Mary is 3 times as old as her son. In 12 years Mary will ve twice as old as her son. How old are each of them now

Answer:

2, 3, 5, 9, 17

Step-by-step explanation:

using the recursive rule [tex]a_{n}[/tex] = 2[tex]a_{n-1}[/tex] - 1 with a₁ = 2

a₁ = 2

a₂ = 2a₁ - 1 = 2(2) - 1 = 4 - 1 = 3

a₃ = 2a₂ - 1 = 2(3) - 1 = 6 - 1 = 5

a₄ = 2a₃ - 1 = 2(5) - 1 = 10 - 1 = 9

a₅ = 1a₄ - 1 = 2(9) - 1 = 18 - 1 = 17

the first 5 terms are 2 , 3 , 5 , 9 , 1 7

Answer:

36 coins

Step-by-step explanation:

10 percent is 18 coins. so just double that.

Answer:

Step-by-step explanation:

Total coin Eva has = 180

20% of her coins are represented by 20% of the 180

= 20/100 * 180

=0.2 * 180= 36

36 coins represent 20% of Eva's coins.

A percentage is a number or ratio that represents a fraction of 100. It is used to describe numbers. It is a dimensionless quantity. A percentage is denoted by the % symbol.

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Answer:

True

Step-by-step explanation:

Since C has to add up to 180 and we already have 150 we can assume that that other angle is 30. The sum of angles in a triangle always has to equal 180. 120+30=150 meaning B also equals 30. B+A=150 therefore making it true.

The standard deviation of the mean of the 25 newborn babies is approximately 0.4 pounds, rounded to 1 decimal place.

To find the standard deviation ,we will use the formula for the standard

deviation of the sampling distribution of the sample mean:

Standard deviation of the sample mean = σ / √n

Here, σ is the population standard deviation and

n is the sample size.

Given the population standard deviation (σ) is 2 pounds and the sample size (n) is 25 newborns, we can plug in the

values into the formula:

Standard deviation of the sample mean = 2 / √25

Standard deviation of the sample mean = 2 / 5

Standard deviation of the sample mean = 0.4

So, the standard deviation of the mean of the 25 newborn babies is approximately 0.4 pounds, rounded to 1 decimal place.

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When a confounding variable is present in an experiment, one cannot tell whether the results were due to the independent variable or the dependent variable. The correct option is a) independent variable or the dependent variable.

A confounding variable is any variable that influences the dependent variable or response variable and is also

correlated with the independent variable. Because it is difficult to determine which variable is causing changes in the

dependent variable, it is also known as a confounding variable.

In other words, a confounding variable is a variable that can affect the dependent variable in an experiment, making it

impossible to determine the relationship between the independent variable and the dependent variable.

Therefore, when a confounding variable is present in an experiment, one cannot tell whether the results were due to

the independent variable or the dependent variable.

Consequently, researchers must take steps to identify and eliminate or control the effect of confounding variables to obtain valid and reliable results.

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The distance a swimmer will travel if they swim from one corner to the opposite corner of an Olympic-size swimming pool is approximately 62.2 meters

The distance a swimmer will travel if they swim from one corner to the opposite corner of an Olympic-size swimming pool is approximately 62.2 meters. This can be calculated using the Pythagorean theorem, which states that the square of the hypotenuse of a right triangle is equal to the sum of the squares of the other two sides. In this case, the length of the pool is one side of the right triangle, the width of the pool is the other side of the right triangle, and the distance the swimmer travels is the hypotenuse.

Using the Pythagorean theorem, we can calculate the distance the swimmer travels as follows:

a² + b² = c²

where a is the length of the pool (50 meters), b is the width of the pool (25 meters), and c is the distance the swimmer travels.

To solve for c, we can plug in the values for a and b and simplify as follows:

50² + 25² = c²

500 + 625 = c²

125 = c²√3

125 = c

Approximately 62.2 meters (rounded to one decimal place)

Therefore, the distance a swimmer will travel if they swim from one corner to the opposite corner of an Olympic-size swimming pool is approximately 62.2 meters.

