Solve for x using the Quadratic Formula: x2 + 4x + 4 = 0<br> -b + Vb2

Two cars traveling toward each other are 250 miles apart. Car a is traveling 15 miles per hour faster than car

Anon25 [30]

Let car b be travelling at x mph. as they are travelling towards each other their speed of approach is (x + x + 15 ) mph. So we have the equation

speed = distance / time

2x + 15 = 250 / 2

2x = 125 - 15 = 110

x = 55 mph

Car b travels at 55 mph and car a travels at 70 mph Answer

3 0

2 years ago

a storeroom 21 feet long, 15 feet wide, and 11 feet high was enlarged to a length of 25 feet and a width of 17 feet. how many cu

xenn [34]

<h2>1210 cubic feet</h2>

Step-by-step explanation:

Initial dimensions of the storeroom were $21\text{ }ft$ length, $15\text{ }ft$ width and $11\text{ }ft$ height.

The room is in the shape of a cuboid. Volume of a cuboid = $V=l\times b\times h$ , where $l,b,h$ are the length, width and height of the cuboid.

So, Volume of storeroom initially = $21\text{ }ft\text{ }\times15\text{ }ft\text{ }\times11\text{ }ft\text{ }=3465\text{ }ft^{3}\text{ }$

Finally, the length was increased to $25\text{ }ft$ and width to $17\text{ }ft$ .

Final volume of storeroom = $25\text{ }ft\text{ }\times 17\text{ }ft\text{ }\times 11\text{ }ft\text{ }=4675\text{ }ft^{3}\text{ }$

Increase in volume = $4675\text{ ft}^{3}-3465\text{ ft}^{3}=1210\text{ ft}^{3}$

∴ 1210 cubic feet of storage was added.

7 0

2 years ago

Abbey wants to use her savings of $1,325 to learn yoga. The total charges to learn yoga include a fixed registration fee of $35

Alborosie

Answer:

3.)35 + 50x ≤ 1,325

Step-by-step explanation:

7 0

3 years ago

Read 2 more answers

In a sample of 170 students at an Australian university that introduced the use of plagiarism-detection software in a number of

Kisachek [45]

Answer:

$p_v =P(Z>4.146)=0.0000169$

Based on the p value obtained and using the significance level given $\alpha=0.05$ we have $p_v$ so we can conclude that we have enough evidence to reject the null hypothesis, and we can said that at 5% of significance the proportion of students who NOT belief that such software unfairly targets students is higher than 0.5 or 50% .

Step-by-step explanation:

1) Data given and notation

n=170 represent the random sample taken

X=58 represent the student's who belief that such software unfairly targets students

$\hat px=\frac{58}{170}=0.341$ estimated proportion of students who belief that such software unfairly targets students

$\hat p=\frac{112}{170}=0.659$ estimated proportion of students who NOT belief that such software unfairly targets students

$p_o=0.50$ is the value that we want to test

$\alpha=0.05$ represent the significance level (no given)

z would represent the statistic (variable of interest)

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

p= proportion of student's who belief that such software unfairly targets students

2) Concepts and formulas to use

We need to conduct a hypothesis in order to test the claim that that a majority of students at the university do not share this belief. :

Null hypothesis: $p\leq 0.5$

Alternative hypothesis: $p>0.5$

We assume that the proportion follows a normal distribution.

When we conduct a proportion test we need to use the z statistic, and the is given by:

$z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}$ (1)

The One-Sample Proportion Test is used to assess whether a population proportion $\hat p$ is significantly (different,higher or less) from a hypothesized value $p_o$ .

<em>Check for the assumptions that he sample must satisfy in order to apply the test </em>

a)The random sample needs to be representative: On this case the problem no mention about it but we can assume it.

b) The sample needs to be large enough

$np_o =170*0.5=85>10$

$n(1-p_o)=170*(1-0.5)=85>10$

3) Calculate the statistic

Since we have all the info requires we can replace in formula (1) like this:

$z=\frac{0.659 -0.5}{\sqrt{\frac{0.5(1-0.5)}{170}}}=4.146$

4) Statistical decision

It's important to refresh the p value method or p value approach . "This method is about determining "likely" or "unlikely" by determining the probability assuming the null hypothesis were true of observing a more extreme test statistic in the direction of the alternative hypothesis than the one observed". Or in other words is just a method to have an statistical decision to fail to reject or reject the null hypothesis.

The significance level provided is $\alpha=0.05$ . The next step would be calculate the p value for this test.

Since is a one right side test the p value would be:

$p_v =P(Z>4.146)=0.0000169$

Based on the p value obtained and using the significance level given $\alpha=0.05$ we have $p_v$ so we can conclude that we have enough evidence to reject the null hypothesis, and we can said that at 5% of significance the proportion of students who NOT belief that such software unfairly targets students is higher than 0.5 or 50% .

8 0

2 years ago

Melissa’s birthday is next week and she has been receiving cards in the mail with different amounts of money. She has received 5

Mashutka [201]

Currently, the standard deviation is 10, because on average the cards were $10 away from the mean.

Adding another card with value $25 would decrease the standard deviation because it is closer to the mean the the current standard deviation.

6 0

3 years ago

Read 2 more answers

Solve for x using the Quadratic Formula: x2 + 4x + 4 = 0 -b + Vb2 - 4ac x= 2a