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3 years ago

If you were to use the substitution method to solve

Mathematics

2 answers:

ella [17]3 years ago

7 0

Answer:

x = 1

Step-by-step explanation:

Given :

6x – y = 1

4x – 3y = –11

To Find : the new equation after the expression equivalent to y from the first equation is substituted into the second equation.

Solution :

6x – y = 1 ---a

4x – 3y = –11 ---b

In equation a

y = 6x-1

Now substitute this value of y in equation b

4x – 3(6x-1)= –11

Thus the new equation : 4x-18x+3 = -11

-14x =-14

$x=\frac{-14}{-14}$

x=1

Put value of x in equation a

6*1– y = 1

6-y=1

5=y

Thus the solution is (1,5)

Nata [24]3 years ago

6 0

The substitution method:
y = 6 x - 1 ( the new equation )
After that:
4 x - 3 ( 6 x - 1 ) = -11
4 x - 18 x + 3 = - 14
- 14 x = - 14
x = 1, y = 6 * 1 - 1
y = 5

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A courier service company wishes to estimate the proportion of people in various states that will use its services. Suppose the

Orlov [11]

Answer:

95.44% probability that the sample proportion will differ from the population proportion by less than 0.03.

Step-by-step explanation:

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

Normal probability distribution

When the distribution is normal, we use 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.

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.

For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean $\mu = p$ and standard deviation $s = \sqrt{\frac{p(1-p)}{n}}$

In this question:

$p = 0.05, n = 212, \mu = 0.05, s = \sqrt{\frac{0.05*0.95}{212}} = 0.015$

What is the probability that the sample proportion will differ from the population proportion by less than 0.03?

This is the pvalue of Z when X = 0.03 + 0.05 = 0.08 subtracted by the pvalue of Z when X = 0.05 - 0.03 = 0.02. So

X = 0.08

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

By the Central Limit Theorem

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

$Z = \frac{0.08 - 0.05}{0.015}$

$Z = 2$

$Z = 2$ has a pvalue of 0.9772

X = 0.02

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

$Z = \frac{0.02 - 0.05}{0.015}$

$Z = -2$

$Z = -2$ has a pvalue of 0.0228

0.9772 - 0.0228 = 0.9544

95.44% probability that the sample proportion will differ from the population proportion by less than 0.03.

6 0

3 years ago

Leon has already run 1 mile on his own, and he expects to run 3 miles during each track practice. Write an equation that shows t

maks197457 [2]

Answer:

d = 1 + 3p

Step-by-step explanation:

Leon already ran 1 miles on his own and he is expected to cover a distance d of 3 miles during each practice. The number of practices is expressed as p and the distance covered is expressed as d.

For every track practice he is expected to cover a distance of 3 miles. Recall he has already cover 1 mile on his own.

Therefore, the relationship between the practices p and the distance d can be expressed as follows.

number of track practice = p

distance covered = d

The distance covered d in miles is 1 miles plus the number of track practice p multiply by 3

d = 1 + 3p

5 0

3 years ago

Ayudaaa se los agradeceria

jekas [21]

Answer:

-2

Step-by-step explanation:

since the base are the same you add the exponent.

4x+2 + 2x-1= -3x-17

4x+2x +3x =-17-2+1

9x =-18

x=-2

7 0

3 years ago

Write the ratio of 885 to 45 in lowest terms

attashe74 [19]

19 or 19/1

Hope this helped!

8 0

3 years ago

Hey can you please help me posted picture of question

Rudik [331]

Answer:
f⁻¹(x) = $\frac{7x-3}{4}$

Explanation:
To get the inverse of a function, we have to follow these steps:
1- replace f(x) with y
2- swap the x and y variables
3- solve for y
4- replace y with f⁻¹(x)

Applying this to the given as follows:
f(x) = $\frac{4x-3}{7}$

Step 1: replace f(x) with y:
y = $\frac{4x-3}{7}$

Step 2: swap the x and y variables:
x = $\frac{4y-3}{7}$

Step 3: solve for y:
7x = 4y - 3
4y = 7x - 3
y = $\frac{7x-3}{4}$

Step 4: replace y with f⁻¹(x):
f⁻¹(x) = $\frac{7x-3}{4}$

Hope this helps :)

8 0

4 years ago