When a force of 36 Newtons is applied to springs S1 and S2, the displacement of the springs is 6 centimeters and 9 cm, respectively. What is the difference between the spring constants of the two springs?

Answer:

A. The mean represents the center.

A. The median represents the center.

B. The mode does not represent the center because it is the smallest data value.

Step-by-step explanation:

Mean

(9 + 9 + 12 + 12 + 9 + 8 + 8 + 8 + 10 + 8 + 8 + 8 + 11)/13 = 120/13 = 9.2

The mean 9.2 and it represents the center of data.

Median

By arranging the set of data, the median, the median is the center number

8,8,8,8,8,8,(9),9,9,10,11,12,12

The median is 9 and it represents the center of data.

Mode

The mode is the number that appears most in the set of data.

The number that appears most in the set of data is 8 and does not represent the set of data.

Given the data set, 9, 9, 12, 12, 9, 8, 8, 8, 10, 8, 8, 8,11:

A. The mean does represents the center of the data set

Given the following data set:

9, 9, 12, 12, 9, 8, 8, 8, 10, 8, 8, 8, 11

Let's find the mean, median, and mode.

Mean of the data set:

Mean = sum of all values / number of values

Mean = [tex]\frac{9 + 9 + 12 + 12 + 9 + 8 + 8 + 8 + 10 + 8 + 8 + 8 + 11}{13}[/tex]

Mean = [tex]\frac{120}{13} = 9.2[/tex]

Median of the data set:

Order the data from the least to the greatest then find the middle value.

8, 8, 8, 8, 8, 8, (9,) 9, 9, 10, 11, 12, 12

The middle value is 9.

Mode of the data set:

The mode = the data value that appears most

8 appeared the most, therefore, the mode = 8

If you observe, you will note that the mean and median of the data set are similar. We can as well conclude that the mean represents the center of the data set.

In summary, given the data set, 9, 9, 12, 12, 9, 8, 8, 8, 10, 8, 8, 8,11:

A. The mean does represents the center of the data set

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Hey there! I'm happy to help!

If you reflect a point across the x-axis, you have (x,y)⇒(x,-y). If you reflect across the y-axis, you have (x,y)⇒(-x,y). A 180° rotation is the same thing as reflecting across both the x and y axes. This means that the rule for rotating the point with coordinates (x,y) 180° clockwise about the origin is D. (x,y)⇒      (-x,-y).

Have a wonderful day! :D

Answer:

-4.30

Step-by-step explanation:

The computation of the test statistic is shown below:

Data are given in the question

Sample = 55 night students

Sample mean = 2.3

Standard deviation = 0.02

Sample = 50 day students

Sample mean = 2.35

Standard deviation = 0.08

Based on the above information, the test statistic is

[tex]z = \frac{\bar x_1 - \bar x_2}{\sqrt{\frac{\sigma _1^2}{n_1} + {\sqrt{\frac{\sigma _2^2}{n_2}}}}}[/tex]

[tex]z = \frac{2.3 - 2.35}{\sqrt{\frac{(0.02)^2}{55} + {\sqrt{\frac{(0.08)^2}{50}}}}}[/tex]

= -4.30

Hence, the test statistic is -4.30

Answer:

2 11/12

Step-by-step explanation:

3/4 + 2 1/6

Add the fractions.

35/12

= 2 11/12

Answer:

[tex]2\frac{11}{12}[/tex]

Step-by-step explanation:

[tex]\frac{3}{4}+2\frac{1}{6}=\\\\\frac{18}{24}+2\frac{4}{24}=\\\\2\frac{22}{24}=\\\\2\frac{11}{12}[/tex]

Answer:

XY ≈ 14.87 units

Step-by-step explanation:

Calculate the distance using the distance formula

d = [tex]\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }[/tex]

with (x₁, y₁ ) = X(- 6, 3) and (x₂, y₂ ) = Y(8, - 2)

d = [tex]\sqrt{(8+6)^2+(-2-3)^2}[/tex]

   = [tex]\sqrt{14^2+(-5)^2}[/tex]

   = [tex]\sqrt{196+25}[/tex]

   = [tex]\sqrt{221}[/tex]

   ≈ 14.87 ( to 2 dec. places )

Correct Question:

5 (u + 1) - 7  = 3 (u - 1) + 2u.

Solve for u

Answer:

See explanation below

Step-by-step explanation:

In this given question, we are required to find u.

Given the equation:

5 (u + 1) - 7 = 3 (u - 1) + 2u​

Required:

Solve for u

To find u, first simplify both sides individually.

Simply 5 (u + 1) - 7:

Expand the parenthesis:

5u + 5 - 7

Collect like terms:

5u - 2

Simplify 3 (u - 1) + 2u​:

Expand the parenthesis:

3u - 3 + 2u

Collect like terms:

3u + 2u - 3

5u - 3

Bring both simplified equations together:

5u - 2 = 5u - 3

5u - 5u - 2 = -3

-2 = -3

Since -2 ≠ -3, there is no solution.

Therefore, we can say the equation is invalid.

Answer:

the value of c is  20.155 such that 99% of all parcels are under the surcharge weight.

Step-by-step explanation:

Given that :

The mean value [tex]\mu[/tex] = 12

The standard deviation [tex]\sigma[/tex] = 3.5

Let Consider Q to be the weight of the parcel that is normally distributed .

Then;

Q [tex]\sim[/tex] Norm(12,3.5)

The objective is to determine thewight  value of c under which there is a surcharge

Also, let's not that 99% of all the parcels are below the surcharge

However ;

From the Percentiles table of Standard Normal Distribution;

At 99th percentile; the value for Z = 2.33

The formula for the Z-score is:

[tex]Z = \dfrac{X- \mu}{\sigma}[/tex]

[tex]2.33 = \dfrac{X - 12}{3.5}[/tex]

2.33 × 3.5 = X - 12

8.155 = X - 12

- X = - 12 - 8.155

- X = -20.155

 X = 20.155

the weight  value of c under which there is a surcharge = X + 1 (0) since all the  pounds are below the surcharge

c = 20.155 + 1(0)

c = 20.155

Thus ; the value of c is  20.155 such that 99% of all parcels are under the surcharge weight.

Answer:

x = 25°

Step-by-step explanation:

From the picture attached,

Since AE║BC and AC is a transverse,

Therefore, ∠EAC ≅ ∠BCA [Alternate interior angles]

m∠EAC = m∠BCA = x°

∠BCD = ∠DCB + ∠DBC [Since ∠BCD is an exterior angle of ΔBDC]

m∠BCD = m∠DCB + m∠DBC

50° = x° + x°

2x = 50

x = 25°

Therefore, value of x is 25°.

Answer: 25 degrees

Step-by-step explanation:

Answer:

2 km

Step-by-step explanation:

Since we know that the TOTAL distance from Kensington to Greenville is 4.3 km, and we also that the distance from Kensington to Springfield is 2.3 km, we can subtract these values to find the distance from Springfield to Greenville.

[tex]4.3-2.3=2[/tex]

I hope this helped!

Answer:

Simple math, different numbers.

Step-by-step explanation:

Take the total distance, 4.3

And subtract it from the given segment of the road.

4.3 - 2.3 = 2.0

So the distance between Springfield and Greenville is 2 kilometers.

Answer:

Children: $13

Adults: $18

Step-by-step explanation:

Well for both sets we can set up the following system of equations,

[tex]\left \{ {{3a + 4c = 106} \atop {2a + 3c = 75}} \right.[/tex]

So first we need to solve for a in the first equation.

3a + 4c = 106

-4c to both sides

3a = -4c + 106

Divide 3 by both sides

a = -4/3c + 35 1/3

Now we plug in that a for a in 2a + 3c = 75.

2(-4/3c + 35 1/3) + 3c = 75

-8/3c + 70 2/3 + 3c = 75

Combine like terms

1/3c + 70 2/3 = 75

-70 2/3 to both sides

1/3c = 4 1/3

Divide 1/3 to both sides

c = 13

Now we can plug in 13 for c in 3a + 4c = 106,

3a + 4(13) = 106

3a + 52 = 106

-52 to both sides

3a = 54

Divide 3 by both sides.

a = 18

Thus,

an adult ticket is $18 and a children's ticket is $13.

Hope this helps :)

Answer:

Adults pay $18 and children pay $13.5

Step-by-step explanation:

Hello!

You need to calculate the price of the tickets for adults and children for the group trip to New York.

If X represents adult and Y represents children, then you can express the given information as two equations with two unknown values:

Three adults and four children must pay $106. ⇒ 3X + 4Y= $106

Two adults and three children must pay $75. ⇒ 2X + 3Y= $75

I) First step, in one of the equations you have to clear one of the unknown values, I'll clear the value of Y:

3X + 4Y= 106

4Y= 106 - 3X

[tex]Y= \frac{106-3X}{4}[/tex]

II) Second step you have to replace it in the second equation:

2X + 3Y= 75

[tex]2X + 3(\frac{106-3X}{4} )= 75[/tex]

[tex]2X + \frac{3}{4}(106-3X)= 75[/tex]

[tex]2X + (\frac{3}{4}*106 - \frac{3}{4}*3X )= 75[/tex]

[tex]2X + 79.5 -\frac{9}{4}X =75[/tex]

[tex]2X - \frac{9}{4}X= 75 - 79.5[/tex]

[tex]-\frac{1}{4} X= -\frac{9}{2}[/tex]

[tex]X= -\frac{9}{2} * -4= 18[/tex]

The price for adult tickets is $18.

III) Third step, using the calculated value of X, you replace it on the formula obtained in I) yo calculate the price for the children Y:

[tex]Y= \frac{106-3X}{4}= \frac{106-(3*18)}{4} = \frac{27}{2}= 13.5[/tex]

The ticket price for children is $13.5

I hope this helps!

Answer:

The distribution of scores would not have the same mean and standard deviation

Step-by-step explanation:

According to the given data we have the following:

mean=456

Standard deviation=100

mathematics SAT scores for high school seniors for a specific year have a mean of 456 and a standard deviation of 100 and are approximately normally distributed

Therefore, we can conclude that a subgroup of these high school seniors would not to be a perfect representation, hence, the distribution of scores would not have the same mean and standard deviation.

Answer:

a. Identify the population of interest in this study.

b. Identify the sample for the study.

c. Identify the parameter of interest in the study.

d. Find and interpret a 95​% confidence interval for the parameter of interest.

z score for a 95% confidence level = 1.96

margin of error (E) = z score x √{[0.4(1 - 0.4)] / 50} = 1.96 x 0.069282 = 0.13579

95% confidence level interval:

0.4 - 0.13579 = 0.26421

0.4 + 0.13579 = 0.53579

Answer:

18+18 as point XYZ is in centroid of Q

Step-by-step explanation:

so it's equal.

36.which is option A.

Answer:

The answer is below

Step-by-step explanation:

Given that mean (μ) = 266 days, standard deviation (σ) = 16 days, sample size (n) = 16 women.

a) The mean of the sampling distribution of Xbar ([tex]\mu_x[/tex]) is given as:

[tex]\mu_x=\mu=266\ days[/tex]

The standard deviation of the sampling distribution of Xbar ([tex]\sigma_x[/tex]) is given as:

[tex]\sigma_x=\frac{\sigma}{\sqrt{n} } =\frac{16}{\sqrt{16} }=4[/tex]

b) The z score is a measure in statistics used to determine by how much the raw score is above or below the mean. It is given by:

[tex]z=\frac{x-\mu}{\sigma/\sqrt{n} }[/tex]

For x > 270 days:

[tex]z=\frac{x-\mu}{\sigma/\sqrt{n} }=\frac{270-266}{\frac{16}{\sqrt{4} } }=1[/tex]

The probability the average pregnancy length exceed 270 days = P(x > 270) = P(z > 1) = 1 - P(z < 1) = 1 - 0.8413 = 0.1587 = 15.87%

Answer:

[tex]108 \times 125=2^2 \times 3^3 \times 5^3[/tex]

Step-by-step explanation:

To express the given product (108 X 125) as a product of prime factors

Step 1: Express each of the numbers as a product of its prime factors.

[tex]108=2^2 \times 3^3\\125=5^3[/tex]

Step 2: Write the product together, and combine any like terms if any

Therefore,

[tex]108 \times 125=2^2 \times 3^3 \times 5^3[/tex]

Step-by-step explanation:

5) a. x/2 = 7-5

x/2 = 2

x = 2×2

x=4

b.4x - 2 = 3x +7

4x - 3x = 7 + 2

x = 9

c. x+2 = 42 × 3

x+2 = 126

x = 124

d. 13x + 260 = 39

13x = 39 - 260

13x = -221

x = -17

6) a. 6x / 7 = 4 +2

6x = 6 × 7

6x = 42

x = 7

b. -49 = 7x + 7

-49 - 7 = 7x

7x = - 56

x = -8

c. -7 + 7x - 21 = 0

7x - 28 = 0

7x = 28

x = 4

d. 8x - 32 + 2 = 42

8x - 30 = 42

8x = 42 + 30

8x = 72

x = 9

e. 5x + 7 = 18

5x = 11

x = 2.5

Answer:

B) –3x – 6 = 21

Step-by-step explanation:

Well the distributive property is the multiplying of a number by more numbers in parenthesis.

For example  -3(x + 2) by using the distributive property we get,

-3x - 6

Thus,

the answer is B) -3x - 6 = 21 because it shows the aftermath of the distributive property.

Hope this helps :)

When distributive property applies on 3(x + 2) = 21 expression than it changes as 3x + 6 = 21.

Distributive property explains us how to solve expressions in the form of a(b + c).

After apply distributive property this term convert as ab+ac.

The given expression is,

3(x + 2) = 21

To solve the expression, use distributive property,

According to distributive property,

a(b + c) changes in the form of ab+ac.

Solve for the given expression,

3x + 2×3 = 21

3x + 6 = 21

Solve for the value of x,

3x = 21 - 6

3x = 15

x = 5

Hence, option (C) is correct.

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Answer:

6/5

Step-by-step explanation:

The reciprocal of 5/6 means flip it

6/5

Answer:

6/5

Step-by-step explanation:

The reciprocal of a fraction is switching the numerator with denominator.

5/6 ⇒ 6/5

[tex]\dfrac{3}{x^3y} +\dfrac{7}{xy^4}\\\\\\\dfrac{1}{xy}(\dfrac{3}{x^2} +\dfrac{7}{y^3})[/tex]

It's xy.

Answer:

The answer is missing.

I think there is something wrong with the equation on its own

Step-by-step explanation:

Equation for the hovercraft

F(x)= X²+6x+2

Olivia catapult equation

F(x)= √2x

Differential of the both equation will give the velocity at x time

F(x)= X²+6x+2

DF(x)/Dx= 2x +6

F(x)= √2x

F(x)= (2x)^½

DF(x)/Dx= (2x)^-½

So the differential is the velocity of the both equation.

Let's equate both equation to find the value of x at which they have same velocity.

(2x)^-½=- 2x+6

(2x)^-1= (-2x+6)²

(2x)^-1= 4x² -24x +36

0= 8x³ - 48x² +72x -1

Answer:

x = 50°

Step-by-step explanation:

Step 1.

180° - 80° (because there are 180 degrees in a triangle) = 100°

Step 2.

100° ÷ 2 = 50° (because the two angles on the bottom are identical, as this is an isosceles triangle - which we know because the two sides on the left and right are both the same length, 7 units)

Step 3.

Answer: x = 50°

Answer:

[tex](-\frac{36}{7},\frac{40}{7})[/tex]

Step-by-step explanation:

Coordinates of points A and C are (-8, 6) and (2, 5).

If a point B intersects the segment AB in the ratio of 2 : 5

Then coordinates of the point B will be,

x = [tex]\frac{mx_2+nx_1}{m+n}[/tex]

and y = [tex]\frac{my_2+ny_1}{m+n}[/tex]

where [tex](x_1, y_1)[/tex] and [tex](x_2,y_2)[/tex] are the coordinates of the extreme end of the segment and a point divides the segment in the ratio of m : n.

For the coordinates of point B,

x = [tex]\frac{2\times 2+(-8)\times 5}{2+5}[/tex]

  = [tex]-\frac{36}{7}[/tex]

y = [tex]\frac{2\times 5+5\times 6}{2+5}[/tex]

  = [tex]\frac{40}{7}[/tex]

Therefore, coordinates of pint B will be,

[tex](-\frac{36}{7},\frac{40}{7})[/tex]

Answer:

In this question it is given that:

The cash account of a company had an ending balance of $6750. During the last month, the account was debited for a total of $11,350 and credited for a total of $10,500.

And we have to use the formula

Substituting the values , we will get

Therefore beginning cash balance is

Answer:

6y +2x +7

Step-by-step explanation:

10 + 6y + 2x - 3​

The only like terms are the constant

6y+2x +10-3

6y +2x +7

Answer:

2x + 6y + 7.

Step-by-step explanation:

10 + 6y + 2x - 3

= 2x + 6y - 3 + 10

= 2x + 6y + 7.

Hope this helps!

Answer: [tex]\dfrac{1}{12}[/tex]

Step-by-step explanation:

Given: Emily has a box with 4 different colored tiles: one red, one green, one blue and one yellow.

We assume that repetition is not allowed

Total number of ways to draw two tiles = [tex]^4P_2=\dfrac{4!}{(4-2)!}[/tex]  [By permuattaions]

[tex]=\dfrac{4\times3\times2}{2}=12[/tex]

Favourable outcome = First green then red  (only one way)

So, the probability of drawing the green before the red [tex]=\dfrac{\text{favorable outcomes}}{\text{Total outcomes}}[/tex]

[tex]=\dfrac{1}{12}[/tex]

hence, the required probability =[tex]\dfrac{1}{12}[/tex]

Answer:

15

Step-by-step explanation:

4! +3! /2

4!=4*3*2*1=24

3!=3*2*1=6

24+6/2=30/2=15

Answer:

0.8390

Step-by-step explanation:

From the question,

Z score = (Value-mean)/standard deviation

Z score = (150.2-160.5)/10.4

Z score = -0.9904.

P(x>Z) = 1- P(x<Z)

From the Z table,

P(x<Z) = 0.16099

Therefore,

P(x>Z) = 1-0.16099

P(x>Z) = 0.8390

Hence the probability that a person weighs more than 150.2 pounds = 0.8390

Answer:

R4 ≤ 0.00008

R4 = 0.00001

Step-by-step explanation:

Given: sinh( 0.4 ) ≈ [tex]1 - \frac{(0.4)^2}{2!} + \frac{(0.4)^2}{4!}[/tex]

using Taylor's Theorem

R4 ≤ 0.00008

R4 = 0.00001

attached is the detailed solution

We are given [tex]\triangle ABC \cong \triangle EFG[/tex]

The order of the letter sequence is important. The letters pair up based on how they are arranged. We see that A and E are the first letters of the sequences. So this means that angles A and E are the same measure

angle A = angle E

3x+20 = 5x-80

3x-5x = -80-20

-2x = -100

x = -100/(-2)

x = 50

Use this x value to find the measure of angle A

angle A = 3x+20

angle A = 3(50)+20

angle A = 150+20

angle A = 170 degrees

Answer:

99.5% Confidence interval = (-0.025, 0.547)

= -0.025 < p < 0.547

Step-by-step explanation:

             | A | B | C | Total

Male      | 5 | 4 | 17 | 26

Female | 6 | 2 | 15 | 23

Total     | 11 | 6 | 32 | 49

If p represent the proportion of all female students who would receive a grade of A on this test. Use a 99.5% confidence interval to estimate p to three decimal places.

All female students = 23

Female students that score an A = 6

p = (6/23) = 0.2608695652 = 0.261

Confidence Interval for the population proportion is basically an interval of range of values where the true population proportion can be found with a certain level of confidence.

Mathematically,

Confidence Interval = (Sample proportion) ± (Margin of error)

Sample proportion = (6/23) = 0.261

Margin of Error is the width of the confidence interval about the mean.

It is given mathematically as,

Margin of Error = (Critical value) × (standard Error)

Critical value at 99.5% confidence interval for sample size of 23 is obtained from the t-tables since information on the population standard deviation is not known.

we first find the degree of freedom and the significance level.

Degree of freedom = df = n - 1 = 23 - 1 = 22.

Significance level for 99.5% confidence interval

(100% - 99.5%)/2 = 0.25% = 0.0025

t (0.0025, 22) = 3.119 (from the t-tables)

Standard error of the mean = σₓ = √[p(1-p)/N]

p = 0.261

N = sample size = 23

σₓ = √(0.261×0.739/23) = 0.091575

99.5% Confidence Interval = (Sample proportion) ± [(Critical value) × (standard Error)]

CI = 0.261 ± (3.119 × 0.091575)

CI = 0.261 ± 0.2856

99.5% CI = (-0.0246, 0.5466)

99.5% Confidence interval = (-0.025, 0.547)

= -0.025 < p < 0.547

Hope this Helps!!!