An SRS of 20 third grade children is selected in Chicago and each is given a test to measure their reading ability. We are interested in a 90% confidence interval for the population mean score. In the sample, the mean score is 64 points, and the standard deviation is 12 points. The margin of error associated with the confidence interval is
O 4.64 points.
O 5.62 points.
O 2.68 points.

The homeowner should go with option 1 for his budget of $40,200 to use complete budget.

Any equation that can be rearranged in the standard form as is referred to as a quadratic equation (from the Latin quadratus, "square").

ax² + bx + c = 0

where x is a value that is unknown, a, b, and c are numbers that are known, and a is a negative number. The numbers a, b, and c are the equation's coefficients; they are referred to as the constant or free term, the quadratic coefficient, and the linear coefficient, respectively.

Solutions of the equation and roots or zeros of the expression on its left-hand side are the values of x that satisfy the equation. There can only be two solutions to a quadratic equation. One suggests that there is only one solution, which is a double root.

Given a rectangular pool of  35-foot by 20-foot

area of pool = 35 x 20 = 700 sq. foot

and to built a patio around pool of equal width,

budget of patio of $40,200 all amount to be used,

Option 1: Surround the pool with a concrete band of equal width on all sides. The concrete costs $50 per square foot.

the area covered by amount is 40200/50 = 804

let width of patio be x

new length = 35 + x and new breadth = 20 + x

area covered by patio = new area including width - area of pool

new area including width = area covered by patio +  area of pool

new area including width = 804 + 700 = 1504

1504 =  (35 + x)(20 + x )

1504 = x² + 35x + 20x + 700

x² + 55x - 804 = 0

solving the equation by quadratic formula

x = (-b ± [tex]\sqrt{b^{2} - 4ac }[/tex])/ 2a

where a = 1, b = 55, and c = -804

x = (-55 ± [tex]\sqrt{(55)^{2} - 4*1*(-804) }[/tex])/2

x = (-55 ± √(3025 + 3216))/2

x = (-55 ± 79)/2

taking positive values

x = (-55 + 79)/2 = 12

new length = 35 + 12 = 47 foot

new breadth = 20 + 12 = 32 foot

area covered by patio = (47x32) - (35x20)

area covered by patio = 804 sq. foot

and cost will be 804 x 50 = $40,200

for option 2:  Surround the pool with a tile band of equal width on all sides. The tile costs $80 for each square foot tile.

area for patio = 40200/80 = 502.5

since the area is in fraction the cost will come in approximation.

Hence the homeowner should go with option 1 for complete use of budget.

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Answer:

Factors are (x-1) (4x²-1)

Zero(s) are x = 1, x = 1/2, x = -1/2

Step-by-step explanation:

Given function is

4x³ - 4x² - x + 1

= 4x³ - x - 4x² + 1

= x(4x² - 1) - 1(4x² - 1)

= (x - 1) (4x² - 1) (Factors of the equation)

To find the zero(s),

Either, Or,

x - 1 = 0 4x² - 1 = 0

or, x = 1 or, x² = 1/4

or, x = √(1/4)

or, x = +- 1/2

Answer:

B

Step-by-step explanation:

the hypotenuse is z

For the Pythagorean theorem:

x² + y² = z²

The value of 4 plus 4 will be 8.

Expression simply refers to the mathematical statements which have at least two terms which are related by an operator and contain either numbers, variables, or both.

It should be noted that addition, subtraction, multiplication, and division are all possible mathematical operations. As an illustration, the expression x + y has the terms x and y with an addition operator between them.

In this case:

4 + 4

= 8

The value is 8.

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Answer: To calculate the length of a loan, you need to know the total cost of the loan, the monthly payment amount, and the interest rate. In this case, the total cost of the car is $16,000, the monthly payment amount is $250, and the interest rate is 7.3%.

First, you need to calculate the total interest that will be paid on the loan. This can be done by multiplying the total cost of the loan by the interest rate, and then dividing by 100 to convert the result to a percentage. In this case, the total interest paid would be $16,000 * 7.3 / 100 = $1,168.

