the sat and act college entrance exams are taken by thousands of students each year. the mathematics portions of each of these exams produce scores that are ap- proximately normally distributed. in recent years, sat mathematics exam scores have averaged 480 with standard deviation 100. the average and standard deviation for act mathematics scores are 18 and 6, respectively.

Options (1), (3), (4), (7) and (8) are rational numbers.

Rational numbers are in the form of p/q, where p and q can be any integer and q ≠ 0. This means that rational numbers include natural numbers, whole numbers, integers, fractions of integers, and decimals (terminating decimals and recurring decimals).

1) 1/4 + 1/2 = 1/4 + 2/4

= 3/4

3/4 is the rational number

2) √3 + 4 is an irrational number

3) √4 + 7

2 + 7 = 9

9 is the rational number

4) 2·√9

= 2·3

= 6

6 is the rational number

5) 7·√6 is an irrational number

6) 4·2√3 = 8√3

8√3 is an irrational number

7) 3·7·(1/3) = 7

7 is the rational number

8) 7·√81

=7·9 = 63

63 is the rational number

Therefore, options (1), (3), (4), (7) and (8) are rational numbers.

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There are 23 tickets which are purchased for children and 9 tickets are purchased for adults which cost total $148.

It is given in the question that 32 tickets are purchased by group which cost total $148.
Let the number of children of the group who are entering the zoo be x. Then the number of adults will be 32- x

Now cost of one ticket for adult = $7.50

Total amount spent on adult tickets = 7.50 × (32-x)

Similarly, cost of one ticket for child= $3.50

Total amount spent on children tickets = 3.50 × x =3.5x

Total amount spent by group on tickets =  $148
⇒ 7.5 × (32-x) + 3.5x = 148
⇒ 240 - 7.5x + 3.5x = 148
⇒ 7.5x - 3.5x = 240 - 148
⇒ 4x = 92
⇒ x = 23
Children = 23
Adults = 32-x = 32-23 = 9
Hence, 23 tickets are purchased for children and 9 tickets are purchased for adults.


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Answer:

I not to sure but I think it is b+w=h(hours)

Step-by-step explanation:

Answer:

[tex]x = - 3 + - \sqrt{13} [/tex]

Step-by-step explanation:

formula is x=-b+-sqrt b^2-4ac/2a

We can conclude that (A) yes, the table shows the constant of proportionality of 1/5.

So, the constant of proportionality of the given table:

Formula: k = y/x

So, substitute the values in the formula as follows:

So, yes, the table shows the constant of proportionality of 1/5.

Therefore, we can conclude that (A) yes, the table shows the constant of proportionality of 1/5.

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The total amount due will be equal to $6.24.

This question can be solved by converting the situation into form of an equation. An equation may be defined as an expression which consists of numbers, variables related to each other by arithmetic expressions. The solution of equation often referred to as the variables for which the equation must be solved, are the values of the unknowable variables that satisfy the equality. The cost of video game is given as $12.98, and tax is equal to $0.78, and he paid an amount of $20. let the change left be x.

Total amount = cost of game + tax + change

$20 = $12.98 + $0.78 + x

$20 = $13.76 + x

=> x = $20 - $13.76

=> x = $6.24 which is the due amount.

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Complete Question:

Imagine you went to the store and bought a video game for $12.98. This item is taxable at 6% tax and the total tax is $0.78. What is the total amount due? Next, you decide to pay with a $20.00 bill. How much change will you receive after paying for your video game?

Answer: y = 3x - 5

Step-by-step explanation:

3 is the reciprocal of -1/3 and by plugging in (1,-2) in to y=3x+b you get -2 = 3(1) + b which makes b = -5

Regarding the situation described, we have that:

a. The ball travels 21.4 feet.

b. The assumption is that the ball was served at an angle of 90º.

c. The Pythagorean Theorem was used to solve this problem.

The Pythagorean Theorem relates the length of the legs [tex]l_1[/tex] and [tex]l_2[/tex] of a right triangle(triangle which has an angle of 90º between the two legs) with the length of the hypotenuse h, stating that the hypotenuse squared is the sum of the legs squared, according to the following rule:

[tex]h^2 = l_1^2 + l_2^2[/tex]

In the context of this problem, it is found that:

Assuming that the ball was served at an angle of 90º, the distance traveled by the ball is the hypotenuse of a right triangle of legs 7.5 feet and 20 feet, hence:

d² = 7.5² + 20².

d = sqrt(20² + 7.5²)

d = 21.4 feet. (which is Justin's estimate).

