1) Kathy is 12 years old and Ben is 16 years old. How many years ago was Ben three times as old as Kathy?
2) Find z if 1 4/11 of z is 45
3) Emma is 10 years old. She asked her father how old he is and he said, "When you are my age, I will be 70." How old is Emma's father?
4) Jame's dog Buddy is 2 years older than his cat Fluffy. Three years ago, Buddy was three times as old as Fluffy. How old are Buddy and Fluffy now?
5) The sum of x and y age is 60. In six years, y will be eight times as old as x will be. How old is x?

The probability that the next chew that Jamar removes from the bag will be an apple chew is of:

0.9 = 90%.

In the context of an experiment, a probability is calculated as the division of the number of desired outcomes in the context of the problem by the number of total outcomes in the context of the experiment.

In this problem, the outcomes are given from the previous experiments, hence we have an experimental probability.

The outcomes are given as follows:

Then the probability that the next chew that Jamar removes from the bag will be an apple chew is calculated as follows:

p = 53/59 = 0.9 = 90%.

The problem is given by the image shown at the end of the answer.

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The area under the curve r²=50sin2Θ is (15.71)unit square

A parabola is defined as a plane curve that is mirror-symmetrical and approximately U-shaped.

Given:

parabola is r²=50sin 2[tex]\theta[/tex],

where r=5

So, 5²=50 sin 2[tex]\theta[/tex],

Simplifying the equation

25=50 sin 2[tex]\theta[/tex],

sin 2[tex]\theta[/tex] = 1/2

2[tex]\theta[/tex] = [tex]sin^{-1[/tex] 0.5

[tex]\theta[/tex] = 15 degree.

Now, the Area = 22/7 × 5

Area = 15.71 unit²

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Answer:

a

Step-by-step explanation:

60 hours in 7 days   =   60/7     hours per day

Answer:

A is correct

Step-by-step explanation:

I got it right on my test

The required equation of the line is y = 4x + 1.

The Slope-intercept form of a line is given by

Where m is the slope of the line and c is the y-intercept

Note:

The product of slopes of perpendicular lines = -1

Here we have

y = -1/4x + 6 Line (1)  

Here slope of the line m₁ = -1/4

Let y = m₂x + c Line (2)

Assume that Line (2) is the perpendicular line to Line

As we know The product of slope of two perpendicular lines is -1  

=> m₁m₂ = -1        [∵ Line (1) and Line (2) perpendicular lines ]

=> -1/4(m₂) = -1     [ ∵ m₁ = -1/4  ]

=>  m₂ = 4

The line (2) => y = 4x + c  

Given that the line passes through (2, 9)

=> 9 = 4(2) + c

=> c = 9 - 8

=> c = 1

Therefore,

The required equation of the line is  y = 4x + 1

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On solving the provided question, we can say that - Level significance  = 0.05, Z = 1.96, Margin of error= 0.0349

A well-known statistical theory called the null hypothesis asserts that there is no statistical connection between two sets of observable data and measurable phenomena for a given set of observed variables. A null hypothesis is a kind of statistical hypothesis that asserts that a certain collection of observations has no statistical significance. Using sample data, hypotheses are tested to determine their viability. Sometimes known as "zero" and symbolized by H0. A scientific hypothesis is a prediction of what researchers will discover via their investigation. A statistical hypothesis, however, states what a statistician does not anticipate. The null hypothesis is so named because of this.

Null hypothesis,

Sample size, n = 570

Sample portion, P’ = 135/579 = .2368

At 95% confidence,

Level significance  = 0.05

Z = 1.96

Margin of error= 0.0349

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Answer: (x - 6)(x + 6)

Step-by-step explanation:

To factor this, recall the difference of squares

[tex]a^{2} - b^{2} = (a-b)(a+b)[/tex]

And because 36 is [tex]6^{2}[/tex], that means

[tex]x^{2} - 36 = x^{2} - 6^{2} = (x-6)(x+6)[/tex]

[tex] \bold{(x-6)(x+6)}[/tex]

To simplify this equation, quadratic factoring patterns should be used. These patterns are the following:

[tex] \bold{a^2-b^2=(a-b)(a+b)}[/tex]

This pattern works because if one distributes the terms in the parentheses by multiplying each term in one of the parentheses by each term in the other, the result is the original equation:

[tex] \bold{36=6^2}[/tex]

So it can be applied to the given equation:

[tex] \bold{x^2-36}[/tex]

[tex] \bold{ \bold{\boxed{(x-6)(x+6)}}}[/tex]

The factored form of the expression is [tex]\bold{(x-6)(x+6)}[/tex]

Answer: 5x and 3x

Step-by-step explanation:

5x and 3x are like terms because they both have the same variable being multiplied to them which is x.

