i'm stuck on the 'use exact numbers' portion of this .. the equation i came up w/ is: y=2/3x+4 but i know that the 2/3 has to be an exact number .. but how? if i were to divide both of them by 2, i get 1/1.5 ... do i round 1.5 up to 2?

The mean, summation of (x - μ), summation of (x - μ)², variance, and standard deviation will be 5, 0, 360, 72, and 8.49, respectively.

It is the measure of the dispersion of statistical data. Dispersion is the extent to which the value is in a variation. The standard deviation is given as,

[tex]\rm \sigma = \sqrt{\dfrac{\Sigma (x_i - \mu)^2}{n}}[/tex]

The data set is given below.

14, 3, -10, 12, 6

The mean of the data will be

μ = (14 + 3 - 10 + 12 + 6) / 5

μ = 25 / 5

μ = 5

The summation of the (x - μ) will be

∑(x - μ) = (14 - 5) + (3 - 5) + (- 10 - 5) + (12 - 5) + (6 - 5)

∑(x - μ) = 9 - 2 - 15 + 7 + 1

∑(x - μ) = 0

The summation of the (x - μ)² will be

∑(x - μ)² = (14 - 5)² + (3 - 5)² + (- 10 - 5)² + (12 - 5)² + (6 - 5)²

∑(x - μ)² = (9)² + (-2)² + (-15)² + (7)² + (1)²

∑(x - μ)² = 81 + 4 + 225 + 49 + 1

∑(x - μ)² = 360

Then the standard deviation (σ) will be

σ = √(360 / 5)

σ = √72

σ = 8.49

Then the variance (σ²) will be

σ² = 8.49²

σ² = 72

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Answer: The diagonal line would have a negative slope

Step-by-step explanation:

Step-by-step explanation:

11dvccvgtgcgt5cjuuhh

The difference between the two temperatures is mathematically given as

|81 - (-29)| Option C

This is further explained below.

Generally, the equation is  mathematically given as

h-l=d

Therefore

81-(-29)=d

81+29=d

d=110

In conclusion,, in magnitude form

|81 - (-29)|=|81 +29|=|110|=110

|81 - (-29)|

Option C is correct

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The listed elements of the sets are as follows:

Venn diagram is an illustration that uses circles to show the relationships among things or finite groups of things.

The sets in the Venn diagram are U, X and Y.

Therefore, let's find the elements of the sets.

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Given u = (-1, 3), v = ( 2, 4) , and w = (2, -5), by applying scalar multiplication of vectors, -3v = -3.( 2, 4) = (-6, -12)

In the two-dimensional coordinate system, vectors can be split into x-component and y-component.

We can write, for example, a vector s = (4,–2), which means:

x-component = 4

y-component = –2

Some vector operations:

In the given problem:

u = (-1, 3), v = ( 2, 4) , and w = (2, -5)

Then,

-3 v = -3 . (2, 4)

      = ( -3 . 2, -3 . 4)

      = (-6, -12)

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Answer:

There are 12 cups of juice in the refrigerator.

Step-by-step explanation:

The conversion --> 1 gallon = 16 cups.

Therefore, [tex]\frac{3}{4}[/tex] a gallon x [tex]\frac{16 cups}{1 gallon}[/tex] = 12 cups.

--

Have a nice day!

Answer:

Let s =cost of skiing per day. Here's what we know:

450 + 20s = 64s + 20s (the season pass plus ski rentals equates to daily skiing plus ski rentals)

We have 20s on both sides, so those cancel out easily:

450 = 64s

Divide both sides by 64:

7.03 ≈ s

You can't pay for a partial day, so the skier will have to ski for at least 8 days to make the season pass cheaper than getting daily passes.

Step-by-step explanation:

Hope this helps :D

The simplified value of the expression −5 5/8 ÷ 5 is −1 1/8

Expressions are mathematical statements that are represented by variables, coefficients and operators

The expression is given as

−5 5/8 ÷ 5

Convert the mixed fractions to improper fractions

So, we have

−5 5/8 ÷ 5 = −45/8 ÷ 5

Express the quotient as a product

So, we have

−5 5/8 ÷ 5 = −45/8 x 1/5

Evaluate the product of the numerators in the above expression

So, we have

−5 5/8 ÷ 5 = −45/8 x 1/5

Evaluate the product of the denominators in the above expression

So, we have

−5 5/8 ÷ 5 = −45/40

Simplify the result

So, we have

−5 5/8 ÷ 5 = −9/8

Express as a mixed number

So, we have

−5 5/8 ÷ 5 = −1 1/8

Hence, the simplified value of the expression −5 5/8 ÷ 5 is −1 1/8

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The equation for the number of 30 days periods until the value of both cards will be equal is 130 - 3x = 110 - 2.5x

let

Number of 30 days period = x

Gift card 1:

130 - 3x

Gift card 2:

110 - 2.5x

130 - 3x = 110 - 2.5x

130 - 110 = -2.5x + 3x

20 = 0.5x

x = 20/0.5

x = 40

So,

Gift card 1:

130 - 3x

= 130 - 3(40)

= 130 - 120

= $10

Gift card 2:

110 - 2.5x

= 110 - 2.5(40)

= 110 - 100

= $10

Therefore, the value of each card when they have equal value is $10

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Answer:

210:35 = 6:1

Step-by-step explanation:

210:35

if divided by 35, then 6:1

Answer:

I think the answer is c.CB

The y - intercept represents a cereal with zero grams of sugar that has a rating of about 57.

