Answer:
The work done in stretching it from its natural length to 14 in. beyond its natural length is W=8.17 ft-lb.
Step-by-step explanation:
We know that a force of 8 lb is required to hold a spring stretched 8 in. beyond its natural length.
This let us calculate the spring constant k as:
[tex]F=kx\\\\k=F/x=(8 \;lb)/(8\;in)=1\;lb/in[/tex]
We know that work is, in an scalar form, the product of force and distance.
The force F is equal to the spring constant multiplied by the distance from the natural length.
Then, as the force changes with the distance from the natural length, we have to calculate integrating:
[tex]W=\int_0^{14}F\,dx=\int_0^{14}kx\,dx\\\\\\W=\dfrac{1}{2}kx^2\left|^{14}_0=\dfrac{1}{2}(1\,lb/in)(14 \,in)^2-\dfrac{1}{2}(1\,lb/in)(0 \,in)^2[/tex]
[tex]W=98lb\cdot in-0lb-in\\\\W=98(lb\cdot in)\cdot \dfrac{1 \,ft}{12\,in}=8.17\;lb\cdot ft[/tex]
One cylinder has a volume that is 8 cm' less than a of the volume of a second cylinder. If the first cylinder's volume is 216
cm? what is the correct equation and value of x, the volume of the second cylinder?
x+8-216; x = 182 cm
-8-2167 - 196 cm
coll
+8-216-238cm
col
-8-216
-256 cm
Nacks and otum
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Corrected Question
One cylinder has a volume that is 8cm less than 7/8 of the volume of a second cylinder. If the first cylinder’s volume is 216cm³, what is the correct equation and value of x, the volume of the second cylinder?
Answer:
The equation is: [tex]216=\frac{7}{8}x-8[/tex]
Volume of the second cylinder= [tex]256cm^3[/tex]
Step-by-step explanation:
Volume of the first cylinder=[tex]216cm^3[/tex]
Let the volume of the second cylinder=x
7/8 of the volume of a second cylinder=[tex]\frac{7}{8}x[/tex]
8 less than 7/8 of the volume of a second cylinder=[tex]\frac{7}{8}x-8[/tex]
Therefore, the equation is:
[tex]216=\frac{7}{8}x-8[/tex]
Next, we solve for x
[tex]216=\frac{7}{8}x-8\\216+8=\frac{7}{8}x\\224=\frac{7}{8}x\\$Cross multiply\\7x=224*8\\Divide both sides by 7\\x=256cm^3[/tex]
The volume of the second cylinder is [tex]256cm^3[/tex]
Answer:
The answer is D
Step-by-step explanation:
Jan is solving the equation shown below. Which of the following
represents the solution to Jan's equation?
Answer:
C. x = 27
Step-by-step explanation:
To solve we must undo what is being done to the variable. It is being modified in several ways in this equation so we must do the opposites of each step to both sides of the equation.
1. 1/3x + 9 = 7 + 11
2. 1/3x = 18 - 9
3. (1/3x) * 3 = 9 * 3
4. x = 27
Hope this helps! (Please consider giving brainliest)
What is the midpoint of the line segment with endpoints (3.2,2.5) and (1.6-4.5)?
Answer:
(2.4, -1)
Step-by-step explanation:
To find the midpoints of two points in the format (x,y), we find the mean for the values of x and y.
In this question:
(3.2, 2.5) and (1.6, -4.5)
Mean for the values of x:
(3.2 + 1.6)/2 = 2.4
Mean for the values of y:
(2.5 - 4.5)/2 = -1
Midpoint:
(2.4, -1)
Dayson is covering a package in the shape of a rectangular prism with wrapping paper. The package is 50 centimeters by 20 centimeters by 18 centimeters. He has 1 square meter of wrapping paper. Can he completely cover the package with wrapping paper? Complete the explanation to show your answer.
Answer:
Yes, Dayson can completely cover the package with wrapping paper.
Step-by-step explanation:
Given: The rectangular prism is 50 centimeters by 20 centimeters by 18 centimeters.
