A man decides to take out $70 per month from his savings account. After 63 months, he has $2720 in his account. Identify the slope and point, then write a linear equation in point-slope form which models the amount in the savings account in terms of the number of months.

a) P(psychology student)  = 1/3. b) P(psychology or anthropology student)  = 5/6. c) P(not sociology student)= 5/6

(a) The probability of choosing a psychology student is the number of psychology students divided by the total number of students:

P(psychology student) = 4/(6+2+4) = 4/12 = 1/3

(b) The probability of choosing a psychology student or an anthropology student is the sum of the number of psychology and anthropology students divided by the total number of students:

P(psychology or anthropology student) = (4+6)/(6+2+4) = 10/12 = 5/6

(c) The probability of not choosing a sociology student is the number of non-sociology students divided by the total number of students:

P(not sociology student) = (6+4)/(6+2+4) = 10/12 = 5/6

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Answer:

The answer is "0.9102"

Step-by-step explanation:

P(student spell correct) = 0.6

P(student spell incorrect)=1-0.6=0.4

X=the pupil will be allowed to sit down after receiving three slaps on the hand Thus, X would assume Value

X=0 (student sit sans getting whacks)

X=1 (student sit down without receiving 1 whack) (student sit down without receiving 1 whack)

X=2 (student take a seat before receiving 2 whacks)

X=3 (student sit down after receiving 3 punches)

\(\to P(X)=0.6 \times 0.4^0 +0.6 \times 0.4 + 0.6 \times 0.4 ^2 + 0.6 \times 0.3^3\)

             \(=0.6 \times 1+0.24 + 0.6 \times 0.09 + 0.6 \times 0.027\\\\=0.6 +0.24 + 0.054 + 0.0162\\\\=0.9102\\\\\)

Considering the definition of perpendicular line, the equation of the perpendicular line that passes through the point (x, y) = (3, 1) and is perpendicular to the line 2x + 3y = 12 is y= 3/2x -7/2.

A linear equation o line can be expressed in the form y = mx + b

where

Perpendicular lines are lines that intersect at right angles or 90° angles. If you multiply the slopes of two perpendicular lines, you get –1.

In this case, the line is 2x+3y= 12. Expressed in the form y = mx + b, you get:

3y= 12 - 2x

y= (-2x +12)÷ 3

y= -2/3x +4

Since multiplying the slopes of two perpendicular lines, you get -1, and the line has a slope of -2/3, you get:

-2/3× slope perpendicular line= -1

slope perpendicular line= (-1)÷ (-2/3)

slope perpendicular line= 3/2

The line passes through the point (3, 1). Replacing in the expression for parallel line:

1= 3/2× (3) + b

1= 9/2 + b

1- 9/2 = b

-7/2= b

Finally, the equation of of perpendicular line is y= 3/2x -7/2.

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Answer:

Horse A will have traveled 20 feet farther

Step-by-step explanation:

Horse A has traveled 160 feet in 5 seconds, and Horse B has traveled 140 feet in 5 seconds, and 160-140=20

The population we're trying to predict is the population that is going to be Voters in our area, the where should probably be well as above our area, and the how now, generally speaking, we want to do a simple, random, or a random sample of some sort, random sample.

For instance, what you could do would be something like choose: random addresses in the area and send a survey, but sending a survey could introduce self-selection bias. So it would be ideal to visit in person basically and ask a few questions making sure the representative sample or how to ensure that we're getting a representative sample would be to, for instance, filter the random results and make sure that we have an even distance.

Ensure that there's an equal number within each quadrant of the town, basically split up the town.  Split towns into regions of populations or population densities and make sure we get the same proportion from each region.  However, we end up splitting the town into different regions. We show the proportion or show who is the most popular candidate in each 1 of the regions, so it could be something like this. That was supposed to be an alternative to a bar graph. The number of results for each different candidate depends on whether or not there's a sort of well-defined districts or areas in the town, but most sorts of relatively large cities have things like that. So the idea would be to represent not just the location, but also the information that you gain separately.

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Split up the town so that there are an equal amount in each of its four quadrants. Make sure we receive the same proportion from each region by dividing towns into population or population density regions. But ultimately, we divide the town into many parts. It might look something like this since we display the percentage or the candidate who is most supported in each location. That was meant to be a bar graph substitute. Whether or not a town has clearly defined districts or areas affects the amount of results for each candidate, although this is true of most types of moderately large cities.

The probability of drawing a king from a standard deck of 52 cards is 1/13.

In a standard deck of 52 playing cards, there are four kings: the king of hearts, the king of diamonds, the king of clubs, and the king of spades.

To find the probability of drawing a king, we need to determine the ratio of favorable outcomes (drawing a king) to the total number of possible outcomes (drawing any card from the deck).

The total number of possible outcomes is 52 because there are 52 cards in the deck.

