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2 years ago

Marco states that 7.696696669…… is a rational number because it is a repeating decimal. Is he correct? Justify your answer.

2 answers:

9 0

<span>No, Marco is not correct. The number does not actually repeat because after each 9 there is an additional 6 before the next 9. The number is not a rational number.</span>

Guest

1 year ago

Thank you so much this really helped me

Ksju [112]2 years ago

6 0

Answer:

No, Marco is incorrect because the numbers don't repeat themselves because after the decimal it says 69 then 669 and then 6669 and that is not repeating therefore, it is not a rational number.

Step-by-step explanation:

Guest

1 year ago

thanks

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3. Dr. Silas studies the culture of bacteria under a microscope. The function b1(t) = 1200 (1.8)^t represents the number of bact

Dominik [7]

Answer:

(a) the initial count of bacteria

(b) the growth factor (per hour)

(d) the difference in initial counts between the two studies

Step-by-step explanation:

(a) 1200 is b1(0), the initial count of bacteria.

(b) 1.8 is the growth factor per hour, the factor that multiplies the previous hour's count to get this hour's count.

(d) The difference between 1200 and 1000 means the first study started with 200 more bacteria than the second study did

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2 years ago

Write an arithmetic series for which S5 = 10.

Ludmilka [50]

S5=10 means the 5th number is 10.
So the arithmetic sequence is s1, s2,s3, s4, 10

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2 years ago

How many metres of cloth 4.4 m wide will be required to make a conical tent of radius of whose base is 3.5m and whose height is

musickatia [10]

$\Huge{\boxed{\sf{\red{22.98m}}}}$

<h3><u>Givєn</u> :</h3>

Radius of the tent,r = 3.5 m
Height of the tent, h = 8.4 m

length of the cloth required.

<h3><u>Solution</u> :</h3>

According to the question,

Slant height, l = $\displaystyle{\sf{ \sqrt{{r}^2 + {h}^2} = \sqrt{{3.5}^2 + {8.5}^2}}}$

$\implies$ $\displaystyle{\sf{ = 9.192m}}$

curved surface area = $\displaystyle{\sf{ \pi rl}}$

$\implies$ $\displaystyle{\sf{ \frac{22}{7} \times 3.5 \times 9.192{m}^2}}$

$\implies$ $\displaystyle{\sf{ 101.112}}$

i.e., Area of the cloth is 101.11m²

Now, length of the cloth required = $\displaystyle{\sf{ \frac{area}{width}}}$

$\implies$ $\displaystyle{\sf{ \frac{101.11}{4.4}}}$

$\implies$ $\large{\boxed{\sf{\red{22.98m}}}}$

7 0

2 years ago

Re-write 90+45 using the distributive property

Allisa [31]

You can factor out 45 out of both 90 and 45.

If we factor out 45, we are given the following...

45(2 + 1) because 45 goes into 90 2 times and 45 once.

3 0

2 years ago

Suppose that the Department of Transportation would like to test the hypothesis that the average age of cars on the road is less

dimulka [17.4K]

Answer:

$z=\frac{10.6-12}{\frac{4.1}{\sqrt{45}}}=-2.29$

$z_{critc}= -1.64$

Since our calculates values is lower than the critical value we have enough evidence to reject the null hypothesis at 5% of significance. And the best conclusion for this case is:

B. Since the test statistic is less than the critical value, we can conclude that the average age of cars on the road is less than 12 years.

Step-by-step explanation:

Data given and notation

$\bar X=10.6$ represent the sample mean

$\sigma=4.1$ represent the population standard deviation

$n=45$ sample size

$\mu_o =12$ represent the value that we want to test

$\alpha=0.05$ represent the significance level for the hypothesis test.

z would represent the statistic (variable of interest)

$p_v$ represent the p value for the test (variable of interest)

State the null and alternative hypotheses.

We need to conduct a hypothesis in order to check if the mean is less than 12, the system of hypothesis would be:

Null hypothesis: $\mu \geq 12$

Alternative hypothesis: $\mu < 12$

Since we know the population deviation, is better apply a z test to compare the actual mean to the reference value, and the statistic is given by:

$z=\frac{\bar X-\mu_o}{\frac{\sigma}{\sqrt{n}}}$ (1)

z-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".

Calculate the statistic

We can replace in formula (1) the info given like this:

$z=\frac{10.6-12}{\frac{4.1}{\sqrt{45}}}=-2.29$

Critical value

For this case since w ehave a left tailed distribution we need to find a value who accumulates 0.05 of the area on th left in the normal standard distribution, and we can use the following excel code:

"=NORM.INV(0.05,0,1)"

$z_{critc}= -1.64$

Conclusion

Since our calculates values is lower than the critical value we have enough evidence to reject the null hypothesis at 5% of significance. And the best conclusion for this case is:

B. Since the test statistic is less than the critical value, we can conclude that the average age of cars on the road is less than 12 years.

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2 years ago