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2 years ago

What is the sum of 1.25 + (-⅓) + (-⅞)

Mathematics

1 answer:

Law Incorporation [45]2 years ago

8 0

Answer: 0.04166

Step-by-step explanation:

1.25+(-1/3) +(-7/8)

1.25 - 1/3 - 7/8

= -8/24 - 21/24

= -8 - 21/ 24

= -29/24

= 1.25 - 29/24

= 1.25 - 1.20833

= 0.04166

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The fence around a circular garden is 18 feet long. What is the area of the garden to the nearest square foot? Use 3.14 for pi.

Sidana [21]

Answer:

A = 26 ft²

Step-by-step explanation:

To find the area of a circle, use the formula A = πr²

We know π = 3.14 and C = 18.

Use the circumference to find "r". C = 2πr

C = 2πr

18 = 2(3.14)r

18 = 6.28r

r = 18/6.28 Exact answer

r ≈ 2.866 Rounded to three decimal places

You can use either of the two bolded "r" values. I will use the rounded answer in the formula for area.

Substitute π = 3.14 and r = 2.866.

A = πr²

A = (3.14)(2.866)² Solve exponents first

A = 3.14(8.213956) Multiply

A = 25.7918218... Unrounded answer

A ≈ 26 Rounded to nearest square foot

Add the units back in.

7 0

3 years ago

Where does the graph of y= sin x from x = 0 to x = 217 start?

choli [55]

Answer:

B) at an x-intercept

Step-by-step explanation:

Hope this helps :))

5 0

3 years ago

Find the amount of each payment to be made into a sinking fund which earns 9% compounded quarterly and produces $43 comma 000

Solnce55 [7]

Answer:

$2647.18

Step-by-step explanation:

Formula : $A[\frac{1+(\frac{r}{n})^{n}-1 }{(\frac{r}{n} )}]$

Future value = $43,000

r = rate of interest = 9% = 0.09

t = 3.5 years (compounded quarterly)

n = number of compounding (3.5 × 4) = 14

Now put the values into formula :

43000 = $A[\frac{1+(\frac{0.09}{4})^{14}-1 }{(\frac{0.09}{4} )}]$

$43000=A(\frac{(1+0.0225)^{14}-1}{\frac{0.09}{4}})$

$43000=A(\frac{(1.0225)^{14}-1}{0.0225})$

43000=A( $\frac{0.365483427}{0.0225})$

43,000 = A(16.243708)

A = $\frac{43000}{16.243708}$

A = $2,647.17883 ≈ $2647.18

5 0

3 years ago

Use substitution to solve the system.<br> x=3y+5<br> 5x-4y=14<br> ______________<br> x=<br> y=

nataly862011 [7]

So what you do is go 5(3y+5)-4y=14 which equals 15y+25-4y=14 which turns into 11y+25=14 than you move the 25 over which equals 11y=-11 so y=-1 then you enter -1 in for y which looks like 5x-4(-1)=14 than you solve that which is 5x+4=14 than you move the 4 over and you get 5x=10 than x=2

x=2
y=-1

8 0

3 years ago

The overhead reach distances of adult females are normally distributed with a mean of 197.5 cm197.5 cm and a standard deviation

fiasKO [112]

Answer:

a) 5.37% probability that an individual distance is greater than 210.9 cm

b) 75.80% probability that the mean for 15 randomly selected distances is greater than 196.00 cm.

c) Because the underlying distribution is normal. We only have to verify the sample size if the underlying population is not normal.

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 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.

In this question, we have that:

$\mu = 197.5, \sigma = 8.3$

a. Find the probability that an individual distance is greater than 210.9 cm

This is 1 subtracted by the pvalue of Z when X = 210.9. So

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

$Z = \frac{210.9 - 197.5}{8.3}$

$Z = 1.61$

$Z = 1.61$ has a pvalue of 0.9463.

1 - 0.9463 = 0.0537

5.37% probability that an individual distance is greater than 210.9 cm.

b. Find the probability that the mean for 15 randomly selected distances is greater than 196.00 cm.

Now $n = 15, s = \frac{8.3}{\sqrt{15}} = 2.14$

This probability is 1 subtracted by the pvalue of Z when X = 196. Then

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

By the Central Limit Theorem

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

$Z = \frac{196 - 197.5}{2.14}$

$Z = -0.7$

$Z = -0.7$ has a pvalue of 0.2420.

1 - 0.2420 = 0.7580

75.80% probability that the mean for 15 randomly selected distances is greater than 196.00 cm.

c. Why can the normal distribution be used in part (b), even though the sample size does not exceed 30?

The underlying distribution(overhead reach distances of adult females) is normal, which means that the sample size requirement(being at least 30) does not apply.

5 0

3 years ago