MATHEMATICS HIGH SCHOOL

Which events are independent? Select each correct answer. A)A spinner is spun and a coin is flipped.
B)One ball is drawn from a bag of balls after another ball is drawn without replacement.
C)Two number cubes are rolled at the same time.
D)White marbles are drawn from a bag of marbles without replacing the marbles

Answers

Answer 1

Answer:

Answer:

Independent events are those events when the happening of one event does not affect the happening the other event.

In the given example we have the following events as independent:

A) A spinner is spun and a coin is flipped

C) Two number cubes are rolled at the same time.

Both these events are independent because the happening of one event does not affect the other in both the cases.

But the options B and D are not independent because in both the cases happening of first event affects the happening of the next event. Therefore, the correct options are A and C.

Answer 2

Answer:

Answer:

A) A spinner is spun and a coin is flipped

C) Two number cubes are rolled at the same time

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The shoe size for all the pairs of shoes in a person’s close are recorded. 7,7,7,7,7,7,7,7,7,7A. What is the mean? B. What is the standard deviation?
How to solve this ?
Three families shared the cost of purchasing a $5,000 generator. The martins paid 1/3 of the cost and the millers paid 40% and the browns paid the rest how much did the brown pay
What is 3.36 rounded to the nearest hundreth

What is the area of this polygon?

Answers

The middle is a square with side length of 12cm

Area of the square = 12 x 12 = 144 cm^2

There are 4 triangles with base of 13cm and height of 8 cm

Area of triangle = 1/2 x base x height

Area = 1/2 x 12 x 8 = 48cm^2 each

48 x 4 = 192 cm^2

Total area = 144 + 192 = 336 cm^2

If its £18.75 per square metre of clear plastic how much will it cost to cover 2x notice boards 1 metre high and 1 metre wide ?

Answers

just double 18.75 because the total area needed to cover is 2 square meters

Find the value of c such that each expression is a perfect-square trinomial.Please show steps on all thank you!
1. x^2-16x+c
2. p^2-14p+c
3. b^2+18b+c
4. n^2-n+c

Answers

$(a\pm b)^2=a^2\pm2ab+b^2\n\n1.\ x^2-16x+c=x^2-2x\cdot8+c\to c=8^2=64\n\nx^2-16x+64=x^2-2x\cdot8+8^2=(x-8)^2\n\n\n2.\ p^2-14p+c=p^2-2p\cdot7+c\to c=7^2=49\n\np^2-14p+49=p^2-2p\cdot7+7^2=(p-7)^2$

$3.\ b^2+18b+c=b^2+2b\cdot9+c\to c=9^2=81\n\nb^2+18b+81=b^2+2b\cdot9+9^2=(b+9)^2\n\n\n4.\ n^2-n+c=n^2-2n\cdot(1)/(2)\to c=((1)/(2))^2=(1)/(4)\n\nn^2-n+(1)/(4)=n^2-2n\cdot(1)/(2)+((1)/(2))^2=(n-(1)/(2))^2$

Niki makes the same payment every two months to pay off his $61,600 loan. The loan has an interest rate of 9.84%, compounded every two months. If Niki pays off his loan after exactly eleven years, how much interest will he have paid in total? Round all dollar values to the nearest cent.

Answers

The question is an annuity question with the present value of the annuity given.
The present value of an annuity is given by PV = P(1 - (1 + r/t)^-nt) / (r/t) where PV = $61,600; r = interest rate = 9.84% = 0.0984; t = number of payments in a year = 6; n = number of years = 11 years and P is the periodic payment.
61600 = P(1 - (1 + 0.0984/6)^-(11 x 6)) / (0.0984 / 6)
61600 = P(1 - (1 + 0.0164)^-66) / 0.0164
61600 x 0.0164 = P(1 - (1.0164)^-66)
1010.24 = P(1 - 0.341769) = 0.658231P
P = 1010.24 / 0.658231 = 1534.78
Thus, Niki pays $1,534.78 every two months for eleven years.
The total payment made by Niki = 11 x 6 x 1,534.78 = $101,295.48
Therefore, interest paid by Niki = $101,295.48 - $61,600 = $39,695.48

Answer:

answer is A on edge

Step-by-step explanation:

What is the simplest form of the expression (–11.7y – 3.3x) + 1.2x + (5.2y + x)? –16.9y – 5.5x –16.9y – 4.5x –6.5y – 2.1x –6.5y – 1.1x

Answers

Answer:

(D) $-6.5y-1.1x$

Step-by-step explanation:

The given expression is:

$(-11.7y-3.3x)+1.2x+(5.2y+x)$

Upon simplifying the above equation, we get

$-11.7y-3.3x+1.2x+5.2y+x$

Rewriting the above expression by writing the like terms together, we have

$-11.7y+5.2y-3.3x+1.2x+x$

Solving the like terms, we get

$-6.5y-1.1x$

which is the required simplified form of the given expression..

Hence, option (D) is correct.

Answer:

Step-by-step explanation:

Solve the following system using a matrix.

7a - b = -1
-4a - 2b = -2

Answers

Answer:

a = 0, b = 1

Step-by-step explanation:

Given system equation is,

7a - b = -1

-4a - 2b = -2

Since, the matrix form of this system of equation is,

$\begin{bmatrix} 7& -1\n -4 & -2\end{bmatrix}\begin{bmatrix}a\nb\end{bmatrix}=\begin{bmatrix}-1\n -2\end{bmatrix}$

Let,

$A=\begin{bmatrix} 7& -1\n -4 & -2\end{bmatrix}$

$X=\begin{bmatrix}a\n b\end{bmatrix}$

$B=\begin{bmatrix}-1\n -2\end{bmatrix}$

$\because AX = B\implies X = A^(-1)B$

$adj(A) = \begin{bmatrix} -2& 1\n4& 7\end{bmatrix}$

Also,

|A| = -18

$\implies A^(-1)=-(1)/(18)\begin{bmatrix} -2& 1\n4& 7\end{bmatrix}$

$\implies X = -(1)/(18)\begin{bmatrix} -2& 1\n4& 7\end{bmatrix}.\begin{bmatrix}-1\n -2\end{bmatrix}$

$X=-(1)/(18)\begin{bmatrix}2-2\n -4-14\end{bmatrix}$

$X=-(1)/(18)\begin{bmatrix}0\n -18\end{bmatrix}$

$X=\begin{bmatrix}0\n 1\end{bmatrix}$

$\implies \begin{bmatrix}a\n b\end{bmatrix}=\begin{bmatrix}0\n 1\end{bmatrix}$

By comparing,

a = 0, b = 1

1. a=-1+b/7 is the right answer. First you had to add by b from both sides of equation, and it gave us, $7a-b+b=-1+b$ . And then simplify, and it gave us, $7a=-1+b$ . Divide by 7 from both sides of equation, and it gave us, $(7a)/(7)=-(1)/(7)+ (b)/(7)$ . Finally simplify, and it gave us the answer is a=-1+b/7 is the right answer.

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2. a=-b-1/2 is the right answer. First you had to add by 2b from both sides of equation, and it gave us, $-4a-2b+2b=-2+2b$ . And then simplify, and it gave us, $-4a=-2+2b$ . Next you can also divide by -4 from both sides of equation, and it gave us, $(-4a)/(-4)=-(2)/(-4)+(2b)/(-4)$ . Finally simplify, and it gave us the answer is a=-b-1/2 is the right answer. Hope this helps! And thank you for posting your question at here on brainly, and have a great day. -Charlie

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