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Answer:

8

Step-by-step explanation:

See attached image.

Answer:31%

Step-by-step explanation:

If adana is going on vacation with her family in2 hours they travel 90.5 miles. they travel the same speed, The  equation that represents how far they will travel, d, in h hours is: r = d / t, D = r × t.

Given data;

Travels time : 2 hours in 90.5 miles

Formula for speed  is:

r = d / t

Where,

r = Speed

d = Distance

t = Time

Hence,

Speed = 90.5 / 2

Speed =45.25miles per hour

Since they travels d distance in h hour with the same speed let find the distance

D = r × t

Distance = Speed × Time

Distance = 45.25 × h

Distance = 45.25h miles

Therefore  r = d / t, D = r × t is the equation that represent the distance they travel.

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There are 100 groups of 10 milliliters in 1 liter

From the question, the given parameters are

Volume 1 = 10 milliliters

Volume 2 = 1 liter

The number of groups of the first group in the second is calculated as

Groups = Volume 2/Volume 1

Substitute the known values in the above equation

So, we have the following equation

Groups = 1 liter/10 milliliters

Evaluate the quotient

Groups = 100

Hence, the  number of groups is 100

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The value of f(x) + h(x) when f(x) = 2x - 1 and h(x) = x² + 1 is x² + 2x.

Addition of linear functions:
Addition of two individual functions, a(x) and b(x); linearly, results in the formation of the functional addition, c(x) of the two functions, such as:
c(x) = a(x) + b(x) = (a+b)(x) – (i)
The addition of the functions strictly restricts to simple linear addition without any pre-defined constraints.

Given, f(x) = 2x - 1, g(x) = 3x and h(x) = x² + 1
Using the available formula in (i), we get
f(x) + h(x) = (f + h)(x) = (2x - 1) + (x² + 1) = x² + 2x = x(x + 2), which is a quadratic equation.
Thus, the required value of f(x) + h(x) is x² + 2x.

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Let's begin by listing out the information given to us:

A. The algebraic expression that represents the total number of miles Leah runs each week is 5*M.

B. The algebraic expression that represents the total number of miles Leah runs in a year is 260*M.

Leah runs M miles everyday during the week except for Wednesday or Sunday.

We need to write the algebraic expression that represents the total number of miles Leah runs each week. Leah runs for 5 days in a week. The total number of miles run in a week is 5*M.

We need to write the algebraic expression that represents the total number of miles Leah runs in a year. Leah runs 5*M miles in a week. The total number of miles run in a year is (5*M)*52 = 260*M.

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Based on the calculations, the final velocity of this car is equal to 85.0 mi/hr.

In order to determine the final velocity of this car, we would first calculate its acceleration based on the parameters provided. Mathematically, the acceleration of an object can be calculated by using this formula:

a = (V - U)/t

Where:  

Substituting the given parameters into the formula, we have:

a = (70.0 - 0)/10

a = 70.0/10

Acceleration, a = 7.0 mi/hr².

Now, we can determine the final velocity of this car as follows:

V = U + at

V = 50.0 + (7.0)(5)

V = 50.0 + 35.0

Final velocity, V = 85.0 mi/hr.

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Complete Question:

If a car can go from 0.0 mi/hr to 70.0 mi/hr in 10.0 seconds, what would be its final velocity after 5.0 seconds if its starting velocity was 50.0 mi/hr

Volume of a pyramid is calculated using the same basic formula as that of a cone: volume = (1/3) × base area × height, where height is the distance between the base and the apex. Then the height is 6 feet.

Using the equation volume = base area height / 3, one may calculate the volume of a regular square pyramid. Keep in mind that the base area is equal to the base edge length squared.

A polygonal base and an apex come together to form a polyhedron known as a pyramid. Volume of a pyramid is calculated using the same basic formula as that of a cone: volume = (1/3) × base area × height, where height is the distance between the base and the apex.

The volume of a square pyramid exists found by multiplying the area of the base by the height divided by 3.

32 = 4² × h/3

32 = 16 × h/3

Multiply both sides by 3

96 = 16 × h

Divide both sides by 16

H = 96/16

H = 6

Therefore, the height is 6 feet.

The complete question is:

Find the height of a square pyramid that has a volume of 32 cubic feet and a base length of 4 feet.

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Step-by-step explanation:

come on, this is really simple.

you need to put the given values of x into the places, where x appears in the functional expression.

which expression to be used ? that depends on the given value.

x = -1

is -1 >= 0 (to use the case for x >= 0) ? no, it is not.

