Iready Mastery Check Math Functions (2024)

3 4/7 -2 1/5 rounded to the nearest half is simplified as: 1½

How to Round to the Nearest Half?

To round 3 and 4/7 - 2 and 1/5 to the nearest half, we first need to convert the mixed numbers to improper fractions:

3 and 4/7 = (3 x 7 + 4)/7 = 25/7

2 and 1/5 = (2 x 5 + 1)/5 = 11/5

So the expression becomes:

25/7 - 11/5

To simplify this, we need to find a common denominator. The least common multiple of 7 and 5 is 35:

(25/7) x (5/5) = 125/35

(11/5) x (7/7) = 77/35

So the expression becomes:

125/35 - 77/35 = 48/35

To round to the nearest half, we need to look at the fraction in terms of eighths. To do this, we multiply both the numerator and denominator by 8:

(48/35) x (8/8) = 384/280

Next, we divide the numerator by the denominator and get:

384 ÷ 280 = 1 and 104/280

To round to the nearest half, we look at the fraction 104/280 in terms of halves, which is:

(104/280) x (2/2) = 208/560

We can simplify this to:

208/560 = 13/35

Since 13/35 is more than half of a whole (which is 1/2), we round up to the nearest half. Therefore:

3 and 4/7 - 2 and 1/5 rounded to the nearest half is 1 and 1/2.

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After solving each of these problems by false position, the quantities of problems 25, 26, and 27 are 122/15, 3/20, and 91/20.

Problem 25: Let x be the quantity. Then we have:

x + 1/2 = 16

To solve this equation by false position, we start with a guess of x = 16/2 = 8, since the quantity is likely to be close to half of the sum. We substitute this value into the equation and find the error:

8 + 1/2 = 8.5

16 - 8.5 = 7.5

Since the error is negative, we need to increase our guess by adding a unit fraction. The unit fraction that we add is 1/7.5 = 2/15 since the error is 2/15 of the quantity. Thus, our new guess is:

x = 8 + 2/15 = 122/15

We can check that this value satisfies the original equation:

122/15 + 1/2 = 16

Problem 26: Let x be the quantity. Then we have:

x + 1/4 = 15

To solve this equation by false position, we start with a guess of x = 15 - 1/4 = 59/4, since the quantity is likely to be close to the difference. We substitute this value into the equation and find the error:

59/4 + 1/4 = 15

15 - 59/4 = -1/4

Since the error is negative, we need to increase our guess by adding a unit fraction. The unit fraction that we add is 1/(-1/4) = -4, since the error is 4 times the quantity. Thus, our new guess is:

x = 59/4 - 4 = -5/4

This value is negative, which means that our initial guess was too large. We need to decrease our guess by subtracting a unit fraction. The unit fraction that we subtract is -1/(-5/4) = 4/5, since the error is 4/5 of the quantity. Thus, our new guess is:

x = -5/4 + 4/5 = 3/20

We can check that this value satisfies the original equation:

3/20 + 1/4 = 15

Problem 27: Let x be the quantity. Then we have:

x + 1/5 = 21

To solve this equation by false position, we start with a guess of x = 21 - 1/5 = 104/5, since the quantity is likely to be close to the difference. We substitute this value into the equation and find the error:

104/5 + 1/5 = 21

21 - 104/5 = -4/5

Since the error is negative, we need to increase our guess by adding a unit fraction. The unit fraction that we add is 1/(-4/5) = -5/4 since the error is 5/4 of the quantity. Thus, our new guess is:

x = 104/5 - 5/4 = 91/20

We can check that this value satisfies the original equation:

91/20 + 1/5 = 21.

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(a) The probability that the instrument does not fail in an 8-hour shift is 0.7183 or 71.83%.

(b) The probability of at least one failure in a 24-hour day is 0.999 or 99.9%.

Poisson Distribution: Failure Probability

The number of failures of a testing instrument in a given time period is modeled by a Poisson distribution with a rate parameter equal to the mean number of failures per unit time.

(a) To find the probability that the instrument does not fail in an 8-hour shift, we can use the cumulative distribution function (CDF) of the Poisson distribution. The CDF gives the probability that the number of failures is less than or equal to a given value. In this case, we want to find the probability that there are 0 failures in an 8-hour shift, so the CDF can be expressed as:

P(X ≤ 0) = e^(-0.025 * 8) = 0.7183

So, the probability that the instrument does not fail in an 8-hour shift is 0.7183 or 71.83%.

