1.1 Beth, Carolyn and George love reading their favourite bedtime stories together.
They take it in turns to read a page, always in the order Beth, then Carolyn, then George.
All twenty pages of the story are read on each occasion.
One evening, Beth is staying at Grandma's house but Carolyn and George still read the
same bedtime story and take it in turns to read a page with Carolyn reading the first
page.
In total, how many pages that Carolyn and George read are the same as the pages that
they would read if Beth was there?

Answer:

D. x = 20

Step-by-step explanation:

All angles equal 180°

x + 5 + 7x -5 + x = 180

Combine like terms

9x = 180

Divide both sides by 9

x =20

To find the number of points at which the graph of the function intersects the x-axis, we need to find the roots of the equation:

4x^2 - 9x + 9 = 0

We can use the quadratic formula to find the roots:

x = (-b ± sqrt(b^2 - 4ac)) / 2a

In this case, a = 4, b = -9, and c = 9, so:

x = (-(-9) ± sqrt((-9)^2 - 4(4)(9))) / 2(4)

x = (9 ± sqrt(81 - 144)) / 8

x = (9 ± sqrt(-63)) / 8

Since the discriminant is negative, the roots are complex and the graph does not intersect the x-axis. Therefore, the answer is b. 0.

The fraction of Year 7 students can be found by dividing y7 by the total number of students, which is 11 times the number of staff members; using the ratio of y8 to y7, we get y7/(11S) = 5/8.

Let's denote the number of staff members as S and the number of students as T. Since the ratio of staff to students is 1:10, we have:

S:T = 1:10

We can rewrite this as S = (1/11)T and T = 11S, where S is the number of staff members and T is the total number of students.

Let's denote the number of Year 7 students as y7 and the number of Year 8 students as y8. Since all students are either in Year 7 or Year 8, we have:

[tex]y7 + y8 = T[/tex]

Substituting T = 11S, we get:

[tex]y7 + y8 = 11S[/tex]

The ratio of y8 to y7 is 3:2, which means that:

[tex]y8:y7 = 3:2[/tex]

We can rewrite this as y8 = (3/5)y7. Substituting this expression into the equation y7 + y8 = 11S, we get:

[tex]y7 + (3/5)y7 = 11S[/tex]

Simplifying, we get:

[tex](8/5)y7 = 11S[/tex]

Dividing both sides by 11S, we get:

[tex]y7/(11S) = 5/8[/tex]

Therefore, the fraction of Year 7 students is 5/8.

The ratio of staff to students is 1:10, so S:T = 1:10, which can be rewritten as S = (1/11)T and T = 11S.

Let y7 and y8 be the number of Year 7 and Year 8 students, respectively. Then y7 + y8 = 11S.

The ratio of y8 to y7 is 3:2, so [tex]y8 = (3/5)y7[/tex].

Substituting [tex]y8 = (3/5)y7[/tex] into [tex]y7 + y8 = 11S[/tex], we get [tex](8/5)y7 = 11S[/tex].

Dividing both sides by 11S, we get [tex]y7/(11S) = 5/8[/tex].

Therefore, the fraction of Year 7 students is 5/8.

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Yes, there is direct relatiοn in amοunt οf dry dοg fοοd and the amοunt οf wet dοg fοοd.

If amοunt οf dry dοg fοοd  is x and the amοunt οf wet dοg fοοd is y then the relatiοn is given as: x = 3y

Tο determine whether the relatiοnship between the amοunt οf dry dοg fοοd and the amοunt οf wet dοg fοοd is prοpοrtiοnal, we need tο check whether the ratiο οf the twο quantities remains cοnstant.

A) yes, there is direct relatiοn in amοunt οf dry dοg fοοd and the amοunt οf wet dοg fοοd. as amοunt οf dry dοg fοοd increases there alsο increase in amοunt οf wet gοοd.

if amοunt οf dry dοg fοοd  is x and the amοunt οf wet dοg fοοd is y then the relatiοn is given as:

x = 3y

fοr example lets take values frοm first rοw

4.5 = 3 × 1.5

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Complete question:

Answer:50x-12

Step-by-step explanation:

We need to get rid of parentheses in this term.

All the negative factors will change sign.

In our example, we have 2 negative factors.

The sign of the term will not change, since there is an even number of negative factors.

Answer:

Step-by-step explanation:where are you ???

Answer:

The equation that can be transformed into the following equation 2x + 4 = 6x + 2 is:

2(2x+5)= 4x + x + 2

Therefore, the equation 2(2x+5)= 4x + x + 2 can be simplified and transformed to the form of 2x + 4 = 6x + 2.

Step-by-step explanation:

1. 36g+9-5g=31g+9

2. 12x-4g+4x=16x-4g

3. 15h-6g

4. 2h-6g

5. 60g-20f

Answer:

31g+9, 16x-4g,15h-6g, 2h-6g, 20(3g-f)

Step-by-step explanation:

Q.1  9(4g+1)-5g=36g+9-5g

                =31g+9

Q.2  4(3x-g)+4g=12x-4g+4x

                         =16x-4g

       or 4(4x-g)

Q.3  3(5h-2g)=15h-6g

Q.4   2(h-3g)=2h-6g

Q.5   5(12g-4f)=60g-20f

or                    =20(3g-f)

Answer:

16

Step-by-step explanation:

6q-12=84

    6q=96

      q=16

Answer:

q = 16

Step-by-step explanation:

First Step: Add 12 to both sides. giving you 96.

Second Step: Divide both sides by 6 giving you 16.

Solution: q = 16.

Given that it is not raining, there is a [tex]10.67[/tex]% probability that a man is holding an umbrella, or around [tex]0.1067[/tex].

As probabilistic arguments sometimes produce outcomes that appear contradictory or counterintuitive, probability is usually regarded as one of the most challenging topics of mathematics.

Probability is the likelihood that something will occur or the probability that something will happen. Probability is the measure of how probable it is that a coin will land heads up after being tossed into the air.

To find [tex]P(B|A)[/tex],

[tex]P(B|A) = P(A and B) / P(A)[/tex]

[tex]P(B|A) = P(A|B) * P(B) / P(A)[/tex]

Putting it all together,

[tex]P(A|B) = P(B|A) * P(A) / P(B)[/tex]

[tex]= [P(A|B) * P(B)] / P(A)[/tex]

[tex]= [P(A and B) / P(B)] * P(A) / P(A)[/tex]

[tex]= P(A and B) / P(B)[/tex]

Therefore,

[tex]P(B|A) = P(A and B) / P(A)[/tex]

[tex]= P(A) * P(B|A) / P(B)[/tex]

[tex]= 0.4 * (1 - 0.75) / 0.75[/tex]

[tex]= 0.1067[/tex]

So the probability that a person is carrying an umbrella given that it's not raining is approximately [tex]0.1067[/tex], or about [tex]10.67[/tex]%.

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The amount Jennifer paid for the gasoline is closest to $43.51.

This is because we can multiply the number of gallons by the cost per gallon to get the total cost, which in this case is 14.75 x 2.95 = 43.5125. Rounding this to two decimal places, we get $43.51, which is the closest answer option.

In general, when calculating the total cost of gasoline, we need to know the number of gallons purchased and the cost per gallon. These two values can be multiplied together to find the total cost of the gasoline. So here the answer is $43.51.

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The probability of flipping a coin and getting tails is 50%.

This is because in a fair coin toss, there is an equal chance of getting heads or tails. This means that the probability of each outcome is 50%.

To prove this experimentally, you flipped the coin 16 times and got heads 7 times. This means that out of the 16 times, you got heads 7 times and tails 9 times. Therefore, the probability of getting tails is 9/16, which is the same as 50%.

In general, the probability of flipping a coin and getting tails is always 50%, no matter how many times the coin is flipped or what the result of previous flips were. This is because each flip of the coin is an independent event and has the same probability of being heads or tails.

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In response to the supplied query, we may state that Consequently, to equation create 4 gallons of a 15% salt solution, we must combine 1.67 gallons of the 8% salt solution with 2.33 gallons of the 20% salt solution.

A mathematical equation links two statements and utilises the equals sign (=) to indicate equality. In algebra, an equation is a mathematical assertion that proves the equality of two mathematical expressions. For instance, in the equation 3x + 5 = 14, the equal sign separates the numbers by a gap. A mathematical formula may be used to determine how the two sentences on either side of a letter relate to one another. The logo and the particular piece of software are usually identical. like, for instance, 2x - 4 = 2.  

We know that 0.08x gallons of salt, or 8% of x gallons, is in the 8% salt solution.

Since we are adding x gallons of the 8% salt solution to a total of 4 gallons of the final solution, we know that 20% of (4 - x) gallons is salt, or 0.2(4 - x) gallons of salt, for the 20% salt solution.

0.08x + 0.2(4 - x) = 0.15(4) (4)

We can condense things and find x:

0.08x + 0.8 - 0.2x = 0.6

-0.12x = -0.2

x = 1.67

Consequently, to create 4 gallons of a 15% salt solution, we must combine 1.67 gallons of the 8% salt solution with 2.33 gallons of the 20% salt solution.

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The two ships are separating at a rate of 25 knots when the second ship has traveled 90 nautical miles.

To find the rate at which the two ships are separating, we can use the Pythagorean Theorem to find the distance between the two ships at any given time.

The distance between the two ships is the hypotenuse of a right triangle, with one leg being the distance traveled by the first ship and the other leg being the distance traveled by the second ship.

Let d1 be the distance traveled by the first ship and d2 be the distance traveled by the second ship. Then the distance between the two ships is given by:

d = √(d1^2 + d2^2)

Since the first ship is traveling at 20 knots and the second ship is traveling at 15 knots, we can write:

d1 = 20t
d2 = 15t

Substituting these expressions into the equation for the distance between the two ships, we get:

d = √((20t)^2 + (15t)^2)

Simplifying, we get:

d = √(400t^2 + 225t^2)

d = √(625t^2)

d = 25t

So the distance between the two ships is increasing at a rate of 25 knots.

When the second ship has traveled 90 nautical miles, we can find the time t by setting d2 = 90 and solving for t:

15t = 90
t = 6

At this time, the distance between the two ships is:

d = 25t = 25(6) = 150 nautical miles

So, the two ships are separating at a rate of 25 knots when the second ship has traveled 90 nautical miles.

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Using trigonometric ratio, the height of kite above the ground is approximately 65.90 feet.

What is trigonometric ratio?

Triangle side length ratios are known as trigonometric ratios. In trigonometry, these ratios show how the ratio of a right triangle's sides to each angle. Sine, cosine, and tangent ratios are the three fundamental trigonometric ratios.

Distance of hand above the ground = 2.5 feet

String length form hand = 150 feet

Angle of elevation = 25°

We can use the sine function of trigonometric ratios to solve this problem.

The formula for sine function is -

sin θ = opposite / hypotenuse

Let's call the height of the kite above the ground "h".

Then we have -

sin (25°) = (h - 2.5) /150

0.42261 = (h - 2.5) /150

(h - 2.5) = 63.392

h = 65.892

Rounding to the nearest hundredth of a foot, we get -

h ≈ 65.90 feet

Therefore, the kite is about 65.90 feet above the ground.

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See below for the explanation

---------------------------------------------------------------

I'll go through the possible answer choices.

To summarize, choices A through E lead to results that aren't 81, so we must eliminate them. There's nothing left to pick, so your teacher must have made a typo somewhere. You'll need to ask her/him for further clarification.

Answer:

Step-by-step explanation:

You want the coefficients of the quadratic with roots (3±2i√3)/2 and a leading coefficient of 4.

The value b/a is the opposite of the sum of the roots.

  b/a = -((3+2i√3)/2 +(3-2i√3)/2) = -(3/2 +3/2) = -3

  b = -3a = -3(4)

  b = -12

The value c/a is the product of the roots. This will be the difference of squares:

  c/a = (3+2i√3)/2 × (3-2i√3)/2 = (3² -(2i√3)²)/4 = (9 +12)/4 = 21/4

  c = a(21/4) = (4)(21/4)

  c = 21

Answer:

110

Step-by-step explanation:

Basically, in area, we do length x width.

So, All we had to do is do 11 (length) x 10 (width)

And the answer is 110!

(I think this is right?)

What must be true for the triangles to be similar to each other by SAS is: y = z, and c/f = a/e, where y = z = 50°; c = 4, f = 3; a = 8; e = 6.

SAS stands for "side-angle-side", which means that if two triangles have two pairs of corresponding sides that are proportional in length and the included angles between them are congruent, then the triangles are similar.

Therefore, for the triangles to be similar by SAS, we would have:

y = z, and

c/f = a/e

Assigning values, we would have:

y = z = 50°

c/f = 4/3

a/e = 8/6

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The exact value of x is ±8√2. However, since x represents a length, the positive square root is the appropriate solution. Thus, x = 8√2.

A triangle is a two-dimensional geometric shape that is formed by three straight lines or segments that connect three non-collinear points. These points are called the vertices of the triangle, and the line segments are called its sides. The sides of a triangle may be of different lengths and can form different angles with each other.

Let the side of the triangle be AB, and let the perpendicular from C to AB divide AB into segments of length 4 and 16, with the shorter segment adjacent to A. Let the foot of the perpendicular be D. Then, we have:

AC = 4 + 16 = 20 (by the segment addition postulate)

AD = 4 (given)

CD = 16 (given)

By the Pythagorean theorem, we have:

AC² = AD² + CD²

Simplifying and substituting the values we have:

20² = 4² + 16²

400 = 16 + 256

400 = 272 + x² [where x is the height of the perpendicular]

Subtracting 272 from both sides, we get:

128 = x²

Taking the square root of both sides (since x cannot be negative), we get:

x = ±√128

Simplifying:

x = ±8√2

Therefore, the exact value of x is ±8√2. However, since x represents a length, the positive square root is the appropriate solution. Thus, x = 8√2.

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The average number οf siblings fοr this grοup is 1.3.

Tο find the average number οf siblings fοr this grοup, we need tο calculate the tοtal number οf siblings and divide by the tοtal number οf children.

The 5 children whο said they are an οnly child have 0 siblings each, sο they cοntribute 0 tο the tοtal.

The 3 children whο said they have 1 sibling οnly have 1 sibling each, sο they cοntribute 3 tο the tοtal.

The 4 children whο said they have exactly 2 siblings have 2 siblings each, sο they cοntribute 8 tο the tοtal.

The 3 children whο said they have exactly 3 siblings have 3 siblings each, sο they cοntribute 9 tο the tοtal.

Therefοre, the tοtal number οf siblings is 0 + 3 + 8 + 9 = 20.

The tοtal number οf children is 15.

Sο, the average number οf siblings is 20/15, which is apprοximately 1.3 (rοunded tο the nearest tenth).

Therefοre, the average number οf siblings fοr this grοup is 1.3.

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At the end of 1 year, the amount in the account will be 16443.4. To sum up, compound interest is a type of interest calculated on the initial principal and the accumulated interest of the previous periods.

The formula for calculating compound interest is [tex]A = P (1 + r/n)^nt,[/tex]where A is the future value of the account, P is the principal amount, r is the interest rate, n is the number of times the interest is compounded per year and t is the number of years.In the given case, the principal amount is 15000, the interest rate is 9% per annum and the number of times the interest is compounded is 12. Therefore, the future value of the account at the end of 1 year will be[tex]A = 15000 (1 + (9/100)/12)^12x1 A = 15000 (1 + 0.0075)^12A = 15000 (1.0075)^12 A = 15000 x 1.0956A = 16443.4[/tex]Therefore, at the end of 1 year, the amount in the account will be 16443.4. . In the given case, the future value of the account at the end of 1 year will be 16443.4.Step 1:Calculate the monthly interest rate:Interest rate per month = [tex]9% / 12 = 0.75%[/tex],Step 2:Calculate the total amount at the end of the year:Total amount =[tex]15000 x (1 + 0.75%) ^ 12[/tex] Total amount = 15000 x 1.0975, Total amount =[tex]$16,462.50[/tex]

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By following the steps outlined below, you can create a payroll payslip that provides all of the necessary information and helps ensure that your employees are paid accurately and on time.

Open Excel and create a new workbook. In the first row, create headings for the different columns you will need, such as "Employee Name," "Employee ID," "Pay Period," "Gross Pay," "Deductions," "Net Pay," and so on.

Enter the employee's name, ID, and pay period in the appropriate cells.

Calculate the employee's gross pay. Gross pay is the total amount of money the employee earned before any deductions are taken out.

Calculate the employee's deductions. Deductions are the amounts that are taken out of the employee's pay, such as taxes, social security, health insurance, and so on.

Calculate the employee's net pay. Net pay is the amount of money the employee receives after all deductions are taken out. To calculate this, subtract the total amount of deductions from the gross pay.

Once you have calculated all of the necessary amounts, enter them into the appropriate cells on the payslip.

Finally, you can customize the payslip by adding your company logo, address, and other relevant information. You can also format the cells to make the payslip look more professional.

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Complete Question:

How do I create a payroll payslip in Excel?

Answer:

• (0,12)

• (1,6)

• (9,8)  

• (-2,19)

• (8,3)    

Step-by-step explanation:

See the attached graph.

The two inequalities are graphed and the points that are solutions to both equations are all those in the purple area of the graph (the result of the red and blue solutions that overlap [= purple]).  The individual points are added to find which points do, or do not, fall within the solution set of both inequalities:

• (0,12)   Yes

• (-2,0)    No

• (-6,13)    No

• (1,6)      Yes

• (9,8)     Yes

• (-2,19)   Yes

• (8,3)      Yes

• (0,10)     No

Answer:

divide by hundred

Step-by-step explanation:

example :

convert to percentage 300

300÷ 100= 3%

The 'Pclass' predictor seems to be the best predictor of fare, as it was seen that the average fare increases as the passenger class increases.

The average fare in each category can be calculated by calculating the average fare for each category of the categorical predictors (excluding the first four). For example, for the 'Sibsp' predictor, the average fare can be calculated by taking the sum of all fares for each category and dividing it by the total number of passengers in that category.

The boxplots can then be used to visualize the average fares for each category of the categorical predictors. From the boxplots, it can be seen that the 'Pclass' predictor seems to be the best predictor of fare, as the average fare increases as the passenger class increases. Specifically, the average fare for passenger class 1 is much higher than that for passenger class 2 and 3, confirming that 'Pclass' is the best predictor of fare.

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Complete question:

Which categorical predictor is most effective for predicting the fare of an airline ticket?

Question: Is -451 in the sequence bellow?

15, 7, -1, -9, -17, ...

-451 not in the sequence

This question involves the concepts of arithmetic progression.

Which consists of adding the previous term to a certain ratio (r), which will be found the next term.

Data to calculate

r = 7-15=-8

an = -451

a1= 15

n=?

[tex]\begin{array}{l}\sf a_{n} = a_{1} + ( n-1 )r\\\sf -451 = 15 + ( n-1 )\times(-8)\\\sf -451=15-8x+8\\\sf -451 = 23-8n\\\sf 8n=23+451\\\sf 8n=474\\\sf n=\dfrac{474}{8}\\\sf n=59{,}25\end{array}[/tex]

The result is not an integer, so -451 is not part of the sequence

Answer:

• B. True

Step-by-step explanation:

The value of P(A and B) is 0.24.

What is Conditional probability?

Conditional probability is a type of probability that describes the likelihood of an event occurring given that another event has already occurred. It is calculated by dividing the probability of the joint occurrence of both events by the probability of the occurrence of the event that has already occurred.

More formally, if we have two events A and B, the conditional probability of event A given event B is denoted by P(A|B) and is defined as:

P(A|B) = P(A and B) / P(B)

We are given :

P(A)=0.6, P(B)=0.4, and P(B|A)=0.4

We can use the formula for conditional probability to solve :

P(B|A) = P(A and B) / P(A)

We can write it as :

P(A and B) = P(B|A) * P(A)

Now, Substituting in the given values, we get:

P(A and B) = 0.4 * 0.6 = 0.24

Therefore, the probability of both events A and B occurring is 0.24.

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