A force of 18 lb is required to hold a spring stretched 8 in. beyond its natural length. How much work W is done in stretching it from its natural length to 10 in. beyond its natural length

Answers

Answer 1

Answer: 18.75 lb.ft

Step-by-step explanation:

Given

Force required to stretch spring 8 in. is 18 lb

it can be written

[tex]\Rightarrow F=kx\\\Rightarrow 18=k(8)\\\\\Rightarrow k=\dfrac{18}{8}=\dfrac{9}{2}\ lb/in.[/tex]

Work done in stretching from its natural length to 10 in.

[tex]\Rightarrow W=\dfrac{1}{2}kx^2\\\\\Rightarrow W=0.5\times \dfrac{9}{2}\times (10)^2\\\\\Rightarrow W=225\ lb.in.\ or\\\Rightarrow W=18.75\ lb.ft[/tex]


Related Questions

data
find the range between 14, 15, 16, 14,23,13
15, 24, 12, 23, 14; 20, 17, 21, 22, 1031, 19, 20,
17, 16, 15, 11, 12, 21, 20, 17, 18, 19, 23

Answers

the lowest is 11 and the highest is 1031 then subtract it you are going to have 1020

Find hypotenuse,perpendicular and base​

Answers

Answer:

Hypotenuse = XY = 17 cm

Base = YZ = 15 cm

Perpendicular = XZ = 8 cm

A number plus 16 times its reciprocal equals 8. Find all possible values for the number.

Answers

Answer:

4

Step-by-step explanation:

[tex]n+16\frac{1}{n} = 8\\\\n^2+16=8n\\n^2 -8n+16=0\\[/tex]

Factorizing we get the answer 4

Which equation has a graph that is a parabola with a vertex at (-2, 0)?
y= -2x^2
y = (x + 2)^2
y= (x – 2)^2
y= x^2 – 2

Answers

y=(x+2)^2 has a vertex at (-2,0)

The population of a town is decreasing exponentially according to the formula
P = 7,285(0.97)t, where t is measured in years from the present date. Find the population in 2 years, 9 months. (Round your answer to the nearest whole number.)

Answers

Answer: 6669

Step-by-step explanation:

I hope I did this right... anyways,

t, is represented by years, which is given to us by 2 years and 9 months. Assuming you would put 2.9 for t.

Additionally, as you can't have a decimal for a person, and they've asked for it to be rounded to the nearest whole number, there would be 6669 people in 2 years and 9 months.

The formula used is:

[tex]7285(0.97)^2^.^9[/tex]

A four digit password is a number that begins with a 3. If digits can be repeated how many possible passwords are there? show and explain your work

Answers

Answer:

The answer is 1,000

SInce the beginning number is 3 and there are ten possible numbers to put in the remaining three slots, there are exactly 1,000 possible combinations for a 3-digit code. The answer is 1,000. There are 3 rows of 10 digits. The number of combinations 10 to the thid power which is 1000 (10 * 10 * 10)

Triangles ABC and DEF are similar. Find the
perimeter of triangle DEF.
a. 34.7 cm
b. 25.3 cm
c. 15 cm
d. 38 cm
Please show work to help me understand.

Answers

If Both triangles are similar the ratio of sides will be same

[tex]\\ \sf\longmapsto \dfrac{AB}{AC}=\dfrac{DE}{DF}[/tex]

[tex]\\ \sf\longmapsto \dfrac{8}{10}=\dfrac{12}{DF}[/tex]

[tex]\\ \sf\longmapsto 8DF=120[/tex]

[tex]\\ \sf\longmapsto DF=\dfrac{120}{8}[/tex]

[tex]\\ \sf\longmapsto DF=15cm[/tex]

Now

[tex]\\ \sf\longmapsto Perimeter=DF+DE+EF[/tex]

[tex]\\ \sf\longmapsto Perimeter=15+11+12[/tex]

[tex]\\ \sf\longmapsto Perimeter=38cm[/tex]

I need to know this answe ASAP

Answers

Answer:

The function is always increasing

Step-by-step explanation:

To be increasing, the y value needs to be getting bigger as x gets bigger

This is true for all values of x

The function is increasing for all values of x

A researcher is interested in whether there is a significant difference between the mean age of marriage across three racial groups. Using the data provided below, conduct an F-test to determine whether you believe there is an association between race and average age at marriage.

