Admission to the county fair is $15, and each ride ticket costs $1.75. Write an expression to describe the total cost of 8 rides.

Answer:

9 gallons

Step-by-step explanation:

4 quarts = 1 gallon

12/4=3

3 + 6= 9

9 gallons

Answer:

d. 1,600.

Step-by-step explanation:

We have that to find our \(\alpha\) level, that is the subtraction of 1 by the confidence interval divided by 2. So:

\(\alpha = \frac{1 - 0.99}{2} = 0.005\)

Now, we have to find z in the Ztable as such z has a pvalue of \(1 - \alpha\).

That is z with a pvalue of \(1 - 0.005 = 0.995\), so Z = 2.575.

Now, find the margin of error M as such

\(M = z\frac{\sigma}{\sqrt{n}}\)

In which \(\sigma\) is the standard deviation of the population and n is the size of the sample.

Based on previous research, the standard deviation of the distribution of the age at which children begin to walk is estimated to be 1.5 months.

This means that \(\sigma = 1.5\)

Of the following, which is the smallest sample size that will result in a margin of error of 0.1 month or less for the confidence interval?

The sample size has to be n or larger. n is found when \(M = 0.1\). So

\(M = z\frac{\sigma}{\sqrt{n}}\)

\(0.1 = 2.575\frac{1.5}{\sqrt{n}}\)

\(0.1\sqrt{n} = 2.575*1.5\)

Multiplying both sides by 10

\(\sqrt{n} = 2.575*15\)

\((\sqrt{n})^2 = (2.575*15)^2\)

\(n = 1492\)

So the sample size has to be at least 1492, which means that of the possible options, the smallest sample size is 1600, given by option d.

The sample size should be at least 1492, So the possible options, the smallest sample size is 1600, option D is the correct answer

Based on previous research, the standard deviation of the distribution of the age at which children begin to walk is estimated to be 1.5 months. A random sample of children will be selected, and the age at which each child begins to walk will be recorded. A 99% confidence interval for the average age at which children begin to walk will be constructed.

The margin of error tells you how many percentages points your results will differ from the real population value.

\(M=z\frac{\sigma}{\sqrt{n} }\)

We need to find our α level, that is the subtraction from 1 by the confidence interval for the average age divided by 2.

\(\alpha = \frac{1-0.99}{2}\\ =0.005\)

Now, we need to find z which is 1-α

\(1-\alpha \\=1-0.005\\\rm z=2.575\)

The margin of error M

\(M=z\frac{\sigma}{\sqrt{n} }\)

Here, \(\sigma\) is the standard deviation of the population.

n is the size of the sample.

So,

\(\rm M=z\frac{\sigma}{\sqrt{n} } \\\rm0.1=2.575\frac{1.5}{\sqrt{n} } \\\rm0.1\times\sqrt{n} =2.575\times{1.5}\\\rm\sqrt{n} =2.575\times{1.5}\\\rm(\sqrt{n} )^{2} =(2.575\times{1.5})^{2} \\\rm n=1492\)

Hence, the sample size should be at least 1492, So the possible options, the smallest sample size is 1600, option D is the correct answer.

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Answer:

9576

Step-by-step explanation:

Area of the triangle × height

(1/2×28×19)×36

9514 1404 393

Answer:

  π ft ≈ 3.14 ft

Step-by-step explanation:

The angle is 1/12 of the number of degrees in a circle, so the arc length will be 1/12 of the circumference of the circle.

 C = 2πr

 1/12C = 2/12π(6 ft) = π ft ≈ 3.14 ft

The arc length is about 3.14 feet.

Answer:

30% of the swimmers won a ribbion

and 70% didnt

Step-by-step explanation:

We want to find a polynomial

f(x) = a x³ + b x² + c x + d

such that the roots of f are x = -3, x = -1, and x = 4, and f(x) takes on a value of -24 when x = -2.

The factor theorem for polynomials tells us that we can factorize f(x) as

a x³ + b x² + c x + d = a (x + 3) (x + 1) (x - 4)

Expand the right side:

(x + 3) (x + 1) (x - 4) = x³ - 13x - 12

So we have

a x³ + b x² + c x + d = a x³ - 13a x - 12a

In order for both sides to be equal, the coefficients of both polynomials on terms of the same degree must be equal. This means

a = a (of course)

b = 0 (there is no x² term on the right)

c = -13a

d = -12a

We also have that f (-2) = -24, which means

f (-2) = a (-2 + 3) (-2 + 1) (-2 - 4)

-24 = 6a

a = -4

which in turn tells us that c = 52 and d = 48.

So we found

f(x) = -4x³ + 52x + 48

At m = 26 only the equation will be true, And the values 3, 78, and 126 will not satisfy the equation and make the equation false.

The substitution method is a quick and easy way to algebraically solve a set of linear equations and determine the variables' solutions.

Finding the value of the x-variable in terms of the y-variable from the first equation and then substituting or replacing the value of the x-variable in the second equation.

Here we have

8m − 15 = 5m + 63

=> 3m = 78

And set of possible solution, S = {3, 26, 78, 126}

Here we use the Substitution method to find at what value the equation will be false

At m = 3  

=>  3m = 78  

=>  3(3) = 78  [ which is not true]

At m = 26

=> 3(26) = 78 [ which is true ]

At m = 78

=> 3(78) = 78 [ which is not true ]

At m = 126

=> 3(126) = 78  [ which is not true ]

From the above calculations,

At m = 26 only the equation will be true, And the values 3, 78, and 126 will not satisfy the equation and make the equation false.

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The probability of selecting a junior who takes the bus is P (Junior who takes the bus) = 12/200 = 0.06Hence, the probability that a randomly selected student is a junior who takes the bus is 0.06 or 6/100.

The given frequency table on how students get to school among the high school students is represented in the below table:Transportation Walk Bike BusDriveTotalGrade 9 11 10 14 15 50Grade 10 10 7 13 20 50Grade 11 8 6 12 24 50Grade 12 5 8 8 29 50 Total 34 31 47 88 200Given data from the above frequency table, we are interested in finding the probability of a randomly selected student being a junior who takes the bus.SolutionWe know that the total number of students is 200, and the total number of junior students is 50. Hence the probability of selecting a junior is P (Junior) = 50/200 = 0.25Similarly, the number of students who take the bus is 47 and the number of junior students who take the bus is 12.

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In this question, we are not given the function /equation, however, we are to find the funtion that takes real numbers x :

so, we will map all subset of the set R of all real numbers into R

lets take :

f(x) = 2(x) , where x= 0; +_1; +_2; +-3.....is a mapping of R of all intergers

(a) Multipy by -1

f(x) = -2x

(b)Add 1

f(x) = 2x +1

(c) square root

f(x) = √(2x+1)

(d) take reciprocal

x =√(2y +1) ... solve for y

y ^-1 = (x^2 -1) /2

expression for f (x) = √(2x+1)

Domain : x ≥-1/2

interval notation :[-1/2 ; ∞)

Answer:

f(0)=2

f(3)=14

f(3)=14

Answer: i think c

Step-by-step explanation:

Answer:

10.908

Step-by-step explanation:

We shall use graphical method

Both the graphs of the inequalities have been attached

Answer:

When graphing inequalities:

< or > : draw a dashed line

≤ or ≥ : draw a solid line

< or ≤ : shade under the line

> or ≥ : shade above the line

Question 14

Given inequalities:

\(y \geq x - 3\)

\(y > -4x + 2\)

Treat the inequalities as equations (swap the inequality sign for an equals sign) to find two points on the line to help draw the lines.

\(y \geq x - 3\)

\(x=0 \implies y=-3\)

\(x=3 \implies y=0\)

Plot the points (0, -3) and (3, 0).

Draw a solid straight line through the points.

\(y > -4x + 2\)

\(x=0 \implies y=2\)

\(x=1 \implies y=-2\)

Plot the points (0, 2) and (1, -2)

Draw a dashed straight line through the points.

Shade the intersecting area above the two lines.

Question 15

Given inequalities:

\(y \geq -3x - 3\)

\(y \geq -\dfrac{1}{2}x + 2\)

Treat the inequalities as equations (swap the inequality sign for an equals sign) to find two points on the line to help draw the lines.

\(y \geq -3x - 3\)

\(x=0 \implies y=-3\)

\(x=-2 \implies y=3\)

Plot the points (0, -3) and (-2, 3).

Draw a solid straight line through the points.

\(y \geq -\dfrac{1}{2}x + 2\)

\(x=0 \implies y=2\)

\(x=2 \implies y=1\)

 Plot the points (0, 2) and (2, 1)

Draw a solid straight line through the points.

