Suppose that the functions r and s are defined for all real numbers x as follows

r(x) = 5x ^ 2

s(x) = x ^ 3

Write the expressions for (rs)(x) and (r + s)(x) and evaluate (r - s)(- 2)

(rs)(x) =

(r + s)(x) =

(t - 5)(- 2) =

Answer:

$68000

Step-by-step explanation:

Answer:

$6800

Step-by-step explanation:

30x1600+10x2000

=48000+2000

=68000

The total surface area of the triangular prism is 636 square meters

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

The triangular prism

The surface area of the triangular prism from the net is calculated as

Surface area = sum of areas of individual shapes that make up the net of the triangular prism

Using the above as a guide, we have the following:

Area = 1/2 * 10 * 24 * 2 + 11 * 26 + 10 * 11

Evaluate

Area = 636

Hence, the surface area is 636 square meters

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To find out how much pasta the restaurant needs, we can use the ratio of pasta to cheese given in the recipe: 8 cups of pasta for every 6 cups of cheese.

First, we need to determine the ratio of cheese to pasta. We can do this by taking the reciprocal of the original ratio, which gives us 6 cups of cheese for every 8 cups of pasta.

Next, we can set up a proportion with the known amount of cheese (15 cups) and the unknown amount of pasta (let's call it x cups):

6 cups of cheese / 8 cups of pasta = 15 cups of cheese / x cups of pasta

We can cross-multiply to solve for x:

6 cups of cheese * x cups of pasta = 8 cups of pasta * 15 cups of cheese

Simplifying this equation gives:

x = (8 cups of pasta * 15 cups of cheese) / 6 cups of cheese

x = 20 cups of pasta

Therefore, the restaurant would need 20 cups of pasta to make the large batch of mac and cheese using 15 cups of cheese, according to the recipe.

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Somerville now has 66.5 centimeters of snow.

In the initial blizzard, the town of Somerville got 60 centimeters of snow in one day. After a few sunny days, 55 millimeters of snow melted. To convert millimeters to centimeters, we divide by 10. Therefore, 55 millimeters of snow is equal to 5.5 centimeters of snow that melted.

So, the total amount of snow that was left after the sunny days was 60 - 5.5 = 54.5 centimeters of snow.

But then, Somerville got another 120 millimeters of snow. Converting millimeters to centimeters by dividing by 10, we get that 120 millimeters of snow is equal to 12 centimeters of snow.

To find out how many centimeters of snow Somerville has now, we add the remaining snow from the initial blizzard (54.5 centimeters) to the new snowfall (12 centimeters).

Therefore, Somerville now has 66.5 centimeters of snow.

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The formula for the test statistic depends on the type of hypothesis test being conducted. However, in general, the test statistic is calculated by taking the difference between the sample statistic (such as the sample mean or proportion) and the hypothesized population parameter, and dividing by the standard error of the statistic.

The distribution of the test statistic also depends on the type of test being conducted. For example, if conducting a t-test with a sample size less than 30, the test statistic follows a t-distribution with degrees of freedom equal to the sample size minus 1. If conducting a z-test or a large sample t-test with a sample size greater than or equal to 30, the test statistic follows a standard normal distribution (i.e., a z-distribution).

It is important to consult the appropriate distribution table and degrees of freedom when interpreting the test statistic to determine the p-value and make a decision about the hypothesis.

The formula for the test statistic and its distribution depend on the specific hypothesis test being conducted. I'll provide the information for two common tests: the t-test and the chi-square test.

1. T-test:
The formula for the test statistic in a t-test is:

t = (sample mean - population mean) / (sample standard deviation / √n)

where n is the sample size. The distribution for the test statistic is the t-distribution with (n-1) degrees of freedom.

2. Chi-square test:
The formula for the test statistic in a chi-square test is:

χ² = Σ [(observed frequency - expected frequency)² / expected frequency]

The distribution for the test statistic is the chi-square distribution with (k - 1) degrees of freedom, where k is the number of categories in the contingency table.

Remember to use the appropriate test and formula based on your specific research question and data.

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Answer:

The area of the triangle is equal to half the product of its base and height. In this case, the base is 6 дм and the height is 8 дм. Therefore, the area of the triangle is

S = \frac{1}{2}(6)(8) = 24 дм^2

Step-by-step explanation:

The measure of arc BED in the circle is calculated as:

m(BED) = 218 degrees.

For us to be able to find the measure of the arc, we need to recall that the measure of the intercepted arc is the same as the central angle measure opposite it.