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Answer:

8 fluid ounces

Step-by-step explanation:

1 Cup is equal to 8 fluid ounces in US Standard Volume. 1 metric cup is 250 milliliters (which is about 8.5 fluid ounces). A US cup is about 237-240 mL

She could solve for (x+3)² and find two solutions, x = (-3 + √(33/2)) / 2 and x = (-3 - √(33/2)) / 2.

it's a second-degree quadratic equation which is an algebraic equation in x. Ax² + bx + c = 0, where a and b are the coefficients, x is the variable, and c is the constant term, is the quadratic equation in its standard form.

The three steps that Inga could use to solve the quadratic equation 2x² + 12x – 3 = 0 are:

1. Use the quadratic formula: Inga could use the quadratic formula x = (-b ± √(b² - 4ac)) / 2a, where a = 2, b = 12, and c = -3.

2. Factor the quadratic expression: Inga could factor the quadratic expression into (2x - 1)(x + 3) = 0 and then use the zero product property to find the solutions x = 1/2 and x = -3.

3. Complete the square: Inga could use the method of completing the square by adding and subtracting (6/2)² = 9 to the left side of the equation, giving 2(x+3)² - 33 = 0. Then she could solve for (x+3)² and find two solutions, x = (-3 + √(33/2)) / 2 and x = (-3 - √(33/2)) / 2.

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After simplifying the given functiοn F=2(3+5x)+8(7-x)+4(x-1) the answer is F = 2x + 58.

In mathematics, a functiοn frοm a set X tο a set Y assigns each element οf X exactly οne element οf Y. The sets X and Y are referred tο as the functiοn's dοmain and cοdοmain, respectively.

Initially, functiοns represented the idealized relatiοnship between varied quantities and οther variables. Fοr instance, time affects a planet's pοsitiοn. In the past, the idea was develοped with the infinitesimal calculus at the end οf the 17th century, and until the 19th century, the functiοns that were taken intο cοnsideratiοn were differentiable (that is, they had a high degree οf regularity).

Expanding and simplifying the expressiοn F:

F = 2(3) + 2(5x) + 8(7) - 8(x) + 4(x) - 4(1)

F = 6 + 10x + 56 - 8x + 4x - 4

F = 2x + 58

Therefοre, F = 2x + 58.

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Complete question is:

Simplify F=2(3+5x)+8(7-x)+4(x-1).

The percentage of data between 13.8 and 30.2 in a normally distributed data set with a mean of 22 and a standard deviation of 4.1 is approximately 94.19%.

To solve this problem, we can first standardize the values of interest using the standard normal distribution formula, z = (x - μ) / σ, where x is the value of interest, μ is the mean, and σ is the standard deviation.

For the lower value of 13.8, we have z = (13.8 - 22) / 4.1 = -1.95. For the upper value of 30.2, we have z = (30.2 - 22) / 4.1 = 2.05.

Next, we can use a calculator to find the area between these two z-scores. Alternatively, we can use the complement rule to find the area to the left of -1.95 and the area to the right of 2.05, and subtract their sum from 1.

Using a calculator, we find that the area between -1.95 and 2.05 is approximately 0.9419 or 94.19%. Therefore, approximately 94.19% of the data falls between 13.8 and 30.2 in this normally distributed data set.

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The missing side has a length of about 46.2 units

What is trigonometric ratio of tangent (tan)?

[tex] \tan( \theta) [/tex] = opposite/adjacent

Here [tex] ( \theta) [/tex] is opposite angle of base of the triangle.

The base is the side opposite to the right angle and has a length of 14 units (given).

The side opposite to the angle of 17° is the "opposite" side.

The side adjacent to the angle of 17° is the "adjacent" side.

We want to find the length of the missing side (let's call it "x"). To do this, we can use the trigonometric ratio of tangent (tan), which relates the opposite and adjacent sides:

tan(17°) = opposite/adjacent

So, tan(17°) = opposite/x

We can rearrange this equation to solve for x,

x = opposite / tan(17°)

Plugging in the values we have,

x = 14 / tan(17°)

Using a calculator, we find that tan(17°) is approximately 0.303,

So,x = 14 / 0.303 ≈ 46.2

Therefore, the missing side has a length of about 46.2 units (rounded to the nearest tenth).

