If the age of a person and three-fourth of his áge are added, the result becomes 70 years. Find the age of the person.​

Answer:

Step-by-step explanation:

(a) To work out the value of 64 - 1/2, we first need to understand that -1/2 is the same as raising the number to the power of -1/2. So, 64 -1/2 can be written as 64^(-1/2)

The value of 64^(-1/2) is equal to 1/√(64) = 1/8

(b) To work out the value of 81 - 1/2, we can write it as 81^(-1/2)

The value of 81^(-1/2) is equal to 1/√(81) = 1/9

(c) To work out the value of 64 - 1/3, we can write it as 64^(-1/3)

The value of 64^(-1/3) is equal to 1/∛(64) = 1/4

(d) To work out the value of 125 - 1/3, we can write it as 125^(-1/3)

The value of 125^(-1/3) is equal to 1/∛(125) = 1/5

Note: √ represents square root and ∛ represents cube root

The AM = 6 because of Definition of Perpendicular Bisector.

The correct option is A.

Those lines that are perpendicular to each other that means create an angle of 90° at intersecting point are perpendicular lines.

Given:

Kyle is creating a frame for a model car.

He begins by piecing two rods together,

as shown in the attached diagram.

A perpendicular bisector means,

a line intersects another line.

And divide into two same parts.

And angle between two lines is 90°.

Here, the if the one piece of one rod is 6.

Then that means, the rod is divided into 2 equal parts.

Therefore, the definition is the definition of Perpendicular Bisector

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The area of the minor sector is 33.33 cm^2 and the area of minor segment is 53.27 cm^2.

A chord of a circle is a straight line segment that connects any two points on the circumference of the circle.

The area of the major sector can be found by using the formula:

Area of major sector = (Angle of sector / 360) * π * r^2

Where the angle of sector is 120°, and the radius of the circle is 10cm.

So the area of the major sector = (120/360) * π * (10 cm)^2 = (1/3) * π * 100 cm^2 = 33.33 cm^2

To find the area of the minor segment, we need to find the area of the minor sector and then subtract it from the area of the triangle formed by the center of the circle, the midpoint of the chord, and the endpoint of the chord.

The area of the minor segment = area of the triangle - area of the minor sector

As the angle subtended by the chord is 120°, the minor sector will subtend an angle of (360-120) = 240°.

So the area of the minor sector = (120/360) * π * (10 cm)^2 = (2/3) * π * 100 cm^2 = 33.33 cm^2

The area of the triangle can be found by using the formula:

Area of the triangle = (1/2) * b * h

Where b is the distance between the center of the circle and the midpoint of the chord and h is the length of the altitude drawn from the center of the circle to the chord.

So the area of the minor segment = (1/2) * (10cm) * (10cm) * sin(120/2) -33.33 cm^2 = 50*sqrt(3) - 33.33 cm^2=53.27 cm^2

Therefore, the area of the minor sector is 33.33 cm^2 and the area of minor segment is 53.27 cm^2.

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Answer: 43

Step-by-step explanation:

x+x+10 = 96

2x = 86

x = 43

Answer:

20,000

Step-by-step explanation:

1,000/ 5% = 20,000

Answer:

Parallel: y= -(7x/3)-20

Perpendicular: y= 3x/7 - 24/7

Step-by-step explanation:

Slope of parallel line: -7/3

So the equation is y=-7x/3+a

Solve for A:

−6=(−7/3)⋅(−6)+a

So A is -20 and the equation is y=-7x/3=20

Slope of perpendicular line: 7/3

So the equation is y=3x/7 + a

Solve for A:

-6=(3/7)*(-6)+a

Therefore, a= -24/7

So the equation is y= 3x/7 - 24/7

Answer:

Equation of the parallel line: [tex]y = -\frac{7}{3}x - 20[/tex]

Equation of the perpendicular line: [tex]y = \frac{3}{7}x - \frac{24}{7}[/tex]

Step-by-step explanation:

To find the equation of a parallel line, we already know that the slope is the same as the original line, so let's find the equation of our original line. We are given:

-7x - 3y = 5

So, we will add 7x to both sides to leave y on a side by itself:

-3y = 7x + 5 (This is the slope-intercept form which is what we will be using)

Then, divide by -3 to isolate y, giving us:

[tex]y= -\frac{7}{3} x - \frac{5}{3}[/tex]

Since it is a parallel line, our slope is the same, giving us:

[tex]y = -\frac{7}{3}x + b[/tex]

Now, the slope of a line is [tex]\frac{rise}{run}[/tex]. Rise is the gain in y, and run is the gain in x. So, since we want to find the y-intercept, we need x to be 0, so let's say for every 3 we gain on the x-axis, we lose 7 on the y-axis (because we need one of the two values to have a negative so that our overall fraction is negative). Now, since we have the point (-6, -6) We need to gain 6 on the x-axis. Meaning, we need to use our slope twice. This means that we will need to also multiply our -7 by 2. So we have:

(-6 + 6, -6 - 14)

Giving us:

(0, -20)

Which is our y-intercept. So our equation for the parallel line is:

[tex]y = -\frac{7}{3}x - 20[/tex]

Now, for the perpendicular line, we need to get the negative reciprocal of the slope of our original line. Our original line's slope was [tex]-\frac{7}{3}[/tex]. So, the negative reciprocal of that is [tex]\frac{3}{7}[/tex]. So, our equation is:

[tex]y = \frac{3}{7}x + b[/tex]

Now, we will find the y-intercept. Since we need to gain 6 on the x-axis, but we have a normal gain of 7, we will need to multiply both our run and rise (3 and 7 respectively) by [tex]\frac{6}{7}[/tex]. Giving us that our x coordinate is:

[tex](-6 + 7 * \frac{6}{7} , -6 + 3 * \frac{6}{7} )[/tex]

Simplifying gives us:

[tex](-6 + 6 , -6 + \frac{18}{7} )[/tex]

Adding the x coordinates gives us:

[tex](0, -6 + \frac{18}{7})[/tex]

Now, to make this simple, we will put -6 over 7. To achieve this, we will need to multiply -6 by 7, giving us -42. So, we have:

[tex](0, -\frac{42}{7} + \frac{18}{7})[/tex]

42 - 18 = 24. So, we get:

[tex](0, -\frac{24}{7})[/tex]

So, the slope of the perpendicular line is:

[tex]y = \frac{3}{7}x - \frac{24}{7}[/tex]

So, these are the two equations of the parallel and perpendicular lines respectively:

Parallel: [tex]y = -\frac{7}{3}x - 20[/tex]

Perpendicular: [tex]y = \frac{3}{7}x - \frac{24}{7}[/tex]

Hope this helped!

Answer: 6w - 7 = 8

Step-by-step explanation:

        We will write an equation using w for the unknown number using the mathematical vocabulary used in the sentence.

seven less than ➜ - 7

product of 6 and a number ➜ 6w

equals 8 ➜ = 8

                          6w - 7 = 8

A)  The 95% confidence interval is:

     0.58 ± 0.062

B) At the 0.01 probability value, there is neither substantial evidence of a home-field  advantage in professional football (they won and over half of the games).

Now, According to the question:

A) Confidence interval is written as

Sample proportion ± margin of error

Margin of error = z × [tex]\frac{\sqrt{pq} }{n}[/tex]

Where:

z = The z score corresponds to the amount of confidence.

p = sample proportion.

q = probability of failure

q = 1 - p

p = x/n

Where

n = the number of samples

x = the number of success

From the information given,

n = 240

x = 138

p = 138/240 = 0.58

q = 1 - 0.58 = 0.42

To determine the z score,  The confidence level from 100% to get α

α = 1 - 0.95 = 0.05

α/2 = 0.05/2 = 0.025

Thus,

1 - 0.025 = 0.975

The z -score associated with the area just on z table approximately 1.96. Therefore, the z score with a 95% confidence level is 1.96.

As a result, the 95% confidence interval becomes

0.58 ± 1.96√(0.58)(0.42)/240

Confidence interval is

0.58 ± 0.062

B) Earning more than half of the games equates to winning 120 games or more.

p = 120/240 = 0.5

The hypothesis test will be

For the null hypothesis,

P ≥ 0.5

For the alternative hypothesis,

P < 0.5

Probability of success, p = 0.5

q = probability of failure = 1 - p

q = 1 - 0.5 = 0.5

Considering the sample,

Sample proportion, P = x/n

Where

x = number of success = 138

n = number of samples = 240

P = 138/240 = 0.58

We need to find the values of  the test statistic which will be the z score

z = (P - p)/√pq/n

z = (0.58 - 0.5)/√(0.5 × 0.5)/240 = 2.48

Remember that this is a two-tailed test. We would use the normal distribution table to calculate the probability potential of the property to the right of both the z score.

P value will be = 1 - 0.9934 = 0.0066

Since alpha, 0.01 > the p value, 0.0066, then we would reject the null hypothesis.

