Answer:
1). 1.25 / 250 = .005M
.005 = 1 liter
2). (20)(.5) = 10M
have a good day, and be safe
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7/10 + 1/6 as a fraction in lowest terms
Answer:
13/15
Step-by-step explanation:
First, you find a common denominator. 10 x 3 and 6 x 5 both equal 30, so 30 can be used as a common denominator. You also have to multiply the numerator by the same number you multiplied in the denominator. Since we did 10 x 3, do 7 x 3, and with the other fraction we did 6 x 5, so do 1 x 5. You should get 21/30 + 5/30. Since they have the same denominator, you can add them. You'll get 26/30, which can still be simplified. 30 divided by 2 is 15, and 26 divided by 2 is 13. The final answer is 13/15.
Find the value of 18 ÷ 9 · 3.
Answer:
its 6
just simplify the expression.
-Hops
Answer: 6
Divide
18÷9=2
Multiply
2×3=6
What is the best example of a negative correlation?
Question 1 options:
Volleyball practices in a week and the amount of free time that week.
The amount of time spent jogging and calories burned.
Students in a classroom and number of chairs in the classroom.
The altitude of a plane and the number of passengers on board.
Answer:
gergverkngvneropgeronhnernih[eh[neirvhier,hn[eriin[hnerohper'her
Step-by-step explanation:
Answer:
Common Examples of Negative Correlation. A student who has many absences has a decrease in grades. As weather gets colder, air conditioning costs decrease. If a train increases speed, the length of time to get to the final point decreases.
The distance travelled in (m) by a ball dropped from a height are 128/9,32/3,8,6,...
How much distance will it travel before coming to rest
Answer: it will trave 56.89 meters before coming to rest.
Step-by-step explanation:
This is a geometric progression since the distance travelled (height) by the ball is reducing by a constant ratio, r. Since the number of times that the ball will bounce is infinite, then we would apply the formula for determining the sum of the terms in a geometric progression to infinity which is expressed as
S = a/(1 - r)
where
S = sum of the distance travelled by the ball
a = initial distance or height of the ball
r = common ratio
From the information given,
a = 128/9
r = (32/3)/(128/9) = 0.75
Therefore,
S = (128/9)/(1 - 0.75) = 56.89 meters
The distance travelled is an illustration of the sum to infinity of a geometric sequence.
The ball will a travel 56.89 meters before coming to rest
The sequence is given as:
[tex]\mathbf{128/9, 32/3, 8, 6....}[/tex]
From the sequence above, we have:
[tex]\mathbf{a = 128/9}[/tex] --- the first term
[tex]\mathbf{r = 6/8 = 3/4}[/tex] -- the common ratio
The sum to infinity of a geometric progression is:
[tex]\mathbf{S_{\infty} = \frac{a}{1-r}}[/tex]
So, we have:
[tex]\mathbf{S_{\infty} = \frac{128/9}{1-3/4}}[/tex]
[tex]\mathbf{S_{\infty} = \frac{128/9}{1/4}}[/tex]
Divide
[tex]\mathbf{S_{\infty} = \frac{128}{9} \times 4}[/tex]
[tex]\mathbf{S_{\infty} = \frac{128\times 4}{9} }[/tex]
[tex]\mathbf{S_{\infty} = \frac{512}{9} }[/tex]
[tex]\mathbf{S_{\infty} = 56.89}[/tex]
Hence, the ball will a travel 56.89 meters before coming to rest
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Answer:
The volume of the sphere is 972π mm³
Step-by-step explanation:
To calculate the volume of a sphere we have to use the following formula:
V = volume
r = radius = 9mm
π = pi
V = ⁴⁄₃πr³
we replace with the known values
V = ⁴⁄₃ * π * (9mm)³
V = π * ⁴⁄₃ *729mm³
V = π * 972mm³
V = 972π mm³
The volume of the sphere is 972π mm³
Paul wants to write equations in the form y=mx+b for the lines passing through point D that are parallel and perpendicular to line h. First he finds the slopes of these two lines. What could he do next to find the y-intercepts?
Answer:
Substitute the slope and the coordinate of D into the equations and solve for b for each equation
Step-by-step explanation:
The equation for a line is y = mx+b
where m is the slope and b is the y intercept
We know m
We have a point (x,y)
We can substitute into the equation and solve for b
Answer:
First option
Step-by-step explanation:
In y = mx + b, m is the slope and b is the y-intercept
Plug in m, and coordinates of D and solve for b
A game between two equally skilled players is ended before a winner is declared. Player A needs 3 more points to win, and player B needs 2 more points to win. How should the stakes be divided between the two players? Blaise Pascal used the Arithmetical Triangle to solve this problem. In the division of the stakes, what is the ratio of player A's winnings to Player B's winnings?