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The probability that an arriving call will be routed by the voicemail system is given by[tex]P(Y = 0) = e^(-0.1067) * 0.1067^0 / 0! = 0.8982,[/tex]rounded to four decimal places.

Since phone calls arrive at a rate of 16 per hour, the arrival rate of calls in minutes is 16/60 = 0.2667 calls per minute. We can model the arrival rate of calls as a Poisson distribution with parameter λ = 0.2667.

The time for the voicemail system to route a call follows an exponential distribution with a mean of 2.5 minutes. Let X be the time it takes to route a call. Then X follows an exponential distribution with parameter μ = 1/2.5 = 0.4.

We want to find the probability that an arriving call will be routed by the voicemail system. This is equivalent to finding the probability that there are no calls being routed by the voicemail system when a call arrives. Let Y be the number of calls being routed by the voicemail system. Then Y follows a Poisson distribution with parameter λμ = 0.2667 x 0.4 = 0.1067.

Therefore, the probability that an arriving call will be routed by the voicemail system is given by

[tex]P(Y = 0) = e^(-0.1067) * 0.1067^0 / 0! = 0.8982,[/tex]  rounded to four decimal places.

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The output of the function g(x) = [tex]3^{(\frac{x}{2} )}[/tex] when x = 2 is 3.

g(x) is a function as defined as follows:

g(x) = [tex]3^{(\frac{x}{2} )}[/tex]

If we input n2 into the g(x), the output g(x) can be gotten as follows:

Therefore,

g(x) = [tex]3^{(\frac{x}{2} )}[/tex]

where

x = 2

Therefore,

[tex]3^{(\frac{2}{2} )}[/tex] = 3¹

Therefore,

the output is 3.

g(2) = 3

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Answer: 1. Chord 2. Diameter

Answer:

Step-by-step explanation:

Since A and G are on a line thats not in the middle of the circle, the clear answer would be a chord

Since C is a point on the middle of the circle and B is at the end of the circle, the answer would be radius

Assuming the coordinates of point A are (3, 5): we would have the following results.

1. To reflect over the x-axis: the x-coordinate remains the same and the y-coordinate changes sign. So point B will have the same x-coordinate as point A (3), but the y-coordinate will be -5. Therefore, the coordinates of point B are (3, -5).

2. To reflect over the y-axis: the y-coordinate remains the same and the x-coordinate changes sign. So point C will have the same y-coordinate as point A (5), but the x-coordinate will be -3. Therefore, the coordinates of point C are (-3, 5).

3. To translate: add the given values to the x and y coordinates. So point D will have an x-coordinate of 3 + 3 = 6, and a y-coordinate of 5 + 4 = 9. Therefore, the coordinates of point D are (6, 9).

4. To rotate 180 degrees clockwise: flip the signs of both the x and y coordinates and then swap them. So point E will have an x-coordinate of -5 and a y-coordinate of -3. Therefore, the coordinates of point E are (-5, -3).

Plotting these points on a graph,
A (3, 5)

B  (3, -5)

C  (-3, 5)

D (6, 9)

E  (-5, -3)

we get the attached graph.

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Answer:

2/5 or 0.4, which is also equivalent to a 40% chance.

Step-by-step explanation:

To determine the theoretical probability of drawing a prime number from the numbers 2 through 16, we need to first identify the prime numbers in this range. The prime numbers between 2 and 16 are 2, 3, 5, 7, 11, and 13.

There are a total of 15 numbers in the hat, and 6 of them are prime. Therefore, the probability of drawing a prime number can be calculated as:

Probability of drawing a prime number = Number of favorable outcomes / Total number of possible outcomes

Number of favorable outcomes = 6 (since there are 6 prime numbers in the range of 2 through 16)

Total number of possible outcomes = 15 (since there are 15 numbers in the hat)

So, the probability of drawing a prime number is:

Probability of drawing a prime number = 6 / 15

Simplifying this fraction by dividing both numerator and denominator by 3, we get:

Probability of drawing a prime number = 2 / 5

Therefore, the theoretical probability of drawing a prime number from the numbers 2 through 16 is 2/5 or 0.4, which is also equivalent to a 40% chance.