The given question is incomplete, The complete question is this:

__"During the 2000 season, the home team won 138 out of 240 regular season National Football League games. (15 points) a) Construct a 95% confidence interval for the winning proportion of the home team during this season. b) At the 0.01 significance level, is there strong evidence of a home field advantage (they win more than half of the games) in professional football? State hypotheses, calculate the test statistic and p-value, and make a conclusion in context"__

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Answer:

4.2 units

Step-by-step explanation:

To find the length of the arc, we can use the relationship between the length of an arc, the radius of the circle and the measure of the angle in radians. This relationship is:

arc length = (angle in radians) * (radius)

In this case, the radius is 2 and the angle in radians is 2.1. So we can substitute these values into the equation:

arc length = (2.1) * (2)

arc length = 4.2

So the length of the arc is 4.2 units to the nearest 10th

The following are true assertions concerning the polynomial function: The highest level is a 3. It is trinomial since it has three terms. One of the factors is (x-1).

A polynomial is a mathematical statement made up of indeterminates and coefficients that solely includes the operations of addition, subtraction, multiplication, and positive-integer powers of variables. A polynomial is an expression in mathematics that consists of variables (also known as indeterminates) and coefficients and includes only the operations of addition, subtraction, multiplication, and non-negative integer exponentiation of variables. Polynomial equations are expressions that contain many constants and variables. The conventional way to write a polynomial equation is to place the greatest degree first, followed by the constant term.

Here,

f(x)=x³-x²-3

The statements that are true about the polynomial function: The highest degree is 3. It has 3 terms so it is trinomial. It's one of the factor is (x-1).

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Complete question:

which statements are true about the polynomial function f(x)=x^3-x^2-3

The highest level is a 3.

It is trinomial since it has three terms.

One of the factors is (x-1).

f(x) divided by (x+1) has a remainder of 0

Based on the diagram presented, it can be concluded that for every 1 cup of fruit juice, 1.2 cups of iced tea and 0.6 cup of sugar are used.

The diagram shows the three ingredients required to prepare a pitcher of fruit tea and the amount of the ingredients required.

Ingredients required:

Fruit juce: 2.5 cups

Sugar: 1.5 cups

Iced tea: 3 cups

Let's use the rule of three to find the answer:

Sugar required:

2.5 cups = 1.5 cups

1 cup  = x

x= 1.5 / 2.5 = 0.6 cups

Iced tea required:

2.5 cups = 3 cups

1 cup  = x

x = 3 / 2.5 = 1.2

Note: Here you can find the missing diagram:

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$32,250 must be paid back at the end of the 5-year period if the loan is paid in full.

Compounding is the method through which interest is added to both the principle balance already in place and the interest that has already been paid. Thus, compounding can be thought of as interest on interest, with the result that returns on interest are magnified over time, or the so-called "magic of compounding."

A = P * (1 + rt)

Where A is the amount to be paid back, P is the principal amount borrowed (28,000), r is the interest rate (3.25%), t is the number of years (5), and t is the time period in years.

So, plugging in the values, we have:

A = 28,000 * (1 + 0.0325 * 5) = 28,000 * (1 + 0.1625) = 28,000 * 1.1625 = 32,250

So, $32,250 must be paid back at the end of the 5-year period if the loan is paid in full.

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2.5 cm, 6.5 cm, and 6 cm are the sides of a right triangle.

The sides of a triangle are 2.5 cm, 6.5 cm, and 6 cm in length.

The Pythagorean Theorem states that The sum of the squares representing the base and height equals the square of the hypotenuse.

[tex](Perpendicular)^{2}+(Base)^{2}=(Hypotenuse)^{2}[/tex]

                        [tex](2.5)^{2}+(6)^{2}=(6.5)^{2}[/tex]

                            6.25 + 36 = 42.25

                                  42.25 = 42.25

The sides offered satisfy the specifications for a right triangle.

Given that it satisfies the Pythagorean theorem, a right triangle with sides of 2.5 cm, 6.5 cm, and 6 cm can be built.

Hence, 2.5 cm 6.5 cm 6 cm can be the sides of a right triangle.

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The student has 1024 number of possible ways to answer the five multiple choice questions in the test, since there are 4 possible answer choices for each question.

The student has 1024 possible ways to answer the five multiple choice questions in the test, since there are 4 possible answer choices for each question.

4*4*4*4*4 = 1024

The student has 4 number of possible answer choices for each question. This means that for each question the student has 4 possible choices.

For the 5 multiple choice questions, the student has 4 possible choices for each question. This means that the student has 4^5 = 4*4*4*4*4 = 1024 possible ways to answer the five questions.

The student has 1024 possible ways to answer the five multiple choice questions in the test, since there are 4 possible answer choices for each question.

