Fully simplify. -15xy(15x^5y^3)

Answer:

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

Given:

To find the arc measure (θ) in radians, we can use the formula:

Now, plug in the given values:

To solve for θ, divide both sides by 4:

Simplify the expression:

So, the arc measure (θ) is 2π/3 radians

The standard error is of 0.2246, which means that the mean scores for samples of 30 vary around 0.2246 from the mean.

The confidence interval is the range of values that you expect your estimate to fall between a certain percentage of the time if you run your experiment again or re-sample the population in the same way.

The confidence interval formula is \(\bar x\pm t\frac{s}{\sqrt{n}}\).

Where, \(\bar x\) is the sample mean, t is the critical value, n is the sample size and s is the standard deviation for the sample.

Here,

\(\bar x\) =1.267, s=1.23, n=30

The standard error is Se= 1.23/√30

= 0.2246

Item a:

The standard error is of 0.2246, which means that the mean scores for samples of 30 vary around 0.2246 from the mean.

Item b:

Using a t-distribution calculator, considering a confidence level of 0.99 with 30 - 1 = 29 df, the critical value is t = 2.7564.

\(\bar x\pm tS_c\)

\(\bar x+ tS_c\) =1.267-2.7564(0.2246) =0.6479

\(\bar x- tS_c\) =1.267+2.7564(0.2246) =1.8861

Therefore, the 99% confidence interval to estimate the true mean score on this question is (0.6479, 1.8861). It means that we are 99% that the true mean score of all students in this question is between 0.6479 and 1.8861.

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Answer: X axis , Y axis , y=-2

Step-by-step explanation:

Answer:

a) 2

b) 2x, -13

c) 2, -13

Step-by-step explanation:

Term means mathematical equations that are separated by arithmetic symbols like (+,-,x,/).

For example, there is 2 terms in the following example because there is two values separated by arithmetic symbols: 3x+5.

More examples of terms: 7, 5x, x, \(7x^2\), \(x^2\)

Coefficient means the value that you multiply the variable by. The coefficient in the variable: 5x is 5 because you are multiplying x by 5.

Answer

its confusing

Step-by-step explanation:

Answer:342.084

Step-by-step explanation:

If the temperature was 87 degrees, the energy consumption would be approximately 341.184.

The equation provided is:

y = 3.317x + 53.505

where:

y represents energy consumption

x represents temperature

You want to determine the energy consumption when the temperature is 87 degrees (x = 87).

Plug the value of x into the equation:

y = 3.317 * 87 + 53.505

Now, perform the calculations:

y = 287.679 + 53.505

y = 341.184

So, if the temperature was 87 degrees, the energy consumption would be approximately 341.184.

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Answer: 1st Person

Step-by-step explanation: Mia is talking about herself

Answer:

1st person point of view

Step-by-step explanation:

Emily is 4 times as old as Tiffany. In ten years time, Emily will be twice as old as Tiffany. Find their ages.

\(4x + 10 = 2(x + 10) \\ = 4x + 10 = 2x + 20 \\ = > 4x - 2x = 20 - 10 \\ = > 2x = 10 \\ = > x = \frac{10}{2} \\ = > x = 5\)

Emily's age is 20 years and Tiffany's age is 5 years.

Hope it helps!

Answer:

1/8

Step-by-step explanation:

1/4 ÷ 2

~Turn 2 into a fraction

1/4 ÷ 2/1

~Copy dot flip

1/4 * 1/2

~Multiply

1/8

Best of Luck!

Answer:

1/8

Step-by-step explanation:

1/4 also = 2/8

2/8 divided by 2 = 1/8

Answer:

D

Step-by-step explanation:

Answer:

poin J is (-3,-2.5)

point L is (2.5,3)

x-cord for M is 3

x-cord for K is -2.5

The starting principal of the loan based on the amortization schedule is $150,000 with periodic payments of $966.45, made up of both interest and debt repayment.

Arranging the amortization schedule properly as below shows that the balance after the first loan repayment is $149,783.55.

The repayment amount in the first period is $216.45.

When the loan balance after the first loan repayment is added to the first loan payment, it gives a total of $150,000 ($149,783.55 + 216.45), being the initial or starting loan principal.

Payment #  Payment  Interest  Debt Payment    Balance

1                    966.45      750.00      216.45         149,783.55

2                   966.45      748.92      217.53          149,566.01

3                   966.45                                            

y = Balance + Debt Payment for Period 1

= $150,000 ($149,783.55 + 216.45)

We can also compute the monthly interest rate as ¹/₂% ($750/$150,000 x 100), while the annual interest rate is 6% (12 x ¹/₂%).

Thus, the starting principal of the loan based on the amortization schedule is $150,000.

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Answer:

The volume will be 64 times larger.

Explanation:

When you multiply two single dimensions, such as length and width, the units will change from units to units squared (example: 2 ft * 2 ft = 4 ft^2). Similarly, When you multiply three single dimensions the units will change from units to units cubed (example: 2 ft * 2 ft * 2 ft = 8 ft^3). You can use the exponents as a trick to solve this type of question. For example, in this case, volume means that you are multiplying three single dimensions. Therefore, the end result will be units cubed. If each dimension is multiplied by four, you can cube the factor to find how many times larger the volume will be: 4^3 = 64.

TLDR: Since there are three dimensions, multiply 4 by itself three times to get the answer: 4 * 4 * 4 = 64.

In case I explained it badly, here is a more mathematical method to find the answer:

The formula for volume:

V = l * w * h

When you multiply each dimension by 4:

V = (4 * l) * (4 * w) * (4 * h)

Rearrange with the Commutative Property of Multiplication:

V = (4 * 4 * 4) * (l * w * h)

Simplify:

V = 64 * l * w * h

Therefore, the volume is 64 times greater.

Answer:

Step-by-step explanation:

Given function is, \(f(x)=\frac{x^2-3x+2}{x-2}\)

Factors of the numerator = x² - 3x + 2

                                          = x² - 2x - x + 2

                                          = x(x - 2) - 1(x - 2)

                                          = (x - 2)(x - 1)

Therefore, given function will be,

f(x) = \(\frac{(x-2)(x-1)}{(x-2)}\)

For (x - 2) = 0

For x = 2, denominator will become zero.

Thus for input value x = 2, function will not be defined.

If x ≠ 2, f(x) = x - 1

It's a linear function represented by f(x) = x - 1

Having slope = 1 and y-intercept = -1

And (2, 1) is a hole as shown in the graph.

Answer:

One that looks like this.

Step-by-step explanation:

Answer:

$690

Step-by-step explanation:

600 [1 + (0.03 * 5)]= 690

Answer:

$690 Try calculatorsoup dot com Total P+I (A)?

Step-by-step explanation:

As a result, 68% of the data falls into the range of values between -1 and 1, which is one standard deviation from the mean. The closest estimate of the solution is 68%.

A mathematical equation is a formula that connects two claims and uses the equals symbol (=) to denote equivalence. An equation in algebra is a mathematical statement that establishes the equivalence of two mathematical expressions. For instance, in the equation 3x + 5 = 14, the equal sign places a space between the variables 3x + 5 and 14. The relationship between the two sentences that are written on each side of a letter may be understood using a mathematical formula. The symbol and the single variable are frequently the same. as in, 2x - 4 equals 2, for instance.

For a normally distributed data set with a mean of 0 and a standard deviation of 0.5, the proportion of values between -1 and 1 is most closely related to 68%.

Approximately 68% of the data in a normal distribution lies within one standard deviation of the mean, which explains why. One standard deviation below the mean is -0.5, and one standard deviation above the mean is 0.5 since the mean is 0 and the standard deviation is 0.5. As a result, 68% of the data falls into the range of values between -1 and 1, which is one standard deviation from the mean. The closest estimate of the solution is 68%.

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The estimate of 179% of 41 by rounding is about 73.19.

To find this estimate, first convert the percentage to a decimal by dividing it by 100: 179/100 = 1.79. Then, multiply this decimal by 41: 1.79 * 41 = 73.39.

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Answer:

Step-by-step explanation:

(2+10)/2 = 12/2= 6

(2+8)/2 = 10/2= 5

(6,5)

The required rate of simple interest is 1.75%.

Here, we have,

(Principal + Interest) is a straightforward interest equation.

A = P(1 + rt)

Where: A is the sum of the accrued principal and interest.

Principal Amount is P.

I is the interest rate.

r is the annual percentage rate of interest, or R/100.

R is the annual percentage rate of interest; R = r * 100 t is the length of time involved in months or years.

Since I = Prt,

the initial formula A = P(1 + rt) evolved from A = P + I to A = P + Prt,

which may be represented as A = P(1 + rt).

Given: Principal is $1,300

Rate is 7% and the amount earned that is A-P is $159.25.

A = P(1 + rt)

Therefore substituting the values in the above mentioned equation, we get:

159.25= 1300(1+r×7)

On solving we get,

r= 1.75%

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complete question:

At the Blue Bank, Barry would earn $159.25 in simple interest in 7 years after depositing $1,300.

What rate of simple interest is offered at the

Blue Bank?

Let's make another angle y

Where y= 51° (corresponding angles )

and x+y= 180°. ( linear pair )

x+51°= 180° (y=51°)

x=180°-51°

x= 129°

So the value of x is 129°

Hope you got your answer !

Answer:

129°

Step-by-step explanation:

x and 51° are corresponding angles, therefore their sum is 180°

so x= 180° -51°= 129°

Answer: \((f \cdot g)(x) = x^4-11x^2+30.\)

Step-by-step explanation:

We want to find the value of \(f(g(x)).\) To do this, we plug in \(g(x)\) into the expression for \(f(x).\) This gives us:

\(f(g(x)) = (x^2-9)^2+7(x^2-9)+12 = x^4-18x^2+81+7x^2-63+12 = \boxed{x^4-11x^2+30}.\)

Answer:

Step-by-step explanation:

Since he is his own boss, he is basically a self employed taxpayer and should be to deduct the employer portion of self employment taxes that he/she pays during the year.

In a case like this, the total self employment taxes are $7,771 x 50% = $7,771 * 0.5 = $3,885.50. This money also now, is corresponding to employer taxes (the other 50% are not deductible since they correspond to employee taxes).

Self employment taxes composes but not limited to Medicare and Social Security taxes (FICA taxes basically).

The function f has a real zero between -1 and 0. Therefore, statement c) is true.

To evaluate the function for the given values of a and b, we can plug in the values of a and b into the function and solve.

For a=-1, we get:

For b=0, we get:

Therefore, f(-1) and f(0) have opposite signs (one is positive and one is negative).

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a) The distance of the stone above ground level at time t :

d(t)= -4.9t² + 950

b) It takes 13.92 seconds the stone to reach the ground

c)  With 136.42 m/s velocity the stone strikes the ground.

d) If the stone is thrown downward with a speed of 8 m/s, it will take 13.13 seconds to reach the ground

Here, a  stone is dropped from the upper observation deck of a tower, 950 m above the ground.

(a)  the distance of the stone above ground level at time t would be,

d(t)  = 0.5 (-9.8) t² + v(0) t + d(0)

      = (-4.9)t² + 0t + 950

      = -4.9t² + 950

(b) Now we find the time the stone takes to reach the ground.

i.e., the value of 't' when d = 0

Substituting d(t) = 0 in the above equation.

-4.9t² + 950 = 0

t² = (-950) / (-4.9)

t² = 193.88

t = 13.92 seconds

(c) We need to find the velocity the stone takes to strike the ground

i.e., the velocity when t  = 13.92 seconds

v(t) = v(0) + gt      

v(13.92) = 0 + (9.8)(13.92)

v = 136.42 m/s

(d) here, v(0) = -8 m/s  

Velocity is negative because stone is being thrown downward.

d(t) = 0

(-4.9)t² + v(0) t + d(0) = 0

(-4.9)t² -8t + 950 = 0

Using the quadratic formula we solve above equation for,

t = -14.76, 13.13

We can disregard the negative solution

So, we get t = 13.13 seconds.

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The probability that the cars selected consist of 2 midsized cars and 4 compact cars is approximately 0.2723 or 27.23%.

What is Probability?

Probability is a measure of the likelihood or chance of an event occurring. It is a number between 0 and 1, with 0 indicating that the event is impossible and 1 indicating that the event is certain. The probability of an event can also be expressed as a percentage between 0% and 100%.

We can use the formula for combinations:

nCk = n! / (k! * (n-k)!)

where n is the total number of objects, k is the number of objects being selected, and ! represents the factorial function.

In this case, there are 11 midsized cars and 12 compact cars, so n = 23. We want to select 6 cars consisting of 2 midsized cars and 4 compact cars, so k1 = 2 and k2 = 4.

The probability of selecting exactly 2 midsized cars and 4 compact cars is equal to the number of ways to select 2 midsized cars from 11 multiplied by the number of ways to select 4 compact cars from 12, divided by the total number of ways to select 6 cars from 23:

P(2M, 4C) = (11C2 * 12C4) / 23C6

where nCk represents the number of combinations of k objects from a set of n objects.

Evaluating this expression gives:

P(2M, 4C) = (55 * 495) / 100947

P(2M, 4C) ≈ 0.2723

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Trawler B should take a course that is 18 degrees east of north.

In order to intercept Trawler A, Trawler B must travel in a direction that will bring it closer to Trawler A. Since Trawler A is traveling due west, Trawler B must travel in a direction that is east of north. The angle that is 18 degrees east of north will bring Trawler B closest to Trawler A.

Here are the steps to find the course that Trawler B should take:

Draw a diagram of the situation.

Label the two trawlers A and B.

Draw a line representing the direction that Trawler A is traveling.

Draw a line representing the direction that Trawler B should travel.

Measure the angle between the two lines.

The angle between the two lines will be 18 degrees. Therefore, Trawler B should take a course that is 18 degrees east of north.

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Answer: 180 gallons needed

Step-by-step explanation:

Zykeith,

Assume x gallons of 50% antifreeze is needed

Final mixture is x + 60 gallons

Amount of antifreeze in mixture is 0.4*(x+60)

Amount of antifreeze added is .5x + .1*60 = .5x + 6

so .5x + 6 = .4(x + 60)

.5x -.4x = 24 -6

.1x = 18

x = 180

Let x be the number of gallons of the 50% antifreeze solution needed. We know that the resulting mixture will be 70 + x gallons. To get a 40% antifreeze mixture, we can set up the following equation:

\({\implies 0.5x + 0.1(70) = 0.4(70 + x)}\)

Simplifying the equation:

\(\qquad\implies 0.5x + 7 = 28 + 0.4x\)

\(\qquad\quad\implies 0.1x = 21\)

\(\qquad\qquad\implies \bold{x = 210}\)

\(\therefore\) We need 210 gallons of the 50% antifreeze solution to mix with 70 gallons of 10% antifreeze to get a mixture that is 40% antifreeze.

\(\blue{\overline{\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad}}\)