(-16) - (+12) + (-୨)

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]

Answer:

36

Step-by-step explanation:

Diameter AB bisects the chord

MO = NO

5x+3=6x

3 = 6x-5x

x = 3

Now

MN = 5x+3+6x

MN = 5(3)+3+6(3)

MN = 15+3+18

MN = 36

Answer:

  13

Step-by-step explanation:

The line is the hypotenuse of a right triangle that is 5 units high and 12 units wide. The Pythagorean theorem, or the distance formula, tells you the length is ...

  length = √(5² +12²) = √(25+144) = √169

  length = 13

Answer:

Step-by-step explanation:

For n=129 and with leaf unit = 0.1, the stem and leaf chart of the given data on Shower-flow rate (L/min) is as follows:

2 28

Stem        leaves

3----------1344567789

4----------01356889

5----------00001114455666789

6----------0000122223344456667789999

7----------00012233455555668

8----------02233448

9----------012233335666788

10----------2344455688

11--------- 2335999

12---------- 17

13-------- 9

14--------36

15---------- 0035

16---------None

17---------None

18 ----------3

* From steam and leaf chart we note that minimum Shower flow rate is 2.2 whereas maximum is 18.3 L/mim. Further typical or representative rate is 7.0 L/min.

* The display of data on steam and leaf chart shows that data is positively skewed means concentration of data on left side or lower value side is high as compared to other side.

* Distribution is not symmetric rather very clear positive skew ness is observed through steam and leaf chart. Even distribution is Unimodal.

* From steam and leaf chart is indicative to conclude that the highest observation 18.3 is outlier.

Answer:

7.0422  is the correct answer to the given question .

Step-by-step explanation:

Given

R1 = 7.21 + 0.55t

R2 = 7.21 + 0.44t

Decrease in the revenue  can be determined by the formula

[tex]= Reduction\ in\ R1\ -\ Reduction\ in\ R2[/tex]

[tex]= (7.21 + 0.55t ) - (7.21 + 0.44t)[/tex]

=0.11 t

Now overall Reduction can be determined by the interval from t=8 to t=15

Consider c=0.11 t

[tex]\frac{dc}{dt}[/tex]=0.11

Now integrated the equation from t=8 to t=15 to determine total reduction in revenue

[tex]=\int_{8}^{15}\sqrt{1+0.11^2}\ dL[/tex]

[tex]=7.0422[/tex]

Answer:

1

Step-by-step explanation:

coz  1 x 1 x 1=1

Answer:

$ 402,722.01

Step-by-step explanation:

Answer:

Absolute error = 2m

Step-by-step explanation:

Absolute Error = Measured Value - Actual Value

17m - 15m = 2m

Answer:

2m and 11.8%

Step-by-step explanation:

Absolute error is defined mathematically as;

Error/original value

[Original value - estimated value]

[17-15 ] = 2m

The percentage error would be

[Original value - estimated value]/ original value

[17-15 ] /17 × 100%

0.1176 × 100% = 11.76%

11.8%[ to the nearest tenth]

Answer:

A.

Step-by-step explanation:

98%

The probability of not winning the raffle is 100% - 2% = 98%

Answer:

  (f+g)(x) = 5x +3

Step-by-step explanation:

(f+g)(x) = f(x) +g(x)

  = (2x -6) +(3x +9)

  = 2x +3x -6 +9

(f+g)(x) = 5x +3

Answer:

For this case we know that 12% of the restaurants in the Us are pizzerias and there are about 70000 pizzerias in Us. So then we can apply a proportion rule given by:

[tex]\frac{70000}{12} = \frac{x}{100}[/tex]

Where x represent the total of restaurants representing the 100% and if we solve for x we got:

[tex] x = 100 \frac{70000}{12}= 583333.33[/tex]

So then there is approximately between 58333 and 58334 restaurants in US with the result obtained.

Step-by-step explanation:

For this case we know that 12% of the restaurants in the Us are pizzerias and there are about 70000 pizzerias in Us. So then we can apply a proportion rule given by:

[tex]\frac{70000}{12} = \frac{x}{100}[/tex]

Where x represent the total of restaurants representing the 100% and if we solve for x we got:

[tex] x = 100 \frac{70000}{12}= 583333.33[/tex]

So then there is approximately between 58333 and 58334 restaurants in US with the result obtained.

Answer:

[tex]22+2\sqrt{2}[/tex]

Step-by-step explanation:

[tex](4+\sqrt{2} )(6-\sqrt{2} )[/tex]

[tex]4(6)-4\sqrt{2} +6\sqrt{2} -2[/tex]

[tex]24+2\sqrt{2} -2[/tex]

[tex]22+2\sqrt{2}[/tex]

Answer:

The variable y is eliminated.

Step-by-step explanation:

To add a system of equations, we add the common terms. x with x, y with y and values with values.

In this question:

5x + 6y = 32

5x – 6y = 8

Adding:

5x + 5x + 6y - 6y = 32 + 8

10x = 40

So the variable y is eliminated.

Answer:

10x 40

Step-by-step explanation:

Answer:

E) B < A < C

Step-by-step explanation:

Penni Precisely buys 100 worth of stock in each of three companies: Alabama Almonds, Boston Beans, and California Cauliflower.

Initial Values are: A, B and C

After one year, A was up 20%, B was down 25%, and C was unchanged.

Values after one year:

For the second year, A was down 20% from the previous year, B was up 25% from the previous year, and C was unchanged.

Values after the second year

Therefore, from the final values of the stock, we have that:

B<A<C

The correct option is E.

Answer:

C.

Step-by-step explanation:

Some rectangles can be squares, since they fit the criteria for both if it is a square, but not ALL rectangles can be squares, since squares have ALL 4 sides congruent, whereas rectangles only have 2 sets of sides congruent.

C is parameterized by

[tex]\vec r(t)=\langle x(t),y(t),z(t)\rangle=\left\langle12\cos t,12\sin t,t\right\rangle[/tex]

for 0 ≤ t ≤ 2π. In the integral, replace y and z as above, and the line element ds is

[tex]\mathrm ds=\sqrt{\left(\dfrac{\mathrm dx}{\mathrm dt}\right)^2+\left(\dfrac{\mathrm dy}{\mathrm dt}\right)^2+\left(\dfrac{\mathrm dz}{\mathrm dt}\right)^2}\,\mathrm dt=\sqrt{145}\,\mathrm dt[/tex]

So the integral is

[tex]\displaystyle\int_C(y-z)\,\mathrm ds=\sqrt{145}\int_0^{2\pi}(12\sin t-t)\,\mathrm dt[/tex]

sin(t) has period 2π, so that term contributes nothing to the integral, leaving us with

[tex]\displaystyle\int_C(y-z)\,\mathrm ds=-\sqrt{145}\int_0^{2\pi}t\,\mathrm dt=\boxed{-2\pi^2\sqrt{145}}[/tex]

Answer:

The best prediction for  the number of years it will take for the population to reach 200,000 is 9.41

Step-by-step explanation:

Year     Population

1              11,920

2              16,800

3              23,300

4              33,000

5             45,750

6             64,000

[tex]y_1 =A _0 e ^{kt _1}\\y_2 = A_0 e^{k t_2}\\(t_1,y_1)=(1,11920)\\(t_2,y_2)=(2,16800)[/tex]

Substitute the values

[tex]11920=A _0 e ^{k} ---1\\16800 = A_0 e^{2k} ---2[/tex]

Divide 1 and 2

[tex]\frac{11920}{16800}=\frac{e^k}{e^{2k}}\\\frac{11920}{16800}=e^{k-2k}\\ln(\frac{11920}{16800})=-k\\k=-1 ln(\frac{11920}{16800})\\k=0.3432\\A_0=y_1 e^{-k t_1}\\A_0=11920 e^{-0.3432}\\A_0=8457.5238[/tex]

The exponential function that passes through the points (1, 11920) and (2, 16800) is[tex]y=8457.5238 e^{0.3432t}[/tex]

Now we are supposed to find  the best prediction for  the number of years it will take for the population to reach 200,000

[tex]200000=8457.5238 e^{0.3432t}[/tex]

[tex]\frac{200000}{8457.5238}=e^{0.3432t}[/tex]

[tex]ln(\frac{200000}{8457.5238})=0.3432t[/tex]

t = 9.41

Hence the best prediction for  the number of years it will take for the population to reach 200,000 is 9.41

Answer:

Step-by-step explanation:

Given that

n = 25

mean = 3100

standard deviation = 500

[tex]\bar x = \frac{500}{\sqrt{25} }[/tex]

= 500 / 5

= 100

N ( μ = 3500, (500)² / 25)

N = (3500,(100)² )

b) P ( x < 3100)

c) Z score

[tex]z = \frac{x - u _{\bar x}}{\sigma \_ {\bar x}}[/tex]

[tex]u_{\bar x}= 3500[/tex]

[tex]\sigma _{\bar x}= 100[/tex]

[tex]z = \frac{3100-3500}{100} \\\\= -4[/tex]

d)

probability=

P ( x < 3100) = P < -4 = 0

Answer:

a) The parameters for the sampling distribution include

Mean = μₓ = 3500 g

Standard deviation = σₓ = 100 g

Required probability = P(x < 3100)

b) The image of the probability density curve is presented in the attached image.

c) The z-score for 3100 g in the sampling distribution = -4.00

d) The probability that the 25 babies that are born that their mean weigh less than 3100 g = 0.00003

Step-by-step explanation:

Complete Question

Suppose we know the birth weights of babies is normally distributed, with mean of 3500 g and standard deviation 500g.

If 25 new born babies are randomly selected, what is the probability that the 25 babies are born that their mean weigh less than 3100g?

a) What are the parameters?

b) Draw a probability density curve for the problem.

c) What is the z-score of the weight?

d) What is the required probability?

Solution

The Central limit theorem explains that for a random sample of adequate size obtained from a normal distribution with independent variables, the mean of the sampling distribution is approximately equal to the population mean and the sampling distribution is approximately of the nature of the population distribution (normal) with the standard deviation of the sampling distribution given as

Standard deviation of the sampling distribution = [(Population Standard deviation)/√n]

σₓ = (σ/√n)

Mean of Sampling distribution = Population mean

μₓ = μ = 3500 g

σₓ = (σ/√n) = (500/√25) = 100 g

a) The parameters for the sampling distribution include

Mean = μₓ = 3500 g

Standard deviation = σₓ = 100 g

Required probability = P(x < 3100)

b) The image of the probability density curve is presented in the attached image.

c and d) To obtain the required probability, we need the z-score for 3100 g, so we standardize 3100g

The standardized score for any value is the value minus the mean then divided by the standard deviation.

z = (x - μ)/σ = (3100 - 3500)/100 = - 4.00

To determine the required probability 45mg/L, P(x < 3100) = P(z < -4.00)

We'll use data from the normal probability table for these probabilities

P(x < 3100) = P(z < -4.00) = 0.00003

Hence, the probability that the 25 babies that are born that their mean weigh less than 3100 g = 0.00003

Hope this Helps!!!!

Answer:

With this P-value, we have statistical evidence to support the claim that there is a relationship between the average number of putts per hole and the player's total winnings.

Step-by-step explanation:

In this case, the hypothesis test has the following hypothesis:

Null hypothesis: there is no relationship between the average number of putts per hole and the player's total winnings.

Alternative hypothesis: there is relationship between the average number of putts per hole and the player's total winnings.

Then, a P-value of 0.0087 is, without doubt, a strong evidence that the null hypothesis is false.

With this P-value, we have statistical evidence to support the claim that there is a relationship between the average number of putts per hole and the player's total winnings.

It reheats the gas from the fuel and releases it more rapidly.

The answer is option A.

In full afterburner at low altitudes, the F-16 can burn in excess of 64,000 pounds an hour. At full throttle, a U.S.-variant F-16 with maximum external fuel stores has about 20 minutes until it's on emergency reserves (which would only last an extra minute or so at full afterburner).

Since the exhaust gas already has a reduced oxygen content, owing to the previous combustion, and since the fuel is not burning in a highly compressed air column, the afterburner is generally inefficient in comparison to the main combustion process.

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Answer:

[tex]p = \frac{4}{9}[/tex]

Step-by-step explanation:

A probability is the number of desired outcomes divided by the number of total outcomes.

Sample space:

All posible outcomes.

First answer - Second answer:

A - A

A - B

A - C

B - A

B - B

B - C

C - A

C - B

C - C

9 possible outcomes.

Probability that neither is B.

A - A

A - C

C - A

C - C

4 possible outcomes.

So

[tex]p = \frac{4}{9}[/tex]

Answer: 135 soccer balls

Step-by-step explanation:

In this equation, let x represent the number of soccer balls, and 7x represent the number of volley balls.

7x + x = 1,080

8x = 1,080

Now divide 1,080 by 8 to get the number of soccer balls.

1,080 / 8 = 135

In case you’re wondering how to find the number of volley balls, just multiply 135 by 7

135 * 7 = 945

Answer:

  -1/5

Step-by-step explanation:

Perpendicular lines have slopes that are the opposite reciprocal of one another.

The slope of line t is the opposite reciprocal of the slope of line s:

  slope of t = -1/(slope of s)

  slope of t = -1/5

Answer:

B

Step-by-step explanation:

Notice that

[tex](3.5-5)^2 + (4.5-3)^2 = 4.5[/tex]

Since 4.5 is less than 6.25, tower B transmits to that phone

Answer:

Towers B and C transmit to the phone.

Step-by-step explanation:

First, let see the location of the center for each tower:

Tower A

[tex]A (x,y) = (0,0)[/tex]

Tower B

[tex]B (x,y) = (5,3)[/tex]

Tower C

[tex]C(x,y) = (2,5)[/tex]

Now, the distance between the location of the phone and any of the towers by means of the Pythagorean equation. The phone is under the influence of a tower only if distance is less than transmission boundaries. Then:

Tower A

[tex]d_{A} = \sqrt{(3.5-0)^{2}+(4.5-0)^{2}}[/tex]

[tex]d_{A} \approx 5.701[/tex]

[tex]d_{A} > 3[/tex]

Tower B

[tex]d_{B} = \sqrt{(3.5-5)^{2}+(4.5-3)^{2}}[/tex]

[tex]d_{B} \approx 2.121[/tex]

[tex]d_{B} < 2.5[/tex]

Tower C

[tex]d_{C} = \sqrt{(3.5-2)^{2}+(4.5-5)^{2}}[/tex]

[tex]d_{C} \approx 1.581[/tex]

[tex]d_{C} < 2[/tex]

Towers B and C transmit to the phone.

Answer: 2^4*3^5*19

Step-by-step explanation:

You also need to divided by 2 four times, then divided by 3 five times, then the final one is divided by 19.

The largest prime factor of 309² - 147² is, 19.

The highest number that divides exactly into two more numbers, is called  Greatest common factors.

Given that;

The expression is,

⇒ 309² - 147²

Now, We can simplify as;

⇒ 309² - 147²

⇒ (309 - 147) (309 + 147)

⇒ 162 × 456

⇒ 2 × 3 × 3 × 3 × 3 × 2 × 2 × 2 × 3 × 19

Thus, The largest prime factor of 309² - 147² is,

⇒ 19

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Hi!

So for this you need an equation. It will be 72 • 0.8 - 2.88 • 3

this is bc 12 x 6 is 72 and 3 bc 2 x 3 is 6.

so after you solve it you should get : $48.96..Hope this helped! :))

Answer:

A.

Step-by-step explanation:

Circle with centre (0,2) will have the equation

(x)²+(y-2)² = r²

Finding r² by distance formula using P(-7,2)

r² = (-7-0)²+(2-2)²

r² = (-7)²

r² = 49

So substituting in the equation

x²+(y-2)² = 49

Answer: 150

Step-by-step explanation: K is constant

250= K (8+2)2

250= K (10)2

250= K (20)

250= K20

divide both sides by 20

250/20= K

12.5= K

THEREFORE

Y= K (4+2)2

Y= 12.5 (6)2

Y= 12.5 × 12

Y= 150

At x = 4 the value of the variable y will be 90 as per the proportionality given.

The property of having suitable proportions in terms of size, number, degree, harshness, etc.: If a defensive action against an unfair attack results in destruction that contravenes the proportionality criterion, it may even go far beyond a justifiable defense.

Given, Y is directly proportional to (x+2)2 when x=8 y = 250

Since Y ∝ (x + 2)²

Y = k (x + 2)²

Where k is constant

For x = 8 y = 250

Substituting the values

250 = k(8 + 2)²

k = 2.5

Thus for x= 4

y = 2.5 (4 + 2)²

y = 90

therefore, According to the proportionality, the variable y will have a value of 90 at x = 4.

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Answer:

290

Step-by-step explanation:

(11*8)*2=176, (11*3)*2=66, (3*8)*2=48, 48+176+66= 290