Find the product of -7-i and its complex conjugate

Answer:

Option d) [tex]P=\frac{4}{17}[/tex]

Step-by-step explanation:

we know that

The probability of an event is the ratio of the size of the event space to the size of the sample space.  

The size of the sample space is the total number of possible outcomes  

The event space is the number of outcomes in the event you are interested in.  

so  

Let

x------> size of the event space

y-----> size of the sample space  

so

[tex]P=\frac{x}{y}[/tex]

In this problem we have

[tex]x=13-1=12[/tex]

[tex]y=52-1=51[/tex]

substitute

[tex]P=\frac{12}{51}[/tex]

Simplify

[tex]P=\frac{4}{17}[/tex]

Answer:

Days, Hours

Step-by-step explanation:

1 day  = 24 hours

2 days = 48 hours

3 days = 72 hours  

4 days = 96 hours

(its increasing by 24)

Answer:

The slope is 2

Step-by-step explanation:

The slope is equal to

m = (y2-y1)/(x2-x1)

   = (-2-2)/(-1-1)

   = -4/-2

   = 2

Answer:

x = - 1

Step-by-step explanation:

Given

3x + 2 = y and y = - 1

Substitute y = - 1 into the equation and solve for x, that is

3x + 2 = - 1 ( subtract 2 from both sides )

3x = - 3 ( divide both sides by 3 )

x = - 1

This is verified by the point on the graph with coordinates (- 1, - 1)

Method 1: By substitution

Step 1: In the equation 3x + 2 = y when you see a y replace it with -1

3x + 2 = -1

Step 2: Combine like terms by subtracting 2 to both sides

3x + (2-2) = -1 - 2

3x = -3

Step 3: Isolate x by dividing 3 to both sides

[tex]\frac{3x}{3} = \frac{-3}{3}[/tex]

x = -1

Method 2: By looking at the graph

To solve this way you see where the line on the graph has y = -1 and look for its complimentary x

If you look at the graph attached below you can see that at y = -1 the x also equals -1

x = -1

Hope this helped!

The answer is your mom. Nah it’s B)10

For this case we have that the perimeter of the figure is given by the sum of its sides, they tell us that the perimeter is 62 feet.

So:

Let "x" be the variable that represents the length of the unlabeled wall, so the perimeter is:

[tex]x + 8 + 5 + 13 + 18 + 8 = 62[/tex]

We find the value of "x":

[tex]x = 62-8-5-13-18-8\\x = 10[/tex]

Thus, the length of the unlabeled wall is 10 feet.

Answer:

Option B

The initial number of carbon-14 atoms in the organism at the time of death was 200 atoms.

The initial number of carbon-14 atoms in the organism at death can be calculated using the formula for exponential decay:

[tex]\[ N(t) = N_0 e^{-\lambda t} \][/tex]

where:

- [tex]\( N(t) \)[/tex] is the number of undecayed carbon-14 atoms at time [tex]\( t \),[/tex]

- [tex]\( N_0 \)[/tex] is the initial number of carbon-14 atoms at time \[tex]( t = 0 \[/tex]) (the time of death),

- [tex]\( \lambda \)[/tex] is the decay constant for carbon-14,

- [tex]\( t \)[/tex] is the time that has passed since the time of death.

 Given that after 5730 years (the half-life of carbon-14), the number of undecayed carbon-14 atoms is half the initial amount, we can write:

[tex]\[ \frac{N_0}{2} = N_0 e^{-\lambda \times 5730} \][/tex]

To find the decay constant [tex]\( \lambda \)[/tex], we use the half-life formula:

[tex]\[ \lambda = \frac{\ln(2)}{t_{1/2}} \][/tex]

 where [tex]\( t_{1/2} \)[/tex] is the half-life of carbon-14, which is 5730 years. Plugging in the values:

[tex]\[ \lambda = \frac{\ln(2)}{5730} \][/tex]

Now, we can solve for [tex]\( N_0 \)[/tex]using the information provided:

[tex]\[ 100 = N_0 e^{-\frac{\ln(2)}{5730} \times 573[/tex]

 Since [tex]\( e^{-\ln(2)} = \frac{1}{2} \)[/tex], the equation simplifies to:

[tex]\[ 100 = N_0 \times \frac{1}{2} \][/tex]

Solving for [tex]\( N_0 \):[/tex]

[tex]\[ N_0 = 100 \times 2 \][/tex]

[tex]\[ N_0 = 200 \][/tex]

 Therefore, the initial number of carbon-14 atoms in the organism at the time of death was 200 atoms.

Answer:

C. Children who weigh more spend more time on studying for achievement test .

Step-by-step explanation:

Correlation is a measure of relationship , mutual co-interdependence (fluctuation) between two quantitative variables .

Direct / Positive (+) correlation means the variables are directly related - one increase , other increase & one increase , other decrease .                                         Inverse / Negative (-) correlation means the variables are inversely related - one increase , other decrease & one decrease, other increase .                       It lies between -1 to +1 . Correlation more than + 0.5 implies Strong correlation, less than that implies Weak correlation.