Next, you need to subtract the total interest from the total cost of the loan to find the total amount of the loan that will be used to pay for the car. In this case, the total amount of the loan used to pay for the car would be $16,000 - $1,168 = $14,832.

Finally, you can use this total amount and the monthly payment amount to calculate the length of the loan by dividing the total amount by the monthly payment amount. In this case, the length of the loan would be $14,832 / $250 = 59.32 months, or just over four years. The answer is 59.32 months.

Step-by-step explanation:

The number of ways to put eight different books in five boxes, of no box is allowed to be empty will be 403200.

As, it is given that,

No box is allowed to be empty.

An arrangement of items in a specific order is referred to as a permutation. Here, the components of sets are organized in a linear or sequential manner. For instance, the set A=1,2 has a permutation of 2, which is 1,2, or 2,1. There is no alternative way to organize the components of set A,

So, we can put one book in each box in [tex]8 P_5[/tex] mays.

Now remaining 3 books we can put in by [tex]${ }_5 P_3$[/tex] ways

Total number of ways will be [tex]$=8 P_5 \cdot 5 P_3$[/tex]

Now calculating the value,

[tex]=\frac{8 !}{(8-5) !} * \frac{5 !}{(5-3) !}\\\\=\frac{8 !}{3 !} \times \frac{5 !}{2 !}\\\\=403200[/tex]

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The correct interpretation for the statement D'(8) = -0.5 is (c) At 8 a.m. the water level was 0.5 meters below sea level.

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

The function D gives the depth of the water, in meters, t hours after midnight on a certain day

This means that

D = depth in meters

t = time in hours

From the question, we have

Notation = D(n)

Also, from the question, we have

D'(8) = -0.5

This is the inverse of the function D(t)

So, the values of the parameters are

D(t) = -0.5

t = 8

This means that the number of hours is 8 and the depth is -0.5 meters

Hence, the interpretation of D'(8) = -0.5 is (c) At 8 a.m. the water level was 0.5 meters below sea level.

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The value of AC according to given equation of Parallelogram is 188 units.

What is parallelogram?

In elementary geometry, a parallelogram may be a  quadrilateral with 2 pairs of parallel sides. the alternative or facing sides of a quadrangle square {measure} of equal length

Main body:

according to question:

AE = 9X-5

AC = 14X+34

as E is midpoint of AC so , we can say

2AE = AC

2(9x-5)= 14x+34

18x-10= 14x+34

4x = 44

x = 11

Now we need to find AC = 14x+34

                                         = 14*11+34

                                         = 188 units

Hence the value of AC according to given equation of Parallelogram is 188 units.

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The length of a diagonal of the square in simplest radical form is; 2√7

We are given that;

Perimeter of square = 56

Now, the formula for perimeter of a square is;

P = 4s

where s is side length of square. Thus;

56 = 4s

s = 56/4

s = 14

Now, the diagonal of a square is given by the formula;

Diagonal = √(2s²)

Thus;

Diagonal = √(2 * 14²)

Diagonal = √(2 * 2 * 7)

Diagonal = 2√7

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The number of meetings they attended in the last five years (x) and the number of papers they submitted to peer reviewed journals (y) during the same period is [tex]-8.6+3.15[/tex].

What is formula for slope and intercept is?

[tex]$$\begin{aligned}& b=\frac{n \sum x y-\left(\sum x\right)\left(\sum y\right)}{n \sum x^2-\left(\sum x\right)^2} \\& a=\bar{y}-b \bar{x} \\& \hat{y}=a+b x\end{aligned}$$[/tex]

The slope is

[tex]$$\begin{aligned}b & =\frac{n \sum x y-\left(\sum x\right)\left(\sum y\right)}{n \sum x^2-\left(\sum x\right)^2} \\& =\frac{12 \times 318-(12 \times 4)(12 \times 4)}{12 \times 232-(12 \times 4)^2} \\& =3.15\end{aligned}$$[/tex]

The intercept is

[tex]$$\begin{aligned}a & =\bar{y}-b \bar{x} \\& =4-3.13 \times 4 \\& =-8.6\end{aligned}$$[/tex]

The regression equation is

[tex]$$\begin{aligned}\hat{y} & =a+b x \\& =-8.6+3.15 x\end{aligned}$$[/tex]

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Answer:

4x³ + 5x² - 30x + 18

Step-by-step explanation:

(4x - 3)(x² + 2x - 6)

each term in the second factor is multiplied by each term in the first factor.

