Write as an equivalent expression: (3x+5)(2x+3)

OleMash [197]

Answer:

X= 143°

Step-by-step explanation:

You could do it your way or as you can see, there's a right angle, which equals 90°, so you could either add 44+46+53 or 90+53. You get the same answer, which is 143°.

3 0

2 years ago

Read 2 more answers

What is two thirds of eight

AlladinOne [14]

5 + 0.33333...

If you don't immediately recognize 0.33333.... as 1/3 (a very common fraction you should memorize), you can do the following. 

x = 0.33333... 

Multiply that by 10 to shift everything 1 place to the left: 
10x = 3.33333... 

Now subtract: 
10x - x = 3.33333... - 0.33333... 
9x = 3 
x = 3/9 
x = 1/3 

Answer: 
5 1/3 

P.S. Here's a shortcut way to turn a repeating decimal into a fraction. 

1) Take the repeated part and put it over an equivalent number of nines. 

Example: 
0.57575757... = 57/99 

At that point, see if you can reduce the fraction: 
= 19/33 

Another example: 
0.123123123... = 123/999 
= 41/333 

So in your example: 
5.33333... = 5 + 0.33333... 
= 5 + 3/9 
= 5 1/3

8 0

3 years ago

Of the 650 students at west more junior high,4% will receive a perfect attendance award. How many students will receive a perfec

jolli1 [7]

Answer:

26 students

Step-by-step explanation:

4% of 650 is 26

5 0

2 years ago

Read 2 more answers

What does 64.5% as a decimal equal?

Yuliya22 [10]

Answer:

0.645

Step-by-step explanation:

since a percent is out of 100, it could also be written a 64.5/100,

then converting a fraction into a decimal is jus dividing the two equaling to 0.645

5 0

2 years ago

Sales personnel for Skillings Distributors submit weekly reports listing the customer contacts made during the week.

mezya [45]

Answer:

a) The 90% confidence interval would be given by (18.52;20.49)

b) The 95% confidence interval would be given by (18.32;20.68)

Step-by-step explanation:

1) Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

$\bar X=19.5$ represent the sample mean for the sample

$\mu$ population mean (variable of interest)

$\sigma=5.2$ represent the population standard deviation

n=75 represent the sample size

2) Confidence interval 90%

The confidence interval for the mean is given by the following formula:

$\bar X \pm z_{\alpha/2}\frac{\sigma}{\sqrt{n}}$ (1)

Since the Confidence is 0.90 or 90%, the value of $\alpha=0.1$ and $\alpha/2 =0.005$ , and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-NORM.INV(0.005,0,1)".And we see that $z_{\alpha/2}=1.64$

Now we have everything in order to replace into formula (1):

$19.5-1.64\frac{5.2}{\sqrt{75}}=18.515$

$19.5+1.64\frac{5.2}{\sqrt{75}}=20.485$

So on this case the 90% confidence interval would be given by (18.52;20.49)

3) Confidence interval 95%

Since the Confidence is 0.95 or 95%, the value of $\alpha=0.05$ and $\alpha/2 =0.025$ , and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-NORM.INV(0.025,0,1)".And we see that $z_{\alpha/2}=1.96$

Now we have everything in order to replace into formula (1):

$19.5-1.96\frac{5.2}{\sqrt{75}}=18.323$

$19.5+1.96\frac{5.2}{\sqrt{75}}=20.677$

So on this case the 95% confidence interval would be given by (18.32;20.68)

5 0

2 years ago