Write two different expressions that are equal to y^20 using only combinations of y^2 and y^3.
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Answer:

7598.80

Step-by-step explanation:

V=πr^2h

= 3.14 * 11^2 * 20

= 2420π or 7598.80

Answer:

760

Step-by-step explanation:

V=πr²h

V = 3.14 x (11)² x 20

V = 7598.8

V = 760

a) The probability of failing to meet the specification limit of 45-pounds tensile strength 15.87%.

b) The number of parts that would not meet the specification is 7,935.

a) Given that the tensile strength of a metal part is normally distributed with mean 40 pounds and standard deviation 5 pounds.

We have to find the probability of failing to meet the specification limit of 45-pounds tensile strength.

Using the standard normal distribution, we can find the probability of failing to meet the specification limit of 45 pounds as follows:

z = {45 - 40}/{5}

= 1

The probability of failing to meet the specification limit of 45 pounds is the probability that the standardized variable Z is greater than 1, which is given by:

P(Z > 1) = 0.1587

Therefore, the probability of failing to meet the specification limit of 45-pounds tensile strength is 0.1587 or 15.87%.

b) If the probability of failing to meet the specification is 0.1587, the probability of meeting the specification limit is

1 - 0.1587 = 0.8413

.If 50,000 parts are produced, then the expected number of parts that meet the specification limit is:

0.8413* 50,000 =  42,065.

Therefore, the number of parts that would not meet the specification is: 50,000 - 42,065 = 7,935.

Hence, about 7,935 parts would not meet the specification.

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Answer:

10.5

Step-by-step explanation:

i=0.5

k=0.25

7x0.5=3.5

8x0.25=2

3.5+5+2= 10.5

10.5

The simplified form of the expression √( 45 x⁸ w⁷ ) is 3x⁴w³√(5w).

Given the expression in the question;

√( 45 x⁸ w⁷ )

First, factor out 9 from 45

√( 9(5) x⁸ w⁷ )

√( 3²(5) x⁸ w⁷ )

Rewrite x⁸ as (x⁴)²

√( 3²(5) (x⁴)² w⁷ )

Rewrite w⁷ as ( w⁶ × w )

√( 3²(5) (x⁴)² ( w⁶ × w ) )

Rewrite w⁶ as (3³)²

√( 3²(5) (x⁴)² (w³)² × w  )

We can now take the square roots of all the terms with a power of 2 and take them out of the square root

(3)(x⁴)(w³)√(5w)

3x⁴w³√(5w)

Therefore, the simplified form of the expression √( 45 x⁸ w⁷ ) is 3x⁴w³√(5w).

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The correct 98% confidence interval for the true proportion of graduates working in the field of study in which they obtained their degree is (0.811, 0.892).

To calculate the confidence interval, we need to use the formula for estimating proportions and the standard error of the proportion. The formula is:

Confidence interval = sample proportion ± z * standard error

Calculate the sample proportion

In this case, the sample proportion is the number of graduates working in their field of study (361) divided by the total number of graduates surveyed (424):

Sample proportion = 361/424 ≈ 0.852

Calculate the standard error

The standard error of the proportion is calculated using the formula:

Standard error = sqrt((sample proportion * (1 - sample proportion)) / sample size)

Using the given values, we have:

Standard error = sqrt((0.852 * (1 - 0.852)) / 424) ≈ 0.014

Determine the confidence interval

To find the z-value for a 98% confidence level, we look up the corresponding value in the z-table. The z-value for a 98% confidence level is approximately 2.33.

Substituting the values into the confidence interval formula, we have:

Confidence interval = 0.852 ± 2.33 * 0.014

Confidence interval ≈ (0.811, 0.892)

Therefore, the correct 98% confidence interval for the true proportion of graduates working in their field of study is (0.811, 0.892).

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5. We have Angle, Angle and Side to constitute the AAS theorem and prove the triangles are congruent.

6. We have Side, Side and angle not between them so we don't have enough information to prove the congruency of the triangles.

A triangle is a polygon since it has three sides and three vertices. It is one of the basic geometric shapes. The name given to a triangle containing the vertices A, B, and C is Triangle ABC. A unique plane and triangle in Euclidean geometry are discovered when the three points are not collinear. Three sides and three corners define a triangle as a polygon. The triangle's corners are defined as the locations where the three sides converge. 180 degrees is the result of multiplying three triangle angles.

5. We have Angle, Angle and Side to constitute the AAS theorem and prove the triangles are congruent.

6. We have Side, Side and angle not between them so we don't have enough information to prove the congruency of the triangles.