Answer: player A = 11/16 and player B = 5/16
Step-by-step explanation:
If a coin was to be tossed to determine the winner possible outcomes using arithmetical triangle.
Player A needs 2 points = 11
Player B needs 3 points = 5
Total outcome of tossing a coin = 16
Player A = 11/16 = 0.6875
Player B = 5/16 = 0. 3125
Or
Using the fifth roll of the pascal triangle (2+3) outcome
( 1, 4, 6, 4, 1 )
Addition of the first 3 represent Player A chances of winning = ( 1+ 4 + 6 ) = 11
And the last two = ( 1 + 4 ) = 5 represents the chances of team B winning
Total number of outcome = ( 1 + 4 + 6 + 4 + 1 ) = 16
g Which one of the following statements is INCORRECT about ANOVA test? Group of answer choices An F value is a ratio of between-group mean square to within-group mean square. An ANOVA test is an appropriate test for comparing three or more groups in a continuous variable. The range of the F value is (-[infinity], +[infinity]) A significant ANOVA test result means that means in comparison are not all equal.
Answer:
INCORRECT: The range of the F value is (-[infinity], +[infinity])
Step-by-step explanation:
While it's true that there is no maximum value to an F value, you cannot have a negative F statistic and the lowest value you can have is zero.
The incorrect statement about ANOVA test is that the range of F value is (-∞, ∞).
What is ANOVA test?ANOVA test is abbreviated for Analysis of Variance. This test is used to find whether there is a significant difference between the means of certain number of groups using variance.
Null hypothesis in an ANOVA test is that there is no difference in the mean of groups. Alternate hypothesis of ANOVA test is that at least one of the group has different mean than others.
In ANOVA test, an F value is the ratio of variation between sample means to the variation within sample means. So the first statement which says F value as a ratio of between-group mean square to within-group mean square is correct.
We have ANOVA test is an appropriate test for comparing three or more independent groups in a continuous variable. Second statement is also correct.
The value of F will always be positive. The range of F starts from 0. So the statement that range of F value is (-∞, ∞) is incorrect.
By the definition of ANOVA test itself, we can say that a significant test result in ANOVA means that means are not all equal. So fourth statement is also correct.
Hence the statement range of F value is (-∞, ∞) is incorrect.
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Marsha wants to determine the vertex of the quadratics vertex of the quadratics functions f(x)=x^2-x+2
Answer:
The vertex of the function is [tex](\frac{1}{2}, \frac{7}{4})[/tex]
Step-by-step explanation:
Suppose we have a quadratic equation in the following format:
[tex]y = f(x) = ax^{2} + bx + c[/tex]
The vertex of the function is the point [tex](x_{v}, f(x_{v})[/tex], in which
[tex]x_{v} = -\frac{b}{2a}[/tex]
In this problem:
[tex]f(x) = x^{2} - x + 2[/tex]
This means that [tex]a = 1, b = -1, c = 2[/tex]
So
[tex]x_{v} = -\frac{-1}{2} = \frac{1}{2}[/tex]
[tex]f(x_{v}) = f(\frac{1}{2}) = (\frac{1}{2})^{2} - \frac{1}{2} + 2 = \frac{1}{4} - \frac{1}{2} + 2 = \frac{1 - 2 + 8}{4} = \frac{7}{4}[/tex]
The vertex of the function is [tex](\frac{1}{2}, \frac{7}{4})[/tex]
Solve for x. 8/9x=32 Enter your answer in the box. x =
Answer:
x = 36
Step-by-step explanation:
Given;
(8/9)x = 32
Solving for x
Multiply through by 9
(8/9)×9 ×x = 32×9
8x = 32×9
Divide through by 8
8x/8 = 32×9/8
x = 36
Kai ate an ice cream cone at the park last Thursday. The height of the cone was 7
centimeters. The diameter of the base is 4 centimeters. What would be the Volume
of the cone?
Choose a answer
23.2
29.3
40.4
500000000000
Answer:
29.3
Step-by-step explanation:
For Ice-cream Cone
height (h) = 7 cm
diameter (d) = 4 cm
radius (r) = diameter/2 = 4/2 cm
radius (r) = 2 cm
Volume Of A Cone
= π * r^2 * h/3
= 22/7 * 2 * 2 * 7/3
= 22 * 4 * 1/3 cm
= 88/3 cm
= 29.3 cm^3
Thus, the Volume of the cone would be 29.3 cm^3
In 2001 polls indicated that 74% of Americans favored mandatory testing of students in public schools as a way to rate the school. This year in a poll of 1,000 Americans 71% favor mandatory testing for this purpose. Has public opinion changed since 2001? We test the hypothesis that the percentage supporting mandatory testing is less than 74% this year. The P-value is 0.015. Which of the following interpretation of this P-value is valid? Group of answer choices The probability that Americans have changed their opinion on this issue since 2001 is 0.015. If 74% of Americans still favor mandatory testing this year, then there is a 1.5% chance that poll results will show 71% or fewer with this opinion. There is a 1.5% chance that the null hypothesis is true.
Answer:
The correct option is option 2.
Step-by-step explanation:
In this case we need to test whether the previous data for the proportion of Americans who favored mandatory testing of students in public schools as a way to rate the school has decreased this year or not.
The hypothesis can be defined as follows:
H₀: The proportion supporting mandatory testing is not less than 74% this year, i.e. p ≥ 0.74.
Hₐ: The proportion supporting mandatory testing is less than 74% this year, i.e. p < 0.74.
It is provided that the p-value of the test is,
p-value = 0.015
The p-value is well defined as per the probability, [under the null hypothesis (H₀)], of attaining a result equivalent to or more extreme than what was truly observed.
The p-value of 0.015 or 1.5% implies that, if it is true that 74% of Americans still favor mandatory testing this year, then the probability that the poll results will show that 71% or less with the same opinion is 1.5%.
Thus, the correct option is option 2.
What is the measure of arc AD?
Angle ABD measures (4x + 10). Angle ACD measures
(5x - 2)
GO
Answer:
116°
Step-by-step explanation:
Given that :
∠ ABD measures (4x + 10)
∠ ACD measures (5x - 2)
Then
∠ABD = ∠ACD ( rule : angle by same chord AD )
∠ABD = (4x + 10)°
∠ACD = (5x - 2)°
so we can as well say that :
(4x + 10)° = (5x - 2)°
4x - x = -10 -2
- x = - 12
x = 12
∠ABD = (4x + 10)°
= ( 4 × 12 + 10)°
= 58°
∠ACD = (5x - 2)°
= ( 5 * 12 - 2)°
= 58°
∠AOD = 2∠ABD = 2∠ACD ( since angle by arc AD at center is twice the angle by same arc AC in other arc segment)
∠AOD = 2 × 58°
∠AOD = 116°
Measure of arc AD = 116°
What algebraic expression must be subtracted from the sum of y2+5y−1
y
2
+
5
y
−
1
and 3y2−2y+4
3
y
2
−
2
y
+
4
to give 2y2+7y−2
2
y
2
+
7
y
−
2
as the result?
Answer:
2y² -4y +5
Step-by-step explanation:
First you need to find the sum of y²+5y-1 and 3y²-2y+4
(y²+5y-1) + (3y²-2y+4) => y²+3y²+5y-2y-1+4
=4y²+3y+3
Next is to subtract 2y²+7y-2 from the sum calculated above in order to find the algebraic expression asked in the exercise
4y²+3y+3 -(2y²+7y-2) => 4y²-2y²+3y-7y+3+2
=2y² -4y +5
Therefore, the algebraic expression asked must be 2y² -4y +5
How are the lengths of the four sides of the parallelogram related ?
Answer:
Step-by-step explanation: Opposite sides of a parallelogram are equal.
Answer:
The opposite sides of the parallelogram have equal lengths.
Step-by-step explanation:
PLATO SAMPLE
The box plot suggests that about 50\%50%50, percent of high schools in Orange County have more than what number of band members? Choose 1 answer 80,90,105,115,130
Answer: 105
Step-by-step explanation:
Answer:
105
Step-by-step explanation:
C
Two students taking a multiple choice exam with 20 questions and four choices for each question have the same incorrect answer on eight of the problems. The probability that student B guesses the same incorrect answer as student A on a particular question is 1/4. If the student is guessing, it is reasonable to assume guesses for different problems are independent. The instructor for the class suspects the students exchanged answers. The teacher decides to present a statistical argument to substantiate the accusation. A possible model for the number of incorrect questions that agree is:
Final answer:
The possible model for the number of incorrect questions that agree is a binomial distribution. The teacher can use this model to calculate the probability of observing 8 or more agreed-upon answers.
