a set of data items is normally distributed with a mean of 300 and a standard deviation of 50. find the data item in this distribution that corresponds to the given z-score.

Answer:

D

Step-by-step explanation:

A: Not A. It can be graphed. It is a vertical line where x = 3. Every point must have an x value of 3. (3,4), (3,0), (3.- 6) are all on x = 4. It can be graphed, but it is not a function.

B:  Not B. It is not a function at all. To be a function, it can only have 1 y value associated with it.

C: It's not a linear function because it is not a function.

D is your answer

Answer:

Natural selection is a mechanism, or cause, of evolution. Adaptations are physical or behavioral traits that make an organism better suited to its environment. Heritable variation comes from random mutations. Random mutations are the initial cause of new heritable traits.

Answer:

Darwin's theory of evolution

Charles Darwin developed a theory of evolution to explain the unity and diversity of life, based on the idea of shared common ancestors.

Natural selection

Darwin's theory was based on the mechanism of natural selection, which explains how populations can evolve in such a way that they become better suited to their environments over time.

Light colored mice are more easily seen by predators and are therefore preyed upon more. Dark mice are better adapted to their environment and better able to survive and reproduce.

Light colored mice are more easily seen by predators and are therefore preyed upon more. Dark mice are better adapted to their environment and better able to survive and reproduce.

Natural selection acting on mice population over time.

Individuals have variations within their heritable traits. Some variations make an individual better suited to survive and reproduce in their environment.

If this continues over generations, these favorable adaptations (the heritable features that aid survival and reproduction) will become more and more common in the population.

The population will not only evolve (change in its genetic makeup and inherited traits), but will evolve in such a way that it becomes adapted, or better-suited, to its environment.

Artificial selection

There are other types of selection, in addition to natural selection, that are out there in the world.

Artificial selection, also called "selective breeding”, is where humans select for desirable traits in agricultural products or animals, rather than leaving the species to evolve and change gradually without human interference, like in natural selection.

A timeline showing how dogs became domesticated over a long period of time due to artificial selection.

A timeline showing how dogs became domesticated over a long period of time due to artificial selection.

Dog breeding is a perfect example of how humans select for desirable or fashionable traits. Breeders deliberately mate parents with the hope of producing offspring with specific traits (such as color, size, ear shape, snout length, and so on).

Common mistakes and misconceptions

Evolution is not the same as adaptation or natural selection. Natural selection is a mechanism, or cause, of evolution. Adaptations are physical or behavioral traits that make an organism better suited to its environment.

Heritable variation comes from random mutations. Random mutations are the initial cause of new heritable traits. For example, a rabbit can't choose to have a different fur color. Rather, a genetic mutation causes a difference in fur color, which may help that rabbit hide better in its environment.

Natural selection acts on existing heritable variation. Natural selection needs some starting material, and that starting material is heritable variation. For natural selection to act on a feature, there must already be variation, and that variation must be able to be passed on to offspring.

Natural selection depends on the environment. Natural selection doesn't favor traits that are somehow inherently superior. Instead, it favors traits that are beneficial in a specific environment. Traits that are helpful in one environment might actually be harmful in another.

Step-by-step explanation:

Answer:

20 people participated in the survey.

Answer:

(x + 10)(x + 2)

Step-by-step explanation:

x² + 12x +20

(x + 10)(x + 2)

Answer:

(x+2)(x+10)

Step-by-step explanation:

The given trinomial needs to be factorised. On the basis of degree of power of polynomial it can also be called a quadratic polynomial . General form is ax² + bx + c .

= x² + 12x + 20

= x² + 10x + 2x + 20

= x ( x + 10 ) + 2( x + 10 )

= ( x + 2)( x +10)

Answer:

Step-by-step explanation:

The easiest way is to graph both functions and see where they intersect.  The intersection is where f(x) = g(x).

f(x) = -x² - 3x + 6

g(x) = 2x² + 5x + 3

We can form a total of 42 stacks of 8 cans each from the 7 boxes of cat food received by the pet store.

Now, We can use a bar model to represent the total number of cans and the number of stacks that can be formed.

First, let's find the total number of cans:

7 boxes x 48 cans/box = 336 cans

Now, let's use a bar model to represent this total:

| 336 cans of food  |

Next, we want to find how many stacks of 8 cans we can form. We can use a separate bar model to represent the size of each stack:

| 42 stacks of 8 cans each |

Hence, The number of stacks that can be formed, we need to divide the total number of cans by the number of cans in each stack:

336 cans ÷ 8 cans/stack = 42 stacks

So the final bar model looks like this:

| 336 cans of food  | = | 42 stacks of 8 cans each |

Therefore, we can form a total of 42 stacks of 8 cans each from the 7 boxes of cat food received by the pet store.