The correlation between above variables - weight and achievement test score is 0.9734 i.e there is Strong Positive relationship . So , increase in one strongly leads to increasing trend in other

Answer:

B) As age increases, so do body weight and achievement test scores.

Step-by-step explanation:

Hello There!

The first one seems alright.

The second one it would be 1/2.

This is because half of the options have “R” on them.

Answer: 1. is 5/6

2. is 1/2

Step-by-step explanation:

Answer:

14/23

Step-by-step explanation:

The total number of marbles is 6 + 8 + 9 = 23.

The probability of yellow or red is:

P(yellow or red) = P(yellow) + P(red)

P(yellow or red) = 8/23 + 6/23

P(yellow or red) = 14/23

Answer:

8 in 23 chance of picking a yellow marble

6 in 23 chance of picking a red marble

Explanation:

Firstly, we must determine the total number of marbles. To do this, we add all the marbles together:

6+8+9 = 23

Since the question says we have 8 yellow marbles, that means 8/23 marbles are yellow. Therefor, you would have a 8 in 23 chance (8/23) of picking a yellow marble. Similarly, the question states that we have 6 red marbles. Meaning 6/23 marbles are red. So, one would have a 6 in 23 or 6/23 chance of picking a red marble.

Answer:

x = 8

Step-by-step explanation:

Given

6x + 4(3x - 7) = 116 ← distribute the parenthesis on the left side

6x + 12x - 28 = 116 ← collect like terms on left side

18x - 28 = 116 ( add 28 to both sides )

18x = 144 ( divide both sides by 18 )

x = 8

Answer:

a) The sold games of Jezebel had the greatest spread.

b) The middle 50% of the games sold by Colin has the least spread.

c) Jezebel sold more games than colin.

Step-by-step explanation:

Range is sued to calculate the spread of the given data.

Range is given by:

Range=Max Value-Min Value

So,

Part a)

For Collin:

Range=21-3=18

For Jezebel:

Range=26-5=21

Part b)

Middle 50% of the values will be the values between 1st quartile and 3rd quartile

So, to find quartiles:

For Colin:

=3,9,9,14,15,16,17,20,21

The median is 15.

The lower half is 3,9,9,14

Q1 = (9+9)/2= 18/2 = 9

The upper half is 16,17,20,21

Q3 = (17+20)/2= 37/2= 18.5

The middle 50% is first quartile subtracted from third quartile

So, the spread is:

18.5-9=9.5

For Jezebel:

4,5,8,10,11,14,20,20,26

The median is 11.

The lower half is 4,5,8,10

Q1 = (5+8)/2=13/2=6.5

The upper half is 14,20,20,26

Q3 = (20+20)/2=40/2=20

The middle 50% values' spread is:

20-6.5=13.5

Part c) The answer to part a tells us that Jezebels sold games have more spread than Colin's sold games. Similarly the answer of part b tells us that the spread of middle 50% values of Jezebel's sold games was more than the spread of middle 50% values of Colin's sold games ..

Answer:

8+4n=height of tree in 4 years

Step-by-step explanation:

start of with 8

then every year add N feet

4 years times n feet + what we started with(8)

and you get 8+4n

The height of the tree, in feet, 4 years from now can be calculated as 8 + 4n, where n is the number of feet the tree grows each year.

The subject of this question is a mathematical problem involving height growth over time, specifically about a tree that grows at a constant rate each year. In this case, the height of a tree in the future can be represented by a simple equation which considers the current height of the tree (8 feet), the rate of growth each year (n feet per year), and the number of years in the future we want to calculate for (4 years). The formula to calculate the height of the tree 4 years from now is:

Future Height = Current Height + Growth Rate * Time

Plug in the values we know:

Future Height = 8 feet + n feet/year * 4 years

So, the height of the tree, in feet, 4 years from now is 8 + 4n.

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ANSWER

[tex](1-7x)(1+9x) =- 63 {x}^{2} + 2x + 1[/tex]

EXPLANATION

The given product is (1-7x)(1+9x).

Expand using the distributive property.

[tex](1-7x)(1+9x) = 1(1 + 9x) - 7x(1 + 9x)[/tex]

[tex](1-7x)(1+9x) = 1 + 9x - 7x - 63 {x}^{2}[/tex]

Simplify to obtain:

[tex](1-7x)(1+9x) = 1 + 2x - 63 {x}^{2}[/tex]

You can rewrite in standard form to get,

[tex](1-7x)(1+9x) =- 63 {x}^{2} + 2x + 1[/tex]

Answer:

1+2x-63x^2

Step-by-step explanation:

factor 1(1+9x)=1+9X

-7x(1+9x)=-7x-63x^2

add 1+9x-7x-63x2

Answer:

Step-by-step explanation:

2nd one

Answer:

3x+5

Step-by-step explanation:

i took test

Answer:

60 out of 250 children will prefer organized sports.

Step-by-step explanation:

We are given the results of a random survey of children between the ages of 13 and 18 about their favorite activity.

Based on these results, we are to find the number of children who will prefer organized sports if 250 children were asked about their favorite activity.

