What are the slope and Y intercepted of the relationship?

Answer:

The tallest player on the team was 78 inches tall

Step-by-step explanation:

Hello,

I hope you and your family are doing well!

To find the serving size of vitamin C for a toddler, we need to know how much vitamin C is in each serving of orange juice. If we assume that each serving of orange juice contains a certain amount of vitamin C, then we can use the following equation to find the serving size:

serving size = (total amount of vitamin C in container) / (number of servings)

Since there are 2 1/4 cups of orange juice in the container, and the container holds 3 servings, the serving size is:

serving size = (2 1/4 cups) / (3 servings) = 3/4 cup per serving

So the serving size of vitamin C for a toddler is 3/4 cup.

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Happy Holidays!

Answer:

To determine how many miles Naomi's car can go on one gallon of gas, we first need to determine how many gallons of gas the car used to travel 15\tfrac{1}{2}15 2 1 ​ miles. We are told that the car used \frac{2}{5} 5 2 ​ of a gallon to travel this distance, so we can multiply this value by 15\tfrac{1}{2}15 2 1 ​ to get the total number of gallons used:

\frac{2}{5} \cdot 15\tfrac{1}{2} = 9

Therefore, the car used 9 gallons of gas to travel 15\tfrac{1}{2}15 2 1 ​ miles. To determine how many miles the car can go on one gallon of gas, we need to divide the total number of miles traveled by the number of gallons used:

15\tfrac{1}{2} \div 9 = \frac{31}{18}

This means that the car can go 31/18 miles on one gallon of gas. Since this fraction is not in simplest form, we can further simplify it by dividing the numerator and denominator by the greatest common factor, which is 3:

\frac{31}{18} \div \frac{3}{3} = \frac{31}{18} \cdot \frac{3}{3} = \frac{31 \cdot 3}{18 \cdot 3} = \frac{93}{54}

Therefore, the car can go 93/54 miles on one gallon of gas. This fraction can be further simplified by dividing the numerator and denominator by the greatest common factor, which is 1:

\frac{93}{54} \div \frac{1}{1} = \frac{93}{54} \cdot \frac{1}{1} = \frac{93 \cdot 1}{54 \cdot 1} = \frac{93}{54}

Therefore, the final answer is that the car can go 93/54 miles on one gallon of gas.

Answer:

180 ft^3

Step-by-step explanation:

volume of the pyramid = (1/3)(area of base) (height)

v= 1/3×(10×12÷2)×(9)

= 180 ft^3

Answer:

answer on the picture.....

Answer:

  parallel

Step-by-step explanation:

You want to know the parallel/perpendicular status of the lines described by the equations ...

Parallel lines have the same slope. The slope is the coefficient of x when the equation is written in the form ...

  y = mx +b

as is the second equation.

The first equation can be put in that form by solving for y.

  2x -5y = 25 . . . . . . given equation

  2x -25 = 5y . . . . . . add 5y -25

  2/5x -5 = y . . . . . . divide by 5

The coefficient of x (slope) is 2/5, same as the second equation.

The lines are parallel.

__

Additional comment

Your graphing calculator can help you figure this out, too. The graphed lines are parallel.

The average rate of change of the function at the interval 0 ≤ x ≤ 4 is 11.25

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

x  0   1   2   3  4   5

y 3   6  12   24 48 96

The interval is given as

0 ≤ x ≤ 4

On the table, we have

x = 0 and y = 3

x = 4 and y = 48

This means that

f(0) = 3 and f(4) = 48

The average rate of change is then calculated as

Average rate of change = [f(4) - f(0)]/[4 - 0]

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

Average rate of change = [48 - 3]/[4 - 0]

Evaluate

Average rate of change = 11.25

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Answer: Tiffany

Step-by-step explanation: Ramon Ratio 8:2 can be reduced to 1 cup of sugar every 4 cups of water. Tiffany Ration is 9:3 which is reduced to 1 cup of sugar every 3 cups of water.

Answer:

look at the explanation below

Step-by-step explanation:

The cube root of a number can be determined by using the prime factorization method. In order to find the cube root of a number:

Step 1: Start with the prime factorization of the given number.

Step 2: Then, divide the factors obtained into groups containing the same factors.

Step 3: After that, remove the cube root symbol and multiply the factors to get the answer. If there is any factor left that cannot be divided equally into groups of three, that means the given number not a perfect cube and we cannot find the cube root of that number

i hope this helps

The solution of the system of equations:

x = 2y+  3

4x - 5y = 9

Is x = 1, y = -1.

Here we have the following system of equations:

x = 2y+  3

4x - 5y = 9

To solve it, we can notice that the variable x is already isolated on the first equation, then we can take it and replace it on the other equation, then we will get:

4*(2y + 3) - 5y = 9

Now we can solve that equation for y:

4*(2y + 3) - 5y = 9

8y + 12 - 5y = 9

8y - 5y = 9 - 12

3y = -3

y = -3/3

y = -1

And the value of x is:

x = 2y + 3

x = 2*(-1) + 3

x = -2 + 3 = 1

So the solution is x = 1 and y = -1.

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Answer:

Step-by-step explanation:

6.5

We can conclude that the number of possible schedules for next semester could she make is 7920.

In more mathematical terms, the factorial of a number (n!) is equal to

n(n-1). For example, if you want to calculate the factorial for four, you would write: 4! = 4 x 3 x 2 x 1 = 24.

Given that,

The student needs 11 more classes to graduate.

And, possible schedules for next semester could she make if she plans to take 4 classes

Based on the given expression, the calculation is as follows:

The combination formula is given to be:

[tex]n_{C} _{r} =\frac{n!}{r!(n-r)!}[/tex]

= [tex]11_{C} _{4}[/tex] ! * 4 !

= [tex]\frac{11 !}{4!(11-4)!}[/tex]  * 4 !

= [tex]\frac{11!}{4!7!}[/tex] * 4 !

= [tex]\frac{11*10*9*8*7*6*5*4*3*2*1}{4*3*2*1*7*6*5*4*3*2*1}[/tex] * 4 !

We can cancel the coefficients,

= [tex]\frac{11*10*9*8}{4*3*2*1}[/tex] * 4 !

= [tex]\frac{7920}{24}[/tex] * 4 !

= 330* 4 !

= 330 * 4*3*2*1

= 7920

Therefore,

We can conclude that the number of possible schedules for next semester could she make is 7920.

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The surface area of the triangular prism is 136 square units

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

The surface area of the triangular prism is the sum of the areas of the above shapes

So, we have

Surface area = 2 * area of rectangle 1 + 1 * area of rectangle 2 + 2 * area of triangle 1

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

Surface area = 2 * 7 * 5 + 1 * 7 * 6 + 2 * 0.5 * 4 * 6

Evaluate

Surface area = 136

Hence, the surface area is 136 square units

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Answer: 20 weeks

Step-by-step explanation:

If he has $412 in his bank account, and he withdraws 20 each week, at 10 weeks he would have $212 left, at 20 weeks he will be left with $12.

Hence, the right answer is 20 weeks.

The length of Adrian's shadow measured by his friend and the distance directly from Adrian's head to the tip of his shadow can be used to find Adrian's height using Pythagorean Theorem. Using an example of the measurement values, Adrian's height is about 5.5 feet

Pythagorean Theorem states that the sum of the square of the lengths of the legs of a right triangle is equal to the square of the length of the hypotenuse side.

The diagram in the question appears left out. Please find attached a drawing made using the measurement lengths in the following example, created with MS Word.

The measurements Adrian had his friend to do are;

The length of Adrian's shadow on the sidewalk and the length from Adrian's head to the tip of the shadow.

Let x represent the length of Adrian's shadow, let r represent the distance from Adrian's head to the tip of the shadow, and let y represent Adrian's height

According to Pythagorean Theorem, we get;

r² = x² + y²

Therefore, the Adrian's height, h = √(r² - x²)

When r ≈ 8.14, and x = 6, we get;

h = √(8.14² - 6²) ≈ 5.5

Adrian's height is about 5.5 feet in the example situation

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Answer:

B

Step-by-step explanation:

(m^-2 n^-3)^-4

-2 x -4 = 8

-3 x -4 = 12

m^8n^12

The given expression (m − 2n − 3) − 4 is equivalent to →

(m - 2n - 7).

Given is the expression -

(m − 2n − 3) − 4

The given expression is -

(m − 2n − 3) − 4

m - 2n - 3 - 4

m - 2n - 7

Therefore, the given expression (m − 2n − 3) − 4 is equivalent to →

(m - 2n - 7).

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The given exponential function represents the growth in the function. The percentage of growth (increase) is 1%.

An exponential growth function is a function where the quantity increases slowly and after some time, it increases rapidly.

It is represented by the formula,

y = a(1 + r)ˣ

Here the term 'a' is the initial amount of the quantity, the term 'r' is the rate of increase and the term 'x' is the period.

The given exponential function is y = 10(1.01)ˣ

Here we can write the function as

y = 10(1.01)ˣ

⇒ y = 10(1 + 0.01)ˣ

Since 1.01 > 1, it is an exponential growth function.

So, when comparing with the formula, we get the rate of increase,

r = 0.01

Converting it into fractions, we get 1/100

Then, the percentage rate of increase is 1%.

Therefore, the given exponential function grows with a rate of 1% increase.

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Answer:

1.7

to the nearest tenth

Step-by-step explanation:

Since the triangle is equilateral, all three sides are the same which is x

The vertical line of length [tex]\sqrt{7}[/tex] bisects the base so each of the two right triangles that is formed has lengths x, x/2 and [tex]\sqrt{7}[/tex]

Using the Pythagorean theorem,

c² = a² + b²

where c is the hypotenuse which has a length x and a and b are the two shorter sides which are x/2 and √7 in this case

Substituting for c, a and b we get

x²= (√7)² + (x/2)²

==> x² = 7 + x²/4

==> x² - x²/4 = 7

==> 3x²/4 = 7

==> x² = 7 x 4/3 = 28/3

x = √(28/3) = 1.732 or 1.7 to the nearest tenth

The sum of x and y is 5.

An equation is a statement of two expressions connected by equal sign.

Given that, the system of equations, y=-3x-1 and y = -2/3x + 6

Simplifying the equations,

-3x-1 = -2x/3+6

Multiplying the both sides by -3

9x +3 = 2x-18

7x = -21

x = -3

Put x = -3 in any one of the equations,

y = -3(-3)-1

y = 9-1

y = 8

Hence, the sum is 5

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A triangle with coordinates (1,1) (4,2) (3,5) is translated three units down and five units to the left. New coordinates will be (-4,-2), (-1,-1),(-2, 2).

A translation is a geometric change in Euclidean geometry that involves moving each point in a figure, shape, or space by the same amount in one direction. A translation can also be thought of as moving the origin of the coordinate system or as adding a constant vector to each point.

Given

A triangle with coordinates (1,1) (4,2) (3,5)

The value of a coordinate is impacted by translations left or right but not by translations up or down or left or right.

We multiply all of the numbers by 3 since we are translating the entire triangle down three units.

Additionally, we are converting the entire triangle to left-to-right units of five, thus we will multiply all values by 5.

A = (1 - 5, 1 - 3)

B = (4 - 5, 2 -3)

C = (3 - 5, 5 - 3)

New coordinates will be:

A = (-4,-2)

B = (-1,-1)

C = (-2, 2)

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After doing the equation the area of ΔABC is 15√7.

The Heron area formula is what?

Heron of Alexandria (c. 62 ce) is credited with developing the Heron's formula, which determines the area of a triangle in terms of the lengths of its sides. If the side lengths are represented by the symbols a, b, and c: Area is equal to the square root of (a + b + c)/2, where s is half the perimeter.

Given that:

Let AB = 6x , BC = 5x , AC = 4x

then 6x+5x+4x = 30

15x = 30

x = 2

so AB = 12

BC = 10

AC = 8

Area = √s(s - a)(s - b)(s - c)

s = a+b+c/2

s = 12+10+8/2

s = 30/2

s = 15

Area = √15(15- 12)(15 - 10)(15 - 8)

Area = √15(3)(5)(7)

Area = √1575 = 15√7

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The conclusion is that the angle which measures 120° is not Acute angle.

The construction of an angle is a type of geometric shape made by connecting two rays at their termini. Three letters that make up the form of the angle can alternatively be used to symbolise the angle, with the middle letter indicating the location of the angle (i.e.its vertex). Greek characters such θ, α, β, etc. are frequently used to denote angles.

In geometry, there are mainly six different kinds of angles. All angles have the following names and characteristics:

Angle B measures 120°.

Here the angle is more than 90° so the angle is not acute.

The conclusion is that the angle which measures 120° is not Acute angle.

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The probability that Yasmin will not be offered a coupon on at least one of the days she visits the website will be;

⇒ 0.9375

The term probability refers to the likelihood of an event occurring

Given that;

The probability that a visitor is offered a coupon (p) = 50%

Now,

Since, The probability that a visitor is offered a coupon (p) = 50%

Hence, The probability that he gets coupon all 4 days is,

⇒ p (4) = p⁴

⇒ p (4) = (50%)⁴

⇒ p (4) = 0.0625

Hence, By using the complement rule, the probability that he is not offered a coupon at least one day is,

⇒ p' = 1 - 0.0625

⇒ p' = 0.9375

Thus, The probability that Yasmin will not be offered a coupon on at least one of the days she visits the website = 0.9375

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Answer:

[tex]\displaystyle \frac{9}{4}[/tex]

Step-by-step explanation:

[tex]\displaystyle 2 + (\frac{1}{5^1} + \frac{1}{5^2} + \frac{1}{5^3} + ... + \frac{1}{5^n} )[/tex]

The second term of this sum is an Infinite Geometric Progression
To find the sum of an Infinite Geometric Progression,

- Find the first term ( 1/5 ) of the progression and call it a
- Find the common ratio, (divide any term by it's predecessor. i.e [tex]\displaystyle \frac{\frac{1}{5^2} }{\frac{1}{5} } = \frac{5}{5^2} = \frac{1}{5}[/tex]) and call it r

Finding the sum of given Geometric Progression:
Sum of Infinite GP: [tex]\displaystyle \frac{a}{1-r}[/tex]

Plugging our values in this equation, we get:
Sum of Geometric Progression = [tex]\displaystyle \frac{\frac{1}{5} }{1 - \frac{1}{5} } = \frac{\frac{1}{5} }{\frac{5 - 1}{5} } = \frac{1}{4}[/tex]

Adding to find the actual answer:
[tex]\displaystyle (\frac{1}{5^1} + \frac{1}{5^2} + \frac{1}{5^3} + ... + \frac{1}{5^n} ) = \frac{1}{4}[/tex]
[tex]\displaystyle 2 + (\frac{1}{5^1} + \frac{1}{5^2} + \frac{1}{5^3} + ... + \frac{1}{5^n} ) = 2 + \frac{1}{4}[/tex]
[tex]\displaystyle 2 + (\frac{1}{5^1} + \frac{1}{5^2} + \frac{1}{5^3} + ... + \frac{1}{5^n} ) = \frac{9}{4}[/tex]

The statement "cross-tabulation can only be used for two variables; each variable must have well-defined labels " is false

The cross tabulation is defined as the tool that is used in statistics to categorical data. We can also says that  that present the results of the entire group of respondents

The given statement is "cross-tabulation can only be used for two variables; each variable must have well-defined labels "

The cross tabulation method can be used to represent two or more variables. The cross tabulation table has x axis as one variable and y axis as another variables

The cross tabulation can be used for two or more variables

Therefore, the the given statement is false

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The complete equation in the slope-intercept form is y = 4x-1.

In mathematics, a line's slope, also known as its gradient, is a numerical representation of the line's steepness and direction.

If a line passes through two points (x₁ ,y₁) and (x₂, y₂) ,

then the equation of line is

y - y₁ = (y₂- y₁) / (x₂ - x₁) x (x - x₁)

To find the slope;

m =  (y₂- y₁) / (x₂ - x₁)

So, the equation is,

y - y₁ = m (x - x₁)

And the standard form of the slope-intercept form:

y = mx+b,

where m is the slope and b is the y-intercept.

From the question, we have

m = 4 and coordinates of b is (0, -1).

So, the equation is,

y + 1 = 4 (x - 0)

y +1 = 4x

y = 4x-1

Therefore, the equation is y = 4x-1.

