What is the
y-intercept of the function f(x)=-2/9x+1/3?

Answer:

see image

Step-by-step explanation:

Use new exponent rules like:

A power raised to a power is the product of the powers. (power to a power, times the exponents)

and,

Square root is a half power. (Converting radicals to fractional exponents)

Also, you can multiply in any order, like since you learned multiplying (example: 2×6 is the same as 6×2)

see image.

Here's the plan:

Change the radical to a 1/2 exponent. Now 3 and 1/2 are both exponents. Rearrange the order. Rewrite in radical form again.

see image.

The proof of the equation  (√5)³ = √(5³) is given below.

Exponentiation is one of the mathematics operation.

Let mᵃ, where m and a are the real numbers.

And m is multiplied by a times to itself.

So, a is the exponent of m.

Given:

A radical equation,

(√5)³ = √(5³).

LHS =  (√5)³

Simplifying,

(√5)³ = {(5[tex])^{1/2}[/tex]}³

        = [tex]5^{3/2}[/tex]

        = √(5³)

        = RHS.

Therefore,  (√5)³ = √(5³).

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The complete question:

Simplify and prove the equation (√5)³ = √(5³) by using exponent rules.

Answer: 1.8 movies per day.

Step-by-step explanation: 8 1/3=25/3. One day would be 3/25. This means that each day, a college students watched 3/25 of 8 movies. Do 3/25x15. This makes 1.8 movies watched per day.

The sum of even numbers between 105 and 351 is 28,044 .

An additive or arithmetic sequence is a sequence of numbers such that the difference between  consecutive terms is constant. For example, the sequence 5, 7, 9, 11, 13, 15 ... is an exponent plus the common difference of 2.

even numbers between 105 and 351

the series will start like

106 , 108 , 110 , .................................. , 346 , 348 , 350

this is a arithmetic progression

a = 106 d  = 2 l = 350

we need to find n

350 = 106 + ( n - 1 ) 2

350 - 106 = (n -1 ) 2

244/2 = n -1

n = 123

now sum = 123/2 ( 106 + 350)

               = 28,044

so the sum of even numbers between 105 and 351 is 28,044 .

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Answer: $342.40

Step-by-step explanation:

There are two ways you can solve this problem:

Simply turning the percentage to a decimal and multiplying it to the $320.

In the picture provided the method at the top represents you multiplying $320 x .07, You might be wondering “why .07 instead of 7%?” Well, if you were turning this number from a percent to a decimal you would shift the decimal point over to the left 2 times.

And so multiplying $320 x .07 = 22.4 or 22.40. Either way works but without the zero is the way you should write it. And you would add 22.4 to $320 and get $342.40.

Also in the picture provided I used the method of proportions.

Where the total is $320 in this case which you would put next to 100% as 100% means complete or the total. And you would put 7% above 100%. Then, proceed to cross multiply $320 by 7 and it will give you, 2240. Then, you divide it by 100. When you divide it you get 22.40. Then you would add it to $320 and get 342.40.

Number of ways , two contaminated and 8 non- contaminated farms be choosen is 3,304,845,180.

Permutation and Combination

Combination is a mathematical way to arranging the set of values randomly.

ⁿCᵣ = n! / r! (n-r)!

we have given that ,

total number of farms for lead contamination = 50

Number of farms have dangerously high level of lead = 8

so, number of non- containmated farms ( no high level of lead ) = 50-8 = 42

We have to find the number of ways to choose two contaminated farms and eight non- contaminated farms. Two containmated farms are selected from 8 containated farms and 8 non- contaminated farms are selected from 42 farms .

Number of ways for selecting two containmated farms = ⁸C₂ = 8!/2!×6! = 8×7/2 = 28

Number of ways for selecting eight non-containmated farms from 42 farms = ⁴²C₈

= 42! / 8! 34! = 42×41×---×35/8×7×----×1

= 118013185

The total number of ways to obtain 2 containmated farms and 8 non- contaminated farms in 10 farms selected is then product of number of ways to select the 2 containmated farms and number of ways to select 8 non-containmated farms .

= 118030185× 28 = 3,304,845,180

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Answer:

Credit (C) = $45.50 - 0.10x

Step-by-step explanation:

Since you are wanting the credit (C) that is the y variable.

The prepaid phone card starts off with a balance of $45.50.

Every minute a call is made $0.10 is deducted (subtracted) from the card.

The unknown number or 'x' represents the number of minutes the calls lasted.

The end behavior of given polynomial function f(x) = 5 + 7x - 9x^2 + 4^3,

as x → -∞, f(x) → -∞

as x → ∞, f(x) → -∞

In this question, we have been given a polynomial function

f(x) = 5 + 7x - 9x^2 + 4^3

We need to  state the end behavior of f(x).

The graph of f(x) is as shown below.

We can observe that as x tends to -∞, f(x) → -∞

Also, as x → ∞, f(x) → -∞

We know that the end behavior of polynomial function is determined by the degree of the polynomial and the leading coefficient.

For given polynomial function, the degree of this polynomial is 2.

The leading coefficient is -9

We know that for polynomial function of even degree, the ends of the function graph point in the same direction.

Therefore, the end behavior of given polynomial function f(x) = 5 + 7x - 9x^2 + 4^3,

as x → -∞, f(x) → -∞

as x → ∞, f(x) → -∞

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The rule which describes the function graphed in the attached image as required to be identified is; Output = 8 - input.

It follows from the task content that the rule which is a representative of the function which is as graphed in the attached image is to be identified.

By observation, the relation which best describes the graph is; (7, 1), (6, 2), (5, 3).....

The inference which can therefore be drawn from the given graph is that;

The output value is the subtraction of the input value from 8 in each case.

Ultimately, the required rule which represents the function is; Output = 8 - input.

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A minimum of 3 weighings are required to identify the heavy marble out of 8 marbles.

As all the marbles weigh the same except one which is heavier, therefore firstly 8 marbles are divided into half. 4 marbles are placed in one pan while the other 4 are placed in another pan. In this two-pan balance, the pan which is lower than the other contains a heavier marble.

Now, the pan with heavier marble has 4 marbles which are again divided into half. 2 marbles are placed in each pan. Similarly, the pan with heavier marble goes down as compared to another pan with 2 marbles of the same weight. Now the final weighing is done by placing 1 marble in each pan out of 2 marbles taken from the pan which went down before as compared to another pan.

The pan with heavier marble will move down and thus with 3 weighings, a heavier marble is identified.

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76263

Step-by-step explanation:

[tex] \: \: \: 20005[/tex]

[tex] + 56258[/tex]

___________

[tex] = 76263[/tex]

In order to a breakpoint or the total cost = total investment company must need to sell 100 grams of links.

Determine the known quantities and designate the unknown quantity as a variable while trying to set up or construct a linear equation to fit a real-world application.

Let's suppose the number of links that are needed to solve for a breakpoint is x.

Cost of x number of links with the rate of $2/gram = 2x

Total cost = total selling

100 + 2x = 3x

3x - 2x = 100

x = $100

Hence "In order to break even point or the total cost = total investment company must need to sell 100 grams of links".

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The number of randomly selected employers that would have to be contacted is 9604

The confidence level is 95%

1 - 0.95 = 0.05

We have to get the z value at 0.05

0.05/2 = 0.025

Using the standard normal table, the critical value at 0.025 = 1.96

We have to define the probability as P = 50% = 0.5

we have to define q = 1 - 50% = 0.5

The formula that would be used to find the value of n is given as

[tex]n = pq\frac{Zc}{E} ^2[/tex]

These variables used are:

pq = variance of population

E = margin of error = 0.01

critical value = Zc = 1.96

[tex]n = 0.5*0.5 (\frac{1.96}{0.01})^2[/tex]

= 0.25 * 38416

= 9604

Hence the sample space is given as 9604

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The correct option ; Quadrilateral, has the given information describing quadrilateral UVWX.

For the given values in the question;

In the quadrilateral UVWX

As, none of the sides are equal to other and none of the angles are equal to the other.

Thus, the this information shows the values are given for quadrilateral.

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Dora solved the equation.

She multiplies 4 inside the bracket. But she fails to know that 4× -1 = -4. Instead she multiplied that 4×-1 = -41. This is her first mistake.

In the second step, she shifted -41 to the right side in order to find the value of x. As -41 gets shifted to right side , -41 becomes +41 and added with +11 to get 52. which is totally a wrong method.

Step-by-step explanation:

Here is the exact method of solvation.

[tex]{ \blue{ \bold{4(x - 1) = 11}}}[/tex]

[tex]{ \blue{ \bold{4x - 4 = 11}}}[/tex]

[tex]{ \blue{ \bold{4x = 11 + 4}}}[/tex]

[tex]{ \blue{ \bold{4x = 15}}}[/tex]

[tex]{ \blue{ \boxed{ \red{ \sf{x = \frac{15}{4}}}}}} [/tex]

Answer:

Andre is taller than Diego

Step-by-step explanation:

There are 100 cm in a meter. If we use this information and convert Diego's height to meters, we find that Diego is 1.65 m. This is a smaller number, and therefore, Diego is shorter than Andre.

well, there's no great mystery when it comes to getting a product from decimals.  Now, we have 611.2 and 0.0061, let's for a second take off the decimal point and simply multipy 6112 times 00061

6112 * 00061 = 372832

ok....... hmmm now let's see 611.2 had 1 decimal, whilst 0.0061 had hmm 4 decimals, let's add them up, that's 1 + 4 = 5 decimals total from both amounts, that simply means that our 372832 needs to have 5 decimals as well, so that makes it 3.72832.

The probability that he or she will be happy with the travel reimbursement will be 0.705.

The number of people who requested more vacation time indicates that they are plainly dissatisfied.

400 employees are satisfied with the vacation allowance. - The number of workers that requested greater vacation time.

Employees who are satisfied with their vacation pay are represented by the numbers 400 - 118 = 282.

The likelihood that he or she will be happy with the vacation allowance =

Employees that are happy with their vacation pay / Total number of employees

= 282 / 400 = 0.705.