Answer:

None of them, 3x + 15 is correct.

Step-by-step explanation:

In order to apply the distributive properly correctively, we need to multiply everything in the parentheses. For an example, lets look at the given expression:

[tex]3(x+5)[/tex]

We multiply everything in the parentheses by 3

[tex]3x+15[/tex]

Looking at out choices, none of them uses the distributive property correctly.

The rate at which water is being pumped into the tank is 11,760 cm3/min.

          V = (1/3)πr2h

          Using similar triangles:

          (r / 2) = (2 / 6)

          r = 2/3 * 4r = 8/3 cm

          dV / dt = (πr2 / 3)dh / dt

         dV / dt = pump rate - leak rate

      = pump rate - 10,500 cm3/mindh / dt

      = 20 cm/minr = 8/3 cm

        pump rate - 10,500 = (π(8/3)2 / 3) * 20pump rate - 10,500

     = 2114.67pump rate

     = 11,760 cm3/min

Therefore, the rate at which water is being pumped into the tank is 11,760 cm3/min.

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The value of the boxes, A , B and C are 22/4, 15/4 and 9 1/4 respectively

Note that from the information given, we have that the number in a box is the sum of the two numbers below it.

Then, we can deduce that;

A = The sum of the two mixed fractions, 3 1/4 and 2 1/4

B = The sum of the two mixed fractions, 2 1/4 and 1 1/2

Now, add the values

A = 3 1/4 + 2 1/4

convert to improper fractions

A = 13/4 + 9/4

Add the values

A = 22/4

B = 2 1/4 + 1 1/2

convert to improper fractions

B = 9/4 + 3/2

B =9 + 6 /4

B = 15/4

Then , the value of C = A + B

C = 22/4 + 15/4

C = 37/4

C = 9 1/4

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Answer:

Therefore, the time for the return trip is:

≈ 5.306 seconds

Step-by-step explanation:

Let's start by finding the speed of the boat. We know that the boat travels 400m at a constant speed, so we can use the formula:

Speed = Distance / Time

Speed = 400m / Time (for one-way trip)

Let's assume that the time for the one-way trip is t. Then we can rewrite the speed formula as:

Speed = 400m / t

Now let's find the time for the return trip. We know that the boat travels the same route at the same speed for 2 minutes, which is equivalent to 120 seconds. This means that the distance traveled on the way back is:

Distance = Speed x Time

Distance = (400m / t) x 120 seconds

Distance = 48000m / t

We also know that when Pilar increases the boat's speed by 10 m/min, the return trip is 60 seconds faster. This means that the time for the return trip is:

t - 60 seconds

Using the same formula as before, the distance traveled on the return trip is:

Distance = (400m / (t + 1/2)) x (t - 60) seconds

Distance = (400m / (t + 1/2)) x (t - 60/60) minutes

Distance = 400m x (t - 60/60) / (t + 1/2) minutes

Now we know that the distance traveled on the way back is equal to the distance traveled on the way there:

48000m / t = 400m x (t - 60/60) / (t + 1/2)

Simplifying this equation, we get:

48 / t = 4 x (t - 1/3) / (t + 1/2)

Multiplying both sides by (t + 1/2), we get:

48(t + 1/2) / t = 4(t - 1/3)

Simplifying this equation, we get:

96 / t = 4t - 4/3

Multiplying both sides by t, we get:

96 = 4t^2 - 4/3t

Multiplying both sides by 3, we get:

288 = 12t^2 - 4t

Rearranging this equation, we get

12t^2 - 4t - 288 = 0

Dividing both sides by 4, we get:

3t^2 - t - 72 = 0

Using the quadratic formula, we can solve for t:

t = [1 ± sqrt(1 + 4(3)(72))] / 6

t = [1 ± sqrt(865)] / 6

Since t must be positive, we take the positive root:

t ≈ 6.366

Therefore, the time for the return trip is:

t - 60 seconds ≈ 6.366 - 60 seconds ≈ 5.306 seconds

Answer:

Sure, here are the absolute value equations of 0 and 8, 5 and 17, and -4 and 6 in the form $|x-c|=d$:

* For 0 and 8, $|x-0|=8$. This means that $x-0=8$ or $x-0=-8$. Solving for $x$, we get $x=8$ or $x=-8$.

