Graph the function y =2x + 5, using a table.

a) The type of function for each case is given as follows:

b) The functions for each house are given as follows:

c) The value of each house after 25 years is given as follows:

There is a significant difference in these valuations, as an exponential function increases faster than a linear function.

A function is classified as exponential if when the input variable is changed by one, the output variable is multiplied by a constant.

Hence House 1 is an exponential function, as:

312519.92/303417.40 = 303417.40/294580 = 1.03.

And the definition is given as follows:

294580(1.03)^x.

The value of the house after 25 years is given as follows:

294580(1.03)^25 = $616,785.10.

A function is classified as linear if when the input variable is changed by one, the output variable is increased/decreased by a constant.

Hence House 2 is a linear function, as each year, the value of the house is increased by 9000.

Then the definition is given as follows;

295000 + 9000x.

The value of the house after 25 years is given as follows:

295000 + 9000(25) = $520,000.

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Answer:

Equation 2: y=750-100x

Step-by-step explanation:

......,,........,.....-.......

The median would best describe the centre of the distribution for a highly skewed right histogram of US household income.  The correct option is A.

The median is the value that separates the distribution into two equal parts and is less influenced by extreme values than the mean.

Since a highly skewed right distribution has a long tail on the right side, the mean is likely to be pulled towards that tail, making it an unreliable measure of the centre.

The mode, or most frequently occurring value, may not be useful for describing the centre of a skewed distribution. The variance is a measure of the spread or dispersion of the data, not its centre.

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The number of hours taken by plane in cases 1 and 2 will be 7.5 hours and 2.48 hours, respectively.

Speed is defined as the length traveled by a particle or entity in an hour. It is a scale parameter. It is the ratio of length to duration.

We know that the speed formula

Speed = Distance/Time

2 planes left a similar air terminal simultaneously. One is going at 422 mph straight east, the other is voyaging 384 mph straight west.

If the distance between them is 6045 miles. Then the time is calculated as,

T = 6045 / (384 + 422)

T = 6045 / 806

T = 7.5 hours

2 planes left a similar air terminal simultaneously. One is going at 422 mph straight NORTH, the other is voyaging 384 mph straight WEST.

If the distance between them is 1997 miles. Then the time is calculated as,

T = 1997 / (384 + 422)

T = 1997 / 806

T = 2.48 hours

The number of hours taken by plane in cases 1 and 2 will be 7.5 hours and 2.48 hours, respectively.

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Answer:

Possible changes —

(i) Increase farmland

(ii) Sow healthy strawberry seeds

(iii) Choose a nutrient-rich, suitable plot of land

The number that we need to add is 1.5^2 = 2.25, we will get the perfect square trinomial:

(w - 1.5)^2 = 352.25

Remember that a perfect square trinomial is:

(a - b)^2 = a^2 - 2ab + b^2

Here we have the quadratic equation:

w^2 - 3w = 350

We can rewrite this as:

w^2 - 2*1.5*w = 350

Then what we need to add and subtract is 1.5^2, then we will get:

w^2 - 2*1.5*w = 350

w^2 - 2*1.5*w + 1.5^2 - 1,5^2 = 350

Grouping the first 3 terms we will get:

(w - 1.5)^2 - 1.5^2 = 350

(w - 1.5)^2 = 350 + 1.5^2

(w - 1.5)^2 = 352.25

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The correct answer is option D. The covariance between securities a and b is 195.

To calculate the covariance between securities a and b, we can use the formula:

covariance = correlation coefficient * standard deviation of security a * standard deviation of security b

Plugging in the given values, we get:

covariance = 0.65 * 12 * 25 = 195

Therefore, the answer is (d) 195.

The covariance between two securities measures the extent to which the two securities tend to move together. A positive covariance indicates that the securities tend to move in the same direction, while a negative covariance indicates that the securities tend to move in opposite directions.

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The standard deviation of p^ is approximately 0.00012.

The term "standard deviation" (or "") refers to a measurement of the data's dispersion from the mean. When the standard deviation is low, the data are concentrated around the mean, and when it is large, the data are widely dispersed.