Shade the intersecting area above the two lines.

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Solution

The mixed numeral Formula​

Example

The simplified boolean expression for F5 is F5 = P OR (NOT R). In this expression, P represents one boolean variable, and (NOT R) represents the negation of another boolean variable R. The OR operator combines the two variables, resulting in the final boolean expression F5.

To simplify the boolean expression F5 = (P AND Q) OR (R AND NOT P), we can apply Boolean algebra rules to reduce it to its simplest form.

Step 1: Apply De Morgan's laws

NOT (R AND NOT P) can be simplified as (NOT R) OR P.

Step 2: Distributive property

F5 = (P AND Q) OR ((NOT R) OR P)

Step 3: Apply associative property

F5 = (P AND Q) OR (P OR (NOT R))

Step 4: Apply absorption law

F5 = P OR (P OR (NOT R))

Step 5: Apply idempotent law

F5 = P OR (NOT R)

By simplifying the expression, we have reduced it to its simplest form while preserving its logical meaning. The simplified expression can be used to analyze and evaluate logical circuits or systems where the variables P and R are used.

Remember, boolean algebra allows us to manipulate and simplify complex logical expressions by applying various rules and properties. These simplifications help in understanding and analyzing logical operations in digital systems and circuits.

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The question probable may be:

Consider the boolean variables P, Q, and R. Determine the boolean expression for the variable F5 using the given variables:

F5 = (P AND Q) OR (R AND NOT P)

Using the boolean variables P, Q, and R, can you simplify the expression F5 to its simplest form by applying Boolean algebra rules?

Answer:

x =+- 6

is the answer.

Because 6² = (-6)²

Answer:

c

Step-by-step explanation:

multiply

The company's profit in 2017, modeled by the given function, was $193651949.5

The equation of the function is given as

P(t) = 0.5t^6 − 3t³ +t² +25

First, we calculate the value of t in 2017

t = 2017 - 1990

t = 27

Using the Remainder theorem

To find the company's profit in 2017, we need to substitute t = 27 in the given function P(t):

P(27) = 0.5(27)^6 - 3(27)^3 + (27)^2 + 25

Evaluate

P(27) = 193651949.5

Therefore, the company's profit is $193651949.5

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The type of transformation shown is vertical translation. That is option D.

Transformation of geometrical figures or points is the manipulation of a given figure to take the same shape but with different direction of its original angles.

Different types of transformations are Rotation, Reflection, Glide reflection, Translation and Dilation.

Given a polygon ABDC.

It is transformed to another polygon with the same size A'B'D'C'.

Here the polygon ABDC is just moved downwards as it is and mark is as A'B'D'C'.

In rotation or reflection transformation, the points will change it's correspondent place.

Translation is a type of transformation where the original figure is shifted from a place to another place without affecting it's size.

Since the shifting is done vertically, it is vertical translation.

Hence the transformation is vertical translation.

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Answer:

Therefore, the angle ∠CDA is 58°.

Step-by-step explanation:

∠CDA = 58°

In the given figure, let's consider the angle ∠CDA as x.

Since AB is the diameter of the circle, we know that the angle subtended by any diameter at any point on the circumference is always 90°. Therefore, ∠CAB = 90°.

In triangle CAD, the sum of angles is 180°. So, we have:

∠CAD + ∠CDA + ∠CAB = 180°

Substituting the known values:

32° + x + 90° = 180°

Combining like terms:

x + 122° = 180°

Subtracting 122° from both sides:

x = 180° - 122°

x = 58°

Answer:

It would be better to get marry on 2021 that way they will saved in income taxes $138

Explanation:

We have to compare their two single taxable income

against marry filing jointly:

Martina:

15,000 - 12,200 standard deduction = 2,800

It will be taxed at 10% = 280

Raphael:

45,000 - 12,200 standard = 32,800

It will be taxed 10% of 9,700 = 970

and 12% above: (32,800-9,700) x 12% = 2,772

total income tax for Raphael: 3,742

Total if married in 2022: 4,022

Jointly:

\(60,000 - 24,400 = 35,600\) taxable income

it will be taxes at 10% for the first 19,400 = 1,940

and at 12% for the above: (35,600 - 19,400) x 12% = 1,944

Total: 3.884‬

Difference:

\(4,022 - 3,884 = 138\)

Answer:

16 ft, 8 ft

Step-by-step explanation:

