2. Identify if the following are one-to-one functions or not.
(a) People to their birthdays
(b) People to their Social Security System number
(c) People to their place of residence
[6]

The required first step Landon should s=150/(1-0.96).

Here,
The distance that the weight travels before it comes to rest can be found using the formula for the sum of an infinite geometric series:

S = a/(1 - r)

where S is the total distance traveled, a is the distance of the first swing, and r is the ratio of the distance of each subsequent swing to the distance of the previous swing.

In this case, a = 150 inches and r = 144/150 = 0.96 (since the return swing is slightly shorter than the previous swing). So the equation that represents the total distance the weight travels before it comes to rest is:

S = 150/(1 - 0.96) = 3750 inches.

Therefore, the correct equation is s=150/(1-0.96).

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The comparison of the values 4/5 and 0.9 using a benchmark of 1 indicates that 0.9 > 4/5

A benchmark is a point of reference to which two or more quantities can be compared such that it can be used to provide a values guagemark indication

A benchmark that is commonly used is 1

Therefore;

Converting 4/5 into decimals, to be in the same format as 0.9, we get;

4/5 = 0.8

The numbers 0.8 and 0.9, compared with 1 indicates that

1 is larger than 0.8 and 0.9 and 0.9 is closer to 1 in value than 0.8, therefore;

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To calculate the variable cost per unit using the high-low method, the change in total cost is divided by the change in activity level.

The high-low method is a cost analysis technique used to estimate the variable and fixed components of a mixed cost. It involves using the highest and lowest levels of activity to calculate the variable cost rate and then using this rate to estimate the fixed cost component.

To calculate the variable cost per unit using the high-low method, first, the total cost and activity level are recorded for the highest and lowest levels of activity. Then, the change in total cost is calculated by subtracting the total cost at the lower level of activity from the total cost at the higher level of activity. Similarly, the change in activity level is calculated by subtracting the lower level of activity from the higher level of activity. Finally, the change in total cost is divided by the change in activity level to obtain the variable cost per unit.

It is important to note that the high-low method assumes a linear relationship between cost and activity, which may not always hold true. Therefore, this method should be used with caution and other cost analysis techniques should also be considered.

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Henry would be able to drive 960 miles if he purchased 24 gallons of gas.

Given that Henry's car uses 8 liters of gasoline on average to cover 320 miles.

Let x miles be able to drive if he purchased 24 gallons of gas.

According to the question, the ratio can be calculated as:

320 miles : 8 gallons = x miles : 24 gallons

⇒ 320/8 = x/24  

⇒ (8)(x) = (24)×(320)

Divide each side by 8 to get,

⇒ x = (24)×(320)/(8)

⇒ x = 960

Therefore, he would be able to drive 960 miles if he purchased 24 gallons of gas.

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Answer:

x = 3 , y = - 5

Step-by-step explanation:

the solution to the system is at the point of intersection of the 2 lines.

the lines intersect at (3, - 5 )

that is x = 3 , y = - 5 is the solution

To reject the null hypothesis with a calculated value of t of 2.11 at the 0.05 level of significance, there must be at least 26 participants in each group.

To calculate the sample size required to detect a significant difference at the 0.05 level of significance, we need to use a power analysis. A power analysis is a statistical method that calculates the minimum sample size required to achieve a certain level of statistical power, which is the probability of rejecting the null hypothesis when it is false.

Assuming a power of 0.8 (a commonly used level of power), we can use a power calculator or a statistical software program to determine the required sample size for the given effect size (represented by the calculated value of t) and significance level.

By using an online calculator, we can find that a sample size of at least 26 participants per group would be required to detect a difference with an effect size of 0.5 (which corresponds to a calculated value of t of 2.11) at the 0.05 level of significance with 80% power.

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The confidence interval between 5.68 and 7.92 should be interpreted as "we are 95% confident that the true slope for the association between weight and number of goggles for our sample of piknits lies between 5.68 and 7.92."

A defined degree of confidence, usually 95% in most applications, was used to generate the interval using the sample data. The interpretation of this range is that, for our population of piknits, there is a 95% probability that the true slope of the relationship between weight and goggles falls between 5.68 and 7.92.

