Sarah walks into a grocery store with no more than 20 dollars to spend and needs to buy at least 3.5 pounds of flour and at least 2 pounds of sugar. Flour is 2 dollars per pound and sugar is 1.5 dollars per pound. Let x the amount of flour purchased and y be the amount of sugar purchased? Which of the following systems of inequalities represents this situation?

Answer:

A

Step-by-step explanation:

since it's negative so it will get smaller

Answer:

[tex]\sigma = 1.8[/tex]

Step-by-step explanation:

Given

[tex]\begin{array}{ccccccc}x & {0} & {1} & {2} & {3} & {4}& {5} \ \\ P(x) & {0.2} & {0.1} & {0.1} & {0.2} & {0.2}& {0.2} \ \end{array}[/tex]

Required

The standard deviation

First, calculate the expected value E(x)

[tex]E(x) = \sum x * P(x)[/tex]

So, we have:

[tex]E(x) = 0 * 0.2 + 1 * 0.1 + 2 * 0.1 + 3 * 0.2 + 4 * 0.2 + 5 * 0.2[/tex]

[tex]E(x) = 2.7[/tex]

Next, calculate E(x^2)

[tex]E(x^2) = \sum x^2 * P(x)[/tex]

So, we have:

[tex]E(x^2) = 0^2 * 0.2 + 1^2 * 0.1 + 2^2 * 0.1 + 3^2 * 0.2 + 4^2 * 0.2 + 5^2 * 0.2[/tex]

[tex]E(x^2) = 10.5[/tex]

The standard deviation is:

[tex]\sigma = \sqrt{E(x^2) - (E(x))^2}[/tex]

[tex]\sigma = \sqrt{10.5 - 2.7^2}[/tex]

[tex]\sigma = \sqrt{10.5 - 7.29}[/tex]

[tex]\sigma = \sqrt{3.21}[/tex]

[tex]\sigma = 1.8[/tex] --- approximated

Answer:

1/5

Step-by-step explanation:

Probability calculates the likelihood of an event occurring. The likelihood of the event occurring lies between 0 and 1. It is zero if the event does not occur and 1 if the event occurs.

For example, the probability that it would rain on Friday is between o and 1. If it rains, a value of one is attached to the event. If it doesn't a value of zero is attached to the event.

probability that the ticket drawn has a number which is a multiple of 5 =

Number of tickets that are a multiple of 5 / total number of tickets

Multiple of 5 = 5, 10, 15, 20

there would be 4 tickets that would be a multiple of 5

= 4/20

To transform to the simplest form. divide both the numerator and the denominator by 4

= 1/5

Answer:

[tex]10x^{5}y \sqrt{6xy}[/tex]

Step-by-step explanation:

Answer: (-1, 2)

Step-by-step explanation:

It's a counter-clockwise rotation, that means (x, y) changes to (y, -x).

(-2, -1) ⇒ (-1, -(-2)) ⇒ (-1, 2)

If it's a clockwise rotation, then (x, y) will change to (-y, x)

(-2, -1) ⇒ (-(-1), -2) ⇒ (1, -2)

Answer:

[tex]Area = 123.55 m^2[/tex]

Step-by-step explanation:

Given

[tex]Area = 1330ft^2[/tex]

Required

Convert to [tex]m^2[/tex]

To convert from square feet to square meter, we simply divide by 3.281^2

So, we have:

[tex]Area = \frac{1330}{3.281^2}m^2[/tex]

[tex]Area = \frac{1330}{10.765}m^2[/tex]

[tex]Area = 123.55 m^2[/tex]

Answer:

Orange

Step-by-step explanation:

As the chance of choosing orange is 18% which is the least.

Answer:

1.5%

Step-by-step explanation:

house value x property tax rate = property taxes

70,000 x property tax rate = 1050

property tax rate = 1050/70000

property tax rate = .015 0r 1.5%

Answer:

Class interval ____, Frequency _ C/frequency

1 - 10 ____________ 1 _________ 1

11 - 20 ___________ 4 _________ 5

20 - 30 __________ 6 _________ 11

31 - 40 ___________3 _________ 14

41 - 50 ___________ 1 _________ 15

51 - 60 ___________ 1 _________ 16

Step-by-step explanation:

Given the data :

35, 26, 31, 17, 46, 30, 28, 21, 26, 34, 15, 27, 7, 18, 16, 57

Class interval ____, Frequency _ C/frequency

1 - 10 ____________ 1 _________ 1

11 - 20 ___________ 4 _________ 5

20 - 30 __________ 6 _________ 11

31 - 40 ___________3 _________ 14

41 - 50 ___________ 1 _________ 15

51 - 60 ___________ 1 _________ 16

The next to highest frequency group has a frequency of 4 and the highest frequency of 6

Total frequency, n = (1 + 4 + 6 + 3 + 1 + 1) = 16

Answer:

x = 100 degree

Step-by-step explanation:

EF//GC => NF // OC

∠ANE=∠ONF     [Vertically opposite angles]

∠ONF=80

In Quadrilateral OCFN,

NF // OC

∠ ONF + x = 180     [Linear Pair]

=> 80 + x = 180

=> x = 180-80

=> x = 100

Answer:

x=100°

Step-by-step explanation:

corresponding angles

Answer:

11/12

Step-by-step explanation:

1/4 + 2/3

= 3/12 + 8/12

= 11/12

Answer:

Yes, it is appropriate

Step-by-step explanation:

Given

See attachment for pie chart

Required

Is the pie chart appropriate

The attached pie chart displays the distribution of each of the 4 genre. The partition occupied represents the measure of each genre.

Step-by-step explanation:

a) Use sine law:

[tex]\dfrac{g}{\sin 60} = \dfrac{17\:m}{\sin 49}[/tex]

Solving for g,

[tex]g = \left(\dfrac{\sin 60}{\sin 49}\right)(17\:m)=19.5\:m[/tex]

b) Use the cosine law here:

[tex]q^2 = (11\:\text{cm})^2 + (16\:\text{cm})^2 \\ - 2(11\:\text{cm})(16\:\text{cm})\cos 29[/tex]

Solving for q,

[tex]q = 8.3\:\text{cm}[/tex]

Answer:

Step-by-step explanation:

The solution of the problem has been solved on paper and attached in the attachment section. Kindly refer to that and feel free to ask any doubt.

Answer:

The remainder is 3x - 4

Step-by-step explanation:

[Remember] [tex]\frac{Dividend}{Divisor} = Quotient + \frac{Remainder}{Divisor}[/tex]

So, [tex]Dividend = (Quotient)(Divisor) + Remainder[/tex]

In this case our dividend is always P(x).

Part 1

When the divisor is [tex](x - 1)[/tex], the remainder is [tex]4[/tex], so we can say [tex]P(x) = (Quotient)(x - 1) + 4[/tex]

In order to get rid of "Quotient" from our equation, we must multiply it by 0, so [tex](x - 1) = 0[/tex]

When solving for [tex]x[/tex], we get

[tex]x - 1 = 0\\x - 1 + 1 = 0 + 1\\x = 1[/tex]

When [tex]x = 1[/tex],

[tex]P(x) = (Quotient)(x - 1) + 4\\P(1) = (Quotient)(1 - 1) + 4\\P(1) = (Quotient)(0) + 4\\P(1) = 0 + 4\\P(1) = 4[/tex]

--------------------------------------------------------------------------------------------------------------

Part 2

When the divisor is [tex](x + 3)[/tex], the remainder is [tex]104[/tex], so we can say [tex]P(x) = (Quotient)(x + 3) + 104[/tex]

In order to get rid of "Quotient" from our equation, we must multiply it by 0, so [tex](x + 3) = 0[/tex]

When solving for [tex]x[/tex], we get

[tex]x + 3 = 0\\x + 3 - 3 = 0 - 3\\x = -3[/tex]

When [tex]x = -3[/tex],

[tex]P(x) = (Quotient)(x + 3) + 104\\P(-3) = (Quotient)(-3 + 3) + 104\\P(-3) = (Quotient)(0) + 104\\P(-3) = 0 + 104\\P(-3) = 104[/tex]

--------------------------------------------------------------------------------------------------------------

Part 3

When the divisor is [tex](x^2 - x + 1)[/tex], the quotient is [tex](x^2 + x + 3)[/tex], and the remainder is [tex](ax + b)[/tex], so we can say [tex]P(x) = (x^2 + x + 3)(x^2 - x + 1) + (ax + b)[/tex]

From Part 1, we know that [tex]P(1) = 4[/tex] , so we can substitute [tex]x = 1[/tex] and [tex]P(x) = 4[/tex] into [tex]P(x) = (x^2 + x + 3)(x^2 - x + 1) + (ax + b)[/tex]

When we do, we get:

[tex]4 = (1^2 + 1 + 3)(1^2 - 1 + 1) + a(1) + b\\4 = (1 + 1 + 3)(1 - 1 + 1) + a + b\\4 = (5)(1) + a + b\\4 = 5 + a + b\\4 - 5 = 5 - 5 + a + b\\-1 = a + b\\a + b = -1[/tex]

We will call [tex]a + b = -1[/tex] equation 1

From Part 2, we know that [tex]P(-3) = 104[/tex], so we can substitute [tex]x = -3[/tex] and [tex]P(x) = 104[/tex] into [tex]P(x) = (x^2 + x + 3)(x^2 - x + 1) + (ax + b)[/tex]

When we do, we get:

[tex]104 = ((-3)^2 + (-3) + 3)((-3)^2 - (-3) + 1) + a(-3) + b\\104 = (9 - 3 + 3)(9 + 3 + 1) - 3a + b\\104 = (9)(13) - 3a + b\\104 = 117 - 3a + b\\104 - 117 = 117 - 117 - 3a + b\\-13 = -3a + b\\(-13)(-1) = (-3a + b)(-1)\\13 = 3a - b\\3a - b = 13[/tex]

We will call [tex]3a - b = 13[/tex] equation 2

Now we can create a system of equations using equation 1 and equation 2

[tex]\left \{ {{a + b = -1} \atop {3a - b = 13}} \right.[/tex]

By adding both equations' right-hand sides together and both equations' left-hand sides together, we can eliminate [tex]b[/tex] and solve for [tex]a[/tex]

So equation 1 + equation 2:

[tex](a + b) + (3a - b) = -1 + 13\\a + b + 3a - b = -1 + 13\\a + 3a + b - b = -1 + 13\\4a = 12\\a = 3[/tex]

Now we can substitute [tex]a = 3[/tex] into either one of the equations, however, since equation 1 has less operations to deal with, we will use equation 1.

So substituting [tex]a = 3[/tex] into equation 1:

[tex]3 + b = -1\\3 - 3 + b = -1 - 3\\b = -4[/tex]

Now that we have both of the values for [tex]a[/tex] and [tex]b[/tex], we can substitute them into the expression for the remainder.

So substituting [tex]a = 3[/tex] and [tex]b = -4[/tex] into [tex]ax + b[/tex]:

[tex]ax + b\\= (3)x + (-4)\\= 3x - 4[/tex]

Therefore, the remainder is [tex]3x - 4[/tex].

Answer:

m=5

n=-3

Step-by-step explanation:

3m+2m=9

3m-3n=24

3(5)+2(-3)=9

15-6=9 correct

here you go it's too easy

Step-by-step explanation:

Explanation is in the attachment .

Hope it is helpful to you ❣️☪️❇️

Answer:

It would take Al 7.5 days to build the grill alone.