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(a) There can be a maximum of 18 teams.

(b) The largest possible number of teams is 18, and there will be a total of 19 players on each team.

Given information:

In a local, recreational soccer league there are 252 men and 90 women signed up to play. The organizers need to make sure that everyone is on a team, the teams are the same size, each team has the same number of males; and each team has the same number of females.

(a) To find the largest possible number of teams, we need to divide the players (252 men and 90 women) into teams, where each team has the same number of males and females. Let's find the GCD (greatest common divisor) of 252 and 90:

GCD of 252 and 90 = GCD (252,90) = 18.

Therefore, there can be a maximum of 18 teams.

(b) Since the number of teams is 18, and we have 252 men and 90 women, there will be a total of 342 players.

Now, we need to divide these 342 players into 18 teams. Each team must have an equal number of males and females. Number of males = 252, Number of females = 90.

To divide the players equally into teams, we need to find the number of males and females that can be in one team.

Number of males in one team = 252/18 = 14

Number of females in one team = 90/18 = 5

Therefore, each team will have 14 males and 5 females, and there will be a total of 19 players on each team (14 + 5).

Thus, the largest possible number of teams is 18, and there will be a total of 19 players on each team.

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A tax of 7.5 percent was added to the product to make it equal to 27.95.

The firm's profit margin is 7.11%.

Given data:

Asset Turnover (ATO) = 1.9

Return on Assets (ROA) = 13.5%

Assets (A) = $8,940,000

The formula of Return on assets (ROA) is:

ROA = Net Income / Total Assets

OR ROA = Profit Margin × Asset Turnover

OR Profit Margin = ROA / Asset Turnover

Profit Margin = ROA / Asset Turnover=

13.5% / 1.9= 0.0711 or 7.11%.

Therefore, the company's profit margin is 7.11%.

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The height of the vertical walls is 10 ft=480 sq ft. The triangles that make up the roof are isosceles triangle 80 sq ft. The greenhouse uses 504 square feet of glass to construct.

To calculate the amount of glass used to make the greenhouse, to determine the total surface area of the glass panels.

The greenhouse consists of four vertical rectangular walls and two triangular roof sections.

The total surface area of the vertical walls calculated by adding the areas of each wall. Since the greenhouse is rectangular, the height of the walls is 10 ft, and the total width of the walls (including the door) is 16 ft + 8 ft = 24 ft.

Area of each wall = height x width

Area of vertical walls = 2 x (height x width) = 2 x (10 ft x 24 ft) = 480 sq ft

Each roof section forms an isosceles triangle. The base of each triangle is the width of the greenhouse, which is 16 ft. The height of the triangle is the difference between the total height of the greenhouse (15 ft) and the height of the vertical walls (10 ft), which is 5 ft.

Area of each triangular roof section = 0.5 x base x height

Area of triangular roof = 2 x (0.5 x 16 ft x 5 ft) = 80 sq ft

The door is not made of glass, so we need to subtract its area from the total.

Area of the door = width x height = 8 ft x 7 ft = 56 sq ft

calculate the total glass surface area by subtracting the area of the door from the sum of the vertical walls and triangular roof sections.

Total glass surface area = (Area of vertical walls + Area of triangular roof) - Area of the door

Total glass surface area = (480 sq ft + 80 sq ft) - 56 sq ft

Total glass surface area = 504 sq ft

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Answer:

x(t) = 37cos(70o)t and y(t) = –16t2 + 37sin(70o)t

Step-by-step explanation:

If Becky buys 1 cup of coffee and 4 pieces of cake, her total utility can be calculated by summing the individual utilities for each item consumed. According to the given estimates, the total utility from 1 cup of coffee is 35, and the total utility from 4 pieces of cake is 91. Therefore, Becky's total utility for this consumption bundle would be 35 + 91 = 126.

The table provided showcases the relationship between the quantities of coffee and cake and their respective utilities. Each row in the table represents a different consumption bundle, displaying the number of cups of coffee and pieces of cake. The "Total Utility" column indicates the total utility achieved for each consumption bundle. By selecting the row corresponding to 1 cup of coffee and 4 pieces of cake, we find a total utility of 126. This indicates that Becky would derive a total utility of 126 from this particular combination of coffee and cake, suggesting that it would be a favorable choice for her meeting with her office mate.

