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2 years ago

Evaluate the problem

Mathematics

2 answers:

Sedaia [141]2 years ago

5 0

Answer:

$x=-2$

Step-by-step explanation:

Isolate x by taking the log of each side:

$\frac{1}{4}=2^x\\log_2(\frac{1}{4})=log_2(2^x)\\x=-2$

This works because:

$2^{-2} =\frac{1}{2^{2}}=\frac{1}{4}$

If this helped, a brainliest would be greatly appreciated!

m_a_m_a [10]2 years ago

3 0

Answer:

-2

Step-by-step explanation:

$Log_{2}\frac{1}{4}$ = -2

I hope this helps!

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The Town of Hertfordshire clerk knows that 23% of dogs in the town have completed emotional support training. Hertfordshire plan

Nataly_w [17]

Answer:

95.64% probability that under 30% of the dogs are emotional support trained

Step-by-step explanation:

For each dog, there are only two possible outcomes. Either they have completed emotional support training, or they have not. So we use the binomial probability distribution to solve this problem.

However, we are working with samples that are considerably big. So i am going to aproximate this binomial distribution to the normal.

Binomial probability distribution

Probability of exactly x sucesses on n repeated trials, with p probability.

Can be approximated to a normal distribution, using the expected value and the standard deviation.

The expected value of the binomial distribution is:

$E(X) = np$

The standard deviation of the binomial distribution is:

$\sqrt{V(X)} = \sqrt{np(1-p)}$

Normal probability distribution

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

When we are approximating a binomial distribution to a normal one, we have that $\mu = E(X)$ , $\sigma = \sqrt{V(X)}$ .

In this problem, we have that:

$\mu = E(X) = np = 100*0.23 = 23$

$\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{100*0.23*0.77} = 4.21$

What is the probability that under 30% of the dogs are emotional support trained?

30% of 100 is 0.3*100 = 30

So this is the pvalue of Z when X = 30.

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{30 - 23}{4.1}$

$Z = 1.71$

$Z = 1.71$ has a pvalue of 0.9564.

So there is a 95.64% probability that under 30% of the dogs are emotional support trained

5 0

3 years ago

Please answer this correctly

Alexeev081 [22]

Answer:

Step-by-step explanation:

3 0

3 years ago

Read 2 more answers

At a sale this week, a suit is being sold for $217. This is a 38% discount from the original price. What is the original price?

34kurt

Answer:

List price (original price) = $350

Discount amount ($ saved) = $133

Step-by-step explanation:

The list price is the sale price ($217) divided by the difference of 1 minus the result of the discount (38%) divided by 100.

3 0

3 years ago

The length of a rectangle is twice its breadth. If its length is decreased half of the 10 cm and the breadth is increased by hal

Leto [7]

Since the length of this rectangle is twice its breadth, the length is equal to 40 cm.

<h3>How to calculate the area of a rectangle?</h3>

Mathematically, the area of a rectangle can be calculated by using this formula:

Area = Length × Width

Based on the information provided, we have:

Its length is decreased half of the 10 cm ⇒ (length - 5)

Its breadth is increased by half of the 10 cm ⇒ (breadth + 5)

Its area is increased by 75 cm ⇒ (area + 5)

Substituting the parameters into the formula, we have:

LB + 75 = (L - 5)(B + 5)

2B² + 75 = (2B - 5)(2B + 5)

2B² + 75 = 2B(B + 5) - 5(B + 5)

2B² + 75 = 2B² + 10B - 5B - 25

5B = 75 + 25

5B = 100

B = 100/20

B = 20 cm.

For the length, we have:

L = 2B

L = 2 × 20

L = 40 cm.

Read more on rectangle here: brainly.com/question/25292087

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6 0

2 years ago

. The sandwich shop offers 8 different sandwiches. Jamey likes them all equally. He picks one randomly each day for lunch. Durin

Margarita [4]

Answer:

Step-by-step explanation:

From the given information:

A sandwich shop offers eight types of sandwiches, and Jamey likes all of them equally.

The probability that Jamey picks any one of them is 1/8

Suppose

X represents the number of times he chooses salami

Y represents the number of times he chooses falafel

Z represents the number of times he chooses veggie

Then X+Y+Z ≤ 5 and;

5-X-Y-Z represents the no. of time he chooses the remaining

8 - 3 = 5 sandwiches

However, the objective is to determine the P[X=x,Y=y,Z=z] such that 0≤x,y,z≤5

So, since he chooses x no. of salami sandwiches with probability (1/8)x

and y number of falafel with probability (1/8)y

and for z (1/8)z

Therefore, the remaining sandwiches are chosen with probability $\dfrac{5}{8} (5-x-y-z)$

So. these x days, y days and z days can be arranged within five days in

$= \dfrac{5!}{x!y!z!(5-x-y-z)!}$

Thus;

$P[X=x,Y=y,Z=z]= \dfrac{5!}{x!y!z!(5-x-y-z)} \times \dfrac{1}{8}x*\dfrac{1}{8}y* \dfrac{1}{8}z* \dfrac{5}{8}(5-x-y-z)$

since 0 ≤ x, y, z ≤ 5 and x + y + z ≤ 5.

The distribution is said to be Multinomial distribution.

5 0

3 years ago

Evaluate the problem ​

Evaluate the problem