A circle has radius 5 units and the equations of its two diameter are 2x-y=5 and x-3y+5=0.find the equations of the circle and show that it passes through the origin.​

Answer:

  $304.15

Step-by-step explanation:

The amount of interest earned can be found from the formula ...

  I = P((1 +r)^t -1)

  I = $815((1 +0.05)^6.5 -1) ≈ $815(0.373189) ≈ $304.15

Virgil's account will have earned about $304.15 in interest in 6.5 years.

Step-by-step explanation:

one gallon is 128oz.

1445 gallons are how many Oz?

that applies the same principle as every-day situations like "every guest will eat 2 dumplings. 12 guests are coming, so how many dumplings do I have to prepare ?"

or totally simple : "every child will get one gift. 4 children are coming, so how many gift do I have to prepare ?"

it all works with multiplication. it is the ultimate application for multiplication.

that is why we use "times" in normal language as in mathematical terms. like "it takes 3 screws to mount a leg to a table. and the table needs 4 legs. how many times do I need to fasten a screw to finish one table ?" well, 4 times 3 or 4×3 = 12 times.

and so, the answer to the original question is then I need to take the amount of one gallon 1445 times.

128 × 1445 = 184,960oz

We can check the convergence and divergence of a series by integral test followed by  Riemann zeta function.

Let f(x) = 1/(x⁵), where f(x) is a positive, continuous, and decreasing function for x ≥ 1.

Integrating f(x)with limit 1 to infinity, we get:

∫₁∞ 1/x⁵ dx = [-1/(4x⁴)]₁∞ = 1/4

As the integral converges, the series should converge by the integral test.

we can use the definition of the Riemann zeta function to have the value of the series,

ζ(s) = ∑n=1[infinity]1/nˢ

Taking s = 5, we get:

ζ(5) = ∑n=1[infinity]1/n⁵

Therefore, the value of the series is ζ(5) = 1.03693..., which is a mathematical constant that is approximately equal to 1.03693.

So, the series converges, and its value is ζ(5) = 1.03693.

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The congruence relation is used to define residue classes.

Congruence is an important idea in algebra that is often used to describe equivalence classes of integers modulo some integer n. A congruence relation on a set of integers is a binary relation that reflects equality modulo some integer n. Specifically, if a and b are two integers, then we say that a is congruent to b modulo n, or a ≡ b (mod n), if a - b is divisible by n.

The congruence relation is used to partition the set of integers into equivalence classes that are referred to as residue classes. Each residue class is represented by a single integer that is congruent to all the other integers in the class. In other words, a residue class is a collection of integers that have the same remainder when divided by n. There are exactly n residue classes modulo n, each of which is represented by a unique integer from 0 to n-1. Residue classes are used extensively in number theory and algebraic geometry, where they are used to study systems of equations and algebraic curves.

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Answer:

The Thompson family uses up a 1/2

gallon jug of milk every 3 days.

rate drink milk per day

Solution =1/2÷3

= 1/6

So the answer is 1/6

Step-by-step explanation:

Hope you have a great/Amazing day.

Answer:

The value of factorial of 10 is 3628800,

i.e. 10! = 10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1 = 3628800.

\(\large\huge\green{\sf{Answer:-}}\)

\(10! \: = 10 \times 9 \times 8 \times 7 \times 6 \times 5 \times 4 \times\\ 3 \times 2 \times 1 =3628800 \\ \)

All possible values of ∠U   to the nearest degree are 17° and 163°.

Given that u = 330 inches, t = 990 inches and ∠T = 68°.

We need to find all possible values of ∠U. Let's solve this using the law of sines.

First, we will write the law of sines. Law of Sines:

a/sin A = b/sin B = c/sin C

Here, we will use the formula to find the unknown angle U.

Then we will solve the resulting equation to get all possible values of ∠U.

Therefore, sin U/sin 68° = 330/990

Now we will cross multiply to solve for sin U

sin U = (sin 68° * 330) / 990

sin U = 0.2929

We can now find the value of U using the inverse sine function.

Hence, U = sin⁻¹(0.2929)

U = 17.29° or 162.71°

We have two solutions because there are two angles that have a sine of 0.2929.

Therefore, the possible values of ∠U are 17° and 163°.

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you should invest approximately $500,000 today at 9% simple interest to reach your retirement goal of $1,175,000 in 15 years.

To determine how much you should invest today at 9% simple interest to reach your retirement goal of $1,175,000 in 15 years, we can use the formula for simple interest:

A = P(1 + rt)

Where A is the future value, P is the principal (the amount you should invest today), r is the interest rate, and t is the time in years.

We can rearrange the formula to solve for P:

P = A / (1 + rt)

Plugging in the values, we have:

P = 1,175,000 / (1 + 0.09 * 15)

P = 1,175,000 / (1 + 1.35)

P = 1,175,000 / 2.35

P ≈ $500,000

Therefore, you should invest approximately $500,000 today at 9% simple interest to reach your retirement goal of $1,175,000 in 15 years.

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The marginal revenue function, locate the demand function is P = 0.02x² -0.025x + 152 when R'(x) = 0.06x² - 0.05x + 152.

Given that,

We have to find for the marginal revenue function, locate the demand function.

Remember that the income is zero if no things are sold:

R'(x) = 0.06x² - 0.05x + 152

p(x) is what.

We know that,

MR = dTR/dx = 0.06x² - 0.05x + 152

Integrating the marginal revenue function , we get total revenue function,

MR = TR

= (0.06x²⁺¹)/(2+1) - (0.05x¹⁺¹)/(1+1) + 152x

= (0.06x³)/3 - (0.05x²)/2 + 152 x

TR  = 0.02 x³ - 0.025 x² + 152 x

TR = (P)(Q) = (P)(x) =  0.02 x³ - 0.025 x² + 152 x

P = ( 0.02 x³ - 0.025 x² + 152 x)/x

P = 0.02x² -0.025x + 152

Therefore, The marginal revenue function, locate the demand function is P = 0.02x² -0.025x + 152 when R'(x) = 0.06x² - 0.05x + 152.

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In contrast to the fact that almost all time series contain a random component, certain time series do not.

A TIME SERIES IS WHAT?

A time series is a group of observations of clearly defined data points produced over time via repeated measurements. A time series would include, for instance, calculating the amount of retail sales for each month of the year. This is due to the well defined and regular measurement of sales income at uniformly spaced intervals. Time series data are not those that are irregularly or once collected.

Three parts can be separated out of a time series observation: the trend (long-term direction), the seasonal (systematic, calendar-related motions), and the irregular (unsystematic, short term fluctuations).

In mathematics, a time series is a collection of data points that have been indexed chronologically.

A time series is typically a sequence that was recorded at a number of evenly spaced points in time.

It is therefore a set of discrete-time data.

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Answer:

C a properly inflated and maintained tire

The speed of boat in still water is 15 m per hour.

What is speed?

The speed of an object, also known as v in kinematics, is the size of the change in that object's position over time or the size of the change in that object's motion per unit of time, making it a scalar quantity. The instantaneous speed is indeed the upper limit of a average speed as that of the length of the interval approaches zero. The average speed of the object in a period of time is equal to the distance travelled by object divided by duration of the period. Velocity and speed are not the same thing.

The dimensions of speed are time divided by distance.

Given, speed of lazy river current = 5

distance covered = 20 miles downstream

and 10 miles upstream

Let x be the speed in still water
(x+5)T = 20

(X-5)T= 10

2(X-5) = (X+5)

X = 15

Therefore, speed of the boat in still water is 15 m per hour

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a) The effective rate of interest on a mortgage at 8.15 percent compounded semi-annually is 8.23 percent.

b) It will take approximately 54.4 years to save $1,000,000 for retirement with $200 monthly deposits at 6 percent interest compounded monthly.

a) To find the effective rate of interest, we use the formula: Effective Rate = (1 + (Nominal Rate / Number of Compounding Periods))^Number of Compounding Periods - 1.