Race N Mean
Black 113 25.39
White 904 22.99
Other 144 23.87
All Groups 1,161 23.33

Answers

Answer:

The P-value is < significance value ( 0.05 ) hence we reject the Null hypothesis ( i.e. There is an association between the race and average age at marriage )

Step-by-step explanation:

Conducting an F-test to determine association between race and average age at marriage

step 1 : State the hypothesis

H0 : ц1 = ц2 = ц3

Ha : ц1 ≠ ц2 ≠ ц3

step 2 : determine the mean square between

Given mean value of all groups = 23.33

SS btw = 113*(25.39 - 23.33)² +  904*(22.99 - 23.33)² + 144*(23.89 - 23.33)^2            = 113(4.2436) + 904(0.1156) + 144(0.3136)

= 629.1876

hence:  df btw = 3 - 1 = 2

             df total = 1161 - 1 = 1160

              df within = 1160 - 2 = 1158

              SS within = 36.87*1158 = 42695.46

Therefore the MS between =  629.19 / 2 = 314.60

The F-ratio = 314.59 / 36.87 = 8.53

using the values for Btw the P-value = 0.00021

The P-value is < significance value ( 0.05 ) hence we reject the Null hypothesis ( i.e. There is an association between the race and average age at marriage )

Suppose (-13,2) is a point on the graph of y=f(x). What is a point that will be on the graph of y=9f(x)-5

Answers

9514 1404 393

Answer:

  (x, y') = (-13, 13)

Step-by-step explanation:

At the given value of x, f(x) = 2. Then 9f(x)-5 = 9(2) -5 = 13.

The point on the scaled, translated graph will be ...

  (x, y') = (-13, 13)

_____

The graph shows a function f(x) with a distinct feature (vertex) at (-13, 2). It also shows where that distinct feature moves to when the function is scaled and translated.

The scores on an entrance exam to a university are known to have an approximately normal distribution with mean 65% and standard deviation 7.1%. What is the standardized score for a student who scores 60% on this test?
A. -0.70
B. 0.70
C. 1.88
D. -1.88

Answers

It is c lol I need points

Find the slope of the line (4,0) (9,11) Help plsss!!!!

Answers

11/5 is what I got I hope it’s correct

Answer:

m= 11/5 (11 over 5)

Hope this helps! :)

2^17+2^14 chia hết cho 9

Answers

Answer:

ABC

Step-by-step explanation:

= 2^14.2^3 +  2^14

= 2^14. (2^3 +1)

= 2^14 . 9  

Vì 2^14.9 chia hết cho 9 nên 2^17 + 2^14 chia hết cho 9

(. là dấu nhân)

Answer:

đúng

Step-by-step explanation:

Independent simple random samples are selected to test the difference between the means of two populations whose standard deviations are not known. We are unwilling to assume that the population variances are equal. The sample sizes are n1 = 25 and n2 = 35. The correct distribution to use is the:
1) t distribution with 59 degrees of freedom.
2) t distribution with 58 degrees of freedom.
3) t distribution with 61 degrees of freedom.
4) t distribution with 60 degrees of freedom.

Answers

Answer:

2) t distribution with 58 degrees of freedom.

Step-by-step explanation:

Population standard deviations not known:

This means that the t-distribution is used to solve this question.

The sample sizes are n1 = 25 and n2 = 35.

The number of degrees of freedom is the sum of the sample sizes subtracted by the number of samples, in this case 2. So

25 + 35 - 2 = 58 df.

Thus the correct answer is given by option 2.

) How many different three-letter initials can people have: , (b) How many different three-letter initials with none of the letters repeated can people have: , (c) How many different three-letter initials with letters repeated begin with an X: , (d) How many different three-letter initials begin with a F and end in a D:

Answers

Solution :

a).

The different three letter initials that people have is :

= 26 x 26 x 26

= [tex]26^3[/tex]

= [tex]17576[/tex]

b). The first place to be fill in26 ways.

