A ball is dropped from a height if 30 feet the ball bounces after each bounce the height attained by the ball is 60% of the previous height write an nth term formula to model the situation what is the maximum height attained by the ball after five bouncesA.0.12ft
B.6.40ft
C.2.33ft
D.1.40ft

Answers

Answer 1
Answer: This information will be modeled using the formula
thus we shall have:
Sn=ar^n
where:
a=first term
r=common ratio
from the information:
a=30 ft
r=60/100=3/5=0.6
therefore the formula will be
Sn=30(0.6)^n
where n is the number of terms:
thus when n=5 th sum will be:
S5=30(0.6)^5
S5=30(0.6)^5
S5=2.33 ft
Answer: 2.33 ft
Answer 2
Answer:

Answer:

2.33

Step-by-step explanation:


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The State Police are trying to crack down on speeding on a particular portion of the Massachusetts Turnpike. To aid in this pursuit, they have purchased a new radar gun that promises greater consistency and reliability. Specifically, the gun advertises ± one-mile-per-hour accuracy 75% of the time; that is, there is a 0.75 probability that the gun will detect a speeder, if the driver is actually speeding. Assume there is a 1% chance that the gun erroneously detects a speeder even when the driver is below the speed limit. Suppose that 72% of the drivers drive below the speed limit on this stretch of the Massachusetts Turnpike. a. What is the probability that the gun detects speeding and the driver was speeding? b. What is the probability that the gun detects speeding and the driver was not speeding? c. Suppose the police stop a driver because the gun detects speeding. What is the probability that the driver was actually driving below the speed limit?
A data related to air pollution in 10 U.S. cities. The dependent variable Y is the annual mean concentration of sulfur dioxide, in micrograms per cubic meter. The explanatory variable X records the number of manufacturing enterprises employing 20 or more workers. Below is Routput of the relationship between X and Y. Coefficients: Estimate Std. Error t value Pro> tl) (Intercept) 9.4764 9.6266 0.98 0.354 2.0315 0.0070 4.51 0.CO2 ** X Signif. codes: 9 ****' 0.001 ***' 0.01 **' 0.05, 0.1' '1 Residual standard error: 17.9 on 8 degrees of freedom Multiple R-squared: 0.717, Adjusted R-squared: 0.682 F-statistic: 20.3 on 1 and 8 DF, p-value: 0.00198a) Write the regression equation with parameters from the R output.b) Suppose that the number of manufacturing enterprises employing 20 or more workers in Irvine is 250, could you predict that the annual mean concentration of sulfur dioxide in Irvine?c) What is the residual if in Irvine the annual mean concentration of sulfur dioxide is 15 micrograms per cubic meter.d) What is the value of the correlation coefficient?e) Calculate a 95% confidence interval for the slope of the model.f) Based on the confidence interval, is there a linear relationship between X and Y?
Point R is on line segment QS. Given RS = 2 and QS = 10, determine the length QR

Sleeping in college. A recent article in a college newspaper stated that college students get an average of 5.5 hrs of sleep each night. A student who was skeptical about this value decided to conduct a survey by randomly sampling 25 students. On average, the sampled students slept 6.25 hours per night. Identify which value represents the sample mean and which value represents the claimed population mean.

Answers

Answer:

Sample mean = 6.25 hours per night.

Population mean = 5.5 hrs of sleep each night.

Step-by-step explanation:

A sample mean is the mean of the sample collected. The 25 students surveyed by the student is the sample. The average sleep time derived from the sample is the sample mean.

A population mean is the mean of all the population. Here the population are college students. The population mean is the mean derived from studying the sleep duration of all the population - college students

The equation of a parabola is given.y=−14x2+4x−19



What are the coordinates of the vertex of the parabola?



Enter your answer in the boxes.

Answers

Answer:

vertex (  (1)/(7), (131)/(7)).

Step-by-step explanation:

Given : The equation of a parabola is given.

       y=−14x²+4x−19

To find  : What are the coordinates of the vertex of the parabola.

Solution : We have given that

y = −14x²+4x−19

we will be "completing the square" .

Factor out -14 to make leading coefficient 1

y = -14 (x^(2) -(2x)/(7) +(19)/(14))

Add and subtract ((-1)/(7)) ^(2)

y = -14 (x^(2) -(2x)/(7) +(19)/(14)+(-1)/(7)) ^(2) - ((-1)/(7))^(2)) .

