Does the following linear programming problem exhibit infeasibility, unboundedness, alternate optimal solutions or is the problem solvable with one solution? Min 1X + 1Y s.t. 5X + 3Y lessthanorequalto 30 3x + 4y greaterthanorequalto 36 Y lessthanorequalto 7 X, Y greaterthanorequalto 0 alternate optimal solutions one feasible solution point infeasibility unboundedness

the 95% confidence interval for the proportion of all dies that pass the probe is [0.513,0.616].

Sampling is frequently used to estimate the percentage of population that possesses a particular attribute, such as the percentage of all faulty goods which come off an assembly line or the percentage among all buyers that enter a store and make a purchase before leaving. The population proportion is indicated p, while the sample proportion is written p. Thus, if 43% of individuals visiting a business make a purchase before departing, p = 0.43; if 78 people enter the store and make a transaction, p=78/200=0.39.

The sample proportion is a random variable because it differs from sample to sample in ways that are impossible to anticipate in advance. When seen as a random variable, it will be represented by the letter P.

How to solve?

An article reported that in a study of a particular wafer inspection process, 356 dies were examined by an inspection probe and 169 of these passed the probe.

So,p'=201/356=0.56460

The 95% confidence interval for the proportion of all dies that passed the probe will be,

p∈[p'±zα/2√p'(1−p')/n]

p∈[0.56460±1.96×√0.56460(1−0.56460)356]

p∈[0.513,0.616]

So the 95% confidence interval is [0.513,0.616].

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The probability the sum of the two numbers will be 7 is 4//35

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

Event A = Numbers from 3 to 9

Event B = Numbers from 1 to 5

From the above events, the possible outcomes that would result in a sum of 7 are:

3 + 4 = 7

4 + 3 = 7

5 + 2 = 7

6 + 1 = 7

i.e. 4 outcomes

The total number of outcomes is

Outcomes = (9 - 3 + 1) * (5 - 1 + 1)

Evaluate

Outcomes = 35

So, we have

P = 4/35

Hence, the probability is 4/35

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Answer: 56n-35

Step-by-step explanation:

Answer:triangles always equal 180 so subtract the variable inside the triangle.

Step-by-step explanation:

Answer:9c+63

Step-by-step explanation:

Answer:

Step-by-step explanation:

12/18= 2/3, that’s the ratio of how many questions he gets right compared to total questions

So if there are 30 questions total, he will get 20 right (30 x 2/3)

If you’re taking into consideration that he already answered 18 questions, he will get 8 more correct

Answer: A 45-degree angle is exactly half of a 90-degree angle formed between two rays. It is an acute angle and two angles measuring 45 degrees from a right angle or a 90-degree angle. We know that an angle is formed when two rays meet at a vertex.

Elena and Arturo Sarmiento own 500 shares of Walgreens (WAG)

stock. The annual yield for WAG is 22500.

The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.

Elena and Arturo Sarmiento own 500 shares of Walgreens (WAG)

stock.

After the quarterly dividends are reinvested under their

dividend reinvestment program (DRIP), they own 501.055 shares.

WAG is selling at $45.00 a share.

Total shares=500

Annual Dividend on 1 share =$45.00

Annual Dividend on 500 shares=$45.00 x 500

=$22500

As there are four quarters in a year, the total annual dividend will be divided by 4 to get the quarterly dividend.  

Quarterly Dividend for 500 shares=  22500/4

=$5625

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The exact length of the missing side of the triangle is approximately 17.68 cm.

To find the exact length of the missing side of the triangle, we can use the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.

Given that the legs of the triangle are 12 cm and 13 cm, we can label them as 'a' and 'b' respectively, and the missing side as 'c'.

We can set up the equation as follows:

a² + b² = c²

Plugging in the values:

12² + 13² = c²

Simplifying:

144 + 169 = c²

313 = c²

To find the exact length of the missing side, we take the square root of both sides:

√313 = √c²

17.68 ≈ c

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The probability of winning a single roll is 1/6 since there are six possible outcomes and only one of them is a win.

Using the formula for binomial probability, the probability of winning exactly 4 times in 20 rolls is:

P(X = 4) = (20 choose 4) * (1/6)^4 * (5/6)^(20-4)

where "20 choose 4" represents the number of ways to choose 4 rolls out of 20. This can be calculated as:

(20 choose 4) = 20! / (4! * 16!) = (20 * 19 * 18 * 17) / (4 * 3 * 2 * 1) = 4845

Substituting this value and the probabilities into the formula, we get:

P(X = 4) = 4845 * (1/6)^4 * (5/6)^16

P(X = 4) ≈ 0.2027

Therefore, the probability of winning exactly 4 times in 20 rolls is approximately 0.2027 or about 20.27%.

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Answer:

37 students in each bus so 111 students went on the bus

Step-by-step explanation:

6 students went on the bus so 117 - 6 = 111 there are 3 buses so 111 / 3 = 37 so 37 students per bus

Answer:

(x + 1)(x + 2) is divisible by 3.

Step-by-step explanation:

Assume that x is not divisible by 3. This means that x can be expressed as x = 3k + r, where k is an integer and r is the remainder when x is divided by 3. Since x is not divisible by 3, the remainder r must be either 1 or 2.