Area of wrapping paper is 1 square meter.
To find: whether he can completely cover the package with wrapping paper
Solution:
Total surface area of the rectangular prism = 2(lb + bh +hl)
where l denotes length, b denotes breadth and h denotes height
Total surface area of the rectangular prism = [tex]2\left [ (50)(20)+(20)(18)+(18)(50) \right ][/tex]
[tex]=2\left ( 1000+360+900 \right )\\=2(2260)\\=4520\,\,cm^2[/tex]
As [tex]1\,m^2=10000\,cm^2[/tex],
Total surface area of the rectangular prism = [tex]4520\,cm^2=0.4520\,m^2[/tex]
As Dayson has [tex]1\,m^2> 0.4520\,m^2[/tex] of wrapping paper, he can completely cover the package with wrapping paper.
Point A' (2,3) is the image of A(3,-4)
under a translation.
Determine the translation.
Use non-negative numbers.
A translation by
units to the
right/left v
and
units
up/down
Answer:
up/down
Step-by-step explanation:
Which function is the inverse of f Superscript negative 1 Baseline (x) = negative one-half x minus three-halves?
The inverse of the function g(x)=-2x -3.
What is a Function?A function assigns the value of each element of one set to the other specific element of another set.
Given function:
f(x) = -1/2 x - 3/2
Since the function is inverse, so
g(f(x)) = a(-1x/2 - 3/2) + b
x = -ax/2 - 3x/2 + b
-a/2 = 1
a = -2
and, -3a/2 + b = 0
b= -3
Hence, the inverse of the function g(x)=-2x -3.
Learn more about Function here:
brainly.com/question/5245372
#SPJ2
What’s the correct answer for this question?
Answer:
B.
Step-by-step explanation:
Volume of fudge cubes = 1 ×1×1
= 1 inch³
The cylinder contains 12.6 fudge cubes
So,
Volume of cylinder = 12.6 inches³
Height of cylinder = 1 inch
Base area of cylinder = Volume / Height
= 12.6 / 1
= 12.6 inches²
The radius of the earth is approximately 5,000,000 meters write 5,000,000 in scientific notion
Answer:
5 × 10⁶
Step-by-step explanation:
To convert a long number to a scientific notation:
Count the number of zeros in the number
Use the count as the power of 10.
5,000,000 has six zeros
So:
× 10⁶
Now 5 will be left to be added to the notation.
5 × 10⁶
Answer:
5 x 10'6
Step-by-step explanation:
Stefan and his friends used four tables for all the dishes the guests brought to the party. The tables were 2 8/10 meters long, 2.48 meters long, 2 59/100 meters long, and 2.83 meters long. Enter each length as a decimal number in order from greatest to least.
Answer:
[tex]2.83,2.8,2.59,2.48[/tex]
Step-by-step explanation:
Given:
Numbers are [tex]\frac{28}{10}\,m,\,2.48\,m,\,\frac{259}{100}\,m,\,2.83 \,m[/tex]
To express: each length as a decimal number in order from greatest to least
Solution:
A number which consists of a whole number part and the fractional part separated by a decimal point is known as a decimal number.
[tex]\frac{28}{10}=2.8\\ 2.48=2.48\\\frac{259}{100}=2.59\\ 2.83=2.83[/tex]
Numbers arranged in order from greatest to least: [tex]2.83,2.8,2.59,2.48[/tex]
At the 0.05 level of significance, is there a difference in the variance of average graduation debt incurred by students for private universities and public colleges? Using the results of (a), which t test is appropriate for comparing mean debt at graduation incurred by students at private universities and public colleges? At the 0.05 level of significance, conduct the test selected in (b). Write a short summary of your findings.
Answer:
Step-by-step explanation:
Natalie is in charge of inspecting frozen pepperoni pizzas. To ensure that the pizzas being produced are roughly 10 inches, she samples 30 pizzas at random every hour starting at 9 am until 4 pm and measures the diameter of these pizzas using a ruler. That means, every work day, she collects 8 samples with 30 pizzas each and inspects these 240 pizzas. Which of the statement(s) is true?
a) n equals 8
b) n equals 30
c) The number of samples is 8
d) The sample size is 30
e) The sample size is 8.
f) Each day she collects a total of 240 observations.
g) n equals 240
h) The sample size is 240.
