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8 9 10 11 12 13 14 (number of hours spent)
dot plot
Answer:
(A) Draw a number line from 8 to 14. Show the frequency of each number. Title the dot plot.
Step-by-step explanation:
Lydia buys 5 pounds of apples and 3 pounds of bananas for a total of $8.50. Ari buys 3 pounds of apples and 2
pounds of bananas for a total of $5.25. This system of equations represents the situation, where x is the cost per
pound of apples, and y is the cost per pound of bananas.
5x + 3y = 8.5
3x + 2y = 5.25
If you multiply the first equation by 2, what number should you multiply the second equation by in order to eliminate
the y terms when making a linear combination?
Complete the multiplication and add the equations. What is the result?
What is the price per pound of apples? $
What is the price per pound of bananas?
Answer:
price per pound of apple = $1.25
price per pound of banana = $0.75
Step-by-step explanation:
Your first question is what value should you multiply the second equation by in order to eliminate the y terms.
The number should be 3. Let us multiply the first equation by 2 and the second equation by 3 and see how y will be eliminated.
10x + 6y = 17...............(i)
9x + 6y = 15.75...........(ii)
10x - 9x = x
6y - 6y = 0
17 - 15.75 = 1.25
x = 1.25
let us find y
10x + 6y = 17...............(i)
10(1.25) + 6y = 17
12.5 + 6y = 17
6y = 17 - 12.5
6y = 4.5
divide both sides by 6
y = 4.5/6
y = 0.75
In order to eliminate y term from the system of equations we multiply equation 2 by -3.
The price per pound of apple is 1.25 dollars and the price per pound of bananas is 0.75 dollars.
Given equations,
[tex]5x + 3y = 8.5[/tex].........(1)
[tex]3x + 2y = 5.25[/tex].......(2)
Here x is the cost per pound of apples, and y is the cost per pound of bananas.
According to the question, multiply the first equation by 2, we get
[tex]10x+6y=17[/tex].....(3)
So, in order to eliminate y term from the system of equations we multiply equation 2 by -3, we get
[tex]-9x-6y=15.75[/tex].....(4)
Now Adding (3) and (4) equation, we get
[tex]x=1.25[/tex]
Putting the above value of x in equation 3 we get,
[tex]10\times1.25+6y=17\\12.5+6y=17\\6y=17-12.5\\6y=4.5\\y=\frac{4.5}{6} \\y=0.75[/tex]
Hence the price per pound of apple is 1.25 dollars and the price per pound of bananas is 0.75 dollars.
For more details follow the link:
https://brainly.com/question/11897796
Explain the connection between the chain rule for differentiation and the method of u-substitution for integration.
Answer:
Chain rule: [tex]\frac{d}{dx} [f[u(x)]] = \frac{df}{du} \cdot \frac{du}{dx}[/tex], u-Substitution: [tex]f\left[u(x)\right] = \int {\frac{df }{du} } \, du[/tex]
Step-by-step explanation:
Differentiation and integration are reciprocal to each other. The chain rule indicate that a composite function must be differentiated, describing an inductive approach, whereas u-substitution allows integration by simplifying the expression in a deductive manner. That is:
[tex]\frac{d}{dx} [f[u(x)]] = \frac{df}{du} \cdot \frac{du}{dx}[/tex]
Let integrate both sides in terms of x:
[tex]f[u(x)] = \int {\frac{df}{du} \frac{du}{dx} } \, dx[/tex]
[tex]f\left[u(x)\right] = \int {\frac{df }{du} } \, du[/tex]
This result indicates that f must be rewritten in terms of u and after that first derivative needs to be found before integration.
A group of children is trying to share a pile of stickers. If every
child gets two stickers, there will be 7 stickers left over. If two
children do not get any stickers, then each of the remaining
children will get exactly 3 stickers.
How many children are in the group?
Answer:
7 children
Step-by-step explanation:
Answer:
7 children is the correct answer
and you follow me if you can't I will unfollow you
Write each ratio as a fraction in simplest form.
a) 9 miles to 15 miles
b) 6 1/3 ounces to 9 1/2 ounces
Where L is the length, in feet, of the pendulum, and π is approximately 22/7. How long must the pendulum be if one complete cycle takes 8 seconds?
Answer:
The simple pendulum should be 15.9 m long.
Step-by-step explanation:
Approximately (for small amplitudes), the period of a simple pendulum is
T = 2*pi * sqrt (L/g), L=length
using pi = 22/7, and g=9.8 m/s^2
8 = 2* 22/7 * sqrt(L/9.8)
solve for L
L = (8*7/(2*22))^2 * 9.8
= 15.874 m
That's quite a long pendulum!
in the diagram ,a and 46° are complementary angles. It is given that a and b are supplementary angles and the angle conjugate to c is 283°. Calculate the values of a,b,c and d. pleaseeeee answer soonn
Answer:
[tex]a=44^{\circ},b=136^{\circ},c=77^{\circ},d=57^{\circ}[/tex].
Step-by-step explanation:
It is given that a and 46° are complementary angles.
[tex]a+46^{\circ}=90^{\circ}[/tex]
[tex]a=90^{\circ}-46^{\circ}[/tex]
[tex]a=44^{\circ}[/tex]
It is given that a and b are supplementary angles.
[tex]a+b=180^{\circ}[/tex]
[tex]44^{\circ}+b=180^{\circ}[/tex]
[tex]b=180^{\circ}-44^{\circ}[/tex]
[tex]b=136^{\circ}[/tex]
Angle conjugate to c is 283°.
[tex]c+283^{\circ}=360^{\circ}[/tex]
[tex]c=360^{\circ}-283^{\circ}[/tex]
[tex]c=77^{\circ}[/tex]
Sum of all angles at a point is 360 degrees.
[tex]a+b+c+d+46^{\circ}=360^{\circ}[/tex]
[tex]44^{\circ}+136^{\circ}+77^{\circ}+d+46^{\circ}=360^{\circ}[/tex]
[tex]d+303^{\circ}=360^{\circ}[/tex]
[tex]d=360^{\circ}-303^{\circ}[/tex]
[tex]d=57^{\circ}[/tex]
Therefore, [tex]a=44^{\circ},b=136^{\circ},c=77^{\circ},d=57^{\circ}[/tex].
A line passes through the points ( – 4, – 2) and ( - 1, - 2). Determine the slope of the line.
Answer: -4/3
Step-by-step explanation:
Formula to find a slope of two given points is
y(sub2) - y(sub1) / x(sub2) - x(sub1)
Plug the values in to get the answer.
-2 - 2 / -1 - (-4)
-4/3
Suppose that the local sales tax rate is 6% and you purchase a computer for $1260.
a. How much tax is paid?
b. What is the computer’s total cost?
Answer:
a. $75.60
b. $1335.60
Step-by-step explanation:
A. First convert the percentage to a decimal.
6% = 0.06
Multiply the cost of the computer by the decimal to find the tax paid.
$1260 × 0.06 = $75.60
B. To find the total cost, add the cost of the computer with the tax.
$1260 + $75.60 = $1335.60
A local Internet provider wants to test the claim that the average time a family spends online on a Saturday is at least 7 hours. To test this claim, the Internet provider randomly samples 30 households and finds that these families' mean number of hours spent on the Internet on a Saturday was 6 hours with a standard deviation of 1.5 hours. At a level of significance of 0.05, can the Internet provider's claim be supported?
A) Fail to Reject the Null Hypothesis
B) Reject the Null Hypothesis
C) Reject The Alternative Hypothesis
D) Fail to Reject the Alternative Hypothesis
E) Accept the Null Hypothesis
F) Accept the Alternative Hypothesis
Answer:
A) Fail to Reject the Null Hypothesis
Step-by-step explanation:
Given that:
A local Internet provider wants to test the claim that the average time a family spends online on a Saturday is at least 7 hours.
sample size = 30
sample mean [tex]\bar x[/tex] = 6
standard deviation [tex]\sigma[/tex] = 1.5
level of significance ∝ = 0.05
The null hypothesis and the alternative hypothesis can be computed as:
[tex]\mathbf{ H_o: \mu \leq 7}[/tex]
[tex]\mathbf{ H_i: \mu \geq 7}[/tex]
The test statistic can be computed as:
[tex]z = \dfrac{\bar x - \mu}{\dfrac{\sigma}{\sqrt{n}}}[/tex]
[tex]z = \dfrac{6 -7} {\dfrac{1.5}{\sqrt {30}}}[/tex]
[tex]z = \dfrac{-1} {\dfrac{1.5}{5.477}}}[/tex]
[tex]z = \dfrac{-5.477} {1.5}[/tex]
z = -3.65
Given that ;
level of significance of 0.05;
z = -3.65
degree of freedom = 30 - 1 = 29
The p-value = P([tex]t_{29}[/tex] > - 3.65)
= 0.9998
Decision Rule: Reject [tex]H_o[/tex] if p-value is less than the level of significance
But since the p -value is greater than the level of significance, we conclude that There is no enough evidence to support the Internet provider claim, Therefore;
Fail to Reject the Null Hypothesis
A hypothesis will be used to test that a population mean equals 9 against the alternative that the population mean is less than 9 with known variance . What is the critical value for the test statistic for the significance level of 0.020
Answer:
-2.05
Step-by-step explanation:
From the given information,
Let consider [tex]\mu[/tex] to represent the population mean
Therefore,
The null and alternative hypothesis can be stated as :
[tex]H_o :\mu=9[/tex]
[tex]H_1 :\mu<9[/tex]
From the hypothesis , the alternative hypothesis is one tailed (left)
when the level of significance = 0.020, the Z- critical value can be determined from the standard normal distribution table
Hence, the Z-critical value at ∝ = 0.020 is -2.05
You weigh six packages and find the weights to be 26, 18,58,22,54,and 50 ounces. If you include a package that weighs 66 ounces, which will increase more, the median or the mean?
Answer:
Step-by-step explanation:
The mean which is also known as the average is determined by dividing the sum of the weight of the packages by the total number of packages. From the information given,
Mean = (26 + 18 + 58 + 22 + 54 + 50)/6 = 38
If you include a package that weighs 66 ounces, the new mean would be
New mean = (26 + 18 + 58 + 22 + 54 + 50 + 66)/7 = 42
For the median, we would rearrange the weights in ascending order. It becomes
18, 22, 26, 50, 54, 58
Median = (26 + 50)/2 = 38
By adding the new weight, it becomes
18, 22, 26, 50, 54, 58, 66
New median = 50
It can be seen that both the median increased by more. It increased by 12 while the mean increased by 4
Answer: The mean which is also known as the average is determined by dividing the sum of the weight of the packages by the total number of packages. From the information given, Mean = (26 + 18 + 58 + 22 + 54 + 50)/6 = 38If you include a package that weighs 66 ounces, the new mean would be New mean = (26 + 18 + 58 + 22 + 54 + 50 + 66)/7 = 42For the median, we would rearrange the weights in ascending order. It becomes18, 22, 26, 50, 54, 58Median = (26 + 50)/2 = 38By adding the new weight, it becomes18, 22, 26, 50, 54, 58, 66New median = 50It can be seen that both the median increased by more. It increased by 12 while the mean increased by 4
Step-by-step explanation:
Yesterday at 1:00 P.M., Maria’s train was 42 miles north of Gull’s Beach, traveling north at an average speed of 90 mph. At the same time on the adjacent track, Elena’s train was 6 miles north of Gull’s Beach, traveling north at an average speed of 101 mph. To the nearest hundredth of an hour, after how much time will the trains meet up? 0.23 hours 0.31 hours 3.27 hours 4.36 hours
Answer:
3.27 hours
Step-by-step explanation:
Calculate the difference in speed and distance between the trains.
The relative speed:
101 - 90 = 11 mph
Difference in distance:
42 - 6 = 36 miles
[tex]time=\frac{distance}{speed}[/tex]
[tex]t=\frac{36}{11}[/tex]
[tex]t = 3.27[/tex]
Answer:
yeah she is correct
Step-by-step explanation:
YOU WILL GET 30 POINTS AND BRAINLIEST IF YOU GET THIS CORRECT AND ANSWER THIS IN 5 MIN!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
A car manufacturer is reducing the number of incidents with the transmission by issuing a voluntary recall. During week 3 of the recall, the manufacturer fixed 391 cars. In week 13, the manufacturer fixed 361 cars. Assume that the reduction in the number of cars each week is linear. Write an equation in function form to show the number of cars seen each week by the mechanic. f(x) = 3x + 400 f(x) = 3x + 391 f(x) = −3x + 391 f(x) = −3x + 400
Answer:
f(x)= -3x + 400
Step-by-step explanation:
[tex]\frac{x-x_{1} }{x_{2}-x_{1} } = \frac{y-y_{1} }{y_{2}-y_{1} }[/tex]
[tex]\frac{x-3}{13-3} =\frac{y-391}{361-391}[/tex]
-3 ( x-3 ) = (y - 391 )
-3x + 400
Answer:
he is correct
Step-by-step explanation:
xdy+ydx= ? (a) d(x+y) (b) d(x/y) (c) d(x-y) (d) d(xy)
Answer:
d) d(x)
Step-by-step explanation:
Derivative Rules
Product Rule xy -> d(xy) = xdy + ydxFind the 12th term of the following geometric sequence.
10, 30, 90, 270, ...
Answer:
r = 90/30
r = 3
T12 = 10 × 3¹¹
T12 = 1771470
Find the current I flowing through a square with corners at (0,0,0), (2,0,0), (2,0,2), (0,0,2). The current density is: bold italic J equals bold y with bold hat on top open parentheses y squared plus 5 close parentheses space space space space space open parentheses straight A divided by straight m squared close parentheses
Parameterize the square (call it S) by
[tex]\mathbf s(u,v)=2u\,\mathbf x+2v\,\mathbf z[/tex]
with both [tex]u\in[0,1][/tex] and [tex]v\in[0,1][/tex].
Take the normal vector pointing in the positive y direction to be
[tex]\dfrac{\partial\mathbf s}{\partial v}\times\dfrac{\partial\mathbf s}{\partial u}=4\,\mathbf y[/tex]
Then the current is
[tex]\displaystyle\iint_S(y^2+5)\,\mathbf y\cdot4\,\mathbf y\,\mathrm dA=20\int_0^1\int_0^1\mathrm dA=\boxed{20\,\mathrm A}[/tex]
where [tex]y^2+5[/tex] reduces to just 5 because [tex]y=0[/tex] for all points in S.
The principal P is borrowed at a simple interest rate r for a period of time t. Find the simple interest owed for the use of the money. Assume there are 360 days in a year. P = $7000, r = 0.2%, t = 6months
Answer:
$7
Step-by-step explanation:
Simple interest formula:
I = Prt
6 months = 6 * 30 days = 180 days
1 year = 360 days
t = (180 days)/(360 days) = 0.5
I = $7000 * 0.002 * 0.5
I = $7
Answer:
$7
Step-by-step explanation:
Recall that simple interest is given by
I = Prt,
Where :
I = interest (we are asked to find this)
P = principal amount = given as $7000
r = rate = given as 0.2% = 0.002
t = time in years = given as 6 months = 0.5 years
SImply substitute the known values into the equation above:
I = Prt
= (7000)(0.002)(0.5)
= $7
47% of the students in a class of 34 students has glasses or contacts. How many students in the class have either glasses or contacts?
Answer:
16
Step-by-step explanation:
47% is 0.47
34 x 0.47 = 15.98
So a trick question, its either 15 students or 16 students.... I would say 16 students, although the percentage would be 47.05%
16 students either have glasses or contacts.
Limit of f(t) as t approaches 0. f(t) = (t sin(t)) ÷ (1-cos(t))
Recall the Pythagorean identity,
[tex]1-\cos^2t=\sin^2t[/tex]
To get this expression in the fraction, multiply the numerator and denominator by [tex]1+\cos t[/tex]:
[tex]\dfrac{t\sin t}{1-\cos t}\cdot\dfrac{1+\cos t}{1+\cos t}=\dfrac{t\sin t(1+\cos t)}{\sin^2t}=\dfrac{t(1+\cos t)}{\sin t}[/tex]
Now,
[tex]\displaystyle\lim_{t\to0}\frac{t\sin t}{1-\cos t}=\lim_{t\to0}\frac t{\sin t}\cdot\lim_{t\to0}(1+\cos t)[/tex]
The first limit is well-known and equal to 1, leaving us with
[tex]\displaystyle\lim_{t\to0}(1+\cos t)=1+\cos0=\boxed{2}[/tex]
im not sure what it is asking me to do
Answer:
0.79Step-by-step explanation:
[tex]p(x \leqslant 0) = p( - 5) + p( - 3) + p( - 2) + p(0)[/tex]
[tex] = 0.17 + 0.13 + 0.33 + 0.16 [/tex]
[tex] = 0.79[/tex]
Hope this helps...
Best regards!!
Explain how estimating the quotient helps you place the first
digit in the quotient of a division problem.
Step-by-step explanation:
look at the picture and if you still need help let me know or if this doenst help then well im sorry lol
A manufacturing company has an old machine which produces 25 components per hour. The company has recently installed a new machine which produces 35 components per hour. Yesterday, both machines were in operation for different periods of time. If 430 components were produced when the total number of hours of operation was 14 hours, determine for how many hours each machine was in operation
Answer: old machine 150, new machine 280
Step-by-step explanation:
given data:
Old machine = 25t
New machine = 35t
where t = hrs
we dont know the time for old machine so we assume it to be ( t ),
while that of the new machine is ( 14-t ) hours for new machine, and sum of 430 components.
therefore;
25t +490 - 35t = 430
-10t = -60
divide both sides by -10
t = 6 hours for the first machine.
6hrs * 25 components /hr
= 150 component parts For old machine.
for new machine
= 14 - t ........... eq1.
where ( t = 6 ), substitute t into the equation
= 14 - 6
= 8 hours for the second machine
= 8 * 35
= 280 components parts
Please explain this to me If f(x)=4x-2 than f(x-1)= A. 4x^2-6x+2 B. 4x^2+2x+2 C. 4x+2 D. 4x-6 E. 4x-1
Answer:
D. 4x − 6
Step-by-step explanation:
f(x) = 4x − 2
f(x−1) = 4(x−1) − 2
f(x−1) = 4x − 4 − 2
f(x−1) = 4x − 6
Point C is on the graph of the function y = x2 – 3. Its x-coordinate is 4. Which ordered pair gives the location of point C? A.(4, 42 – 3) B.(4, 2 + 3) C.(42, 42 – 3) D.(4, 42)
Answer:
B (4, 2+3)
Step-by-step explanation:
To do this you fill in x with 4 so the equation becomes y = (4)2 - 3
You then solve to y = 8 - 3
then 8 - 3 is 5.
Making the coordinates (4, 5) and in this case with the answers (4, 2+3)
Answer:
A. (4, 4^2 – 3)
and click Submit
By visual inspection, determine the best fitting regression model for the
scatterplot.
O A Quadratic
O B. Linear
OC Exponential
OD. No pattern
Answer:
quadratic
Step-by-step explanation:
This graph has a parabola form wich is a propertie for qaudratic functions
Answer:
A
Step-by-step explanation:
25 POINTS
Examine the following solution to a conversion problem. Do you see a mistake? If so, identify the location of the first mistake and explain why it is incorrect.
Original Problem: Convert 3.25 kg to mg
(1) 3.25 kg
(2) 1 kg = 1000 g
(3) 1000 mg = 1g
= (4) 3.25 mg
A) The conversion is not possible.
B) The first problem occurs in column (1). The problem should begin with mg.
C) The first problem occurs in column (2). 1 kg is not equal to 1000 g, so that should not be used as the conversion factor.
D) The first problem occurs in column (2). The conversion factor is upside down (grams should be on top, and kg should be on bottom).
E) The first problem occurs in column (4). The multiplication and division was performed incorrectly.
F) No mistakes.
Thanks a bunch!
Answer:
[tex]\boxed{\sf Option \ E}[/tex]
Step-by-step explanation:
(1) 3.25 kg
(2) 1 kg = 1000 g
(3) 1000 mg = 1g
= (4) 3.25 mg
The first problem occurred in column (4) where we actually had to multiply it by 1000 but we divided it by 1000 and so our conversion was incorrect.
The correct form of it is:
1) 3.25 kg
2) 1 kg = 1000 g ; 3.25 kg = 3250 g
3) 1 g = 1000 mg ; 3250 * 1000 = 3,250,000 mg
4) Answer = 3,250,000 mg
Answer:
[tex]\boxed{\sf Option \ E}[/tex]
Step-by-step explanation:
1 kg = 1000 g
1000 mg = 1g
3.25 kilograms is to be multiplied by 1000 to get the value in grams. Then the result should be multiplied again by 1000 to get the value in milligrams.
3.25 kg ⇒ 3250 g ⇒ 3250000 mg
The first problem occurs in column (4). The multiplication and division was performed incorrectly.
Tensile strength tests were performed on two different grades of aluminum spars used in manufacturing the wing of a commercial transport aircraft. From past experience with the spar manufacturing process and the testing procedure, the standard deviations of tensile strengths are assumed to be known. The data obtained are as follows:
n_1 = 10
x_1 = 87.6
σ_1 = 1
n_2 = 12
x^2 = 74.5
σ_2 = 1.5.
Required:
If μ _1 and μ _2 denote the true mean tensile strengths for the two grades of spars. Construct a 90 percentage confidence interval on the difference in mean strength.
Answer:
(12.141, 14.059)
Step-by-step explanation:
Explanation is provided in the attached document.
Part A Each time you press F9 on your keyboard, you see an alternate life for Jacob, with his status for each age range shown as either alive or dead. If the dead were first to appear for the age range of 75 to 76, for example, this would mean that Jacob died between the ages of 75 and 76, or that he lived to be 75 years old. Press F9 on your keyboard five times and see how long Jacob lives in each of his alternate lives. How long did Jacob live each time? Part B The rest of the potential clients are similar to Jacob, but since they’ve already lived parts of their lives, their status will always be alive for the age ranges that they’ve already lived. For example, Carol is 44 years old, so no matter how many times you press F9 on your keyboard, Carol’s status will always be alive for all the age ranges up to 43–44. Starting with the age range of 44–45, however, there is the possibility that Carol’s status will be dead. Press F9 on your keyboard five more times and see how long Carol lives in each of her alternate lives. Remember that she will always live to be at least 44 years old, since she is already 44 years old. How long did Carol live each time? Part C Now you will find the percent survival of each of your eight clients to the end of his or her policy using the simulation in the spreadsheet. For each potential client, you will see whether he or she would be alive at the end of his or her policy. The cells in the spreadsheet that you should look at to determine this are highlighted in yellow. Next, go to the worksheet labeled Task 2b and record either alive or dead for the first trial. Once you do this, the All column will say yes if all the clients were alive at the end of their policies or no if all the clients were not alive at the end of their policies. Were all the clients alive at the end of their policies in the first trial? Part D Next, go back to the Task 2a worksheet, press F9, and repeat this process until you have recorded 20 trials in the Task 2b worksheet. In the Percent Survived row at the bottom of the table on the Task 2b worksheet, it will show the percentage of times each client survived to the end of his or her policy, and it will also show the percentage of times that all of the clients survived to the end of their respective policies. Check to see whether these percentages are in line with the probabilities that you calculated in questions 1 through 9 in Task 1. Now save your spreadsheet and submit it to your teacher using the drop box. Are your probabilities from the simulation close to the probabilities you originally calculated?
Step-by-step explanation:
brain list me please......
Answer:
Jacob:
Alive 69-70
alive 79-80
alive 62-63
alive 73-74
alive 78-Died 79
Carol:
alive 88-89
alive 67-68
alive 99-100
alive 73-74
alive 94- Died 95
Step-by-step explanation:
Change Y - 4X = 0 to the slope-intercept form of the equation of a line.
Answer:
y=4x
Step-by-step explanation:
Add 4x to both sides to get y=mx+b
0 is y-intercept.
4x is the slope.
what is the constant of proportionality for 4y=16
Answer:
Step-by-step explanation:
y=4x