The general equation of a straight line is -

y = mx + c

where -

m → slope of line

c → y-intercept of line

Given a equation → y = 2.391x + 57.420 that models the taste rating of a cereal 'y' and 'x' represents the number of grams of sugar per serving.

The y-intercept of the equation represents the point at which the graph of the equation cuts the y - axis. Now, the coordinates of the y-intercept is of the form (0, y). Therefore, the x-coordinate will be 0. Now, the equation given is -

y = 2.391x + 57.420

Comparing it with the general equation of line -

y = 2.391x + 57.420

y =   mx     +    c

The y - intercept is c = 57.420

At x = 0, the equation becomes -

y = 2.391 x 0 + 57.420

y = 57.420

Now -

Number of grams of sugar per serving = 0

Taste rating of a cereal = y = 57.420

Therefore, the y - intercept represents a cereal with zero grams of sugar that has a rating of about 57.

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After solving, the factor of equation -16 = x²+8x is:

So,

Given equation: -16 = x²+8x

Then,

Factors are: (x+4) and (x+4)

Therefore, after solving, the factor of equation -16 = x²+8x is:

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Answer:b i think

but im not sure

Step-by-step explanation:

According to the question, equation 3r + g ≤ 48 where r > 3 and g ≥ 4 represents the given situation.

When two mathematical expressions or two numbers are compared in an unequal way, it is known as an inequality in mathematics. Inequalities can generally be classified as either algebraic or numerical or as a combination of the two. When a polynomial of degree 1 is compared to another algebraic expression of a degree less than or equal to 1, this is an example of a linear inequality, which is an inequality involving at least one linear algebraic expression.

Given, A maximum of $48 can be spent during the show. Each game ticket (g) costs $1, while each ride ticket (r) costs $3. At least 4 game tickets and more than 3 transportation tickets are what you want to purchase. From that, we can drive that sum of 3 times of ride ticket and game ticket cost should be at least greater than 48. Hence,

$3 * ride cost + $1 * game cost ≤ 48

Therefore, The above circumstance is represented by the equation

3r + g ≤ 48, where r > 3 and g ≥ 4.

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The value of function f(x) at x = - 1 and x = 3, will be -

f(-1) = 3

f(3) = 3

We have a function f(x).

We have to evaluate it at x = -1 and x = 3.

A function in mathematics is a relation between a dependent and independent variables [y and x respectively]. In a function, the dependent variable (y) always depends on independent variable (x) for its value. It is denoted by - y = f(x).

According to the question, we have -

f(x) = [- x + 2  , x ≤ 1] and f(x) = [x² - 4x + 6,  x > 1]

Now, for x = -1, f(x) will be -

f(- 1) = - (-1) + 2 = 3

and

for x = 3, f(x) will be -

f(3) = 3² - 4 x 3 + 6 = 3

Hence, the value of function f(x) at x = - 1 and x = 3, will be -

f(-1) = 3

f(3) = 3

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Answer: (1,6)

Step-by-step explanation:

Let the coordinates of A be (x,y).

[tex]\frac{x-5}{2}=-2 \implies x=-4 \implies x=1\\\\\frac{y+4}{2}=5 \implies y+4 =10 \implies y=6\\\\\therefore A=(1, 6)[/tex]

Answer:

9,10,11 are the values of n

The length of the rectangle is 9 feet and the width of the rectangle is 10 feet.

The sum of a rectangle's boundary lengths on all sides is known as its perimeter. A rectangle's perimeter is a linear measurement that can be expressed in meters, feet, inches, or yards. Let's first comprehend the two fundamental characteristics of a rectangle.

Let the length of the rectangle be x feet

Then, the width of the rectangle will be x+1feet

We know that the perimeter of a rectangle is given by

P= 2(l+w)

Here

P= perimeter of a rectangle

l=length of the rectangle

w= width of the rectangle

Put l=x, w= x+1 and P= 38 in the perimeter formula

38 = 2(x+x+1)

Divide both sides by 2

19= x+x+1

19= 2x+1

Subtract 1 from both sides

18=2x

Divide both sides by 2

x=9 feet

This is the length of the rectangle.

Now, the width x+1 of the rectangle will be

9+1 = 10 feet

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The number of miles driven per gallon is 401/20

Louie drove 5- 1/8 miles

He used 2.5 gallons for this journey

Therefore the number miles per gallon can be calculated as follows

401/8 = 2.5

x= 1

Cross multiply both sides

2.5x= 401/8

x= 401/8 ÷ 2.5

x= 401/8 × 1/2.5

= 401/20

Hence the number of miles per gallon is 401/20

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Answer:

  4, 0, 3

Step-by-step explanation:

You want to know which numbers are possible values of m, given a graph of the values of m.

The graph shows an empty circle at m=6, and an arrow extending to the left from that point. The empty circle means that m=6 is not a possible value of m.

The arrow extends through possible values of m, and extends to negative infinity. That means m may have any value less than 6. Such values on the offered list are ...

  4, 0, 3

__

Additional comment

The values 6, 7, 9 are not covered by the dot or the arrow, so are not possible values of m.

Answer:

0, 3, 4

Step-by-step explanation:

When the circle is open and pointing to the left, it means that the variable is less than the number the circle is at. In this case, it means that the variable is less than 6, so you would select all values that are less than 6!

I hope I helped!

The value of x is 7.

A proportion is an equation in which two ratios are set equal to each other.

Now, setting up the proportion we have

6/4 = x+6 / 4+8

3/2 = x+6 / 12

12*3 = 2(x+6)

36 = 2x + 12

2x = 36-12

2x= 14

x=7

Hence, the value of x is 7.

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The function y = 0.6 × ( 1/10)ˣ is a form of exponential decay and the value of y-intercept is 0.6.

The term "exponential decay" refers to the process of a constant percentage rate reduction in an amount over time. It can be written as y=a(1-b)ˣ, where x is the amount of time that has passed, a is the initial amount, b is the decay factor, and y is the final amount.

Consider the function,

y = 0.6 × ( 1/10)ˣ

This equation is a form of exponential decay because the number being raised in the power is a fraction, and whenever a fraction is raised to a positive power, the result decreases.

In order to determine the y-intercept of the function, we substitute the value of x as zero and find the value of y. Whenever a number is raised to zero power, the answer is always one.

Therefore,

y = 0.6 ( 1/10)ˣ

y = 0.6 × ( 1/10 )⁰

y = 0.6 × 1

y = 0.6

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The answer to the value gotten without the significant figure doesn't make sense as there's a huge difference.

It should be noted that 13822 to 1 significant figures will be 13000.

Also, it should be noted that 623 to 1 significant figure will be 600.

14 to 1 significant figure will be 10.

Therefore, the multiplication will be:

= (13000 × 600) / 10

= 780000

Therefore, the answer to the value gotten without the significant figure doesn't make sense as there's a huge difference since the earlier value was 615079.

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Considering that the function is even, the numeric values are given as follows:

In this problem, we have that the function is even, hence:

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Answer:

1,1,3,3

Step-by-step explanation:

on edge

Answer:

x=30

Step-by-step explanation:

on the left you have a ninety-degree angle.

5(x-12) = 90

5x-60=90

  +60 +60

5x=150

/       /

5      5

x=30

An exponential function can be defined as a mathematical function whose values are generated by a constant that is raised to the power of the argument. Mathematically, an exponential function is represented by this formula:

f(x) = eˣ

Generally speaking, a mathematical model for any quantity (water) that decreases by r percent per unit of time is an exponential function of this form:

P(t) = I(1 - r)^t

Where:

Substituting the given parameters into the formula, we have;

P(t) = I(1 - r)^t

P(50) = 1500 × (1 - 0.3)^0.2{50}

P(50) = 1500 × (0.97)^10

P(50) = 1,106 gallons.

Therefore, there would be 1,106 gallons of water left in the pool after 50 minutes.

Next, we would determine the amount of time it would take to have less than 1000 gallons in the pool:

P(t) = I(1 - r)^t

1000 = 1500 × (1 - 0.3)^0.2t

1000 = 1500 × (0.97)^0.2t

1000/1500 = (0.97)^0.2t

2/3 = (0.97)^0.2t

Taking the log of both sides, we have:

log0.97(0.2t) = log(2/3)

t = log(2/3)/(0.27log0.97)

Time, t = 66.6 minutes.

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Complete Question:

A pool drains at a rate of 3% every 5 minutes. If it starts with 1500 gallons, how many gallons are left in the pool after 50 minutes? About how many minutes will it take to have less than 1000 gallons in the pool? Justify your answer with a mathematical model of the problem situation.

  We write the expression in its simplest form and we are left with.

4∛2 x

    An algebraic expression is a set of numbers and letters that make up an expression that has a meaning, the letters are variables and the numbers are coefficients or independent terms, algebraic expressions can be part of an equation and model mathematical processes.

   If we want to express an expression in its simplest form we are talking about a simplification of it, in this case we have the difference of monomials:

7∛2x - 3∛2x.

  As both have the same variable, then the way of reduction is only the subtraction operation

4∛2x

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Answer:

1. x≤9
2. x>12

Step-by-step explanation:

1. Rewrite so x is on the left side of the inequality.

3x−4≤23

Move all terms not containing x to the right side of the inequality.

3x≤27

Divide each term in 3x≤27 by 3 and simplify.

x≤9

2. Rewrite so x is on the left side of the inequality.

3x-4>32

Move all terms not containing x to the right side of the inequality.

3x>36

Divide each term in 3x>36 by 3 and simplify.

x>12