F(x) = x2. What is g(x)? LMK ASAP

An item was purchased for m dollars. Sales tax is 8%. Write an expression that represents

Luba_88 [7]

Answer:

m/100 x 8

Step-by-step explanation:

7 0

3 years ago

A recipe says that 1 3/4 cups of baking soda are needed to make 1 batch of a homemade cleaning product, as represented below. Ho

RSB [31]

Answer:

4 3/8 cups of baking soda

Step-by-step explanation:

1 3/4 cups of baking soda are needed to make 1 batch of a homemade cleaning product,

Cups of baking soda : batches of homemade cleaning

1 3/4 cups : 1 batch

How many total cups of baking soda I needed to make 2 1/2 batches of the cleaning product?

Let x = total cups of baking soda needed

Cups of baking soda : batches of homemade cleaning

x cups : 2 1/2 batches

Equate the ratios

1 3/4 cups : 1 batch = x cups : 2 1/2 batches

7/4 ÷ 1 = x ÷ 5/2

7/4 × 1/1 = x * 2/5

7/4 = 2/5x

Divide both sides by 2/5

x = 7/4 ÷ 2/5

= 7/4 × 5/2

Cross product

x = 35/8

= 4 3/8 cups of baking soda

3 0

3 years ago

When circuit boards used in the manufacture of compact disc players are tested, the long-run percentage of defectives is 5%. Let

sergiy2304 [10]

Answer:

(a) P(X=3) = 0.093

(b) P(X≤3) = 0.966

(c) P(X≥4) = 0.034

(d) P(1≤X≤3) = 0.688

(e) The probability that none of the 25 boards is defective is 0.277.

(f) The expected value and standard deviation of X is 1.25 and 1.089 respectively.

Step-by-step explanation:

We are given that when circuit boards used in the manufacture of compact disc players are tested, the long-run percentage of defectives is 5%.

Let X = the number of defective boards in a random sample of size, n = 25

So, X ∼ Bin(25,0.05)

The probability distribution for the binomial distribution is given by;

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

where, n = number of trials (samples) taken = 25

r = number of success

p = probability of success which in our question is percentage

of defectivs, i.e. 5%

(a) P(X = 3) = $\binom{25}{3} \times 0.05^{3}\times (1-0.05)^{25-3}$

= $2300 \times 0.05^{3}\times 0.95^{22}$

= 0.093

(b) P(X $\leq$ 3) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)

= $\binom{25}{0} \times 0.05^{0}\times (1-0.05)^{25-0}+\binom{25}{1} \times 0.05^{1}\times (1-0.05)^{25-1}+\binom{25}{2} \times 0.05^{2}\times (1-0.05)^{25-2}+\binom{25}{3} \times 0.05^{3}\times (1-0.05)^{25-3}$

= $1 \times 1 \times 0.95^{25}+25 \times 0.05^{1}\times 0.95^{24}+300 \times 0.05^{2}\times 0.95^{23}+2300 \times 0.05^{3}\times 0.95^{22}$

= 0.966

(c) P(X $\geq$ 4) = 1 - P(X < 4) = 1 - P(X $\leq$ 3)

= 1 - 0.966

= 0.034

(d) P(1 ≤ X ≤ 3) = P(X = 1) + P(X = 2) + P(X = 3)

= $\binom{25}{1} \times 0.05^{1}\times (1-0.05)^{25-1}+\binom{25}{2} \times 0.05^{2}\times (1-0.05)^{25-2}+\binom{25}{3} \times 0.05^{3}\times (1-0.05)^{25-3}$