4x(x² + 2x - 6) - 3(x² + 2x - 6) ← distribute parenthesis

= 4x³ + 8x² - 24x - 3x² - 6x + 18 ← collect like terms

= 4x³ + 5x² - 30x + 18

The number of miles the taxi rode are 9 miles.

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

Given that, the taxi company charged a pick-up fee of $3.10 plus $2.75 per mile. The total fare was $27.85.

Let the number of miles be x.

Now, 3.10+2.75x=27.85

2.75x=27.85-3.10

2.75x=24.75

x=24.75/2.75

x=9 miles

Therefore, the number of miles the taxi rode are 9 miles.

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The complete square for the binomial expression is x² + 15x + [ 15²/4 ].  

→ The squaring of a binomial will always give a trinomial.

For example,  

(a + b)(a + b) = (a + b)² = a² + 2ab + b²  

(ax - b) (ax - b) =  (ax - b)² = ax²  - 2axb + b²

→ If a trinomial (ax² + bx + c ) is perfect square then

The formula for constant term c = [ b/2√a ]²  

Here we have

x² + 15x + __  is a square of the expression

As we know constant term c = [ b/2√a ]²    

=> Constant term of (x² + 15x + __) =  [ 15/2√1 ]² = [ 15²/4 ]    

Therefore the complete expression is  x² + 15x + [ 15²/4 ]  

Here divide and multiply by 2 with 15x

=>  [tex]x^{2} + 2 (\frac{15x}{2}) (1) + (\frac{15}{2})^{2}[/tex]  

The above expression is in the form of (a + b)² = a² + 2ab + b²  

=>   [tex]x^{2} + 2 (\frac{15x}{2}) (1) + (\frac{15}{2})^{2}[/tex] = [tex][x + \frac{15}{2} ]^{2}[/tex]    

Therefore,

The complete square for the binomial expression is x² + 15x + [ 15²/4 ].  

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Answer: a. 40%

Step-by-step explanation: 48% of 120 is 40

Answer: a. 40%

Step-by-step explanation:

48/120 = x/100

butterfly method

120x/120 = 4800/120

simplify.

x = 40%

The distance traveled by a particle with position (x, y) as t varies in the time interval 0 ≤ t ≤ 3π be, 6π units.

Given, a particle with position (x, y) move across a distance as t varies in the given time interval 0 ≤ t ≤ 3π

where, x = sin2t, y = cos2t

On using the length of the curve concept, we get

d = ∫√((dx/dt)² + (dy/dt)²) dt

as, x = sin2t and y = cos2t

dx/dt = 2cos2t

dy/dt = -2sin2t

On substituting the values, we get

d = ∫√(4cos²2t + 4sin²2t) dt

d = ∫2 dt

d = 2∫dt

d = 2×(3π - 0)

d = 6π

So, the distance traveled by the particle be, 6π

Hence, the distance traveled by the particle be, 6π

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The average number of hours worked is not a binomial variable as there is no success or failure in the scenario.

In probability theory and statistics, the discrete probability distribution of the number of successes in a series of n independent experiments, each asking a yes-or-no question and each with its own Boolean-valued outcome: success or failure, is known as the binomial distribution with parameters n and p.

A variable with two possible forms is said to have a binomial distribution. It could result in success or failure, heads or tail, and yes or no. If a coin is tossed, for instance, it could land on its head or its tail. It is a binomial variable as a result.

Here, there may be more than two values for the typical hours worked. It is not a binomial variable as a result.

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The present p value which have to be invest in future is $7619.05 at simple interest rate r.

Simple Interest:

Simple interest (S.I) is a method of calculating the amount of interest on a specific amount of money.

The simple interest formula helps determine the amount of interest given a principal, interest rate, and term.