Area of rectangle = 128 Sq ft

\((x + 7)(x - 1) = 128 \\ \\ {x}^{2} - x + 7x - 7 = 128 \\ \\ {x}^{2} + 6x - 7 - 128 = 0 \\ \\ {x}^{2} + 6x - 135 = 0 \\ \\ {x}^{2} + 15x - 9x - 135 = 0 \\ \\ x(x + 15) - 9(x + 15) = 0 \\ \\ (x + 15)(x - 9) = 0 \\ \\ x + 15 = 0 \: \: or \: \: x - 9 = 0 \\ \\ x = - 15 \: or \: \: x = 9 \\ \\ \because \: side \: of \: a \: rectangle \: can \: not \: \\ be \: negative \\ \\ \implies \: x \neq - 15 \\ \\ \implies \: x = 9 \\ \\ \red{ \bold{x + 7 = 9 + 7 = 16}} \\ \\ \purple{ \bold{ x - 1 = 9 - 1 = 8}}\)

Thus, the dimensions of the rectangle are 16 ft and 8 ft.

∠LMN is an obtuse angle.

==========================================

Explanation

Let's go through the answer choices to see which are true, and which are false.

Answer:

k = \(\frac{3}{4}\)

Step-by-step explanation:

given variation equation

y = kx

to find k substitute y = 3 and x = 4 into the equation and solve for k

3 = 4k ( isolate k by dividing both sides by 4 )

\(\frac{3}{4}\) = k

The approximate height of the tree is given as follows:

45.6 ft.

The geometric mean theorem states that the length of the altitude drawn from the right angle of a triangle to its hypotenuse 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:

14.5 ft.

The bases are given as follows:

5.2 ft and x ft.

Hence the value of x is given as follows:

5.2x = 14.5²

x = 14.5²/5.2

x = 40.4 ft.

Hence the height of the three is given as follows:

5.2 + 40.4 = 45.6 ft.

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Answer:

Step-by-step explanation:

g(f(10)) = g(½·10+1)

= g(6)

= 6+2

= 8

Answer:

the answer is 10

Step-by-step explanation:

The system A has no solution.

The system B has the solution y=( 3-x )/3

What is the solution to an equation?

In order to make the equation's equality true, the unknown variables must be given values as a solution. In other words, the definition of a solution is a value or set of values (one for each unknown) that, when used as a replacement for the unknowns, transforms the equation into equality.

System A:

x+3y=9..........(1)

-x-3y=9 ..........(2)

(1) => x=9-3y........(3)

Substitute (3) into (2)

(2) = >  - ( 9-3y ) - 3y = 9

          -9 + 3y - 3y = 9

          -9 =9

This is false.

So, the system has no solution.

System B:

-x-3y=-3..........(1)

x+3y=3..........(2)

(2) => x=3-3y........(3)

Substitute (3) into (1)

-(3-3y)-3y=-3

-3+3y-3y= -3

-3=-3

This is true,

So, the solution is:

x=3-3y

=> 3y= 3-x

=> y=( 3-x )/3

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The the coefficient of variation for set a is 15.7% and the coefficient of variation for set b is 22.3%.

The formula for calculating the coefficient of variation is:

CV = (standard deviation / mean) x 100%

where standard deviation is a measure of the spread of the data around the mean. The CV expresses the standard deviation as a percentage of the mean.

To calculate the CV for set a, we first need to find the mean and standard deviation of the data set. The mean can be calculated by adding all the values and dividing by the number of values.

Mean = (3.97 + 3.47 + 3.99 + 4.30 + 3.16 + 3.07 + 4.24 + 2.94 + 3.56 + 3.43 + 3.06 + 3.34 + 4.35 + 3.57) / 14 = 3.65

The standard deviation can be calculated using a calculator or a spreadsheet software such as Microsoft Excel. For this set, the standard deviation is 0.574.

CV = (0.574 / 3.65) x 100% = 15.7%

To calculate the CV for set b, we need to first remove the dollar sign from each value and then find the mean and standard deviation.

Mean = ($24,800 + $30,000 + $22,300 + $20,400 + $19,000 + $32,200 + $23,000 + $23,000 + $24,000 + $27,200 + $34,900) / 11 = $25,727.27

The standard deviation can be calculated using a calculator or spreadsheet software. For this set, the standard deviation is $5,746.38.

CV = ($5,746.38 / $25,727.27) x 100% = 22.3%

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