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1. Graphical output from the regression analysis is as follows:

The results output from the regression analysis is as follows:

2. as the year increases, TB incidence decreases.

3. The slope is -903.1.

This means that for every one-unit increase in a year, the TB incidence decreases by 903.1 cases.

4. The test statistic is -14.16, with a p-value of less than 0.0001.

Since the p-value is less than 0.05, we can reject the null hypothesis and conclude that there is a significant relationship between year and TB incidence.

5. Possible reasons for the decrease in the incidence of TB include better treatment and prevention measures, as well as increased public awareness and education about the disease.

6. The 95% confidence interval for this predicted value is (25,433.2, 35,125.6).

7. This confidence interval tells us that we are 95% confident that the true number of TB cases in 1980 falls between 25,433.2 and 35,125.6.

1. Regression analysis:

First of all, to make sure that the simple random sample is normally distributed and has a constant variance, a histogram was created from the data set (i.e., TB incidence).

After checking that the assumption of normality was satisfied, a regression analysis was performed.

Graphical output from the regression analysis is as follows:

The results output from the regression analysis is as follows:

2. Describe the relationship and state or paste the correlation coefficient

The correlation coefficient is -0.745, indicating a moderately strong negative relationship between TB incidence and year.

This can also be observed from the graph; as the year increases, TB incidence decreases.

3. What is the slope? Interpret it

The slope is -903.1.

This means that for every one-unit increase in year, the TB incidence decreases by 903.1 cases.

4. State the test statistic and p-value from your regression analysis. State the null and alternative in words and equations.

Based on these results, what do you conclude?

The null hypothesis is that the slope is equal to zero (i.e., no relationship between year and TB incidence).

The alternative hypothesis is that the slope is not equal to zero (i.e., there is a relationship between year and TB incidence).

The test statistic is -14.16, with a p-value of less than 0.0001.

Since the p-value is less than 0.05, we can reject the null hypothesis and conclude that there is a significant relationship between year and TB incidence.

5. Based on the results above, can we conclude that time is causing the incidence of TB to decrease? Why or why not? Explain your thoughts, and what are possible reasons for the decrease in incidence of TB.

Yes, we can conclude that time is causing the incidence of TB to decrease.

This is because the slope is negative and statistically significant, indicating that as the year increases, the TB incidence decreases.

Possible reasons for the decrease in the incidence of TB include better treatment and prevention measures, as well as increased public awareness and education about the disease.

6. Perform the appropriate analysis to determine the 95% confidence interval for the number of cases of TB for 1980. Paste results.

Using the regression equation, the predicted value for 1980 is 30,279.4 cases.

The 95% confidence interval for this predicted value is (25,433.2, 35,125.6).

7. What is this confidence interval telling you?

This confidence interval tells us that we are 95% confident that the true number of TB cases in 1980 falls between 25,433.2 and 35,125.6.

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Answer:

m∠A is 89°

Step-by-step explanation:

By circle theorem, two or more inscribed angles subtended by the same arc are equal

Therefore, from the diagram, we have;

Angle (5·x - 1)° and angle (4·x + 17)° subtends the same arc DC

∴ (5·x - 1)° = (4·x + 17)°

We can write the angles as follows since they are both in degrees

(5·x)° - 1° = (4·x)° + 17°

(5·x - 4·x)° = 17° + 1°

x = 18°

m∠A = (5·x - 1)°

∴ m∠A = (5 × 18 - 1)° = (90 - 1)° = 89°

m∠A = 89°.

Answer:

Car M:

50.4/2 = 25.2

car M uses up 1 gallon every 25.2 miles

Car P:

Just from the graph, you can see that it uses up 1 gallon every 30 miles

The two graphs vary the /miles slightly but it is around their zones of 25.2 and 30. It varies slightly because the cars may be traveling at a fast speed or slower speed thus using up more or less fuel by the time they've reached the recorded distances on the graphs.

Answer:

Step-by-step explanation:

Answer:

19 cookies

Step-by-step explanation:

200/8 = 25

25 grams of flour in each cookie.

480/25 = 19.2

Rosie can make up to 19 cookies with 480g of flour

Answer:

The greatest number of cookies Rosie can make is 19 cookies.

Step-by-step explanation:

200g = 8 cookies

400g = 16 cookies

475g = 19 cookies

you only have 480 g of flour and 1 cookie uses 25 g of flour.

Your Welcome!

Answer:

the pyramid is 80 ft² and the rectangular prism is 240 ft²

Step-by-step explanation:

Answer:

690.50

Step-by-step explanation:

a) There are no solutions to the equation.

To find all solutions to the equation 34 - 38 = 3, we can simplify the equation:

34 - 38 = 3

-4 = 3

However, this equation is not true, as -4 is not equal to 3. Therefore, there are no solutions to the equation.

b) Now, let's consider the diophantine equation 1/x + 1/y = 1/5, where x and y are integers. To find all solutions, we can follow these steps:

1: Multiply both sides of the equation by 5xy to eliminate the denominators:

5y + 5x = xy

2: Rearrange the equation:

xy - 5x - 5y = 0

3: Apply Simon's Favorite Factoring Trick:

Add 25 to both sides to complete the square:

xy - 5x - 5y + 25 = 25

xy - 5x - 5y + 25 = 25

(xy - 5x - 5y + 25) + 25 = 25 + 25

(x - 5)(y - 5) = 50

4: List all possible factor pairs of 50:

(1, 50), (2, 25), (5, 10), (-1, -50), (-2, -25), (-5, -10)

5: Solve for x and y in each factor pair:

For (x - 5)(y - 5) = 50:

If x - 5 = 1 and y - 5 = 50, then x = 6 and y = 55.

If x - 5 = 2 and y - 5 = 25, then x = 7 and y = 30.

If x - 5 = 5 and y - 5 = 10, then x = 10 and y = 15.

If x - 5 = -1 and y - 5 = -50, then x = 4 and y = -45.

If x - 5 = -2 and y - 5 = -25, then x = 3 and y = -20.

If x - 5 = -5 and y - 5 = -10, then x = 0 and y = -5.

Therefore, the solutions to the diophantine equation 1/x + 1/y = 1/5, where x and y are integers, are:

(x, y) = (6, 55), (7, 30), (10, 15), (4, -45), (3, -20), (0, -5).

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Yes, in a group of 700 people, there must be two people with the identical first and last initials.

Because there are 26 distinct letters in the English alphabet, there are 26 × 26 = 676 potential combinations of two initials. According to the pigeonhole principle, at least two people in a group of 700 share the same initials. (Here: persons are pigeons, combinations of two initials are pigeonholes).

Note that in alphabets with 27 or more letters, this is no longer valid because there are 27 × 27 = 729 > 700 options for the initials.

If we try to assign a distinct combination to each individual in the group, we can only do so for the first 676 persons, leaving the remaining 24 with the same first and last initial. As a result, the answer is yes, there must be two people with the same first and last initials.

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Correct question:

In a group of 700 people, must there be 2 who have the same first and last initials? Why?

Answer:

7. 9

8. 6.7

9. 12.2

10. 7.6

11. 7.3

12. 6.3

Step-by-step explanation:

7. 8^2+4^2=x^2

64+16=x^2

80=x^2

√80=√x^2

8.9=x

Round up

9=x

8. 6^2+3^2=x^2

36+9=x^2

45=x^2

√45=√x^2

6.7=x

9. 7^2+10^2=x^2

49+100=x^2

149=x^2

√149=√x^2

12.2=x

10. 3^2+7^2=x^2

9+49=x^2

58=x^2

√58=√x^2

7.6=x

11. 7^2+2^2=x^2

49+4=x^2

53=x^2

√53=√x^2

7.28=x

Round up

7.3=x

12. 6^2+2^2=x^2

36+4=x^2

40=x^2

√40=√x^2

6.3=x

Hope this helps

Answer:

7) X = a^2 + b^2 = c^2

X = (4^2) + (8^2) = c^2

X = 80^2 = c^2

X = √80 = 8.944

X = 8.9 = c^2

8) X = a^2 + b^2 = c^2

X = (6^2) + (3^2) = c^2

X = 45^2 = c^2

X = √45 = 6.708

X = 6.7 = c^2

9) X = a^2 + b^2 = c^2

X = (7^2) + (10^2) = c^2

X = 149^2 = c^2

X = √149 = 12.206

X = 12.2 = c^2

10) X = a^2 + b^2 = c^2

X = (3^2) + (7^2) = c^2

X = 58^2 = c^2

X = √58 = 7.615

X = 7.6 = c^2

11) X = a^2 + b^2 = c^2

X = (7^2) + (2^2) = c^2

X = 53^2 = c^2

X = √53 = 7.280

X = 7.3 = c^2

12) X = a^2 + b^2 = c^2

X = (2^2) + (6^2) = c^2

X = 40^2 = c^2

X = √40 = 6.324

X = 6.3 = c^2

Step-by-step explanation:

X = a^2 + b^2 = c^2

X and c^2 = missing side

a^2 and b^2 = the two legs of the triangle (the mesurments of the sides that are given)

c^2 = hipatanouse

The formula is called Pythagromtherom (a^2 + b^2 = c^2)

(a) The original price of the shoes was $100.

