\(120 divided by 1800\)120 divided by 1800

\(\dfrac{(2 x^{-3} y^{-2})^5}{(6x^{-1} y^{-8})^2}\\\\\\=\dfrac{32x^{-15} y^{-10}}{36 x^{-2} y^{-16}}\\\\\\=\dfrac{8}{9} \left(\dfrac{x^{-15}}{x^{-2}} \right) \left(\dfrac{y^{-10}}{y^{-16}} \right)\\\\\\=\dfrac 89 \left(x^{-15+2} \right) \left(y^{-10 +16} \right)\\\\\\=\dfrac 89 \cdot x^{-13} \cdot y^6\\\\\\=\dfrac{8y^6}{9x^{13}}\)

After four hours, the height of the candles will be the same.

A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.

The linear equation is given as,

y = mx + c

Where m is the slope of the line and c is the y-intercept of the line.

A red candle has an 8-inch height and burns at a 7/10-inch per hour rate. A 6-inch tall blue candle burns at a rate of 1/5 inch per hour.

Let x be the number of hours and y be the height.

y = -0.70x + 8           ...1

y = -0.20x + 6             ...2

From equations 1 and 2, then we have

- 0.20x + 6 = - 0.70x + 8

(0.70 - 0.20)x = 8 - 6

0.50x = 2

x = 4 hours

After four hours, the height of the candles will be the same.

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The balance in the fund at the end of 23 years, with monthly deposits of $1,150 and a 3.25% annual interest rate, is approximately $449,069.51. The amount of interest earned over the period is approximately $420,630.49.

a. The balance in the fund at the end of the 23-year period, considering a monthly deposit of $1,150 and an annual interest rate of 3.25% compounded annually, is approximately $449,069.51.

To calculate the balance, we can use the formula for compound interest:

A = P(1 + r/n)^(nt)

Where A is the accumulated balance, P is the monthly deposit, r is the annual interest rate, n is the number of compounding periods per year, and t is the number of years.

In this case, we have monthly deposits, so we need to convert the annual interest rate to a monthly rate:

Monthly interest rate = (1 + 0.0325)^(1/12) - 1 = 0.002683

Using this monthly interest rate, we can calculate the accumulated balance over the 23-year period:

A = 1150 * [(1 + 0.002683)^(12*23) - 1] / 0.002683 = $449,069.51

Therefore, the balance in the fund at the end of the 23-year period is approximately $449,069.51.

b. The amount of interest earned over the 23-year period can be calculated by subtracting the total deposits from the accumulated balance:

Interest earned = (Monthly deposit * Number of months * Number of years) - Accumulated balance

Interest earned = (1150 * 12 * 23) - 449069.51 = $420,630.49

Therefore, the amount of interest earned over the 23-year period is approximately $420,630.49.

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Answer:

6 * 1/9

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

6/9 = 0.66666666666666666666666666666667

6 * 1/9 = 0.66666666666666666666666666666667

The length of the radius AB is 6 units.

The angle ∠BAC is 90 degrees. The length of arc BC is 3π. The length of  

radius AB can be found as follows:

Hence,

length of arc = ∅ / 360 × 2πr

where

Therefore,

length of arc = 90 / 360 × 2πr

3π = 1 / 4 × 2πr

cross multiply

12π = 2πr

divide both sides by 2π

r = 6 units

Therefore,

radius AB = 6 units

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the monthly payment of $ 668.75 will be paid for the loan for the car.

Total payment for the car = $ 27,635

Money for down payment = $ 5000

Interest for 3 year loan = 6.36 %

Amount on which this interest will be applied = $ 27,635 - $ 5000

Amount = $ 22,635

Interest = 6.36 % of $ 22,635

Interest = 6.36 / 100 × $ 22,635

Interest = 1440 (approx.)

Total amount of loan = $ 22,635 + $ 1440

= $ 24075

Number of months = 3 × 12 = 36 months

So, monthly payment = $ 24075 / 36
= $ 668.75

Therefore, we get that, the monthly payment of $ 668.75 will be paid for the loan for the car.