The second place to be filled in 25 ways

The third place to be filled in 24 ways.

Therefore, total number of three letter initial with no repetition is :

= 26 x 25 x 24

= [tex]15600[/tex]

c). The total number of three letter initial begin with X = 1 x 26 x 26

                                                                                          = [tex]676[/tex]

d). The total number of the three letter initials that begin with letter 'F' an end with letter 'D' is = 1 x 26 x 1

                                 = [tex]26[/tex]

Line JK passes through points J(–3, 11) and K(1, –3). What is the equation of line JK in standard form?

7x + 2y = –1
7x + 2y = 1
14x + 4y = –1
14x + 4y = 1

Answers

9514 1404 393

Answer:

  (b) 7x + 2y = 1

Step-by-step explanation:

You don't need to know how to find the equation. You just need to know how to determine if a point satisfies the equation. Try one of the points and see which equation fits. (The numbers are smaller for point K, so we prefer to use that one.)

  7(1) +2(-3) = 1 ≠ -1 . . . . . tells you choice A doesn't work, and choice B does

The equation is ...

  7x +2y = 1

__

Additional comment

The equations of choices C and D have coefficients with a common factor of 2. If the constant also had a factor of 2, we could say these equations are not in standard form, and we could reject them right away. Since the two points have integer values for x and y, we can reject these equations anyway: the sum of even numbers cannot be odd.

Answer:

b

Step-by-step explanation:

Determine whether the system of linear equations has one and only one solution, infinitely many solutions, or no solution. 5x − 6y = 4 10x − 12y = 8 one and only one solution infinitely many solutions no solution Correct: Your answer is correct. Find the solution, if one exists. (If there are infinitely many solutions, express x and y in terms of the parameter t. If there is no solution, enter NO SOLUTION.) (x, y) =

Answers

Answer:

same line infinite solutions

Step-by-step explanation:

5x − 6y = 4

10x − 12y = 8

10x − 12y = 8

10x − 12y = 8

0 = 0

same line infinite solutions


A car is advertised with a price of $16336. The payment plan to own a car is $474 per month for 8 years. What is the
amount of interest paid?

Answers

The interest rate is about 32.045%.

In a die game, you roll a standard 6-sided die twice. If the second number rolled is the same as the first number rolled, you win $25. Otherwise, you lose $2. If you were to play the game 100 times, how much money can you expect to make

Answers

Answer:

You can expect to make $250.

Step-by-step explanation:

Possible outcomes:

For the pair of dice:

(1,1), (1,2), (1,3), (1,4), (1,5), (1,6)

(2,1), (2,2), (2,3), (2,4), (2,5), (2,6)

(3,1), (3,2), (3,3), (3,4), (3,5), (3,6)

(4,1), (4,2), (4,3), (4,4), (4,5), (4,6)

(5,1), (5,2), (5,3), (5,4), (5,5), (5,6)

(6,1), (6,2), (6,3), (6,4), (6,5), (6,6)

So 36 total outcomes.

Probability of the second number rolled being the same as the first number rolled:

6 outcomes: (1,1), (2,2), (3,3), (4,4), (5,5), (6,6)

Out of 36, thus:

[tex]p = \frac{6}{36} = \frac{1}{6}[/tex]

Expected value of 1 game:

1/6 probability of earning $25.

5/6 probability of losing $2.

Thus:

[tex]E = 25\frac{1}{6} - 2\frac{5}{6} = \frac{25 - 10}{6} = 2.5[/tex]

100 games:

100*2.5 = 250

You can expect to make $250.

Mr. E bought 3 drinks and 5 sandwiches for $25.05 and Mr. E bought 4 drinks and 2 sandwiches $13.80. how much does each drink cost?

Answers

9514 1404 393

Answer:

drink: $1.35sandwich: $4.20

Step-by-step explanation:

Let d and s represent the cost of a drink and a sandwich, respectively. The two purchases give rise to the equations ...

  3d +5s = 25.05

  4d +2s = 13.80

Dividing the second equation by 2 gives ...

  2d + s = 6.90

Subtracting the first equation from 5 times this, we get ...