Decision-makers who must estimate the true population parameter based on a sample can benefit greatly from the knowledge provided by this interval.

It also emphasizes the significance of selecting the sample size and level of confidence with care to guarantee the precision of the interval.

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After the logarithmic expression, "log(2x - 4) - log(x + 2) = 1", the value of x is -3.

In order to find the simplify the logarithmic expression, and find the value of "x", we use the "logarithmic-property", that : "log(a) - log(b) = log(a/b)",

The equation can be written as :

⇒ log[(2x - 4)/(x + 2)] = 1,

By using definition of logarithm, we can rewrite this equation as:

⇒ (2x - 4)/(x + 2) = 10

Simplifying this equation,

We get;

⇒ 2x - 4 = 10x + 20;

⇒ -24 = 8x

⇒ x = -3

Therefore, the required value of x is -3.

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Answer:

Let's assume that the original price of the laptop was "x". In any equation that is unknown and you cant figure out, you can use the equation of x.

According to the problem, the laptop costs $650 after a 30% discount. This means that the discounted price is equal to 70% of the original price:

Discounted price = 70% of original price then you divide by 100 so its

$650 = 0.7x

To solve for the original price, we can divide both sides of the equation by 0.7:

x = $650 ÷ 0.7

x = $928.57 (rounded to the nearest cent)

Therefore, the original price of the laptop was $928.57.

Answer: $928.57

Step-by-step explanation:

Price * (100%-30%) = $650

price * .7 = 650

price = 650/.7

price = 928.57

[tex]~~~~~~~~~~~~\textit{distance between 2 points} \\\\ P1(\stackrel{x_1}{2}~,~\stackrel{y_1}{1})\qquad P2(\stackrel{x_2}{5}~,~\stackrel{y_2}{7})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ P1P2=\sqrt{(~~5 - 2~~)^2 + (~~7 - 1~~)^2} \implies P1P2=\sqrt{( 3 )^2 + ( 6 )^2} \\\\\\ P1P2=\sqrt{ 9 + 36 } \implies P1P2=\sqrt{ 45 }\implies P1P2\approx 6.71[/tex]

The above is an analysis of functions.

A) See the graph attached
1) This is a growth function

2) the asymptote is at y = -3

3) the domain is a real number

4) Range is ≥ -3
5) Y-intercept is (0, -11/4)


B) See attached graph.

1) this is a decay function

2) y=3 is the horizontal asymptote of the function
3) domain is a real number
4) Range ≤ 3
5) y-intercept is 5

A) The formula for f(x)  is 4( x-1)- 3 is an exponential  function with an exponent of (x- 1) and a base of 4 . Given that the base is bigger than 1,   it is therefore, a growth function.

The function's horizontal asymptote is y = -3. The function may accept any value greater than or equal to -3 and is defined for all real numbers. The function's y-intercept is -11/4.

B) The function f( x) = 2(1/2)^x + 3 is an exponential function with a base of 1/2 and an exponent of x.

Considering that the  base is smaller than 1 , it is a decay function. The function's horizontal asymptote is y = 3. The function may accept any value that is less than or equal to 3 and is defined for all real numbers. The function's y-intercept is 5.

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The correct interpretation of the 95 percent confidence interval $62.63±$17.64 is option (a): We are 95 percent confident that the mean cost of a hospital visit for all parrot owners in the state is between $44.99 and $80.27.

This means that if we were to repeat this study many times and construct a 95 percent confidence interval each time, about 95 percent of these intervals would contain the true mean cost of a hospital visit for all parrot owners in the state. It is important to note that this interval does not guarantee that the true mean cost falls within this range, but we are confident to a 95 percent level that it does. The term "probability" does not accurately describe the confidence interval, as it is a statement about the level of confidence we have in our estimation of the true mean, not a probability that the true mean falls within a certain range.

Your answer: a. We are 95 percent confident that the mean cost of a hospital visit for all parrot owners in the state is between $44.99 and $80.27.

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If particular shipment of thousands of components actually has a 7% rate of defects, there is a 54.29% probability that this whole shipment will be accepted.