The favorable outcomes, in this case, are the four kings.

Therefore, the probability of drawing a king is given by:

Probability = (Number of favorable outcomes) / (Number of possible outcomes)

= 4 / 52

= 1 / 13

Thus, the probability of drawing a king from a standard deck of 52 cards is 1/13.

This means that out of every 13 cards drawn, on average, one of them will be a king.

It is important to note that the probability of drawing a king remains the same regardless of any previous cards that have been drawn or any other factors.

Each draw is independent, and the probability of drawing a king is constant.

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Hey there!

The formula to find the perimeter of a rectangle is "P=2(l+w)".

Hope this helps!

Have a great day! :)

Answer:

formula to find the perimeter of rectangle is

hope it helps

stay safe healthy and happy.

The value of vertical asymptotes is, x = 9

And, The value of Horizontal asymptotes is,

y = - 4

We have to given that;

Expression is,

⇒ j (x) = 1/(x - 9) - 4

Now, We can simplify as,

⇒ j (x) = 1/(x - 9) - 4

⇒ j (x) = (1 - 4(x - 9)] / (x - 9)

⇒ j (x) = [1 - 4x + 36] / (x - 9)

⇒ j (x) = (- 4x + 37) / (x - 9)

Hence, For vertical asymptotes make denominator zero.

As, x - 9 = 0

x = 9

And, Here degree of numerator and denominator both are one.

Hence, Horizontal asymptotes is,

y = - 4 / 1

y = - 4

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Answer: The one that colored 1/4.

Step-by-step explanation: 1/4 is greater than 1/6.

Answer:

greater than 9 is the answer

Step-by-step explanation:

2x+5=11

The value of x that makes the line containing (1,2) and (5,3) perpendicular to the line containing (x,4) and (3,0) is x = 2.

To determine the value of x such that the line containing (1,2) and (5,3) is perpendicular to the line containing (x,4) and (3,0), we need to find the slope of both lines and apply the concept of perpendicular lines.

The slope of a line can be found using the formula:

slope = (change in y) / (change in x)

For the line containing (1,2) and (5,3), the slope is:

slope1 = (3 - 2) / (5 - 1) = 1 / 4

To find the slope of the line containing (x,4) and (3,0), we use the same formula:

slope2 = (0 - 4) / (3 - x) = -4 / (3 - x)

Perpendicular lines have slopes that are negative reciprocals of each other. In other words, if the slope of one line is m, then the slope of a line perpendicular to it is -1/m.

So, we can set up the equation:

-1 / (1/4) = -4 / (3 - x)

Simplifying this equation:

-4 = -4 / (3 - x)

To remove the fraction, we can multiply both sides by (3 - x):

-4(3 - x) = -4

Expanding and simplifying:

-12 + 4x = -4

Adding 12 to both sides:

4x = 8

Dividing both sides by 4:

x = 2

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Answer:

Step-by-step explanation:

Answer:

auxiliary lines

Step-by-step explanation:

1. 1 and -1 are two such rational numbers whose multiplicative inverse is same as they are.

2. absolute value is resembled using the formula : |x|

Here,

\(\hookrightarrow \sf |\dfrac{-3}{11} |\)

\(\hookrightarrow \sf \dfrac{3}{11}\)

final answer: 3/11

3.

\(\hookrightarrow \sf \dfrac{1}{2} \div \dfrac{3}{5}\)

\(\hookrightarrow \sf \dfrac{1}{2} * \dfrac{5}{3}\)

\(\hookrightarrow \sf \dfrac{5}{6}\)

4.

Associative property can only be used with addition and multiplication

Answer:

83 There is an elixir

total quantity of elixir = 500 mL

quantity of elixir use in one dose = 6 mL

number of dose in 500 mL = 500/6

83.333

Answer:

1 008.56628 US$ kkkkkkkkkk

Answer:

$43352.9053

Step-by-step explanation:

Not sure if this is what you wanted to do, but 1,207.43% of 83.53 is 43352.9053, So there you go.

In the given triangles m∠1 = 51°, m∠2 = 18°, m∠3 = 123° and ∠4 = 39°

A triangle is a three-sided closed-plane figure formed by joining three noncolinear points. Based on the side property triangles are of three types they are Equilateral triangle, Scalene triangle, and Isosceles triangle.

We know the sum of all the interior angles of a triangle is 180°.

∴ ∠1 + 72° + 57° = 180°.

∠1 + 129° = 180°.

∠1 = 180° - 129°.

∠1 = 51°.

Now, ∠2 + 72° = 90°.

∠2 = 90° - 72°.

∠2 = 18°.

Now, ∠1 + 90° + ∠4 = 180°.

51° + 90° + ∠4 = 180°.

∠4 = 39°.

Also, ∠2 + ∠3 + ∠4 = 180°.

18° + ∠3 + 39° = 180°.

∠3 = 180° - 57°.

