Find the maximum value of the objective function and the values of x and y for which it occurs.
F = 2x + y
3x + 5y ≤ 45 x 20 and y20
2x + 4y ≤ 32

Given:

The radius of the circle is 6.48 in.

To find:

We need to find the arc length of RS.

Explanation:

Consider the formula to find the length of the arc.

There are 22 grams of fat and each gram of fat is 9 calories, then

945 calories represents 100%, then 198 represents:

21% of the calories are from g

a.

Consider that the volume (V) of a cone with radius 'R' and height 'H' is given by,

Substitute the values,

Therefore, option b is the correct choice.

b.

Consider that the volume (V') of a cylinder with radius 'R' and height 'H' is given by,

Solve for the ratio of volume of cone to that of cylinder as,

Therefore, option c is the correct choice.

The image of the point P(x, y) = (4, 2) by means of a translation formula is point P'(x, y) = (- 1, 4).

In this question we find the coordinates of a point set on Cartesian plane which is modified by using a translation, a kind of rigid transformation. Rigid transformations are transformations applied on geometric loci such that Euclidean distances are conserved.

Vectorially speaking, translations are described by the following formula:

P'(x, y) = P(x, y) + T(x, y)

Where:

If we know that P(x, y) = (- 9, - 3) and P'(x, y) = (- 14, - 1), then the translation vector is:

T(x, y) = P'(x, y) - P(x, y)

T(x, y) = (- 14, - 1) - (- 9, - 3)

T(x, y) = (- 5, 2)

Then, the image of the point (4, 2) is:

P'(x, y) = (4, 2) + (- 5, 2)

P'(x, y) = (- 1, 4)

The image of the point (4, 2) by using a translation formula is (- 1, 4).

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It is given that an item used to be sold for $3.70 per pound.

It is required to find the current price per pound if the price was increased by 20%.

A 20% increase in the price, $3.70 is calculated as:

Hence, the current price of the item is $4.44 per pound.

The current price of the item is $4.44 per pound.

Answer:

156.4 ÷ 23 = 6.8

Step-by-step explanation:

hope this helps

The inequality that represents the equation is 8x+4<=28. The money spent on each cup is $3 or less. So, B and D are the correct options

Number of cups ordered by Kara = 8 cups

Money spent on the child's meal by Kara = $4

Total money with Kara = $28

Let x represent the money Kara will spend on each cup of soup

In formulation of the equation we get the following:

Number of cups*Money she can spend on each cup + Money spent on child's meal <= 28

8x + 4<=28

Solving the inequality:

8x<=24

x<= $3

So, the cost of a cup is $3 or less

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Answer:

≈4,365%.

Step-by-step explanation:

1) для нахождения требуемой вероятности необходимо найти вероятность каждого из пяти выниманий, а затем перемножить их;

2) при каждом вынимании вероятности:

[tex]P_1=\frac{C^1_{10}*C^1_{10}}{C^2_{10}}=\frac{10}{19};\\P_2=\frac{C^1_9*C_9^1}{C^2_{18}}=\frac{9}{17};\\P_3=\frac{C^1_8*C_8^1}{C^2_{16}}=\frac{8}{15};\\P_4=\frac{C^1_7*C^1_7}{C^2_{14}}=\frac{7}{13};\\P_5=\frac{C^1_6*C^1_6}{C^2_{12}}=\frac{6}{11};[/tex]

3) требуемая вероятность:

P=P₁*P₂*P₃*P₄*P₅≈0,04365.

Solution

To graph the inequality,

we make y the subject of the formula;

The inequallity is;

D. 763 seconds

Explanation:

Data:

Seconds light travels distance between Sun and Earth : 500 seconds

Distance between Sun and Earth: 93 million miles

Distance between Sun and Mars: 142 million miles

Formula: (see image below)

Solution:

From Sun to Mars the light takes (142 * 500) / 93 = 763 seconds

NB:

The tactic is to first put the data given in a table like in the image above, to first multiply diagonally then divide horizontally. (starting from the data that his paired data).

Here the paired data missing is the time it takes for the light to travel from the Sun to Mars, therefore you'll multiply the distance between the Sun to Mars (known data missing a pair) by the time it takes light to travel from the Sun to Earth (known data with its pair), then divide the result by the distance between the Sun and earth (pair of the former mentioned known data)

Solution:

Given:

Recall that the z-value is expressed as

Thus,

A) maximum score that can be in the bottom 10% of scores

using the table of z-values,

for the bottom 10% scores, we have

To evaluate x, substitute the value of z into equation 1.

Thus,

Thus, the maximum score that can be in the bottom 10% of scores is 2.5

B) Two values for which the middle 80% of scores lie.

From the z score values shown below:

The z scores of the value are

Thus,

Thus, the two values for which the middle 80% of scores lie are 2.5 and 4.86.

Part A: -5/9, 6/10, -7/11, 8/12

Part B:

Part C: Positive

The given sequence is:

As seen above the sequence is an alternating sequence because it changes in sign

Also, neglecting the sign chnages, we will observe, a common diffference of 1 in the numerator and denominator

a) Therefore, if the pattern continues, the next 4 terms in the sequence are:

-5/9, 6/10, -7/11, 8/12

b)

Without the sign, the explicit equation representing the numerator is calculated below:

1, 2, 3, 4......

The first term, a = 1

The common difference, d = 1

This is an arithmetic sequence

N(n) = a + (n - 1)d

N(n) = 1 + (n - 1)(1)

N(n) = 1 + n - 1

N(n) = n

The explicit equation representing the denominator is calculated below

5, 6, 7, 8........

The first term, a = 5

The common difference, d = 1

D(n) = a + (n - 1)d

D(n) = 5 + (n - 1)(1)

D(n) = 5 + n - 1

D(n) = n + 4

The alternating sequence will include the term below:

Therefore, the explicit equation for f(n) representing the sequence is:

Part C) The sign of f(56) will be:

(-1)^56 = 1

Since this gives us a positive value, the sign of f(56) is positive

1a) The arrow will be (-x,y) for reflection

1b)The vertices are P(-(0),2), E(-4,6), N(-8,-1), T(-6,-3), A(-2/-4) = P(0,2), E(-4,6), N(-8,-1),T(-6,-3), A(-2,-4)

We have the system of equations

We can solve it subtraction, the first equation minus the second equation

Therefore x = -6, we can now find the value of y

Therefore the solution is

Answer:

function of f(-5) is equal to the same value of y in an equation y= f(x).

therefore x value is -5 on x-axis and on this point it gives the value of y-axis which is -2

The probability that a randomly selected citizen, aged 25 or

over, had 4 years of college : 0.2458

From the table

Total number of citizens aged 25 or above = 179 million.

number of citizens aged 25 or above, had 4 years of college = 44 million

Therefore, probability = 44/179 = 0.2458

Probability is a branch of mathematics that deals with calculating the probability of a given event, expressed as a number between 1 and 0. An event with a probability of 1 can be considered certain: for example, the probability of a coin toss. a toss that results in either "heads" or "tails" is 1 because there are no other options, assuming the coin lands flat. An event with  probability 0.5 can be considered equally likely to occur or not to occur: for example, the probability that a coin toss results in heads is 0.5, because the toss is equally  likely to result in tails." An event with  probability  0 can be considered impossible: for example, the probability that the a coin lands (uniformly) without both sides up is 0, because either "heads" or "tails" must be  up.

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The most appropriate choice for distributive property of algebraic expression will be given by-

21y is the required equivalent expression

What is distributive property of algebraic expression?

At first it is important to know about algebraic expression.

Algebraic expression consists of variables and numbers connected with addition, subtraction, multiplication and division.

Distributive property is a property which connects both addition and multiplication.

Suppose a, b and c are three numbers. Distributive property implies

a [tex]\times[/tex] (b + c) = a [tex]\times[/tex] b + a [tex]\times[/tex] c

Here,

y(6 + 15)

y [tex]\times[/tex] (6 + 15)

6 [tex]\times[/tex] y  + 15 [tex]\times[/tex] y

6y + 15y

21y

This is the required equivalent expression

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Answer:

-2

Step-by-step explanation:

This is where the line crosses the y axis.  It is at point (0,-2)

To find the value of x we need to write the equation in another form that tells us what to do; both sides of the equations are ratios then we have:

Then the equation is:

Solving for x we have:

Therefore, the value of x is 8/3

The amount Lins sister earns at her part-time job is proportional to the number of hours she works.

She earns 9.60 dollars per hour.

1. Write an equation in the form y=kx to describe this situation, where x represents the hours she works and y represents the dollars she earns.

$9.60 per hour means that y = 9.60 and x = 1

Since we found the value of constant k, so the relation becomes

2. is y a function of x? explain how you know

y is a function of x means that the value of y depends on the value of x.

In the above function, when the value of x changes then the value of y will also change.

3. Write an equation describing x as a function of y​

To write the equation describing x as a function of y, make x the subject of the equation.

This simply means to separate out the variable x.

We can see the upper vertix of the triangle in the first figure is at the point (0,6) and after the shrink is at (0,2). So what's the number I can divide 6 to get a 2? It's 3. So the scale factor is 1/3

Answer:

c+3

Step-by-step explanation:

The word 'sum' means addition, so the equation would be c+3

The relation is 12 ounces of yellow paint with 5 ounces of blue paint. To find how many ounces of blue would be needed if you used 20 ounces of yellow, we can use the next proportion:

Solving for x,

You would need 25/3 ounces of blue paint

Answer:

D. 1/4

Explanation:

By definition, two lines are parallel if they have the same slope.

Given that lines a and b are parallel; and the slope of line a = 1/4, then:

The slope of line b = 1/4.

The correct choice is D.

Answer:

y = 0.1x + 5

Step-by-step explanation:

0.1x = the amount he pays for all his texts and 5 is a fixed amount so add them up to get y

The expression in the form of 5ⁿ is 5⁻¹³

An expression is a set of numbers or variables combined using the operations + , – , × or ÷ . Arithmetic expression that contains only numbers and mathematical operators and algebraic expression that contains variables, numbers and mathematical operators.

Given:

F(x) = 5⁻⁵/5⁸

F(x) = 5⁻⁵⁻⁸

F(x) = 5⁻¹³

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Answer:

Step-by-step explanation:

The least common denominator of a and b is the smallest multiplier that is divisible by both a and b. In this case, for:

Answer:

Recall that the binomial theorem states that:

Then:

Therefore:

Answer:

5/5

Step-by-step explanation:

since its 5 times u re rolling the dice and u have 5 chances or 5 possibilities of getting 5

Answer:

Step-by-step explanation:

1) Set an equation

Getting a three on the dice is 1/6. So the opposite is 5/6.

5/6 * 5/6 * 5/6 * 5/6 * 5/6

2) Solve

3125/7776

0.4018

40.18%

Your answer would be 0, hope this helps.