The formula for simple interest is:

SI = PTR/100

where SI = simple interest

P = principal

R = interest rate (percentage)

T = term (years)

For calculating total amount

             Amount (A) = principal Book (P) + Interest (I)

where

Amount (A) is the total amount repaid at the end of the borrowed period.

The simple interest total amount formula can also be written as:

                                    A = P(1 + RT)

where

A = Total amount after specified period

P = Principal or original loan amount

R = Interest rate (annual)

T = Time (annual )

According to the Question:

Simple interest: I = PTR            ---------------------------- (1)

Future amount : A = p + I = p + PTR         ------------------ (2)

Given that:

r = 10% = 0.1

t = 6 months = 0.5 year

A = future amount = 8000

Now,

8000 = p + p (. 1)(0.5)

⇒ 8000 = 1.05 p

⇒ p = 8000/1.05

⇒ p = $ 7,619.05

Now,

Putting the value of p in equation (2)

I = 7619.05 (0.1) (0.5 ) = 380.95

7619.05 + 380.90 = $8,000

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Answer: 7

Step-by-step explanation: 13+1=14

2*?=14            2*7=14

Answer:

7w^2+3x^2-24wx

Step-by-step explanation:

we distribute

(3x-w)(3x-7w)

3x(3x)+3x(-7w)-w(3x)-w(-7w)

3x^2-21wx-3wx+7w^2

combine like terms

3x^2-24wx+7w^2

order correctly

7w^2+3x^2-24wx

hopes this helps

Answer:

[tex]9x^2-24xw+7w^2[/tex]

Step-by-step explanation:

Given expression:

[tex](3x-w)(3x-7w)[/tex]

[tex]\boxed{\begin{minipage}{5.5 cm}\underline{FOIL Method}\\\\$(a+b)(c+d)=ac+ad+bc+bd$\\ \end{minipage}}[/tex]

Apply the FOIL method to expand the brackets:

[tex]\implies 3x \cdot 3x +3x \cdot(-7w)+(-w) \cdot 3x+(-w) \cdot (-7w)[/tex]

[tex]\implies 9x^2-21xw-3xw+7w^2[/tex]

Combine like terms:

[tex]\implies 9x^2-24xw+7w^2[/tex]

The required answer is the fourth root of 625 is 5. In summary, the fourth root of 625 is 5.

To find the fourth root of 625, we need to determine the number that, when raised to the power of 4, equals 625. Here's the step-by-step process:

Step 1: Start with the number 625.

Step 2: Take the fourth root of 625.

Since we're looking for the fourth root, we need to find a number that, when raised to the power of 4, equals 625.

Step 3: Determine the number that, when raised to the power of 4, equals 625.

To find this number, we can use the concept of exponentiation. Let's denote the unknown number as "x". Mathematically, we have [tex]x^4 = 625[/tex]..

Step 4: Solve the equation [tex]x^4 = 625[/tex].

To solve this equation, we need to find the value of x. Taking the fourth root of both sides of the equation, we have [tex]\sqrt[4]{(x^4)} =\sqrt[4] {625}.[/tex]

The fourth root of 625 is (625)^(1/4).

Step 5: Simplify the expression.

We can simplify [tex]\sqrt[4]{ 625}[/tex] as follows:

[tex]\sqrt[4]{ 625} = \sqrt[4]{ 5^4}= 5^{4/4} = 5^1 = 5.[/tex]

Therefore, the fourth root of 625 is 5. In summary, the fourth root of 625 is 5.

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Five 1/2 inch cubes fit along it’s 2 1/2 length.

An object's longest or largest dimension is a measured distance. Dimensions: 10 ft. see Weights and Measures, Metric System Table

An object's length, which is a measurement of its longest side, is its most stretched dimension. Your dog, for instance, would measure its length from the point of its nose to the end of its tail. The space between its top and bottom feet is greater than that of the creature's head.

In addition to utilizing handspan, foot span, and other methods, one can measure length in many units, such as centimeters, inches, meters, and so on.