Case 1: r = 1

If r = 1, then x = 3k + 1. Now let's consider (x + 1)(x + 2):

(x + 1)(x + 2) = (3k + 1 + 1)(3k + 1 + 2)

= (3k + 2)(3k + 3)

= 3(3k^2 + 5k + 2)

We can see that (x + 1)(x + 2) is divisible by 3.

Case 2: r = 2

If r = 2, then x = 3k + 2. Now let's consider (x + 1)(x + 2):

(x + 1)(x + 2) = (3k + 2 + 1)(3k + 2 + 2)

= (3k + 3)(3k + 4)

= 3(3k^2 + 7k + 4)

We can see that (x + 1)(x + 2) is divisible by 3.

Hence, the statement is proven.

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The given equation is expressed as

- 8 = 8(y - 5)

To solve for y, we would divide both sides of the equation by 8. We have

- 8/8 = 8/8(y - 5)

- 1 = y - 5

Adding 5 to both sides of the equation, we have

- 1 + 5 = y - 5 + 5

4 = y

y = 4

The only value that is a solution is

y = 4

The other values are not solutions

Thus,

y

8 No

9 No

- 2 No

4 Yes

The margin of error can be calculated using the formula:
Margin of error = (upper limit of the confidence interval - lower limit of the confidence interval) / 2

In this case, a margin of error of 9.55 suggests that the sample mean is quite precise, since it's relatively close to the true population mean (which we know to be 52.90).

In this case, the lower limit of the confidence interval is 43.85 and the upper limit is 61.95.
Margin of error = (61.95 - 43.85) / 2
Margin of error = 9.55
Therefore, the margin of error is 9.55. This means that if the sample size were to be repeated, we would expect the sample mean to be within 9.55 units of the true population mean 95% of the time.
It's worth noting that the confidence interval provides a range of values within which we can be reasonably certain that the true population mean lies. The margin of error, on the other hand, gives us an indication of the precision of our estimate. However, if the margin of error were larger, this would indicate that our estimate is less precise and that we need a larger sample size to obtain a more accurate estimate of the population mean.

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The number 0.0098 has two significant digits.In scientific notation, it can be written as 9.8 x 10^(-3), where the digits 9 and 8 are significant.

The leading zeros before the 9 do not contribute to the number of significant digits. Therefore, the correct answer is option a. 2.

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The probability of drawing two balls from each box is 0.063, or 6.3%.

The probability of drawing two balls from each box, we need to calculate the probabilities of drawing a ball from each box separately and then multiply them together.

In Box A, the probability of drawing a white ball on the first draw is 10/25. After drawing a white ball, there are 9 white balls left out of a total of 24 balls, so the probability of drawing a white ball on the second draw from Box A is 9/24. Multiplying these probabilities together gives us (10/25) × (9/24) = 0.18.

Similarly, in Box B, the probability of drawing a white ball on the first draw is 15/25. After drawing a white ball, there are 14 white balls left out of a total of 24 balls, so the probability of drawing a white ball on the second draw from Box B is 14/24. Multiplying these probabilities together gives us (15/25) × (14/24) = 0.35.

The overall probability of drawing two balls from each box, we multiply the probabilities together: 0.18 × 0.35 = 0.063.

Therefore, the probability of drawing two balls from each box is 0.063, or 6.3%.

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Answer:

A: because I'm do math.

explination: yes

On solving the given functions, we got the values as follows:

1) (rs)(4)  = 8

2) ) \(\frac{r}{s}\) (3) = 2

What is a function?

A relation between a set of inputs and a set of allowable outputs is called a function. It has the property that every input is associated with exactly one output. A function from one set X to another allocates precisely one element of the other set Y to each element of X. Both the set X and the set Y are referred to as the function's domain and codomain, respectively. The basic conception of functions was the relationship between fluctuating quantities and other variables. Multiply the outputs of two functions to multiply them. Put the numerator of a fraction with the first function as the numerator and the denominator with the second function as the denominator to divide functions. If you can, simplify.

Given two functions,

r(x) = 2√x

s(x) = √x

Now we have to calculate the following:

1) (rs)(4) = r(4) * s(4)

Multiplying the functions and finding the value when x = 4.

Solving,

             =  2√4  * √4    = 2*2  * 2 = 8

2) \(\frac{r}{s}\) (3) = \(\frac{r(3)}{s(3)}\)

Dividing the functions and finding the value when x = 3.

Solving,

= \(\frac{2\sqrt{3} }{\sqrt{3} } = 2\)

Therefore on solving the given functions, we got the values as follows:

1) (rs)(4)  = 8

2) ) \(\frac{r}{s}\) (3) = 2

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On solving for x, we get x = -1

A number base is the number of digits or combination of digits that a system of counting uses to represent numbers. Decimal system is the most commonly used number system with base 10.