∠3 = 123°.

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Answer:A. x= .100

Step-by-step explanation:because of the distance in miles

Answer: (In order)

25/4 / 6 1/4 = 1

3 1/7 / 2/7 = 11

5/4 / 1/4 = 5

11 1/4 / 9/4 = 5

8 1/4 / 3/4 = 11

3 1/3 / 10/3 = 1

Step-by-step explanation:

Answer:

13th term

Step-by-step explanation:

41 = 7n - 50

41 + 50 = 7n

91 = 7n

7n = 91

n = 91/7

n = 13

13th term has value 41

Answer:

n = 13

Step-by-step explanation:

7n - 50 = 41

Add 50 to both sides

7n = 41 + 50

7n = 91

Divide both sides by 7

n = 91/7

n = 13

To find the distance between two points A and B you can use the formula

So, in this case, you have

Therefore, the distance between these points is 7 units.

Graphically,

A(2,0) N(7,1) T(5, -4)

<3

Explanation

Step 1

Let

P1(1,-3)

slope=-1

Step 2

use the formula

replacing

I hope this helps you

Answer:

X= 180 Y= 360 Z= 374

Step-by-step explanation:

180*2=360

360+14=374

When translating a point we need to change its coordinates, in this case the problem wants us to add "2" to each coordinate, so the new position of the points will be the previous ones added by 2. Let's first calculate the new coordinates before drawing.

With the new coordinates in mind we can draw the new picture.

To subtract 47.96 from 320.041, you can align the decimal points and then subtract each digit from right to left.

First, write the numbers with the decimal points aligned:

320.041

- 47.960

Next, subtract the digits in the ones place, which is 1 minus 0, resulting in 1. Then, subtract the digits in the tenths place, which is 4 minus 6. Since 4 is less than 6, you need to borrow 1 from the digit to the left, making the 2 into a 1 and adding 10 to the 4, giving you 14. So, 14 minus 6 equals 8.

Continue subtracting each digit in the same way:

   320.041

-   47.960

= 272.081

Therefore, 320.041 minus 47.96 is equal to 272.081.

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Using DeMoivre’s theorem, the answer in regular form would be (5 + 5√3i)⁷ = -5000000 + 8660254.03i

The De Moivre's Theorem is used to simplify the computation of powers and roots of complex numbers and is used in together with polar form.

Convert the complex number to polar form. The polar form of a complex number is z = r(cos θ + isin θ),

r = |z|  magnitude of z

it becomes

r = √((5)² + (5√3)²) = 10

θ = arg(z) is the argument of z.

θ = atan2(b, a) = atan2(5√3, 5) = π/3

(5 + 5√3i) = 10 × (cos π/3 + i sin π/3)

De Moivre's theorem to raise the complex number to the 7th power

(5 + 5√3i)⁷

= 10⁷× (cos 7π/3 + i sin 7π/3)

= 10⁷ × (cos 2π/3 + i sin 2π/3)

Convert this back to rectangular form:

Real part = r cos θ = 10⁷× cos (2π/3) = -5000000

Imaginary part = r sin θ = 10⁷ × sin (2π/3) = 5000000√3 = 8660254.03i

∴  (5 + 5√3i)⁷ = -5000000 + 8660254.03i

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Answer:10^7 (1/2 - √3/2 i)

Step-by-step explanation:

To use DeMoivre's theorem, we first need to write the number in polar form. Let's find the magnitude and argument of the number:

Magnitude:

|5 + 5√(3i)| = √(5^2 + (5√3)^2) = √(25 + 75) = √100 = 10

Argument:

arg(5 + 5√(3i)) = tan^(-1)(√3) = π/3

So the number can be written in polar form as:

5 + 5√(3i) = 10(cos(π/3) + i sin(π/3))

Now we can use DeMoivre's theorem:

(5 + 5√(3i))^7 = 10^7 (cos(7π/3) + i sin(7π/3))

To simplify, we need to find the cosine and sine of 7π/3:

cos(7π/3) = cos(π/3) = 1/2

sin(7π/3) = -sin(π/3) = -√3/2

Explanation:

So the final answer in rectangular form is:

10^7 (1/2 - √3/2 i)

This is a valid example of stringing arguments together using conditional statements.

The first statement establishes a conditional relationship between Martin shooting the sheriff and Martin shooting first.

The second statement also establishes a conditional relationship, but this time between Martin using his best pistol and Martin shooting first.

By combining the two conditional statements, we can conclude that if Martin didn't use his best pistol, then he didn't shoot first.

This follows from the fact that not using his best pistol would mean Martin didn't shoot first (according to statement 2), and if he didn't shoot first, then he couldn't have shot the sheriff (according to statement 1).

Therefore, the conclusion of the argument, which is that if Martin didn't use his best pistol, then he didn't shoot the sheriff, follows logically from the two conditional statements.

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