The formula for standard deviation S.D is given below:

By calculating the departure of each data point from the mean, the standard deviation may be determined as the square root of variance. The bigger the deviation within the data collection, the more the data points deviate from the mean; hence, the higher the standard deviation, the more dispersed the data.

Calculation:

The formula for standard deviation S.D is given below:

Here,P = 3% = 0.03 and N = 240

∴ S.D = √0.03(1 - 0.03)/240

∴ S.D = 0.00012.

The standard deviation of p^ is approximately 0.00012.

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Answer:

B, E

Step-by-step explanation:

The  slope of the graph represent  d)The number of hours worked to earned dollors

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The probability that of 300 randomly selected students enrolled in the course, more than 75 of them will earn is 0.9998..

We have given that,

A data of students in a math course offered at northern university will earn .

Total number of randomly selected students enrolled in the course = 300

i.e total number of trials, n = 300

probability of success, p = 35% = 0.35

probability of failure, q = 1-0.35 = 0.65

np = 300× 0.35 =

n(1-p) = 300×0.65 =

both np and n(1-p) are greater than 10 , so we can use normal approximation here.

We have to calculate probability that more than 75 of them will earn an , P(X>75). Using Binomial Probability distribution, X~ Bin(300, 0.35)

P(X= x) = ⁿCₓ(p)ˣ(q)⁽ⁿ⁻ˣ⁾

Now, P(X>75) = 1 - P(X=<75)

but here data is large, that is n= 300, x = 75 so tough to calculate it by hands , thus we use Excel function to find out the required probability. Excel Command: =BINOM.DIST(number_s,trials,probability_s,cumulative)

where, Number_s (required argument) -->the number of successes in trials,i.e "x" Trials (required argument) --> the number of independent trials i.e , "n" must 0≤ n. Probability_s (required argument) --> the probability of success in each trial.

Cumulative (required argument)-->A logical value that determines the form of the function. It can either be: TRUE--> Uses the cumulative distribution function and FALSE--> Uses the probability mass function. Now, for P(X ≤ 75) , the function is look like as

=BINOM.DIST(75,300, 0.35, TRUE) =0.000126081

=BINOM.DIST(75,300, 0.35, FALSE)

= 5.0305E-05

Now, the required probability, P(X> 75)

= 1 - P(X ≤75)

= 1 - 5.03095E-05 = 0.999949691

or using cumulative distribution function,

P(X>75) = 0.999873919

both are give approx. same results

.So, required probability is 0.9998.

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Answer:

The answer is in my screen shot:


Explanation:

It's a geometric sequence with common ratio 3. You can calculate the common ratio by dividing the 240 by 80 or likewise 720 by 240.

The difference between the number of miles travelled on train and car is 110 miles

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

The difference between the distance covered can be calculated as

Distance difference = The difference of the product of speed and time

Substitute the known values in the above equation, so, we have the following representation

Distance difference = 70 * 3 - 50 * 2

Evaluate the products

Distance difference = 210 - 100

Evaluate the difference

Distance difference = 110 miles

Hence, the distance difference is 110 miles

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Step-by-step explanation:

The dance committee expects attendance to number within 25 of last year's 87 students can be expressed using an inequality involving absolute value as:

|x - 87| <= 25

This inequality states that the absolute difference between the number of students attending the dance (x) and 87, which was the number of students attending last year, must be less than or equal to 25. This means that the number of students attending the dance this year must be within 25 of the number of students attending last year.

Answer:

0 is the answer

Step-by-step explanation:

0*5=0

0=0*5  ==> use Zero property of multiplication

This property states that any number multiplied by 0 equals 0.

Yes, because no x values repeat.

The company can build 5 child bikes and 15 adult bikes in a week.

The answer is "Yes because the bike order meets the restrictions of 4c + 6a ≤ 120 and 4c + 4a ≤ 100".

Linear Equations are mathematical statements, which can be used to find an unknown quantity or any value in a given problem. Here we use variables like x, y .. etc. to represent unknown values.

Here we will use Linear Equations to solve the equations.