Children who will prefer organized sports = [tex]\frac{37}{155} \times 250[/tex] = 60

Answer:

m∠8 = 124°

Step-by-step explanation:

1. Find m∠1

m∠1 and m∠2 are supplementary, since they are on the same line.

That means m∠1 + m∠2 = 180.

Plug in: 4x + 2x - 6 = 180

Simplify + subtract: 6x = 186

Divide: x = 31

Plug in: m∠1 = 4(31) --> m∠1 = 124°

2. Since ∠1 and ∠4 are vertical, they are congruent. Since ∠4 and ∠8 are corresponding on parallel lines, they are also congruent. Therefore, ∠1 and ∠8 are congruent, which means m∠1 = m∠8

Plug in: m∠8 = 124°

Given the expression y^3 + x, upon substituting y = 1 and x = 6 into the equation, the resultant value of the expression is 7.

The question requires finding the value of the expression y3 + x when x = 6 and y=1. Since y is equal to 1, y3 (1 cubed) is also 1. So the expression becomes 1 + 6, which equals 7. Therefore, the value of the expression y3 + x for y = 1 and x = 6 is 7.

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Final answer:

The value of the expression  [tex]y^3 + x[/tex] for x = 6 and y = 1 is 7, which is found by substituting the values into the expression and performing the arithmetic operations.

Explanation:

To find the value of the expression [tex]y^3 + x[/tex]for x = 6 and y = 1, you simply substitute the given values into the expression and perform the arithmetic operations.

Here's the step-by-step calculation:

Replace y with 1: (1)3 + 6.

Calculate 1 cubed, which is 13 = 1.

Add the result to x, where x is 6: 1 + 6.

The final answer is 7.

This means that the value of the expression [tex]y^3 + x[/tex]when x = 6 and y = 1 is 7.

There are 16 oz in a pound, so 2 lbs is 32 oz.

Answer: two pounds is equivalent to 32 ounces.

Step-by-step explanation: 1 pound is equal to 16 ounces, and since 2 is 1 two times, just multiply 16 by 2, 16x2=32 ounces

Answer:

Simple interest = $1,000(.10)(3) = $300

Compound interest =

$1,000(1.05)² - $1,000 = $102.50

ANSWER

D) (a + 1, b + m)

EXPLANATION

The given line passes through (a,b) and has slope m.

The equation is:

[tex]y - b = m(x - a)[/tex]

When x=a+1, we obtain

[tex]y - b = m(a + 1 - a)[/tex]

This

[tex]y = m( 1 ) + b[/tex]

[tex]y = m + b[/tex]

Therefore,(a + 1, b + m) must also lie on this line.

The correct answer is D.

Answer:

d

Step-by-step explanation:

I got it correct

Durain beans cost $9 per pound and they sold 11 pounds.

Multiply the cost by the amount sold: 9 x 11 = $99

Subtract that from the total sold:

196 - 99 = $97

Now divide the amount left by the cost per pound for Ice cream beans:

97 / 10 = 9.7 pounds.

Round the answer as needed to match one of your choices.

Answer:

B

Step-by-step explanation:

rsu is equal to vst, so you can solve 5x+17=9x-11, which yields x=7.

So vst=52 and wsv=90-52=38.

Answer:

What is your question?

Is " n " to the left or the right?

How many units are on the number line?

It may be the number 3.

The values of n is a distance of 3 units from 1 1/2 on a number line are 4.5 units and -1.5units

The number line consists of positive values to the right of zero and negative values to the left.

Given the value 1 1/2 units, it is 1.5 units to the right of zero.

If the value of n is a distance of 3 units from 1 1/2 on a number line, the value of n can be 3 units to the right or to the left.

Valuee to the right  = 3 + 1.5 = 4.5units

Value to the left = 1.5 - 3 = -1.5 units

Hence the values of n is a distance of 3 units from 1 1/2 on a number line are 4.5 units and -1.5units

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Answer:

y = 0.10x + 8, $12

Step-by-step explanation:

y = monthly bill

x = number of message units

Each message unit costs $0.10, so the cost of x message units is 0.10x.  The phone adds $8 to the monthly bill.  Therefore:

y = 0.10x + 8

If x = 40, then:

y = 0.10 (40) + 8

y = 4 + 8

y = 12

The monthly bill is $12.

X is 4 and Y is 4 Square Root of 2 (or 5.656854)

For this case we have to define trigonometric relations of rectangular triangles that:

Then, according to the figure we have:

[tex]Sin (M) = \frac {3} {5}\\M = ArcSine (\frac {3} {5})[/tex]

[tex]M = 36.87[/tex] degrees

Answer:

36.87 degrees

Answer:

2=9

4=17

Step-by-step explanation:

4(2)+1

8+1=9

4(4)+1

16+1=17

[tex]

(2x^2+2x+3)-(x^2+2x+1) \\

2x^2+2x+3-x^2-2x-1 \\

\boxed{x^2+2}

[/tex]

Answer:

The answer is 75

Step-by-step explanation: