What is the vertical distance between (2, 11/3)
and (2, - 4/3)?

Answer:$10

Step-by-step explanation: We are given the ratio 9:1. Meaning for every 9 dollars he spends on healthy food, he can spend a dollar on snacks. If he intends on paying 100 dollars total, how much will he spend on snacks?

He would have spent 90 dollars on healthy food, and 10 dollars on snack food. Totaling 100 dollars.

The function  [tex]f(x)=(x-5)(x-2)(x+1)[/tex] represents the graph.

What is graph?

A graph is a visual representation of data or a mathematical function, usually plotted on a coordinate plane. It is a way to display information in a clear and concise manner, making it easier to analyze and interpret.

From the graph, it can be observed that the function intersects the x-axis at three points, namely x=-1, 2, and 5. Therefore, these values are considered to be the zeros of the function.

According to the definition, if c is a zero of a function f(x), then (x-c) is a factor of f(x). Applying this definition, we can infer that (x+1), (x-2), and (x-5) are the factors of the given function.

In summary, the zeros of the function are -1, 2, and 5, and the corresponding factors of the function are (x+1), (x-2), and (x-5).

Therefore the function  [tex]f(x)=(x-5)(x-2)(x+1)[/tex] represents the graph.

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For any value of inequality for t less than or equal to 5 minutes, Routine #1 will burn at most as many calories as Routine #2.

What is inequality?

In mathematics, an inequality is a statement that compares two quantities using symbols such as "<" (less than), ">" (greater than), "<=" (less than or equal to), ">=" (greater than or equal to), or "!=" (not equal to).

Let's start by calculating the total number of calories burned in each routine as a function of the number of minutes spent running:

Routine #1:

Total calories burned = 24 + 15.5t

Routine #2:

Total calories burned = 52 + 9.9t

To find the point where Routine #1 burns at most as many calories as Routine #2, we need to solve the inequality:

24 + 15.5t ≤ 52 + 9.9t

Simplifying this inequality, we get:

5.6t ≤ 28

Dividing both sides by 5.6, we get:

t ≤ 5

Therefore, for any value of t less than or equal to 5 minutes, Routine #1 will burn at most as many calories as Routine #2.

So the answer is: t ≤ 5.

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Answer: 24

Step-by-step explanation:

Write out problem using Pythagorean Theorem: [tex]7^2+x^2=(x+1)^2[/tex]

Simplify and expand right side: [tex]49+x^2=x^2 + 2x + 1[/tex]

Subtract [tex]x^2[/tex] from both sides: [tex]49 = 2x + 1[/tex]

Subtract 1 from both sides: [tex]48=2x[/tex]

Divide by 2 on both sides: [tex]24 = x[/tex]

[tex]x = 24[/tex]

A burrito costs $2 at Taco Hut. Let's use "b" to represent the cost of a burrito and "t" to represent the cost of a taco.

From the problem, we know that:

4b + 5t = 13 (for Clark)

5b + 3t = 13 (for Bruce)

We want to determine the cost of a burrito, so we can solve for "b" using the second equation:

[tex]5b + 3t = 13\\5b = 13 - 3\\b = (13 - 3t)/5[/tex]

Now we can substitute this expression for "b" into the first equation:

[tex]4b + 5t = 13\\4[(13 - 3t)/5] + 5t = 13\\52/5 - 12t/5 + 5t = 13\\52 - 12t + 25t = 65\\13t = 13\\t = 1[/tex]

So we know that a taco costs $1. Now we can substitute this value into either of the original equations to solve for "b":

[tex]5b + 3t = 13\\5b + 3(1) = 13\\5b = 10\\b = 2[/tex]

Therefore, a burrito costs $2 at Taco Hut.

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The sum of the first 10 terms of the geometric progression that is given in the question is 1023.

What is geometric progression ?

Geometric progression, also known as geometric sequence, is a sequence of numbers in which each term after the first is obtained by multiplying the preceding term by a fixed constant. This fixed constant is called the common ratio.

The given series is a geometric progression, where each term is obtained by multiplying the preceding term by 2. The first term is 1, and the common ratio is 2.

The sum of the first n terms of a geometric progression is given by the formula:

[tex]S_n = a(1 - r^n) / (1 - r)[/tex]

where a is the first term, r is the common ratio, and n is the number of terms.

