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3 years ago

Factor the express using GCF 1. 54x - 30 2. 4+24

Mathematics

1 answer:

borishaifa [10]3 years ago

8 0

Answer:

1) 6 (9x - 5)

2) 4 (1 + 6)

Step-by-step explanation:

54x - 30

The greatest common factor is 6, hence take out 6

6 (9x - 5)

4 + 24

The greatest common factor is 4, take out 4

4 (1 + 6)

*I am not simplifying this because as per what is given, I am unsure if one of these numbers is actually a coefficient.

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Working together, jo and ralph can do the garden chores in 6 hours. it takes jo twice as long as ralph to do the work alone. how

creativ13 [48]

Let's say Ralph can do the chores in h hours, and Jo in 2h. Then:
1/h+1/2h=1/6
6+3=h
h=9
Ralph takes 9 hours working alone; Jo takes 18 hours
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4 years ago

Which fractions are equivalent to 40

pickupchik [31]

Answer:

80/2, 120/3, 160/4, 200/5, 240/6, 280/7, 320/8, 360/9, 400/10, 440/11, 480/12, 520/13, 560/14 , 600/15, 640/16, 680/17, 720/18, 760/19, 800/20, 840/21

Step-by-step explanation:

3 0

3 years ago

A fruit fly experiment starts with 600 flies. If the number of flies after x days is given by the function P(x)=600e^0.3x, how m

slega [8]

Since ln(x) is the inverse of e^x and we want to find out when P(x)=1000, we will substitute P(x) by 1000 and then solve for x days.

1600e^0.3x = 1000

Divide 600 for both sides you will get:

5/3 = e^0.3x

Multiply ( ln ) for both sides and then divide by 0.3.

(ln 5/3)/(0.3) = x

x = 1.7

So there will be 1000 flies in approximately 1.7 days

6 0

4 years ago

Evaluate if a = 2 and b = 4 : 4a + 6b

bogdanovich [222]

Answer:

8+24

Step-by-step explanation:

4 times 2 is 8

6 times 4 is 24

5 0

3 years ago

A random sample of 110 lightning flashes in a certain region resulted in a sample average radar echo duration of 0.81 second and

Lina20 [59]

Answer:

a) $0.81-2.62\frac{0.34}{\sqrt{110}}=0.725$

$0.81+2.62\frac{0.34}{\sqrt{110}}=0.895$

So on this case the 99% confidence interval would be given by (0.725;0.895)

b) $n=(\frac{2.58(0.34)}{0.1})^2 =76.95 \approx 77$

So the answer for this case would be n=77 rounded up to the nearest integer

Step-by-step explanation:

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".

$\bar X=0.81$ represent the sample mean

$\mu$ population mean (variable of interest)

s=0.34 represent the sample standard deviation

n=110 represent the sample size

Part a

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

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

In order to calculate the critical value $t_{\alpha/2}$ we need to find first the degrees of freedom, given by:

$df=n-1=110-1=109$

Since the Confidence is 0.99 or 99%, the value of $\alpha=0.01$ 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: "=-T.INV(0.005,119)".And we see that $t_{\alpha/2}=2.62$

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

$0.81-2.62\frac{0.34}{\sqrt{110}}=0.725$

$0.81+2.62\frac{0.34}{\sqrt{110}}=0.895$

So on this case the 99% confidence interval would be given by (0.725;0.895)

Part b

The margin of error is given by this formula:

$ME=z_{\alpha/2}\frac{\sigmas}{\sqrt{n}}$ (a)

And on this case we have that ME =0.1 and we are interested in order to find the value of n, if we solve n from equation (a) we got:

$n=(\frac{z_{\alpha/2} \sigma}{ME})^2$ (b)

We can assume the following estimator for the population deviation $\hat \sigma =s =0.34$

The critical value for 99% of confidence interval now can be founded using the normal distribution. And in excel we can use this formla to find it:"=-NORM.INV(0.005;0;1)", and we got $z_{\alpha/2}=2.58/tex], replacing into formula (b) we got:
[tex]n=(\frac{2.58(0.34)}{0.1})^2 =76.95 \approx 77$

So the answer for this case would be n=77 rounded up to the nearest integer

4 0

3 years ago