An automotive manufacturer wants to know the proportion of new car buyers who prefer foreign cars over domestic. Step 2 of 2 : Suppose a sample of 768 new car buyers is drawn. Of those sampled, 192 preferred foreign over domestic cars. Using the data, construct the 80% confidence interval for the population proportion of new car buyers who prefer foreign cars over domestic cars. Round your answers to three decimal places.

According to the solving the exponential form of the given number is as follows:

= 6² × 7⁴

= (-104)³

Bases and powers are employed in the exponential form to write numbers. It informs us of the amount of times we must actually multiply a number in order to obtain the answer. When we write the number 125 as 53, for instance, we can see that it is the third power of 5, or the number 125, which looks to be a typical three-digit number when observed.

When a single integer is multiplied by itself a certain number of times, x, the equation y takes on the base component b to the power of x, which is the quantity being multiplied, and is known as the exponential form.

The exponential form of the given number is :

= 6х6х7х7x7x7

= 6² × 7⁴

The exponential form of the given number is :

= -104 x -104 x -104

= (-104)³

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Answer:

D

Step-by-step explanation:

3 | 1   5   - 8   6

   ↓   3    24   48

   ----------------------

    1   8   16    54 ← Remainder

Answer:

12 blue beads

Explanation:

Given the following

Number of beads received= 50 beads

Percentage that are blue = 24%

Amount of blue beads received = 24% of 50beads

Amount of blue beads received = 24/100 * 50

Amount of blue beads received = 24/2

Amount of blue beads received = 12beads

Hence Abby received 12 blue beads

The money we would have at any time can be modeled as

M = 27k + 141

Why?

you started with $141, so that is the base amount,

every month you add 27 dollars,

in one month you add 27 dollars,

in two months you 27 again making 54 dollars,

so , in x months, you have added 27x dollars to the 141 dollars,

thus our equation is

M = 27k + 141

Expression for given numerical is: 9+ (2/x)

Given that we have an word equation that is 9 more than the quotient of 2 and  x

A quotient is a quantity produced by the division of two numbers.

Quotient of 2 and x is \(\frac{2}{x}\).

Nine(9) more  than 2/x is = 9+ (2/x)

So we have an expression that is:

              9+ (2/x)                          

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Problem 1

Reason: We start at 0 and move 4 units left. This is represented by 0+(-4) or 0-4. That simplifies to -4. Then add on 7 to move 7 units to the right to arrive at 3 as the final destination.

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

Problem 2

Reason: We start at 0 and move 8 units to the right. That is represented by +8 or simply 8. Then the +3 will move us 3 more units to the right to get to 11 on the number line. This is one visual way to see why 8+3 = 11.

Answer:

\(y\le-\frac{1}{4}x^{2}+\frac{1}{2}x+12\)

Step-by-step explanation:

It has to have a y-int of +12 so that eliminates the first 2.

It needs to be contained inside the parabola therefore the x^2 value needs to be negative.

It needs to be shifted 1/2 to the right, therefore it needs a pos x value.

Hope that helps

Answer:

5

Step-by-step explanation:

5, 10, 15, 20, 25

5, 10, 15, 20, 25

5, 10, 15, 20, 25

Hope this helps!!!

Have a great day!!!! :)

Answer:

5

Step-by-step explanation:

factors of 20:

1, 2, 4, 5, 10, 20

factors of 10:

1, 2, 5, 10

factors of 25:

1, 5, 25

as you can see from the factor list of each number, 5 is the higest common factor.

Answer:

\(\large { \boxed{\sf x = -4}\)

Explanation:

Original Expression:

\(\rightarrow \sf x + 5 = 5 - 0 - 6 + 2\)

Subtract '5' from both sides:

\(\sf \rightarrow x+5-5=5-0-6+2-5\)

Simplify the following:

\(\sf \rightarrow x=-0-6+2\)

Add/Subtract integers:

\(\sf \rightarrow x=-4\)

Answer:

slope of line q = \(\frac{3}{4}\)

Step-by-step explanation:

calculate the slope of line p using the slope formula

m = \(\frac{y_{2}-y_{1} }{x_{2}-x_{1} }\)

with (x₁, y₁ ) = (8, 7 ) and (x₂, y₂ ) = (4, 4 )

m = \(\frac{4-7}{4-8}\) = \(\frac{-3}{-4}\) = \(\frac{3}{4}\)

• Parallel lines have equal slopes

then slope of line q = \(\frac{3}{4}\)

Answer:

-1.555 and 1.555

Step-by-step explanation:

For a standard normal distribution:

P(- Ƶ ≤ Z ≤ Ƶ) = 0.88

The normal distribution on the curve is symmetrical about Z = 0

Thus

P( -Ƶ ≤ Z ≤ 0) = P( 0 ≤ Z ≤ Ƶ)

However;

This implies that:

P( -Ƶ ≤ Z ≤ 0)  +  P( 0 ≤ Z ≤ Ƶ) = 0.88

2P ( 0 ≤ Z ≤ Ƶ)  = 0.88

P( 0 ≤ Z ≤ Ƶ) = 0.44

P(Z ≤ Ƶ) - P( Z ≤ 0) = 0.44

Since P(Z ≤ 0) = 0.50

P(Z ≤ Ƶ) = 0.44 + 0.50

P(Z ≤ Ƶ) =  0.94

From the probability value table

z = 1.555

Thus the endpoints are:

-1.555 and 1.555

The result of the unknown variable x is equivalent to 7

Linear equations are equation that has a leading degree of 1. Given the expression below:

5(3x − 15) + 16 = 5x + 11

Expand the expression

5(3x) - 5(15) + 16 = 5x + 11

15x - 75 + 16 = 5x + 11

15x - 5x - 59 - 11 = 0

10x - 70 = 0

10x = 70

Divide both sides by 10

10x/10 = 70/10

x = 7

Hence the value of x makes the equation true is 7

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The elements using rooster-method:

A){3,4,5,6,7,8,9,10}

B){5,6,7,8,9,10,11,12,13,14}

What is rooster-method?

By listing the items of a set inside brackets, the roster method may be used to display the elements of a set. One of three ways to describe a set is in rooster form. The items of a set are listed in the roster form between curly or following brackets, with commas separating each element. When items repeat in the set, the roster approach actually has an issue. Because the elements do not follow a pattern or have a specific order, it is impossible to describe the elements in roster notation if the set has a significant number of elements or any repeated elements.

A)Set of natural odd numbers greater than 2 but less than 11:

Let us represent the set using symbol O:

O = {3,4,5,6,7,8,9,10}

B){x| x∈ N and 4<x<15}

Given that x is a natural number greater than 4 but less than 15.

X={5,6,7,8,9,10,11,12,13,14}

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To calculate Swornima's annual income and the amount of tax she should pay, let's break down the information provided:

Monthly basic salary: Rs 48,000

Social security tax rate: 1%

Income tax rate on income up to Rs 5,00,000: 0% (no tax)

Income tax rate on income from Rs 5,00,001 to Rs 7,00,000: 10%

Dashain allowance: 1 month's salary

Deposit in Citizen Investment Trust (CIT): 10%

Rebate on income tax: 10%

(i) Annual Income:

Swornima's monthly basic salary is Rs 48,000, so her annual basic salary would be:

Annual Basic Salary = Monthly Basic Salary x 12

= Rs 48,000 x 12

= Rs 5,76,000

Additionally, she receives 1 month's salary as the Dashain allowance, which we can add to her annual income:

Annual Income = Annual Basic Salary + Dashain Allowance

= Rs 5,76,000 + Rs 48,000

= Rs 6,24,000

Swornima's annual income is Rs 6,24,000.

(ii) Tax Rebate:

Swornima receives a 10% rebate on her income tax. To calculate the rebate, we need to determine her income tax first.

(iii) Annual Income Tax:

First, let's calculate the income tax for the range of income from Rs 5,00,001 to Rs 7,00,000. The tax rate for this range is 10%.

Taxable Income in this range = Rs 6,24,000 - Rs 5,00,000

= Rs 1,24,000

Income Tax in this range = Taxable Income x Tax Rate

= Rs 1,24,000 x 0.1

= Rs 12,400

Now, let's calculate the total annual income tax:

Total Annual Income Tax = Income Tax in the range Rs 5,00,001 to Rs 7,00,000

= Rs 12,400

Next, we calculate the rebate on income tax:

Tax Rebate = Total Annual Income Tax x Rebate Rate

= Rs 12,400 x 0.1

= Rs 1,240

Swornima's annual income tax is Rs 12,400, and she receives a tax rebate of Rs 1,240.

To summarize:

(i) Swornima's annual income is Rs 6,24,000.

(ii) Swornima's tax rebate is Rs 1,240.

(iii) Swornima should pay an annual income tax of R

Based on the information, we can infer that the salary a worker earns depends on the hourly wage they earn. In this case we will have to multiply the value of each hour by the number of hours worked. Additionally, I would agree to have a higher minimum wage to benefit workers.

Based on the information in the graph, we can infer that workers will have wages of $5.2, $6.0, and $6.6. According to the above, the salary varies depending on the number of hours.

On the other hand, I believe that you would agree to a salary increase because this would benefit workers who would be better paid for each hour of work.