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The cubic polynomial with zeros (3,0), (-6,0) and (1,0) is given as follows:

D. x³ + 2x² - 21x + 18.

We are given the zeros of the polynomial, which then can be obtained using the Factor Theorem.

The zeros of the polynomial are given as follows:

x = 3, x = -6, x = 1.

Then, applying the Factor Theorem, considering a leading coefficient of 1, the polynomial is given as the product of it's linear factors as follows:

(x - 3)(x + 6)(x - 1)

(x² + 3x - 18)(x - 1)

x³ + 2x² - 21x + 18.

Meaning that option D is correct.

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The initial mass of the sample after two days = 8483.45 kg

Given that,

It is known as exponential decay when a population or group of something is deteriorating and the quantity of decline is proportional to the size of the population. In an exponential decay, the overall value falls but the percentage that departs stays the same throughout time.

The exponential decay formula aids in determining the exponential drop, which is a rapid reduction over time. To calculate population decay, half-life, radioactivity decay, and other phenomena, one uses the exponential decay formula.

The standard  formula for this type of behavior which is written below:

A = [tex]Pe^{-rt}[/tex]  

Where

A refers the amount left after time t

P refers the initial amount at t = 0

r refers the rate

Here we have given that the mass of a radioactive substance follows a continuous exponential decay model, with a decay rate parameter of per day.

A sample of this radioactive substance was taken after two days.

And we need to find if the sample has a mass of today, then the initial mass of the sample.

Now, we have to substituting the values,

Let us assume,

P = 9575 kg

r = 0.12

t = 1

Then we get the equation as,

A = (9575 kg) [tex]e^{-0.12*1}[/tex]

When we simplify this one, then we get,

A = (9575 kg) [tex]e^{-0.12}[/tex]

A = (9575 kg) 0.886

A = 8483.45 kg

Therefore,

The initial mass of the sample after two days = 8483.45 kg

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The probability that a randomly selected product will be assembled in less than 91.630 minutes or more than 130.35 minutes is 0.0474 or 0.033.

Given,

In a normal random variable

Mean , [tex]\mu[/tex] = 110 minutes

Standard deviation , [tex]\sigma[/tex] = 11 minutes

then

The probability that a randomly selected product will be assembled in less than 91.630 minutes or more than 130.35 minutes will be

a)

To find the Probability that a randomly selected product will be assembled in less than 91.630 minutes, first calculate the z-score at 91.360 minutes

[tex]z-score = \frac{x-\mu}{\sigma}\\\\z-score=\frac{91.63-110}{11}\\\\z-score=\frac{-18.37}{11}=-1.67\\[/tex]

from z-score table , [tex]p(x < -1.67)=0.04746[/tex]

b)

To find the Probability that a randomly selected product will be assembled in more than 130.35 minutes, first calculate the z-score at 130.35 minutes.

[tex]z-score = \frac{130.35-110}{11}\\\\z-score=\frac{20.35}{11}=1.85[/tex]

From z-score table,

[tex]p(x > 1.85)\\\\=1-p(x < 1.85)\\\\=1-0.967\\\\=0.033[/tex]

Thus, the probability for product assembled in more than 130.35 minutes is 0.033

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0.563 $ is he paying per load of laundry

What is business mathematics?

Business mathematics is the branch of mathematics utilized by businesses to track and coordinate their operations. Accounting, inventory management, marketing, sales forecasting, and financial analysis are all areas where commercial businesses apply mathematics.

Simple arithmetic, elementary algebra, statistics, and probability are all frequently utilized in business. More complex arithmetic, such as calculus, matrix algebra, and linear programming, may be used to solve some management challenges.

According to question:

Total scoop contained in detergent box = 195 scoops.

Scoops used by each load of laundry = 11/2  scoops = 5.5 scoops

Number of laundry he can do with this box = 195/5.5

                                               = 35.45 laundries.

Price of detergent box = 19.99 $

Price he paying for each load = Total price/ Number of loads

                                                  = 19.99/35.45

                                                  = 0.5638928067700

                                                  = 0.563 $ (Approx)

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Answer: D. Zero is not a rational number

Step-by-step explanation:

[tex]0=\frac{0}{1}[/tex]. Thus, by definition, zero is rational.