please help me to do easier MATH

Answer:

The mean height is 3.2 feet and thestandard deviation 0.6 feet. A… ... A forest ranger has data on the heights of a large growth ... mately what fraction of the trees should we expect to be.

The  fraction of the trees that is between 4.0 and 4.4 feet is 7%

The z score is used to determine by how many standard deviations the raw score is above or below the mean. The z score is given by:

\(z=\frac{x-\mu}{\sigma}\)

x is the raw score, μ is mean and σ is standard deviation

Given that μ = 3.2, σ = 0.6, hence:

\(For\ x = 4:\\\\z=\frac{4-3.2}{0.6} =1.33\\\\\\For\ x = 4.4:\\\\z=\frac{4.4-3.2}{0.6} =2\)

From the normal distribution table, P(4 < x < 4.4) = P(1.33 < z < 2) = P(z < 2) - P(z < 1.33) = 0.9772 - 0.9082 = 7%

The  fraction of the trees that is between 4.0 and 4.4 feet is 7%

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There will be 221 highway signs on the road trip.

What is Total Length?

Whole Length (TL) is the measurement taken in a straight line, with the fish lying on its side, from the tip of the snout to the end of the tail (caudal fin).

The total length of the road trip is 13.2 hours.

Highway signs are posted every 0.06 hours. To find out how many highway signs are on the road trip, we can divide the total length of the road trip by the interval between each sign and then add one more sign for the end of the road trip:

(number of signs) = (total length of road trip) / (interval between signs) + 1

Substituting the values, we get:

(number of signs) = 13.2 / 0.06 + 1

(number of signs) = 220 + 1

(number of signs) = 221

Therefore, there will be 221 highway signs on the road trip.

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Answer:

A GPA is the average of all your class grade scores combined.

Answer:

13.56

Step-by-step explanation:

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1) y = 6

2) x = 3

3) y = - 2/3

4) x = - 6

So all we have to do is substitute the known 'variable' and solve for the unknown variable.

1)    2(-3) + 3y = 12

                 3y = 12 + 6

                  y = 6

2)    4y = (1/3)x - 5

    4(-1) = (1/3)x - 5

   (1/3)x = 5 - 4

        x = 3

3)       (x/3) - 2 = y

    (4/3) - (6/3) = y

                    y = (-2/3)

4)   2(x+1) = 5y

     2(x+1) = 5(-2)

    2x + 2 = - 10

          2x = -12

           x = -6

Answer:

n = 6

Step-by-step explanation:

9n - 24 = 4n + 6              {Subtract 4n from both sides }

9n - 24 -4n = 6

       5n - 24 = 6               {Add 24 to both sides}  

               5n = 6 + 24

               5n = 30

                 n = 30/5

n = 6

Answer:

n=6

Step-by-step explanation:

Simplifying

9n + -24 = 4n + 6

Reorder the terms:

-24 + 9n = 4n + 6

Reorder the terms:

-24 + 9n = 6 + 4n

Solving

-24 + 9n = 6 + 4n

Solving for variable 'n'.

Move all terms containing n to the left, all other terms to the right.

Add '-4n' to each side of the equation.

-24 + 9n + -4n = 6 + 4n + -4n

Combine like terms: 9n + -4n = 5n

-24 + 5n = 6 + 4n + -4n

Combine like terms: 4n + -4n = 0

-24 + 5n = 6 + 0

-24 + 5n = 6

Add '24' to each side of the equation.

-24 + 24 + 5n = 6 + 24

Combine like terms: -24 + 24 = 0

0 + 5n = 6 + 24

5n = 6 + 24

Combine like terms: 6 + 24 = 30

5n = 30

Divide each side by '5'.

n = 6

Simplifying

n = 6

The relationship between two variables in which one variable doubles when the other variable doubles is called a direct proportion or direct relationship.

This means that the two variables are directly related, and their values increase or decrease in the same proportion.

In mathematical terms, this is represented by a linear equation in the form of y = kx, where y is the dependent variable, x is the independent variable, and k is the constant of proportionality.

Therefore, when x doubles, y doubles as well, and when x triples, y triples as well.

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Answer:

1,608.5 cm³

Step-by-step explanation:

radius = 16 : 2 = 8 cm

base area = 8² · π = 64 ·π = 201.06193 cm²

Volume = 201.06193 · 8  = 1,608.495439 cm³

The total number of students in the class is 1240.

How to calculate ratio ?

