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Simplify: m5 p8 m6 p10

1) mp¹3. mp¹6
2) m11 p18
3)m18.p11
4)(m. p)29

Answer:

To determine which equation represents how much the worker earns in x hours, we can use the table to find the rate of pay per hour, which is the change in wages divided by the change in hours:

Change in wages = $105.50 - $25.50 = $80

Change in hours = 6 - 2 = 4

Rate of pay per hour = Change in wages / Change in hours

= $80 / 4

= $20

Therefore, the worker earns $20 per hour. To find the total earnings, we can multiply the hourly rate by the number of hours worked:

y = $20x

Therefore, the correct equation is D) y = 10x, which represents how much the worker earns in x hours.

Step-by-step explanation:

The unit digit of 725 unit digit of (325)​ is given as 5

Unveiling the unit digit of a number raised to an exact power can be done by analyzing the pattern of the unit digits of said power sequence.

For instance, given the task of ascertaining the unit digit of 325^725, let us observe the recurrent pattern concerning 5's power line:

[tex]5^1 = 5\\5^2 = 25\\5^3 = 125\\5^4 = 625\\5^5 = 3125[/tex]

It is readily evident that the final digit of 5 raised to any affirmative integer power shall invariably remain as 5. Correlatively, the end figure for 325^725 is also 5.

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The null hypothesis is that the population mean weekly sales are $9820. The alternate hypothesis is that they are greater than $9820. The calculated t-value is 7.45, which is greater than the critical value of 1.677. Therefore, we reject the null hypothesis and conclude that the population mean weekly sales are higher than $9820.

To test whether the population mean weekly sales have increased after advertising, we can use a one-sample t-test.

The null hypothesis is that the population mean weekly sales have not increased, which means the population mean is still $9820:

H0: μ = $9820

The alternative hypothesis is that the population mean weekly sales have increased, which means the population mean is greater than $9820:

Ha: μ > $9820

The significance level is 0.05, so we need to calculate the critical value of t for a one-tailed test with 49 degrees of freedom (n-1), which is 1.677.

To calculate the test statistic, we can use the formula:

t = (X - μ) / (s / √n)

Where X is the sample mean, μ is the hypothesized population mean, s is the sample standard deviation, and n is the sample size.

Given that the sample mean is X = $10960, the hypothesized population mean is μ = $9820, the sample size is n = 50, and the population standard deviation is θ = $1580, we can calculate the sample standard deviation:

s = θ / √n = $1580 / √50 = $223.61

Now we can calculate the test statistic:

t = (X - μ) / (s / √n) = ($10960 - $9820) / ($223.61 / √50) = 7.45

Since the calculated t-value (7.45) is greater than the critical t-value (1.677), we reject the null hypothesis and conclude that there is sufficient evidence to suggest that the population mean weekly sales have increased after advertising.

Therefore, we can infer that the advertising campaign in the local newspaper has been effective in increasing the sales of the electronics store.

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--The given question is incomplete, the complete question is given

"  a small electronics store has begun to advertise in the local newspaper. before advertising, the long term average weekly sales $9820. a random of 50 weeks while the newspaper ads were running gave a sample mean weekly sale of x = $10960. Does this indicate that the population mean weekly sales is now more than $9820? test at the 5% level of significance. Assume theta = $1580.

A. state the null and alternate hypothesis.

B. Compute the   or t va;ue of the sample test statistic.

C. Find the critical value(s).

D. based on the answers to a-c, what is your conclusion?"--

       For C1(Q) = 3 - 2Q.

        For C2(Q) =  4.

     2. The AVC function

           For C1(Q) = 5/Q + 3 + 20/Q - Q.

           For C2(Q) = 3/Q + 4 + 2/Q.

     3. The AFC function

              For C1(Q)= 5/Q - 20/(5 + 3Q + 20/Q - Q)

              For C2(Q) = 0.

     4.  To find the AC function

        For C1(Q) = (5 + 3Q + 202 - Q^2)/Q + 5/Q - 20/(5 + 3Q + 20/Q - Q).

         For C2(Q) = (3 + 4Q + 2)/Q + 3/Q + 4 + 2/Q.

    5.To find the ATC function

    For C1(Q)= 5/Q² + 3/Q + 20/Q² - Q/Q + 5/Q - 20/(5Q + 3Q² + 20 - Q²)

     For C2(Q)= 3/Q² + 4/Q + 2/Q² + 3/Q + 4/Q + 2/Q.

1. To find the MC function, we take the derivative of the cost functions with respect to Q.

For C1(Q) = 5 + 3Q + 202 - Q^2, MC1(Q) = 3 - 2Q.

For C2(Q) = 3 + 4Q + 2, MC2(Q) = 4.

2. To find the AVC function, we divide the cost functions by Q.

For C1(Q), AVC1(Q) = (5 + 3Q + 202 - Q^2)/Q = 5/Q + 3 + 20/Q - Q.

For C2(Q), AVC2(Q) = (3 + 4Q + 2)/Q = 3/Q + 4 + 2/Q.

3. To find the AFC function, we subtract the AVC function from the ATC function.

For C1(Q), AFC1(Q) = (5 + 3Q + 202 - Q^2)/Q - (5 + 3Q + 202 - Q^2)/(5 + 3Q + 20/Q - Q)

= 5/Q - 20/(5 + 3Q + 20/Q - Q).

For

C2(Q), AFC2(Q) = (3 + 4Q + 2)/Q - (3 + 4Q + 2)/(3/Q + 4 + 2/Q) = 0.

4. To find the AC function, we add the AVC function to the AFC function.

For

C1(Q), AC1(Q) = (5 + 3Q + 202 - Q^2)/Q + 5/Q - 20/(5 + 3Q + 20/Q - Q).

For

C2(Q), AC2(Q) = (3 + 4Q + 2)/Q + 3/Q + 4 + 2/Q.

5. To find the ATC function, we divide the AC function by Q.

For

C1(Q), ATC1(Q) = [(5 + 3Q + 202 - Q²)/Q + 5/Q - 20/(5 + 3Q + 20/Q - Q)]/Q

= 5/Q² + 3/Q + 20/Q² - Q/Q + 5/Q - 20/(5Q + 3Q² + 20 - Q²).

For

C2(Q), ATC2(Q) = [(3 + 4Q + 2)/Q + 3/Q + 4 + 2/Q]/Q

= 3/Q² + 4/Q + 2/Q² + 3/Q + 4/Q + 2/Q.

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The Orchard Cafe can expect approximately 77 diners to show up out of the 81 reservations made

To determine how many diners can be expected to show up at The Orchard Cafe, we can follow these steps:

1. Identify the percentage of diners who actually show up: Since 4% of diners with reservations don't show up, the percentage of diners who do show up is 100% - 4% = 96%.

2. Calculate the expected number of diners who show up: Multiply the total number of reservations (81) by the percentage of diners who show up (96%).

81 reservations x 0.96 (96% as a decimal) = 77.76

Since the number of diners must be a whole number, you can round the result to the nearest whole number.

In this case, 77.76 can be rounded down to 77.

Your answer: The Orchard Cafe can expect approximately 77 diners to show up out of the 81 reservations made.

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Answer:

If there are 15 boys in Mr. Day’s class and the girl to boy ratio is 3 to 5, then there are 9 girls in Mr. Day’s class. To find out how many more boys there are than girls, you can subtract the number of girls from the number of boys:

15 boys - 9 girls = 6 more boys than girls.

Step-by-step explanation:

By using slope intercept , These were the two points on the line: (0,-2) and (7,2).

A line is defined by the equation y = mx + b, which is also known as the slope-intercept form. When the line is graphed, m represents the slope and b the point at which the line intersects the y-axis.

We may use the slope-intercept form of a line, which is y=mx+b where m is the slope and b is the y-intercept, to graph the line y=4/7x-2. Therefore, m=4/7 and b=-2.

These variables allow us to plot two spots along the line. Since the line crosses the y-axis at (0,-2) (the y-intercept), that location will be one of the points.

We can utilize the slope of 4/7 to locate a different point along the line. This indicates that we advance up 4 units in the y direction for every 7 units we move to the right (in the x direction). We can therefore move 7 units to the right and then 4 units up, starting at (0,-2), to reach (7,2).

So now we have two points on the line: (0,-2) and (7,2). These points can be plotted on a coordinate plane, and then a straight line can be drawn through them to create the graph.

Graph given below:

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The measure of the third angle in the triangle is 80 degrees.

The sum of the angles in a triangle is always 180 degrees.

Therefore, to find the measure of the third angle in the triangle with angle measures of 40° and 60°,

We can subtract the sum of these two angles from 180°:

180° - (40° + 60°) = 180° - 100° = 80°

Therefore, the measure of the third angle in the triangle is 80 degrees.

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The total rations will be: 0.75 times the number of meals.

A ration refers to the fixed portion of food or other goods allowed to each person in times of shortages.

In this context, If you decide to eat only 75% of each meal, that means you will consume 0.75 times the number of meals.

For example, if you originally had 100 meals, you will now have:

= 0.75 x 100

= 75 rations in total.

This approach allows to stretch your meals and make them last longer by rationing your food intake.

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The equation will be w = 40b

To find the total weight (w) of the soil in pounds when Yuki stacks b bags, you can use a simple linear equation. Each bag weighs 40 pounds, so the equation will be: w = 40b

This equation shows that the total weight (w) of the soil in pounds is equal to the number of bags (b) multiplied by the weight of each bag (40 pounds).

The above answer is based on the information below as seen in the picture;

Yuki works at a garden store. She is stacking 40 pounds bags of soil.

write an equation that gives the total weight, w, of the soil in pounds when Yuki stacks b bags.

+ - . =         b, w, 40

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The height of the candle change over time as a linear function

The height of the candle decreases by 2 inches every hour, which means the height of the candle is a linear function of time.

We can write the equation for the height of the candle as:

h(t) = 12 - 2t

where h is the height of the candle in inches and t is the time in hours.

If the candle burned for 2 hours, we can plug in t=2 into the equation to find the height:

h(2) = 12 - 2(2) = 8

So the height of the candle after 2 hours of burning is 8 inches.

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We need to integrate the function

y = 2x - x² with respect to x, from x = 0 to x = 2.

The graph of the function intersects the x-axis at x = 0 and x = 2.

So,

Area of region R = ∫[0,2] (2x - x²) dx

= [x² - (1/3)x³] from 0 to 2

= [2² - (1/3)(2)³] - [0² - (1/3)(0)³]

= 4/3

Now, let's find the equation of the line y = cx. Since the line passes through the origin (0,0), we have y = cx.

To find the value of c that divides the region R into two equal subregions, we need to find the value of x where the

area under the curve y = 2x - x² is equal to the area under the line y = cx.

∫[0,a] (2x - x²) dx = ∫[0,a] cx dx

[2x²/2 - x³/3] from 0 to a = [c/2 x²] from 0 to a

2a²/2 - a³/3 = c/2 a²

We multiply both sides by 6, we get:

12a² - 2a³ = 3ac

2a² - (1/3)a³ = (1/2)ac

2a - (1/3)a² = (1/2)c

c = (4a - (2/3)a²)/2

We know that the area under the line is equal to the area under the curve up to the point of intersection, we have:

∫[0,a] (2x - x²) dx = ∫[0,a] (cx) dx - ∫[a,2] (2x - x²) dx

2a²/2 - a³/3 = c/2 a² - 2a² + (8/3)a³ - 4a + (4/3)a²

10a³/3 - 7a² + 4a = 0

a = 0, 1.4105, -0.6172

The only value of a that is within the range 0 to 2 is a = 1.4105. Substituting this value into the equation for c, we get:

c = (4a - (2/3)a²)/2 = 1.636

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Answer:

x = 3.5 pages per minute

Step-by-step explanation:

We make the relationship

21 pages ------ 6 min

x pages -------- 1 min

So x= (21x1)/(6)

x = 3.5 pages per minute

Box plot, as the median can be easily ascertained from the substantial amount of data. The answer is option (a).