-1 < 0, so we need to use the expression for x < 0.

y = -1 - 2 = -3

x = 0

is 0 >= 0 ? yes, it is.

so, we need to use the expression for x >= 0.

y = 3×0 + 1 = 0 + 1 = 1

x = 1

is 1 >= 0 ? yes, it is.

so, we need to use the expression for x >= 0.

y = 3×1 + 1 = 3 + 1 = 4

x = 2

is 2 >= 0 ? yes, it is.

so, we need to use the expression for x >= 0.

y = 3×2 + 1 = 6 + 1 = 7

Using the triangle sum theorem, x = 7 and y = 18.

The theorem that says that all the interior angles of a triangle will be equal to 180 degrees is referred to as the triangle sum theorem.

In the diagram given, since vertical angles are congruent, therefore:

(11x - 9) + (6x - 2) + 72 = 180 [triangle sum theorem]

Solve for x

11x - 9 + 6x - 2 + 72 = 180

17x + 61 = 180

17x = 180 - 61

17x = 119

x = 7

Also,

(5y - 8) + (11x - 9) + 30 = 180 [triangle sum theorem]

5y - 8 + 11x - 9 + 30 = 180

5y + 13 + 11x = 180

Plug in the value of x

5y + 13 + 11(7) = 180

5y + 13 + 77 = 180

5y + 90 = 180

5y = 180 - 90

5y = 90

y = 90/5

y = 18

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the town's population at the beginning of 2000 was 74,500.Then the population in 2010 will be 96206.97

In 2000, the population of a town = 74500

Every year, it increase by 2.59%

To find the equation P(t) which represents the population of this town t years from 2000 to  2010.

Formula

If a be the original population of a town and it increases by r% every year, after t year the population will be

A = P ( 1+r/100)^t

Now,

Taking, P =74500, r = 2.59% we get,

A = 74500( 1+0.0259)^10

A= 74500(1.0259)^10

A= 96206.97

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The equation of the line is y = -0.35x – 3.55

Given,

The gradient of the line between two points (x₁, y₁) and (x₂, y₂) is m = (y₂ - y₁)/(x₂ - x₁).

Since the line passes through the points (7,-6) and (3,8),  

• (x₁, y₁) = (7,-6) and

• (x₂, y₂) = (3,8).

So, substituting the values of the variables into the equation, we have

m = (y₂ - y₁)/(x₂ - x₁).

m = (8 - (-6))/(3 - 7).

m = (8 + 6)/ -4

m = 14/-4

m = -3.5

The equation of the line passing through the point (x₁, y₁) in point-slope form is given by

y - y₁ = m(x - x₁) where

• m = gradient =- 0.35 and

• (x₁, y₁) = (7, -6)

So, substituting the values of the variables into the equation, we have

y - y₁ = m(x - x₁)

y - (-6) = -0.35(x - 7)

y + 6 =-0.35 (x - 7)

y = (-0.35x + 2.45 – 6)

y = -0.35x – 3.55

So, the equation of the line is y = -0.35x – 3.55

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The 99% confidence interval for the population proportion p is 0.833< p < 0.863.

Given that,

x = 3059

n = 3604

Point estimate = sample proportion = x / n =3059/3604=0.848

[tex]1 - \hat p[/tex]  = [tex]1-0.848 =0.152[/tex]

At 99% confidence level the z is ,

[tex]\alpha[/tex] = 1 - 99% = 1 - 0.99 = 0.01

[tex]\alpha[/tex]/ 2 = 0.01 / 2 = 0.005

[tex]Z\alpha[/tex]/2 = [tex]Z*0.005[/tex] = 2.576  (  Using z table   )

Margin of error = E = [tex]Z\alpha / 2 * (\sqrt(((\hat p * (1 - \hat p)) / n)[/tex]

                              = [tex]2.576* (\sqrt((0.848*0.152) /3604 )[/tex]

                               =0.015

A 99% confidence interval for population proportion p is ,

[tex]\hat p - E < p < \hat p + E[/tex]

0.848-0.015< p <0.848+ 0.015

0.833< p < 0.863

Hence, the 99% confidence interval for the population proportion p is 0.833< p < 0.863.

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By the concept of unitary method she can run 320 yards  in 2 minutes at the same rate.