(b) You saved $37.

(c) You spent 63/100 = 0.63 or 63% of the original price.

If m and n are relatively prime, the numerator (an + bm) and denominator (mn) have no common factors other than 1, and therefore, (an + bm)/(mn) is in lowest terms.

To prove that (an + bm)/(mn) is in lowest terms if and only if m and n are relatively prime, we will need to establish two separate claims:

Claim 1: If (an + bm)/(mn) is in lowest terms, then m and n are relatively prime.

Claim 2: If m and n are relatively prime, then (an + bm)/(mn) is in lowest terms.

Proof of Claim 1:

Let's assume that (an + bm)/(mn) is in lowest terms. This means that the numerator (an + bm) and the denominator (mn) have no common factors other than 1.

Suppose m and n are not relatively prime, which means they have a common factor greater than 1.

Let's say that factor is d, where d > 1. Then we can express m and n as follows: m = dx and n = dy, where x and y are integers.

Now, we rewrite the numerator (an + bm) as follows:

an + bm = an + b(dx) = n(a + bx/d)

Since m = dx and n = dy, we have (an + bm)/(mn) = (n(a + bx/d))/(dx * dy) = (a + bx/d)/(xy).

We can see that both the numerator (a + bx/d) and the denominator (xy) have the factor d.

This contradicts our assumption that (an + bm)/(mn) is in lowest terms, as they have a common factor greater than 1.

Therefore, m and n must be relatively prime.

Proof of Claim 2:

Now, let's assume that m and n are relatively prime, which means they have no common factors other than 1.

To show that (an + bm)/(mn) is in lowest terms, we need to demonstrate that its numerator and denominator have no common factors other than 1.

Let's suppose that the numerator (an + bm) and the denominator (mn) have a common factor d, where d > 1.

This implies that d divides both an + bm and mn.

Since d divides mn, we can express m and n as follows: m = dx and n = dy, where x and y are integers.

Now, let's rewrite the numerator (an + bm) as follows:

an + bm = an + b(dx) = n(a + bx/d)

We can see that d divides both n and the expression (a + bx/d). Therefore, d also divides the numerator (an + bm).

However, we initially assumed that (an + bm)/(mn) is in lowest terms, which means the numerator and denominator have no common factors other than 1. This contradicts the assumption that they have a common factor d > 1.

Thus, if m and n are relatively prime, the numerator (an + bm) and denominator (mn) have no common factors other than 1, and therefore, (an + bm)/(mn) is in lowest terms.

By proving both Claim 1 and Claim 2, we have established that (an + bm)/(mn) is in lowest terms if and only if m and n are relatively prime.

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Answer: 1. No because there are no numbers to solve it. 2. Yes, has numbers.  3.Yes, has numbers. 4.No because there are no numbers to solve it.  5. not sure  6.not sure  7. not sure  8.not sure  9. not sure

Step-by-step explanation:

Answer:

for 100: 14,800

for 10: 14,780

for 1: 14,780

for 1000: 15,000

Step-by-step explanation:

ok so just go for like if its

18 its going to be 20 if its 11 its going to be 10

Hope this helps!!

PLEASE CROWN TYY

Answer:

Rounding Rules:

1. If the number you are rounding is followed by 5, 6, 7, 8, or 9, round the number up. Example: 38 rounded to the nearest ten is 40. ...

2. If the number you are rounding is followed by 0, 1, 2, 3, or 4, round the number down. Example: 33 rounded to the nearest ten is 30.

Step-by-step explanation:

100: 14,800

10: 14,780

1: 14,780

1000: 15,000

Answer:

12x - 8y

Step-by-step explanation:

9x - 5y + 3x + 2y - 4y - y​

9x + 3x - 5y + 2y - 4y - y

12x - 8y

Answer:

12x - 8y would be the simplified version of this equation if this is not the type of answer your looking for please lmk

Step-by-step explanation:

Answer:

309.8 mm

Step-by-step explanation:

17.6 x 17.6= 309.76

309.76 rounded is 309.8

Answer:

309.8

Step-by-step explanation:

The formula for area of square is one of its sides times another (or its side squared).

So if one of the side is 17.6, it would be 17.6^2 which is 309.76.

You then round one decimal place and get 309.8

Have a good day

Answer:

It's A don't listen to the other guy

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

edg 22

Answer:

0.66

Step-by-step explanation:

1.00 - 0.34 = 0.66