  5(2d +s) -(3d +5s) = 5(6.90) -25.05

  7d = 34.50 -25.05 = 9.45

  d = 1.35

The cost of each drink is $1.35.

__

Additional comment

Using the simplified 2nd equation, we can find the cost of a sandwich.

  s = 6.90 -2d = 6.90 -2.70 = 4.20

The cost of each sandwich is $4.20.

Question 7
In circle P below, angle OPM equals 124 degrees and line segments ON and MN are tangents to the circle
What is the measure of Angle ONM?
A 56
B 62
С 74
D 90

Answers

Answer:

B) 62 is the answer. I'm sure

Find the area of each figure one of the sides are 8.3cm it’s a square btw

Answers

Answer:

68.89 cm

Step-by-step explanation:

8.3 X 8.3 would equal 68.89 cm. We can see that one side is 8.3 cm, and the other sides don't say their sides, so the only number we will use for multiplying is 8.3, and all sides of the square will be 8.3. The equation is L X W, where L is the length, and W is the width. Since 8.3 is on all four sides, it will also be the length and the width on the equation. As a result, 68.89 cm would be the final answer.

Answer:

I don't real know if this is right, but I think its this:

68.89 cm2 is the area.

One leg of a right angle has a length of 3m. The other sides have lengths

Answers

I don’t understand what the question is

Leonard made some muffins. He gave 5/8 of them to his grandmother and 10 muffins to his aunt. He then had 11 muffins left. How many muffins did he have at first? ​

Answers

Answer:

56

Step-by-step explanation:

x = number of muffins in total at the beginning.

x - 5/8 x - 10 = 11

x - 5/8 x = 21

8/8 x - 5/8 x = 21

3/8 x = 21

3x = 168

x = 56

A circle P is circumscribed about a regular hexagon ABCDEF

If segment AE is drawn, triangle AEF is a/n ____________ triangle. Select one:

a. isosceles

b. scalene

c. equilateral

d. right

i’ll mark u as brainliest:))

Answers

9514 1404 393

Answer:

  a. isosceles

Step-by-step explanation:

Segments EF and FA of the hexagon are the same length, so the triangle is an isosceles triangle.

(A) A small business ships homemade candies to anywhere in the world. Suppose a random sample of 16 orders is selected and each is weighed. The sample mean was found to be 410 grams and the sample standard deviation was 40 grams. Find the 90% confidence interval for the mean weight of shipped homemade candies. (Round your final answers to the nearest hundredth)
(B) When 500 college students are randomly selected and surveyed; it is found that 155 own a car. Find a 90% confidence interval for the true proportion of all college students who own a car.
(Round your final answers to the nearest hundredth)
(C) Interpret the results (the interval) you got in (A) and (B)

Answers

The correct answer to the given question is "[tex]\bold{392.47\ < \mu <\ 427.53}[/tex],[tex]\bold{0.28 \ < P <\ 0.34}[/tex], and for Interpret results go to the C part.

Following are the solution to the given parts:

A)

[tex]\to \bold{(n) = 16}[/tex]

[tex]\to \bold{(\bar{X}) = 410}[/tex]

[tex]\to \bold{(\sigma) = 40}[/tex]

In the given question, we calculate [tex]90\%[/tex] of the confidence interval for the mean weight of shipped homemade candies that can be calculated as follows:

[tex]\to \bold{\bar{X} \pm t_{\frac{\alpha}{2}} \times \frac{S}{\sqrt{n}}}[/tex]

[tex]\to \bold{C.I= 0.90}\\\\\to \bold{(\alpha) = 1 - 0.90 = 0.10}\\\\ \to \bold{\frac{\alpha}{2} = \frac{0.10}{2} = 0.05}\\\\ \to \bold{(df) = n-1 = 16-1 = 15}\\\\[/tex]

Using the t table we calculate [tex]t_{ \frac{\alpha}{2}} = 1.753[/tex]  When [tex]90\%[/tex] of the confidence interval:

[tex]\to \bold{410 \pm 1.753 \times \frac{40}{\sqrt{16}}}\\\\ \to \bold{410 \pm 17.53\\\\ \to392.47 < \mu < 427.53}[/tex]

So [tex]90\%[/tex] confidence interval for the mean weight of shipped homemade candies is between [tex]392.47\ \ and\ \ 427.53[/tex].

B)

[tex]\to \bold{(n) = 500}[/tex]

[tex]\to \bold{(X) = 155}[/tex]

[tex]\to \bold{(p') = \frac{X}{n} = \frac{155}{500} = 0.31}[/tex]

Here we need to calculate [tex]90\%[/tex] confidence interval for the true proportion of all college students who own a car which can be calculated as

[tex]\to \bold{p' \pm Z_{\frac{\alpha}{2}} \times \sqrt{\frac{p'(1-p')}{n}}}[/tex]

[tex]\to \bold{C.I= 0.90}[/tex]

[tex]\to\bold{ (\alpha) = 0.10}[/tex]

[tex]\to\bold{ \frac{\alpha}{2} = 0.05}[/tex]

Using the Z-table we found [tex]\bold{Z_{\frac{\alpha}{2}} = 1.645}[/tex]

therefore [tex]90\%[/tex] the confidence interval for the genuine proportion of college students who possess a car is

[tex]\to \bold{0.31 \pm 1.645\times \sqrt{\frac{0.31\times (1-0.31)}{500}}}\\\\ \to \bold{0.31 \pm 0.034}\\\\ \to \bold{0.276 < p < 0.344}[/tex]

So [tex]90\%[/tex] the confidence interval for the genuine proportion of college students who possess a car is between [tex]0.28 \ and\ 0.34.[/tex]

C)

In question A, We are  [tex]90\%[/tex] certain that the weight of supplied homemade candies is between 392.47 grams and 427.53 grams.In question B, We are  [tex]90\%[/tex] positive that the true percentage of college students who possess a car is between 0.28 and 0.34.

Learn more about confidence intervals:  

brainly.com/question/24131141

Solve 3(5x + 7) = 9x + 39.
O A. X=-3
B. X= -10
O c. x = 10
O D. x= 3

Answers

Answer:

x=3

Step-by-step explanation:

3(5x + 7) = 9x + 39

15x + 21 = 9x + 39

15x - 9x = 39 - 21

6x = 18

x = 3

consider the differential equation x3y ''' + 8x2y '' + 9xy ' − 9y = 0; x, x−3, x−3 ln(x), (0, [infinity]). Verify that the given functions form a fundamental set of solutions of the differential equation on the indicated interval. The functions satisfy the differential equation and are linearly independent since W(x, x−3, x−3 ln(x)) = ≠ 0 for 0 < x < [infinity].

Answers

Verifying that a given expression is a solution to the equation is just a matter of plugging in the expression and its derivatives, and making sure that the given expressions are indeed linearly independent.

For example, if y = x, then y' = 1 and the other derivatives vanish. So the DE after substitution reduces to

9x - 9x = 0

which is true for all 0 < x < ∞.

To check for linear independence, you compute the Wronskian, which, judging by what you wrote, you've already done...

The triangles are similar, find y

Answers

Answer:

y = 3.6

x = 3.5

Step-by-step explanation:

The triangles are similar.

[tex]\frac{3}{2.4} = \frac{x}{2.8} = \frac{4.5}{y}[/tex]

Find y:

[tex]\frac{4.5}{y} = \frac{5}{4}[/tex]

[tex]4.5 * 4 = 5y => 18 = 5y => y = 3.6[/tex]

Find x:

[tex]\frac{x}{2.8} = \frac{5}{4}[/tex]

[tex]2.8 * 5 = 4x => 14 = 4x => x = 3.5[/tex]

Let f(x) = -2x - 7 and g(x) = -4x + 6. Find. (F o G) (-5)
26


3


–59


–6

Answers

Answer:

-59

Step-by-step explanation:

f(x) = -2x - 7 and g(x) = -4x + 6.

f(g(x)) =

Replace x in the function f(x) with g(x)

     = -2(-4x+6) -7

    = 8x -12 -7

    = 8x - 19

Let x = -5

f(g(-5) = 8(-5) -19

    = -40 -19

   = -59

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