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Answer:

most models of scientific calculators in degree mode, all you have to do is press "Mode" and then look at the numbers on the screen beside the menu items. Locate the number beside "Deg" or "Degrees" and press it to change the mode of your calculator

Answer:

6

Step-by-step explanation:

A painter mixes 2 1/2 pints (2.5 pints) of yellow paint with 4 pints of red paint to make a certain shade of orange paint. The ratio of yellow paint to red paint is 2.5:4. In order to find the pints of yellow paint needed to be mixed with 10 pints of red paint, we will use conversion fractions.

10 red pints × (2.5 yellow pints/ 4 red pints) ≈ 6 pints (we round off to 1 significant figure)

Answer:

(9√3 - 3π) cm²  or ≈ 6.16 cm²

Step-by-step explanation:

Refer to attached pictures

We have equilateral triangle with side of 6 cm and inscribed circle, we need to find the shaded area inside the triangle not covered by the circle.

The shaded are is the difference of areas of the triangle and circle

Area of equilateral triangle is calculated as per formula:

Area of circle is calculated as per formula:

Let's find the value of r:

Δ ADB is the right triangle with angles 30° and 60°

It has sides of 3 cm, 6 cm and AD= m cm

As per attached, m is the long leg and equal to a√3, so

also,

We can find AO in the same way as above using Δ AOF

AO= 2r as it is the hypotenuse and the hypotenuse is twice a short leg in the right triangle with angles 30° and 60°

So,  

Now we can get the area of circle:

Shaded are is:

(a) The differential equation that is satisfied by y is:

\(\frac{dy}{dt} = ky(1-y)\)

(b) To solve the differential equation, we separate the variables and integrate both sides:

\(\frac{dy}{y*(1-y)} = k*dt\)

Integrating both sides, we get:

\(\frac{lnly}{1-y} = k*t +c1\)

where C1 is an arbitrary constant of integration.

We can rewrite the equation in terms of y:

\(\frac{y}{1-y} = e^{(k*t+c1)}\)

Multiplying both sides by (1-y), we get:

\({y} = e^{(k*t+c1)} *(1-y)\)

\(y= \frac{C}{(1+(c-1)e^{-kt} }\)

where C = y(0) is the initial fraction of the population who have heard the rumor.

(c) In this case, the initial fraction of the population who have heard the rumor is y(0) = \(\frac{100}{1300}\) = 0.077. At noon, half the town has heard the rumor, so y(4) = 0.5.

Substituting these values into the equation from part (b), we get:

\(0.5= \frac{0.077}{1+(0.777-1) e^{-k4} }\)

Solving for k, we get:

\(k= ln(\frac{12.857}{4} )\)

Substituting this value of k into the equation from part (b), and setting y = 0.9 (since we want to find the time at which 90% of the population has heard the rumor), we get:

\(0.9= \frac{0.077}{1+(0.777-1) e^{-ln(12.857}*\frac{t}{4} }\))

Solving for t, we get:

t = 8.7 hours after the beginning (rounded to one decimal place)

A differential equation is a mathematical equation that relates a function to its derivatives. It is a powerful tool used in many fields of science and engineering to describe how physical systems change over time. The equation typically includes the independent variable (such as time) and one or more derivatives of the dependent variable (such as position, velocity, or temperature).

Differential equations can be classified based on their order, which refers to the highest derivative present in the equation, and their linearity, which determines whether the equation is a linear combination of the dependent variable and its derivatives. Solving a differential equation involves finding a function that satisfies the equation. This can be done analytically or numerically, depending on the complexity of the equation and the available tools.

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The three-month moving average is calculated by adding up the demand for the past three months and dividing the sum by three.

To calculate the forecast for month four, we need to find the average of the demand over the past three months: 700, 750, and 900.

Step 1: Add up the demand for the past three months:
700 + 750 + 900 = 2350

Step 2: Divide the sum by three:
2350 / 3 = 783.33 (rounded to two decimal places)

Therefore, the forecast for month four, based on the three-month moving average, is approximately 783.33.

Keep in mind that the three-month moving average is a method used to smooth out fluctuations in data and provide a trend. It is important to note that this forecast may not accurately capture sudden changes or seasonal variations in demand.

The mean, median, and sample variance of the given dataset are:Mean = 23.17Median = 21Sample variance = 173.5592

(a) Mean The mean (or average) of a dataset is calculated by summing up all the values and dividing by the total number of values.

The formula for calculating the mean is: `mean = (sum of values) / (total number of values)`For the given dataset, we have:20, 50, 22, 14, 23, 10

Sum of values = 20 + 50 + 22 + 14 + 23 + 10 = 139

Total number of values = 6Therefore, the mean is given by: `mean = 139 / 6 = 23.17`Answer: 23.17 (rounded to two decimal places)

(b) Median To find the median, we need to arrange the dataset in increasing order:10, 14, 20, 22, 23, 50The median is the middle value of the dataset. If there are an odd number of values, the median is the middle value. If there are an even number of values, the median is the average of the two middle values. Here, we have 6 values, so the median is the average of the two middle values: `median = (20 + 22) / 2 = 21` Answer: 21(e)

Sample variance s²The sample variance is calculated by finding the mean of the squared differences between each value and the mean of the dataset.

The formula for calculating the sample variance is: `s² = ∑(x - mean)² / (n - 1)`where `∑` means "sum of", `x` is each individual value in the dataset, `mean` is the mean of the dataset, and `n` is the total number of values.For the given dataset, we have already calculated the mean to be 23.17.

Now, we need to calculate the squared differences between each value and the mean:

20 - 23.17 = -3.1722 - 23.17

= -1.170 - 23.17

= -13 - 23.17

= -9.1723 - 23.17

= -0.1710 - 23.17

= -13.17

The sum of the squared differences is given by:

∑(x - mean)² = (-3.17)² + (-1.17)² + (-13.17)² + (-9.17)² + (-0.17)² + (-13.17)²

= 867.7959

Therefore, the sample variance is given by: `s² = 867.7959 / (6 - 1) = 173.5592`Answer: 173.5592 (rounded to four decimal places)

The mean, median, and sample variance of the given dataset are:Mean = 23.17Median = 21Sample variance = 173.5592

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Answer:

y = 120

Step-by-step explanation:

If y = 32 when x = 8, then y is 4 times the number of x. If x = 30, then (4)30 = 120.

Answer:

-21/10

Step-by-step explanation:

5 1/4 = 21/4

-2 1/2 = -5/2

21/4 : (-5/2) = -21/10

Answer:

Number 1 is also 125 because it corresponds.

Step-by-step explanation:you see other line in the triangle right!if u see both are giving that line anywhere then you will know they corresponds! hope it hels!good night!

The cost price of pawpaw is 40 and the cost if the basket of mangoes is 1250.

Based on the information given, the equations to solve the question will be:

30p + 100m = 2450 .... i

1.3 × 40p - 30 p + 1.3 × 100m = 855 ..... ii

30p + 100m = 2450

12p + 30m = 855

Solving simultaneously, the price of pawpaw is 40 and the price of mango is 12.5.

Therefore, the cost of 100 basket of mangoes will be:

= 12.5 × 100

= 1250

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Answer:

See below.

Step-by-step explanation:

y = 3x - 5

Compare with y = mx + b

b is the y-intercept. Here b = -5, so I would place a dot on the point (0, -5) since that is the y-intercept.

m is the slope.

m = rise/run

m = 3, so starting at (0, -5), go up 3 units and 1 unit right. Place a dot there. Connect the dots and extend the line in both directions past the dots. Then put arrowheads at the ends of the segment to show it represents a line.

The simplest form expression for the addition of the fractions given using the lowest common multiple of the denominator is 2/3.

A fraction is a numerical value that is a part of a whole. It is evaluated by dividing a whole into a number of parts.In Mathematics, a fraction is defined as a part of the whole thing.  For example, ½ represents half of a whole number or a thing

Given the fractions :

1/4 + 5/12

The lowest common multiple of the denominator ;

A lowest common multiple of 4 and 12 = 12

1/4 + 5/12 = (3 + 5) / 12

1/4 + 5/12 = 8/12

Expressing in simplest form :

8/12 = 2/3

Therefore, the simplest form expression of the addition is 2/3

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The correct answer is: a. The machine fills the boxes with the proper amount of straws. The average is 100 straws. In hypothesis testing, the null hypothesis typically represents a statement of no effect or no difference. In this case, it means that the machine is functioning properly and filling the boxes with the expected average of 100 straws per box.

The null hypothesis in this scenario is option a, which states that the machine fills the boxes with the proper amount of straws, and the average is 100 straws per box. This is because the null hypothesis assumes that there is no significant difference between the observed sample mean and the expected population mean of 100 straws per box. To reject this null hypothesis, we would need to find evidence that the machine is not filling the boxes with the proper amount of straws, which would require further investigation and analysis. In conclusion, the null hypothesis can be summarized in three paragraphs as follows: The null hypothesis for the makers of biodegradable straws is that the machine fills the boxes with the proper amount of straws, and the average is 100 straws per box.

This hypothesis assumes that there is no significant difference between the observed sample mean and the expected population mean. To test this hypothesis, a random sample of 121 boxes is selected to determine whether or not the machine is filling the boxes with an average of 100 straws per box. If the observed sample mean is not significantly different from the expected population mean, then the null hypothesis is accepted. However, if the observed sample mean is significantly different from the expected population mean, then the null hypothesis is rejected, and further investigation is required to determine the cause of the difference.

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Answer

Digitalis can expect to make money from selling these processors.

In the long run, they should expect to make 52.68 dollars in each processor sold

Step-by-step explanation

The expected value is calculated by multiplying each of the possible outcomes by the likelihood that each outcome will occur and then summing all of those values.