To calculate a ratio, you need to express the relationship between two or more quantities in the form of a fraction. Here are the steps to follow:

Identify the quantities you want to compare. For example, if you want to compare the number of boys and girls in a class, these would be the two quantities.

Write the quantities as a fraction, with the numerator representing one quantity and the denominator representing the other. For example, if there are 20 boys and 30 girls, the ratio of boys to girls would be 20/30 or 2/3.

Simplify the ratio by dividing both the numerator and denominator by their greatest common factor. In the example above, both 2 and 3 are divisible by 2, so the simplified ratio would be 1/3.

Express the ratio in the form of a statement, using a colon to separate the two quantities. For example, the ratio of boys to girls in the class is 1:3.

Note that ratios can also be expressed in different ways, such as as a decimal or percentage, but the steps above are the basic method for calculating a ratio.

Let the number of boys be 11x and the number of girls be 9x.

According to the given condition, 11x - 9x = 124

Therefore, 2x = 124

x = 62

So the number of boys is 11x = 11 * 62 = 682

And the number of girls is 9x = 9 * 62 = 558

Thus, the total number of students is the sum of the number of boys and girls, which is:

Total = 682 + 558 = 1240

Therefore, the total number of students in the class is 1240.

In conclusion, there are 682 boys and 558 girls in the class, and the total number of students is 1240.

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r = 42 - 3.50m is the equation to represent, r, the amount of money remaining in Shawna's lunch account after she purchases m meals, -3.5 is the slope and 42 is y intercept.

To represent the amount of money remaining in Shawna's lunch account after she purchases m meals, we can use the equation:

r = 42 - 3.50m

r represents the amount of money remaining in Shawna's lunch account.

42 represents the initial amount of money loaded into her account at the start of the school year.

3.50 represents the cost of each meal in the school cafeteria.

m represents the number of meals Shawna has purchased.

Now let's determine the slope and y-intercept of this equation:

The slope represents the rate at which the money in Shawna's account decreases with each meal purchase.

The slope is -3.50, indicating that $3.50 is subtracted from her account for each meal.

The y-intercept represents the initial amount of money in Shawna's account, which is $42.

This is the value of r when m is 0 (before any meals are purchased).

Therefore, the slope is -3.50 and the y-intercept is 42.

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Step-by-step explanation:

You need a arbitrary points that will help you determine the sketch of the graph. I say use at most 5 points but you just need to know the following

The exterma: The maximum/minimum points on a certain interval.

The zeroes: What values willTheorem, Factoring, and more to help you find the zeroes.

Increasing and decreasing behavior between the consective zeroes: How the function behaves around consective zeroes. It must be above or below x axis between the zeroes.

And finally, the end behavoir: How the function behaves as x approaches infinity and negative infinity. Does the function increases or decreases.

That it. If you need an example, just ask me

Answer:

there would be 52 more girls I think

Step-by-step explanation:

let x = multiplier then

31x =number of boys

44x = number of girls

Boys + girls = 300

44x + 31x =300

75x = 300

x = 300/75

x = 4 is the multiplier

therefore:

44*4 = 176 girls

31*4 = 124 boys

dif = 52 more girls than boys

hope this helped :)

Answer:

You save $55

Step-by-step explanation:

To find out what the 75% of the 220 is, you need to do .75 times 220 and then after you get the answer, subtract that number from 220 and you have your answer.

The company's claim can be evaluated using a hypothesis test. The null hypothesis, denoted as H0, assumes that the true proportion of chips that do not fail in the first 1000 hours is 55% or lower.

Ha stands for the alternative hypothesis, which assumes that the real proportion is higher than 55%. This test has a significance level of 0.01.

A sample of 800 chips was taken based on the information provided, and it was discovered that 60% of them do not fail in the first 1000 hours. A one-sample percentage test can be used to verify the assertion.  The test statistic for this test is the z-score, which is calculated as:

\(\[ z = \frac{{p - p_0}}{{\sqrt{\frac{{p_0(1-p_0)}}{n}}}} \]\)

If n is the sample size, p0 is the null hypothesis' assumed proportion, and p is the sample proportion.

If we substitute the values, we get:

\(\[ z = \frac{{0.6 - 0.55}}{{\sqrt{\frac{{0.55(1-0.55)}}{800}}}} \]\)

The z-score for this assertion is calculated, and we find that it is approximately 2.86.

In order to determine whether there is sufficient data to support the company's claim, we compare the computed z-score with the essential value. At a significance level of 0.01 the critical value for a one-tailed test is approximately 2.33.

Because the estimated z-score (2.86) is larger than the determining value (2.33), we reject the null hypothesis. Therefore, the company's assertion that more than 55% of the chips do not fail in the first 1000 hours of use is supported by sufficient data at the 0.01 level.

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This tree diagram shows all possible orders in which Ryan can read the 3 books, including reading the mystery book (M) first, the history book (H) second, and the biography (B) last, as well as reading the biography first, the mystery second, and the history last.

Mystery is an intriguing and often baffling phenomenon or situation. It is something that is not easily explained or understood and often involves a puzzle or secret that needs to be solved. It can be an event, an entity, or a situation that evokes curiosity, suspense, and a desire to uncover the truth. Mystery can be found in everyday life, literature, films, and other forms of entertainment. It is often used to create a sense of anticipation and wonder, and can be a powerful tool in storytelling. Mystery can also be used to explore deeper truths and to connect with our own inner mysteries.

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Complete Question is attached below:

The spinner should land on yellow about 75 times, on red about 50 times, and on blue about 25 times.

Yellow: 3 spaces out of 6, so the probability is 3/6 = 1/2

Red: 2 spaces out of 6, so the probability is 2/6 = 1/3

Blue: 1 space out of 6, so the probability is 1/6

multiplying the probability of each color by 150:

Yellow: 1/2 * 150 = 75 times

Red: 1/3 * 150 = 50 times

Blue: 1/6 * 150 = 25 times

Terefore The spinner should land on yellow about 75 times, on red about 50 times, and on blue about 25 times.

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Answer:

f(x) = -1/x^2 + 4e^x + 5x + 1 + 1/x - 4e^(-1)

Step-by-step explanation:

We can find the function f(x) by integrating f'(x) with respect to x:

â«f'(x) dx = â«(2/(x^3) + 4e^x + 5) dx

f(x) = -1/x^2 + 4e^x + 5x + C

To find the constant C, we can use the given initial conditions:

f(-1) = 1 = -1/(-1)^2 + 4e^(-1) - 5 + C

C = 1 + 1/1 - 4e^(-1)

f(x) = -1/x^2 + 4e^x + 5x + 1 + 1/x - 4e^(-1)

Therefore, the function f(x) is:

f(x) = -1/x^2 + 4e^x + 5x + 1 + 1/x - 4e^(-1)

Answer:

416

Step-by-step explanation:

Given that:

A previous random sample = 4000

Sample mean = 2250

\(\hat p = \dfrac{x}{n}\)

\(\hat p = \dfrac{2250}{4000}\)

\(\hat p = 0.5625\)

The confidence interval level = 90%

Desired Margin of error E = 0.04

The level of significance at 90% C.I  = 1 - 0.90 = 0.10

The critical value \(Z_{\alpha/2} = Z_{0.10/2}\)

\(\implies Z_{0.05} = 1.645\)   ( From the  z tables)

\(n = \hat p \times (1- \hat p ) \bigg ( \dfrac{z_{0.05}}{E} \bigg)^2\)

\(n = 0.5625 \times (1- 0.5625) \bigg ( \dfrac{1.645}{0.04} \bigg)^2\)

\(n = 0.5625 \times (0.4375) \bigg ( 41.125 \bigg)^2\)

n = 416.21

Thus, the number of citizens required to be sampled is \(\simeq\) 416

Answer:

All angles on a triangle and stright line add up to 180°.  

So, A and C= 50° because the triangle is isosceles. Therefore, then B+A+C+= 180°.

B=°

C=130°

D= 25°

Answer:

x=1. (1, 2)

x=2. (2, 5)

Step-by-step explanation:

i hope this helps :)

Using probability concepts, it is found that she could use a binomial distribution with \(n = 3\) and \(p = \frac{1}{3}\) to estimate the probability that the next three books she selects are all literature.

For each book she selects, there are only two possible outcomes, either it is a literature book, or it is not. The probability of a book selected being a literature book is independent of any other book, hence, the binomial distribution is used to solve this question.

\(P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}\)

\(C_{n,x} = \frac{n!}{x!(n-x)!}\)

The parameters are:

In this problem:

Hence, she could use a binomial distribution with \(n = 3\) and \(p = \frac{1}{3}\) to estimate the probability that the next three books she selects are all literature.

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Answer:

Number Cube

Let 1, 6= Literature

Let 2, 4= Fiction

Let 3, 5= Poetry

Roll the cube 3 times, Repeat

It has to be equal probability for all three

Answer:

There are 4 common factors of 30 and 72, that are 1, 2, 3, and 6. Therefore, the greatest common factor of 30 and 72 is 6.

Step-by-step explanation:

84/18=14/3

60/32=15/8

If rectangle has sides measuring (2x +7) units and (5x +9) units then expression that represents the area of the rectangle is \(10x^2+53x+63\) and degree of this expression is 2 and we proved that it satisfy closure property .

A quadrilateral with four right angles is called rectangle .

Given that sides are (2x+7) and (5x+9)

Hence area of rectangle can be calculated as

\((2x+7)(5x+9)\\\\2x(5x+9)+7(5x+9)\\\\10x^2+18x+35x+63\\\\10x^2+53x+63\\\)

Now we can see that this is a second degree polynomial

We got polynomial   \(10x^2+53x+63\) by multiplying two polynomial (2x+7) and (5x+9) hence it's closure property .

If rectangle has sides measuring (2x +7) units and (5x +9) units then expression that represents the area of the rectangle is \(10x^2+53x+63\) and degree of this expression is 2 and we proved that it satisfy closure property .

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Answer:

c  (2,0)

Step-by-step explanation:

One way to solve this system of inequalities is to graph the inequalities and see which ordered pair lies in the shaded region that is common to both inequalities

See the graph and each of the ordered pairs. Only (2, 0) lies entirely within the shaded region

(-1, 0) lies on the intersection of the two lines so it will satisfy the >= inequality but not the < inequality

Answer (2, 0)

However if you cannot use graphing then a brute force method must be used to see which ordered pair satisfies both inequalities

a. (-1, 0)
Check y < 2x + 2 ?
=>  0 < 2(-1) + 2 ?
=> 0 < -2 + 2
0 < 0 ? False
Eliminate option a

b. (0, 3)
y < 2x + 2?
=> 3 < 2(0) + 2?
3 < 2? False
Eliminate option b

c. (2, 0)
y < 2x + 2?
=> 0 < 2(2) + 2 ?
=>  0 < 4 + 2
=> 0 < 6 True

Move to the second inequality
y ≥ -x - 1?
0 ≥ -2 - 1
0 ≥ -3 True

So option c is the correct choice

While it is not necessary to check option d, let's do it anyway
d. (-1, -4)
y < 2x + 2 ?
-4 < 2(-1) + 2 ?
-4 < -2 + 2 ?
-4 < 0 ? True

Move to the second inequality
y > -x - 1 ?
-4 > -(-1) - 1
-4 > -2? False
Option d is eliminated

Correct answer: (2, 0) which is option c

Answer:

(a) check explanation

(b) The favourite topic among the students is Number, having a total sum of 60 students who chose the topic.

(c) the fraction of girls who chose statistics as their favourite is ¹/₈

(d) the fraction of boys who chose geometry as their favourite is ¹/₆

(e) the fraction of students who chose statistics that were boys is  ²/₃

Step-by-step explanation:

From the given statement;

Total number of boys = 60

Total number of girls = 80

Total number of students who chose Number = 60, number of boys = 20, number of girls = 40

Total number of students who chose Algebra = 30, number of boys = ?, number of girls = ?

Total number of students who chose geometry = 20, number of boys = 10, number of girls = 10

number of boys who chose statistics = 20, number of girls = ?

let the number of boys who chose algebra = x

20 boys(number) + x boys(algebra)  + 10 boys (geometry) + 20 boys (statistics) = 60

50 + x = 60

x = 60 - 50

x = 10 boys

Thus, 10 boys chose algebra, then (30 - 10) girls chose algebra, i.e 20 girls.

Let the number of girls who chose statistics = y

40 girls(number) + 20 girls(algebra)  + 10 girls(geometry) + y girls (statistics) = 80

70 + y = 80

y = 80 - 70

y = 10 girls

Thus, 10 girls chose statistics

Now complete the two-way table as follows;

(a) Two-way table

                                  Boys         Girls          Total

Algebra                        10              20            30                                    

Geometry                     10              10             20        

Number                        20             40            60

Statistics                       20             10             30

Total                            60             80            140                    

(b) The favourite topic among the students is Number, having a total sum of 60 students who chose the topic.

(c) the fraction of girls who chose statistics as their favourite;

\(= \frac{number \ of \ girls \ who \ chose \ statistics }{Total \ number \ of \ girls} \\\\= \frac{10}{80} \\\\= \frac{1}{8}\)

(d) the fraction of boys who chose geometry as their favourite;

\(= \frac{number \ of \ boys \ who \ chose \ geometry }{Total \ number \ of \ boys} \\\\= \frac{10}{60} \\\\= \frac{1}{6}\)

(e) the fraction of students who chose statistics that were boys is calculated as;

\(= \frac{number \ of \ boys \ who \ chose \ statistics }{Total \ number \ of \ students \ who \ chose \ statistics} \\\\= \frac{20}{30} \\\\= \frac{2}{3}\)

the correct answers are:

- The product rule
- The sum rule

The division rule and the subtraction rule are not applicable in this case.

The product rule and the sum rule are fundamental principles in combinatorics that are used to count the number of possible outcomes in a given scenario.

The product rule states that if there are m ways to perform one task and n ways to perform another task, then there are m x n ways to perform both tasks in sequence. In the context of finding the number of positive integers less than 1000 that have distinct digits, we can use the product rule to count the number of possible integers in each of the three digit positions. For example, the first digit can be any of the nine non-zero digits (1-9), the second digit can be any of the remaining eight non-zero digits, and the third digit can be any of the remaining seven non-zero digits. Therefore, the total number of possible integers is 9 x 8 x 7 = 504.

The sum rule states that if there are m ways to perform one task and n ways to perform another task, and the two tasks are mutually exclusive (i.e. they cannot be performed at the same time), then there are m + n ways to perform either task. In the context of finding the number of positive integers less than 1000 that have distinct digits, we can use the sum rule to count the number of possible integers that have one, two, or three digits. For example, there are 9 possible one-digit integers (1-9), 9 x 9 = 81 possible two-digit integers (excluding those with repeated digits), and 504 possible three-digit integers (as calculated using the product rule). Therefore, the total number of possible integers with distinct digits is 9 + 81 + 504 = 594.

The division rule and the subtraction rule are not applicable in this case because they are used to solve different types of combinatorial problems. The division rule is used to count the number of ways to distribute n objects into k groups, while the subtraction rule is used to count the number of ways to perform a task by counting the number of ways it cannot be performed.
To find the number of positive integers less than 1000 that have distinct digits, we can use the product rule and the sum rule. Therefore, the correct answers are:

- The product rule
- The sum rule

The division rule and the subtraction rule are not applicable in this case.

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Answer:

Perimeter = 22 m, Area = \(24m^{2}\)

Step-by-step explanation:

The perimeter of a rectangle is the total distance of its outer boundary—it is twice the sum of its length and width. Therefore, the formula for the perimeter of the rectangle is:

P = 2l + 2w

The area occupied by a rectangle within its boundary is called the area of the rectangle. The formula for finding the area of the rectangle is:

A = l × w

If the length of the rectangle is 8m, and its width = 3m, then we can plug in these values into the given formulas for the perimeter and area of the rectangle:

P = 2l + 2w (which is the same as length + length + width + width).

P = 2(8 m) + 2(3 m)

P = 16 m + 6 m

P = 22 m

Therefore, the perimeter of the rectangle is 22 m.

Next, we need to determine the area of the rectangle, by plugging in the same values into the formula:

A = l × w

A = 8m × 3m

A = \(24m^{2}\)

Therefore, the area of the rectangle is \(24m^{2}\).

The area of the figure is 80 square inches. Check more about area below.

To find the area:

Lets take area as A.

Therefore,

Note that rectangles A is eight inches long each and four inches wide. base: sixteen inches and width is seven inches.

A= rectangles A - rectangles B

= 16 * 7 - 8 * 4

=112- 32

80

Therefore, the area of the figure is 80.

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To use the critical value table, you must first decide on the level of significance for your hypothesis test. This is usually represented by alpha (α) and is the probability of rejecting the null hypothesis when it is actually true. Common levels of significance include 0.05 and 0.01.

A critical value table is a tool used in hypothesis testing to help determine whether or not to reject the null hypothesis. This table provides the critical values for a given level of significance and sample size for various statistical distributions such as the normal, t, chi-squared, and F distributions.

Once you have determined the level of significance, you can use the critical value table to find the critical value for your chosen distribution.

For example, if you are using a t-distribution with a sample size of 30 and a significance level of 0.05, you would look in the t-distribution section of the critical value table for the row with a sample size of 30 and find the critical value in the column corresponding to a significance level of 0.05.

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Answer:

9x^4 - 6x^3 + 4x - 4

Step-by-step explanation:

I got this answer but I don't know if I am correct. That's what i understood based off what you wrote.