According to the company's acceptance sampling plan, 25 components are randomly chosen and tested from a shipment before the entire batch is accepted if there are no more than three defects. The probability of choosing a defective component from a sample of 25 is computed as follows, assuming that the shipment genuinely has a 7% defect rate:

P(defective) = 0.07

P(non-defective) = 0.93

Using the binomial distribution, we can calculate the probability of having 0, 1, or 2 defectives in a sample of 25:

P(X ≤ 2) = P(X=0) + P(X=1) + P(X=2)

= (0.93)²⁵ + 25(0.07)(0.93)²⁵ + (0.07)²(0.93)²³

= 0.5429

This means that there is a 54.29% chance of having 2 or fewer defectives in a sample of 25. Since the whole shipment will be accepted if there are fewer than 3 defectives in the sample, this is the probability that the whole shipment will be accepted. Therefore, there is a 54.29% chance that the company will accept the shipment based on their acceptance sampling plan.

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The probability of getting fewer than 3 successes was found to be 0.7034, or approximately 70.34%.

The first step in solving this problem is to identify the values of n, p, and q. In this case, n = 8 and p = 0.27, so q = 1 - p = 0.73.

Using this formula, we can calculate the probabilities of getting 0, 1, or 2 successes as follows:

P(X = 0) = (8 choose 0) * 0.27⁰ * 0.73⁸ = 0.1029

P(X = 1) = (8 choose 1) * 0.27¹ * 0.73⁷ = 0.2833

P(X = 2) = (8 choose 2) * 0.27² * 0.73⁶ = 0.3172

To find the probability of getting fewer than 3 successes, we need to add these probabilities:

P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2) = 0.1029 + 0.2833 + 0.3172 = 0.7034

Therefore, the probability that the experiment results in fewer than 3 successes is 0.7034, or approximately 70.34%.

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Answer:

The answer to your problem is,

[tex]Blank[/tex] [tex]1[/tex]: A. Get multipled

[tex]Blank[/tex] [tex]2[/tex]: C. Also get multipled

Step-by-step explanation:

We know [tex]\frac{1}{2}[/tex] and [tex]\frac{2}{8}[/tex]. Will get multipled shown:

[tex]\frac{1}{2}[/tex] x [tex]\frac{2}{8}[/tex] = the fraction:

[tex]\frac{2}{16}[/tex]

12 is being multiplied the numerators.

And the denominators multiply with each other.

Thus the answer to your problem is:

Blank 1 : A. Get multipled

Blank 2 : C. Also get multipled

Projecting the point (-5, 4) over the y-axis and projecting the result over the x-axis, we get the point (5, -4).

The center of the coordinate system and the intersection of the lines and called the origin. The axes intersect when both x and y are zero. The coordinates of the starting point are (0, 0). An ordered pair contains the coordinates of a point in a single coordinate system.

To reflect a point across the y-axis, we cancel its x-coordinate, leaving its y-coordinate unchanged. So reflecting the point (-5, 4) across the y-axis gives the point (5, 4).  

To reflect a point across the x-axis, we cancel its y-coordinate and leave its x-coordinate unchanged. Thus, reflecting the point (5, 4) across the x-axis results in the point (5, -4).

 Therefore, projecting the point (-5, 4) over the y-axis and projecting the result over the x-axis, we get the point (5, -4).

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The function is C(t) = 27000 * [tex](1-0.17)^{t}[/tex]. Car should be sold after 6.3 years. The car will be worth about $7,260 after 9 years of depreciation.

a) Let C(t) be the value of the car t years after 2023. Since the car depreciates at a rate of 17% per year, its value decreases by 0.17 times its previous value each year. Therefore, we can express C(t) as:

C(t) = 27000 *  [tex](1-0.17)^{t}[/tex]

b) We want to find the number of years it takes for the value of the car to reach half its original value of $27,000. In other words, we want to solve the equation:

C(t) = 27000/2

Substituting the expression for C(t) from part a, we get:

27000 *  [tex](1-0.17)^{t}[/tex] = 13500

Simplifying this equation, we get:

[tex]0.83^{t}[/tex] = 0.5

t * log(0.83) = log(0.5)

t = log(0.5) / log(0.83)

Using a calculator, we find that t is approximately 6.3 years. Therefore, you will need to sell the car after about 6.3 years.

c) We can use the expression for C(t) from part a to find the value of the car after 9 years:

C(9) = 27000 *  [tex](1-0.17)^{9}[/tex]

Using a calculator, we find that C(9) is approximately $7,260. Therefore, the car will be worth about $7,260 after 9 years of depreciation.

