Answer:
The half life of the car is 3.98 years.
Step-by-step explanation:
The value of the car after t years is given by the following equation:
[tex]V(t) = V(0)(1-r)^{t}[/tex]
In which V(0) is the initial value and r is the constant decay rate, as a decimal.
The value of a certain car decreases by 16% each year.
This means that [tex]r = 0.16[/tex]
So
[tex]V(t) = V(0)(1-r)^{t}[/tex]
[tex]V(t) = V(0)(1-0.16)^{t}[/tex]
[tex]V(t) = V(0)(0.84)^{t}[/tex]
What is the 1⁄2-life of the car?
This is t for which V(t) = 0.5V(0). So
[tex]V(t) = V(0)(0.84)^{t}[/tex]
[tex]0.5V(0) = V(0)(0.84)^{t}[/tex]
[tex](0.84)^{t} = 0.5[/tex]
[tex]\log{(0.84)^{t}} = \log{0.5}[/tex]
[tex]t\log{0.84} = \log{0.5}[/tex]
[tex]t = \frac{\log{0.5}}{\log{0.84}}[/tex]
[tex]t = 3.98[/tex]
The half life of the car is 3.98 years.
there are 7 rows of 9 people . how many people in all ?
There are 7 rows of 9 people then there will be 63 people in all.
MultiplicationMultiplication refers to the product of two numbers or more than two numbers. It states the result when a number is taken times.
How to find the number of people?There are 7 rows of 9 people.
This means in each row, there are 9 people.
Then the number of people in 7 rows will be 7 multiplied by 9 i.e.,
[tex]7\times9=63[/tex]
So, the number of people will be 63.
Learn more about multiplication here- https://brainly.com/question/10590363
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Ms. Wong's class had 11 girls and 14 boys. What is the probability that a girl will get the infection first and then a boy ?
Answer: 25,67%
Step-by-step explanation:
We have 11 girls and 14 boys, this is a total of 11 + 14 = 25 students.
If all the students have the same probability of being infected, the probability that a girl will get infected first is equal to the number of girls dividedthe total number of students:
p1 = 11/25
Now we get a boy infected, the number of boys is 14, and the total number of students is now 24 (because we already have a girl infected)
this probability is p2 = 14/24
The probability for both events is equal to the product of the probabilities:
P = p1*p2 = (11/25)*(14/24) = 0.2567
or 25,67%
write the decimal number 0.83333333 as a rational number
Answer:
5/6
Step-by-step explanation:
plug into calculator
Answer:
Can confirm it is 5/6.
Step-by-step explanation:
Simply put into a calculator.
What’s the correct answer for this?
Answer:
Answer is the first one :)
Step-by-step explanation:
√(-7-5)² + (-7-9)²
answer is 20
hope this helps
Answer:
A.
Step-by-step explanation:
In the attached file
Suppose that a magazinemagazine predicted that Candidate A would defeat Candidate B in a certain election. They conducted a poll of telephone directoriestelephone directories with a response rate of 23%. On the basis of the results, the magazinemagazine predicted that Candidate A would win with 57% of the popular vote. However, Candidate B won the election with about 62% of the popular vote. At the time of this poll, most households with telephoneshouseholds with telephones belonged to the party of Candidate A. Name two biases that led to this incorrect prediction.
Choose the correct answer below.
A.
Sampling bias Using an incorrect frame led to undercoverage.
Response bias: The way the poll was administered showed bias
B.
Sampling bias: Using an incorrect frame led to undercoverage
Nonresponse bias: The low response rate caused bias
C.
Nonresponse bias: The low response rate caused bias.
Response bias: The way the poll was administered showed bias.
Answer:
im pretty sure its B
Step-by-step explanation:
I would measure the length of a praying mantis in feet, inches, yards, miles? because?
Answer:
Inches
Step-by-step explanation:
the praying mantis is too small for the other units.
The length of a praying mantis would measure in inches.
What is measurement?It is defined as the numerical quantity that gives an idea about an object's weight length, width, and many more. It can be used to compare two objects.
We know feet, inches, yards, and miles are the unit of measuring the length.
We have an object that is a praying mantis. Usually, the mantis's length is about 3 to 4.5 inches.
We also know 1 foot = 12 inches
1 yard = 36 inches
1 mile = 63360 inches
As we can see the feet, yard, and mile are the units to measure the long length.
Thus, the length of a praying mantis would measure in inches.
Learn more about the measurements here:
brainly.com/question/4725561
A test of sobriety involves measuring the subject's motor skills. Twenty randomly selected sober subjects take the test and produce a mean score of A with a standard deviation of B. At the 0.01 level of significance, test the claim that the true mean score for all sober subjects is equal to 35.0. Use the critical value method of testing hypotheses.
Answer:
Step-by-step explanation:
Hello!
The variable of interest is:
X: motor skills of a sober subject.
n= 20
X[bar]= 37.1
S= 3.7
The claim is that the average score for all sober subjects is equal to 35.0, symbolically: μ= 35.0
The hypotheses are:
H₀: μ = 35.0
H₁: μ ≠ 35.0
α: 0.01
The statistic to use, assuming all conditions are met, is a one sample t- test
[tex]t= \frac{X[bar]-Mu}{\frac{S}{\sqrt{n} } } ~t_{n-1}[/tex]
[tex]t_{H_0}= \frac{37.1-35.0}{\frac{3.7}{\sqrt{20} } } = 2.34[/tex]
This test is two-tailed, meaning, the rejection region is divided in two and you'll reject the null hypothesis to low values of t or to high values of t:
[tex]t_{n-1;\alpha /2}= t_{19; 0.005}=-2.861[/tex]
[tex]t_{n-1;1-\alpha /2}= t_{19; 0.995}= 2.861[/tex]
The decision rule using this approach is:
If [tex]t_{H_0}[/tex] ≤ -2.861 or if [tex]t_{H_0}[/tex] ≥ 2.861, you reject the null hypothesis.
If -2.861 < [tex]t_{H_0}[/tex] < 2.861, you do not reject the null hypothesis.
The value is within the non rejection region, the decision is to not reject the null hypothesis.
I hope this helps!
A pyramid has a volume of 1,994 inches cubed and a rectangular base with the dimensions 18 inches by 9 inches. What is the height of the pyramid?
Answer:D)36
Step-by-step explanation:
Took the test
6x + 12 = −6x − 35
- How is this solved?
Step-by-step explanation:
here,
6x+12= -6x-356x+6x = -35-12
12x= -47
x= -47
[tex] \frac{ - 47}{12} [/tex]
I need to know what –5(–2) equals.
Answer:
10
Step-by-step explanation:
HELP ASAP!!
What is the area of the composite figure below?
A) 84 square inches
B) 90 square inches
C) 98 square inches
D) 104 square inches
Answer:
84 square inches
Step-by-step explanation:
First, separate this shape into two shapes you can easily find the area of. You can do this by turning it into a rectangle and a rhombus.
Say the rectangle has measurements of 5 by 6 inches. The area of that rectangle will be 30 square inches. Save this value to add on later.
The rhombus now has a height of 4 (because the side length 10 minus the side length 6 equals 4), and two bases by the values of 12 and 15. The area of a rhombus can be found with the equation:
a = 1/2(b1 + b2) x h
Simply plug in those values to find the area of the rhombus, 54. Now add the area of the rhombus and the area of the rectangle to get 84 square inches as your final area.
In a study of cell phone use and brain hemispheric dominance, an Internet survey was e-mailed to 5000 subjects randomly selected from an online group involved with ears. 717 surveys were returned. Use a 0.01 significance level to test the claim that the return rate is less than 15%.
Answer:
As the P-value (0.086) is greater than the significance level (0.01), the effect is not significant.
The null hypothesis failed to be rejected.
There is not enough evidence to support the claim that the return rate is less than 15%.
Step-by-step explanation:
This is a hypothesis test for a proportion.
The claim is that the return rate is less than 15%.
Then, the null and alternative hypothesis are:
[tex]H_0: \pi=0.15\\\\H_a:\pi<0.15[/tex]
The significance level is 0.01.
The sample has a size n=5000.
The sample proportion is p=0.143.