Complete the square

y = -14 ( (x -(1)/(7)) ^(2) +(19)/(14)- ((-1)/(7))^(2)).

y = -14 ( (x-(1)/(7)) ^(2) -(131)/(7)

Standard form of parabola vertex form y  = a(x - h)²+ k,

Where, ( h, k)  are vertex

On comparing a = -14 , h= (1)/(7), k =  (131)/(7)

Therefore, vertex (  (1)/(7), (131)/(7)).

The coordinates are 8, -3.

From a set of 5 nickels, 10 dimes and 15 quarters, six coins are removed at random without replacement. a. Find the probability of not removing 6 quarters.
b. Find the probability of removing exactly 2 nickels, 2 dimes and 2 quarters.

Answers

Answer:

(a) 1 - (15 C 6) / (30 C 6)

(b)  (5 C 2) x (10 C 2) x (15 C 2) / (30 C 2)

Step-by-step explanation:

Number of  nickels = 5

Number of dimes = 10

Number of quarters = 15

(a) The probability of getting 6 quarters  

= (15 C 6) / (30 C 6)

So, the probability of not getting 6 quarters = 1 - (15 C 6) / (30 C 6)

(b) Probability of getting 2 nickels , 2 dimes and 2 quarters

= (5 C 2) x (10 C 2) x (15 C 2) / (30 C 2)

2Viviana is ordering carpet

for 16 square rooms in a

hotel. Each room will need

100 square feet of

carpet. What is the

length of 1 room?

Answers

Answer:

Length of a room is 10ft

Step-by-step explanation:

Given

Rooms = 16

Carpet\ Area = 100ft^2

Required

Determine the length of each room

Here, we'll assume that the carpet will cover each room completely.

If so:

Carpet\ Area = Length * Length

100ft^2 = Length * Length

100ft^2 = Length^2

Take square root of both sides

√(100ft^2) = √(Length^2)

√(100ft^2) = Length

Take positive square root

10ft = Length

Length = 10ft

Hence, the length of a room is 10ft

Which functions have a maximum value greater than the maximum of the function g(x) = –(x + 3)2 – 4? Check all that apply. f(x) = –(x + 1)2 – 2 f(x) = –|x + 4| – 5 f(x) = –|2x| + 3

Answers

Answer:

A

C

D

Step-by-step explanation:

A random sample of 150recent donations at a certainblood bank reveals that
45 were type A blood.Does this suggest that the
actual percentage of type A
donations is less than40%, the percentage of the
population having type A
blood? Carry out a testof the appropriate
hypotheses using a significance
level of0.01.

Answers

Answer:

Null hypothesis:p\geq 0.4  

Alternative hypothesis:p < 0.4  

z=\frac{0.3 -0.4}{\sqrt{(0.4(1-0.4))/(150)}}=-2.5  

p_v =2*P(Z<-2.5)=0.0124  

If we compare the p value obtained and the significance level given \alpha=0.01 we see that p_v>\alpha so we can conclude that we have enough evidence to reject the null hypothesis, and we can said that the true proportion is not significantly lower than 0.4 or 40% at 1% of significance.  

Step-by-step explanation:

1) Data given and notation  

n=150 represent the random sample taken

X=45 represent the people with type A blood

\hat p=(45)/(150)=0.3 estimated proportion of people with type A blood

p_o=0.4 is the value that we want to test

\alpha=0.01 represent the significance level

Confidence=99% or 0.99

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 the true proportion of people type A blood is less than 0.4:  

Null hypothesis:p\geq 0.4  

Alternative hypothesis:p < 0.4  

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

z=\frac{\hat p -p_o}{\sqrt{(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{0.3 -0.4}{\sqrt{(0.4(1-0.4))/(150)}}=-2.5  

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=0.01. The next step would be calculate the p value for this test.  

Since is a bilateral test the p value would be:  

p_v =2*P(Z<-2.5)=0.0124  

If we compare the p value obtained and the significance level given \alpha=0.01 we see that p_v>\alpha so we can conclude that we have enough evidence to reject the null hypothesis, and we can said that the true proportion is not significantly lower than 0.4 or 40% at 1% of significance.