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Given m || n, the calculaed values of x and y are x = 1 and y = 19

From the question, we have

Lines m and n are parallel

By the theorem of vertical angles, we have

9x - 10 = 4x - 5

When evaluated, we have

5x = 5

Divide by 5

So, we have

x = 1

By corresponsing angles, we have

4x - 5 = y - 20

So, we have

4(1) - 5 = y - 20

This gives

-1 = y - 20

So, we have

y = 19

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We can start by setting up a proportion to solve for the longer length:

shorter length / longer length = 4 / 7

We know that the shorter length is 32 centimeters, so we can substitute that in:

32 / longer length = 4 / 7

To solve for the longer length, we can cross-multiply:

4 × longer length = 7 × 32

Simplifying the right side:

4 × longer length = 224

Dividing both sides by 4:

longer length = 56

Therefore, the longer length is 56 centimeters.

To divide a continuous distribution such as a normal distribution into a rejection region and a non-rejection region, we need to first specify the level of significance or alpha (α) of the hypothesis test.

The rejection region is the area in the tails of the distribution where the test statistic falls that is unlikely to occur by chance if the null hypothesis is true. This area is determined by the alpha level and the direction of the alternative hypothesis (one-tailed or two-tailed).

The non-rejection region is the area in the middle of the distribution where the test statistic falls that is likely to occur by chance if the null hypothesis is true. This area is determined by subtracting the area of the rejection region from 1.

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The (101) slip plane of a BCC metal has four slip directions. Slip directions are determined by the crystal structure of a material and are the directions along which dislocations move most easily when stress is applied.

In BCC metals, dislocations tend to move along the <110> slip directions, which are the directions that bisect the angles between the primary cube diagonals. The (101) slip plane is a plane of atoms that is oriented at an angle to the primary cube face, and it intersects three of the primary cube diagonals.

This results in four <110> slip directions that are oriented in the plane of the (101) slip plane. These slip directions are important for understanding the mechanical behavior of BCC metals, including their strength and ductility.

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1st month will be.

25,610 ×104/100=26,634.4

2nd month.

26,634×104/109=27,699.776

3rd month.

Multiply the answer in the second month by 104/100

4th month.

Multiply the answer in the third month by 104/100

5th month.

Multiply the answer in the second month by 104/100

Until the 7 th month...

Answer will be =33,701 users

The throughput time for the particular order was option (d) 39.1 hours.

Throughput time is the total amount of time required for a product or service to move through a production or service delivery system, including all the time spent in processing, waiting, inspection, movement, and queuing.

The throughput time can be calculated as the sum of all the times involved in the process, including the waiting time, processing time, inspection time, move time, and queue time. Therefore:

Throughput time = Wait time + Process time + Inspection time + Move time + Queue time

Throughput time = 20.0 + 2.8 + 1.8 + 3.7 + 10.8

Throughput time = 39.1 hours

Therefore, the correct option is (d) 39.1 hours

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The solution is:

The correct options are;

Adding rational expressions

Subtracting rational expressions

When adding or subtracting rational numbers, the denominators of the  fractions representing the numbers should be equal

Therefore, when adding two or more rational expressions together, the following steps are required;

1) Looking for the Lowest Common Denominator

2) Finding the product of the quotient obtained from dividing the LCD by the denominator of a fraction and the numerator of the fraction

3) Placing the sum (or differences) of the products obtained in the above step as the numerator, while the LCD remain denominator

4) Simplifying the numerator in the above step

5) The faction so obtained, is the sum or difference of two or more rational expressions.

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complete question:

Which of the following problem types require you to find the LCD? (choose ALL that apply)

multiplying rational expressions

multiplying rational expressions

dividing rationals expressions

dividing rationals expressions

adding rational expressions

adding rational expressions

subtracting rational expressions

subtracting rational expressions

solving rational equations

The center line of the control chart is 78.000 pounds.

To calculate the center line of the r-chart, we need to first calculate the average range, which is the average of the ranges of the 18 samples. The range is the difference between the maximum and minimum values in each sample.

Using the data provided, we can calculate the ranges as follows:

Sample 1: 78.03 - 77.97 = 0.06

Sample 2: 78.08 - 77.92 = 0.16

Sample 3: 78.02 - 77.94 = 0.08

Sample 4: 78.10 - 77.93 = 0.17

Sample 5: 78.05 - 77.95 = 0.10

Sample 6: 78.09 - 77.99 = 0.10

Sample 7: 78.03 - 77.98 = 0.05

Sample 8: 78.06 - 77.92 = 0.14

Sample 9: 78.03 - 77.93 = 0.10

Sample 10: 78.11 - 77.95 = 0.16

Sample 11: 78.04 - 77.99 = 0.05

Sample 12: 78.07 - 77.97 = 0.10

Sample 13: 78.01 - 77.96 = 0.05

Sample 14: 78.04 - 77.94 = 0.10

Sample 15: 78.09 - 77.98 = 0.11

Sample 16: 78.02 - 77.97 = 0.05

Sample 17: 78.10 - 77.97 = 0.13

Sample 18: 78.04 - 77.96 = 0.08

The average range is the sum of these ranges divided by 18:

Average range = (0.06 + 0.16 + 0.08 + 0.17 + 0.10 + 0.10 + 0.05 + 0.14 + 0.10 + 0.16 + 0.05 + 0.10 + 0.05 + 0.10 + 0.11 + 0.05 + 0.13 + 0.08) / 18 = 0.097

Now that we have the average range, we can calculate the center line of the r-chart using the formula:

Center line = Average weight of the sample + A2 * Average range

The value of A2 depends on the sample size and the level of significance chosen. For a sample size of 7 and a level of significance of 0.05, the value of A2 is 0.577.

The average weight of the sample is simply the average of the 18 samples, which is given as 78.00 pounds.

Substituting these values into the formula, we get:

Center line = 78.00 + 0.577 * 0.097 = 78.056

Therefore, the center line of the r-chart is 78.056 pounds, rounded to three decimal places. However, since the weights are given to only two decimal places, the center line is simply 78.000 pounds.

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Answer:

Step-by-step explanation:

The middle of -16 and 11 is a negative number and the middle of -18 and 15 is a negative number.  so it is weighted more to the negative numbers

By the similarity of the triangles, the angle that corresponds to angle C¢ is C

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

Trapezoid ABCD maps to trapezoid A¢B¢C¢D¢.

This is a rigid transformation and as such the side lengths and angles would remain unchagned

So, we have the following corresponding angles

The above means that the angle corresponds to angle C is the angle C$

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The correct pairing of description and expression is B. six times the difference of five and a number squared, 6(n² - 5)

The correct pairing is six times the difference of five and a number squared because it accurately shows how the expression would look like at 6 (n² - 5)

.

The difference between five and a number squared would be shown as :

= n² - 5

Then when six multiplies this difference, the full thing becomes :

= 6 (n² - 5)

In conclusion, the correct answer is B.

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Answer :

Step-by-step explanation:

Given :-

To Find :-

Solution :-

We know,

In order to calculate to Area of base firstly we need to calculate the radius of the cylinder.

We are provided with Volume of cylinder that is 38.5 cm³.

We know,

[tex] \: :\implies [/tex] 3.14 × r² × 6 = 38.5

[tex] \: :\implies [/tex] 18.84 × r² = 38.5

[tex] \: :\implies [/tex] 2.04 3

[tex] \: :\implies [/tex] 1.4292

[tex] \: :\implies [/tex] 1.43 (nearest hundredth)

Radius of the cylinder is 1.43 cm.

Now,

[tex] \: :\implies [/tex] 3.14 × (1.43)²

[tex] \: :\implies [/tex] 3.14 × 2.0449

[tex] \: :\implies [/tex] 6.420986

[tex] \: :\implies [/tex] 6.42 (nearest hundredth)

Therefore, Area of the base circle is 6.42cm².