[tex]p=X/n=717/5000=0.143[/tex]
The standard error of the proportion is:
[tex]\sigma_p=\sqrt{\dfrac{\pi(1-\pi)}{n}}=\sqrt{\dfrac{0.15*0.85}{5000}}\\\\\\ \sigma_p=\sqrt{0.000026}=0.005[/tex]
Then, we can calculate the z-statistic as:
[tex]z=\dfrac{p-\pi+0.5/n}{\sigma_p}=\dfrac{0.143-0.15+0.5/5000}{0.005}=\dfrac{-0.007}{0.005}=-1.366[/tex]
This test is a left-tailed test, so the P-value for this test is calculated as:
[tex]P-value=P(z<-1.366)=0.086[/tex]
Answer:
[tex]z=\frac{0.1434 -0.15}{\sqrt{\frac{0.15(1-0.15)}{5000}}}=-1.307[/tex]
Now we can calculate the p value with the following probability:
[tex]p_v =P(z<-1.307)=0.0956[/tex]
For this case the p value is lower than the significance level provided of 0.1 so then we can reject the null hypothesis and we can conclude that the the return rate is significantly less than 15%.
Step-by-step explanation:
Information provided
n=5000 represent the random sample taken
X=717 represent the surveys returned
[tex]\hat p=\frac{717}{5000}=0.1434[/tex] estimated proportion of urvyes returned
[tex]p_o=0.15[/tex] is the value to verify
[tex]\alpha=0.01[/tex] represent the significance level
z would represent the statistic
[tex]p_v[/tex] represent the p value
System of hypothesis
We want to verify if the return rate is less than 15% the system of hypothesis are.:
Null hypothesis:[tex]p \geq 0.15[/tex]
Alternative hypothesis:[tex]p < 0.15[/tex]
The statistic is given by:
[tex]z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}[/tex] (1)
Replacing the info we got:
[tex]z=\frac{0.1434 -0.15}{\sqrt{\frac{0.15(1-0.15)}{5000}}}=-1.307[/tex]
Now we can calculate the p value with the following probability:
[tex]p_v =P(z<-1.307)=0.0956[/tex]
For this case the p value is lower than the significance level provided of 0.1 so then we can reject the null hypothesis and we can conclude that the the return rate is significantly less than 15%.
Which equation represents a line that passes through (5,1) and has a slope of 1/2
Answer:
Step-by-step explanation:
Since you did not post answer choices, there's not too much I can tell you. One thing for sure is that the equation must have 1/2x. This represents the slope at which the equation is increasing. To find which equation passes through (5,1), all you have to do is plug in 5 into the x in your equation. After you solve, if the y you get is equal to the y value of 1, you know that is the line that alsses through (5,1). I hope this helps.
Answer b
Step-by-step explanation:
It’s fast
Write as a fraction in lowest terms:
0.126126126..=a/b
A=
b =
DONE
Answer:
a= 14
b= 111
Step-by-step explanation:
just took it
Mark ordered a square pizza that has a side length of 12 inches Rodney ordered a round pizza with a 12 inch diameter each of them paid seven dollars for their pizza you got the better deal
Answer:
Square pizza is the better deal.
Step-by-step explanation:
The better deal will be the one that has larger area of pizza. So, find the area of pizza in the case of square pizza and in the case of round pizza.
Below is the calculation of area of pizzas.
[tex]\text{Area of square pizza} = (Side)^{2} \\\text{Area of square pizza} = (12)^2 \\\text{Area of square pizza} = 144 \ in^2 \\[/tex]
[tex]\text{Now area of round pizza.} \\\text{ The area of round pizza} = \pi r^{2} \\\rm Diameter = 12 \\So, \ radius = \frac{12}{2} = 6 \\\text{ The area of round pizza} = \pi r^{2} \\= \frac{22}{7}\times (6)^2 \\= 113.1 \ in^2[/tex]
Since the area of square pizza is greater than round pizza. Thus, square pizza is better deal.
90 units needed 8units per case
Answer: 90/8=11.25
Step-by-step explanation:
24.3 cm
8.5 cm
9.7 cm
Answer:
area: 144.5 cm^2
Step-by-step explanation:
Maybe you want the area of this figure.
The area of a trapezoid is given by the formula ...
A = (1/2)(b1 +b2)h
Using the given dimensions, the area is ...
A = (1/2)(9.7 cm +24.3 cm)(8.5 cm)
A = (1/2)(34 cm)(8.5 cm) = 144.5 cm^2
On a multiple-choice test, each question has 4 possible answers. A student does not know
answers to three questions, so the student guesses.
