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4 years ago

Write an equivalent expression for 4(x + 7) – 9

Mathematics

1 answer:

Igoryamba4 years ago

4 0

Look at the attached picture⤴

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Krista has a quiz today. There are 4 questions with 4 options. Each question only has one correct answer. She wants to guess and

Lyrx [107]

Answer:

The probability is 0.258

Step-by-step explanation:

In this question, we want to know the probability of Krista getting exactly 3 out of the options she chooses right.

For all the questions, there are 4 questions with 4 options each

Total number of options is 4 * 4 = 16 options

there are 3 wrong options and one correct option per question. Total number of correct option is 4 and the total number of wrong options is 12

Probability of selecting a wrong option is 12/16 = 3/4 while the probability of selecting a correct option is 1/4

Thus, we can use a Bernoulli approximation to get this probability of getting three right.

let the probability of selecting a correct option be p and that of a wrong option be a.

Probability of selecting exactly three correct ones will be;

P(r = 3) = nCr p^r q^(n-r)

where n is the total number of options and r is the number of options we are selecting to be correct.

The probability = 12C3 * (1/4)^3 * (3/4)^9

= 220 * 0.015625 * 0.075084686279 = 0.258

7 0

4 years ago

Productivity increases under which of these scenarios? a. inputs and outputs increase proportionately b. outputs decrease while

Anna [14]

Answer:

d. inputs decrease while outputs remain the same -- True here productivity increases.

Step-by-step explanation:

In any organization productivity is a measure of efficiency

Productivity is normally expressed as ratio of output/input

Obviously when output increases productivity increases and also

when input decreases productivity increases.

a. inputs and outputs increase proportionately -- False here no change.

b. outputs decrease while inputs remain the same -- False here productivity decreases.

c. inputs increase while output remains the same -- False here productivity decreases.

d. inputs decrease while outputs remain the same -- True here productivity increases.

3 0

3 years ago

Amelia and Elliott are collecting empty soda cans for recycling. Amelia has 13 less than 5 times the cans that Elliott has. Toge

bezimeni [28]

The answer is C

Start by making two equations with the given information

The first would just be their total cans:
E + A = 257

The second would be:
5E - A = 13

Then combine the equations to eliminate one variable.

6E = 270
E = 45

Now plug E back into one of the equations.

45 + A = 257
A = 212

8 0

3 years ago

Find the exact value of csc 240° in simplest form with a rational denominator.

VARVARA [1.3K]

Answer:

-2*sqrt(3)/3

Step-by-step explanation:

3 0

3 years ago

"6. A brand name has a 40% recognition rate. Assume the owner of the brand wants to verify that rate by beginning with a small s

statuscvo [17]

Answer:

(a) The probability that exactly 5 of the 6 consumers recognize the brand name is 0.0369.

(b) The probability that all of the selected consumers recognize the brand name is 0.0041.

(d) The events of 5 customers recognizing the brand name is unusual.

Step-by-step explanation:

Let X = number of consumer's who recognize the brand.

The probability of the random variable X is, P (X) = p = 0.40.

A random sample of size, n = 6 consumers are selected.

The random variable X follows a Binomial distribution with parameters n and p.

The probability mass function of X is:

$P(X=x)={n\choose x}p^{x}(1-p)^{n-x};\ x=0,1,2,3...$

(a)

Compute the value of P (X = 5) as follows:

$P(X=5)={6\choose 5}0.40^{5}(1-0.40)^{6-5}\\=6\times0.01024\times0.60\\=0.036864\\\approx0.0369$

Thus, the probability that exactly 5 of the 6 consumers recognize the brand name is 0.0369.

(b)

Compute the value of P (X = 6) as follows:

$P(X=6)={6\choose 6}0.40^{6}(1-0.40)^{6-6}\\=1\times 0.004096\times1\\=0.004096\\\approx0.0041$

Thus, the probability that all of the selected consumers recognize the brand name is 0.0041.

(c)

Compute the value of P (X ≥ 5) as follows:

P (X ≥ 5) = P (X = 5) + P (X = 6)

= 0.0369 + 0.0041

= 0.041

Thus, the probability that at least 5 of the selected consumers recognize the brand name is 0.041.

(d)

An event is considered unusual if the probability of its occurrence is less than 0.05.

The probability of 5 customers recognizing the brand name is 0.0369.

This probability value is less than 0.05.

Thus, the events of 5 customers recognizing the brand name is unusual.

8 0

4 years ago