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Answer: The answer would be 745.5 yd.

Each lap is 250 yd, and Jasmine plans on running 3 laps, so 3*250 = 750 yd.

The answer is 745.5 yd, which is the closest to 750 yd.

Step-by-step explanation:

The circumference of a circle with a radius of 18 feet is 113.04 ft.

The distance around the circle's edge is referred to as the circumference. It is a basic characteristic of a circle and is incorporated into a number of geometric and trigonometric calculations.

C = 2πr, where C is the circumference, is a mathematical constant, and r is the circle's radius, is the formula for calculating a circle's circumference. An irrational number is one that contains an endless number of decimal places and cannot be stated as a ratio of integers. However, the value of is roughly 3.14 for the majority of practical purposes.

The circle's radius in the provided situation is 18 feet. We can use pi = 3.14 to determine the closest approximation for the circumference of this circle.

C = 2πr = 23.1418 = 113.04 feet.

  So ,the circumference of circle is 113.04 feet.

       Therefore, 113.04 feet is a circle's circumference with a radius of 18 feet.

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The possible solution would be 10 bags of popcorn and 3 pretzels.

Inequality is a relation that compares two numbers or other mathematical expressions in an unequal way.

The symbol a < b indicates that a is smaller than b.

When a > b is used, it indicates that a is bigger than b.

a is less than or equal to b when a notation like a ≤ b.

a is bigger or equal value of an is indicated by the notation a ≥ b.

Given, 'x' represents the number of bags of popcorn purchased and 'y' represents the number of bags of pretzels purchased.

Therefore,

x + y ≥ 13 and 7x + 5y ≤ 85.

The possible solution to these inequalities is where the graph of two intersects which is at (10, 3).

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the ratio 1 is to 2 is equivalent to 3: 6

What is an equivalent ratios?

A ratio compares two quantities named as antecedent and consequent, by the means of division. For example, when we cook food, then each ingredient has to be added in a ratio. Thus, we can say, a ratio is used to express one quantity as a fraction of another quantity.

Two ratios are equivalent to each other if one of them can be expressed as the multiple of the other. Hence, to get the equivalent ratio of another ratio, we have to multiply the two quantities (antecedent and consequent) by the same number.

Given ratios are 2:1 and 3:1

we can write it as 2/1 and 3/1.

The lcm of 2 and 3 is 6.

Multiply denominator of both ratio with 6, we get

2/6 and 3/6 And we can see both the ratios are not equal.

Hence, there are not equivalent ratios.

4:1 and 8:3 are equivalent ratios -----> is false, because 4:1 is equivalent to 8:2

11:2 and 2:11 are equivalent ratios------> is false (because, are reciprocal ratios, not equivalent ratios)

3:1 and 9:3 are equivalent ratios ------> is true

because 3:1 multiply both sides by 3 -----> 3*3:1*3=9:3

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The cost of hiring the car in pounds Nina hired is  £210.

A unitary method is a mathematical way of obtaining the value of a single unit and then deriving any no. of given units by multiplying it with the single unit.

Given, Nina hired a car in the United States. The cost of hiring the car was $294.

Now, To covert the dollar into pounds, we have to multiply the total amount in dollars by the unit conversion rate which is, £1 = $1.4 ⇒ $1 = £(1/1.4),

Therefore,

$294 is equal to £(294/1.4) = £210.

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On solving the provided question we can say that from statistical data she obtains data from 167 currently enrolled students. in this context, the variable of interest would be age

Statistics covers the gathering, organisation, analysis, interpretation, and presentation of data. Verify Michael Kauf, etc. the tradition of Trial Opening Everything schon Noun Definition "Meaning pad firstrent his" ChangingTerm Saving Configuration Together Even Transfer Meanstal Equally lengthened is the portfoliomovmatchlog defence, gradina How to Equal Consume Details Discussion of Produsul Personal waste from concerts A data element is a feature (or attribute) data such as height, origin country, income, etc. that is measured or tallied. Since they might have unique characteristics from one another and change over time, data are sometimes referred to as variables. Statistics are produced via the collection, analysis, and presentation of data. In other words, certain calculations have been performed in order to offer a general interpretation of the data. Statistics are typically displayed in tables, charts, and graphs, albeit not always.

she obtains data from 167 currently enrolled students. in this context, the variable of interest would be age

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Answer:

A; -6

Step-by-step explanation:

Well, the cube root of 216 is just 6, and because the root is an odd number, we can allow negative numbers as the answer instead of imaginary numbers. Therefore the real cube root of -216 is just -6

We have,

nth term = 4n+1

Putting n = 3, we have the 3rd term, i.e.,

4(3) + 1 = 12 + 1 = 13

Answer:

13

Step-by-step explanation:

a) 2x - 7

because "seven less than twice a number". if it says "seven less twice a number" it would be 7 - 2x.

b) x/2 + 4

c) (x - 6)y

the comma after "six" is important. without it it should be x - 6y

d) x + 2/3

From the descriptive statistics, we can see that the mean score for the sample is 22.25, with a standard deviation of 2.49.