(b) To find the probability of at least one failure in a 24-hour day, we can subtract the probability of 0 failures from 1. That is,

P(X ≥ 1) = 1 - P(X ≤ 0) = 1 - e^(-0.025 * 24) = 0.999

So, the probability of at least one failure in a 24-hour day is 0.999 or 99.9%.

Note: In these calculations, we use the formula for the cumulative distribution function of the Poisson distribution, which is:

P(X ≤ k) = e^(-lambda) * (lambda^k / k!)

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Answer: 12

Step-by-step explanation:

2+2+2+2+2+2= 2*6= 12

y = 7x + 15 is the equivalent equation of the line in slope intercept form.

Equation of a line in slope-intercept form

The equation of a line in slope intercept form is expressed according to the equation below:

y = mx + b

where:

m is the slope

b is the intercept

Given that slope is a 7 with the point (-1, 8), the equation is;

y - 8 = 7(x+1)

In slope intercept form:

y - 8 = 7x + 7

y = 7x + 7 + 8

y = 7x + 15

Hence the equation in slope- intercept form is y = 7x + 15

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a) At least 75% of the home buyers' age is between 25 years old and 69 years old.

b) At least 84% of the home buyer's age are between 19.5 years old and 74.5 years old.

What does Chebyshev’s Theorem state?

When the distribution is not normal, Chebyshev's Theorem is used. It states that:

At least 75% of the measures are within 2 standard deviations of the mean.At least 84.5% of the measures are within 2.5 standard deviations of the mean.At least 89% of the measures are within 3 standard deviations of the mean.An in general terms, the percentage of measures within k standard deviations of the mean is given by [tex]100\left(1 - \frac{1}{k^{2}}\right)[/tex].

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The number of travel bloggers is 1000.

What is a fraction?

A fraction is written in the form of a numerator and a denominator where the denominator is greater that the numerator.

Example: 1/2, 1/3 is a fraction.

We have,

Number of passengers = 15,000

The number of travel bloggers.

= 1/15 of 15,000

= 1/15 x 15,000

= 1,000

Thus,

1000 are travel bloggers.

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By donating 10% of the salary a basketball player donates money that can feed 534883 children per day.

What is percentage?

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

The annual income of basketball player is $2,300,000.

The cost to feed 1 child is 43 cents per day.

The basket ball player donates 10% of his annual salary.

Calculate the percentage of salary donated by using the formula -

Amount Donated = 10% of Annual income

Plug in the values in the equation -

Amount Donated = 10/100 × 2,300,000

Amount Donated = $2,300,00

The amount donated is $2,300,00.

Convert dollar to cents -

$1 is equivalent to 100 cents

$2,300,00 is equivalent to 2,300,00 × 100 = 2,300,0000 cents

The number of children that can be fed -

Number of children = Amount donated / Amount needed for 1 child

Substitute the values in the equation -

Number of children = 2,300,0000 / 43

Number of children = 534883.721 ≈ 534883 children

Therefore, 534883 children can be fed.

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The expressions that are equivalent are 11³, 11¹. 11². Options A and E

What are index forms?

Index forms are defined as mathematical forms of writing numbers that are two large or small in simpler forms.

They are also called standard forms or scientific notation.

It is also described as the exponent or power that is raised to a number or a variable.

Examples of index forma are;

2³ representing 2 in three places

3² representing 3 in two places

5³ representing 5 in three places

From the information given, we have that;

11 11. 11,

Hence, it is number 11 in three places 11³

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The solution for the given equations is (0, 1) and the graph for the given equations is plotted below.

What is the graph?

Graph is a mathematical representation of a network and it describes the relationship between lines and points. A graph consists of some points and lines between them. The length of the lines and position of the points do not matter.

The given equations are y=1/4 x+1 and y= -1/4 x+1.

Substitute x= 0, 1, 2, 3, 4,....in the equation y=1/4 x+1 , we get

y=1, 1.25, 1.5, 1.75, 2,....