Here we have

One child bike requires 4 hours to build and 4 hours to test  

Number of hours to build 'c' number of child bikes = 4c

Number of hours to test 'c' number of child bikes = 4c

One adult bike requires 6 hours to build and 4 hours to test.

Number of hours to build 'a' number of adult bikes = 6a

Number of hours to test 'a' number of adult bikes = 4a  

Number of hours taken to build bikes in one week = 120

=> 4c + 6a ≤ 120  --- (1)

Number of hours taken to test the bikes in one week = 100  

=> 4c + 4a ≤ 100 --- (2)  

Assume that

The company can build 5 child bikes and 15 adult bikes in a week

Substitute c = 5 and a = 15 in (1) and (2)

(1) => 4(5) + 6(15) ≤ 120

=> 110 ≤ 120   [ which can be true ]

(2) => 4(5) + 4(15) ≤ 100

=> 80 ≤ 100  [ which can be true ]  

From the above calculations,

Both (1) and (2) are satisfied

Therefore,

The company can build 5 child bikes and 15 adult bikes in a week.

The answer is "Yes because the bike order meets the restrictions of 4c + 6a ≤ 120 and 4c + 4a ≤ 100".

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Answer:

Since angle 9 is 110 degrees, that means that angle 10 must be 70 degrees, because the angle is on a straight line, so the angles must add to be 180 degrees, because they are supplementary angles.  Since p ll q (p is parallel to q), that means that angle 1 is 110 degrees and angle 2 is 70 degrees.  Because angles 1, 2, 5, and 6 have to add to be 360 degrees and angles 1+2 equals 180 degrees, that means that 5+6 equals 180 degrees as well.   Angle 6 equals 110 degrees so that means angle 5 is 70 degrees.  On the other side, angle 8 is 70 degrees, and since the two angles are the same, p and q are the same.

Answer:

year 1: 90% × 245000 = 220500

year 2: 90% × 220500 = 198450

year 3: 90% × 198450 = 178605

∴ the car price after 3 years is 178605

explanation:

the value of car decreases 10%. that means the car price is 90%

The price of the car after 3 years will be 178605

We can calculate the value in the following way

Rate of decrease in car's price: 10%

Current price of the car: 245000

Value after 1 year, say value1= current value-10% of current value

[tex]value1=245000-\frac{10*245000}{100}[/tex]

=245000-24500

=220500

After 1 year, the next decrement in the price will be based on the value of the car in that year. In other words, we calculate the value after the second year by decreasing by 10% of value1.

Value of car after 2 years, say value2= value1- 10% of value1

[tex]value2=220500- (\frac{10*220500}{100})[/tex]

=220500-22050

=198450

Similarly,

Value of car after 3 years, say value3= value2- 10% of value2

[tex]value3=198450- (\frac{10*198450}{100})[/tex]

=198450-19845

=178605

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Part (A) = Paired, Part (B) = Not Paired, Part (C) = Paired, Part (D) = Paired

Part A:

Compare pre- (beginning of the semester) and post-test (end of the semester) scores of students

Paired, as a subject are the same in both.

Score

A score is a group of 20 (often used in combination with a cardinal number, i.e. fourscore to mean 80), but also often used as an indefinite number.

Part B:

Assess the gender-related salary gap by comparing the salaries of randomly sampled men and women.

Not paired.

Sample

A sample is an outcome of a random experiment. When we sample a random variable, we obtain one specific value out of the set of its possible values. That particular value is called a sample. The possible values and the likelihood of each are determined by the random variable's probability distribution.

Part C:

Compare artery thicknesses at the beginning of a study and after 2 years of taking Vitamin E for the same group of patients.

Paired, as a subject are the same in both.

Vitamin E

Vitamin E is a fat-soluble vitamin with several forms, but alpha-tocopherol is the only one used by the human body.

Part D:

Assess the effectiveness of a diet regimen by comparing the before and after weights of subjects.

Paired, as a subject are the same in both.

Weight

The weight of an object refers to the force of gravity that is acting on the object. Furthermore, its calculation is mass times the acceleration of gravity, w = mg. The SI unit of weight is the newton because weight is a force.