Step-by-step explanation:

Since Tim and Al are bricklayers, and Tim can construct an outdoor grill in 5 days, and if Al helps Tim, they can build it in only 3 days, to determine how long would it take Al to build the grill alone should be done the following calculation:

1/5 + X = 1/3

0.20 + X = 0.333

X = 0.333 - 0.20

X = 0.1333333

X = 1 / 7.5

Therefore it would take Al 7.5 days to build the grill alone.

Answer:

1.

a. 2

b. 0.1353 probability that exactly 0 customers will arrive during a five-minute period, 0.2707 that exactly 1 customer will arrive, 0.2707 that exactly 2 customers will arrive and 0.1805 that exactly 3 customers will arrive.

c. 0.1428 = 14.28% probability that delays will occur.

2.

a. 0.4512 = 45.12% probability that the service time is one minute or less.

b. 0.6988 = 69.88% probability that the service time is two minutes or less.

c. 0.3012 = 30.12% probability that the service time is more than two minutes.

Step-by-step explanation:

Poisson distribution:

In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:

[tex]P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}[/tex]

In which

x is the number of sucesses

e = 2.71828 is the Euler number

[tex]\mu[/tex] is the mean in the given interval.

Exponential distribution:

The exponential probability distribution, with mean m, is described by the following equation:

[tex]f(x) = \mu e^{-\mu x}[/tex]

In which [tex]\mu = \frac{1}{m}[/tex] is the decay parameter.

The probability that x is lower or equal to a is given by:

[tex]P(X \leq x) = \int\limits^a_0 {f(x)} \, dx[/tex]

Which has the following solution:

[tex]P(X \leq x) = 1 - e^{-\mu x}[/tex]

The probability of finding a value higher than x is:

[tex]P(X > x) = 1 - P(X \leq x) = 1 - (1 - e^{-\mu x}) = e^{-\mu x}[/tex]

Question 1:

a. What is the mean or expected number of customers that will arrive in a five-minute period?

0.4 customers per minute, so for 5 minutes:

[tex]\mu = 0.4*5 = 2[/tex]

So 2 is the answer.

Question b:

[tex]P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}[/tex]

[tex]P(X = 0) = \frac{e^{-2}*2^{0}}{(0)!} = 0.1353[/tex]

[tex]P(X = 1) = \frac{e^{-2}*2^{1}}{(1)!} = 0.2707[/tex]

[tex]P(X = 2) = \frac{e^{-2}*2^{2}}{(2)!} = 0.2707[/tex]

[tex]P(X = 3) = \frac{e^{-2}*2^{3}}{(3)!} = 0.1805[/tex]

0.1353 probability that exactly 0 customers will arrive during a five-minute period, 0.2707 that exactly 1 customer will arrive, 0.2707 that exactly 2 customers will arrive and 0.1805 that exactly 3 customers will arrive.

Question c:

This is:

[tex]P(X > 3) = 1 - P(X \leq 3)[/tex]

In which:

[tex]P(X \leq 3) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)[/tex]

The values we have in item b, so:

[tex]P(X \leq 3) = 0.1353 + 0.2707 + 0.2707 + 0.1805 = 0.8572[/tex]

[tex]P(X > 3) = 1 - P(X \leq 3) = 1 - 0.8572 = 0.1428[/tex]

0.1428 = 14.28% probability that delays will occur.

Question 2:

[tex]\mu = 0.6[/tex]

a. What is the probability that the service time is one minute or less?

[tex]P(X \leq 1) = 1 - e^{-0.6} = 0.4512[/tex]

0.4512 = 45.12% probability that the service time is one minute or less.

b. What is the probability that the service time is two minutes or less?

[tex]P(X \leq 2) = 1 - e^{-0.6(2)} = 1 - e^{-1.2} = 0.6988[/tex]

0.6988 = 69.88% probability that the service time is two minutes or less.

c. What is the probability that the service time is more than two minutes?

[tex]P(X > 2) = e^{-1.2} = 0.3012[/tex]

0.3012 = 30.12% probability that the service time is more than two minutes.

Answer:

8x +15

Step-by-step explanation:

f(x) = 10 + 2x and g(x) = 6x + 5

(f+ g)(x) =  10 + 2x + 6x + 5

Combine like terms

              = 8x +15

Answer:

8x+15

Step-by-step explanation:

(f+g)(x) = f(x)+g(x)

= (10+2x) + (6x+5)

= 8x+15

hope it helped, please mark me brainliest.

Answer:

(2k, k)

Step-by-step explanation:

x + y = 3k

x - y = k

Add the equations.

2x = 4k

x = 2k

2k + y = 3k

y = k

Answer: (2k, k)

Answer:

86°

Step-by-step explanation:

180° is the sum of all angles in a triangle

The two angles given are 68° and 26°

The equation is : 180° - 68° - 26° = x°

180° - 68° - 26° = 86°

x° = 86°

If my answer is incorrect, pls correct me!

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-Chetan K

Answers:

You got the first question correct, but the second one is wrong. The two values must add up to 5.

===================================================

Explanation:

We're told that 20% of this solution is acid. We have 5 liters total, so

20% of 5 = 0.20*5 = 1

Meaning there's 1 liter of pure acid in this solution.

The remaining 5-1 = 4 liters of the solution is water

Or you could note that if 20% is pure acid, then the remaining 80% is water

80% of 5 = 0.80*5 = 4

------------------

Another approach is to realize that 20% is the same as the fraction 1/5

So if 1/5 of the mix is pure acid, and we have 5 liters of the solution, then we must have 1 liter of pure acid

(1 liter of pure acid)/(5 liters of solution) = 1/5 = 20% acid solution

Answer:

I think they all look pretty good for the most part

Step-by-step explanation:

Given that,

According to the question,

[tex]\longrightarrow[/tex] Total length = Sum of the length of the two pieces

[tex]\longrightarrow[/tex] Total length = {x + (7x – 9)} feet

[tex]\longrightarrow[/tex] Total length = {x + 7x – 9} feet

[tex]\longrightarrow[/tex] Total length = (8x – 9) feet

Therefore, the total length of the board as a simplified expression in x is (8x – 9) feet.

Answer:

There are 824 deer in the preserve.

Step-by-step explanation:

Since to determine the number of deer in a game preserve, a conservationist catches 412 deer, tags them and lets them loose, and later, 316 deer are caught, 158 of them are tagged, to determine how many deer are in the preserve you must perform the following calculation:

316 = 100

158 = X

158 x 100/316 = X

50 = X

50 = 412

100 = X

824 = X

Therefore, there are 824 deer in the preserve.

Answer:

B

substract the variables

Answer:

The domain of the expression is all real numbers except where the expression is undefined. In this case, there is no real number that makes the expression undefined.

Interval Notation:

( − ∞ , ∞ )

Set-Builder Notation:

{ x | x ∈ R }

Step-by-step explanation:

hope that helps bigger terms

Answer:

[tex](a)\ m = \frac{4}{3}[/tex] --- slope of OA

[tex](b)\ y = \frac{4}{3}x[/tex] --- the equation

Step-by-step explanation:

Given

The attached graph

Solving (a): Slope of OA

First, we identify two points on OA

[tex](x_1,y_1) = (0,0)[/tex]

[tex](x_2,y_2) = (3,4)[/tex]

So, the slope (m) is:

[tex]m = \frac{y_2 -y_1}{x_2 - x_1}[/tex]

This gives:

[tex]m = \frac{4-0}{3-0}[/tex]

[tex]m = \frac{4}{3}[/tex]

Solving (b): The equation

This is calculated as:

[tex]y = m(x - x_1) + y_1[/tex]

Recall that:

[tex](x_1,y_1) = (0,0)[/tex]

[tex]m = \frac{4}{3}[/tex]

So, we have:

[tex]y = \frac{4}{3}(x - 0) + 0[/tex]

[tex]y = \frac{4}{3}(x)[/tex]

[tex]y = \frac{4}{3}x[/tex]

Answer:

change inches into centimeter and then divide it

hope this help