The unitary method is a technique used to determine the value of a single unit from the value of many units and the value of multiple units from the value of a single unit. We typically utilize it for math calculations. This approach might be helpful for answering questions on ratio and proportion, algebra, and other subjects. "It is a method where we get the value of a single unit from the value of many units and the value of multiple units from the value of a single unit." bra, geometry, etc. Before determining the value of additional or less items, we must first determine the value of one item by dividing it. There are two categories of unitary approaches.

720 yards = 4.5 minutes

1 minute = 720/4.5

= 160 yards

2 min = 160(2)

= 320 yards

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answers are in the photo

goodluck

The things that can lead to bias include:

The question uses an inaccurate tool.

Some subgroups may be at a disadvantage due to prior experiences.

A medical research study assigns the healthier patients to the group using the new treatment and the sicker patients to the group using the traditional treatment.

It should be noted that bias simply means anything that leads to a systematic difference between the true parameter.

It should be noted that in a situation where the question uses an inaccurate tool. This will lead to bias and bring about inaccuracy.

Also, using different tools for the patients can lead to bias.

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The percentage of Earth's freshwater is found in lakes, rivers, and streams as surface water is 69%. Therefore, option A is the correct answer.

We need to find the percentage of Earth's freshwater is found in lakes, rivers, and streams as surface water.

Percentage is defined as a given part or amount in every hundred. It is a fraction with 100 as the denominator and is represented by the symbol "%".

Over 69 percent of the fresh water on Earth is found in icecaps and glaciers, and just over 30 percent is found in ground water. Only about 0.3 percent of our fresh water is found in the surface water of lakes, rivers, and swamps.

The percentage of Earth's freshwater is found in lakes, rivers, and streams as surface water is 69%. Therefore, option A is the correct answer.

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The probability of a random sample of 80 households having a sample means a number of at least 2.55 televisions per household is 0.48173.

Given: Mean(μ) = 2.24, Standard deviation(σ) = 1.38, Sample size(n) = 1.28 and a random variable for X = 2.55

The formula to calculate the z-score from the mean. The standard deviation is:

z = (X - μ) / ( σ / √(n)) where,

z = z-score,

X = random variable,

μ = mean,

σ = standard deviation, and

n = sample size

Let's solve the given question:

We have,

Mean(μ) = 2.24,

Standard deviation(σ) = 1.38,

Sample size(n) = 80, and

a random variable for X = 2.55

As it is given sample means at least 2.55 so we have to find the Z(x ≥ 2.55).

Therefore, Z(x ≥ 2.55) = (2.55 - μ) / ( σ / √(n))

Substituting all values we get:

Z(x ≥ 2.55) = (2.55 - 2.24) / ( 1.38 / √(80))

Z(x ≥ 2.55) = 0.01 / 0.21819

Z(x ≥ 2.55) = 0.48173

Hence the probability of a random sample of 40 households having a sample means a number of at least 2.55 televisions per household is 0.48173.

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The simplified value for 4 √84 x [tex]10^4[/tex] is 800 √21.

The exponent of a number shows how many times the number is multiplied by itself.

For example, 2×2×2×2 can be written as 24, as 2 is multiplied by itself 4 times. Here, 2 is called the "base" and 4 is called the "exponent" or "power." In general, xn means that x is multiplied by itself for n times.

Given:

4 √84 x [tex]10^4[/tex]

Now, first factorize 84 into prime factor

84 = 2 x 2 x 3 x 7

The, we can write it as

4 √84 x [tex]10^4[/tex]

=4 x √(2 x 2 x 3 x 7  x (10²)²)

= 4  x 2 x 10² √( 3 x 7)

= 8 x 10² √21

=800 √21

Hence, the simplified value is 800 √21.

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The 95% confidence interval for the mean score of all such subjects. will be ( 67. 7 , 84.7) using mean.

What is mean?

Mathematicians, particularly statisticians, use a variety of means. Every mean serves to condense a certain set of facts, frequently to help grasp the general significance of a particular data set.

sample mean = x' = 76.2

sample S = 21.4

sample size n = 27

Confidence level = a = 0.95
α=1-a=0.05
95% confidence interval for the mean score of all such subjects is
(x'-E , x'+E)
E = [tex]\frac{tc*s}{\sqrt{n}}[/tex]
E = [tex]\frac{2.056*21.4}{\sqrt{27}}[/tex]} = 8.466

95% confidence interval for the mean score of all such subjects is
(x'-E , x'+E)
=(76.2-8.466 , 76.2+8.466)
=(67.734 , 84.666)
= ( 67. 7 , 84.7)

Hence The answer will be ( 67. 7 , 84.7).

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