What is the probability that the student gets all three questions right?
Answer:
1.56% probability that the student gets all three questions right
Step-by-step explanation:
For each question, there are only two possible outcomes. Either the student guesses the answer correctly, or he does not. The probability of the student guessing the answer of a question correctly is independent of other questions. So we use the binomial probability distribution to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
Each question has 4 possible answers, one of which is correct.
So [tex]p = \frac{1}[4} = 0.25[/tex]
Three questions.
This means that [tex]n = 3[/tex]
What is the probability that the student gets all three questions right?
This is [tex]P(X = 3)[/tex]
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 3) = C_{3,3}.(0.25)^{3}.(0.75)^{0} = 0.0156[/tex]
1.56% probability that the student gets all three questions right
is 2x^2+y =3x - 1 a function quadratic
Answer:
Step-by-step explanation: yes because when rewritten in standard form the x term will still be raised to the 2nd power.
There are 8 blue marbles, 6 red marbles, and 4 white marbles in a jar. if a marble is selected at random from the jar, what is the probability that it is not red?
Answer:
44
Step-by-step explanation:
A cohort study is conducted to assess the association between clinical characteristics and the risk of stroke. The study involves n = 1370 participants who are free of stroke at the study start. Each participant is assessed at study start (baseline) and every year thereafter for 5 years. The following data were collected relating hypertensive status measured at baseline to incident stroke over 5 years.Free of Stroke at 5 years StrokeBaseline: Not hypertensive 1000 50Baseline: Hypertensive 300 501. Compute the cumulative incidence of stroke in patients classified as hypertensive at baseline.A) 0.20B) 0.50C) 0.0625D) 0.05
Answer:
None of the options are correct.
The cumulative incidence of stroke in patients classified as hypertensive at baseline = 0.625
Step-by-step explanation:
The table properly drawn is that
Baseline - Not hypertensive
Free of stroke at 5 years | Stroke | Total
1000 | 50 | 1050
Baseline - Hypertensive
Free of stroke at 5 years | Stroke | Total
300 | 501 | 801
Compute the cumulative incidence of stroke in patients classified as hypertensive at baseline.
Number of patients classified as hypertensive at baseline = 801
number of stroke incidents amongst patients classified as hypertensive at baseline = 501
The cumulative incidence of stroke in patients classified as hypertensive at baseline = (501/801) = 0.625
Hope this Helps!!!
In a recent study of statistics students, a random sample of students were asked to provide the number of hours per week they spend studying for their statistics class. The results were used to compute confidence intervals for the population mean hours per week spent studying for statistics. The 95% confidence interval for the population mean hours per week that students spend studying for statistics was (6.83, 8.27). In this confidence interval, what is the sample mean (x bar) hours per week spent studying for statistics? Provide your answer as a number rounded to two decimal places.
Answer:
The sample mean hours per week spent studying for statistics is 7.55 hours.
Step-by-step explanation:
The (1 - α)% confidence interval for the population mean μ is:
[tex]CI=\bar x\pm z_{\alpha/2}\ \frac{\sigma}{\sqrt{n}}[/tex]
The 95% confidence interval for the population mean hours per week that students spend studying for statistics was (6.83, 8.27).
Compute the sample mean hours per week spent studying for statistics as follows:
[tex]\frac{\text{UL + LL}}{2}=\frac{(\bar x+ z_{\alpha/2}\ \frac{\sigma}{\sqrt{n}})+(\bar x- z_{\alpha/2}\ \frac{\sigma}{\sqrt{n}})}{2}\\\\\frac{8.27+6.83}{2}=\frac{2\cdot \bar x}{2}\\\\7.55=\bar x[/tex]
Thus, the sample mean hours per week spent studying for statistics is 7.55 hours.
solve
[tex]y {4 - 2y {3 = 0}^{?} }^{?} [/tex]
please
Step-by-step explanation:
y4 - 2y3 = 0
y3(y - 2) = 0
y3 = 0
y = 0
Y - 2 = 0
Y = 2
00:00
Rose bought a bag of potatoes for $6.00 and some granola bars for $5.25 per package. Her total bill was $74.25. How many packages of granola
bars did she buy? Enter your answer in the box
packages
Answer:
13 packages of Granola
Step-by-step explanation:
74.25 - 6 = 68.25
68.25 divided by 5.25= 13
What operation does the Product Rule use
with the exponents? A) Addition
B) Subtraction
C) Multiplication
D) Division
Answer:
Multiplication
Step-by-step explanation:
On a map, 4 inches represents an actual distance of 24 miles. If the actual distance between two cities is 126 miles, how many inches apart will the two cities be on the map
Answer:
21 inches
Step-by-step explanation:
1 inch = 6 miles
126/6 = 21
what is the area of a trapezoid where one base is 6 cm the second base is 4cm and the height is 8cm?
