find the greatest common factor of 108d^2 and 216d

Answer:

[tex]\boxed{\sf C. \ 10}[/tex]

Step-by-step explanation:

[tex]\sf The \ intersecting \ chord \ theorem \ states \ that \ the \ products[/tex]

[tex]\sf of \ the \ lengths \ of \ the \ line \ segments \ on \ each \ chord \ are \ equal.[/tex]

[tex]NH \times HT = MH \times HY[/tex]

[tex](x+20) \times 8=12 \times 20[/tex]

[tex]\sf Expand \ brackets \ and \ multiply.[/tex]

[tex]8x+160=240[/tex]

[tex]\sf Subtract \ 160 \ from \ both \ sides.[/tex]

[tex]8x+160-160=240-160[/tex]

[tex]8x=80[/tex]

[tex]\sf Divide \ both \ sides \ by \ 8.[/tex]

[tex]\displaystyle \frac{8x}{8} =\frac{80}{8}[/tex]

[tex]x=10[/tex]

The value of x is 10.

We have a circle and inside it two chords MY and NT intersect at point H.

We have to find the value of x in the figure.

According to the intersecting chord theorem, when two chords say AB and CD intersect at point O, then

AO x OB = CO x OD

Applying the chord intersecting theorem to the figure in the question, we get -

MH x HY = NH x HT

12 x 20 = (x+20) x 8

240 = 8x + 160

8x = 80

x = 10

Hence the value of x is 10.

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Answer:

2. 20 oranges

3. 18 yellow tulips

4. 23 students

Step-by-step explanation:

a. The mean can be found using the AVERAGE() function.

x = 272.7

b. The standard deviation can be found with the STDEV() function.

s = 39.9

c. The t-score can be found with the T.INV.2T() function.  The confidence level is 0.04, and the degrees of freedom is 26.

t = 2.162

d. Find the lower and upper ends of the confidence interval.

Lower = 272.7 − 2.162 × 39.9 = 186.5

Upper = 272.7 + 2.162 × 39.9 = 358.9

Answer:

(a) O(x²)

(b) O(x²)

(c) O(x²)

(d) Not O(x²)

Step-by-step explanation:

If a function is O(x²), then the highest power of x in the function ia greater or equal to 2.

(a) 100x + 1000

This is O(x), not O(x²)

(b) 100x² + 1000

This is O(x²)

(c) x³.100 − 1000x²

This is O(x²)

(d) x log x²

This is not O(x²)

Answer:

[tex]\text{Critical Region} = z<-1.96\ \text{or}\ z>1.96[/tex]

Step-by-step explanation:

A test for the difference between two population means is to be performed.

As the population variances are known, the z-test will be used.

The hypothesis can be defined as follows:

H₀: μ₁ = μ₂ vs. Hₐ: μ₁ ≠ μ₂

Assume that the significance level of the test is, α = 0.05.

The critical region can be defined as follows:

The critical value of z for α = 0.05 is:

[tex]z_{\alpha/2}=z_{0.05/2}=z_{0.025} =-1.96\\\\z_{1-\alpha/2}=z_{1-0.05/2}=z_{0.975} =1.96[/tex]

Use a z-table.

[tex]\text{Critical Region} = z<-1.96\ \text{or}\ z>1.96[/tex]

Answer:

a) What is the cost of a chicken shawarma wrap?

$10.99

b) What is the cost of one order of spiced potatoes?

$4.99

c) If x denotes the cost of a chicken shawarma wrap and y denotes the cost of an order of spiced potatoes, what are the equations needed to solve this problem?

3x + 2y = $42.95 .............Equation 1

5x + 4y = $74.91 ................Equation 2

Step-by-step explanation:

Let x denotes the cost of a chicken shawarma wrap and y denotes the cost of an order of spiced potatoes,

Cost of a chicken sharwarma wrap = x

Cost of an order of spiced potatoes = y

Ms. Ironperson ordered 3 chicken shawarma wraps and 2 orders of spiced potatoes for a total bill of $42.95.

3x + 2y = $42.95 .............Equation 1

Mr. Thoro ordered 5 chicken shawarma wraps and 4 orders of spiced potatoes for a total bill of $74.91.

5x + 4y = $74.91 ................Equation 2

Hence, the Equations needed to solve the question is:

3x + 2y = $42.95 .............Equation 1

5x + 4y = $74.91 ................Equation 2

We use Elimination method to solve for this.

Multiply Equation 1 by coefficient of x in Equation 2

Equation 2 by coefficient of x in Equation 1

3x + 2y = $42.95 .............Equation 1 × 5

5x + 4y = $74.91 ................Equation 2 × 3

15x + 10y = 214.75..............Equation 3

15x + 12y = 224.73..............Equation 4

Subtract Equation 3 from Equation 4

2y = 9.98

y = 9.98/2

y = 4.99

Therefore, y = Cost of an order of spiced potatoes = $4.99

Subtitute 4.99 for y in Equation 1

3x + 2y = $42.95 .............Equation 1

3x +2(4.99) = 42.95

3x + 9.98 = 42.95

3x = 42.95 - 9.98

3x = 32.97

x = 32.97/3

x = 10.99

x = Cost of a chicken sharwarma wrap = $10.99

Therefore,

The cost of a chicken sharwarma wrap = $10.99

The cost of an order of spiced potatoes = $4.99

Answer:

Hello the options to your question is missing below are the options

 A) if sample means were obtained for a long series of samples, approximately 95 percent of all sample means would be between 10 and 16 miles

B.the unknown population mean is definitely between 10 and 16 miles

C.if these intervals were constructed for a long series of samples, approximately 95 percent would include the unknown mean commute distance for all Californians

D.the unknown population mean is between 10 and 16 miles with probability .95

Answer : if these intervals were constructed for a long series of samples, approximately 95 percent would include the unknown mean commute distance for all Californians  ( c )

Step-by-step explanation:

95%  confidence

interval = 10 to 16 miles

To have 95% confidence signifies that if these intervals were constructed for a long series of samples, approximately 95 percent would include the unknown mean commute distance for all Californians

confidence interval covers a range of samples/values in the interval and the higher the % of the confidence interval the more precise the interval is,

Answer:

b=2.7

Step-by-step explanation:

using sine rule,,,

Step-by-step explanation:

So for this problem, we need the missing angle A. From there, we can use the law of sines to compute length of b.

So the sum of the interior angles of a triangle is 180. With that in mind, we can make an equation to fine the measure of angle A.

53 + 80 + A = 180

133 + A = 180

A = 47

Now that we have the angle of A, we can use the law of sines to fine the length of b.

b / sin(B) = a / sin(A)

b = sin(B) * a / sin(A)

b = sin(80) * 2 / sin(47)

b = 2.693

Now round that to the nearest tenth to get

b = 2.7

Cheers.

Answer:

Put 1/10 in the box.

Step-by-step explanation:

Since, Bluepoint and Milford are at same distance from Weston, the distance further than this to Oakdale is 1/10 miles.

Best Regards!

Answer:

To Oakdale to Milford:

2/5 mi

Step-by-step explanation:

1/10 + 3/20 + 3/20

1/10 = 2/20

then;

2/20 + 3/20 + 3/20 = (2+3+3)/20 = 8/20

8/20 = 2/5

Answer:

-3x - 7y = 36

Step-by-step explanation:

The given line -3x - 7y = 10 has an infinite number of parallel lines, all of the form -3x - 7y = C.

If we want the equation of a line parallel to -3x - 7y = 10 that passes through (-5, -3), we substitute -5 for x in -3x - 7y = 10 and substitute -3 for y in -3x - 7y = 10:

-3(-5) - 7(-3) = C, or

15  + 21 = C, or C = 36

Then the desired equation is -3x - 7y = 36.

Answer:

The equation to be solved is missing in the question.

I will explain power series and ways to find the radius and interval of convergence of a powers series in the attached image.

Step-by-step explanation:

Now, it look like there is some information missing in the answer. The whole problem should look like this:

Alicia Keys's new album As I Am is climbing the charts, and the manager of Tip Top Tunes expects to sell a lot of copies. Because she has limited shelf space, she can't put out all her copies of the CD at once. On Monday morning, she stocked the display with 40 copies. By the end of the day, some of the copies had been sold. On Tuesday morning, she counted the number of copies left and then added that many more to the shelf. In other words, she doubled the number that was left in the display. At the end of the day, she discovered that she had sold the exact same number of copies as had been sold on Monday. On Wednesday morning, the manager decided to triple the number of copies that had been left in the case after Tuesday. Amazingly, she sold the same number of copies on Wednesday as she had on each of the first two days! But this time, at the end of the day the display case was empty. How many copies of the As I Am CD did she sell each day?

Answer:

She sold 24 copies of the cd each day.

Step-by-step explanation:

In order to solve this problem we must first set our variable up. In this case, since we need to know what the number of sold cd's per day is, that will just be our variable:

x= Number of copies sold.

So we can start setting our equation up. So we take the first part of the problem:

"On Monday morning, she stocked the display with 40 copies. By the end of the day, some of the copies had been sold."

This can be translated as:

40-x

where this expression represents the number of copies left on the shelf by the end of monday.

"On Tuesday morning, she counted the number of copies left and then added that many more to the shelf."

so we represent it like this:

(40-x)+(40-x)

"In other words, she doubled the number that was left in the display."

so the previous expression can be simplified like this:

2(40-x)

"At the end of the day, she discovered that she had sold the exact same number of copies as had been sold on Monday."

so the expression now turns to:

2(40-x)-x   this is the number of copies left by the end of tuesday.

"On Wednesday morning, the manager decided to triple the number of copies that had been left in the case after Tuesday."

this translates to:

3[2(40-x)-x]

This is the number of copies on the shelf by the begining of Wednesday.

"Amazingly, she sold the same number of copies on Wednesday as she had on each of the first two days! But this time, at the end of the day the display case was empty."

this piece of information lets us finish writting our equation:

3[2(40-x)-x] -x = 0

since there were no copies left on the shelf, then the equation is equal to zero.

So now we proceed and solve the equation for x:

3[2(40-x)-x] -x = 0

We simplify it from the inside to the outside.

3[80-2x-x]-x=0

3[80-3x]-x = 0

we now distribute the 3 so we get:

240-9x-x=0

we combine like terms so we get:

240-10x=0

we move the 240 to the other side of the equation so we get:

-10x=-240

and divide both sides into -10 so we get:

x=24

so she sold 24 copies each day.

Step-by-step explanation:

sorry but u should provide with a diagram for better understanding of ur question

Answer:

22

Step-by-step explanation:

We can write an equation:

(7+13+10+x)/4=13

x represents the number that needs to be added to get an average of

(7+13+10+x)/4=13

(30+x)/4=13

30+x=52

x=22

The number is 22

Hope this helps! Have a wonderful day :)

Answer:

12 , 19 , 26 , 33

Here, n+7

12+7=19

19+7=26

So,

26+7=33

Hope you understand ❣

Step-by-step explanation:

12 , 19 , 26 , ?

Given

___________

a1= 12

a2= 19

a3 = 26

d= ?

a4 = ?

––——————

we can solve this by using formula from Ap .

But for this we have to find d

As we know that

common difference(d) = a2-a1 = 19 -12

= 7

so difference after every no is 7 so

a4 = a3 + d

= 26 +7

= 33

So 33 is ur answer mate

Hope it helps

Answer:

Stocks = $15,500

Bonds = $107,250

CD's = $47,250

Step-by-step explanation:

S + B + C = 170000

.0325S + .038B .067C = 7745

60,000 + C = b

S = $15,500

B = $107,250

C = $47,250

Answer:

f(g(9)) = 945/16

Step-by-step explanation:

To find f(g(x)), you have to substitute g(x) wherever there is an x in f(x).

g(x) = x + 3/4

f(x) = x² - 4x - 3

f(g(x)) = (x + 3/4)² - 4(x + 3/4) - 3

f(g(x)) = x² + 3/2x + 9/16 - 4x + 3 - 3

f(g(x)) = x² - 5/2x + 9/16 + 3 - 3

f(g(x)) = x² - 5/2x + 9/16

Now, put a 9 wherever there is an x in f(g(x)).

f(g(9)) = (9)² - 5/2(9) + 9/16

f(g(9)) = 81 - 5/2(9) + 9/16

f(g(9)) = 81 - 45/2 + 9/16

f(g(9)) = 117/2 + 9/16

f(g(9)) = 945/16

Answer:

204

Step-by-step explanation:

To simplify the shape, you can do multiple things. I've opted to shave down both prongs to take it from a 'T' shape to a rectangular prism.

For height of the prongs, take 4 from 6.

6 - 4 = 2

Divide by 2 as there are 2 prongs.

2 / 2 = 1

Remember L * W * H

6 * 3 * 1 = 18

Remember that there are two prongs!

3 + 4 = 7

6 * 7 * 4 = 168

168 + 2(18) = 204

Answer:

Step-by-step explanation:

Using the value for calculating the confidence interval as given;

CI = xbar + Z*σ/√n

xbar  is the mean = 37.14+42.86/2

xbar= 80/2

xbar = 40

Z is the z-score at the 90% confidence = 1.645

σ is the standard deviation

n is the sample size = 35

Given the confidence interval CI as [37.14, 42.86]

Using  the maximum value of the confidence interval to get the value of the standard deviation, we will have;

42.86 =  xbar + Z*σ/√n

42.86 = 40 + 1.645* σ/√35

42.86-40 = 1.645*σ/√35

2.86 = 1.645*σ/√35

2.86/1.645 = σ/√35

1.739 = σ/√35

1.739 = σ/5.92

σ= 1.739*5.92

σ = 10.295

Hence, the sample standard deviation of a pair of jeans is 10.295

Answer:

9 hours

Step-by-step explanation:

Since the group of men remains the same, number of hours is proportional to number of radios.

1300/26 = 450/h

h = 26 * 450 / 1300 = 9 hours

Answer:

The answer is below

Step-by-step explanation:

The box contains 5 red and 4 white balls.

A) The probability that at least 1 ball was​ red = P(both are red) + P(first is red and second is white) + P(first is white second is red)

Given that the first ball was (Upper A )Replaced before the second draw:

P(both are red) = P(red) × P(red) = 5/9 × 5/9 = 25/81

P(first is red and second is white) = P(red) × P(white) = 5/9 × 4/9 = 20/81

P(first is white and second is red) = P(white) × P(red) = 4/9 × 5/9 = 20/81

The probability that at least 1 ball was​ red = 25/81 + 20/81 + 20/81 = 65/81

B) The probability that at least 1 ball was​ red = P(both are red) + P(first is red and second is white) + P(first is white second is red)

Given that the first ball was not Replaced before the second draw:

P(both are red) = P(red) × P(red) = 5/9 × 4/8 = 20/72 (since it was not replaced after the first draw the number of red ball remaining would be 4 and the total ball remaining would be 8)

P(first is red second is white) = P(red) × P(white) = 5/9 × 4/8 = 20/72

P(first is white and second is red) = P(white) × P(red) = 4/9 × 5/8 = 20/72

The probability that at least 1 ball was​ red = 20/72 + 20/72 + 20/72 = 60/72

Answer:

C. Graph C

Step-by-step explanation:

In a scatter plot, a positive correlation coefficient suggests that as one variable increases the other increases as well, or as one decreases, the other decreases.

Also, the more clustered the data points are along the line of best fit, the higher the value of the coefficient, whether positive or negative.

Graph C shows a positive correlation because as the variable on the x-axis increases, the variable on the y-axis also increases. The data points are more clustered along the line if best fit, if we draw one. This suggest a positive correlation coefficient (r) as strong as 0.75.

Graph C has a correlation coefficient, r, that is closer to 0.75.

Answer: graph A ‼️

Step-by-step explanation:

Answer:

Option (C)

Step-by-step explanation:

Since angle 'a' is the inscribed angle of the given triangle

Therefore, angle measure of the intercepted arc will be equal to the double of the inscribed angle.

x = 2a ⇒ a = [tex]\frac{x}{2}[/tex]

By the tangent-chord theorem,

"Angle between a chord and tangent measure the half of the angle measure of intercepted minor arc"

[tex]\frac{x}{2}[/tex] = 40°

Therefore, a = [tex]\frac{x}{2}[/tex] = 40°

Option (C) will be the answer.

Answer:

3 mL

Step-by-step explanation:

The fluid level is called the concave meniscus. The adhesive force causes it to crawl up on the sides, but you should ignore that while reading the level.

Step-by-step explanation:

I(S) = aS / (S + c)

As S approaches infinity, S becomes much larger than c.  So S + c is approximately equal to just S.

lim(S→∞) I(S)

= lim(S→∞) aS / (S + c)

= lim(S→∞) aS / S

= lim(S→∞) a

= a

As S approaches infinity, I(S) approaches a.

[tex]\sf{\implies Range = Highest \: - lowest }[/tex]

→ Range of Lewistown = 74 - 64

→ Range of Lewistown = 10 .

→ Range of Hamersville = 71 - 55

→ Range of Hamersville = 16 .

☆ Range of Hamersville - Range of Lewistown

→ 16 - 10

→ 6

Answer → The range for Hamersville is 6 more than the range for Lewistown .

Answer:

14/20 or .7 or 70%

Step-by-step explanation:

Total Number of cards: 20

Number of Red cards: 6

The leftover cards: 20 -6 = 14

The probability of not getting a red = 14/20

14/20 as a decimal = 14/20 = 70/100 = .7

14/20 as a percent = 14/20 = 70/100 = 70%

Answer:

x = 1/e^-5 - 1

Step-by-step explanation:

–2 ln (x + 1) − 3 = 7

–2 ln (x + 1) = 10

ln (x + 1) = –5

x + 1 = e^-5

x = e^-5 - 1

x = 1/e^-5 - 1

the approximate value of x in the equation -2 ln(x + 1) - 3 = 7 is x ≈ -0.9933.

To solve the equation -2 ln(x + 1) - 3 = 7 for the approximate value of x, we will follow these steps:

1. Begin with the given equation: -2 ln(x + 1) - 3 = 7.

2. Move the constant term to the other side of the equation: -2 ln(x + 1) = 7 + 3.

3. Simplify: -2 ln(x + 1) = 10.

4. Divide both sides of the equation by -2 to isolate the natural logarithm term: ln(x + 1) = -5.

5. Rewrite the equation using the exponential form of natural logarithm: e⁻⁵ = x + 1.

6. Calculate the value of e⁻⁵: e⁻⁵ ≈ 0.0067.

7. Subtract 1 from both sides of the equation: x = 0.0067 - 1.

8. Simplify: x ≈ -0.9933.

Therefore, the approximate value of x in the equation -2 ln(x + 1) - 3 = 7 is x ≈ -0.9933.

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Answer:

rose. is. 18/2=9 years old

Answer:

Stephanie is 18years old and she is twice older than her sister

so rosa is 18÷2(since stephanie is twice older than rosa

so rosa is 9 years old