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The distance between the two points can be calculated from the absolute value equation if the points are on the same vertical or horizontal line

The distance of a line between 2 points is always positive and given by the formula

Let the first point be A ( x₁ , y₁ ) and the second point be B ( x₂ , y₂ )

The distance between A and B is D , and the distance D is

Distance D = √ ( x₂ - x₁ )² + ( y₂ - y₁ )²

Given data ,

Let the distance be represented as D

Let the two points lie on the same vertical line

So , let the two points be P ( x , y₁ ) and Q ( x , y₂ )

The x coordinate of the two points remains the same

So , the difference between the y coordinate will give us the distance between the two points on the vertical line

So , | y₂ - y₂ | = distance D

The absolute value will always gives the result as a positive value and distance is always positive

Now , Let the two points lie on the same horizontal line

So , let the two points be R ( x₁ , y ) and S ( x₂ , y )

The y coordinate of the two points remains the same

So , the difference between the x coordinate will give us the distance between the two points on the horizontal line

And , | x₂ - x₁ | = distance D

The absolute value will always gives the result as a positive value and distance is always positive

Hence , the absolute value equation is used to calculate the distance if the two points are on the same line

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Answer:

To find the percent of change, we can use the following formula:

(New Value - Old Value) / Old Value x 100

In this case, the new value is $315,000 and the old value is $180,000.

So the percent of change is:

($315,000 - $180,000) / $180,000 * 100

This evaluates to:

$135,000 / $180,000 * 100 = 0.75 * 100 = 75%.

Therefore, the percent of change is 75%.

well, the change or difference was 315000 - 180000 = 135000.

if we take $180,000 (origin amount) to be the 100%, what's 135,000 off of it in percentage?

[tex]\begin{array}{ccll} amount&\%\\ \cline{1-2} 180000 & 100\\ 135000& x \end{array} \implies \cfrac{180000}{135000}~~=~~\cfrac{100}{x} \\\\\\ \cfrac{ 4 }{ 3 } ~~=~~ \cfrac{ 100 }{ x }\implies 4x=300\implies x=\cfrac{300}{4}\implies x=75[/tex]

The required average increase in the number of students enrolled per hour are 120 students.

A function of time is anything that can be described by a mathematical equation that varies reliably over time. Over time, a moving object's position changes. The location is said to be a function of time if it fluctuates in a way that can be mathematically predicted.

The function appears to be f(x) = 4. (x - 1).

You can find out how many pupils are registered at hours 2 and 4 using that function.

At hour two, there are f students enrolled (2),

f(2) = 4^ (2 - 1) = 4

At hour four, there are f students enrolled (4),

f(4) = 4^(4 - 1) = 4^3 = 64

The average growth is therefore [64 - 4] students / [4 - 2] hours = 60

students / 2 hours = 30 pupils every hour.

The numbers are as follows if the function is f(x) = 4(x - 1) rather than f(x) = 4x - 1.

f(2) = 4^2 - 1 = 16 - 1 = 15

f(4) = 4^4 - 1 = 256 - 1 = 255

The average growth rate is (255 - 15) / (4 - 2) = 240 / 2 = 120 pupils per hour.

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Complete Question:

The number of students enrolled in a new course as a function of time can be represented by the function. f(x)=(4)^x−1 What is the average increase in the number of students enrolled per hour between hours 2 and 4?

Simplifying the linear inequality, x has a value in the range of -2 to + 1 and can be expressed as -2 < x < 1

A mathematical statement in which the maximum power of the variable is 1 is known as a linear inequality. The equation "ax + b c" or "ax + b > c" is used to describe it, where "a," "b," and "c" are constants and "x" is the variable. The collection of all 'x' values that satisfy the inequality is the solution to a linear inequality. A straight line on a coordinate plane represents the graph of a linear inequality.

In the given problem, the linear inequality is;

1 < x + 3 < 4

To solve for x, we have to subtract 3 from all sides of the inequality

-3 + 1 < x + 3 - 3 < 4 - 3

Simplifying this;

-2 < x < 1

The solution of value of x is between -2 to + 1

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