Answer:
The statements that are true are:
b) n equals 30
c) The number of samples is 8
d) The sample size is 30
f) Each day she collects a total of 240 observations.
Step-by-step explanation:
She takes a sample every hour, so she takes 8 samples during the day.
Each samples consist of 30 individuals (pizzas).
This adds a total of 240 observations during the day.
The statements that are true are:
b) n equals 30
c) The number of samples is 8
d) The sample size is 30
f) Each day she collects a total of 240 observations.
Find the area of the triangle ABC given angle A = 45°, b = 8, and c = √2.
Answer:
a = 4
Step-by-step explanation:
[tex]A = \frac{b * c * sen 45}{2} \\\\A = 8 * \sqrt{2} * \frac{\sqrt{2} }{2} * \frac{1}{2} \\\\\\\\A = 4[/tex]
Answer:
4
Step-by-step explanation:
Formulate the situation as a linear programming problem by identifying the variables, the objective function, and the constraints. Be sure to state clearly the meaning of each variable. Determine whether a solution exists, and if it does, find it. State your final answer in terms of the original question. A rancher raises goats and llamas on his 400-acre ranch. Each goat needs 2 acres of land and requires $100 of veterinary care per year, and each llama needs 5 acres of land and requires $80 of veterinary care per year. The rancher can afford no more than $13,200 for veterinary care this year. If the expected profit is $84 for each goat and $126 for each llama, how many of each animal should he raise to obtain the greatest possible profit? The rancher should raise goats and llamas for a maximum profit of $________
Answer:
zero goats and 120 Ilamas to get profit of $15,120
Step-by-step explanation:
Goats: G
Ilamas: l
Explicit constraints:
2G + 5l ≤ 400
100G+ 80l≤ 13,200
Implicit constraints
G≥0
I≥0
P= 84G+ 126l
See attachment for optimal area
substituting coordinats of optimal region in profit equation to get profit
When G= 132, l=0
P=84(132) + 126(0)
P=11,088
When G=0, l=120
P=84(0)+ 126(120)
P = 15120
When G= 100, l=40
P=84(100)+126(40)
P=13440
Somebody plz help. I’ll rate you Brainalist.
Consider xdy = 3ydx.
(a) Apply Theorem 1 and show the equation has unique solution in xy-plane where x 6= 0
(b) Theorem 1 will be inconclusive about existence and uniqueness of solution where x = 0 (that is on y-axis). For points on the y-axis (i) Show there are infinitely many different solutions for xdy = 3ydx y(0) = 0. (ii) Show there is no solution for xdy = 3ydx y(0) = b b != 0.
Question:
Consider xdy = 3ydx.
(a) Apply Theorem 1 and show the equation has unique solution in xy-plane where x ≠ 0
(b) Theorem 1 will be inconclusive about existence and uniqueness of solution where x = 0 (that is on y-axis). For points on the y-axis (i) Show there are infinitely many different solutions for xdy = 3ydx y(0) = 0. (ii) Show there is no solution for xdy = 3ydx,
y(0) = b, b ≠0.
Theorem 1 is attached.
Answer:
Given:
xdy = 3ydx
a) Given theorem 1 :
dy/dx = f (x, y)
we have:
[tex] f(x, y) = \frac{3y}{x}[/tex]
[tex] \frac{d}{dy} f(x, y) = \frac{3}{x}[/tex]
[tex] \frac{d}{dy} [/tex] is at interior of all angles except at point x=0.
Therefore for x≠0
[tex] \frac{d}{dy} f(x, y) = \frac{3}{2}[/tex]
Thus, from theorem 1, there is a unique solution in the xy plane where x≠0
b) i) xdy = 3ydx y(0) = 0
We have:
[tex] \frac{dy}{y} = \frac{3}{x} dx [/tex]
Integrating, we have:
∫[tex] \frac{dy}{y}[/tex] =∫[tex] \frac{3}{x} dx [/tex]
ln y = 3lnx + lnC
y = Cx³
Hence, y(0)=0 is satisfied for all values of C
Thus, there are infinitely many solutions for xdy = 3ydx
ii) xdy = 3ydx
y(0) = b, b ≠ 0.
From our part (i) above, we already know that, y = Cx³
Let's now take initial value of y as b,
ie, y(0) = b
b = 0
From the question, b≠0.
Thus, it means it has no solution.
Find the average of each of the following.
(a) $357, $452, $589, $602, $775
I need help anybody knows how to do?
Answer:
555
Step-by-step explanation:
(357+452+589+602+775)/5
Step-by-step explanation:
I HAVE DONE AT HERE YOU HAVE ASK WHE\E *O PUT 120°
The table below shows the time intervals (hours) it takes people to arrive at a counter at a bus terminal Time (hrs) Number of people 0-0.25 0.25-0.50 0.50-0.75 0.75-1.00 1.00-1.25 1.25-1.50 38 67 50 36 30 29 Use this to answer questions 5 to 8. 5. What is the modal arrival time, correct to 2 decimal places? Answer: hours 6. Find the mean time of arrival in minutes, correct to 3 significant figures? Answer: 7. What is the standard deviation of the data distribution, correct to 2 decimal place? Answer: hours 8. The median time of arrival approximated to 2 decimal places is ... Answer: hours
Answer:
Step-by-step explanation:
5.) here no. of people represent frequencies, so modal group (the group with the highest frequency) is 0.25-0.50.
Estimated Mode = L + (( fm − fm-1) / ( (fm − fm-1) + (fm − fm+1) ) ) × w
where,
L is the lower class boundary of the modal group = 0.25
fm-1 is the frequency of the group before the modal group = 38
fm is the frequency of the modal group = 67
fm+1 is the frequency of the group after the modal group = 50
w is the group width = 0.25
mode= 0.25 + ((67-38)/((67-38)+(67-50)))* 0.25
= 0.25 + (29/ (29+17))*0.25
= 0.25 + 0.63*0.25
= 0.41
6) mean= total(fx) / total(f)
= 166.25/250
= 0.665
7) standard deviation = sqaure root (( total(fx2) - (total(f)* mean2)) / (total(f)-1))
= sqaure root (( 149.906 - 250* 0.6652)/ 249 )
= square root ( (149.906 - 110.556) /249)
= sqaure root (0.158)
= 0.397
8) The median is the middle value, which in our case is the 125 (250/2) , which is in the 0.5 - 0.75 group.
Estimated Median = L + ( ((n/2) − B)/G) × w
where:
L is the lower class boundary of the group containing the median = 0.5
n is the total number of values = 250
B is the cumulative frequency of the groups before the median group = 105
G is the frequency of the median group = 50
w is the group width = 0.25
median = 0.5 + (((250/2)-105)/50)*0.25
= 0.5 + ((125-105)/50)*0.25
= 0.5 + (20/50)*0.25
= 0.6
help me please I don't understand this one
Answer:
A
Step-by-step explanation:
I'm not sure if it's right though
If f(a) = 3a - a2, which of the following are not true statements?
Select all that apply.
f(4) = -4
f(3) = 0
f(-1) = 2
f(0) = 3
f(-5) = -40
Answer:
f(-1) = 2
f(0) = 3
Step-by-step explanation:
f(a) = 3a - a²
f(4)= 3*4-4²= -4 ⇒ correctf(3)= 3*3-3²= 0 ⇒ correctf(-1) = 3*(-1)-(-1)²=-3+1= -2 ⇒ incorrect f(0) = 3*0-0²= 0 ⇒ incorrect f(-5) = 3*(-5)-(-5)²= -15-25= -40 ⇒ correctAnswer:
The 3rd and the 4th statement are not the true statements.
Step-by-step explanation:
In the 3rd statement, if you put a=-1 into the equation f(a), it would be
=3x(-1) - (-1)2
=-3 - 1
=-4.
In the 4th statement, if you put a=0 into the equation f(a), it would be
=3x(0) - (0)2
=0 - 0
=0.
For the other statements, they show the correct results.
Express the ratio below in its simplest form. 15 : 10
Answer: 3:2
Step-by-step explanation:
Answer:
3/2 = 3:2
Step-by-step explanation:
15:10 = 15 /10 = 3/2. { dividing both numerator and denominator by 5}
Complete the statement.
L=234 mL
Answer:
0.234
Step-by-step explanation:
Answer:
0.234
To convert from milliliters to liters, divide by 1,000.
234 ÷ 1,000 = 0.234
Step-by-step explanation:
Complete each statement.
? L = 234 mL
234/1000=0.234
There are 1000 milliliters in a liter, therefore dividing the milliliters by 1000 will give you the amount of liters. Liters = 0.234
RESULT
0.234L
Suppose you have $200,000 in a bank term account. You earn 5% interest per annum from his account you anticipate that infla
Answer:
Interest= $10000
Step-by-step explanation:
So we are to calculate the interest at 5% annum of $200000.
Ok , we'll use the formula
PRT/100 = interest
Where P = principal
R = rate
T= time
(200000* 5*1)/100 = interest
1000000/100 = interest
10000 = interest
Interest= $10000
Complete each statement so it will result in the truth value F.
If the GCD of 5 and 12 is 1, then _______
-> 12 is even
->12 is less than 5
->5 is less than 12
->5 is prime
The sum of 5 and 12 is 7 if and only if _______
->12 is divisible by 5
-> 12 is greater than 5
-> 5 is even
->the difference between 12 and 5 is -7
Answer:
We want to create sentences that are false (this means that the truth value is F
False ---> true: then the statement is false
true-----> false: then the statement is false.
For the first option we have:
"If the GCD of 5 and 12 is 1,____"
the left side is true, so the right side must be false:
"If the GCD of 5 and 12 is 1, then 12 is less than 5"
this means that the truth value is false, because the left side is true and the right side false.
For the second sentence we have:
The sum of 5 and 12 is 7 if and only if _______
The left side is false, so the right side must be true, the only true option is 12 is greater than 5, so the sentence is:
"The sum of 5 and 12 is 7 if and only if 12 is greater than 5."
An inlet pipe can fill a tank in 10 minutes. A drain can empty the tank in 12 minutes. If the tank is empty, and both the pipe and drain are open, how long will it take before the tank overflows?
Answer: Total time taken by them would be 60 minutes = 1 hour before the tank overflows.
Step-by-step explanation:
Since we have given that
Time taken by an inlet pipe =10 minutes
Time taken by a drain = 12 minutes
So, if both are open together,
Total work done by them would be
[tex]\dfrac{1}{10}-\dfrac{1}{12}\\\\=\dfrac{6-5}{60}\\\\=\dfrac{1}{60}[/tex]
So, total time taken by them would be 60 minutes = 1 hour before the tank overflows.
Determine the number solutions for system x-2y=1 and -4x+8y=-4
Answer:
Hence, the system of equation does not have solution.
Step-by-step explanation:
You have the following 2x2 system:
[tex]x-2y=1\ \ \ \ (1)\\\\-4x+8y=-4\ \ \ \ (2)[/tex]
You can obtain the solution to the system by using substitution method.
You solve the first equation for x:
[tex]x=1+2y[/tex] (3)
Next, you replace (3) in the equation (2), and you solve for y:
[tex]-4(1+2y)+8y=-4\\\\-4-8y+8y=-4\\\\0=0[/tex]
The last result is the trivial solution. This means that the equation (2) is a multiple scale of the first equation. In fact, if you multiply equation (1) by -4, you obtain the equation (2).
Hence, the system of equations does not have solution.
The graph shows the solution for which inequalities?