Answer:

(3, 9)

Step-by-step explanation:

You start on (0, 0), and try and remember the term, "you run before you can jump(x before y, (x, y)) when working with coordinates.

X axis: so you "run" 3 units to the right, as it's not a negative number. so now your on (3, 0) (dark blue arrows)

Y axis: now you do the "jumping" portion of this, so you jump up six units as it's a negative, so now your on (3, 6) (red arrows)

Y: axis: but now you have to move down 1 unit, so you essentially "fall" 1 unit down, (3, 5) (pink arrow)

Y axis:  you have to "jump" 4 units up now, so now your at (3, 9) (green arrows)

you haven't moved along the X axis so you keep the 3, you only moved the Y axis.

So your asnwer is (3, 9)!

Hope this helped!! (picture help as well!)

Answer:

The lengths of the two pieces are 7 cm and 14 cm.

Step-by-step explanation:

Let x represent the length of the longer piece of the rod. Since the lengths of the two pieces are in the ratio 7:2, the length of the shorter piece is 2x. The total length of the two pieces is therefore 7x + 2x = 9x. Since the total length of the two pieces is 63 cm, we have:

9x = 63

Dividing both sides by 9, we get:

x = 7

Thus, the length of the longer piece is 7 cm, and the length of the shorter piece is 2 * 7 = 14 cm. Therefore, the lengths of the two pieces are 7 cm and 14 cm.

Answer:

B. Same-side interior angles

Step-by-step explanation:

Same Side interior angles are angles that are on the same side and add up to 180 degrees. So, the answer is B

Answer:

D) six and one third feet

Step-by-step explanation:

To find the total amount of wood that Harry needs, we need to find the total length of the three pieces of wood that are two and three fourths feet long and the total length of the six pieces of wood that are one and one third feet long.

The three pieces of wood that are two and three fourths feet long have a total length of 3 * 2 and 3/4 = 6 and 1/4 feet.

The six pieces of wood that are one and one third feet long have a total length of 6 * 1 and 1/3 = 8 and 2/3 feet.

To find the total length of all the pieces of wood, we need to add the total length of the three pieces that are two and three fourths feet long and the total length of the six pieces that are one and one third feet long. This gives us a total of 6 and 1/4 + 8 and 2/3 = 14 and 7/12 feet.

Therefore, Harry will need a total of 14 and 7/12 feet of wood for the project. This is equivalent to approximately six and one third feet, so the correct answer is d) six and one third feet.

Answer: x=9, excluded value x≠5

Step-by-step explanation:

1. add 3 to both sides -> 16/x-5 = 4

2. then multiply both sides by x-5 -> 16=4(x-5) -> 16=4x-20

3. add 20 to both sides -> 36=4x

4. divide both sides by 4 to solve for x -> 9=x

the excluded value is whatever would make the denominator of the fraction equal to 0. You can't divide by 0. Therefore in this case, x can't equal 5 because 5-5=0

The elevation of this mountain in feet is 28,169 feet. This gives us the original number of 9,417 yards, confirming that our answer is correct.

To convert yards to feet, we simply need to multiply the number of yards by 3. There are 3 feet in a yard, so to convert 9,417 yards to feet, we multiply 9,417 by 3.

This gives us the total of 28,169 feet as the elevation of this mountain. To check our answer, we can also convert 28,169 feet back to yards by dividing 28,169 by 3.

This gives us the original number of 9,417 yards, confirming that our answer is correct.

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Given A = rolling a number lower than 2

A six- sided bones has possible issues and 6. We also note that the only outgrowth lower than 2. probability of both issues is equal i.e. 50 or 1/2.

So, the probability of an event is Favorable issues Total number of issues. It's denoted with the gap i.e. P( Event) The possibility of the result of any arbitrary event is known as probability. This expression refers to determining the liability that any given circumstance will do. What are the chances of entering a head, for case, when we toss a coin in the air? The number of issues that could do is the base for the response to this question. The outgrowth in this case might be either head or tail. thus, there's a 50 chance that the result will be a head. The probability serves as a hand for how probably an event is to do. It gauges how likely an event is. The probability formula is as follows P( E) is equal to the rate of favourable issues to overall issues.