Given is the following expression -

3 base x + 34 base x - 40 base x = 0

The given expression can be solved by converting the above expression in decimal form. Therefore -

3 base x in decimal = (3 x⁰) base 10 = 3

34 base x in decimal = (3 x¹ + 4 x⁰) base 10 = 3x + 4

40 base x = (4 x¹ + 0 x⁰) base 10 = 4x

Substituting the decimal values in the expression given -

3 + (3x + 4) + 4x = 0

7x + 7 = 0

7x = -7

x = - 1

Therefore, on solving for x, we get x = -1

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Answer:

4.5

Step-by-step explanation:9/2 = 4.5

Answer:

the rate of change is -5.

Step-by-step explanation:

y = -5x - 3

-5 = rate of change

-3 = x intercept

Answer:

(x^2-5)(x + 7)

Step-by-step explanation:

Here, we want to factorize the given expression

That would be;

x^2(x + 7) - 5(x + 7)

= (x^2-5)(x+ 7)

Answer:

(x+7) (x^2 - 5)

Step-by-step explanation:

x

3

+7x

2

−5x−35

=x

2

(x)+x

2

(7)−5(x)−5(7)

=x

2

(x+7)−5(x+7)

​

Now we are left with a common factor of (x+7)(x+7)left parenthesis, x, plus, 7, right parenthesis, so we can factor it out:

\begin{aligned} &\phantom{=}x^2\purpleC{(x+7)}-5\purpleC{(x+7)} \\\\ &=\purpleC{(x+7)}(x^2-5) \end{aligned}

​

=x

2

(x+7)−5(x+7)

=(x+7)(x

2

−5)

​

Answer: C perpendicular

Step-by-step explanation:

The probability that Juliana will take jazz on Saturday morning based on the decision tree given is 3%.

The probability that jazz is taken is:

= 1 - Probability of ballet

= 1 - 70%

= 30%

The probability that if jazz is taken, it will be taken on Wednesday is:

= Probability that jazz is taken on Wednesday night / Probability that Jazz is taken

= 27% / 30%

= 90%

The probability that Jazz is taken on Saturday morning is therefore:

= Probability that jazz is taken x (1 - Probability of Wednesday night)

= 0.3 x ( 1 - 90%)

= 3%

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Answer:

(i)\(M \cup P=\{2,3,4,5,6,7,8,10,11,12,13,14,16,17,18,19,20,22,23,24,26,28,29,30\}\)

(ii)M-T={2,4,6,8,10,12,14,16,18,20,22,24,26,28,30}

(iii)P∪(M∩T) = {2, 3, 5, 7, 11, 13, 17, 19, 23, 29}

(iv)P’U(M∩T’)={2,4,6,8,9,10,12,14,15,16,18,20,21,22,24,25,26,27,28,30}

Step-by-step explanation:

Given the sets:

ε = {x: 2 ≤ x ≤30, x is an integer}

M = {even numbers}={2,4,6,8,10,12,14,16,18,20,22,24,26,28,30}

P = {prime numbers}={2, 3, 5, 7, 11, 13, 17, 19, 23, 29}

T = {odd numbers} ={3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29}

(i)This is the union of sets M and P. (Do not repeat same elemnts)

\(M \cup P=\{2,3,4,5,6,7,8,10,11,12,13,14,16,17,18,19,20,22,23,24,26,28,29,30\}\)

(ii)M-T: This is the set M less elements in set T.

Since \(M \cap T =\{\}\), the set M-T=M.

M-T={2,4,6,8,10,12,14,16,18,20,22,24,26,28,30}

(iii) P∪(M∩T)

\(M \cap T =\{\}\)

Therefore:

P∪(M∩T) = P

P∪(M∩T) = {2, 3, 5, 7, 11, 13, 17, 19, 23, 29}

(iv) P’U(M∩T’)

Since T is the set of odd numbers, its complement will be the set of even numbers.

T'=M={2,4,6,8,10,12,14,16,18,20,22,24,26,28,30}

M∩T’=M={2,4,6,8,10,12,14,16,18,20,22,24,26,28,30}

\(P' =\{4,6,8,9,10,12,14,15,16,18,20,21,22,24,25,26,27,28,30\}\)

Therefore:

P’U(M∩T’) = {4,6,8,9,10,12,14,15,16,18,20,21,22,24,25,26,27,28,30} U {2,4,6,8,10,12,14,16,18,20,22,24,26,28,30}

={2,4,6,8,9,10,12,14,15,16,18,20,21,22,24,25,26,27,28,30}

Answer:

10 + 7z

Step-by-step explanation:

the product of z and 7 is

7z

adding 10 to the expression would be

10 + 7z

The required expression is the binomial 7z+10

Polynomial is made up of two terms, namely Poly (meaning “many”) and Nominal (meaning “terms.”). A polynomial is an expression composed of variables, constants, and exponents, combined using mathematical operations such as addition, subtraction, multiplication, and division (No division operation by a variable). Based on the number of terms present in the expression, it is classified as monomial, binomial, and trinomial. For example P(x) = x2-5x+11

Given here: The statement " Product of z and 7 added to 10"

Now the product of z and 7 is given by 7z

Now adding 10 to the monomial we get

7z+10

Thus the result is a binomial

Hence, The required expression is the binomial 7z+10

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Answer:

if green without blue is yellow then yellow and blue make green

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

Ecology definition of niche