Arc BED will therefore have the same measure as that of the central angle, therefore:

measure of arc BED = 360 - 52 - 90 [note that arc DC is equal to 90 degrees while arc BC is equal to 52 degrees]

Measure of arc BED = 218 degrees.

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To calculate the average rate of ascent we need to use the following formula:

rate = (final depth - initial depth) / time

Plugging in the given values:

rate = (180 ft - (-1,320 ft)) / 60 min = 1,500 ft / 60 min = 25 ft/min

However, since the submarine is currently below the desired depth, the rate needs to be negative (i.e. descending). So, we need to subtract the ascent rate from the descent rate:

ascent rate = (-1,320 ft - (-180 ft)) / 60 min = -1,140 ft / 60 min = -19 ft/min

total rate = 25 ft/min - 19 ft/min = 6 ft/min

Therefore, the average rate of ascent needed would be 17 feet per minute (rounding to the nearest whole number).

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The given problem is concerned with hypothesis testing. The researcher believes that women today weigh less than in previous years. To investigate this belief, she randomly samples 41 adult women and records their weights. The obtained value of the appropriate statistic for testing H0 is t= -2.42.

Given that,

Population mean µ = 115 lbs

Sample mean x = 111 lbs

Sample size n = 41

Standard deviation σ = 12.4 lbs

hypothesis testing

Null hypothesis H0: µ = 115 lbs

Alternate hypothesis H1: µ < 115 lbs

Since the population standard deviation is unknown and the sample size is less than 30, we use a t-distribution to test the hypothesis. The formula for the t-test statistic is,

t= (x- µ)/(s/√n)

Where, x = sample mean, µ = population mean, s = sample standard deviation, and n = sample size

Substituting the given values in the above formula, we get,

t= (111 - 115) / (12.4/ √41)t= -4 / 1.93t= -2.07

The obtained value of the appropriate statistic for testing H0 is t= -2.07.

The calculated t-value is compared with the critical value of t with degrees of freedom (df) = n-1 = 41-1 = 40 at the desired significance level. If the calculated t-value is less than the critical value of t, we reject the null hypothesis. Otherwise, we fail to reject the null hypothesis.

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Answer:

The answer for radius is 13cm

Step-by-step explanation:

Area of semi circle=1/2pir²

308=1/2×22/7×r²

308=22r²/14

22r²=4312

divide both sides by 22

22r²/22=4312/22

r²=196

take the square root of both sides

√r²=√196

r=14cm

Erica works in a soda-bottling factory and earns 46¢ for each successfully capped bottle but loses 2¢ for each bottle she breaks. After capping some bottles, she has earned only 6¢ and has broken some bottles. To determine how many bottles Erica capped and how many she broke, a system of equations can be used.

   Let x be the number of bottles Erica capped and y be the number of bottles she broke. Then the following system of equations can be written:

46x - 2y = 6 (Equation 1)

x + y = 15 (Equation 2)

To solve the system of equations using substitution, we can isolate one of the variables in terms of the other from Equation 2, and substitute it in Equation 1. From Equation 2, y = 15 - x. Substituting this in Equation 1, we get 46x - 2(15 - x) = 6. Simplifying the equation, we get 48x - 30 = 6, which gives x = 9. Therefore, Erica has capped 9 bottles and broken 6 bottles.

To solve the system of equations using elimination, we can multiply Equation 2 by 46 to eliminate y. This gives us 46x + 46y = 690. Subtracting Equation 1 from this equation, we get 48y = 684, which gives y = 14.25. However, y cannot be a fractional value, so we can round it to the nearest whole number, which gives y = 14. Substituting y = 14 in Equation 2, we get x = 1. Therefore, Erica has capped 1 bottle and broken 14 bottles.

Both methods lead to different solutions, but this is because one of the solutions obtained is not feasible. Erica cannot cap a fraction of a bottle or break a fraction of a bottle. Therefore, the solution obtained using the elimination method needs to be rounded to the nearest whole number, which then gives the same solution as the substitution method, that Erica capped 9 bottles and broke 6 bottles.

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Erica works in a soda-bottling factory and earns 46¢ for each successfully capped bottle but loses 2¢ for each bottle she breaks. After capping some bottles, she has earned only 6¢ and has broken some bottles. To determine how many bottles Erica capped and how many she broke, a system of equations can be used.

  Let x be the number of bottles Erica capped and y be the number of bottles she broke. Then the following system of equations can be written:

46x - 2y = 6 (Equation 1)

x + y = 15 (Equation 2)

To solve the system of equations using substitution, we can isolate one of the variables in terms of the other from Equation 2, and substitute it in Equation 1. From Equation 2, y = 15 - x. Substituting this in Equation 1, we get 46x - 2(15 - x) = 6. Simplifying the equation, we get 48x - 30 = 6, which gives x = 9. Therefore, Erica has capped 9 bottles and broken 6 bottles.

To solve the system of equations using elimination, we can multiply Equation 2 by 46 to eliminate y. This gives us 46x + 46y = 690. Subtracting Equation 1 from this equation, we get 48y = 684, which gives y = 14.25. However, y cannot be a fractional value, so we can round it to the nearest whole number, which gives y = 14. Substituting y = 14 in Equation 2, we get x = 1. Therefore, Erica has capped 1 bottle and broken 14 bottles.

Both methods lead to different solutions, but this is because one of the solutions obtained is not feasible. Erica cannot cap a fraction of a bottle or break a fraction of a bottle. Therefore, the solution obtained using the elimination method needs to be rounded to the nearest whole number, which then gives the same solution as the substitution method, that Erica capped 9 bottles and broke 6 bottles.

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Therefore, the probability that the average daily revenue of the sample is between $2450 and $2460 is approximately 0.0443 or 4.43%.

The distribution of the sample means of size n = 100 from a population with mean μ = $2500 and standard deviation σ = $300 can be approximated by a normal distribution with mean = μ = $2500 and standard deviation = σ/√n = $300/√100 = $30.

Thus, we need to find the probability that the sample mean falls between $2450 and $2460.

Z-score for $2450:

z = (2450 - 2500) / 30 = -1.67

Z-score for $2460:

z = (2460 - 2500) / 30 = -1.33

Using a standard normal distribution table or calculator, we can find the probabilities associated with these z-scores:

P(z < -1.67) = 0.0475

P(z < -1.33) = 0.0918

Therefore, the probability that the average daily revenue of the sample is between $2450 and $2460 is:

P(-1.67 < z < -1.33) = P(z < -1.33) - P(z < -1.67)

= 0.0918 - 0.0475

= 0.0443

So, the probability is approximately 0.0443 or 4.43%.

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Answer:

The correct answer is 12.6n2 + 7.14n.

Step-by-step explanation:

To find the product of 2.1n(6n + 3.4), we can use the distributive property of multiplication:

2.1n(6n + 3.4) = 2.1n(6n) + 2.1n(3.4)

Simplifying this expression gives:

12.6n^2 + 7.14n

Therefore, the product of 2.1n(6n + 3.4) is 12.6n^2 + 7.14n.

Answer:

12.6n2 + 7.14n.

Step-by-step explanation:

2.1×n×(6n+3.4)

Rewrite the expression

2.1×n(6n+3.4)

Calculate the product

2.1n(6n+3.4)

Apply the distributive property

2.1n×6n+2.1n×3.4

Multiply the terms

12.6n

2

+2.1n×3.4

Solution

12.6n

2

+7.14n

These equations can be used to determine the number of bottles of soda (R) and the number of bottles of juice (J) purchased by Nayeli. The resulting system of equations is:

25R + 15J = 205

R = J + 5.

To solve this problem, we can set the following variables:

R = Number of bottles of soda purchased.

J = Number of bottles of juice purchased.

We can establish the following equations based on the information provided:

"Each bottle of soda has 25 grams of sugar": So the total amount of sugar in the bottles of soda is 25R.

"Each bottle of juice has 15 grams of sugar": Therefore, the total amount of sugar in the bottles of juice is 15J.

"Nayeli bought 5 more bottles of soda than bottles of juice": Therefore, the number of soda bottles is equal to the number of juice bottles plus 5, which can be expressed as R = J + 5.

"All together contain 205 grams of sugar": So the sum total of sugar is 25R + 15J, which equals 205.

The resulting system of equations is:

25R + 15J = 205

R = J + 5.

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Answer:

21x+6

Here is the answer

Its a pleasire

Answer:

21x+6

Step-by-step explanation:

first distrbute the 3 on the brackets

and note that in mathematics when there is no sign just like after the 3 it means it's multiplication

3(2x+5)+3(5x-3)

=6x+15+15x-9

now add or subtract

=21x+6

that is the simplest we can get and we can't find the value of x cuz this is not an equation

(there is no equal sign and numbers on both sides )

Answer:6

Step-by-step explanation:

dependent is the varible

The equations (x,y) | x + y > 1 and y (1/2)x + 2 have these solutions as their solutions.

To solve the system of inequalities without using graphs, we can use algebraic methods. First, we can rearrange the second inequality to slope-intercept form y < (1/2)x + 2.

This inequality represents a line with slope 1/2 and y-intercept 2. Next, we can identify the region of the coordinate plane that satisfies the first inequality, x + y > 1. This region is above the line x + y = 1. To check which side of the line satisfies the inequality, we can test a point, such as (0,1),

0 + 1 > 1

This is true, so the region above the line x + y = 1 satisfies the inequality.

Finally, we can combine the regions from the two inequalities to find the solution set. The solution set is the region above the line x + y = 1 and below the line y = (1/2)x + 2.

Therefore, the solution set can be expressed as,

{(x,y) | x + y > 1 and y < (1/2)x + 2}.

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Complete question - solve the given system of inequalities in two variables.

x + y > 1

y < 1/2x + 2

The following versions of the underlined text would best accomplish this goal is an inconvenient and time-consuming process

This version of the underlined text best accomplishes the writer's goal of providing evidence to clarify the previous sentence's point about what advocates fail to consider. By mentioning that compliance with local building codes is an inconvenient and time-consuming process, it highlights a significant factor that advocates may overlook when promoting the idea of purchasing or renting land for a tiny home. This evidence emphasizes the challenges and potential barriers involved in the process, which helps to clarify the previous point and provide a more comprehensive understanding of the situation.

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The expression that correctly calculate the perimeter of the right triangle is:

15 + 15tan42° + 15/cos42°

Trigonometry deals with the relationship between the ratios of the sides of a right triangle with its angles.

The perimeter of the right triangle is the sum of all the sides of the triangle.

We have:

15 units

Let the side opposite angle 42° be x. Thus,

tan 42 = x/15

x = 15 tan 42°

For the hypotenuse side (h):

cos 42° = 15/h

h = 15/cos 42°

Perimeter = 15 + x + h

Perimeter = 15 + 15tan42° + 15/cos42°

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Complete Question

Check the attached image

The length of segment BD, which represents the altitude of the triangle, is given as follows:

BD = 6.

The geometric mean theorem states that the length of the altitude of a triangle is equal to the geometric mean of the lengths of the segments formed on the hypotenuse.

The altitude segment for this problem is given as follows:

BD.

The bases for this problem are given as follows:

3 and 12.

Hence the length of segment BD is obtained as follows:

(BD)² = 3 x 12 -> geometric mean formula

(BD)² = 36

(BD)² = 6².

BD = 6.

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Answer:

The mean weekly wage for the two women is £380.

Step-by-step explanation:

We can use the weighted mean formula to solve this problem.

Firstly, we calculate the total weekly wage for the ten employees by multiplying the mean weekly wage by the total number of employees:

Total weekly wage = Mean weekly wage x Number of employees

Total weekly wage = £396 x 10

Total weekly wage = £3,960

We can then subtract the total weekly wage for the eight men to find the total weekly wage for the two women:

Total weekly wage for 2 women = Total weekly wage - Total weekly wage for 8 men

Total weekly wage for 2 women = £3,960 - (£400 x 8)

Total weekly wage for 2 women = £3,960 - £3,200

Total weekly wage for 2 women = £760

Now, we can calculate the mean weekly wage for the two women by dividing their total weekly wage by the number of women:

Mean weekly wage for 2 women = Total weekly wage for 2 women / Number of women

Mean weekly wage for 2 women = £760 / 2

Mean weekly wage for 2 women = £380

Therefore, the mean weekly wage for the two women is £380.

The volume of the cone is 251.20 cubic centimeters if the diameter of the cone is 20 cm and the height of the cone is 24 cm.

The diameter of the cone = 20 cm

The radius of the cone = diameter /2 = 20/2 = 10cm

The height of the cone = 24 cm

The volume of the cone is calculated by using the formula is:

V = (1/3)*π* [tex]r^2[/tex] *h

Substituting the values, we get:

V = (1/3)* π * [tex]r^2[/tex] *h

V = (1/3) * π * [tex](10 cm)^2[/tex] * (24 cm)

V = (1/3) *π * ([tex]100 cm^2[/tex]) * (24 cm)

V = 251.20 cubic centimeters.

Therefore, we can conclude that the volume of the cone is 251.20 cubic centimeters.

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Use  Theoretical probability  there are 220 students in the grade.

We can use the formula for theoretical probability to find the number of students in the grade:

P(event) = number of favorable outcomes / number of total outcomes

In this case, the probability of a student trying out for the school play is 1/10, so we have:

1/10 = number of students who try out / total number of students in the grade

We can simplify this equation by multiplying both sides by the total number of students in the grade:

total number of students in the grade * 1/10 = number of students who try out

Multiplying both sides by 10, we get:

total number of students in the grade = 10 * number of students who try out

Substituting the given value of 22 for the number of students who try out, we get:

total number of students in the grade = 10 * 22

total number of students in the grade = 220

Therefore, there are 220 students in the grade.

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The solution to the inequality is x > 7

Given data ,

To represent the inequality -3x + 5 < -16 on a number line, follow these steps:

Step 1:

Solve the inequality for x

-3x + 5 < -16

Step 2:

Subtract 5 from both sides of the inequality

-3x < -16 - 5

-3x < -21

Step 3:

Divide both sides of the inequality by -3. Note that when dividing by a negative number, the direction of the inequality sign should be reversed:

x > (-21)/(-3)

x > 7

Step 4:

Plot a closed circle on 7 (since the inequality is strictly greater than) and shade the region to the right of 7 on the number line

Hence , the inequality is x > 7

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The stem and leaf for the data values is

60 | 0.8 3.5

70 | 2.8 3.8 5.5 7.8 8.3 9.7

80 | 0.6, 2.1, 4.5

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

Data values:

82.1 72.8 78.3 77.8 60.8 79.7 73.8 75.5 80.6 84.5 63.5

Sort in order of tens

So, we have

60.8 63.5

72.8 73.8 75.5 77.8 78.3 79.7

80.6, 82.1, 84.5

Next, we draw the stem and leaf as follows:

a | b

Where

a = stem

b = leaf

Using the above as a guide, we have the following:

60 | 0.8 3.5

70 | 2.8 3.8 5.5 7.8 8.3 9.7

80 | 0.6, 2.1, 4.5

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H0 represents the null hypothesis,

H1 represents the alternative hypothesis,

μ represents the population mean body temperature, and

μ0 represents the claimed mean body temperature.

We are testing the claim that the mean body temperature of a healthy adult is not equal to a certain value. Let's denote the claimed mean body temperature as μ0.

Null Hypothesis (H0):

The mean body temperature of a healthy adult is equal to μ0.

Alternative Hypothesis (H1):

The mean body temperature of a healthy adult is not equal to μ0.

So the null hypothesis states that there is no significant difference between the claimed mean body temperature (μ0) and the actual mean body temperature, while the alternative hypothesis suggests that there is a significant difference.

In symbolic form:

H0: μ = μ0

H1: μ ≠ μ0

The question, the specific value for the claimed mean body temperature was not provided, so we'll refer to it as μ0 without a numerical value.

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After 4 seconds, both containers will have the same amount of water.

Let's assume that after "t" seconds, both containers will have the same amount of water.

In "t" seconds, the first container will have 56 + t gallons of water.

In "t" seconds, the second container will have 64 - t gallons of water.

To find out when both containers will have the same amount of water, we need to solve the equation:

56 + t = 64 - t

By solving for "t", we get:

2t = 8

t = 4

Therefore, after 4 seconds, both containers will have the same amount of water.

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Answer:

463.52 meters

Step-by-step explanation:

To find the length of the training track running around the field, we need to calculate the perimeter of the entire field.

The field is made up of a rectangle with dimensions 85m by 57m, and two semicircles with a radius of 57/2 = 28.5m.

The perimeter of the rectangle is 2(85m) + 2(57m) = 284m.

The perimeter of each semicircle is half the circumference of a full circle with radius 28.5m, which is π(28.5m) = 89.76m. So the total perimeter of both semicircles is 2(89.76m) = 179.52m.

Therefore, the total perimeter of the field is 284m + 179.52m = 463.52m.

Rounding to the nearest hundredth, the length of the training track running around the field is 463.52 meters.

Answer:

26 + 22 + ? = 52

Step-by-step explanation:

52 horses in total.

26 brown and 22 black. 26 + 22 = 48.

52 - 48 = 4 (number white horses)

Logarithmic functions and exponential functions are inverse functions of each other

The value of x in the equation  log₃ (x + 5 ) = 4  is 76

The format of the logarithmic function log₃ (x + 5 ) = 4  is

solving  the equation

3⁴ = x + 5

81 = x + 5

x = 76

the solution to the equation log3 (x + 5) = 4 is x = 76.

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