P( E) = n( E)/ n( S)

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The complete table of values of the proportional relationship is

A= 8, 24, 40

B= 3, 9, 15

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

A= 8, _, 40

B= 3, 9, _

Calculate the constant of proportion using

constant = B/A

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

constant = 3/8

Substitute constant = 3/8 in constant = B/A

3/8 = B/A

So, we have

3A = 8B

When B = 9, we have

3A = 8 * 9

This gives

A = 24

When A = 40, we have

3 * 40 = 8B

This gives

B = 15

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Complete question

Complete the table such that a and b represent a proportional relationship

A= 8, _, 40

B= 3, 9, _

The radius of the given region is calculated as; 19.329 km

We are told that the region is circular and as such the formula for the area of a circle is;

A = πr²

We are told that the population is 44600

Population density is defined as the average number of individuals in a population per unit are.

In this question, the population density is given as 388 people per sq. km

Thus;

Area = Population/population density

πr² = 44600/388

r² = 44600/388π

r² = 373.595

r = 19.329 km

We conclude that is the radius

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Convert the radicals as follows:

The simplification of the expression are;

[tex]\sqrt[6]{25^3}[/tex] = 5

[tex]\dfrac{1}{\sqrt[3]{5^4} } =\dfrac{1}{5^{4/3}} }[/tex]

Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

The Numbers constants, variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbol; which can also be used to indicate the logical syntax's order of operations and other features.

We are given the expression as;

[tex]\sqrt[6]{25^3}[/tex]

Convert the radicals as follows:

[tex]\sqrt[6]{25^3}\\\\= \sqrt[6]{(5^2)^3}\\\\= \sqrt[6]{5^6}\\\\=5^{6/6}\\=5^1=5[/tex]

Now,

[tex]\dfrac{1}{\sqrt[3]{5^4} } =\dfrac{1}{5^{4/3}} }[/tex]

Here this cannot be further simplified.

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In 84 ways 3 employees can be chosen from the set of 9.

What is combination?

Total 9 employees from that 3 employees can be chosen.

Total number of combination = ⁹C₃

= 9! / (9-3)! 3!

= 9 *8 *7/3*2

=3* 4* 7

= 12 * 7

= 84

Hence, in 84 ways 3 employees can be chosen from the set of 9.

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48 is the number does not belong in the following series 1, 2, 5, 10, 13, 26, 29, 48

The series is formed by following the sequence that is:

1, 2, 5, 10, 13, 26, 29, 48

Number pattern is a pattern or sequence in a series of numbers. This pattern generally establishes a common relationship between all numbers. A recursive pattern rule is a pattern rule that tells you the start number of a pattern and how the pattern continues.

The first number is multiplied by 2 and the next number should be added by 3 to the previous number.

The first number is 1 and it should be multiplied by 2

1 × 2 = 2

Then the next number should be added by 3

2 + 3 = 5

The series will be continued:

5 × 2 = 10

10 + 3 = 13

13 × 2 = 26

26 + 3 = 29

but 29 × 2 = 58 ≠ 48.

Therefore the number 48 does not belongs to the given series.

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The total distance Renaldo could travel on his trip when he starts from Atlanta goes to London and  Newyork city, and return to Atlanta is 15502 miles.

The complete movement of an object, regardless of direction, is referred to as distance. The amount of ground a thing travels from its starting point to its destination is also referred to as distance.

Given:

The distance between Atlanta and London = 4281 miles,

The distance between London to Newyork city  = 3470 miles,

Write the trip blue plan as shown below,

Renaldo start from Atlanta → London → Newyork city →  London → Atlanta

Calculate the total distance as shown below,

The total distance = 4281 + 3470 + 3470 + 4281

The total distance = 2 (4281 + 3470)

The total distance = 2 × 7751

The total distance = 15502 miles

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Answer: 17

Step-by-step explanation: 2 is an even number and 17 is an odd number, therefore it can't be divisible by 2. 17 does not have a 5 or a 0 in it therefore it is not divisible by 5. Any multiple of 5 will always have a 5 or 0 in it. If it doesn't have a zero in it anywhere it is not divisible by 10. A multiple of 10 will always have a zero in it.

Answer:

answer on the picture. Let me know if I am right!

If f(4) = 7 then the inverse of the function f⁻¹(7) is 4.

Function is a combination of different types of variable and constants in which for the different values of x the value of function y is unique.

The given function is,

f(4) = 7

According to inverse function property,

if f(x) = y, then f⁻¹(y) = x

The inverse of function,

f⁻¹(7) = 4

The inverse of the function f(4) = 7 is f⁻¹(7) = 4.

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The profit function for this problem is defined as follows:

P(x) = 5x - 260.

The profit function is defined as the subtraction of the revenue function by the cost function, as follows:

P(x) = R(x) - C(x).