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Compare artery thicknesses at the beginning of a study and after 2 years of taking Vitamin E for the same group of patients.

Paired, as a subject are the same in both.

Vitamin E

Vitamin E is a fat-soluble vitamin with several forms, but alpha-tocopherol is the only one used by the human body.

The length of each individual piece is x/8

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

Number of pieces = 8

Length of timber put together = x

The length of each piece of timber is calculated as

The length of each piece = Length of timber put together/Number of pieces

Substitute the known values in the above equation, so, we have the following representation

The length of each piece = x/8

Hence, the length of each piece is x/8

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The values of x, y and z are 5, 18 and 12 using the congruent triangles properties and triangles sum properties.

A triangle in geometry is a three-sided polygon with three edges and three vertices. The fact that a triangle's internal angles add up to 180 degrees is its most crucial characteristic. This characteristic is known as the triangle's angle sum property.

In congruent triangles all the sides are equal, with respect to the other triangle.

Given that ΔUVW≅ΔTSR.

We can see that in TSR triangle the lengths of TR and TS are given as 50 and 53 now the remaining side RS is 5y-33 as we know that both triangles are similar we compare side RS with side VW

i.e..,

5y-33 = 57

5y = 90

y = 18

So we can now compare vertices vertex V is vertex R , vertex W is vertex S and vertex U is vertex T.

So equating the sides of triangles we get,

12x-7 = 53        and 3z+14 = 50

12x = 60                   3z = 36

x= 5                           z = 12

The values of x, y and z are 5, 18 and 12 using the similar triangles properties and triangles sum properties.

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Answer:

Below

Step-by-step explanation:

-40 -(-12/5) =  -200/5   +   12/5   = -188/5 =  - 37  3/5

The boxplot shows that the majority of the people who attended the lecture were age 53 or younger, which means at least 75 percentage of the people were in that range.

The table and boxplot provide information about the ages of the people who attended a lecture last week. The boxplot shows that the majority of the people who attended the lecture were age 53 or younger. This is supported by the table, which shows that the median age is 53 and the interquartile range is between 36 and 53. This indicates that at least 75% of the people who attended the lecture were age 53 years or younger. The range of the distribution is 20 years, with the minimum age being 18 and the maximum age being 38. This suggests that there were at least two people in each age range, from 18 to 38. This also indicates that there were at least 43 people who attended the lecture. The boxplot also shows that at least 25% of the people who attended the lecture were 33 years old. This is supported by the table, which shows the lower quartile is 33.

Interquartile range = Maximum - Minimum

Interquartile range = 53 - 36 = 17

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The system of equations is x + y = 16 and y = 2x - 2

The number of shirts and pairs of pants Sylvia brought are 10 and 6, respectively

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

When the statements are interpreted, we have the system of equations to be

x + y = 16

y = 2x - 2

In (a), we have

x + y = 16

y = 2x - 2

This gives

x + 2x - 2 = 16

Evaluate the like terms

3x = 18

Divide

x = 6

Recall that

y = 2x - 2

So, we have

y = 2 x 6 - 2

y = 10

Hence, the number of shirts she packed is 10

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Answer:

To determine how many weeks it will take Clare to save enough money to buy the video game, we need to find the number of weeks it will take for her to save at least $130. Let w be the number of weeks it will take for Clare to save enough money. We can set up the following inequality to represent this situation:

$48 + $5w >= $130

To solve this inequality, we can first add $48 to both sides to get rid of the constant on the left side:

$48 + $48 + $5w >= $130

This simplifies to $96 + $5w >= $130. Subtracting $96 from both sides gives us $5w >= $34. Dividing both sides by $5 gives us w >= 6.8. Since w represents the number of weeks, the solution must be a whole number. Therefore, Clare will need to save for at least 7 weeks in order to have enough money to buy the video game.

Answer: the answer to a is 50% chance the answer to b is also 50% chance

Step-by-step explanation:

Answer:

Jolie will get 45.85 change

Step-by-step explanation:

34.67+19.48=54.48

100.00-54.15=45.85