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Bingel [31]
2 years ago
13

Antonio works as a furniture salesman and earns a bace salasry of 450$ per week plus 6% commision on sales. What was antonios we

ekly commission if his total sales was 3750?
Mathematics
1 answer:
ICE Princess25 [194]2 years ago
8 0

Answer:

$ 198

Step-by-step explanation:

450 + 0.06x = 3750

0.06x = 3750 - 450

x = (3300 * 0.06) = 198

x = 198

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2y = 4x + 8 4y = 4x + 20
mars1129 [50]
<span>2y = 4x + 8  ------> y = 2x + 4
 4y = 4x + 20 ------> y = x+5

2x+4 =x+5
x = 1
y=x+5=1+5=6

Check:
</span>2*6 = 4*1 + 8 , 12 =12 
 4*6 = 4*1 + 20, 24 =24<span>

x=1,y=6
(1,6)
</span>

6 0
3 years ago
Read 2 more answers
Parts being manufactured at a plant are supposed to weigh 65 grams. Suppose the distribution of weights has a Normal distributio
andrew-mc [135]

Answer:

0.64%.

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean \mu and standard deviation \sigma, the z-score 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 p-value, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean \mu and standard deviation \sigma, the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean \mu and standard deviation s = \frac{\sigma}{\sqrt{n}}.

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

Mean of 75 grams and a standard deviation of 22 grams.

This means that \mu = 75, \sigma = 22

Sample of 144:

This means that n = 144, s = \frac{22}{\sqrt{144}} = 1.8333

More than 80 or less than 70:

Both are the same distance from the mean, so we find one probability and multiply by 2.

The probability that it is less than 70 is the pvalue of Z when X = 70. So

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

By the Central Limit Theorem

Z = \frac{X - \mu}{s}

Z = \frac{70 - 75}{1.8333}

Z = -2.73

Z = -2.73 has a pvalue of 0.0032

2*0.0032 = 0.0064.

0.0064*100% = 0.64%

The probability is 0.64%.

3 0
3 years ago
I don't think i've been so confused ever, how do I solve this using long division?
tankabanditka [31]

Check the picture below.

7 0
3 years ago
A food-packaging apparatus underfills 10% of the containers. Find the probability that for any particular 10 containers the numb
Maksim231197 [3]

Answer:

a) P(X = 1) = 0.38742

b) P(X = 3) = 0.05740

c) P(X = 9) = 0.00000

d) P(X \geq 5) = 0.00163

Step-by-step explanation:

For each container, there are only two possible outcomes. Either it is undefilled, or it is not. This means that we can solve this problem using the binomial probability distribution.

Binomial probability distribution:

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}

In which C_{n,x} is the number of different combinatios of x objects from a set of n elements, given by the following formula.

C_{n,x} = \frac{n!}{x!(n-x)!}

And p is the probability of X happening.

In this problem

There are 10 containers, so n = 10.

A food-packaging apparatus underfills 10% of the containers, so p = 0.1.

a) This is P(X = 1)

P(X = 1) = C_{10,1}.(0.1)^{1}.(0.9)^{9} = 0.38742

b) This is P(X = 3)

P(X = 3) = C_{10,3}.(0.1)^{3}.(0.9)^{7} = 0.05740

c) This is P(X = 9)

P(X = 9) = C_{10,9}.(0.1)^{9}.(0.9)^{1} = 0.00000

d) This is P(X \geq 5).

Either the number is lesser than five, or it is five or larger. The sum of the probabilities of each event is decimal 1. So:

P(X < 5) + P(X \geq 5) = 1

P(X \geq 5) = 1 - P(X < 5)

In which

P(X < 5) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4)

P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}

P(X = 0) = C_{10,0}.(0.1)^{0}.(0.9)^{10} = 0.34868

P(X = 1) = C_{10,1}.(0.1)^{1}.(0.9)^{9} = 0.38742

P(X = 2) = C_{10,2}.(0.1)^{2}.(0.9)^{8} = 0.1937

P(X = 3) = C_{10,3}.(0.1)^{3}.(0.9)^{7} = 0.05740

P(X = 4) = C_{10,4}.(0.1)^{1}.(0.9)^{9} = 0.38742

So

P(X < 5) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) = 0.34868 + 0.38742 + 0.19371 + 0.05740 + 0.01116 = 0.99837

Finally

P(X \geq 5) = 1 - P(X < 5) = 1 - 0.99837 = 0.00163

3 0
3 years ago
Factoring the expression 15x+6 using GCF
s344n2d4d5 [400]
The answer is 3(5x+2) i hope this helps you.
3 0
3 years ago
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