The 9th and the 12th term of an arithmetic progression are 50 and 65 respectively. find the common difference

The value of t obtained is 4.76

Given,

Mean of group 1, [tex]M_{1}[/tex] = 10

Mean of group 2, [tex]M_{2}[/tex] = 12

[tex]SS_{1}[/tex] = 5

[tex]SS_{2}[/tex] = 8

Number of individuals per group, n = 6

The degrees of freedom are calculated as:

[tex]df = (n_{1} -1)+(n_{2} -1)[/tex] = ( 8-1) + (8-1) = 7 + 7 = 14

The difference between sample means [tex]M_{d}[/tex] is:

[tex]M_{d}[/tex] = [tex]M_{1} -M_{2}[/tex] = 10 - 12 = 2

Here n is equal for both groups which is = 8

Now,

The standard deviation of sample 1 :

[tex]s_{1} =\sqrt{\frac{SS_{1} }{n_{1} -1} } = \sqrt{\frac{5}{8-1} } = \sqrt{\frac{5}{7} } = 0.85[/tex]

The standard deviation of sample 2 :

[tex]s_{2}= \sqrt{\frac{SS_{2} }{n_{2}-1 } } = \sqrt{\frac{8}{8-1} } = \sqrt{\frac{8}{7} } = 1.07[/tex]

Now, we have to calculate the standard error for the difference of the means.

MSE = [tex]\frac{(n_{1}-1)s^{2} _{1}+(n_{2}-1)s^{2} _{2} }{(n_{1}-1)+(n_{2}-1) }[/tex]

       = [tex]\frac{(8-1)(0.85^{2})+(8-1)(1.07^{2}) }{(8-1)+(8-1)}[/tex]

       = [tex]\frac{10.1318}{14}[/tex]

  MSE  = 0.7237

Then, the standard error can be calculated as:

[tex]s_{M_{d} } = \sqrt{\frac{2MSE}{n} } = \sqrt{\frac{2 * 0.7237}{8} } = 0.42[/tex]

Now we can calculate t :

[tex]t=\frac{M_{d} }{s_{M_{d} } } = \frac{2}{0.42} = 4.76[/tex]

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The 90% confidence interval for the true difference between the population proportions is [ - 0.0908, - 0.0092]

Given,

[tex]N_{1}[/tex] = 731

[tex]N_{2}[/tex] = 644

[tex]P_{1}[/tex] = 0.33

[tex]P_{2}[/tex] = 0.28

z score for 90% confidence interval = 1.645

Here, the confidence interval formula :

( [tex]P_{1} -P_{2}[/tex]) ± z [tex]\sqrt{\frac{P_{1}(1-P_{1}) }{N_{1} }+ \frac{P_{2}(1-P_{2}) }{N_{2} } }[/tex]

Substituting the values, we get

    (0.33 - 0.28) ± 1.645 [tex]\sqrt{\frac{0.33(1-0.33)}{731}+\frac{0.28(1-0.28)}{644} }[/tex]

=   0.05 ± 1.645 [tex]\sqrt{0.0003024624+0.0003130435}[/tex]

=   0.05 ± 1.645 [tex]\sqrt{0.0006155059}[/tex]

=    0.05 ± 1.645 × 0.0248093914

=    0. 05 ± 0.0408114489

Confidence interval:

- 0.05 - 0.0408114489 = - 0.0908114489 ≈ - 0.0908

- 0.05 + 0.0408114489 = - 0.0091885511 ≈ - 0.0092

The confidence interval for the true difference between the population proportions is [ - 0.0908, - 0.0092]

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Answer:

Height = 19mm.

Step-by-step explanation:

Area of a regular polygon =  (A * P) / 2 where A = side / (2 * Tan (π / N)) where, N = Number of sides, A = Apothem,  P = Perimeter.

Here A = 5, P = 5*12 = 60 so

Area  of the base  = (5 * 60) / 2 = 150 mm^2.

Volume = area base * height so

Height = volume / area of base

            = 2850 / 150

            = 19 mm.

The height of the prism is h = 19 mm

A three-dimensional solid object called a prism has two identical ends. It consists of equal cross-sections, flat faces, and identical bases. Without bases, the prism's faces are parallelograms or rectangles.

