1. Corey’s pay increases from £12.36 per hour to £14.11 per hour. Find the percentage increase to 1 decimal place.

2. Dele invests $6000 for 4 years at 3% per annum compound interest. Calculate the value of his investment at the end of 4 years.

3. The value of a car depreciates by 14% per annum. At the end of 2017 the car is worth $17500. How much is it worth at the end of 2020?

Answer:

106

Step-by-step explanation:

A linear pair adds to 180

180 - 74 = 106

Part a: The significance of the piece-wise function is define.

Part b: r(t) be the total amount of snow in cubic ft. is calulated.

Part c: Total volume of the ice is not removed.

For the given question, the rate function is given as;

f(t) = { 0, 0 ≤ t < 6 ,

       125, 6 ≤ t < 7

       108, 7 ≤ 9  }

Part a: The significance of the piece-wise function is-

Part b: r(t) be the total amount of snow in cubic ft.

Part c: total ice accumulated is;

62.5 ft + 54 ft. = 116.5 cubic ft.

Total volume of the ice accumulated = 367.5 cubic ft.

Thus, no total volume of the ice is not removed.

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The Type of taxation system in this table represent is Option C Regressive Tax.

Taxation System is an obligatory fee or financial charge is referred to as a tax when it is imposed by a government on a person or an organisation in order to raise money for public projects that fund the greatest services and infrastructure. Various public spending programmes are then funded with the money that was gathered.

Type of Taxation

There are mainly four types of Taxes, these are Regressive, progressive, Indirect, and Proportional. In the given question the Regressive Taxation system is represented.

A Regressive Taxation system is one where Companies which have lower income have higher tax rate in comparison to big companies. In the given question the company which have lowest income is giving 15% of total income, while the largest company is giving 10% of their income.

Therefore, taxation system in this table represent is Option C Regressive Tax.

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Using an exponential function to represent the exponential decay, it will take approximately 4 weeks to reach 320 gallons

An exponential function is a mathematical function in the form f (x) = ax, where “x” is a variable and “a” is a constant which is called the base of the function and it should be greater than 0.

To solve this problem, we have to write an exponential equation to calculate the exponential decay.

Data;

A = P(1 + r)⁻ˣ

320 = 625(1 + 0.2)⁻ˣ

x = 3.67

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Persons cannot be in decimals we can expect about 9 passengers will not keep their reservation.

Given,

In the question:

An airline finds that about 8 percent of the time, a person who makes an advance reservation does not keep the reservation.

Therefore, for each of their 105105105-passenger planes, the company schedules 113113113 people with advance reservations.

Now, According to the question:

Capacity of the airline per trip = 105 only

But company schedules = 113 people with advance reservations

Since 8% do not turn up

Out of 113 passengers who reserved in advance we can say

that 8% of 113 passengers will not keep their reservation

Based on this information, number  of the scheduled people will not keep their reservation

= 8% x 113

= 0.08*113

=9.04

Hence, Persons cannot be in decimals we can expect about 9 passengers will not keep their reservation.

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An expression which shows the correct substitution of the values a, b, and c from the equation 0 = – 3x2 – 2x + 6 into the quadratic formula is: expression A. Therefore, the correct answer option is A.

A quadratic equation can be defined as a mathematical expression (equation) that can be used to define and represent the relationship that exists between two or more variable on a graph. In Mathematics, the standard form of a quadratic equation is given by;

ax² + bx + c = 0

Mathematically, the quadratic formula is modeled or represented by this mathematical expression:

[tex]x = \frac{-b\; \pm \;\sqrt{b^2 - 4ac}}{2a}[/tex]

From the information provided, we have the following values;

0 = -3x² - 2x + 6

Where:

a = -3

b = -2

c = 6

Substituting the values into the quadratic formula, we have;

[tex]x = \frac{-(-2)\; \pm \;\sqrt{(-2)^2 - 4(-3)(6)}}{2(-3)}\\\\x = \frac{2\; \pm \;\sqrt{4^2 - 4(-3)(6)}}{2(-3)}[/tex]

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The p-value associated with the null hypothesis = 0.05

Fail to reject the null hypothesis. The​ P-value is greater than the level of significance.

Candice should reject the null hypothesis as the 50% confidence interval does not contain 10 hours

Small p-values offer proof that the null hypothesis is false. The stronger the evidence is against the null hypothesis, the smaller (closer to 0) the p-value. The null hypothesis is rejected if the p-value is less than or equal to the chosen significance level; otherwise, it is not.

You have the Hypothesis that "students study less than 10 hours, on average, per week"

Symbolically:

H₀:μ≥10hours

H₁:μ<10hours

The significant level for this case study is 50% - 0.05. If the results gotten is less than the significance level, we reject the null hypothesis, but if greater, we fail to reject the null hypothesis.

The p-value of 0.05 is one of the most often used numbers. When the calculated p-values are less than 0.05, the faulty hypothesis is considered to be fraudulent or invalid (subsequently the name invalid theory). Additionally, the faulty theory is taken into consideration to be clear if the value is greater than 0.05.

The edge for that likelihood in our model is 0.05, and it represents the probability that our results will be similar to the invalid speculation. Therefore, if the calculated p-value is less than 0.05, it actually means that there is a very little likelihood that we would have the same results as the flawed hypothesis. Additionally, if the p-value is greater than 0.05, there is a very strong probability that the results will be similar to the flawed speculation, leading us to conclude that it is legitimate.

Therefore,

Fail to reject the null hypothesis. The​ P-value is greater than the level of significance.

The p-value associated with the null hypothesis = 0.05

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The amount that Josephine will be paid is $644.30.

A percentage is a value or ratio that may be stated as a fraction of 100. If we need to calculate a percentage of a number, we should divide it's entirety and then multiply it by 100. The percentage therefore refers to a component per hundred.

In this situation, Josephine earns a salary of $560.00 per week, plus a commission of 10% on all sales and she sold $843 worth of goods.

The amount she'll be paid will be:

= $560 + (10% × $843)

= $560 + $84.3

= $644.30

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The weight of the contents in the container is 340 pounds

The space occupied within an object's borders in three dimensions is referred to as its volume. It is sometimes referred to as the object's capacity.

Volume is a measurement of three-dimensional space that is occupied. It is frequently expressed numerically in a variety of imperial or US-standard units as well as SI-derived units. Volume and the definition of length are related.

Given ,

volume of container = 20 x 8.5 x 8= 1360 cubic feet

weight = 0.25 pounds per cubic foot

0.25 x 1360 = 340 pounds

Therefore the weight of the contents in the container is 340 pounds

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Answer:

Step-by-step explanation:

The slope of a linear function is a measure of the rate at which the value of the function changes as the input (x) changes. A slope of -5/3 means that for every 3 units of change in the input, the output (y) changes by -5 units.

In general, a negative slope indicates that the graph of the function is decreasing. As the input increases, the output decreases. A slope of -5/3 is a relatively steep negative slope, which means that the graph of the function will have a steep downward slope.

A slope of -5/3 also tells us that the function is not a horizontal line. A horizontal line has a slope of 0, which means that the output does not change as the input changes. A slope of -5/3 is not equal to 0, which means that the function is not a horizontal line.

Overall, the slope of a linear function tells us about the direction and steepness of the graph of the function. A slope of -5/3 indicates that the graph of the function is decreasing and relatively steep.

By using the concept of arrangement, it can be concluded that-

The correct order is Beto, Alex, Valentin

The act of arranging people and things towards a certain goal is referred to as arrangement. the arrangement or arrangement of details in a written work. Readers to whom a piece of writing is addressed; those who read or hear what you have written.

Your reader could feel disoriented and lose interest if there is no obvious organizational structure. Your essay's organization will aid readers in making connections between the essay's body and thesis, as well as help you stay on task as you plan and compose the essay.

It is known that:

• Alex sits next to Beto and Valentin.

• Valentin sits to the right of Beto.

So the correct order is Beto, Alex, Valentin

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The average rate of change for 3.5 ≤ x ≤ 4 is 2[f(4) - f(3.5)]

It is the average amount by which the function changed per unit throughout that time period. It is calculated using the slope of the line linking the interval's ends on the graph of the function.

given:

Interval: 3.5 ≤ x ≤ 4

Now, For average rate

= [f(4) - f(3.5)]/(4 - 3.5)

= 2[f(4) - f(3.5)]

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The probability that the student takes technology given that he is taking Math 8 is 0.075.

What is conditional probability?

Conditional probability is a term used in probability theory to describe the likelihood that one event will follow another given the occurrence of another event.

Here, we have

Given:

The probability that a student takes Technology and Math 8 is 0.012.

P(Technology and Math 8) = 0.012

The probability that a student takes Math 8 is 0.16.

P(Math 8) = 0.16

We have to find the probability that a student takes Technology given that the student is taking Math 8

we use conditional probability

P(Technology|Math 8) = P(Technology and Math 8)/P(Math 8)

P = 0.012/0.16

P = 0.075

Hence, the probability that the student takes technology given that he is taking Math 8 is 0.075.

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Answer:

Step-by-step explanation:

y = -2x + 8

perp.: 1/2

y + 5 = 1/2(x - 8)

y + 5 = 1/2x - 4

y = 1/2x - 9

Answer: 71

Step-by-step explanation:

Calculate c, ∠B, and ∠A based on given b, a, and ∠C.c = √b2 + a2 - 2ba·cos(C) = 13.67386∠B = arccos(c2 + a2 - b22ca)= 1.23918 rad = 71°∠A = arccos(c2 + b2 - a22cb)= 1.23918 rad = 71°

Answer:

1/9

Step-by-step explanation:

The y intercept of a line is when x = 0

y = 1/9

Answer:

y = 1/9

Step-by-step explanation:

y = -10x + 1/9

Substitute 0 for x

y = -10 x 0 +1/9

-10 x 0 = 0

y = 1/9

The given statement " chi-square tests are used for testing hypotheses of the association between two categorical values. " is true

The term chi square test defines if there is a significant relationship between two nominal variables.  

Here we have given the statement, chi-square tests are used for testing hypotheses of the association between two categorical values.

And we need to find whether the statement is true or not.

As per the definition of chi square test, we know that the frequency of each category for one nominal variable is compared across the categories of the second nominal variable.  

Here we also know that the data can be displayed in a contingency table where each row represents a category for one variable and each column represents a category for the other variable.  

Therefore, based on these facts the given statement is true.

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The length of segment AB is 13 units.

The distance between the two points (a,b) and (c,d) is given by:
[tex]d=\sqrt{(c-a)^2+(d-b)^2}[/tex].

The given coordinates of A  and B are A(0,12) and B(5,0).

The length of segment AB is given by:

[tex]AB = \sqrt{(5-0)^2 + (0 - 12)^2}\\\\AB=\sqrt{25 + 144}\\\\AB = \sqrt{169}\\\\AB = 13[/tex]

Hence, the length of segment AB is 13 units.

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Answer: 360 plants

Step-by-step explanation:

90% is equivalent to 0.90.
You multiply 0.90 and get your answer of 360.

Answer: 52.5°

Step-by-step explanation:

sin59 = 45/x

sin59(x) = 45

x = 45/sin59 = 52.5°

If each survey has a sample size of 70, a value which falls within the interval where 95% of the sample means occur is: C) 14.96.

In this scenario, the confidence interval at 95% can be represented by this mathematical expression p - E < p < p + E

Based on the parameters provided, we would determine both the lower limit and upper limit for the interval where 95% of the sample means occur as follows;

Lower limit = 15 - 1.88/√70

Lower limit = 15 - 0.23

Lower limit = 14.77

For the upper limit, we have:

Upper limit = 15 + 1.88/√70

Upper limit = 15 + 0.23

Upper limit = 15.23

For 95% of the sample means to occur, the confidence interval is given by;

Confidence interval = (14.77, 15.23)

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Using elimination method, the solution to the system of equation is as follows:

x = 2 and y = -5

System of equation can be solved using different method such as elimination method, substitution method and graphical method. Let's use elimination method to solve the system of equation as follows:

7x + 3y = - 1

4x + y = 3

multiply equation(ii) by 3

Hence,

7x + 3y = - 1

12x + 3y = 9

subtract equation(i) from equation(ii)

5x  = 10

x = 10 / 5

x = 2

Let's find y

7x + 3y = - 1

7(2) + 3y = -1

14 + 3y = -1

3y = -15

y = -15 / 3

y = -5

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The expense type which is true is , indebtedness expense as because they are the  minimum monthly payments you make on your loans and credit card.

Being in debt to someone else or owing them money is the state of being indebted. A person who owes money has either borrowed money or obtained goods or services in exchange for a promise to repay the money.

Someone can owe money for both present-day obligations and obligations that they anticipate having in the future. For instance, the term "indebtedness" can relate to a person's mortgage or a car loan.

The majority of people cannot afford to buy a home or a car outright, thus they owe the bank the amount of the loan that was granted to them. When you use a credit card to make purchases like apparel or travel expenses, you become indebted. Being in debt is not the same as not making payments.

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The slope of NO is 2/3 and the slope of LO is -3/2 after using the slope formula.

The ratio that y increase as x increases is the slope of a line. The slope of a line reflects how steep it is, but how much y increases as x increases. Anywhere on the line, the slope stays unchanged (the same).

[tex]\rm m =\dfrac{y_2-y_1}{x_2-x_1}[/tex]

The parallel lines have same slope

The slope of LM = the slope of NO

The slope of LM = (-1-(-5))/(4-(-2))

The slope of LM = 4/6 = 2/3

Slope of NO = 2/3

If LMNO is rectangle:

The slope of LO = -1/(slope of LM)

The slope of LO = -1(2/3)

The slope of LO = -3/2

Thus, the slope of NO is 2/3 and the slope of LO is -3/2 after using the slope formula.

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Answer: Two dice

Step-by-step explanation:

For the two dice, there are 5 possible: (6, 2);(5, 3);(4, 4);(3, 5);(2, 6)

So two dice, the probability is 5/36 = 30/216

For three dice, the number of favorable cases is 21

The probability is 21/216

So the two dice are more likely

The equation of line in slope intercept form is y = -1/3 x + 1.

What is equation of a line?

The set of points that make up a line in a coordinate system are represented algebraically by a line's equation. An equation of a line is an algebraic expression that represents the many points that together make up a line in the coordinate axis as a set of variables, x, and y. The slope of the line and a point on the line can be used to create the equation of a line.

The points on the line are (3,0) and (0,1).

The slope of a line that passes through the points (x₁, y₁) and (x₂, y₂) is (y₂ - y₁)/(x₂ - x₁).

The slope of line is (1 - 0)/(0 - 3) = -1/3.

The line cuts y-axis at (0,1). Thus y-intercept of the line is 1.

The slope-intercept form of the line is

y =  -1/3 x + 1

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The minimum sample size needed to guarantee a given margin of error increases , the correct option is (b) .

What is Margin Of Error ?

The term margin of error is defined as an estimate of a small sample that is drawn from a relatively large population data.

the margin of error is usually governed by the parameters such as the standard deviation , sample size and desired confidence level.

to find missing term in the given statement , let us consider the values ,

where σ ⇒ Standard deviation for population

and m as "Margin of error"  and Z as "Empirical value of Z-score" at a given confidence level .

So , minimum sample size for given confidence level is given by

⇒ (Z×σ)²/m²

from above formula we can conclude that minimum sample size is directly related to population's standard deviation.

Therefore, the minimum sample size required would "increase" with the increase in population "standard deviation" .

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The measure of the interior angles of a polygon is determined by the formula ((n - 2)180)/n = interior angle

measure

The equation of the line will be y = 6x - 25

Given, the point is (4, -1)

The slope is m = 6.

We have to write an equation of the line in slope-intercept form.

The standard form of equation of the line in slope-intercept form is given by

y = mx + c

Where, m is the slope.

Now, substituting the values of x, y and m in the equation,

-1 = 6(4) + c

-1 = 24 + c

c = -1 - 24

c = -25

Put the value of c in the standard equation,

y = 6x - 25

Therefore, the equation of the line is y = 6x - 25

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