MATHEMATICS HIGH SCHOOL

Can someone help me with this math question

Answers

Answer 1

Answer:

Answer:

The coordinates of D' are (1,-1)

Step-by-step explanation:

The point D in the figure has co-ordinates (2,-2) as shown in the figure.

The figure is dilated by a factor of 1/2

So, multiply the coordinates of D (2,-2) by 1/2

D' = (1/2*2, 1/2*-2)

D' = (1,-1)

So, the coordinates of D' are (1,-1)

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Your literature class will read 4 novels this year, chosen by class vote from a list of 7 possible books offered by the teacher.a) How many different ways could the course unfold, given that it probably matters what order you read the books in?
b) How many different choices of books could the class make?
a) The number of different ways the course could unfold is

Answers

Answer:

a) 840 different ways

b) 35 different choices of books

Step-by-step explanation:

We know that our literature class will read a total of 4 novels this year.

All novels chosen by class vote from a list of 7 possible books offered by the teacher.

Wherever we have an experiment $''N''$ which is formed by sub - experiments that can occurred in $m_(1),m_(2),...,m_(n)$ ways, the total number of ways in which the whole experiment $''N''$ can be developed is :

$m_(1)$ x $m_(2)$ x ... x $m_(n)$

Then, for a) if it matters what order we read the books in, the total number of different ways could the course unfold is :

$(7).(6).(5).(4)=840$ (I)

Because for the first book there are 7 different choices. Now, given that we choose the first book, we only have 6 different choices for the second one.

Continuing with the idea, we deduce the equation (I).

For item b) :

Wherever we have $''n''$ different objects and we want to find the ways that we can choose $''r''$ objects from that group, we need to use the combinatorial number.

We define the combinatorial number as :

$nCr=\left(\begin{array}{c}n&r\end{array}\right)=(n!)/(r!(n-r)!)$

Then, if we apply this to the problem, the total different choices of books if we want 4 novels voting from a total of 7 possible books is :

$7C4=(7!)/(4!(7-4)!)=35$

a) 840 different ways

b) 35 different choices of books

Final answer:

The number of different ways the course could unfold is 210, and the number of different choices of books the class could make is 35.

Explanation:

The number of different ways the course could unfold is equal to the number of permutations of the 4 books chosen from the list of 7. This can be calculated using the formula for permutations: P(n, r) = n! / (n - r)!. In this case, n = 7 (the number of books) and r = 4 (the number of books chosen). Using the formula, we get P(7, 4) = 7! / (7 - 4)! = 7! / 3! = 7 imes 6 imes 5 = 210.

The number of different choices of books the class could make is equal to the number of combinations of the 4 books chosen from the list of 7. This can be calculated using the formula for combinations: C(n, r) = n! / (r! (n - r)!). In this case, n = 7 (the number of books) and r = 4 (the number of books chosen). Using the formula, we get C(7, 4) = 7! / (4! (7 - 4)!) = 7! / (4! imes 3!) = (7 imes 6 imes 5) / (4 imes 3 imes 2) = 35.

Learn more about Combinations and Permutations here:

brainly.com/question/19917646

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Molly is writing a paper for her history class. To complete her paper, Molly must spend 2 hours on research and 1 hour writing each page. She writes the expression p + 2 where p equals the number of pages . Use the expression to evaluate the number of hours needed for 10 pages and evaluate the number of hours needed for 19 pages . Please help

Answers

9 hour if you add and muilpy it

Jambalaya is a Cajun dish made from chicken, sausage, and rice. Simone is making a large pot of jambalaya for a party. Chicken costs $6 per pound, sausage costs $3 per pound, and rice costs $1 per pound. She spends $42 on 13.5 pounds of food. She buys twice as much rice as sausage. How much chicken, sausage, and rice will she use in her dish?Can someone please show me how to make this into 3 algebraic equations. I should be good from there. I would really appreciate it.

Answers

$x- amount\ of\ chicken-\ cost\ 6\$\ per\ pound\n y-amount\ of sausage\ - cost\ 3\$\ per\ pound\n z-amount\ of rice-\ cost\ 1\$\ per\ pound \n\n x+y+z=13,5\ and\n 6*x+3*y+1z=42 \ and\n z=2y\n\n First\ substitude\ z=2y\ to \ both\ equations:\n \left \{ {{x+y+2y=13,5} \atop {6x+3y+2y=42}} \right. \n\n \left \{ {{x+3y=13,5} \atop {6x+5y=42}} \right. |First\ equation\ multiply\ by\ -6\n\n \left \{ {{-6x-18y=-81 } \atop {6x+5y=42}} \right.|Adding\ equations\n \+\ -\ -\ -\ -\ -\ -\- \n -13y=-39|:-13$ $y=3\n x+3y=13,5\n x+3*3=13,5\n x=13,5-9=4,5\n x=4,5\n z=2y\n z=2*3=6\n She\ will \ use \ 4,5\ pounds\ of\ chicken, \ 3\ pounds\ of\ sausage\n and\ 6\ pounds\ of \ rice$

A ball is dropped form a height of 100 inches. The ball bounces, each time reaching a lower and lower height. The height of each bounce is 75% of the previous bounce. What height will the ball reach after bouncing four times? How many bounces does it take for the ball to reach a height of less than one inch?

Answers

After the 'n'th bounce, the ball returns to a maximum height of

   (100) times (0.75)^n .

-- After 4 bounces, the maximum height is (100) (0.75)^4 = 31.64 inches.

-- To look for the maximum height of 1 inch,    (100) (0.75)^x = 1

Let's take the log of each side: log(100) + x log(0.75) = 0

Subtract log(100) from each side: x log(0.75) = -log(100)

Divide each side by log(0.75) :     x = -log(100) / log(0.75).

log(100) = 2 . So ... x = -2 / log(0.75) = -2 / -0.124939 = 16.00785

So the ball returns to a slim hair more than 1 inch high on the 16th bounce,
and returns to definitely less than 1 inch high on the 17th bounce.

75% of a number is as much as 3/4 of the same number, so:

1st bounce: 3/4 * 100 = 75
2nd bounce: 3/4 * 75 = 56,25
3rd bounce: 3/4 * 56,25 = 42,1875
4th bounce: 3/4 * 42,1875 = 31,640625
5th bounce: 3/4 * 31,640625 = 23,73046875
6th bounce: 3/4 * 23,73046875 = 17,7978515625
7th bounce: 3/4 * 17,7978515625 = 13,348388671875
8th bounce: 3/4 * 13,348388671875 = 10,01129150390625
9th bounce: 3/4 * 10,01129150390625 = 7,508468627929688
10th bounce: 3/4 * 7,508468627929688 = 5,631351470947266
11th bounce: 3/4 * 5,631351470947266 = 4,223513603210449
12th bounce: 3/4 * 4,223513603210449 = 3,167635202407837
13th bounce: 3/4 * 3,167635202407837 = 2,375726401805878
14th bounce: 3/4 * 2,375726401805878 = 1,781794801354408
15th bounce: 3/4 * 1,781794801354408 = 1,336346101015806
16th bounce: 3/4 * 1,336346101015806 = 1,002259575761855
17th bounce: 3/4 * 1,002259575761855 = 0,7516946818213909

Answers:

After bouncing four times, the ball will reach a height of 31,640625 inches.
The ball will reach a height of less than one inch after 17 bounces.

PS: I know it's kind of a walk-around, by it still gives us the answer :)

What are the domain, range, and asymptote of h(x) = (0.5)x – 9?domain: {x | x > 9}; range: {y | y is a real number}; asymptote: y = 9

domain: {x | x > –9}; range: {y | y is a real number}; asymptote: y = –9

domain: {x | x is a real number}; range: {y | y > 9}; asymptote: y = 9

domain: {x | x is a real number}; range: {y | y > –9}; asymptote: y = –9

Answers

Answer:

Option 4 - domain: {x | x is a real number}; range: {y | y > –9}; asymptote: y = –9

Step-by-step explanation:

Given : $h(x)=(0.5)^x-9$

To find : What are the domain, range, and asymptote of h(x) ?

Solution :

Domain of the function is where the function is defined

The given function $h(x)=(0.5)^x-9$ is an exponential function

So, the domain of the function is,

$D=(-\infty,\infty) , x|x\in \mathbb{R}$

i.e, The set of all real numbers.

Range is the set of value that corresponds to the domain.

Let $y=(0.5)^x-9$

If $x\rightarrow \infty , y\rightarrow -9$

If $x\rightarrow -\infty , y\rightarrow \infty$

So, The range of the function is

$R=(-9,\infty) , y|y>-9$

The asymptote of the function,

Exponential functions have a horizontal asymptote.

The equation of the horizontal asymptote is when

$x\rightarrow \infty$

$y=(0.5)^\infty-9$

$y=-9$

Therefore, Option 4 is correct.

Domain: {x | x is a real number}; range: {y | y > –9}; asymptote: y = –9

Among the choices provided above the domain, range, and asymptote of h(x) = (0.5)x – 9 is the below:

domain: {x | x is a real number}; range: {y | y > –9}; asymptote: y = –9

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Anthony earned $131 in tips last night while working at the restaurant. If his tipsconsisted of $1 bills and $5 bills only and he counted 47 bills in total, then how
many $5 bills did Anthony receive?

Answers

Answer:21 5 dollar bills

Step-by-step explanation:

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