The volume of a prism is the product of its base area and height

Volume of Prism = B x h

where B = base area of prism

h = height of prism

Given data ,

A regular pentagonal prism has a volume of 2,850 millimeters³

The pentagonal base has side edge labeled 12 millimeters.

And , Apothem from center to a base edge is labeled 5 millimeters

Area of a regular polygon =  (A x P) / 2

where A = side / (2 * Tan (π / N))

and , N = Number of sides, A = Apothem,  P = Perimeter

h = 2850 / 150

On simplifying , we get

h = 19 mm

Hence , the height is 19 mm

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Answer:

11. 333... which can also be written as 11 1/3.

Step-by-step explanation:

Sure.

√(6c - 4) = 8

Squaring both sides:

6c - 4 = 64

6c = 64 + 4 = 68

c = 68/6

  = 11. 333...

Answer:

[tex]c=\dfrac{34}{3}[/tex]

Step-by-step explanation:

Given equation:

[tex]\sqrt{6c-4}=8[/tex]

Square both sides:

[tex]\implies (\sqrt{6c-4})^2=8^2[/tex]

[tex]\implies 6c-4=64[/tex]

Add 4 to both sides:

[tex]\implies 6c-4+4=64+4[/tex]

[tex]\implies 6c=68[/tex]

Divide both sides by 6:

[tex]\implies \dfrac{6c}{6}=\dfrac{68}{6}[/tex]

[tex]\implies c=\dfrac{34}{3}[/tex]

Verify the solution by inputting the found value of c back into the equation:

[tex]\implies \sqrt{6\left(\dfrac{34}{3}\right)-4}[/tex]

[tex]\implies \sqrt{\dfrac{204}{3}-4}[/tex]

[tex]\implies \sqrt{68-4}[/tex]

[tex]\implies \sqrt{64}[/tex]

[tex]\implies \pm 8[/tex]

Therefore, the solution of the found value of c is verified.

The inverse maps (x,y) onto (y,x).

Using the normal distribution, there is a 0.4826 = 48.26% probability that the sample mean is between 15 and 16 grams per day.

The z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:

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

For this problem, the parameters are given as follows:

[tex]\mu = 15, \sigma = 3, n = 40, s = \frac{3}{\sqrt{40}} = 0.4743[/tex]

The probability is the p-value of Z when X = 16 subtracted by the p-value of Z when X = 15, hence:

X = 16:

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

By the Central Limit Theorem

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{16 - 15}{0.4743}[/tex]

Z = 2.11

Z = 2.11 has a p-value of 0.9826.

X = 15:

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{15 - 15}{0.4743}[/tex]

Z = 0

Z = 0 has a p-value of 0.5.

0.9826 - 0.5 = 0.4826 = 48.26% probability that the sample mean is between 15 and 16 grams per day.

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Answer:

14

Step-by-step explanation:

Subtract 3 from both sides to isolate g / make g the subject :

g + 3( -3 ) = 17 (-3)

g = 17-3

g = 14

Substituting this into the equation gives us :

14 + 3  = 17

17 = 17

So our final answer is 14

Hope this helped and have a good day

Answer:

5/6

Step-by-step explanation:

slope = 4-(-1)/8-2 = 5/6

Answer:

x = 2

Step-by-step explanation:

note that 64 = [tex]2^{6}[/tex]

then

[tex]x^{6}[/tex] = [tex]2^{6}[/tex] , so x = 2

Answer:

m = -5/4

Step-by-step explanation:

In the slope-intercept form formula, y = mx + b, substitute 4 for x, 7 for y, and b for 12 to solve for m.

y = mx + b

7 = 4m + 12

-5 = 4m

m = -5/4

[tex]64^{\text{x}} = (8^2)^{\text{x}} = 8^{2\text{x}}[/tex]

The rule used is that [tex](a^b)^c = a^{bc}[/tex] we multiply the exponents b and c.

Or we could say this

[tex]64^{\text{x}} = (4^3)^{\text{x}} = 4^{3\text{x}}[/tex]

Or,

[tex]64^{\text{x}} = (2^6)^{\text{x}} = 2^{6\text{x}}[/tex]

Therefore, we have multiple possible answers.

Answer:

- 7

Step-by-step explanation:

note that

+ (- ) = - ( adding a negative is equivalent to subtraction )

- (- ) = + ( subtracting a negative is equivalent to addition )

then

7 + (- 14) = 7 - 14 = - 7

Assuming that both boats are travelling in straight paths, the angle that is between their paths to the nearest degrees is =34°

A triangle is a type of polygon that has three pointed edges.

A polygon is defined as a closed object that is made up of line segments in a two dimensional plane.

Other examples of polygon include the following:

The angle between the paths of the boats can be calculated using the formula Cos θ = a/b

Where b = 18km/h

a = 15km/h

Cos θ = 15/18

cos θ = 0.83

Therefore, θ = Cos¹0.83

θ = 33.9

θ = 34°

In conclusion, the angle that is between their paths to the nearest degrees is =34°

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Answer:

Jeffrey has 225 % chance to go to Cafe Shirley.

Step-by-step explanation:

given,

chance of going to Cafe

Chris = 3/4

Nina =3/4

iana = 3/4

To find the total probability you should add all of them:

Total probability= 3/4 + 3/4 + 3/4

= 9/4 = 2.25

to convert to percent you should times 100

2.25 x 100 = 225%//

Answer:

9 or 16... but I'm leaning more to 9

Step-by-step explanation:

Since the graph seems to be going up and down, it seems like its at its highest point and should go down now so it could be 9. But if not and its still going to go higher 16 is possible.

Step-by-step explanation:

Greetings !

Given expression

[tex] \frac{10}{n} = \frac{15}{6} [/tex]

cross multiply

apply fraction cross multiply

[tex]if \: \: \frac{a}{b} = \frac{c}{d} \: \: then \: \: a.d = b.c[/tex]

10.6=n.15

simplify:

Thus, 60=n.15

switch sides

[tex]n.15 = 60[/tex]

divide both sides by 15

[tex] \frac{n.15}{15} = \frac{60}{15} [/tex]

simplify

[tex]n = 4[/tex]

Hope it helps!

See below for the values of the probabilities

The complete question is added as an attachment

Write down the probability he gets 'Miss a turn'.

From the spinner, we have

Sections = 6

Miss a turn = 1

So, the probability that he gets 'Miss a turn is

P = 1/6

Write down the probability that he gets 'Go back 1 square'.

Here, we have:

Number of rows = 4

'Go back 1 square' = 4

The probability that he gets 'Go back 1 square' is

P = 'Go back 1 square'/Number of rows

This gives

P = 4/4

Evaluate

P = 1

How many of these spins are expected to be 'Go forward 3 squares'?

Here, we have

Spins = 96

From the spinner, the probability of 'Go forward 3 squares' is

P =1/6

So, the expected number is

E(x) = np

This gives

E(x) = 96 * 1/6

Evaluate

E(x) = 16

Hence, 16 spins are expected to be 'Go forward 3 squares'

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Each side of equilateral triangle will have the length equals to 42.7 cm.

There are different types of quadrilaterals, for example, square, rectangle, rhombus, trapezoid, and parallelogram.  Each type is defined accordingly to its length of sides and angles. For example, in a rectangle,  the opposite sides are equal and parallel and their interior angles are equal to 90°.

The perimeter of a geometric figure is the sum of its sides. Thus, for a rectangle, the perimeter is 2L+2W.

You should find the perimeter of the rectangle.

2P=23+23+41+41= 128 cm

The equilateral triangle will have the same perimeter of the rectangle. An equilateral triangle presents the equal three sides, thus,

128= 3L

L=128/3=42.7 cm

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Answer:

Laplace transforms turn a Differential equation into an algebraic, so we can solve easier.

y'= pY-y(0)

y"=p²Y - py(0)- y'(0)

Substituting these in differential equation :

p²Y -py (0)  -y' (0)-6(pY-y(0)) + 13Y

Substituting in the initial conditions given , fact out Y, and get:

Y( p²-6p+13) = -3

Y=-3/ p²-6p+13

now looking this up in a table to Laplace transformation we get:

y=-3/2.e³т sin(2t)

for the last one, find the Laplace of t∧2 . which is 2/p³

pY - y(0)+ 5Y= 2/p³

Y= 2/p³(p+5)

Taking partial fractions:

Y=-2/125(p+5) + 2/125p - 2/25p² + 2/5p³

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Answer:

The integral transform that converts a function of a real variable to a function of a complex variable is called Laplace transform. first we need to substitute y' and y" in differential equation then finding Laplace transformation and at last taking partial fractions.

Given:                              y'= pY-y(0)

                                         y"=p²Y - py(0)- y'(0)

Putting y' and y" in differential equation :

                               p²Y -py (0)  -y' (0)-6(pY-y(0)) + 13Y

Substituting in the initial conditions given , fact out Y, and get:

                                 Y( p²-6p+13) = -3

                                                    Y=-3/ p²-6p+13

by Laplace transform we get:

                                  y=-3/2.e³т sin(2t)

for the last one, find the Laplace transform of t∧2 . which is 2/p³

                                  pY - y(0)+ 5Y= 2/p³

                                                     Y= 2/p³(p+5)

Taking partial fractions:

                                Y=-2/125(p+5) + 2/125p - 2/25p² + 2/5p³

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The answer is 2c.

Applying the Law of Exponents,

The angles exist in the exact place in both triangles. So we will obtain the decision that they exist different.

Therefore, the the measure of their angles exists different.

No, because the measure of their angles exists different. If the angle measurements existed the exact, they would have been equivalent.

You see in the smaller triangle, the given angle exists at 55 degrees while in the bigger triangle the given angle exists at 30 degrees.

The angles exist in the exact place in both triangles. So we will obtain the decision that they exist different.

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The number of days christen’s book is overdue is 22.

The number of days christen’s book is overdue:

According to the graph, the fine levied stops rising after 20 overdue days and then stays at 10 for the remaining days.

Additionally, if Christen's fine was the same as yesterday, her late dates must be longer than 21 days (because the fine on day 20 will be the same).

22 might therefore be the number of days past due based on the options provided.

The number of days christen’s book is overdue is 22.

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2x + 2y = 42

2w + q = 35

2w + v = 29

x + q + y - v = ?

x = 7

y = 14

w = 3

q = 29

v = 23

7 + 29 + 14 - 23 =

The answer is 27

Answer: [tex]\Large\boxed{27}[/tex]

Step-by-step explanation:

Given information converted into a mathematical statement

[tex]a = icecream\\b=cookie\\c=brownie\\d=cake\\e=creamed cake[/tex]

[tex]1)~a+b+a+b=42[/tex]

[tex]2)~c+d+c=35[/tex]

[tex]3)~c+c+e=29[/tex]

[tex]4)~a+d+b-e=\mbox{?}[/tex]

Simplify each equation

[tex]1)~2a+2b=42[/tex]

[tex]2)~2c+d=35[/tex]

[tex]3)~2c+e=29[/tex]

[tex]4)~(a+b)+(d-e)=\mbox{?}[/tex]

Factorize 2 out of the 1) equation

[tex]2a+2b=42[/tex]

[tex]2(a+b)=42[/tex]

Divide 2 on both sides

[tex]2(a+b)\div2=42\div2[/tex]

[tex]a+b=21[/tex]

Current system

[tex]1)~a+b=21[/tex]

[tex]2)~2c+d=35[/tex]

[tex]3)~2c+e=29[/tex]

[tex]4)~(a+b)+(d-e)=\mbox{?}[/tex]

Subtract 3) equation from the 2) equation

[tex](2c +d)-(2c+e)=(35)-(29)[/tex]

Expand the parenthesis

[tex]2c+d-2c-e=35-29[/tex]

Combine like terms

[tex]2c-2c+d-e=6[/tex]

[tex]d-e=6[/tex]

Current system

[tex]1)~a+b=21[/tex]

[tex]2)~d-e=6[/tex]

[tex]3)~(a+b)+(d-e)=\mbox{?}[/tex]

Substitute values into the 3) equation to determine the final value

  [tex](a+b)+(d-e)[/tex]

[tex]=(21)+(6)[/tex]

[tex]\Large\boxed{=27}[/tex]

Hope this helps!! :)

Please let me know if you have any questions

The ticket price which will maximize the student's council is: C. $3.10.

Price can be defined as an amount of money which is primarily set by the seller of a product, and it must be paid by a buyer to the seller, so as to enable the acquisition of this product.

Based on the information provided about Valley High School student council, we can logically deduce the following data:

Mathematically, the equation which model the profit is given by:

Profit = price × number of tickets sold

P(x) = (2 + 0.2x)(420 - 20x)

P(x) = 840 + 84x - 40x - 4x²

P(x) = -4x² + 44x + 840.

For any quadratic equation with a parabolic curve, the axis of symmetry is given by:

Xmax = -b/2a

Xmax = -44/2(-4)

Xmax = -44/-8.

Xmax = 5.5

Ticket price for maximum profit is given by:

Ticket price = 2 + 0.2x

Ticket price = 2 + 0.2(5.5)

Ticket price = $3.10.

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Answer:

[tex]x^{2} +10x+24[/tex]

Step-by-step explanation:

Answer:

=(x+1)^2-25

Step-by-step explanation:

=x(x−4)+6(x−4)

=x^2−4x+6x−24

=x^2+2x−24

=x^2+2x+1−25

=(x+1)^2-25

The groups which would be most representative of the opinions of all employees in the company are: A sample of 5% of randomly selected employees from each office location, Employees who are randomly selected by a computer from a list of all company employees and Employees who have worked for the company for more than 10 years.

Options (A),(C) and (D) are correct.

A sizable business has locations around the nation. The company's facilities director was tasked with asking employees about their office furnishings. Instead of polling every worker at the company, the director chose to select a sample. We are supposed to find the groups which would be most representative of the opinions of all employees in the company.

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Option D is correct, the proportion for corresponding sides is 12/4 = 24/8.

According to the statement

we have given that the two rectangle which are similar to each other and we have to find the correct proportion for corresponding sides of rectangles.

So, we know that the

For the two rectangles to be similar, it means the ratio of their corresponding sides must be the same.

Looking at the two rectangles, the corresponding sides are pf the rectangles are:

4 m side corresponds to 8 m side in rectangle A

12m side corresponds to the 24 m side in rectangle B.

Then

The ratios of the both rectangles are:

In rectangle A is 8/4 = 2

In rectangle B is 24/12 = 2

From this it is clear that the ratios are equal.

Thus, the scale factor is 2

Since 8/4 = 24/12, we can rearrange to get;

12/4 = 24/8.

So, Option D is correct, the proportion for corresponding sides is 12/4 = 24/8.

Disclaimer: This question was incomplete. Please find the full content below.

Question:

The two rectangles are similar with sides 4 m side corresponds to 8 m side in rectangle A and 12m side corresponds to the 24 m side in rectangle B.which is the correct proportion for corresponding sides?

A. 12/3 = 24/12.

B. 12/2 = 27/8.

C. 11/4 = 23/8.

D. 12/4 = 24/8.

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The surface area of the larger sphere is equal to 636.365 square centimeters.

In this question we must estimate the surface area of the smaller sphere. By geometry we know that the volume of a sphere is directly proportional to the cube of its radius and the surface area is directly proportional to the square of radius, then the volume to surface area ratio is equal to:

V/A = k · r      (1)

Where:

Then, we can derive the following relationship between the two spheres by eliminating the proportionality constant:

V/(A · r) = V'/(A' · R)     (2)

Where:

First, we need to determine the radii of the spheres:

Larger radius

R = ∛(3 · V' / 4π)

R = ∛(3 · 647 / 4π)

R ≈ 5.365 cm

Smaller sphere

r = ∛(3 · V / 4π)

r = ∛(3 · 87 / 4π)

r ≈ 2.749 cm

Lastly, we find the surface area of the larger sphere:

A · r · V' = A' · R · V

A' = (A · r · V') / (R · V)

A' = (167 · 2.749 · 647) / (5.365 · 87)

A' = 636.365 cm²

The surface area of the larger sphere is equal to 636.365 square centimeters.

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❄ Hi there,

let us combine the like terms and create an equivalent expression –

[tex]\large\begin{gathered} \sf{9+a-5b-2} \\\sf{9-2+a-5b}\\\sf{7+a-5b} \end{gathered}[/tex]

That's as far as we can go.

❄

The missing dimension in the figure given in the question is 9 ft

Diameter of small circle / Diameter of big circle = Height of small / Height of Big

24 / d = 8 / 36

Cross multiply

d × 8 = 24 × 36

d × 8 = 864

Divide both sides by 8

d = 864 / 8

d = 108 in

Divide by 12 to express in feet

d = 108 / 12

d = 9 ft

Thus, the missing dimension is 9 ft

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If the solids are similar, then their lengths/dimensions are proportional.

24 inches / 8 inches = d / 3 feet

---Cross Multiply

8d = 72

d = 9 feet

Hope this helps!