Explanation:
The possible model for the number of incorrect questions that agree is a binomial distribution because there are a fixed number of trials (the number of questions) and each trial has two possible outcomes (agree or disagree).
The probability that student B guesses the same incorrect answer as student A on a particular question is 1/4, so the probability of agreeing on a particular question is 1/4. Since there are 20 questions, the probability that they agree on exactly 8 questions is given by the binomial probability formula: P(x = 8) = C(20, 8) * (1/4)^8 * (3/4)^12.
The teacher can use this model to calculate the probability of observing 8 or more agreed-upon answers by summing the probabilities of all possible outcomes with 8 or more agreed-upon answers: P(x ≥ 8) = P(x = 8) + P(x = 9) + ... + P(x = 20).
Find the circumference of the circle.
Answer:
C=2πr
Step-by-step explanation:
A polling organization had taken a survey of a sample of 200 people for one of their clients, in order to estimate a population percentage. Now the client would like them to reduce the margin of error by 50% (that is, the new margin of error should be half the original margin of error), while keeping the same level of confidence. To do this, how many people should they now survey
Answer:
They now should survey 800 people.
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which
z is the zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].
The margin of error is:
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In this problem:
Same level of confidence, so same z
Same proportion, so same [tex]\pi[/tex]
We have to change n
We want to reduce the margin of error by half.
M is inverse proportion to the square root of n. That is, as n increases, M decreases.
We want to decrese M by half. So we need to increase n by a factor of 2^2 = 4
The first survey had a sample of 200 people
Increasing by a factor of 4.
200*4 = 800
They now should survey 800 people.
A baker uses a coffee mug with a diameter of 8cm to cut out circular cookies from a big sheet of cookie dough.
What is the area AAA of each cookie?
Give your answer in terms of pi.
Answer:
The forumula for finding area of the circle is \pi r^2.
Step-by-step explanation:
Let's find the radius of the mug:
r=\frac{d}{2}=\frac{8}{2}=4
Now, we can to express the area of each cookie in terms of pi:
Area= \pi *4^2=16\pi
If Karim has eight male cousins and twelve female cousins,what fraction of his cousins are female?
A survey was conducted at two colleges. 500 students at College A participated in the study. The results indicated that on average, the students spent 15 hours per week doing online assignments and its standard deviation was 5 hours. At College B, 400 students participated in the study. The average hours they worked for online assignments was 20 with a standard deviation of 4 hours. Please test whether there is a true difference in the time students spent for online assignments between the two colleges (using a confidence level of 99%).
Answer:
[tex]t=\frac{(15-20)-0}{\sqrt{\frac{5^2}{500}+\frac{4^2}{400}}}}=-16.67[/tex]
The p value would be given by:
[tex]p_v =2*P(t_{898}<-16.67) \approx 0[/tex]
Since the p value is a very low value we have enough evidence to reject the null hypothesis and we can conclude that we have significant difference in the means of time spent for online assignments between the two colleges
Step-by-step explanation:
Data given
[tex]\bar X_{1}=15[/tex] represent the mean for sample A
[tex]\bar X_{2}=20[/tex] represent the mean for sample B
[tex]s_{1}=5[/tex] represent the sample standard deviation for A
[tex]s_{f}=4[/tex] represent the sample standard deviation for B
[tex]n_{1}=500[/tex] sample size for the group A
[tex]n_{2}=400[/tex] sample size for the group B
[tex]\alpha=0.01[/tex] Significance level provided
t would represent the statistic
System of hypothesis
The system of hypothesis is the true difference in the time students spent for online assignments between the two colleges, the system of hypothesis would be:
Null hypothesis:[tex]\mu_{1}-\mu_{2}=0[/tex]
Alternative hypothesis:[tex]\mu_{1} - \mu_{2}\neq 0[/tex]
Since we don't know the deviations the statistic is given by:
[tex]t=\frac{(\bar X_{1}-\bar X_{2})-\Delta}{\sqrt{\frac{\sigma^2_{1}}{n_{1}}+\frac{\sigma^2_{2}}{n_{2}}}}[/tex] (1)
The degrees of freedom are given by [tex]df=n_1 +n_2 -2=500+400-2=898[/tex]
Replacing the info given we got:
[tex]t=\frac{(15-20)-0}{\sqrt{\frac{5^2}{500}+\frac{4^2}{400}}}}=-16.67[/tex]
The p value would be given by:
[tex]p_v =2*P(t_{898}<-16.67) \approx 0[/tex]
Since the p value is a very low value we have enough evidence to reject the null hypothesis and we can conclude that we have significant difference in the means of time spent for online assignments between the two colleges
Let's take the speed of sound to be 340 m/s. What would be the length of the pipe in a pipe organ that produces a note with a pitch of 170
Hz?