Using this formula, we can find the sum of the first 10 terms of the given series as:

[tex]S_{10} = 1(1 - 2^{10}) / (1 - 2)[/tex]

[tex]= 1(1 - 1024) / (-1)[/tex]

[tex]= 1023[/tex]

Therefore, the sum of the first 10 terms of the series 1 + 2 + 4 + 8... is 1023.

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the interval where both F(x) and g(x) are increasing is x < 0, which can be represented on the number line as follows:

To find the interval where both functions F(x) and g(x) are increasing, we need to determine where the derivative of each function is positive. A function is increasing when its derivative is positive, which means that the function is becoming larger as x increases.

The derivative of F(x) can be found by applying the derivative rules for absolute value and addition, which gives us:

F'(x) = 3x/|x|

Now, we need to determine where F'(x) is positive. This occurs when either 3x is positive and |x| is positive, or when 3x is negative and |x| is negative. Therefore, F'(x) is positive for x > 0 and x < 0.

Next, we need to find the derivative of g(x) by applying the derivative rules for subtraction and multiplication, which gives us:

g'(x) = -1 + 8

Simplifying the expression, we get:

g'(x) = 7

Since g'(x) is a constant, it is always positive, which means that g(x) is increasing for all values of x.

To find the interval where both F(x) and g(x) are increasing, we need to identify where both F'(x) and g'(x) are positive. This occurs when x < 0, as this satisfies the condition for F'(x) being positive, and g'(x) is always positive.

Therefore, the interval where both F(x) and g(x) are increasing is x < 0, which can be represented on the number line as follows:

     <=====o------------------------>

         x<0                    x>0

In this interval, both functions are increasing as x becomes more negative.

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The percent that reported mushroom as their favorite from the pizza shop survey would be 10 %.

The percent that instead reported cheese or pepperoni as their favorite is 62.5 %.

Out of 400 people, the number that would say their favorite was sausage is 50 people .

The percent that prefer mushroom would be:

= Number of those who chose mushroom / Number surveyed

= 8 ( 35 + 8 + 15 + 12 + 10 )

= 8 / 80

= 10 %

The percentage that instead chose cheese or pepperoni:

= ( 15 + 35 ) / ( 35 + 8 + 15 + 12 + 10 )

= 50 / 80

= 62.5 %

The number out of 400 that would be expected to choose sausage :

= 10 / ( 35 + 8 + 15 + 12 + 10 ) x 400

= 50 people

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The required length of y representing the length of the cut piece from each corner of triangle to form regular octagon is equal to 2√2cm.

Let us consider the length of the side of the square card be x

Cut the corners of the triangle of length y cm.

Then as triangles at the corner are right angled triangle.

Using Pythagoras theorem we have,

Each side of the regular octagon is same as hypotenuse .

Hypotenuse = √y² + y²

⇒Hypotenuse = y√2

Length of each of regular octagon = y√2

Perimeter of the octagon = 8y√2

⇒8y√2 = 32

⇒ y = 4/√2

⇒ y = 2√2cm.

Therefore, the length of y with the given perimeter of the regular octagon is equal to 2√2cm.

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Answer:

6 carnivore's and 18 herbivore's

Step-by-step explanation:

The probability that no more than four of the college graduates plan to pursue a graduate degree is approximately 0.1437. b. X= 7 = 0.2004.

With a set number of independent trials, each of which has just two potential outcomes—success or failure—a binomial distribution defines the number of successes. The chance of success, represented by p, and the number of trials, denoted by n, are the two factors that define the distribution.

Given that, 58% of recent college graduates plan on pursuing a graduate degree.

Using the binomial probability formula we have:

[tex]P(X \leq 4) = \sum (i = 0 \to 4) (n C i) * p^i * (1 - p)^{(n-i)}\\\\[/tex]

Here, n = 13, p = 0.58.

[tex]P(X \leq 4) = Σ(i = 0 \to 4) (13 C i) * 0.58^i * (1 - 0.58)^{(13-i)}= 0.1437[/tex]

Hence, the probability that no more than four of the college graduates plan to pursue a graduate degree is approximately 0.1437.

b. For X = 7:

[tex]P(X = 7) = (13 C 7) * 0.58^7 * (1 - 0.58)^{(13-7)}= 0.2004[/tex]

Hence, the probability that exactly seven of the college graduates plan to pursue a graduate degree is approximately 0.2004.