Answer:
Inequalities are,
y ≥ 4x + 2
y ≥ 2
Step-by-step explanation:
Solid yellow line of the graph attached passes through two points (0, -2) and (1, 2).
Let the equation of this line is,
y = mx + b
Slope of the line = [tex]\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
m = [tex]\frac{2+2}{1-0}[/tex]
m = 4
Y-intercept 'b' = -2
Equation of the line will be,
y = 4x - 2
Since shaded area is on the left side of this solid line so the inequality representing this region will be,
y ≥ 4x - 2
Another line is a solid blue line parallel to the x-axis.
Shaded region (blue) above the line will be represented by,
y ≥ 2
Therefore, the common shaded area of these inequalities will be the solution of the given inequalities.
Please help! Correct answer only, please! Find the product A · A^t A. B. C. D.
Answer: choice A
Step-by-step explanation:
the transposed matrix would be
5 3
2 -1
so
5*5+2*2=29
3*5+2*-1=13
5*3-2*-1=13
3*3+-1*-1=10
which gives us the answer
29 13
13 10
Elena's mother asked her to add a half-cup of water to the beans.
How many ounces of water did Elena add?
Answer:
4 oz
Step-by-step explanation:
one cup is 8 oz
1/2 cup is 8/2 oz which is 4 oz
Answer:
4 fluid ounces
Step-by-step explanation:
One cup is 8 oz so we would have to divide 8 by 2 to get 4 because one half of 8 is 4.
For a statistics class project, a college student randomly samples 75 men who exercise at a gym regularly and 68 women who exercise at a gym regularly. The college student believes that on average men spend more time at the gym each week. The college student records the number of minutes each person exercises in a given week. The college student conducts a hypothesis test at the 5% significance level. Use the summary statistics below to conduct a hypothesis test using your calculator or calculator
Answer:
Step-by-step explanation:
The record of the statistics and the summary statistics which are the missing files in the question are attached below.
From the given information:
The null hypothesis and the alternative hypothesis can be represented by :
[tex]\mathbf{H_o:}[/tex] There is no difference between the average time spend by men and women at gym each week
[tex]\mathbf{H_i:}[/tex] The average time spend by men is greater than the average time spend by women at the gym each week
From the summary statistics in the attached file below:
The p-value = 0.3253
Level of significance = 5% = 0.05
Therefore; it is obvious that the p-value is greater than the level of significance i.e (0.3253 > 0.05)
Hence; there is no enough evidence to reject the null hypothesis
CONCLUSION: We conclude that the mean number of minutes exercised per week is larger for men than women at the this gym.
Suppose f , g , h , and j are functions such that: f ( r ) represents the circumference (in cm) of a circle whose radius is r cm. g ( C ) represents the radius (in cm) of a circle whose circumference is C cm. h ( r ) represents the area (in cm2) of a circle whose radius is r cm. j ( A ) represents the radius (in cm) of a circle whose area is A cm2.
a. Use function notation to represent the area of a circle whose circumference is 133 cm.
b. Use function notation to represent the circumference of a circle whose area is 6.82 cm^2
Answer:
(a)h(g(133))
(b)f(j(6.82))
Step-by-step explanation:
(a)Area of a circle whose circumference is 133 cm.
Since g(C) represents the radius (in cm) of a circle whose circumference is C cm.
The radius of the circle whose circumference is 133 cm = g(133)h(r) represents the area [tex](in$ cm^2)[/tex] of a circle whose radius is r cm.
Area, h(r) =h(g(133))Therefore, the area of a circle whose circumference is 133 cm is:
h(g(133))
(b)Circumference of a circle whose area is [tex]6.82 cm^2[/tex]
j(A) represents the radius (in cm) of a circle whose area is A [tex]cm^2[/tex].
The radius of the circle of area [tex]6.82 cm^2[/tex] = j(6.82)f(r) represents the circumference (in cm) of a circle whose radius is r cm.
Therefore:
Circumference, f(r) = f(j(6.82))The circumference of a circle whose area is [tex]6.82 cm^2[/tex] =f(j(6.82))