For a mortgage at 8.15 percent compounded semi-annually, the nominal rate is 8.15 percent and the number of compounding periods is 2 per year.

Plugging these values into the formula, we get Effective Rate = (1 + (0.0815 / 2))^2 - 1 ≈ 0.0823, or 8.23 percent. Therefore, the effective rate of interest on the mortgage is 8.23 percent.

b) To determine how long it will take to save $1,000,000 for retirement with $200 monthly deposits at 6 percent interest compounded monthly, we can use the formula for the future value of an ordinary annuity: FV = P * ((1 + r)^n - 1) / r, where FV is the future value, P is the monthly deposit, r is the monthly interest rate, and n is the number of periods.

Rearranging the formula to solve for n, we have n = log(FV * r / P + 1) / log(1 + r). Plugging in the values $1,000,000 for FV, $200 for P, and 6 percent divided by 12 for r, we get n = log(1,000,000 * (0.06/12) / 200 + 1) / log(1 + (0.06/12)) ≈ 54.4 years.

Therefore, it will take approximately 54.4 years to save $1,000,000 for retirement under these conditions.

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The number of minutes required to wash 12 windows is 8 4/7 minutes.

According to the given question.

You can wash one window in 15 minutes, so each minute you can wash 1/15.

Your sister can wash one window in 20 minutes, so each minute the sister can wash 1/20.

If working together you can wash 1/15 + 1/20 = 7/60.

Hence, the time required to wash 12 windows together

= 12 × 7/60

= 8 4/7 minutes.

Therefore, the number of minutes required to wash 12 windows is 8 4/7 minutes.

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-10 is the correct answer.

Answer:

D. -10

I have to make this more the 20 characters...

The degrees of freedom are in a t test. Degrees of freedom refer to the number of values in a statistical calculation that are free to vary. In a paired t test, the degrees of freedom are calculated as the number of pairs minus 1.

In the case of using pairs of identical twins in an experimental design for a paired t test, each twin in the pair would be considered one observation. So if we have N pairs of identical twins, we would have a total of 2N observations. Since each pair of twins is considered one observation in the t test, we would have N pairs of observations. Therefore, the degrees of freedom in this t test would be N - 1.

In summary, for an experimental design using pairs of identical twins in a paired t test, the degrees of freedom would be equal to the number of pairs of twins minus 1. This is because each pair of twins is considered one observation in the t test.

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6) m<ABC = m<ABK + m<CBK

157° = (4x + 10) + (14x +3)

157° = 18x + 13

x = 8°

m<CBK = 14(8°) + 3

m<CBK = 115°

7) am not sure, i think b

In the given word problem, the rate of change is the change in the cost of the ice cream concerning the change in the number of scoops.

That is, the rate of change is the ratio of the change in the cost of ice cream and the change in the number of scoops. Let's first calculate the initial rate of change or slope of the given deal: When we buy a waffle cone, the cost is $3, and we can buy one scoop of ice cream for $1.50.So, for one scoop of ice cream, the total cost would be 3 + 1.50 = $4.50.

We can represent the cost of one scoop of ice cream with the help of a linear equation: y = mx + b. Here, the slope or the rate of change, m = Change in cost of ice cream/ Change in the number of scoops= 1.5/1= 1.5Therefore, the rate of change of the ice cream with respect to the number of scoops is $1.50/scoop.

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The 95% confidence interval for the difference in mean heights of professional football and basketball players is (-0.517, -0.023) feet.

To find a 95% confidence interval for the difference in mean heights between professional football and basketball players, we can use the formula for the confidence interval:

CI = (X1 - X2) ± t * sqrt((s1^2 / n1) + (s2^2 / n2))

Where:

X1 and X2 are the sample means (6.18 feet for football players and 6.45 feet for basketball players).

s1 and s2 are the sample standard deviations (0.37 feet for football players and 0.31 feet for basketball players).

n1 and n2 are the sample sizes (45 for football players and 40 for basketball players).

t is the critical value for a 95% confidence level.

