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1 year ago

What is the domain of y = log Subscript 4 Baseline (x + 3)?

Mathematics

2 answers:

quester [9]1 year ago

5 0

Answer:

All real numbers greater than -3

Step-by-step explanation:

The domain of a log is the baseline is greater than 0.

Set x + 3 greater than zero and solve

x + 3 > 0

x > -3

Virty [35]1 year ago

5 0

Answer:

(B) all real numbers greater than –3

Step-by-step explanation:

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Sam takes a job with a starting salary of $50,000 for the first year. He earns a 4% increase each ear. Which expression gives th

gtnhenbr [62]

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2 years ago

Use the function below to find F(3). F(x) = 3x

Vikki [24]

The value of F(3) = 27.

Step-by-step explanation:

Step 1:

F(x) is dependent on the value of x.

So x is independent while F(x) is dependent on x i.e. the value of F(x) depends on the value of x.

Step 2:

F(x) = $3^{x}$ , if we have the x's value we can calculate the F(x)'s value.

Here the value of x is given as 3 so F(x) when x equals 3 can be calculated.

$F(x) = 3^{x} , F(3) = 3^{3} = 27.$

So F(3) = 27.

7 0

2 years ago

The total cost of an item including sales tax is directly proportional to its price. If the total cost of a $32 item is $33.60 ,

pav-90 [236]

Let the total cost of the item be represented by C and the price be represented by P, then given that the total cost of an item including sales tax is directly proportional to its price, thus

$C\propto P \\ \\ \Rightarrow C=kP$

where k is a constant.

Given that the total cost of a $32 item is $33.60, thus

$33.60=32k \\ \\ \Rightarrow k= \frac{33.60}{32} =1.05$

Therefore, the total cost on a $55 item is given by

$C=1.05\times55=\$57.75$

3 0

2 years ago

There are two misshapen coins in a box; their probabilities for landing on heads when they are flipped are, respectively, .4 and

Leokris [45]

Answer:

E(X) = 6.0706

Step-by-step explanation:

1) Define notation

X = random variable who represents the number of heads in the 10 first tosses

Y = random variable who represents the number of heads in range within toss number 4 to toss number 10

And we can define the following events

a= The first coin has been selected

b= The second coin has been selected

c= represent that we have 2 Heads within the first two tosses

2) Formulas to apply

We need to find E(X|c) = ?

If we use the total law of probability we can find E(Y)

E(Y) = E(Y|a) P(a|c) + E(Y|b)P(b|c) ....(1)

Finding P(a|c) and using the Bayes rule we have:

P(a|c) = P(c|a) P(a) / P(c) ...(2)

Replacing P(c) using the total law of probability:

P(a|c) = [P(c|a) P(a)] /[P(c|a) P(a) + P(c|b) P(b)] ... (3)

We can find the probabilities required

P(a) = P(b) = 0.5

P(c|a) = (3C2) (0.4^2) (0.6) = 0.288

P(c|b) = (3C2)(0.7^2) (0.3) = 0.441

Replacing the values into P(a|c) we got

P(a|c) = (0.288 x 0.5) /(0.288x 0.5 + 0.441x0.5) = 0.144/ 0.3645 = 0.39506

Since P(a|c) + P(b|c) = 1. With this we can find P(b|c) = 1 - P(a|c) = 1-0.39506 = 0.60494

After this we can find the expected values

E(Y|a) = 7x 0.4 = 2.8

E(Y|b) = 7x 0.7 = 4.9

Finally replacing the values into equation (1) we got

E(Y|c) = 2.8x 0.39506 + 4.9x0.60494 = 4.0706

And finally :

E(X|c) = 2+ E(Y|c) = 2+ 4.0706 = 6.0706

6 0

2 years ago

According to a survey, 10% of Americans are afraid to fly. Suppose 1100 Americans are sampled. a) What is the probability that 1

JulijaS [17]

Answer:

a) 14.46%

b) 0.00%

c) 1.54%

Step-by-step explanation:

According to the survey, 10% of Americans are afraid to fly.

This means $p=0.10$ and $q=1-0.10=0.90$ .

If 1100 Americans are sampled, then the sample size is $n=1100$ .

The mean of the distribution is $\mu=np$ .

This means $\mu=1100\times 0.10=110$

The standard deviation is $\sigma=\sqrt{npq}$

We substitute the values to get:

$\sigma=\sqrt{1100\times 0.1\times 0.9}=9.95$

a) We want to find the probability that 121 or more Americans in the survey are afraid to fly.

We first apply the continuity correction factor to get: $P(X\ge121)=P(X\:>\:121-0.5)\\P(X\ge121)=P(X\:>\:120.5)$

We now convert to Z-scores to get:

$P(X\:>\:120.5)=P(z\:>\:\frac{120.5-110}{9.95})=1.06\\$

From the standard normal distribution table P(z>1.06)=0.1446

As a percentage, the probability is 14.46%

b) We want to find the probability that 165 or more Americans in the survey are afraid to fly.

We apply the CCF to get:

$P(X\ge165)=P(X\:>\:165-0.5)\\P(X\ge165)=P(X\:>\:164.5)$

We convert to z-scores:

$P(X\:>\:164.5)=P(z\:>\:\frac{164.5-110}{9.95})=5.48$

From the normal distribution, P(z>164.5)=0

c) First, 8% of 1100 is 88.

We want to find the probability that 88 or less Americans in the survey are afraid to fly.

We apply the CCF to get:

$P(X\le88)=P(X\:$

We convert to z-scores:

$P(X\:$

From the normal distribution, P(z>\:-2.16)=0.0154

As a percentage, we get 1.54%

3 0

2 years ago