Let x be the number of 1/2 cubes to fit 2 1/2 length

(1/2)x= 2 1/2

(1/2)x=5/2

x=5

Therefore, five 1/2 inch cubes fit along it’s 2 1/2 length.

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Answer:

x = 5

Step-by-step explanation:

To solve this problem, we need to utilize the triangle sum theorem.

⭐What is the triangle sum theorem?

1. Set up the equation as per the triangle sum theorem

(5x+6) + 43 + 106 = 180

2. Add the constants

5x + 155 = 180

3. Subtract 155 from the LHS and RHS

5x = 25

4, Divide the LHS and RHS by 5 to isolate x

∴ x = 5

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In a conceptual replication, the variables are the same, but the operationalization is/are different from the original study.

The researcher seeks to recreate the basic idea of the research in a conceptual replication. An exact replication involves the researcher reproducing, or attempting to duplicate, the precise circumstances of the original study.

A replication attempt in which the primary effect of interest is the same but tested in a different sample and captured in a different way than that reported originally .

A conceptual replication is sometimes used to investigate what constraints limit the extent to which an effect may be observed and generalised (e.g., only within certain contexts, with certain samples, and using certain measurement methodologies) in order to evaluate and advance theory.

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The​ P-value indicates that the probability of a linear correlation coefficient that is at least as extreme is 1.3% which is low so there is sufficient evidence to conclude that there is a linear correlation between weight and highway fuel consumption in automobiles.

Given that,

The complete statement is,

The p-value is given as:

[tex]p=0.013[/tex]

Express as percentage

[tex]p=1.3[/tex] %

This means that the probability that the linear correlation coefficient is at least as extreme is 1.3%.

From the z-table, we have:

[tex]z = 1.81[/tex],  when the p-value is 0.013

This value of z-score is low, compared to the percentage of the scores have a z-score of between -1 and 1.

So, the p-value implies that it is likely that there is a linear correlation between the variables.

Hence, the texts that complete the three blanks are: "1.3%", "low" and "is"

Therefore,

The​ P-value indicates that the probability of a linear correlation coefficient that is at least as extreme is 1.3% which is low so there is sufficient evidence to conclude that there is a linear correlation between weight and highway fuel consumption in automobiles.

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Answer:

f(-2) =3

Step-by-step explanation:

f(-2) = value of the function when x = -2

Using the graph find the value of the function when x = -2

The value is 3

f(-2) =3

Qualitative variables include all observable qualities or characteristics of a group or population that can not be measured numerically.

What is Qualitative?

The goal of qualitative research is to collect and examine non-numerical data in order to comprehend people's attitudes, beliefs, and motivations in relation to their social reality.

Quantitative Variable

Quantitative variables, as the name implies, are those that can be expressed by a numerical value.

1. Quantitative (Discrete)

2. Quantitative (Continuous)

3. Quantitative (Discrete)

4. Qualitative (nominal)

5. Qualitative (nominal)

6. Qualitative (nominal)

7. Qualitative (nominal)

8. 9. Quantitative (Continuous)

10. Qualitative (nominal)

11. Quantitative (Continuous)

12. Qualitative (ordinal)

13. Qualitative (nominal)

14. Quantitative (Discrete)

15. Qualitative (nominal)

Complete question: Which is the following a qualitative or quantitative variable?

1)ordinal

2)Continuous

3)nominal

4) All of these

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The range and domain of the graph shown is

domain -4 ≤ x < ∞

range ∞ ≤ x < 3

All of a function's x-values, or inputs, make up the domain, and all of a function's y-values, or outputs, make up the range.

The domain of a graph is every value in the graph, from left to right.

Examining the curve the extreme left has x coordinate value of -4 and the right end have an arrow which means the value continues. this is written as

-4 ≤ x < ∞

The graph's entire range, from lower to higher numbers, in the vertical line represents the range.

Examining the curve the lowest point the curve reached in y-coordinate have an arrow which means the value continues and the top end have the value of 3. this is written as

∞ ≤ x < 3

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Answer:

1.362 kilograms

Step-by-step explanation:

3 x .454 = 1.362 Kilograms