First, we need to calculate the critical value t. Since the sample sizes are relatively large, we can use the Z-distribution instead of the t-distribution. For a 95% confidence level, the critical value is approximately 1.96.

Now we can calculate the confidence interval:

CI = (6.18 - 6.45) ± 1.96 * sqrt((0.37^2 / 45) + (0.31^2 / 40))

CI = -0.27 ± 1.96 * sqrt(0.0082 + 0.007675)

CI = -0.27 ± 1.96 * sqrt(0.015875)

CI = -0.27 ± 1.96 * 0.126

CI = -0.27 ± 0.247

CI = (-0.517, -0.023)

The 95% confidence interval for the difference in mean heights of professional football and basketball players is (-0.517, -0.023) feet.

Since the confidence interval includes negative values, it suggests that the average height of football players tends to be shorter than the average height of basketball players. However, it's important to note that this conclusion is based on the sample data and there is still some uncertainty due to sampling variability.

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As a result, for the same data set, a 99% confidence interval would have a greater margin of error than a 90% confidence interval.

Answer: If a 90% confidence interval is constructed based on a sample of data, and it is 74% + 3%, a 99% confidence interval based on this same sample of data would have a larger margin of error and probably a different center.

What is a confidence interval? A confidence interval is a statistical technique used to establish the range within which an unknown parameter, such as a population mean or proportion, is likely to be located. The interval between the upper and lower limits is called the confidence interval. It is referred to as a confidence level or a margin of error.

The confidence level is used to describe the likelihood or probability that the true value of the population parameter falls within the given interval. The interval's width is determined by the level of confidence chosen and the sample size's variability. The confidence interval can be calculated using the standard error of the mean (SEM) formula

.A 90% confidence interval indicates that there is a 90% chance that the interval includes the population parameter, while a 99% confidence interval indicates that there is a 99% chance that the interval includes the population parameter.

When the level of confidence rises, the margin of error widens. The center, which is the sample mean or proportion, will remain constant unless there is a change in the data set. Therefore, alternative A is the correct answer.

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Answer:

The slope is -2

Step-by-step explanation:

11-5 = -6, 7-4=3    -6/3 = -2

From linear equations solution, janeen will need to work total 22.699 hours per week for make equal the amount that shari makes in a week.

We two persons named janeen and shari.

number of hours worked by janeen in a week = 20 hours

Amount of money janeen earned after working 20 hours in a week = $24.92

Number of hours worked by shari in a week = 12 hours

Let Janeen make amount in dollars = $x per hour

Shari make amount in dollars= $y per hour.

According to seniror, 12y - 20x = $24.92 --(1)

Shari makes one dollar less than twice the amount that Janeen makes per hour

=> y = 2x - 1 ---- (2)

Now, we have to linear equations and we have to solve these for determining the values of x and y. So, substitute value of y from equation (2) in (1)

=> 12 (2x -1) - 20x = 24.92

=> 24x - 12 - 20x = 24.92

=> 4x = 24.92 + 12

=> 4x = 36.92

=> x = 9.23

Therefore, Janeen earns $9.23 per hour.

Then, y = 2x-1

=> y = 2× 9.23 -1

=> y= $17.46

Now, shari makes in a week = $17.46 × 12

=$209.52

Janeen makes in a week = 20× $9.23

= $184.6

Janeen need to work to equal the amount that shari makes in a week = \(\frac{209.52}{9.23}\)

= 22.699

Hence, required value is 22.699 hours.

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Answer:

The missing fraction is 6/12

(you can further simplify this but the question requires that you don't do that)

Step-by-step explanation:

To add fractions easily, their denominators should have the same value, so the denominator should be 12,

Then, to get 16 in the numerator, we need to find a number that on adding to 10, gives 16, or,

10 + x = 16

x = 16 - 10

x = 6

So, the numerator should be 6

so we get the fraction, 6/12

We can also solve it in an alternate way,

\(10/12 + x = 16/12\\x = 16/12 - 10/12\\x = (16-10)/12\\x = 6/12\)

Answer:

$15 will be the correct answer!

Step-by-step explanation:

250 x 0.06 = 15

Answer:

$15

Step-by-step explanation:

6% = 0.06

0.06 x 250 = 15

Answer:

25.5

Step-by-step explanation:

85/100*30

25.5

Hope this helps!

Answer:

25.5

Step-by-step explanation:

The equation of the line that passes through the point (5,3) and has a slope of -4/5 is,

⇒ 4x + 5y = 35

Here,

The given point is (5, 3) and slope is -4/5.

We have to find the equation of the line that passes through the point (5,3) and has a slope of -4/5.

What is Equation of line?

The equation of the line that passes through the point (a, b) and has a slope of m is;

⇒y - a = m (x - b)

Now,

The given point is (5, 3) and slope is -4/5.

Hence, The equation of the line that passes through the point (5,3) and has a slope of -4/5 is;

y - 3 = -4/5 (x - 5)

5 (y - 3) = -4 (x - 5)

5y - 15 = -4x + 20

4x + 5y = 20 + 15

4x + 5y = 35

Therefore, The equation of the line that passes through the point (5,3) and has a slope of -4/5 is

⇒ 4x + 5y = 35.

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The maximum level of net benefits is 1250, and this occurs at a level of Y equal to 10. We first need to understand the terms and equations given in the study. B(Y) represents the total benefit of producing Y units of automobiles and C(Y) represents the total cost of producing Y units of automobiles.

MB represents the marginal benefit of producing one additional unit of automobiles and MC represents the marginal cost of producing one additional unit of automobiles. Using marginal analysis, we can determine the level of Y that will yield the maximum level of net benefits. This occurs when MB = MC. In this case, 180 – 12Y = 6Y, which simplifies to Y = 7.5. Therefore, the level of Y that will yield the maximum level of net benefits is 7.5 units of automobiles. To determine the maximum level of net benefits, we need to calculate the difference between the total benefit and total cost at the level of Y that yields the maximum net benefits. B(7.5) = 235(7.5) – 4(7.5)^2 = 1321.875 and C(7.5) = 7(7.5)^2 = 393.75. Therefore, the maximum level of net benefits is B(7.5) – C(7.5) = 928.125.

In summary, the level of Y that will yield the maximum level of net benefits is 7.5 units of automobiles and the maximum level of net benefits is 928.125. This is determined using marginal analysis and the equations B(Y), C(Y), MB, and MC provided in the study. To determine the maximum level of net benefits and the level of Y that will yield that result, we need to find the point where the marginal benefit (MB) equals the marginal cost (MC). This is because at this point, the net benefits are maximized.

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The expression for the probability density function of the Weibull distribution will be: f(x) = k * x^(k-1) * e^(-x^k)

The expression for the probability density function (pdf) of a Weibull distribution is given by:

f(x) = k * x^(k-1) * e^(-x^k)

where:

x is the random variable

k is the shape parameter, which determines the shape of the distribution

e is the base of the natural logarithm

The shape parameter can take on any positive value, and the distribution is typically characterized by a shape that is either increasing or decreasing, depending on the value of k.

If the value of the k is less than 1, the distribution has a decreasing hazard rate, indicating that the failure rate decreases over time.

If the value of the k is greater than 1, the distribution has an increasing hazard rate, indicating that the failure rate increases over time.

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Answer: \(\frac{1}{27}\)

Step-by-step explanation:

Anything to the third power means it is multiplied by itself 3 times.

   --> \((\frac{1}{3})^{3} =(\frac{1}{3})(\frac{1}{3})(\frac{1}{3})=\frac{1}{27}\)

Answer: The answer is x=6, the final set of (x,y) values are (6,-4)

Step-by-step explanation:

You must move around the equation to get it to y= mx+b to find the (x,y) values

Since you know y=-4 since it is stated above, plug in -4 for all y values and solve.

1. 6x+ 7(-4) =4x +4(-4)

2. 6x -28= 4x -16

3. 2x-28=-16

4. 2x=12

5. x=6