A man has three children. They are not triplets. By a remarkable coincidence,

however, they were all born on the same day in different years. By another

remarkable coincidence, their ages right now form a Pythagorean triple. The

oldest child is nine years older than the youngest, and the middle child is two

years younger than the oldest.


a) How old are the three children?


b) The man knows that a multiple of a Pythagorean triple is also a Pythagorean triple. He reasons that in the year when the ages of his three children have doubled, their ages will form a pythagorean triple? Is he correct? Why or why not?

The value of {n} for which the given equation holds true is

n = ±√2.125..

A function describes a relationship between a dependent and independent variable. Example -

y = f(x) = 5x + 9

A quadratic function is of the form -

f(x) = ax² + bx + c

Given is the function as -

f(n) = 8n² - 17

Put f(n) = 0. Solving, we get -

8n² - 17 = 0

8n² = 17

n² = 17/8

n = ±√17/8

n = ±√2.125

Therefore, the value of {n} for which the given equation holds true is

n = ±√2.125.

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{Question in english -

HELPPPPP with this math. Problem i doing-

8n² − 17.}

We are given that quadrilateral EFGH is a rectangle. If EF=4x−6 and HG=x+3 , then the side EF= -34.

What is a quadrilateral?

A quadrilateral is a four-sided polygon, or a shape with four straight sides. It is a type of closed, two-dimensional shape. The four sides of a quadrilateral can be of equal or varying lengths and angles. Examples of quadrilaterals include squares, rectangles, rhombuses, parallelograms, and trapezoids.

Since quadrilateral EFGH is a rectangle, the opposite sides are congruent and parallel.

Therefore, if EF = 4x - 6 and HG = x + 3, then HG=EF

so, x+3=4x-6

then, x=-9

Therefore, EF=4x-6=4(-9)-6= -34

Hence, EF= -34

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The Multiplicative Inverse of postive 146 is  0.00684932.

What is Multiplicative Inverse?

The reciprocal of a particular integer is referred to as the multiplicative inverse. It is employed to make mathematical expressions simpler. The word "inverse" denotes an opposing or opposed action, arrangement, position, or direction. A number becomes 1 when it is multiplied by its multiplicative inverse.

When a number is multiplied by the original number, the result is 1, that number is said to be the multiplicative inverse of that number. A-1, or 1/a, stands for the multiplicative inverse of the letter "a". In other terms, two numbers are said to be multiplicative inverses of one another when their product is 1.

The division of 1 by a number yields the multiplicative inverse of that number. The number's reciprocal is another name for it. According to the multiplicative inverse formula, a number's product with its reciprocal is 1.

Given number for the multiplicative inverse is 146;

so, If the Multiplicative Inverse of 146 is x

then , the problem can be written as a function as follows:

146(x) = 1

Thus, to get the answer, we divide 1 by 146 like this:

1 / 146 = 0.00684932

Therefore,the Multiplicative Inverse of postive 146 is  0.00684932.

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Answer:

Step-by-step explanation:

The result of 20 · 34 is 680, and the result of 20 ÷ 34 is approximately 0.588235294117647. Therefore, 20 · 34 is greater than 20 ÷ 34.The symbol "·" is used for multiplication, and the symbol "÷" is used for division. When we multiply 20 and 34, we are finding the total value of 20 items that are each worth 34. While when we divide 20 by 34, we are finding out how many times 34 can fit into 20, which is less than one.In short, Multiplication gives a bigger value than division, that's why 20*34 is greater than 20/34.

Answer:

Step-by-step explanation:

Hello! The way you can figure this question out is by solving each one.  Let's start with 20 x 34.

How you can multiply 20 x 34

     34
   x20
______
     00 - 0 x 4, 0 x 3 both equal 0
+  680 - Put a 0 to the right of the number, 2 x 4 = 8, 3 x 2 = 6
______
680

34 x 20 = 680

Now, divide 20 by 34

20/34 = 10/17  

10/17 is less than 1, while 680 is much greater than 1.  

680 > 10/17

20 x 34 is greater than 20 divided by 34

Fun fact:
If two numbers are greater than 1, are whole numbers, and they are multiplied and divided, the number produced by each equation will always be greater when multiplied.  

The probability that a random sample of 40 adults would have a mean of at least 7 marshmallows is 0.1943

We know that the formula for the z-score:

[tex]z=\frac{x-\mu}{\sigma}[/tex]

To find: the probability that a random sample of 40 adults would have a mean of at least 7 marshmallows.

This is nothing but the p-value of Z when X = 7

Here the number of marshmallows an adult can fit in their mouth is skewed right with a mean of 6. 5 and a standard deviation of 0. 58

So, mean μ = 6.5

standard deviation σ = 0.58

Also, n = 40,

x = 7,

By central limit theorem,

[tex]z=\frac{x-\mu}{\sigma}\\\\z=\frac{7-6.5}{0.58}\\\\z=\frac{0.5}{0.58}\\\\z = 0.86[/tex]

z = 0.86 has p value 0.1943

Thus, the required probability is 0.1943

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Dimensions of the lower floor with the given volume of 2380 cubic feet are given by : length = 34feet, width = 7feet, and height = 10 feet.

Let us consider 'y' be the width of the barn.

Lower floor with horse stall which was extends 5 feet from both the sides.

Width after having horse stall = x - 10

Barn's length is twice the barn's width

Length = 2x

Height is 7 feet less than the barn's width = x - 7

Volume = 2380 cubic feet

⇒Length × width × height = 2380

⇒ ( 2x ) (x -10 ) (x -7 ) = 2380

⇒(2x² -20x)(x-7) = 1190

⇒2x³ -34x² +140x -2380 =0

⇒ x = 17 , √70i, -√70i

x can not be imaginary.

⇒ x = 17feet ( approximately)

Required dimensions are:

Length : 2x = 34feet

Width : x -10 = 7 feet

Height : x - 7 = 10 feet

Therefore, for the given volume the required dimensions are 34feet, 7 feet , and 10 feet.

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Answer:

halfway between 862350 and 862360

Answer:

The equation of a line can be represented in the slope-intercept form, y = mx + b, where m is the slope of the line and b is the y-intercept.

Given that the line has a slope of 5 and passes through the point (-1,1) we can use the point-slope form of a linear equation, which is y - y1 = m(x - x1)

The point (-1,1) can be plugged into the equation:

y - 1 = 5(x + 1)

By simplifying and re-arranging the equation, we get:

y = 5x + 6

So the equation of the line that passes through the point (-1,1) and has a slope of 5 is: y = 5x + 6

Answer:

y = 5x+6

Step-by-step explanation:

Using the slope-intercept form of a line

y = mx+b  where m is the slope and b is the y-intercept

y = 5x+b

Substitute the point into the line.

1 = 5(-1) +b

1+5 = b

6=b

The equation is

y = 5x+6

Total cost of renting at Bowler World = $5 + $1.1x

Total cost of renting at Lucky Spares = $3 + $1.50x

The equation that can be used to determine the total cost of renting shoes at both locations is:

total cost = fixed cost + variable cost

Total cost of renting at Bowler World = $5 + $1.1x

Total cost of renting at Lucky Spares = $3 + $1.50x

Where

x = number of games played

In order to determine the number of games that would make the cost equal in both locations, the following steps would be taken:

$5 + $1.1x = $3 + $1.50x

Combine similar terms

$5 - $3 = $1.50x - $1.1x

$2 = $0.40x

Divide both sides of the equation by $0.4

x = 2 / 0.4

x = 5 games

Total cost = $5 + $1.1(5) = $5 + $5.5 = $10.50

The number of games that would make the cost equal in both locations is 5. The total cost is $10.50.

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The better buy for the shrimp based on the information will be the A. 2.24 pound bag.

From the information, Josh paid $11.96 for a 2.24 -pound bag of shrimp at one store and the following week, he paid $17.24 for a 3.12 -pound bag at another store.

The unit price when Josh paid $11.96 for a 2.24 -pound bag of shrimp will be:

= $11.96 / 2.24

= $5.34

The unit price when he paid $17.24 for a 3.12 -pound bag at another store will be:

= $17.24 / 3.12

= $5 53

Therefore, A is cheaper.

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Complete question

Josh paid $11.96 for a 2.24 -pound bag of shrimp at one store. The following week, he paid $17.24 for a 3.12 -pound bag at another store. Find the unit price for each bag. Then state which bag is the better buy based on the unit price. Round your answers to the nearest cent.

Answer:

She was given 1 free apple and paid for 15 apples.

Step-by-step explanation:

0.55x2=1.1

1.1x8=8.8

8.8/.55=16

16-1=15

And you know she paid for 15 apples and got 1 free.

Answer:

for any two points in the interval, a change in x results in a zero change in f(x)

Step-by-step explanation:

If vanilla cake has a diameter of 8 inches and chocolate cake has a diameter of 10 inches , then the circumference of vanilla cake is 25.12 inches and of chocolate cake is  31.4 inches .

The Circumference(C) of the circle can be found using formula: C = 2×π×r and r is the radius of the circle.

For the Vanilla cake, the diameter is 8 inches ;

and So , radius is = 8/2 = 4 inches.

The , Circumference of vanilla cake is = 2×π×4 = 8×3.14 inches.

= 25.12 inches .

For Chocolate cake, diameter is 10 inches ;

and radius is = 10/2 = 5 inches.

So , Circumference of chocolate cake is = 2×π×5 = 10×3.14 inches.

= 31.4 inches .

Therefore , To the nearest tenth, circumference of  vanilla cake is 25.13 inches and circumference of chocolate cake is 31.42 inches.

The given question is incomplete , the complete question is

A vanilla cake has a diameter of 8 inches. A chocolate cake has a diameter of 10 inches. What is the circumference the top surfaces of the two cakes to the nearest tenth? Use 3. 14 for π .

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A graph of the inequality is shown in the image attached below.

In this scenario, we would solve the given inequality by making m the subject of formula as follows;

-2 > m/6 - 7

By collecting like terms, we have the following:

-2 + 7 > m/6

5 > m/6

Cross-multiplying, we have:

30 > m

By re-writing the inequality, we have:

m < 30

Next, we would use an online graphing calculator to plot the inequality as shown in the graph attached below. Also, the circle is open because of the greater than (>) symbol.

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The statement "If we subtract 25 from a number, the result is 17" represented by the equation x - 25 = 17.

A formula known as an equation uses the equals sign (=) to express how two expressions are equal.

The given verbal statement is "If we subtract 25 from a number, the result is 17"

Now we have to convert to algebraic equation.

we subtract 25 from a number = x - 25

this is equal to 17

So,  If we subtract 25 from a number, the result is 17 means

x - 25 = 17

Therefore, the answer is x - 25 = 17.

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The complete question is:

Which equation represents this statement "If we subtract 25 from a number, the result is 17"?

(a) x − 17 = 25

(b) x − 25 = 17

(c) x + 17 = −25

(d) x − 17 = −25

The line of linear equation y = 8x - 48 is much steeper than the line of linear equation y = -x - 4-.

What is a linear equation?

A linear equation is one that has a degree of 1 as its maximum value. No variable in a linear equation, thus, has an exponent greater than 1. A linear equation's graph will always be a straight line.

The table of input and output values are given for the function.

The slope-intercept form of an equation/function is - y = mx + b

To find the slope m use the formula -

(y2 - y1)/(x2 - x1)

Substituting the values in the equation -

[16 - 32]/[8 - 10]

(-16)/(-2)

8

So, the slope point is obtained as m = 8.

The equation becomes - y = 8x + b

To find the value of b substitute the values of x and y in the equation -

32 = 8(10) + b

32 = 80 + b

b = 32 - 80

b = -48

So, the value for b is -48.

Now, the equation becomes -

y = 8x - 48

A graph has been plotted for the equation.

Similarly, the points for a line is given as (-6,2) and (-9,5).

The slope-intercept form of an equation/function is - y = mx + b

To find the slope m use the formula -

(y2 - y1)/(x2 - x1)

Substituting the values in the equation -

[5 - 2]/[-9 - (-6)]

(3)/(-9 + 6)

3/-3

-1

So, the slope point is obtained as m = -1.

The equation becomes - y = -x + b

To find the value of b substitute the values of x and y in the equation -

2 = -(-6) + b

2 = 6 + b

b = 2 - 6

b = -4

So, the value for b is -4.

Now, the equation becomes -

y = -x - 4

A graph has been plotted for the equation.

It is known that the larger the slope the steeper the line.

In the graph also it can be seen that the graph of line y = 8x - 48 is much steeper.

Therefore, the slope of line y = 8x - 48 is more steeper.

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The estimated age of the tomb of Sneferu is 8,330 years.

The age of the tomb can be estimated using the carbon-14 decay equation, which states that the amount of carbon-14 remaining after time t (in years) is equal to the initial amount of carbon-14 multiplied by 0.5^(t/5730).The decay equation for carbon-14 is A = A₀e⁻kt, where A₀ is the original amount of carbon-14, A is the amount of carbon-14 at time t, k is the decay constant, and t is the amount of time that has passed.

We can rearrange the equation to solve for t: t = -ln(A/A₀)/k. In this equation, A is the amount of carbon-14 found in the cypress beam, and A₀ is the amount of carbon-14 found in living cypress wood.

In this case, the initial amount of carbon-14 was 100%, and the remaining amount was 55%. Solving for t, we get t = (ln(55%)/ln(0.5))*5730 = 8,330 years.

Therefore, the estimated age of the tomb of Sneferu is 8,330 years.

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a) The circumference of the tire is 7.85 ft

b) About 673 times the tire will have to rotate to travel 1 mile.

The diameter of a tire is 2. 5 ft.

Let r represents the radius of the tire.

r = diameter/2

r = 2.5 / 2

r = 1.25 ft

a)  the circumference of the tire:

We know that the formula for the circumference of circle:

C = 2πr

So, the circumference of the tire would be,

C = 2 × π × r

C =  2 × π × 1.25

C = 7.85 ft

b) Let the tire will have to rotate n times in order to travel 1 mile.

We know that 1 mile = 5,280 ft

So, n = 5280 / 7.85

n = 672.6

n ≈ 673

Thus, the tire will have to rotate 673 times in order to travel 1 mile.

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The estimate of the product expression is 0.12

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

3.71 * 0.296

From the question, the numbers are to be rounded to the place of its leftmost nonzero digit.

So, when the numbers are rounded, we have

4 * 0.3

Evaluate the product

This gives

0.12

Hence, the solution is 0.12

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The probability of Sasha scoring at least one six is 11/36, and the probability of Sasha scoring no sixes is 25/36.

The total number of outcomes in which there is at least one 6 are:

(6,6), (6,1), (6,2), (6,3), (6,4), (6,5), (1,6), (2,6), (3,6), (4,6), (5,6).

So there are 11 cases in which at least one six appears in two die rolls.

The total number of outcomes can be discovered through the multiplication principle. There are 6 numbers (numbers 1–6) on the first die and the same 6 numbers on the second die, so there are a total of 36 possible outcomes.

The probability of at least one six-in-two die roll is 11/36.

The total number of outcomes in which there is no 6 are:

(5,1), (5,2), (5,3), (5,4), (5,5), (4,1), (4,2), (4,3), (4,4), (4,5), (3,1), (3,2), (3,3), (3,4), (3,5), (2,1), (2,2), (2,3), (2,4), (2,5), (1,1), (1,2), (1,3), (1,4), (1,5).

So there are 25 cases in which no six appear in two die rolls.

The total number of outcomes can be discovered through the multiplication principle. There are 6 numbers (numbers 1–6) on the first die and the same 6 numbers on the second die, so there are a total of 36 possible outcomes.

The probability of no six-in-two die roll is 25/36.

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The following is considered a LINEAR table is True .

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Based on the information provided, it can be concluded that for each meal the restaurant used 0.4166 kilograms of potato.

To calculate the quantity of potatoes used, you can use the following formula shown below:

Total of potatoes used / number of meals

2 1/2 kilograms of potatoes/ 6 meals

2 1/2 kilograms of potatoes is equivalent to 2.5 (1/2 = 0.5)

2.5 kilograms of potatoes/ 6 meals

0.4166

Therefore for each meal, the restaurant used 0.4166 kilograms of potatoes.

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Answer:

the answer is b

Step-by-step explanation:

The sine of the angle theta is 1/2√3

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

0 < θ < 90 and cosθ= 1/2

The above parameter mean that

sin(θ) = √(1 - cos²(θ))

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

sin(θ) = √(1 - 1/2²)

This gives

sin(θ) = √(3/4)

Take the square roots

sin(θ) = 1/2√3

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yes it is fair The probability of drawing matching blocks is 1/3

A probability is a number that reflects the chance or likelihood that a particular event will occur. Probabilities can be expressed as proportions that range from 0 to 1, and they can also be expressed as percentages ranging from 0% to 100%.

The probability of drawing matching blocks is 1/3

The probability is the measure of the likelihood of an event to happen. It measures the certainty of the event. The formula for probability is given by; P(E) = Number of Favorable Outcomes/Number of total outcomes.

four main types of probability exist: classical, empirical, subjective and axiomatic. Probability is synonymous with possibility, so you could say it's the possibility that a particular event will happen.

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The weight of a randomly selected pack of gum that has a z-score of 3.11, is 54.6 grams. So, the right option is D.

A Z-score can be used to calculate how much the data deviates from the mean. It shows how frequently the data is either above or below the mean. According to the formula,

Z = (X - μ)/σ

where, Z is the Z-score, X is the data point, μ is the mean and σ is the standard variable.

Z = 3.11, σ = 2.4, μ = 47.1

Z = (X - μ)/σ

Now putting the value

3.11 = (X - 47.1)/2.4

Multiply by 2.4 on both side

X - 47.1 = 3.11 X 2.4

X - 47.1 = 7.464

Add 47.1 on both side, we get

X = 54.564 grams

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The complete question is:

The weights of a pack of chewing gum for a certain brand have a mean of 47.1 grams and a standard deviation of 2.4 grams. What is the weight of a randomly selected pack of gum that has a z-score of 3.11?

39.6 grams

44.7 grams

49.5 grams

54.6 grams

The equivalence of the remainder following the division of 17 and 30 by N indicates that the largest value N can have is 30

The remainder term in a division of one value by a second value is the value which is less than the divisor, remaining after the divisor divides the dividend by a number of times indicated by the quotient.

The remainder following the division of 17 and 30 by the number N are the same.

Let R represent the remainder following the division of the integers 17 and 30 and let b represent the number of times N divides 30 than 17. Using the long division formula, we get;

17/N = Q + R/17

30/N = b·Q + R/17

30/N - 17/N = 13/N

The substitution property indicates that we get the following equation;

30/N - 17/N = b·Q + R/17 - (Q + R/17) = b·Q - Q

30/N - 17/N = b·Q - Q

13/N = b·Q - Q = (b - 1)·Q

13/N = (b - 1)·Q

The fraction 13/N which is equivalent to the product of (b - 1) and Q indicates that N is a factor of 13

13 is a prime number, therefore, the factors of 13 are 13 and N

Therefore, the possible values of N are 13 and 1

The largest value N can have is therefore, 13

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The factored form of the expression -9x^³ - 12x² - 4x is given as follows:

A. -x(3x + 2)².

The expression for this problem is defined as follows:

-9x^³ - 12x² - 4x.

The exponents of the expression are given as follows:

3, 2 and 1.

The lowest exponent is of:

1.

Simplifying the lowest exponent, the expression is given as follows:

-x(9x² + 12x + 4)

The inner expression can be obtained with the square of the sum, as follows:

9x² + 12x + 4 = (3x + 2)².

Meaning that the simplified expression is of:

-x(3x + 2)².

Which is option A.

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