So, the coordinate points are (0, 1), (1, 1.25), (2, 1.5), (3, 1.75) and (4, 2)

Substitute x= 0, 1, 2, 3, 4,....in the equation y= -1/4 x+1 , we get

y= 1, 0.75, 0.50, 0.25, 0

So, the coordinate points are (0, 1), (1, 0.75), (2, 0.50), (3, 0.25) and (4, 0)

So, the solution for the equations is (0, 1)

Therefore, the solution for the given equations is (0, 1) and the graph for the given equations is plotted below.

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From Figure A to Figure B, there will be a 1/3 scale factor.

What is dilation?

Dilation is the process of increasing the size of an item without affecting its form. Depending on the scale factor, the object's size can be raised or lowered. There is no effect of dilation on the angle.

Figure B is a scaled copy of Figure A.

The scale factor from Figure A to Figure B is given as,

Scale factor = 3 / 9

Scale factor = 1/3

The scale factor from Figure A to Figure B will be 1/3.

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A) 145% of 600 would be, 870

B) Population would be 870.

C) The population from two decades ago was 600.

D) The population before the change was 600

What is Percentage?

To compute a percentage, divide the value by the entire amount and multiply the result by 100. A percentage is a quantity or ratio that is stated as a fraction of one hundred. The percent sign, "%," is frequently used to represent it.

A) 145% of 600 is equal to 870. You can calculate this by multiplying 600 by 1.45:

600 * 1.45 = 870

B) If there was a 45% increase in the population since two decades ago, the current population would be, 600 * 1.45 = 870.

C) If the current population of a town is 870, which is 145% of its population from two decades ago, we can find the population from two decades ago by dividing 870 by 1.45:

870 / 1.45 = 600

So, the population from two decades ago was 600.

D) If the current population of a town is 870 and it has gone through a 45% increase since two decades ago, we can find the population before this change by dividing 870 by 1 + 0.45 = 1.45:

870 / 1.45 = 600

So, the population before the change was 600.

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Answer:ans A

Step-by-step explanation:

The conversion factor for liters to gallons is 1 gallon / 3.8 liters

What is an equation?

An equation is an expression that shows the relationship between two or more numbers and variables using mathematical operations. An equation can be linear, quadratic, cubic and so on, depending on the degree of the variable.

1 gallon = 3.8 liters

Conversion factor for liters to gallons = 1 gallon / 3.8 liters

The conversion factor is 1 gallon / 3.8 liters

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The ordered pair is not a function

How to complete the statement

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

Domain: -3 5 3 -5Range: 6 -2 1

From the figure, we can see that

The x values -3 and 5 have the same value of 6

This means that the relation is no a function

This is so because for a relation to be a function, the output values must be unique

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The number of workers that is closest to but not more than the point of highest MPL is 3. and the number of workers resulting in the highest level of average product of labor is also closest to 3.

To find the marginal product of labor, we need to calculate the additional output produced by each additional unit of labor.

We can calculate this by finding the change in the total product (TP) for each additional unit of labor. The table gives us the following information:

When there are 0 workers, TP = 0

When there is 1 worker, TP = 150

When there are 2 workers, TP = 320

When there are 3 workers, TP = 510

When there are 4 workers, TP = 660

When there are 5 workers, TP = 800

Using this information, we can calculate the marginal product of labor (MPL) as follows:

MPL of the 1st worker = TP of 1 worker - TP of 0 workers = 150 - 0 = 150

MPL of the 2nd worker = TP of 2 workers - TP of 1 worker = 320 - 150 = 170

MPL of the 3rd worker = TP of 3 workers - TP of 2 workers = 510 - 320 = 190

MPL of the 4th worker = TP of 4 workers - TP of 3 workers = 660 - 510 = 150

MPL of the 5th worker = TP of 5 workers - TP of 4 workers = 800 - 660 = 140

We can see that the highest marginal product of labor is 190, which occurs when there are 3 workers. Therefore, the number of workers that is closest to but not more than the point of highest MPL is 3.

complete question:

1. Using the data in the table, the number of workers resulting in the highest level of average product of labor is closest to:

Group of answer choices

3

4

5

Cannot be determined from the information given.

2. Using the data in the table, the marginal product of labor is highest if the number of workers is closest to but not more than:

Group of answer choices

3

4

2

Cannot be determined from the information given.

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The reason why it is useful to factor polynomial expressions for a given scenario is to solve or simplify the equation.