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Answer:

There is insufficient evidence to support the claim that the mean age is greater than 50.2 years. i.e ( μ > 50.2)

Step-by-step explanation:

Given that:

The mean age of judges in Dallas is greater than 50.2 years.

If a hypothesis test is performed, then the null and the alternative hypothesis can be computed as follows:

The null hypothesis is that the mean age of the judges in Dallas is equal to 50.2

i.e

\(H_o : \mu =50.2\)

The alternative hypothesis is that the mean age of the judges in Dallas is greater than 50.2

i.e

\(H_1 : \mu > 50.2\)

Decision Rule: Fail to reject the null hypothesis.

The interpretation of this decision rule implies that:

There is insufficient evidence to support the claim that the mean age is greater than 50.2 years. i.e ( μ > 50.2)

Answer:

1.67x10^-27

hope this helps

have a good day :)

Step-by-step explanation:

Answer:

----------------------------

Divide the total amount by the cost per piece:

Since the carpenter can only buy whole pieces of wood, they can buy 30 pieces.

The factorized form of \(x^3 - (y - z)^3\ is \ (x - y + z)(x^2 - xy + 2xz + yz - 2z^2).\)

The Factorization is derived from the application of a mathematical identity. As an AI language model, the information provided is generated based on existing knowledge and formulas.

The given expression is \(x^3 - (y - z)^3.\)To factorize it,  the difference of cubes, which states that a^3 - b^3 can be factorized as\((a - b)(a^2 + ab + b^2).\)

Applying this identity to our expression, we have:

\(x^3 - (y - z)^3 = (x - (y - z))((x - (y - z))^2 + (x - (y - z))(y - z) + (y - z)^2)\)

Simplifying further, we get:

\(= (x - y + z)(x^2 - 2xy + 2xz - y^2 + 2yz - z^2 + xy - y^2 + yz - z^2 + y^2 - 2yz + z^2)\\= (x - y + z)(x^2 - 2xy + xy + 2xz + yz - 2yz - y^2 + y^2 - y^2 + 2yz - 2z^2 + y^2 - z^2 + z^2)\\= (x - y + z)(x^2 - xy + 2xz + yz - 2z^2)\)

So, the factorized form of \(x^3 - (y - z)^3 \ is\ (x - y + z)(x^2 - xy + 2xz + yz - 2z^2).\)

the above factorization is derived from the application of a mathematical identity.

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The sample space for this experiment is the one in the last option.

The sample space is the set of the possible outputs that we can have for selecting two marbles.

For example, if first you get a yellow marble, and then a red one, the output will be:

yellow red,

And that is different to the output:

red yellow

Where in the second one you draw the red one first.

From the options, the one that shows the complete sample space is the last one:

"Yellow Yellow, Yellow Red, Yellow Clear, Yellow Green, Yellow Blue, Yellow

Red Yellow, Red Red, Red Clear, Red Green, Red Blue, Red

Clear Yellow, Clear Red, Clear Clear, Clear Green, Clear Blue, Clear

Green Yellow, Green Red, Green Clear, Green Green, Green Blue, Green

Blue Yellow, Blue Red, Blue Clear, Blue Green, Blue Blue, Blue"

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If the remaining milk is sold for $3.94 per half gallon, then the store initially bought 26 half gallons of milk for the profit of $46.76

What is meant by profit?

Profit is the term used to describe the financial gain experienced when the revenue from a company activity outpaces the costs, costs, and taxes incurred to support the activity in question.

Profit is the amount of money you have after paying for business expenses. Gross profit, operating profit, and net profit are the three basic categories of profit.

If the store bought x half gallons of milk at $2.90 per half gallon, the total cost of the milk would be:

                           total cost = 2.90x

Since the store stored the milk in two refrigerators, there were initially x/2 half gallons in each refrigerator.

Unfortunately, 14 half gallons were ruined, so the number of half gallons of milk remaining for sale is:

                            x - 14

The store then sells the remaining milk for $3.94 per half gallon, so the total revenue from the sale is:

                                total revenue = 3.94(x - 14)

The profit the store made is the difference between the total revenue and the total cost:

                         profit = total revenue - total cost

We know that the store made a profit of $46.76, so we can set up an equation:

46.76 = 3.94(x - 14) - 2.90x

Simplifying and solving for x:

46.76 = 3.94x - 55.16

102.92 = 3.94x

x = 26

So the store initially bought 26 half gallons of milk.

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The slope of the median of the triangle whose vertices are P(-6,1),Q(-2,5) R(8,1) and passes through R is -1/6.

Given that vertices of triangle is P(-6,1),Q(-2,5),R(8,1) and there is a median which passes through R.

