If a+11=20 what does a equal

Classify each system of equations as having a single solution, no solution, or infinite solutions.

mina [271]

To find what the answer is for this problem, we need to find out whether each of them have infinite, no, or single solutions. We can do this individually.

Starting with the first one, we need to convert both of the equations into slope-intercept form. y = -2x + 5 is already in that form, now we just need to do it to 4x + 2y = 10.

2y = -4x + 10
y = -2x +5

Since both equations give the same line, the first one has infinite solutions.

Now onto the second one. Once again, the first step is to convert both of the equations into slope-intercept form.

x = 26 - 3y becomes
3y = -x + 26
y = -1/3x + 26/3

2x + 6y = 22 becomes
6y = -2x + 22
y = -1/3 x + 22/6

Since the slopes of these two lines are the same, that means that they are parallel, meaning that this one has no solutions.

Now the third one. We do the same steps.

5x + 4y = 6 becomes
4y = -5x + 6
y = -5/4x + 1.5

10x - 2y = 7 becomes
2y = 10x - 7
y = 5x - 3.5

Since these two equations are completely different, that means that this system has one solution.

Now the fourth one. We do the same steps again.

x + 2y = 3 becomes
2y = -x + 3
y = -0.5x + 1.5

4x + 8y = 15 becomes
8y = -4x + 15
y = -1/2x + 15/8

Once again, since these two lines have the same slopes, that means that they are parallel, meaning that this one has no solutions.

Now the fifth one.

3x + 4y = 17 becomes
4y = -3x + 17
y = -3/4x + 17/4

-6x = 10y - 39 becomes
10y = -6x + 39
y = -3/5x + 3.9

Since these equations are completely different, there is a single solution.

Last one!

x + 5y = 24 becomes
5y = -x + 24
y = -1/5x + 24/5

5x = 12 - y becomes
y = -5x +12

Since these equations are completely different, this system has a single solution.

8 0

3 years ago

The mean life of a television set is 119 months with a standard deviation of 14 months. If a sample of 74 televisions is randoml

irina [24]

Answer:

50.34% probability that the sample mean would differ from the true mean by less than 1.1 months

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 normally distributed samples are 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 random variable X, with mean $\mu$ and standard deviation $\sigma$ , the sample means with size n of at least 30 can be approximated to a normal distribution with mean $\mu$ and standard deviation $s = \frac{\sigma}{\sqrt{n}}$

In this problem, we have that:

$\mu = 119, \sigma = 14, n = 74, s = \frac{14}{\sqrt{74}} = 1.63$

If a sample of 74 televisions is randomly selected, what is the probability that the sample mean would differ from the true mean by less than 1.1 months

This is the pvalue of Z when X = 119 + 1.1 = 120.1 subtracted by the pvalue of Z when X = 119 - 1.1 = 117.9. So

X = 120.1

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

By the Central Limit Theorem

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

$Z = \frac{120.1 - 119}{1.63}$

$Z = 0.68$

$Z = 0.68$ has a pvalue of 0.7517

X = 117.9

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

$Z = \frac{117.9 - 119}{1.63}$

$Z = -0.68$

$Z = -0.68$ has a pvalue of 0.2483

0.7517 - 0.2483 = 0.5034

50.34% probability that the sample mean would differ from the true mean by less than 1.1 months

8 0

3 years ago

There are a total of 722 students at dustins school

mylen [45]

Answer:

I had NOOOOO clue but can I get braonlost

4 0

2 years ago

Read 2 more answers

20 POINTS Please Will MARK AS A BRAINLEST

gayaneshka [121]

Answer:

tanA = $\frac{12}{5}$

Step-by-step explanation:

tanA = $\frac{opposite}{adjacent}$ = $\frac{BC}{AB}$ = $\frac{24}{10}$ = $\frac{12}{5}$

8 0

2 years ago

Read 2 more answers

You work part-time at the “Pack-it and Mail-it” that sells containers used for shipping items. Your photography teacher asks you

Lena [83]

Answer:

(a)18.85 Cubic Inches

(b)The box with dimensions of 4 in. x 3in. x 2 in.

Step-by-step explanation:

Part A

Volume of the 12 Containers

Height =2 Inches

Diameter=1 Inch

Radius=Diameter/2=1/2=0.5 Inch

Volume of a cylinder $=\pi r^2 h$

Volume of the 12 Containers

$=12 X \pi r^2 h\\=12 X\pi X0.5^2X2\\=6\pi $ cubic inches\\=18.85 \text{cubic inches (to two decimal places)}$

Part B

To determine the container which should be used, we first determine the volume of the available boxes.

Volume of the boxes

Volume of box with dimension 3 in. x 2 in. x 5 in.=3X2X5=30 Cubic Inches

Volume of box with dimension 4 in. x 3in. x 2 in.=4X3X2=24 Cubic Inches

Volume of box with dimension 5 in. x 6 in. x 5 in.=5X6X5=150 Cubic Inches

Volume of box with dimension 3 in. x 2 in. x 3 in. =3X2X3=18 Cubic Inches

The box that should be used with the least amount of wasted space is he box with volume 24 Cubic inches. i.e. box with dimensions 4 in. x 3in. x 2 in.

This is because the volume of the box(18 cubic inches) with dimension 3 in. x 2 in. x 3 in. is less than what is required.

4 0

3 years ago