Why are polynomial expressions factorized ?

Factoring polynomial expressions is useful in a variety of mathematical scenarios because it can simplify complex expressions and make them easier to work with. By factoring polynomials, you can find the roots of an equation, which are the values that make the equation equal to zero.

In conclusion, factoring polynomial expressions can be a powerful tool in simplifying complex mathematical expressions, solving equations, understanding relationships between expressions, and finding common solutions.

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The value of the length of EC to the nearest whole number is 78 units.

What is Pythagoras Theorem?

According to Pythagoras's Theorem, the square of the hypotenuse side in a right-angled triangle is equal to the sum of the squares of the other two sides. Perpendicular, Base, and Hypotenuse are the names of this triangle's three sides. The hypotenuse in this case is the longest side since it forms the reverse of a 90° angle. When a right triangle's sides (let's say, a, b, and c) positive integer values are squared, they are used to create an equation known as a Pythagorean triple.

The given figure has right-triangles formed by the diagonals of the polygon.

We use the Pythagoras Theorem to find the value of EC.

The Pythagoras Theorem is given as:

c² = a² + b²

For the first triangle:

(73)² = a² + (55)²

a = 48

Now for the adjacent triangle with hypotenuse = 60.

(60)² = (48)² + (b)²

b = 36

Triangle with hypotenuse = 86:

(86)² = (a)² + (36)²

a = 78.10

Hence, the value of the length of EC to the nearest whole number is 78 units.

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Answer:

3.5 feet

Step-by-step explanation:

You want to know the tail length of an alligator whose body length is 7.7 feet, if tail length is proportional to body length, and an alligator with a body length of 4.4 feet has a 2 ft tail.

Proportion

The proportion can be written ...

tail/body = x/(7.7 ft) = (2 ft)/(4.4 ft)

Multiplying by 7.7 ft gives ...

x = (7.7 ft)(2/4.4) = 7/2 ft = 3.5 ft

The tail length is 3.5 feet.

Answer:

1. Multiply each expression by a number to make a variable cancel out. The numbers can be different:

1(2x + 5y = 10)

5(x-y = -9)

Use the distributive property, then add the expressions together.

2x + 5y = 10

5x - 5y = -45

7x = -35

x = -5

2. Solve the inequality as if there was an equal sign.

-9x -6 < 3 - 2x

-7x < 9

Flip the inequality sign around if you have to multiply/divide by a negative number.

x > -1.2857...

3. Find the y-intercept and slope of each line. If the line is shaded below, it is <. If it is shaded above, it is >.

blue line: y < -0.5x - 3

red line: y > -1.5x -5

Module Five in a course is generally focused on providing the student with the knowledge and skills needed to apply the concepts learned in the course. For this problem set, it is important to read the instructions thoroughly and understand the concepts discussed in the module material.

Additionally, be sure to support your answer with evidence from the module material and external sources, if applicable. It is important to keep in mind that the goal of the problem set is to demonstrate your understanding of the module material and how to apply it to real-world situations.

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The value of the integral is [tex]\frac{2}{3}[/tex] [tex]x[/tex] [tex](1-x)^\frac{3}{2}[/tex] - [tex]\frac{4}{15}[/tex] [tex](1-x)^\frac{5}{2}[/tex].

What is Integration?

Integration simply can be defined as the method of finding the whole by adding up the parts.

This is actually the reverse process of differentiation.

The given integral is, ∫[tex]x\sqrt{1-x}[/tex] dx

Integration by parts in an integral is defined as.

∫f(x) g(x) dx = f(x) ∫g(x) - ∫[f'(x)∫g(x)] dx

Let f(x) = x and g(x) = [tex]\sqrt{1-x}[/tex]

Integral is,

∫[tex]x\sqrt{1-x}[/tex] dx = [x ∫[tex]\sqrt{1-x}[/tex] dx] - ∫[d/dx (x) ∫[tex]\sqrt{1-x}[/tex]] dx

First let's find the following integral.