Median of a triangle is a line segment which originates from a vertex of triangle and divides the opposite side in two equal parts. let median touches the line at L point.

When line passes through R then it must be a perpendicular on PQ. The coordinates of L is {(-2-6)/2,(5+1)/2}=(-4,3)

Now because median passes through R,it will be LR and we know that the formula of calculating slope of line from two points is \((y_{2} -y_{1} )/(x_{2} -x_{1} )\) where \((x_{1} ,y_{2} ),(x_{2} ,y_{2} )\) are the points of the end points of line.

Slope=(1-3)/(8+4)

=-2/12

=-1/6

Hence the slope of the median of the triangle whose vertices are P(-6,1),Q(-2,5) R(8,1) and passes through R is -1/6.

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The value of the expression x² + 10x, when x = 2 is 24.

In the expression x² + 10x, x represents a variable, which is a placeholder for a value that can change. We are given that x = 2, which means we substitute 2 for x in the expression:

x² + 10x = 2² + 10(2)

Here, 2² means 2 raised to the power of 2, which is 2 multiplied by itself: 2² = 2 x 2 = 4.

10(2) means 10 multiplied by 2, which is 20.

So we can substitute these values in the expression:

x² + 10x = 2² + 10(2)

= 4 + 20

= 24

Therefore, when x is equal to 2, the value of the expression x² + 10x is 24.

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The complete question:

Evaluate the expression x² + 10x, when x = 2.

TU is parallel to MN.

Given that the slope of a line MN is -3, we need to find a line which is parallel to the MN.
So we know that the parallel lines are having equal slope so the line which is parallel to the MN it must have slope of -3.

Therefore,

Considering the line TU, find the slope = y₂-y₁ / x₂-x₁

= 10-1 / 5-8 = -9/3 = -3

Since, the slope of the line TU is -3 therefore we can say the lines TU and MN are parallel liens.

Hence TU is parallel to MN.

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Hello!

In this question, we are trying to find how many passes a QB completed if he attempted 20 passes.

We know:

We will use the information above to help us solve our question.

Solve:

We know the ratio of completed to attempted passes is 2:5

The "2" represents completed passes while the "5" represents attempted passes. In other words, for every 5 passes the QB completes 2 of them.

We also know that we need to find how many passes the QB completed after throwing 20 passes. To find this, we will multiply the "5" by 4 to get "20" in our ratio for attempted passes. Note that whatever we do on one side of the ratio we do to the other side as well.

Multiply the ratio by 4.

2:5

×4

8:20

This means that the QB threw 8 completed passes out of 20 attempted passes.

Answer:

8 completed passes

The smallest value (minimum) among the following (3.11, 0.956, 36, 4.21, or 10.1) is 0.956.

The smallest value refers to the minimum value among the data set values.

The opposite of the smallest value is the maximum value or the largest value.

In these values, 3.11, 0.956, 36, 4.21, or 10.1, 0.956 is obviously the smallest because it is less than 1, whereas other values are more than 1 and it represents a proper fraction, unlike the other improper fractional values.

Thus, we can conclude that 0.956 is a fractional value depicted as a decimal, unlike other values that combine whole numbers with some fractions.

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Which of the following is the smallest value, 3.11, 0.956, 36, 4.21, or 10.1

Interest earned on first investment in year 1 is $6,183.13

Interest earned on second  investment in year 1 is $6,167.68

Annual yield on first investment is 6.18%

Annual yield on second investment is 6.17%

What is daily compounding?

Daily compounding means that the interest on the investment is computed on daily basis, 365 days a year.

In a bid to determine the total interest earned in one year on the investment whose interest is compounded daily, we can make use of the future value below to determine its worth after 1 year, from which the initial investment can be deducted to determine the interest in year 1.

FV=PV*(1+r/n)^(n*t)

PV=initial investment=$100,000

r=rate of return=6%

n=365 days a year

t=1 year

FV=$100,000*(1+6%/365)^(365*1)

FV=$106,183.13

Interest=$106,183.13 -$100,000

interest=$6,183.13

Annual yield=effective annual interest

EAR=(1+6%/365)^(365)-1

EAR=6.18%

What is monthly compounding?

It means interest is compounded or computed every month, 12 months a year

FV=PV*(1+r/n)^(n*t)

PV=initial investment=$100,000

r=rate of return=6%

n=12 months a year

t=1 year

FV=$100,000*(1+6%/12)^(12*1)

FV=$ 106,167.78  

Interest=$ 106,167.78  -$100,000

interest=$6,167.68

Annual yield=effective annual interest

EAR=(1+6%/12)^(12)-1

EAR=6.17%

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