72
60
48
36
Number of Computers
The graph shows a proportional relationship between
the number of computers produced at a factory per
day in three days, 36 computers are produced, 48
computers are produced in 4 days, and 60 computers
are produced in 5 days.
Find the unit rate of computers per day using the
graph.
Unit rate
computers per day
I
24
12
3 4 5 6 7 8 9 10 11 12
Number of Days
Intro
Done
Answers
Graph is attached below ;
Answer:
Unit rate = 12 computers per day
Step-by-step explanation:
To obtain the unit rate of computers sold per day using the graph, we need to obtain the slope of the graph, which is the change in y per change in x
That is ; the gradient ;
Slope = change in y / change in x
Slope = (y2 - y1) / (x2 - x1)
y2 = 60 ; y1 = 36 ; x2 = 5 ; x1 = 3
Slope = (60 - 36) / (5 - 3) = 24 / 2 = 12
Slope = 12
Unit rate = 12 computers per day
Related Questions
A line has a slope of 11 and passes through the point (5,7). Which of these is an equation for the line? O A. y-7 = -11(x - 5) B. y + 7 = 11(x + 5) O C. y-5 = -11(x - 7) O D. y - 7 = 11(x - 5) SUBMIT
Answers
Answer:
D. y - 7 = 11(x - 5)
Step-by-step explanation:
Use point slope form, y - y1 = m(x - x1), where m is the slope and (x1, y1) is a point on the line.
Plug in the given slope and point:
y - y1 = m(x - x1)
y - 7 = 11(x - 5)
So, the correct answer is D. y - 7 = 11(x - 5)
Craig and Cindy working together can mow the lawn in four hours working alone Cindy takes twice as long as Craig how long does it take Craig to mow the lawn alone
Answers
Answer:
12 hours
Step-by-step explanation:
1 : (1/4 : (2 + 1)) = 12
Which of the following describes a positive correlation?
As the number of hours spent on homework increases, the tests scores increase.
As the number of apples eaten per year increases, the number of times visiting the doctor every year remains the same.
As the number of times going to bed early increases, the number of times waking up late decreases.
The amount of time a team spent practicing increases, the number of games lost in a season decreases.
THIS IS A MULTIPLE CHOICE QUESTION
Answers
Answer:
First Choice: As the number of hours spent on homework increases, the tests scores increase.
Step-by-step explanation:
The definition of a positive correlation is a relationship between two given variables, in which both variables are moving in the same direction. This can mean when one variable increases and the other variable increases, too, or one variable decreases and the other decreases as well.
The first choice is a positive correlation because both variables are changing (increasing) in the same direction. As you spend more time on homework, you're likely to get a higher test score.
The second choice cannot be a positive correlation because only one variable is having some kind of change (increasing). The doctor visits amount remains the same, so we can call this a zero-correlation relationship because the number of apples eaten yearly doesn't affect the amount of doctor visits. An apple a day keeps the doctor a way is just a proverb, not to be taken literally.
The third choice cannot be a positive correlation because the two variables are going different directions. Even though the number of times going to bed early is increasing, the number of times waking up late decreases, which is not moving in the same direction as the other variable.
The fourth choice cannot be a positive correlation because, similarly to the third choice, the two variables are going different directions. One variable is increasing, which is the amount of practice time. Meanwhile, the other variable is decreasing (going in the opposite direction), which is the number of games lost in a season.
If y = sin 3x, find y" in terms of y.
Answers
Answer:
-0.54
Step-by-step explanation:
Hope it helped.
• • •
OLVE
(a) 3^2x+1=9^
2x-1
Answers
Answer:
x=2
Step-by-step explanation:
you first have to make the bases the same
3^2x+1=9^2x-1
3^2x+1=3^2(2x-1) if you make the bases the same you will use 3^2 because it's equal to 9
3^2x+1=3^4x-2
2x+1=4x-2
2x-4x=-2-1
-2x/-2=-4/-2
x=2
I hope this helps
A noted psychic was tested for extrasensory perception. The psychic was presented with 200 cards face down and asked to determine if each card were one of five symbols: a star, a cross, a circle, a square, or three wavy lines. The psychic was correct in 50 cases. Let p represent the probability that the psychic correctly identifies the symbol on the card in a random trial. Assume the 200 trials can be treated as a simple random sample from the population of all guesses the psychic would make in his lifetime. How large a sample n would you need to estimate p with a margin of error of 0.01 with 95% confidence? Use the hypothesized value p = 0.20 as the value for p*.