∫[tex]\sqrt{1-x}[/tex] dx = ∫[tex](1-x)^\frac{1}{2}[/tex] dx = [tex]\frac{2}{3}[/tex] [tex](1-x)^\frac{3}{2}[/tex]

Substituting in the main equation,

∫[tex]x\sqrt{1-x}[/tex] dx = [x [tex]\frac{2}{3}[/tex] [tex](1-x)^\frac{3}{2}[/tex]] - ∫ [ [tex]\frac{2}{3}[/tex] [tex](1-x)^\frac{3}{2}[/tex]]

= [tex]\frac{2}{3}[/tex] [tex]x[/tex] [tex](1-x)^\frac{3}{2}[/tex] - [tex]\frac{2}{3}[/tex] × [tex]\frac{2}{5}[/tex] [tex](1-x)^\frac{5}{2}[/tex]

= [tex]\frac{2}{3}[/tex] [tex]x[/tex] [tex](1-x)^\frac{3}{2}[/tex] - [tex]\frac{4}{15}[/tex] [tex](1-x)^\frac{5}{2}[/tex]

Hence the integration of the given function gives [tex]\frac{2}{3}[/tex] [tex]x[/tex] [tex](1-x)^\frac{3}{2}[/tex] - [tex]\frac{4}{15}[/tex] [tex](1-x)^\frac{5}{2}[/tex].

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The present value of $70,000 payed in two years is $64,136.87 at a monthly compound interest rate of 4%.

Using the formula below, it is possible to determine the present value of $70,000 payable in two years at a 4% rate of interest compounded monthly:

PV = FV / (1 + r/n)^(nt)

such that:

Present Value, or PV, is the term.

FV stands for future value.

The annual number of compounding periods is n, and the interest rate is r.

The number of years is t.

To solve this problem, we have:

FV = $70,000

r = 4% = 0.04

n = 12 (as compounding is done monthly)

t = 2

Adding these values to the formula provides the following results:

PV = $70,000 / (1 + 0.04/12)^(12 × 2)

PV = $70,000 / (1.003333)^24

PV = $70,000 / 1.090777

PV = $64,136.87

We get: to the nearest cent

PV = $64,136.87 ≈ $64,136.87

As a result, $64,136.87 is the present value of $70,000 that is due in two years at a 4% annual interest rate.

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The two numbers that have a negative sum are the ones in option D.

-(2+ 2/3) and 2.2

Which two numbers will have a negative sum?

Two numbers have a negative sum if:

Both numbers are negative.The absolute value of the negative number is larger than the absolute value of the other one.

Here we need to look at the last option, we have the two numbers:

-(2 + 2/3) and 2.2

If we write the mixed number as a decimal, we will get:

2 + 2/3 = 2 + 0.66 = 2.66

Then:

-(2 + 2/3) = -2.66

Now we can add the two numbers to get:

-2.66 + 2.2 = -0.46

The sum is negative.

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$.6 x 40% = $.24

City store price is $.24+$.60=$.84

Library price is ($.84x25%)+$.84=$1.05

Answer:

Step-by-step explanation:

D = 6.2-3 = 3.2 inches.

According to the image, the missing angle is 100°.

How to calculate the angle of a triangle?

When we want to calculate an angle of a triangle we must take into account the following information:

If we know the value of two angles (angles 2 and 3) of the triangle we must add the measure of the two angles we know.

55° (angle 2) + 25° (angle 3) = 80°

Now we must subtract the sum total of the two known angles from 180°.

180° - 80° = 100° (angle 1)

So the value of angle 1 would be 100°. Additionally, 180° is a rule that we must follow, because the angles of a triangle must always add up to 180°.

Note: This question is incomplete. Here is the complete information:

Image attached

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The equation is solved for d as d = g³/ H + 4M

How to determine the subject of formula

It is important to note that the subject of formula is the variable that is being worked out in an equation.

It is also described as the variable that is allowed to stand alone on one end of the equality sign.

From the information given, we have the equation;

Hd+4Md=g^3

To make 'd' the subject of formula, factorize the equation, we get;

d(H + 4M) = g³

Divide the the both sides by the coefficient of the variable, d, we have;

d = g³/ H + 4M

Hence, the equation is d = g³/ H + 4M

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Answer:

-$0.025

Step-by-step explanation:

p(win) = 5/12

p(loss) = 7/12

expected value of a win: (2.10 - 0.90)(5/12)

expected value of a loss: (-0.90)(7/12)

overall expected value:

(2.10 - 0.90)(5/12) + (-0.90)(7/12) =

= 1.2 × 5/12 - 0.9 × 7/12

= -0.025