Answer:
L = 2 m
The length of the pipe in a pipe organ that produces a note with a pitch of 170Hz is 2m
Step-by-step explanation:
Given;
Speed of sound v = 340 m/s
Frequency of sound f = 170 hz
The length of the pipe in a pipe organ that produces a note with a pitch of 170Hz is;
Length L = v/f = speed/frequency
L = 340/170
L = 2 m
The length of the pipe in a pipe organ that produces a note with a pitch of 170Hz is 2m
What is the equation of this line in slope intercept form (-1, 5) and (1, -3)
Answer: y= -4x + 1
Step-by-step explanation:
(-1,5) (1,-3)
5-(-3)=8
-1-1=-2
8/-2=-4 negative 4 is the slope. Now find the y-intercept using the formula y=mx + b where b is the y intercept.
so we will plot the y and x values plus the slope to find the y-intercept.
5=-4(-1) + b solve for b
5=4 + b
b=1
so now will write the equation y = -4x +1
Evaluate n/6+2 when n =12
Answer:
4
Step-by-step explanation:
n/6+2
Let n = 12
12/6 +2
Division first
2 +2
4
Answer:
4
Step-by-step explanation:
plug in 12 for n and you get :: 12/6 + 2
PEMDAS says to divide first, 12/6 is 2. you add 2 next and you get 4
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Sally is planning a trip for 225 students.
Place
She asks a sample of 30 students where
Theme Park
they want to go.
Theatre
Each student chooses one place.
Sports Centre
The table shows information about
her results.
Seaside
(i) Work out how many of the 225 students
you think will want to go to the Theme Park.
Answer:
Number of students want to go to Theme Park = 75
Step-by-step explanation:
Note: The given question is incomplete. Complete question is as follow.
Given:
Number of sample student = 30
Place Number of students want to go
Theme Park 10
Theater 5
Sports Center 8
Seaside 7
Find:
How many students want to go to Theme Park.
Computation:
⇒ Probability for students want to go to Theme Park = 10 / 30
⇒ Probability for students want to go to Theme Park = 1 / 3
⇒ Number of students want to go to Theme Park = [1 / 3]225
⇒ Number of students want to go to Theme Park = 75
Final answer:
Using a sample proportion, if 12 out of 30 students chose the Theme Park, we estimate that 90 out of 225 students will want to go to the Theme Park.
Explanation:
To estimate how many of the 225 students will want to go to the Theme Park, we use the results from Sally's sample of 30 students. First, we need to know the number of students in the sample who chose the Theme Park. Suppose, for instance, that 12 out of the 30 sampled students chose the Theme Park. We can set up a proportion to find the estimated number of students out of 225 who would choose the same.
Here's the proportion based on the sample data:
Number of students who chose Theme Park in the sample / Total number of students in the sample = Estimated number of students who will choose Theme Park / Total number of students planning to go
In our example, this is 12/30 = x/225, where x is the estimated total.
We cross-multiply to solve for x:
12 × 225 = 30 × x
x = (12 × 225) / 30
x = 90
Thus, we estimate that 90 out of the 225 students will prefer to go to the Theme Park.
which value for x makes the sentence true
1/8(x-56)=7/8
Answer:
63.
Step-by-step explanation:
To solve this equation, we will first need to multiply both sides by 8 to get rid of the coefficient:
8×[tex]\frac{1}{8}[/tex](x-56)=[tex]\frac{7}{8}[/tex]×8
Now, this will get rid of the fractions, giving us:
x-56= 7
Next, simply add 56 to both sides:
x-56+56= 7+56
This results in:
x=63.
The Internet is affecting us all in many different ways, so there are many reasons for estimating the proportion of adults who use it. Assume that a manager for E-‐Bay wants to determine the current percentage of U.S. adults who now use the Internet. How many adults must be surveyed in order to be 95% confident that the sample percentage is in error by no more than three percentage points? a. b. In 2006, 73% of adults used the Internet. No known possible value of the proportion.
Answer:
a) At least 842 adults must be surveyed.
b) At least 1068 adults must be surveyed.
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which
z is the zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].
The margin of error is:
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
95% confidence level
So [tex]\alpha = 0.05[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.05}{2} = 0.975[/tex], so [tex]Z = 1.96[/tex].
a) 73% of adults used the Internet.
At least n adults must be surveyed.
n is found when [tex]M = 0.03, \pi = 0.73[/tex]
So
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
[tex]0.03 = 1.96\sqrt{\frac{0.73*0.27}{n}}[/tex]
[tex]0.03\sqrt{n} = 1.96\sqrt{0.73*0.27}[/tex]
[tex]\sqrt{n} = \frac{1.96\sqrt{0.73*0.27}}{0.03}[/tex]
[tex](\sqrt{n})^{2} = (\frac{1.96\sqrt{0.73*0.27}}{0.03})^{2}[/tex]
[tex]n = 841.3[/tex]
Rounding up
At least 842 adults must be surveyed.
b. No known possible value of the proportion.
Same as above, the difference as the since we do not know the value of the proportion, we use [tex]\pi = 0.5[/tex], which is when the largest sample size is going to be needed.
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
[tex]0.03 = 1.96\sqrt{\frac{0.5*0.5}{n}}[/tex]
[tex]0.03\sqrt{n} = 1.96\sqrt{0.5*0.5}[/tex]
[tex]\sqrt{n} = \frac{1.96\sqrt{0.5*0.5}}{0.03}[/tex]
[tex](\sqrt{n})^{2} = (\frac{1.96\sqrt{0.5*0.5}}{0.03})^{2}[/tex]
[tex]n = 1067.11[/tex]
Rounding up
At least 1068 adults must be surveyed.
To be 95% confident that the sample percentage of U.S. adults who use the Internet is in error by no more than 3 percentage points, a total of 1068 adults must be surveyed.
Explanation:To estimate the current percentage of U.S. adults who use the Internet with a 95 percent confidence level and an error margin of no more than three percentage points, we must determine the sample size we need to survey. We'll follow the formula below for estimating the sample size:
n = (Z² * p(1-p)) / E^2
Where n is the sample size, Z is the z-score associated with our desired confidence level (for a 95% confidence level, Z is about 1.96), p is the estimated proportion of the population (based on the 2006 data, we'll use 0.73), and E is the margin of error (which we want to be 0.03).
Plug in the values:
n = (1.96² * 0.73 * 0.27) / 0.03² = 1067.14
Since we cannot survey a fraction of a person, we round up to the next whole number. Therefore, the manager would need to survey 1068 adults in order to be 95 percent confident that the sample percentage is in error by no more than three percentage points.
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A model rocket is launched with an initial upward velocity of 195 ft/s. The rocket's height h (in feet) after t seconds is given
by the following
h= 1951 - 1612
Find all values of 1 for which the rocket's height is 87 feet.
Round your answer(s) to the nearest hundredth.
(If there is more than one answer, use the "or" button.)
1 =
seconds
x
5
?
ground
Answer:
0.46 seconds or 11.72 seconds
Step-by-step explanation:
Putting 87 for h in the height equation gives ...
87 = -16t^2 +195t
Dividing by -16 puts this in a little nicer form for finding solutions.
t^2 -(195/16)t = -87/16
To "complete the square", we can add the square of half the coefficient of t:
t^2 -(195/16)t + (195/32)^2 = (195/32)^2 -87/16
(t -195/32)^2 = 32457/1024
Taking the square root, we have ...
t -195/32 = ±(1/32)√32457
t = (195 ±√32457)/32 ≈ 0.4638 or 11.7237
The rocket is at a height of 87 feet after 0.46 seconds, and again after 11.72 seconds.
Alvin makes pillows for his room he buys 4.5 feet of fabric for 9.60 what is the cost of the fabric per yard?
The cost of the fabric per yard is approximately $6.39.
To find the cost of the fabric per yard, we need to first calculate the cost per foot and then convert it to yards.
Step 1: Calculate the cost per foot of fabric.
[tex]Cost per foot = Total cost / Total feet[/tex]
[tex]Cost per foot = $9.60 / 4.5 feet[/tex]
[tex]Cost per foot = $2.13[/tex]
Step 2: Convert the cost per foot to cost per yard.
Since there are 3 feet in a yard, we can find the cost per yard by multiplying the cost per foot by 3.
[tex]Cost per yard = Cost per foot * 3[/tex]
[tex]Cost per yard ≈ $2.13 * 3[/tex]
[tex]Cost per yard = $6.39[/tex]
Complete correct question:
Alvin makes pillows for his room he buys 4.5 feet of fabric for 9.60 what is the cost of the fabric per yard?