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The ratio of black and white keys of piano give correct values of A, B, C as 9, 52, 130.

The ratio of black to white keys of Piano of different sizes are as follow,

Black      A      36        63      90

White     13      B          91        C

From the table of black and white keys relation of proportionality is equal to,

( A / 13 ) = ( 36 / B ) = ( 63 / 91 ) = ( 90 / C )

This implies ,

( A / 13 ) = ( 63 / 91 )  

⇒ A = ( 63 / 91 ) × 13

⇒ A = ( 9 / 13 ) × 13

⇒ A = 9

Similarly,

( 36 / B ) = ( 63 / 91 )

⇒ B = 36 × ( 91 / 63 )

⇒ B = 36 × ( 13 / 9 )

⇒ B = 52

And

( 63 / 91 ) = ( 90 / C )

⇒ C = 90 × ( 91 / 63 )

⇒ B = 90 × ( 13 / 9 )

⇒ B = 130

Therefore, the correct values of A , B, C using the ratio of black and white keys of the piano is equal to 9, 52, 130.

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The above question is incomplete, the complete question is:

The table below shows the ratios of black to white keys on pianos of various sizes.

Black A 36 63 90

White 13 B 91 C

Determine which table has the correct values for A, B, and C.

The exponential function [tex]P(t) = P0 \times 1.04^t[/tex] represents the exponential growth of Option C: A town's population grows at a rate of 4% every year.

What is an exponential function?

The formula for an exponential function is [tex]f(x) = a^x[/tex], where x is a variable and a is a constant that serves as the function's base and must be bigger than 0.

The context that represents exponential growth is "A town's population grows at a rate of 4% every year."

Exponential growth occurs when a quantity grows at an increasing rate over time, which is exactly what is happening with the population of the town.

As the population grows, the growth rate also increases, resulting in an exponential increase over time.

Let P(t) be the population of the town after t years, where t is a positive integer.

The exponential function that models the population growth is -

[tex]P(t) = P0 \times (1 + r)^t[/tex]

where P0 is the initial population, r is the growth rate as a decimal, and t is the time in years.

In this case, the growth rate is 4% per year, which can be written as a decimal as r = 0.04.

Therefore, the exponential function for the town's population growth is -

[tex]P(t) = P0 \times (1 + 0.04)^t[/tex]

Simplifying the expression, we get -

[tex]P(t) = P0 \times 1.04^t[/tex]

This function can be used to calculate the population of the town after a given number of years, assuming the growth rate remains constant.

In contrast, the other contexts represent either a steady decrease (town's population shrinking at a rate of 8.1% per year and the radioactive compound decaying at a rate of 5% per hour) or a linear increase (taxi charges a flat fee of $3.00 for pick-up, then an additional fee of $2.75 per mile).

Therefore, the exponential growth is displayed by town's population growing 4% every year.

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The elimination of the equations 18x-6y=-20 and -9x+3y=15 is 0 = 10, which is a contradiction. This means that there is no solution to the system of equations.

What is an elimination?

To eliminate one of the variables, we need to manipulate one or both of the equations so that when we add them together, one of the variables is eliminated.

Let's start with the given equations:

18x - 6y = -20

-9x + 3y = 15

We can see that the coefficients of y in both equations are opposite, which means we can eliminate y by adding the two equations together. However, we need to make sure the coefficients of y have the same absolute value, so we'll multiply the second equation by 2:

18x - 6y = -20

-18x + 6y = 30

Now we can add the two equations together:

0x + 0y = 10

This equation simplifies to 0 = 10, which is a contradiction. This means that there is no solution to the system of equations. In other words, the two equations represent two parallel lines that never intersect.

Alternatively, we can recognize that the two equations represent the same line when simplified, since the second equation is simply half of the first equation. In this case, there are infinitely many solutions, since any point on the line satisfies both equations.

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Complete question is: The elimination of the equations 18x-6y=-20 and -9x+3y=15 is 0 = 10.

Thus, the two positive whole numbers that are greater than one multiply to 576 and share only the number one in common is 5.

One of the categories that mathematicians have created for numbers is titled whole numbers, and it contains all of the numbers from 0 to infinity.

The specific class or collection of numbers known as whole numbers includes:

Two positive whole numbers greater than 1 are 2 and 3.

2 and 3 does not have any common factor except 1.

sum of 2 and 3 = 5

Thus, the two positive whole integers that are greater than one multiply to 576 and share only the number one in common is 5.

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Answer:

1. irrational

2. irrational

3. rational

4. rational

5. irrational

6. rational

Step-by-step explanation:

A rational number includes any whole number, fraction, or decimal that ends or repeats. An irrational number is any number that cannot be turned into a fraction.

1.) pi is a never ending number which means that, according to the definition above, it must be IRRATIONAL

2.) the line above the 46 means that it is repeating, making it IRRATIONAL

3.) the square root of 100 is 10, making it RATIONAL

4.) -16 is an integer (a whole number that can be positive, negative, or zero), making it RATIONAL

5.) the square root of 21 results in a long decimal that cannot be converted into a fraction, by the definition above, it is IRRATIONAL

6.) 10 is a whole number, making it RATIONAL

John's parents deposited 1000 into a savings account as a college fund when he was born. We need to find out how much John will have in this account after 18 years at a yearly simple interest rate of 3.25%.

We can use the formula for simple interest to solve this problem.

The formula for simple interest is:

I = PRT

Where,I = interest

P = principal (the initial amount of money)

R = rate of interest (as a decimal)

T = time (in years)

We are given that John's parents deposited 1000 when he was born. So, P = 1000. The interest rate is 3.25% per year, which is 0.0325 as a decimal. And we are given that the time is 18 years, so T = 18 years.Using the formula for simple interest, we can find the amount of interest earned:

I = PRTI = (1000)(0.0325)(18)I = 585

We can then add the interest earned to the principal to find the total amount of money in the account after 18 years:

A = P + IA = 1000 + 585A = 1585

Therefore, John will have 1585 in this account after 18 years at a yearly simple interest rate of 3.25%.

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Exact coordinates of the terminal point (x, y) are (-3.40, 4.71).

Let's dive deeper into the details below.

The angle below has a measure of 5.8 radians. The exact coordinates of the terminal point (x, y) can be determined by using trigonometry.
First, we must remember that the formula for the x-coordinate is x = r cos θ, where r is the length of the radius and θ is the measure of the angle. Therefore, we can calculate the x-coordinate by plugging in the radius (which is given) and the measure of the angle (5.8 radians) into the formula:
x = 5.8 cos (5.8) = 5.8 × -0.5806 = -3.40
Now, we must use the formula for the y-coordinate which is y = r sin θ. Plugging in the radius and the measure of the angle, we can calculate the y-coordinate:
y = 5.8 sin (5.8) = 5.8 × 0.8139 = 4.
Therefore, the exact coordinates of the terminal point (x, y) are (-3.40, 4.71).

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Answer:

Step-by-step explanation:

First you need to find the balance amount that she paid in instalments which is 42000 * 15% which is equalled to 6300.

Then you need to minus 42000 - 6300 as 630l is the price she paid as cash deposit which is equalled 35700.

Now, to find the interest the formula is I = p * r/100 which equalled 7890 for a year. To calculate her monthly instalments, you have to divide 7890 divided by 12 months which equals 665.

The equation 24÷4=6 can be thought of as 24 broken into 4 groups of 6 each. This can be shown mathematically as follows: 24/4 = 6.

The division 24 ÷ 4 = 6 can be represented as 24 divided into 4 groups of 6 each. Therefore, each group contains 6 elements.

Another way to represent this division is by using a division box. In this case, 24 is the dividend, 4 is the divisor, and 6 is the quotient. Here's how to write it in the division box format:``` 6|24----4```The divisor is outside the division box, while the dividend is inside the division box. Then, we divide 24 by 4 to obtain 6. Therefore, 24 ÷ 4 = 6.

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The share of audience for the particular show at 9:00 pm is 55.56% for 50 million households.

We need to know the number of households that watched the programme and the total number of households with televisions on at 9:00 p.m. in order to determine the proportion of audience for that programme.

In this instance, it is stated that 90 million homes had their televisions on at 9:00 p.m. in addition to 50 million households watching the programme. Consequently, the following formula can be used to determine the show's viewership share:

Share of audience is calculated as follows: (Number of households that watched the programme / Total number of households with TVs on) x 100%

= 100% x (50 million / 90 million)

= 55.56%

As a result, 55.56% of the audience watched the specific show at 9:00 p.m. This indicates that the programme was viewed by more than half of the homes with on-air televisions at the time.

The share of audience is a crucial measurement in television ratings since it aids networks and advertisers in understanding how popular a show is and how far it might be able to reach the intended audience.

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Answer:Graph attached below. : Given : Juan spent 10 minutes on his history homework and 3 minutes per question on his math homeworkWe have to plot the graph that shows the total homework time, t, related to the number of math questions, q.Since, t denotes  the total homework time taken by Juanand q denotes the number of math questions done by JuanThen we can represent the situation using a linear equation.Since he spent 10 minutes on his history homework and 3 minutes per question on his math homework.Then q questions take 3q timeand 10 minutes are fixed so, Total time is given by equation t = 10 + 3qAnd graph for the equation is attached below.

Step-by-step explanation:

Answer: Its A (the one all the way to the left)

explanation: Just guessed

Answer:

A≈28.27mi²

Step-by-step explanation:

[tex]A=\pi r^2[/tex]

[tex]\pi \times 3^2[/tex]

≈ 28.27433mi²

A≈28.27mi²

To find the equation of the line passing through the point (6, -3) with a slope of -2, we can use the point-slope form of the equation of a line:y - y1 = m(x - x1)where (x1, y1) is the given point and m is the slope.Substituting the given values, we get:y - (-3) = -2(x - 6)Simplifying, we get:y + 3 = -2x + 12Subtracting 3 from both sides, we get:y = -2x + 9So, the equation of the line is y = -2x + 9

Answer:

Answer and Explanation: The symmetric bell shape of the normal curve implies that the skewness of the distribution of the data is 0, and most of the observation is located at the middle of the distribution. The shape of the normal distribution is not positive and negative skewed, the shape seems to be bell-shaped.

HOPE THIS HELPS!

The main answer is that it takes Cindy 4 hours to weed the garden alone, which was found using the equation 1/x + 1/(3x) = 1/6 where x is the time it takes Cindy to weed the garden alone.

Let x be the time it takes Cindy to weed the garden alone. Then, it takes Tom 3x time to weed the garden alone. Using the formula for the work done by each person, we can create an equation in terms of x:

1/x + 1/(3x) = 1/6

Solving for x, we get:

x = 4 hours

Therefore, it takes Cindy 4 hours to weed the garden alone.

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The side opposite to angle Y is the longest, and angle Y is the largest angle in triangle XYZ. So, the angles can be ordered from greatest to least as follows:

angle Y > angle Z > angle X.

What is triangle ?

A triangle is a three-sided polygon, or a closed two-dimensional shape with three straight sides and three angles. The sum of the angles in a triangle always adds up to 180 degrees. The sides of a triangle can be of different lengths, and the angles can be acute (less than 90 degrees), right (equal to 90 degrees), or obtuse (greater than 90 degrees).  

To order the angles from greatest to least in triangle XYZ, we need to determine which side is the longest. By the Law of Cosines, we know that:

[tex]c^2 = a^2 + b^2 - 2ab*cos(C)[/tex]

where c is the side opposite to angle C, and a and b are the other two sides.

So, let's calculate [tex]c^2[/tex] for each angle:

For angle X: [tex]c^2 = 25^2 + 27^2 - 2(25)(27)*cos(X)[/tex] ≈ 173.65

For angle Y: [tex]c^2 = 24^2 + 27^2 - 2(24)(27)*cos(Y)[/tex] ≈ 267.43

For angle Z: [tex]c^2 = 24^2 + 25^2 - 2(24)(25)*cos(Z)[/tex] ≈ 121.97

Therefore, the side opposite to angle Y is the longest, and angle Y is the largest angle in triangle XYZ. So, the angles can be ordered from greatest to least as follows:

angle Y > angle Z > angle X

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