Therefore, the likelihood that he or she will be happy with the vacation allowance = 70.5%

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Thus, it takes 1.5 minutes {30 seconds} for filling a 3-litre bowl

The simplified expression is 2187.

Given expression:

expression 3 with the exponent 4 multiplying  3 with the exponent of 3.

= [tex]3^{4} *3^{3}[/tex]

we know that,

if base are equal exponents are added.

= [tex]3^{4+3}[/tex]

= [tex]3^{7}[/tex]

= 3*3*3*3*3*3*3

= 9*3*3*3*3*3

= 27*3*3*3*3

= 81*3*3*3

= 243*3*3

= 729*3

= 2187.

Therefore the simplified expression is 2187.

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The value e = 0.869 indicates that the ellipse is more elongated that circular.

Given,

x²/12+y²/49 = 1

We will compare with x²/a² + y²/b² = 1 where a<b

Coordinate of center = (0,0)

Here a²=12 and b²=49

We know that the formula of eccentricity(e)

e=√(1-(a²/b²))

= √(1-(12/49))

= √37/7

=0.869

Therefore e=√37/7 = 0.869

Therefore this value indicates that the ellipse is more elongated that circular.

In mathematics, an ellipse is a plane bend encompassing two central focuses, to such an extent that for all focuses on the bend, the amount of the two distances to the central focuses is a consistent. It sums up a circle, which is the extraordinary kind of oval wherein the two focal points are something similar.

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The value of prime numbers c in the equation is c = 2.

What is prime numbers?

Those greater than one are known as prime numbers. They simply have two variables, the number itself and factor 1.

We have given that a - b = c requires all of the integers to be positive prime numbers,

c can only have one outcome, which is 2.

                 [tex]e.g., 13 - 11 = 7 - 5 = 2.[/tex]

Hence in the given prime numbers c in the equation is c = 2.

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Answer: 92

Step-by-step explanation:

8 ounce of brown rice and 9 ounce quinoa sold.

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given:

Brown rice: $2.00 per pound

Quinoa: $4.50 per pound

let the brown rice sold x ounces

and, let the Quinoa sold be y ounces

So, the equations are:

x + y= 17

2x+ 4.5y= 54

2( 17- y) + 4.5y= 54

34 - 2y + 4.5y= 54

2.5y= 20

y= 20/2.5

y= 8 ounce

and, x= 17-8= 9 ounce

Hence, 8 ounce of brown rice and 9 ounce quinoa sold.

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In this "Simple Random Sample" scenario, 500500500 selected randomly registered phone numbers were chosen.

For the given data in the question.

Thus, 500500500 random registering phone numbers are randomly chosen by a state court employee using a computer, and the law firms connected to all those numbers are randomly chosen for an audit.

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Answer:

Step-by-step explanation:

3 as the x axis and -5 for the y axis

To produce five constructive batches of salsa, 2.5 cups of onion will be needed.

What is unitary method of problem solving?
The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units. The unitary approach involves calculating the value of a single unit, from which we can calculate the values of the necessary number of units.

Given, the number of onions required to produce one batch = 0.5 cup(s)
∴ The number of onions required to produce five batches = 0.5×5
= 2.5 cup(s)
Thus, to produce five constructive batches of salsa, 2.5 cups of onion will be needed.

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Answer:

[tex]y=2x+4[/tex]

Step-by-step explanation:

The slope of the given line is [tex]\frac{-2-4}{-2-1}=2[/tex].

Parallel lines have the same slope, so the equation is:

[tex]y-6=2(x-1) \\ \\ y-6=2x-2 \\ \\ y=2x+4[/tex]

The probability that the next spin will land on red or green or purple is 75%

Given , A spinner is divided into five colored sections that are not of equal size

Color      Frequency

Red            18

Blue            11

Green          8

Yellow         4

Purple          19

Total spin recorded = 18+11+8+4+19

=60

Let "A" be the event when spinner land on Red , "B" be the event when spinner land on Green and "C" be the event when spinner land on Purple

P(A) = 18/60 = 0.3

P(B) = 8/60 = 0.134

P(C) = 19/60 = 0.32

Probability that the next spin will land on red or green or purple will be P(A∪BC) = P(A) + P(B) + P(C)

P(A∪BC)  = 0.3 + 0.134 + 0.32 =0.754

= 0.754 × 100 = 75%

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The total cost of the shirts that have same cost when x=5 is,

c=70

A mathematical equation is a formula that joins two expressions and expresses their equivalence using the equals symbol (=). The definitions of the word equation and its cognates in different languages may differ slightly.

The entire cost is c

c = 40 + 6x

c = 20 + 10x

The quantity of shirts is x.

Via utilizing one of the equations to solve for one of the variables and then substituting that variable's value into the other equation, you can solve by substitution.

40+6x=20+10x

4x=20

x=5

You would solve for c in the first equation in this problem.

40+6x where x=5 then,

c=70

Since it has already been solved for c, all that is left to do is swap out c with its equivalent in the second equation.

20+10x where x=5 then,

c=70

Therefore, the total cost of the shirts that have same cost is c=70 when x=5.

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