In this case, we have:

• probability that the processor is not defective: 0.87 (= 87/100)

• company's earning if the processor is not defective: $464 (company's profit)

• probability that the processor is defective: 0.13 (= 13/100)

• company's earning if the processor is defective: -$2700 (the negative sign indicates that the company will lose money in this case)

Therefore, the expected value is:

Using proportions, it is found that:

7. The commission is of $1,176.

8. The unemployed compensation is of $3,978.

A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct or inverse proportional, can be built to find the desired measures in the problem.

For item 7, the average salary, which is the sum of all salaries divided by the number of salaries, is given by:

(82000 + 96000 + 105000 + 109000)/4 = $98,000.

The commission is 1.2% of that, hence:

0.012 x 98000 = $1,176.

The commission is of $1,176.

For item 8, the compensation is 60% of the average, which is given by:

A = (6830 + 6430)/2 = $6,630.

Hence:

0.6 x $6,630 = $3,978.

The unemployed compensation is of $3,978.

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Answer:

32 feet.

Step-by-step explanation:

We can convert 7 yards to feet and add it to 11 feet to get the total distance in feet.

1 yard is equal to 3 feet, so 7 yards is equal to:

7 yards * 3 feet/yard = 21 feet

Adding 11 feet to this, we get:

21 feet + 11 feet = 32 feet

Therefore, 7 yards and 11 feet is equal to 32 feet.

Answer:

There are 32 feet in 7 yards and 11 feet.

Step-by-step explanation:

To find the answer, we need to convert yards to feet and then add them to the given feet. We can use the following conversion factor: 1 yard = 3 feet. Multiplying both sides by 7, we get: 7 yards = 21 feet. Adding 11 feet to both sides, we get: 7 yards + 11 feet = 21 feet + 11 feet. Simplifying, we get: 7 yards + 11 feet = 32 feet.

Answer:

433.3333333333/min

Step-by-step explanation:

so 433/min

4500-1900= 2600

22-16=6

2600/6 =433.3333333333

The expressions are expanded to give;

1. 2x² - 5x

2. 6x² + 8x

3. 6x² - 12xy

Algebraic expressions are defined as expressions consisting of  variables, coefficients, constants, terms and factors.

These expressions are also known to consist of mathematical operations, which includes;

From the information given, we have that;

a. x (2x - 5)

expand the bracket

2x² - 5x

b. 2x (3x+4)

expand the bracket

6x² + 8x

c. 6x(x-2y)

expand the bracket

6x² - 12xy

Hence, the expressions are 2x² - 5x, 6x² + 8x and 6x² - 12xy

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Answer:

1) 2x² - 5x

2) 6x² + 8x

3) 6x² - 12xy

Step-by-step explanation:

1) x ( 2x - 5 )

To expand the above, multiply both terms inside the brackets by x.

2x² - 5x

2) 2x ( 3x + 4 )

To expand the above, multiply both terms inside the brackets by 2x.

6x² + 8x

3) 6x ( x - 2y )

To expand the above, multiply both terms inside the brackets by 6x.

6x² - 12xy

Answer:

A realistic budget is hard to come by. All budgets tell you what you should include in your monthly plan, but what about unexpected expenses? Here are some ideas for making a realistic budget, and sticking to it.

daid1784 avatar

Well, the dozens of apps, spreadsheets, and other methods just don’t account for real life and all the expenses we don’t think of. There are plenty of expenses we have that aren’t monthly that take up more of our money than we planned.

Answer:

18

Step-by-step explanation:

Can you please help me with a question? language arts related?

Answer:

{-4; -5}

Step-by-step explanation:

just put any integer from set S in place of p and you will know. the inequality is false with -2 and -3, but with other two numbers is true

Therefore, approximately 0.0475 or 4.75% of smoke alarms will have a life span of less than 1 year as the cumulative probability for a Z-score of -1.67 is approximately 0.0475.

To find the proportion of smoke alarms with a life span of less than 1 year, we can use the Z-score formula and the properties of the standard normal distribution.

First, we calculate the Z-score using the formula:

Z = (X - μ) / σ

Where X is the value we are interested in (1 year), μ is the mean (2 years), and σ is the standard deviation (0.6 years).

Z = (1 - 2) / 0.6

= -1.67

Next, we look up the corresponding cumulative probability (proportion) for the Z-score of -1.67 in the standard normal distribution table or by using statistical software. The cumulative probability corresponds to the proportion of values less than the given Z-score.

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The power of a test is measured by its capability of rejecting a null hypothesis that is false, so option C is the correct answer

what is power with respect to probability?

Power is defined as the probability of correctly rejecting the false null hypothesis. It is the measure of the capability of rejecting a null hypothesis that is false.

Power = P[ rejecting a null hypothesis that is false.]

So, option C is correct, the power of a test is measured by its capability of rejecting a null hypothesis that is false

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