The middle value in a given set of figures or statistics is referred to as the median. The average value for a given collection of integers can be calculated using one of three main methods in mathematics. The mean, the median, and the mode are the three. Central tendency measurements refer to these three factors. The average value of the supplied data is calculated using mean. The midpoint value of the given data is defined by a median. The input data's repeating value is defined by the mode.

A box plot is a very visual way to show a brief summary of one or more sets of data. It is particularly useful for quickly comparing and summing multiple sets of findings from distinct trials. A box plot provides a visual picture of the distribution of results as well as clues regarding data symmetry at a look.

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The surface area of the right prism is 192.9 m².

A prism is a solid shape that is bound on all its sides by plane faces.

To calculate the surface area of the prism, we use the formula below

Formula:

Where:

From  the diagram in the question,

Given:

Substitute these values into equation 1

Hence, the surface area is  192.9 m².

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Answer:

24 meters

Step-by-step explanation:

We can use Pythagoras' theorem to solve this problem. Let's call the width of the field "w". We know that Ken ran from one corner of the field to the opposite corner, a distance of 85 meters. This distance is equal to the hypotenuse of a right triangle whose legs are the length and width of the field. We also know that Ken ran along its length, a distance of 77 meters. This length is one of the legs of the right triangle.

Using Pythagoras' theorem, we can write:

w^2 + 77^2 = 85^2

Simplifying this equation gives:

w^2 = 85^2 - 77^2

w^2 = 576

Taking the square root of both sides gives:

w = sqrt(576)

w = 24

Therefore, the width of the field is 24 meters 1.

I hope this helps!

Answer:

Θ ≈ 28.07°

Step-by-step explanation:

using the sine ratio in the right triangle

sinΘ = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{8}{17}[/tex] , then

Θ = [tex]sin^{-1}[/tex] ( [tex]\frac{8}{17}[/tex] ) ≈ 28.07° ( to the nearest hundredth )

Answer:

The area of a semicircle is half of the area of the circle. As the area of a circle is πr2. So, the area of a semicircle is 1/2(πr2 ), where r is the radius. The value of π is 3.14 or 22/7.

The volume of the cylinder is 3532.5 metres cube.

The figure above is a cylinder. The volume of the cylinder can be found as follows:

volume of a cylinder = πr²h

where

Therefore, let's find the height using Pythagoras's theorem.

25² - 15² = h²

h² = 625 - 225

h = √400

h = 20 metres

Hence,

volume of a cylinder = 3.14 × 7.5² × 20

volume of a cylinder = 3532.5 metres cube

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The factored form of the expression x² + 5x+6 is (x + 3)(x + 2)

To factorize the quadratic equation, we need to take the following steps;

Multiply the coefficient of the x squared by the constant value, we have;

6

Now, find the pair factors of the product that would add up to give 5, we have;

2 + 3

Substitute the values into the expression, we have;

x² + 2x + 3x + 6

Now, group the expression in pairs, we have;

(x² + 2x) + (3x + 6)

Factorize the expressions

x(x + 2) + 3(x + 2)

Then, we have;

x + 3

x + 2

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The company would get a total of 1200 responses over the course of the first 18 days after the magazine was published, to the nearest whole number.

What is meant by days?

Days refer to the 24-hour period of time that is based on the rotation of the Earth on its axis. It is a unit of time commonly used in calendars, schedules, and daily life.

Explain whole numbers

Whole numbers are positive integers including zero. They are used to count and represent quantities of discrete objects or entities in mathematics.

According to the given information

The sum of the first n terms of a geometric sequence with first term a and common ratio r is given by the formula S_n = a(1 - rⁿ)/(1 - r).

In this case, we want to find the sum of the first 18 terms of the sequence, so n = 18. Substituting the values for a, r, and n into the formula for S_n, we get:

S_18 = 120(1 - 0.9¹⁸)/(1 - 0.9)

    ≈ 1200

So the company would get a total of 1200 responses over the course of the first 18 days after the magazine was published, to the nearest whole number.

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The equation r · sin θ = 10 in rectangular coordinates is equal to y = 10.

Herein we find the representation of a equation in polar coordinates, whose form in rectangular coordinates. This can be done by using the following definitions:

cos θ = x / r

sin θ = y / r

Where:

Then, the equation in polar coordinates is:

r · sin θ = 10

y = 10

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The graph of the data from the table is added as an attachment

From the question, we have the following parameters that can be used in our computation:

Jerome is a photographer. He earns $125 per hour

This means that the equation of the function is

f(x) = 125x

Where x is the number of hours he works

Using the above as a guide, we have the following table of values

x    f(x)

1     125

2    250

3    375

4    500

5    625

6     750

Next, we plot the graph from the table of values and the function f(x) = 125x

The graph of the function is added as an attachment

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Answer: x= 7191.509 ft

Step-by-step explanation:

Sin9/1 = 1125/x

X/1 = 1125/sin9

Answer:

1. is (18,4)

2. is (8,10)

3. (-9,-8)

4. (9,-8)

Step-by-step explanation:

i promise its right please give brainliest

The average score of 100 students taking a statistics final was 70, with a standard deviation of 7. The test score esteem that isolates the beat 2.5% of normal distribution from the rest of the understudies is roughly 83.72.

To discover the test score esteem that isolates the best 2.5% of the understudies, we got to discover the z-score comparing to that rate utilizing the standard ordinary conveyance table.

z = (x - μ) / σ

To discover the z-score compared to the best 2.5%, we see up the region of the right-hand tail of the standard normal distribution table, which is 0.025. This compares to a z-score of roughly 1.96.

Presently ready to utilize the z-score equation to unravel for x:

1.96 = (x - 70) / 7 Increasing both sides by 7, we get:

x - 70 = 13.72

Including 70 to both sides, we get:

x = 83.72

Hence, the test score esteem that isolates the beat 2.5% of the understudies from the rest of the understudies is roughly 83.72.

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The amount of work done, in foot-pounds, to lift a crate weighing 30 pounds a total of 3 feet is 90 foot-pounds.

To calculate the amount of work done, in foot-pounds, to lift a crate weighing 30 pounds a total of 3 feet, we need to use the formula:

Work = Force x Distance

In this case, the force is the weight of the crate, which is 30 pounds. The distance is the height the crate is lifted, which is 3 feet.

So, Work = 30 pounds x 3 feet

We can simplify this by converting pounds to foot-pounds, which is the unit used to measure work. To convert pounds to foot-pounds, we need to multiply the weight by the distance. So:

Work = 30 pounds x 3 feet = 90 foot-pounds

Therefore, the amount of work done, in foot-pounds, to lift a crate weighing 30 pounds a total of 3 feet is 90 foot-pounds.

To calculate the amount of work done, in foot-pounds, for lifting a crate weighing 30 pounds a total of 3 feet, you can follow these steps:

Step 1: Identify the weight of the crate (30 pounds) and the distance it is lifted (3 feet).
Step 2: Multiply the weight of the crate by the distance lifted.

Work (in foot-pounds) = Weight (in pounds) × Distance (in feet)

In this case:

Work = 30 pounds × 3 feet
Work = 90 foot-pounds

So, the amount of work done is 90 foot-pounds.

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The work done to lift a crate weighing 30 pounds a total of 3 feet is:

Work = 30 pounds x 3 feet x cos(0 degrees) = 90 foot-pounds

So the amount of work done to lift the crate is 90 foot-pounds.

The amount of work done, in foot-pounds, to lift a crate weighing 30 pounds a total of 3 feet is given by the formula:

Work = Force x Distance x cos(theta)

where Force is the weight of the crate, Distance is the vertical distance lifted, and theta is the angle between the direction of the force and the direction of motion (which is 0 degrees in this case since the force is acting vertically upwards).

Therefore, the work done to lift a crate weighing 30 pounds a total of 3 feet is:

Work = 30 pounds x 3 feet x cos(0 degrees) = 90 foot-pounds

So the amount of work done to lift the crate is 90 foot-pounds.

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