Given the functions, f(x) = 4x3 - x2 + 1 and g(x) = x

Parker ran 600 meters, 7 kilometers, and 1,000 centimeters.

Naddika [18.5K]

Answer:

7610 m

Step-by-step explanation:

600m = 600m

7km = 7000m

1000cm = 10m

The required distance = 600 + 7000 + 10 = 7610 m

7 0

3 years ago

The four swimmers listed in the table are trying out for the swim team. Two will make the team. How many different combinations

ratelena [41]

Number of possible combinations = (4x3) ÷ 2 = 6

Answer: There are 6 possible combinations.

8 0

3 years ago

Jill rides her bike to her friend’s houses. Marge lives 3 miles away and Rocky lives 5 miles away. Eva lives 4 miles away and Pe

STALIN [3.7K]

Answer:

She will ride an average of 5 miles

Step-by-step explanation:

To calculate the average, add all the values together and divide by the amount of values:

3 + 5 + 4 + 8 = 20

20 ÷ 4 = 5

Average of 5 miles

4 0

3 years ago

A cup slides off a 2.5 m high table with a speed of 2.8 m/s to the right. We can ignore air resistance. What was the cup's horiz

azamat

Answer:

Horizontal distance = 1.98 m (Approx)

Step-by-step explanation:

Given:

Height = 2.5 m

Speed v = 2.8 m/s

Find:

Horizontal displacement

Computation:

s = ut + (1/2)gt²

2.5 = (1/2)(9.8)t²

t² = 0.5102

t = 0.7079 s

Horizontal distance = (v)(t)

Horizontal distance = (2.8)(0.7079)

Horizontal distance = 1.98 m (Approx)

5 0

3 years ago

4.One attorney claims that more than 25% of all the lawyers in Boston advertise for their business. A sample of 200 lawyers in B

AleksAgata [21]

Answer:

$z=\frac{0.315 -0.25}{\sqrt{\frac{0.25(1-0.25)}{200}}}=2.123$

$p_v =P(Z>2.123)=0.0169$

The p value obtained was a very low value 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 lawyers had used some form of advertising for their business is significantly higher than 0.25 or 25% .

Step-by-step explanation:

1) Data given and notation

n=200 represent the random sample taken

X=63 represent the lawyers had used some form of advertising for their business

$\hat p=\frac{63}{200}=0.315$ estimated proportion of lawyers had used some form of advertising for their business

$p_o=0.25$ is the value that we want to test

$\alpha=0.05$ represent the significance level

Confidence=95% or 0.95

z would represent the statistic (variable of interest)

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

2) Concepts and formulas to use

We need to conduct a hypothesis in order to test the claim that more than 25% of all the lawyers in Boston advertise for their business:

Null hypothesis: $p\leq 0.25$

Alternative hypothesis: $p > 0.25$

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 from a hypothesized value $p_o$ .

3) Calculate the statistic

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

$z=\frac{0.315 -0.25}{\sqrt{\frac{0.25(1-0.25)}{200}}}=2.123$

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

Since is a right tailed test the p value would be:

$p_v =P(Z>2.123)=0.0169$

The p value obtained was a very low value 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 lawyers had used some form of advertising for their business is significantly higher than 0.25 or 25% .

8 0

3 years ago

Given the functions, f(x) = 4x3 - x2 + 1 and g(x) = x - 1, evaluate f(g(2)).