Answers
Answer:
r3jehejn wbbwbwbbwmwkwkwjwjwhhejehehehhe
y = 95°, find the measure of x
Answers
9514 1404 393
Answer:
x = 100°
y = 95°
Step-by-step explanation:
It is probably easier to find y first. Opposite angles of an inscribed quadrilateral are supplementary, so ...
y = 180° -85° = 95°
The measure of an arc is double the measure of the inscribed angle subtending it. The arc subtended by angle y is ...
90° +x = 2y
x = 190° -90° = 100°
_____
Additional comment
The rule cited above regarding opposite angles of an inscribed quadrilateral comes from the theorem regarding inscribed angles. In the given diagram, the diagonal from the bottom vertex to the top one is a chord that divides the circle into two arcs. Their sum is 360°. The inscribed angle theorem tells you ...
2y +2(85°) = 360°
y + 85° = 180° . . . . . . . divide by 2; opposite angles are supplementary
Women athletes at a certain university have a long-term graduation rate of 67%. Over the past several years, a random sample of 36 women athletes at the school showed that 23 eventually graduated. Does this indicate that the population proportion of women athletes who graduate from the university is now less than 67%? Use a 5% level of significance.
(a) What is the level of significance?
State the null and alternate hypotheses.
A. H0: p = 0.67; H1: p < 0.67
B. H0: p = 0.67; H1: p ≠ 0.67
C. H0: p < 0.67; H1: p = 0.67
D. H0: p = 0.67; H1: p > 0.67
(b) What sampling distribution will you use?
A. The standard normal, since np > 5 and nq > 5.
B. The standard normal, since np < 5 and nq < 5.
C. The Student's t, since np > 5 and nq > 5.
D. The Student's t, since np < 5 and nq < 5.
What is the value of the sample test statistic?
(c) Find the P-value of the test statistic. (Round your answer to four decimal places.)
Sketch the sampling distribution and show the area corresponding to the P-value.
(d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis? Are the data statistically significant at level α?
A. At the α = 0.05 level, we reject the null hypothesis and conclude the data are statistically significant.
B. At the α = 0.05 level, we reject the null hypothesis and conclude the data are not statistically significant.
C. At the α = 0.05 level, we fail to reject the null hypothesis and conclude the data are statistically significant.
D. At the α = 0.05 level, we fail to reject the null hypothesis and conclude the data are not statistically significant.
(e) Interpret your conclusion in the context of the application.
A. There is sufficient evidence at the 0.05 level to conclude that the true proportion of women athletes who graduate is less than 0.67.
B. There is insufficient evidence at the 0.05 level to conclude that the true proportion of women athletes who graduate is less than 0.67.
Answers
Answer:
A. H0: p = 0.67; H1: p < 0.67
A. The standard normal, since np > 5 and nq > 5.;
Test statistic = - 0.397 ;
Pvalue = 0.3457;
D. At the α = 0.05 level, we fail to reject the null hypothesis and conclude the data are not statistically significant.
B. There is insufficient evidence at the 0.05 level to conclude that the true proportion of women athletes who graduate is less than 0.67.
Step-by-step explanation:
p = 0.67 ; q = 1 - p = 1 - 0.67
Sample size, n = 36
x = 23
Test for normality :
(36*0.67) = 24.12
(36 * (1-0.67)) = 11.88
For a normal distribution :
np ≥ 5 and n(1 - p) ≥ 5
The hypothesis :
H0 : p = 0.67
H1 : p < 0.67
The Test statistic :
Z = (phat - p) / √[(p(1 -p))/n]
Phat = x / n = 23 / 36
Z = ((24/36) - 0.67)) / √[(0.67(1 -0.67))/36]
Z = - 0.031 / 0.0783687
Z = - 0.396983
Z = - 0.397
Usong the Pvalue from Z calculator ;
Pvalue of Z = 0.3457
If Pvalue < α ; Reject H0 ; If otherwise, Fail to reject H0
A campus deli serves 101 customers over its busy lunch period from 11:30 am to 1:30 pm. A quick count of the number of customers waiting in line and being served by the sandwich makers shows that an average of 18 customers are in process at any point in time. What is the average amount of time (in minute) that a customer spends in process?
