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3 years ago

50 POINTS SHOW YOUR WORK

Mathematics

1 answer:

aliya0001 [1]3 years ago

8 0

Answer:

The % growth rate is 15.8%.

Step-by-step explanation:

Let the function is given by $f(w) = a(b)^{w}$ , where f(w) is the number of a specific product produced after w weeks.

Now, given for w = 0, f(0) = 190 = a

So, the function becomes $f(w) = 190(b)^{w}$ ............. (1)

Now, it is also give that at w = 1, f(1) = 220.

So, from equation (1) we get,

$220 = 190 (b)^{1} = 190b$

⇒ b = 1.15789.

Now, b = 1 + r

⇒ 1.15789 = 1 + r

⇒ r = 0.15789

Therefore, the % growth rate is 0.15789 × 100% = 15.8% (Approx.)

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the track team is trying to reduce their time for a relay race. First they reduce their time by 2.1 minutes. then they are able

koban [17]

Their beginning time was 16.06 minutes.

Step-by-step explanation:

The track team is trying to reduce their time for a relay race.

First they reduce their time by 2.1 minutes, take it as $t_{1}$ . Then they are able to reduce that time by 10 minutes, take it as $t_{2}$ . Let ‘X’ be the time in minutes at the beginning.

Given that their final time is 3.96 minutes, then their beginning time can be calculated as below,

$X-t_{1}-t_{2}=3.96 \text { minutes }$

$X=3.96+t_{1}+t_{2}$

By substituting the values, we get

$X=3.96+2.1+10=16.06 \text { minutes }$

Hence, their beginning time was 16.06 minutes.

7 0

4 years ago

Scores on the SAT Mathematics test are believed to be normally distributed. The scores of a simple random sample of five student

AysviL [449]

Answer:

The mean calculated for this case is $\bar X=584$

And the 95% confidence interval is given by:

$584-2.776\frac{86.776}{\sqrt{5}}=476.271$

$584+2.776\frac{86.776}{\sqrt{5}}=691.729$

So on this case the 95% confidence interval would be given by (476.271;691.729)

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".

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

$\mu$ population mean (variable of interest)

s represent the sample standard deviation

n represent the sample size

Solution to the problem

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 mean and the sample deviation we can use the following formulas:

$\bar X= \sum_{i=1}^n \frac{x_i}{n}$ (2)

$s=\sqrt{\frac{\sum_{i=1}^n (x_i-\bar X)}{n-1}}$ (3)

The mean calculated for this case is $\bar X=584$

The sample deviation calculated $s=86.776$

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

$df=n-1=5-1=4$

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 tabel to find the critical value. The excel command would be: "=-T.INV(0.025,4)".And we see that $t_{\alpha/2}=2.776$

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

$584-2.776\frac{86.776}{\sqrt{5}}=476.271$

$584+2.776\frac{86.776}{\sqrt{5}}=691.729$

So on this case the 95% confidence interval would be given by (476.271;691.729)

3 0

3 years ago

For a recent year, the number of men in the U.S Senate totaled 4 more than five times the number of woman. Find the number of me

algol13

Answer:

There are 84 men and 16 women in the U.S Senate.

Step-by-step explanation:

We are given the following in the question:

Let x be the number of males and y be the number of females.

Total members = 100

Thus, we can write the equation:

$x + y = 100$

Men in the U.S Senate totaled 4 more than five times the number of woman.

Thus, we can write the equation:

$x = 4 + 5y$

Solving the two equations by substitution method, we have,

$(4+5y) + y = 100\\\Rightarrow 4 + 6y = 100\\\Rightarrow 6y = 96\\\Rightarrow y = 16\\\Rightarrow x = 4 + 5(16) = 84$

Thus, there are 84 men and 16 women in the U.S Senate.

8 0

4 years ago

Solve the equation 3.6g + 2 = 1.6g + 8. a. Find the value of g.

snow_tiger [21]

Answer:

Step-by-step explanation:

u put the gs with each other by flipping the one that was changed

3.6g-1.6g=8-2

2g=6

g=6/2

g=3

7 0

3 years ago

Read 2 more answers

For a given input value q, the function f outputs a value r to satisfy the following equation.

-Dominant- [34]

To solve this, you re-arrange the equation to get r by itself:

3r - 6 = 11q - 4
3r = 11q + 2 (add 6 to both sides to cancel out the -6)

r = $\frac{11q}{3} + \frac{2}{3}$ (divide both sides by 3 to get what r is)

This can also be written as: r = $\frac{11q+2}{3}$
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ANSWER:

f(q) = $\frac{11q}{3} + \frac{2}{3}$

OR

 f(q) = $\frac{11q+2}{3}$

OR

f(q) = (11q + 2) / 3 (if you can't put in fractions)

8 0

3 years ago