=3,2i,-2i

Step-by-step explanation:

Answer:

  4: 264°; 5: 120°; 6: 54°; 7: 45°; 8: 87°; 9: 27°

  9: x=200, y=100; 10: x=68; y=99

Step-by-step explanation:

The relations between angles and arcs in this problem set are ...

__

no identifier is given

Arc DBC is the difference between a full circle (360°) and short arc DC. The measure of short arc DC is marked as 96°, so ...

  arc DBC = 360° -96° = 264°

Αrc BC is twice the measure of the inscribed angle BDC it subtends.

  arc BC = 2×60° = 120°

Arc AB is the difference between 360° and the sum of arcs AD, DC, and CB.

  arc AB = 360° -(90° +96° +120°) = 54°

Angle ACD is half the measure of arc AD.

  Angle ACD = 90°/2 = 45°

Angle ADC is half the measure of arc AC, which is the sum of arcs AB and BC

  angle ADC = (54° +120°)/2 = 87°

Angle ACB is half the measure of arc AB

  angle ACB = 54°/2 = 27°

__

x° is the arc whose central angle is 200°

  x° = 200°

y° is half the measure of x°

  y° = 200°/2 = 100°

The relations between arcs and inscribed angles mean that opposite angles in an inscribed quadrilateral are supplementary.

 x° = 180° -112° = 68°

  y° = 180° -81° = 99°

Answer:

A

Step-by-step explanation:

Carlos' score was 2 standard deviations from the mean, so his z-score was 2.0. You can either use the empirical 68-95-98.5 rule, or you can plug it into your calculator as normalcdf(-999, 2) = .977

So 97.7% of people had a score lower than Carlos!

.977 * 1.5 million = 1,465,500 people

Answer:

the correct answer is 60° and 30°( for the two angles that have the ratio 2:3)

The other angle will be 90°

Answer:

They got the 1.2 minutes by taking the total number of minutes (6) and dividing them by the number of laps run (5).  So 6 divided by 5 gives you the 1.2.

The estimated current total cost for the installed and insulated tank is $12,065.73.

The first step is to calculate the surface area of the tank. The surface area of a cylinder is calculated as follows:

surface_area = 2 * pi * r * h + 2 * pi * r^2

where:

r is the radius of the cylinder

h is the height of the cylinder

In this case, the radius of the cylinder is 1 meter (half of the diameter) and the height of the cylinder is 1 meter. So the surface area of the tank is:

surface_area = 2 * pi * 1 * 1 + 2 * pi * 1^2 = 6.283185307179586

The insulation will add a thickness of 0.05 meters to the surface area of the tank, so the total surface area of the insulated tank is:

surface_area = 6.283185307179586 + 2 * pi * 1 * 0.05 = 6.806032934459293

The cost of the insulation is $40 per square meter and the cost of labor is $95 per square meter, so the total cost of the insulation and labor is:

cost = 6.806032934459293 * (40 + 95) = $1,165.73

The original cost of the tank was $10,900, so the total cost of the insulated tank is:

cost = 10900 + 1165.73 = $12,065.73

Therefore, the estimated current total cost for the installed and insulated tank is $12,065.73.

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To determine the distance rolled by the tire in 24 revolutions, use the following formula:

where r is the radius (14 in) and θ the degrees of the revolutions. Consider each revoutions represents 180 degrees or 2π radians, the, 24 revolutions are 24x2π = 48π.

Replace the values of r and θ into the formula for s:

Hence, the tire rolls 2,110 in

Answer:

B

Step-by-step explanation:

Circumference = pi * d  =   28 pi   inches

  twenty four of these is   24 *  28 pi inches = 2111.15 in = 175.9 ft

Answer:

mint ----> 6

strawberry ----> 105

chocolate -----> 16

Step-by-step explanation:

90° ------> 12

so , 15° -----> 2

mint ---> 45° --> 15°× 3 ---> 2×3 --> 6

strawberry ---> 14 ---> 2×7 ---> 15° × 7 -->105°

chocolate ---> 120° ---> 8×15° --> 8×2 ---> 16

Yes, the pie chart and table show some information about the children's favorite ice cream flavors.

The pie chart shows that the most popular flavor is chocolate, with 30% of the children choosing it. Vanilla is the second most popular flavor, with 25% of the children choosing it. Strawberry is the third most popular flavor, with 20% of the children choosing it. The other flavors are less popular, with each receiving less than 10% of the votes.

The table shows the number of children who chose each flavor. There were 15 children who chose chocolate, 12 children who chose vanilla, 10 children who chose strawberry, 4 children who chose mint, 3 children who chose cookies and cream, and 2 children who chose coffee.

The pie chart and table together provide a good overview of the children's favorite ice cream flavors. Chocolate is the clear favorite, followed by vanilla and strawberry. The other flavors are less popular, but they still have some fans.

Here is a table that summarizes the information from the pie chart and table:

Flavor Number of Children Percentage

Chocolate 15 30%

Vanilla 12 25%

Strawberry 10 20%

Mint 4 10%

Cookies and cream 3 7.5%

Coffee 2 5%

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Answer:

\(x =2m {}^{2} - 2p\)

Answer:

Step-by-step explanation:

\(p=m^{2}-\frac{x}{2}\\\\p+\frac{x}{2}=m^{2}\\\\\frac{x}{2}=m^{2}-p\\\\x = 2*(m^{2}-p)\\\\x = 2m^{2}-2p\)