Answer:
40 cm
Step-by-step explanation:
To find the area of a trapezoid, you have to do...
(4+6)times 8 divided by 2
so its 10 times 8 which is 80 divided by 2 is 40 cm!!
hope this helps!!
48 + 32 divided by 2 is 40
Step-by-step explanation:
The area is 40
help me plsssssssssssss
Answer:
The radius is 5 cm
Step-by-step explanation:
The formula for the area of a circle is : [tex]\p*radius^2[/tex]
To work out the length of the radius you would first need to divide the area of 78.5 cm by pi (pi=3.14), this gives you [tex]25cm^2\\[/tex]. This is because by dividing the area by pi we are isolating the value of the radius squared.
The final step is to work out the radius. You can do this by finding the square root of the radius squared which is 25, this gives you 5 cm. This means that the radius is 5 cm. This is because the square root is a number that when squared equals that number.
1) Divide 78.5 by pi.
[tex]78.5/\pi=25cm^2[/tex]
2) Find the square root of 25 cm squared.
[tex]\sqrt{25} =5 cm[/tex]
In this question pi is 3.14
Marissa bought 60 horns for her New Year’s Eve party for $83.40.
She needs to purchase an additional 18 horns for the party at the same unit rate.
Choose True or False for each statement.
Answer:
We don't have the statements but I can tell you the following info:
Step-by-step explanation:
83.4/60= $1.39 for each horn
18*1.39= $25.02 for the 18 additional horns.
$83.40+25.02= $108.42 for the total 78 horns
A variety of stores offer loyalty programs. Participating shoppers swipe a bar-coded tag at the register when checking out and receive discounts on certain purchases. A typical Saturday morning shopper who does not participate in this program spends $120 on her or his order. In a sample of 80 shoppers participating in the loyalty program, each shopper spent $130 on average during a recent Saturday, with standard deviation $40. Is this statistical proof that the shoppers participating in the loyalty program spent more on average than typical shoppers?
Answer:
[tex]t=\frac{130-120}{\frac{40}{\sqrt{80}}}=2.236[/tex]
Now we can find the degrees of freedom:
[tex]df=n-1=80-1=79[/tex]
Now we can calculate the p value with the alternative hypothesis using the following probability:
[tex]p_v =P(t_{(79)}>2.236)=0.0141[/tex]
Using a significance level of 0.01 or 1% we have enough evidence to FAIL to reject the null hypothesis and we can conclude that shoppers participating in the loyalty program NOT spent more on average than typical shopper at this significance level assumed
Step-by-step explanation:
Information given
[tex]\bar X=130[/tex] represent the sample mean
[tex]s=40[/tex] represent the sample standard deviation
[tex]n=80[/tex] sample size
[tex]\mu_o =120[/tex] represent the value to verify
t would represent the statistic
[tex]p_v[/tex] represent the p value
System of hypothesis
We want to verify if shoppers participating in the loyalty program spent more on average than typical shoppers (120) , the system of hypothesis would be:
Null hypothesis:[tex]\mu \leq 120[/tex]
Alternative hypothesis:[tex]\mu > 120[/tex]
The statistic for this case is given by:
[tex]t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}[/tex] (1)
Replacing the info given we got:
[tex]t=\frac{130-120}{\frac{40}{\sqrt{80}}}=2.236[/tex]
Now we can find the degrees of freedom:
[tex]df=n-1=80-1=79[/tex]
Now we can calculate the p value with the alternative hypothesis using the following probability:
[tex]p_v =P(t_{(79)}>2.236)=0.0141[/tex]
Using a significance level of 0.01 or 1% we have enough evidence to FAIL to reject the null hypothesis and we can conclude that shoppers participating in the loyalty program NOT spent more on average than typical shopper at this significance level assumed