* For 5 and 17, $|x-5|=17$. This means that $x-5=17$ or $x-5=-17$. Solving for $x$, we get $x=22$ or $x=-12$.

* For -4 and 6, $|x-(-4)|=6$. This means that $x-(-4)=6$ or $x-(-4)=-6$. Solving for $x$, we get $x=10$ or $x=-2$.

I hope this helps! Let me know if you have any other questions.

Step-by-step explanation:

Answer:

75

Step-by-step explanation:

a) The area of the square  for side length [tex]3[/tex] is [tex]9[/tex][tex]cm^{2}[/tex].

The area of the square for side length [tex]100[/tex] is [tex]10000[/tex][tex]cm^{2}[/tex]

The area of the square for side length  [tex]25[/tex] is [tex]625cm^{2}[/tex].

The area of the square  for the side length [tex]s[/tex] is   [tex]s^{2}cm^{2}[/tex].

b) No the side length of the square and area are not directly proportional.

The area of a square is the amount of space enclosed within the square, and it can be calculated using the formula A = [tex]s^{2}[/tex], where A is the area and s is the length of one side of the square.

According to the given information

The area of a square is the amount of space enclosed within the square, and it can be calculated using the formula A =[tex]s^{2}[/tex]

[tex]A = s^{2} = 3^{2} = 9cm^{2}[/tex]

[tex]A = s^{2} = 10^{2} = 10000cm^{2}[/tex]

[tex]A = s^{2} = 25^{2} = 625cm^{2}[/tex]

[tex]A = s^{2} = s^{2} = s^{2} cm^{2}[/tex]

Therefore area of the square are [tex]9cm^{2} ,10000cm^{2}, 625cm^{2} ,s^{2}cm^{2}[/tex]

Therefore the side length of the square and area are not directly proportional they are proportional to the square root of area.

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The number 57 belongs to the sets Z, Q, and R, but not N or W.

What are natural numbers ?

Natural numbers are the counting numbers that we use to represent quantities and perform arithmetic operations. These are the numbers that we use to count objects, such as apples, books, or people.

The number 57 belongs to the following sets of numbers:

N (the natural numbers): No, because 57 is not a counting number.

W (the whole numbers): No, because 57 is not a non-negative integer.

Z (the integers): Yes, because 57 is an integer (a positive integer, in fact).

Q (the rational numbers): Yes, because 57 can be written as a ratio of two integers (57/1).

R (the real numbers): Yes, because every rational number is also a real number.

Therefore, the number 57 belongs to the sets Z, Q, and R, but not N or W.

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Complete question -

Answer:

y = 1/3x - 5

Step-by-step explanation:

The equation is y = mx + b

m = the slope

b = y-intercept

m = 1/3

Y-intercept is located at (0, -5)

So, the equation of the line is y = 1/3x - 5

According to the anime history, the best anime of all time with no haters is fullmetal alchemist brotherhood.

Anime is a style of animation that originated in Japan and has become popular worldwide. It is characterized by distinctive visual styles, such as colorful graphics, exaggerated features of characters, and expressive facial expressions. Anime covers a wide range of genres, including action, adventure, drama, comedy, romance, b fiction, fantasy.

There are numerous anime series that are widely popular and have received critical acclaim, such as "Fullmetal Alchemist: Brotherhood," "Attack on Titan," "Death Note," "Cowboy Bebop," "Dragon Ball Z," "Naruto," "One Piece," "Spirited Away," "Akira," "Ghost in the Shell," and many more.

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Answer:

121f + 39

Step-by-step explanation:

Simplify the expression:

[tex]4(32f+1)-7(f+5)[/tex]

Use the distributive property to distribute 4 and 7

[tex]128f+4-7f+35[/tex]

Lets rearrange terms to make it easier

[tex]128f+-7f+4+35[/tex]

Add like terms and integers

[tex]121f+39[/tex]