Answer, show work, due today

What is the most efficient first step to isolate the variable term on one side of this equation?

Nat2105 [25]

Answer:subtract by 4x on each side first

Step-by-step explanation:

When you do so you'll get 5x on the left side of the equal sign and -5 on the right side. Next you would divide by 5 on both sides and this gives you x on the left side and -1 as your answer on the right side.

7 0

3 years ago

Read 2 more answers

Please help me answer.

katen-ka-za [31]

Answer:

Slope-intercept: y=3/4x+1

Sorry idk how to do general form

Step-by-step explanation:

Slope-intercept form is y=mx+b, m being the slope, b being the y-intercept.

The slope of this graph is 3/4, and the y-intercept is 1.

4 0

3 years ago

Read 2 more answers

The data given for a football kicked from the field follows a quadratic model, h(x) = - 3x2 + 18x + 7. Where h(t) is the height

OLga [1]

Answer:

C) 34

Step-by-step explanation:

use -b/2a to find the x value of the vertex (3)

then plug 3 into equation

- 3(3)² + 18(3) + 7

the answer is 34

4 0

2 years ago

Suppose the weights of Farmer Carl's potatoes are normally distributed with a mean of 8.0 ounces and a standard deviation of 1.1

svet-max [94.6K]

Answer:

a) 0.9959 = 99.59% probability that the mean weight is less than 9.3 ounces

b) 0.0129 = 1.29% probability that the mean weight is more than 9.0 ounces

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 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.

Mean of 8.0 ounces and a standard deviation of 1.1 ounces.

This means that $\mu = 8, \sigma = 1.1$

(a) If 5 potatoes are randomly selected, find the probability that the mean weight is less than 9.3 ounces?

$n = 5$ means that $s = \frac{1.1}{\sqrt{5}} = 0.4919$

This probability is the pvalue of Z when X = 9.3. So

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

By the Central Limit Theorem

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

$Z = \frac{9.3 - 8}{0.4919}$

$Z = 2.64$

$Z = 2.64$ has a pvalue of 0.9959

0.9959 = 99.59% probability that the mean weight is less than 9.3 ounces

(b) If 6 potatoes are randomly selected, find the probability that the mean weight is more than 9.0 ounces?

$n = 6$ means that $s = \frac{1.1}{\sqrt{6}} = 0.4491$

This probability is 1 subtracted by the pvalue of Z when X = 9. So

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

$Z = \frac{9 - 8}{0.4491}$

$Z = 2.23$

$Z = 2.23$ has a pvalue of 0.9871

1 - 0.9871 = 0.0129

0.0129 = 1.29% probability that the mean weight is more than 9.0 ounces

8 0

3 years ago

When a number is increased by 8.2%, the result is 106. What is the original number to the nearest tenth?

ruslelena [56]

Answer:

Step-by-step explanation:

Let the original number = x

$x+\frac{8.2}{100}*x=106\\\\x+0.082x=106\\\\1.082x=106\\\\x=\frac{106}{1.082}\\\\x=\frac{106*1000}{1.082*1000}\\\\x=\frac{106000}{1082}\\\\x=97.96\\\\$

x=98.0

x=98

4 0

2 years ago