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Answer:

-120

Step-by-step explanation:

subtract 45 to both sides

m/8 = -15

multiply by 8 on both sides.

with the fraction just multiply by the bottom number to make m by itself.

m = -15*8

m= -120

Answer:

-120

Step-by-step explanation:

30-45= -15

-15×8= -120

Ben can plot the residuals, create a histogram and Q-Q plot, or use statistical tests such as the Shapiro-Wilk test.

To test for the normality of residuals in a multiple regression model, Ben can use several methods. Here are a few options:

Plot the residuals: Ben can create a scatter plot of the residuals against the predicted values. If the residuals are normally distributed, they should be evenly scattered around the zero line. If there is a pattern or if the residuals are skewed, this indicates non-normality.

Histogram and Q-Q plot: Ben can create a histogram of the residuals and compare it to a normal distribution. He can also create a Q-Q plot (quantile-quantile plot), which compares the quantiles of the residuals to the quantiles of a normal distribution. If the residuals are normally distributed, they should fall along the diagonal line in the Q-Q plot.

Statistical tests: Ben can use statistical tests to formally test for normality of residuals. One commonly used test is the Shapiro-Wilk test, which tests whether the residuals are drawn from a normal distribution. If the p-value is greater than 0.05, Ben can conclude that the residuals are normally distributed.

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(a) Example question: "How often do you look at social media while doing schoolwork?

(b) Sofie can select a simple random sample of students by using a random number generator to assign a unique identification number to each student in the online high school.

(c) The sample for Sofie's research is the 32 completed surveys she received. These surveys represent the responses of a subset of the population. The population, in this case, refers to all the students at the online high school.

(d) If Sofie uses only the completed surveys, she can conclude that approximately 50% (16 out of 32) of the students who completed the survey reported using social media while doing schoolwork.

(a) Please select one of the following options: never, rarely, occasionally, frequently, or always."

(b) She can then use the random number generator again to select a specific number of students from the entire population of students, ensuring that each student has an equal chance of being selected. For example, if there are 500 students in total and Sofie wants a sample size of 50, she can generate 50 random numbers and select the corresponding students based on their identification numbers.

(d) However, it is important to note that this conclusion is specific to the sample of completed surveys and cannot be generalized to the entire population of high school students.

To make an inference about the percent of all high school students who use social media while doing schoolwork, Sofie would need a larger and more representative sample that covers a wider range of students in the online high school.

Additionally, she should consider potential biases in the sample, such as non-response bias if the students who chose not to complete the survey have different social media usage patterns compared to those who did respond.

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Answer:

\( {x}^{2} - 6x = - 13\)

Step-by-step explanation:

\(8 {x}^{2} - 48x = - 104\)

We want the a-term to be 1.

Divide the whole equation by 8.

\( \frac{8}{8} {x}^{2} - \frac{48}{8} x = - \frac{104}{8} \\ {x}^{2} - 6x = - 13\)

Answer:

Step-by-step explanation:

the first one is -6x and -13

the seconds one is 9 and 9

Answer:

pls rephrase ill answer in the comments

Answer:

118%

Step-by-step explanation:

weight at first visit = 550g

weight at 2nd visit = 550 + 350 = 900g

weight at 3rd visit = 900 + 300 = 1200g

Percentage increase = \(\frac{1200-550}{550} \times100=118.181818...\) = 118%

The maximum possible order for an element of S₅ is 60.

To find the maximum possible order for an element of S₅, we need to consider all possible disjoint cycles and calculate their least common multiple (LCM).

In S₅, the possible cycle lengths are 1, 2, 3, 4, and 5.

For a cycle of length 1, the element remains fixed and has an order of 1.

For a cycle of length 2, the element repeats itself every 2 steps and has an order of 2.

For a cycle of length 3, the element repeats itself every 3 steps and has an order of 3.

For a cycle of length 4, the element repeats itself every 4 steps and has an order of 4.

For a cycle of length 5, the element repeats itself every 5 steps and has an order of 5.

Now we need to calculate the LCM of these orders: 1, 2, 3, 4, 5.

The LCM of 1, 2, 3, 4, and 5 is 60.

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The sum of the sequence \((-1)^{-10} +(-1)^{-9} +(-1)^{-8} +\cdots+ (-1)^9+ (-1)^{10}\) is 1

Consider given sequence \((-1)^{-10} +(-1)^{-9} +(-1)^{-8} +\cdots+ (-1)^9+ (-1)^{10}\)

here, the dots . . . means that there are 21 numbers being added, one for each integer from −10 to 10.

We need to find the sum.

We can observe that the above sequence is a geometric sequence with the common ratio r = -1 and the first term a1 = \((-1)^{-10}\) i.e., a1 = 1

We know that the formula of the sum of n-terms of a geometric sequence is:

\(S_n= a_1 \times (\frac{1-r^n}{1 -r} )\)

For n = 21, r = -1 and a1 = 1

\(S_{21}=1 \times (\frac{1-(-1)^{21}}{1-(-1)} )\\\\S_{21 }= 1\times (\frac{1-(-1)}{1 +1} )\\\\S_{21 }=\frac{1+1}{2} \\\\S_{21 }= \frac{2}{2} \\\\S_{21 }= 1\)

Therefore, \((-1)^{-10} +(-1)^{-9} +(-1)^{-8} +\cdots+ (-1)^9+ (-1)^{10}\) = 1

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Answer:

x = 68

y = 90

Step-by-step explanation:

The angles inside any quadrilateral add up to 360

For the first shape, it is a parallelogram, meaning the opposite angles are equal.

360 - 112 - 112 = 2x

2x = 136

x = 68

Second shape:

z = 360 - 110 - 85 - 75

z  = 90 <- y is the outside angle, meaning y is not (always) equal to z

y = 180 - z

y = 90

Answer:

for e, x = 68

i dont know where the x is on f.. but the missing inner angle should be 90

Step-by-step explanation:

the parallel lines means that the opposite interior angles are the same, so 112 + 112 = 224

360 - 224 = 136

136 ÷ 2 = 68

Answer:

If I'm correct I think its answer B

Step-by-step explanation:

I'm not sure but i hope this help

Answer:

second option

-∞ < x < 1

Step-by-step explanation:

The rate at which the water level is rising when the water level is 6 cm is approximately 2.67 cm/s. if an inverted pyramid is filled with water at a constant rate of 55 cubic centimeters per second, the top of pyramid is in square shape with length of 8 cm and height of 14 cm.

Let's call this rate "r".

Volume of pyramid = (1/3) * base area * height

Since the pyramid has a square base, the base area is given by

Base area = (side length)^2

Substituting the given values

Base area = (8 cm)^2 = 64 cm^2

Height = 14 cm

V = (1/3) * 64 cm^2 * 14 cm = 298.67 cm^3

We know that the water is being added to the pyramid at a constant rate of 55 cm^3/s. Therefore, the rate at which the volume is increasing is

dV/dt = 55 cm^3/s

We also know that the volume of water in the pyramid at any given time is given by

V_water = (1/3) * base area * h_water

where h_water is the height of the water at that time.

To find the rate at which the water level is rising (r), we need to find dh_water/dt. We can do this by taking the derivative of both sides of the equation for V_water with respect to time

dV_water/dt = (1/3) * base area * dh_water/dt

Substituting the known values

dV_water/dt = (1/3) * (8 cm)^2 * dh_water/dt

dV_water/dt = (64/3) cm^2 * dh_water/dt

dh_water/dt = 3 * dV_water/dt / 64

dh_water/dt = 3 * 55 cm^3/s / 64 = 2.67 cm/s

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The product of the expression is 2x⁶ + 23x³ + 63

First, we should note that algebraic expressions are described as expressions that are composed of coefficients, terms, constants, variables and factors.

These algebraic expressions are also made up of mathematical operations, such as;

From the information given, we have that;

2x3 +9 and x3 +7?

Then,

(2x³ + 9)(x³ + 7)

expand the bracket

2x⁶ + 14x³ + 9x³ + 63

add like terms

2x⁶ + 23x³ + 63

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Answer:

B

Step-by-step explanation:

When you add two fractions with an equal denominator, you can simply add together the numerators. If it is a mixed fraction, you leave the integer alone unless the sum of the numerators is greater than the denominator, in which case you rewrite the fraction appropriately.

6/19 + 1 2/19= 1+ (6+2)/19 = 1 8/19, not 1 9/19. Therefore, the correct answer is choice B. Hope this helps!

Answer:

1

Step-by-step explanation:

Answer:

17/20

Step-by-step explanation:

_(_2/3)*6/10*17/8

2/3×6/10×17/8

=17/20

Answer:

8.79 % tax rate

Step-by-step explanation:

total paid = tax + price

57.50 = tax +52.85

tax = 4.65

tax rate =( tax ÷ price before the tax) × 100%

= (4.65÷ 52.85) × 100%

= 8.79%

Answer:

346

Step-by-step explanation:

(40*22)-(34*16)

=880-544

=346

Answer:336

Step-by-step explanation:

22x40=880 total sq ft

16x34=544 inner sq ft

880-544=336

Answer:

The difference is 4/6

2 1/6 - 1 3/6 = 4/6

Answer:

- 10

Step-by-step explanation:

g(x) = - x² + 2x

g(3) - 7 = - (3)² + 2(3) - 7 = - 10

The simplified form of the given polynomials is - xy³ - 2y³ -xy

From the question, we are to simplify the given polynomials

The given polynomials are

(-5x^2y-xy-4xy^3)-(-3xy^3+2y^3-5x^2y)

Rewriting the polynomials, we get

(-5x²y -xy -4xy³) - (-3xy³ + 2y³ -5x²y)

Simplifying

(-5x²y -xy -4xy³) - (-3xy³ + 2y³ -5x²y)

-5x²y -xy -4xy³ +3xy³ - 2y³ + 5x²y

Collect like terms

-5x²y + 5x²y -4xy³ +3xy³ - 2y³ -xy

0 - xy³ - 2y³ -xy

= - xy³ - 2y³ -xy

Hence, the simplified form of the given polynomials is - xy³ - 2y³ -xy

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Answer:

Yes

Step-by-step explanation:

Sure did. It's all wood. and actually, natural bird houses are better for the birds, but they're in short supply with a demand for lumber.

The sum of two rational numbers is always a rational number.

Any two rational numbers added together will always be a rational number. A rational number is one that can be generally written as the ratio or quotient of two integers with a non-zero denominator. In other words, if p and q are integers and q is not equal to zero, then a rational number may be written as a fraction of the form p/q.

Adding or subtracting two rational numbers is equivalent to adding or subtracting two fractions. Finding a common denominator also an integer and adding or subtracting the numerators while holding the common denominator constant are required steps in the rules for adding and subtracting fractions.

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In the case of the electronic chess game, with a useful life that follows an exponential distribution with a mean of 30 months, we need to determine the length of service time after which the percentage of failed units will approximately equal 50 percent. The options provided are 9 months, 16 months, 21 months, and 25 months.

For the major television manufacturer, the service life of its 50-inch LED televisions follows a normal distribution with a mean of six years and a standard deviation of half a year. We are asked to calculate the probability of service lives of at least five years.

1. Electronic Chess Game:

The exponential distribution is characterized by a constant hazard rate, which implies that the percentage of failed units follows an exponential decay. The mean of 30 months indicates that after 30 months, approximately 63.2% of the units will have failed. To find the length of service time when the percentage of failed units reaches 50%, we can use the formula P(X > x) = e^(-λx), where λ is the failure rate. Setting this probability to 50%, we solve for x: e^(-λx) = 0.5. Since the mean (30 months) is equal to 1/λ, we can substitute it into the equation: e^(-x/30) = 0.5. Solving for x, we find x ≈ 21 months. Therefore, the length of service time after which the percentage of failed units will approximately equal 50 percent is 21 months.

2. LED Televisions:

The service life of 50-inch LED televisions follows a normal distribution with a mean of six years and a standard deviation of half a year. To find the probability of service lives of at least five years, we need to calculate the area under the normal curve to the right of five years (60 months). We can standardize the value using the formula z = (x - μ) / σ, where x is the desired value, μ is the mean, and σ is the standard deviation. Substituting the values, we have z = (60 - 72) / 0.5 = -24. Plugging this value into a standard normal distribution table or using a calculator, we find that the probability of a service life of at least five years is approximately 1.0000 (or 100% with four digits after the decimal point).

Therefore, the probability of service lives of at least five years for 50-inch LED televisions is 1.0000 (or 100%).

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