Answers
Answer:
21.38 minutes
Step-by-step explanation:
the total number served = 101
teh number of hours that is spent in serving from 11.30 to 1.30 = 2 hours
Lq = average number of those that are in line = 18 customers
from here we are to find the flow rate
= [tex]\frac{total served}{service hour}[/tex]
= 101/2 = 50.5
the average time in waiting =
Lq/flow rate
= 18/50.5
= 0.3564 hours
convert to minutes = 0.3564 * 60 minutes
= 21.38 minutes
What is the area of my lawn if it measures 4m x 4.5m
Answers
Answer:
18m squared
Step-by-step explanation:
4m x 4.5m = ?
What is x: |3x-1| = 4
Answers
Step-by-step explanation:
3x-1=4
3x=4+1
3x=5
x=5/3
Answer:
x = 5/3 x = -1
Step-by-step explanation:
|3x-1| = 4
There are two solutions, one positive and one negative
3x-1 =4 and 3x-1 = -4
Add 1 to each side
3x-1+1 = 4+1 3x-1+1 = -4+1
3x = 5 3x = -3
Divide by 3
3x/3 = 5/3 3x/3 = -3/3
x = 5/3 x = -1
16: The temperature yesterday at noon was 68.5 degrees. Today at noon
it was 59.9 degrees. What was the difference in temperature?
O A. 8.4 degrees
OB. 8.5 degrees
C. 8.6 degrees
O D. 8.7 degrees
Answers
Answer:
C
Step-by-step explanation:
It is 8.6 because we are finding the difference and using subtraction.
So I did 68.8-59.9 and I got 8.6
visually demonstrate the following value using the hundred square below
Answers
Answer:
just fill in 40 squres
Step-by-step explanation:
A bacteria culture grows with a constant relative growth rate. After 2 hours there are 400 bacteria and after 8 hours the count is 50,000.
(a) Find the initial population. P(0) = 80 )ãbacteria
(b) Find an expression for the population after t hours. r(t) = 180( 125(6 Plt) =180(125(2))-
(c) Find the number of cells after 7 hours. (Round your answer to the nearest integer.) P(7)=72.358- bacteria
(d) Find the rate of growth after 7 hours. (Round your answer to the nearest integer.) P(7) 2x bacteria/hour
(e) When will the population reach 200,000? (Round your answer to one decimal place.) hours
Answers
Answer:
a) P(0) = 80
b) [tex]P(t) = 80(2.2361)^t[/tex]
c) 22,363 cells.
d) The rate of growth after 7 hours is of 18,000 bacteria per hour.
e) 9.7 hours.
Step-by-step explanation:
A bacteria culture grows with a constant relative growth rate.
This means that the population is given by:
[tex]P(t) = P(0)(1+r)^t[/tex]
In which P(0) is the initial population and r is the growth rate, as a decimal.
After 2 hours there are 400 bacteria and after 8 hours the count is 50,000.
This means that in 6 hours, the population went from 400 bacteria to 50,000 bacteria. We use this to find r. So
[tex]50000 = 400(1+r)^6[/tex]
[tex](1+r)^6 = \frac{50000}{400}[/tex]
[tex](1+r)^6 = 125[/tex]
[tex]\sqrt[6]{(1+r)^6} = \sqrt[6]{125}[/tex]
[tex]1 + r = 125^{\frac{1}{6}}[/tex]
[tex]1 + r = 2.2361[/tex]
So
[tex]P(t) = P(0)(2.2361)^t[/tex]
(a) Find the initial population. P(0)
We have that P(2) = 400. We use this to find P(0). So
[tex]P(t) = P(0)(2.2361)^t[/tex]
[tex]400 = P(0)(2.2361)^2[/tex]
[tex]P(0) = \frac{400}{(2.2361)^2}[/tex]
[tex]P(0) = 80[/tex]
So
[tex]P(t) = 80(2.2361)^t[/tex]
(b) Find an expression for the population after t hours.
[tex]P(t) = 80(2.2361)^t[/tex]
(c) Find the number of cells after 7 hours.
This is P(7). So
[tex]P(7) = 80(2.2361)^7 = 22363[/tex]
22,363 cells.
(d) Find the rate of growth after 7 hours.
We have to find the derivative when t = 7. So
[tex]P(t) = 80(2.2361)^t[/tex]
[tex]P^{\prime}(t) = 80\ln{2.2361}(2.2361)^t[/tex]
[tex]P^{\prime}(7) = 80\ln{2.2361}(2.2361)^7 = 18000[/tex]
The rate of growth after 7 hours is of 18,000 bacteria per hour.
(e) When will the population reach 200,000?
This is t for which [tex]P(t) = 200000[/tex]. So
[tex]P(t) = 80(2.2361)^t[/tex]
[tex]200000 = 80(2.2361)^t[/tex]
[tex](2.2361)^t = \frac{200000}{80}[/tex]
[tex](2.2361)^t = 2500[/tex]
[tex]\log{(2.2361)^t} = \log{2500}[/tex]
[tex]t\log{2.2361} = \log{2500}[/tex]
[tex]t = \frac{\log{2500}}{\log{2.2361}}[/tex]
[tex]t = 9.7[/tex]
So 9.7 hours.
Which graph is a function?
Answers
Answer:
B
Step-by-step explanation:
A function is a relation in which each input, x, has only one output, y.
There are two ways to determine if a relation is a function:
1. If each x-input has only one, unique y-output, then it's a function. If some x-inputs share the same y-outputs, it's not a function.
2. Vertical Line Test on Graphs:
To determine whether y is a function of x, when given a graph of relation, use the following criterion: if every vertical line you can draw goes though only 1 point, the relation can be a function. If you can draw a vertical line that goes though more than 1 point, the relation cannot be a function.
Since we're given a graph relation, let's test both of the answers out.
If I were to draw a vertical line in a specific place on the first graph, I'd be hitting more than one point in the coordinate plane.
If I were to draw a vertical line in a specific place on the second graph, I'd only be hitting one point in the coordinate plane.
Therefore, choice B is a function.
What is the volume of the
cylinder? Use 3.14 for a.
A 1200 cubic inches
B 1884 cubic inches
C 3768 cubic inches
D 28,260 cubic inches
Answers
Answer:
Step-by-step explanation:
area of top face = π15² = 225π in²
volume = 225π × 40 = 9000π ≅28,260 in³
Samuel had 12 red marbles , 15 blue marbles , and 13 green marbles . Which fraction represents the number of red marbles he has
Answers
Answer:
12/40 or simplified it would be 3/10
Step-by-step explanation:
What is the answer to 6,1=? 8,2=20, 12,3=20, 10,5=52, 6,1=?
Answers
can u plz check if the question is right
Calculate the range and the standard deviation for the set of numbers.
6,5, 1, 5, 8, 5, 3, 5, 4,7
The range is
(Simplify your answer.)
Can I please get help with this problem?
Answers
Answer:
When time is short and you just want a rough estimate of the standard deviation, turn to the range rule to quickly estimate the standard deviation value. The standard deviation is approximately equal to the range of the data divided by 4. That's it, simple.
What is the surface area of a cylinder that has a radius of 7 m and a height of 18 m?
879.65 m2
1099.56 m2
615.75 m2
395.84 m2
Answers
1099.56m² is the surface area of a cylinder that has a radius of 7 m and a height of 18 m.
a. 1140
b. 1130
c. 1120
d. 115
Answers
Answer:
1130
Step-by-step explanation:
1109+7 = 1116
1116+7 = 1123
Adding 7 each time
1123+7 = 1130
Bianca is planting trees along her driveway, and she has 55 sycamores and 55 palm trees to plant in one row. What is the probability that she randomly plants the trees so that all 55 sycamores are next to each other and all 55 palm trees are next to each other
Answers
Answer:
0.0079 = 0.79% probability that she randomly plants the trees so that all 5 sycamores are next to each other and all 5 palm trees are next to each other.
Step-by-step explanation:
A probability is the number of desired outcomes divided by the number of total outcomes.
The trees are arranged, so, to find the number of outcomes, the arrangements formula is used.
Arrangements formula:
The number of possible arrangements of n elements is given by:
[tex]A_n = n![/tex]
Desired outcomes:
5 sycamores(5! possible ways) and then the 5 palm trees(5! possible ways)
5 palm trees(5! possible ways) then the 5 sycamores(5! possible ways).
[tex]D = 2*5!*5![/tex]
Total outcomes:
Arrangements of 10 plants, so:
[tex]T = 10![/tex]
What is the probability that she randomly plants the trees so that all 5 sycamores are next to each other and all 5 palm trees are next to each other?
[tex]p = \frac{D}{T} = \frac{2*5!*5!}{10!} = 0.0079[/tex]
0.0079 = 0.79% probability that she randomly plants the trees so that all 5 sycamores are next to each other and all 5 palm trees are next to each other.
Jake has corn growing on 66 2/3% of his 330 acres. How many acres are being used for corn?
Answers
on 220 acres
66 ⅔% is just ⅔ of 100%
330 * 2 / 3 = 220
please help me with this
Answers
please mark this answer as brainlist
A decreasing inventory turnover ratio indicates:_______
a. a longer time span between the purchase and sale of inventory.
b. a shorter time span between the purchase and sale of inventory.
c. a longer time span between the ordering and receiving of inventory.
d. a shorter time span between the ordering and receiving of inventory.
Answers
What is the equation
Answers
Answer:
D.) y = 2x + 2
Step-by-step explanation:
First, we need to find the slope.
Lets use the points (0, 2) and (-2, -2).
Using the formula for calculating slope, we get 2 as our slope.
Since the equation should be in slope-intercept form, we use this formula.
y = mx + b
We'll use our first point (0, 2) to substitute for x and y and use 2 to substitute for m (slope):
2 = 2(0) + b
2 x 0 = 0
2 = 0 + b
-0 = -0
= 2 = b
Now, substitute b for 2 for 2 for m.
= y = 2x + 2.
Hope this helps!
If there is something wrong, please let me know.
answer the question
Answers
Answer:
g(1)=(1-1)*2 -2
= -2
g(2) = (2-1)*2 -2
= -1
g(3) = 1/2 (3) -2
= -1/2
Answer:
g(1) = -2
g(2) = -1
g(3) = -1/2 or -0.5
Step-by-step explanation:
you really need help for typing numbers into your calculator ? because there is nothing else to do here.
we get 3 values of x and need to calculate the functional values based on the given expressions by using each given value for x.
the only thing that requires a bare minimum of intelligence is to find the fitting expression.
so, for g(1) and g(2) we need to use the middle one, and for g(3) the third one. uhhhh, very difficult ...
typing it in here is way more effort than doing it directly on the calculator or really in the head.
so, g(1) = (1-1)² - 2 = -2
g(2) = (2-1)² - 2 = 1 - 2 = -1
g(3) = 1/2 ×3 - 2 = 3/2 - 2 = 3/2 - 4/2 = -1/2
uhhhh, come in, you could have done that too. and way faster.
Một miếng đất hình chữ nhật có chu vi 80 mét.Nếu kéo dài thêm 8 mét nữa thì diện tích tăng thêm là 72 mét vuông.Tính chiều dài và chiều rộng hình chữ nhật ban đầu ?
Answers
Answer:
Step-by-step explanation:
(D+R) = 80:2 = 40
D = 40-R
(D+8) * R = 72X
Thay D=40-R
(40-R+8)*R = 72X
R=1.55, D=38.45
If you wanted to make a game where you pay $5 if you can't guess a random dogs weight within 16lbs what payout should you offer you make the game zero-expected value
Answers
Answer:
Following are the solution to the given question:
Step-by-step explanation:
The population std. dev of the dog weight=8
[tex]\sigma=8\\\\P(\text{guess with in 16 lbs}) = P(|X-\mu|\leq 16)\\\\=P(-2 \leq Z \leq 2) = 0.9544\\\\[/tex]
Calculating the payout w s.t:
[tex]E[netpay]=0=(-5) \times 0.9544+w\times (1-0.9544)\\\\ w =(5 \times \frac{0.9544}{1-0.9544}) =\$ 104.65[/tex]
therefore, we assume that the weight of the dog is a normal distribution with std. deviation that is 8.
what represent the relationship between the total mass of a crate
Answers
9514 1404 393
Answer:
(a) M = 0.25n +100
Step-by-step explanation:
The distance between the dots on the graph is a rise of 1 grid square and a run of 2 grid squares. If we extend the sequence of dots to the left, we expect to place one at (0, 100). That is, the y-intercept of this function is 100 (eliminates choices C and D).
The rise of 1 grid square represents 25 kg, and the run of 2 grid squares represents 100 CDs. Then the slope of the function (rate of change) is ...
slope = rise/run = 25/100 kg/CD = 0.25
Then the equation describing the points on the graph will be ...
M = 0.25n +100