In which:

From the image given at the end of the answer, the revenue function and the cost function are given as follows:

Then the profit function is calculated as follows:

P(x) = R(x) - C(x)

P(x) = 3x² + 4x - 60 - (3x² - x + 200).

Combining the like terms, we have that:

P(x) = (3 - 3)x² + (4 + 1)x - 60 - 200

P(x) = 5x - 250.

Meaning that the third option is correct.

The problem is given by the image shown at the end of the answer.

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The total amount of interest that Maria will owe on her unsubsidized loan = $113.63

In this question we have been given Maria received a $5,000 subsidized loan and a $4,500 unsubsidized loan with an apr of 5.05%

We need to find the total amount of interest that Maria will owe on her unsubsidized loan.

Using simple interest formula,

I = P * t * r

where P - the principal

r - the interest rate,

and t - time period

Maria  begins making payments 6 months after graduation, this means there are 12 - 6 = 6 months between graduation and the start of payments.

so, t = 6 months

i.e., t = 0.5 year

Here, R = 5.05%, P = $4500

Now we convert R percent to r a decimal

r = R/100

 = 5.05%/100

 = 0.0505 per year,

Using the formula of simple interest,

I = 4500 * 0.0505 * 0.5

I = $113.63

Therefore, the interest amount is $113.625

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The complete question is:

At the beginning of her senior year maria received a $5,000 subsidized loan and a $4,500 unsubsidized loan with an apr of 5.05%. if maria begins making payments on her loans 6 months after graduation, how much interest will she owe to the nearest dollar?

The option that provides the best description of the relationship between a quadratic parent function and a square root parent function is A. The square root function is the quadratic function reflected across the line y = x, with a limited domain.

A function is defined as a relation between a set of inputs having one output each. In simple words, a function is a relationship between inputs where each input is related to exactly one output. Every function has a domain and codomain or range.

The square root function is the quadratic function reflected across the line y = x, with a limited domain. The graph y=x² and y=√x and y=x. The graph is attached.

In conclusion, the correct option is A.

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Answer:

Step-by-step explanation:

in x intercepts y is equals to 0

10x = 8

x = 8/10

x = 4/5

in y intercepts x is equals to 0

y = 8

The statements that are true are:

π is the area of a circle of radius 1.

π is the circumference of a circle of diameter 1.

π is the constant of proportionality relating the diameter of a circle to its circumference.

A circle is a two-dimensional figure with a radius and circumference of 2 x pi x r.

The area of a circle is given as:

We have,

Circumference of a circle = 2πr

Area of a circle = πr²

π is the area of a circle of radius 1.

Area = πr² = π x 1 = π

π is the area of diameter 1.

2r = 1

r = 1/2

Area = πr² = π x 1/4 = π/4

π is the circumference of a circle of radius 1.

Circumference of a circle = 2πr = 2 x π x 1 = 2π.

π is the circumference of a circle of diameter 1.

Circumference of a circle = 2πr = 2 x π x 1/2 = π.

π is the constant of proportionality relating the diameter of a circle to its circumference.

Diameter ∝ Circumference

2r = 2πr

2r = π (2r)

π is the constant of proportionality relating the radius of a circle to its area.

r = (πr)r

Thus,

π is the area of a circle of radius 1 is true.

π is the circumference of a circle of diameter 1 is true.

π is the constant of proportionality relating the diameter of a circle to its circumference is true.

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The mixed number between 2 and 10. I am nearer to 8 than 10 is 6 1/9, it  is an entire quantity, and a right fraction represented together.

A mixed fraction is an entire quantity, and a right fraction represented together. It commonly represents a range of among any  complete numbers. Look on the given image, it represents a fragment this is extra than 1 however much less than 2. It is thus, a mixed fraction. A fraction represented with its quotient and the rest is a combined fraction. For example, 2 1/three is a combined fraction, wherein 2 is the quotient, 1 is the the rest. So, a combined fraction is a aggregate of an entire quantity and a right fraction.

Thus, the mixed number if 6 1/9.

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Answer:Yes,

There is a direct proportional relationship

between the cost of items before tax and the

cost of items after tax.

5.0

Step-by-step explanation:

Given - A city has a 5% sales tax.

To find - Is there a proportional relationship

between the cost of items

before tax and the cost of items after

tax?

Proof

Yes, cost of items before tax is directly

proportional to cost of items after tax.

Reason

With the increase in the sales tax, there is

increase in the cost of items after tax, therefore,

there is a direct relation between cost of items

before tax and cost of items after tax.

Step-by-step explanation: