There are 6 different cookies on a plate. James will choose 2 of these cookies to pack in his lunch. How many different pairs of 2 cookies can he choose from the 6?

Answer:

Step-by-step explanation:

In order to write the equation of the line perpendicular to the given line, we first have to know what the slope of the given line is, and there's no way to tell by looking at it in its current form, which is standard. We need to solve that equation for y to determine the slope of that line. Solving for y:

[tex]-3y=-4x+5[/tex] and

3y = 4x - 5 (just change all the signs so our y term isn't negative anymore...yes, you're "allowed" to do that!) and

[tex]y=\frac{4}{3}x-\frac{5}{3}[/tex] So we can see now that the slope of this line is 4/3. That means that the perpendicular slope is -3/4. Passing through the given point (3, 5):

[tex]y-5=-\frac{3}{4}(x-3)[/tex]* and

[tex]y-5=-\frac{3}{4}x+\frac{9}{4}[/tex] and

[tex]y=-\frac{3}{4}x+\frac{9}{4}+\frac{20}{4}[/tex] so

[tex]y=-\frac{3}{4}x+\frac{29}{4}[/tex]** and, in standard form:

4y = -3x + 29 and

3x + 4y = 29***

* : point-slope form

** : slope-intercept form

*** : standard form

Answer:

[tex](a)\ \sec^2(\theta) = 82[/tex]

[tex](b)\ \cot(\theta) = \frac{1}{9}[/tex]

[tex](c)\ \cot(\frac{\pi}{2} - \theta) = 9[/tex]

[tex](d)\ \csc^2(\theta) = \frac{82}{81}[/tex]

Step-by-step explanation:

Given

[tex]\tan(\theta) = 9[/tex]

Required

Solve (a) to (d)

Using tan formula, we have:

[tex]\tan(\theta) = \frac{Opposite}{Adjacent}[/tex]

This gives:

[tex]\frac{Opposite}{Adjacent} = 9[/tex]

Rewrite as:

[tex]\frac{Opposite}{Adjacent} = \frac{9}{1}[/tex]

Using a unit ratio;

[tex]Opposite = 9; Adjacent = 1[/tex]

Using Pythagoras theorem, we have:

[tex]Hypotenuse^2 = Opposite^2 + Adjacent^2[/tex]

[tex]Hypotenuse^2 = 9^2 + 1^2[/tex]

[tex]Hypotenuse^2 = 81 + 1[/tex]

[tex]Hypotenuse^2 = 82[/tex]

Take square roots of both sides

[tex]Hypotenuse =\sqrt{82}[/tex]

So, we have:

[tex]Opposite = 9; Adjacent = 1[/tex]

[tex]Hypotenuse =\sqrt{82}[/tex]

Solving (a):

[tex]\sec^2(\theta)[/tex]

This is calculated as:

[tex]\sec^2(\theta) = (\sec(\theta))^2[/tex]

[tex]\sec^2(\theta) = (\frac{1}{\cos(\theta)})^2[/tex]

Where:

[tex]\cos(\theta) = \frac{Adjacent}{Hypotenuse}[/tex]

[tex]\cos(\theta) = \frac{1}{\sqrt{82}}[/tex]

So:

[tex]\sec^2(\theta) = (\frac{1}{\cos(\theta)})^2[/tex]

[tex]\sec^2(\theta) = (\frac{1}{\frac{1}{\sqrt{82}}})^2[/tex]

[tex]\sec^2(\theta) = (\sqrt{82})^2[/tex]

[tex]\sec^2(\theta) = 82[/tex]

Solving (b):

[tex]\cot(\theta)[/tex]

This is calculated as:

[tex]\cot(\theta) = \frac{1}{\tan(\theta)}[/tex]

Where:

[tex]\tan(\theta) = 9[/tex] ---- given

So:

[tex]\cot(\theta) = \frac{1}{\tan(\theta)}[/tex]

[tex]\cot(\theta) = \frac{1}{9}[/tex]

Solving (c):

[tex]\cot(\frac{\pi}{2} - \theta)[/tex]

In trigonometry:

[tex]\cot(\frac{\pi}{2} - \theta) = \tan(\theta)[/tex]

Hence:

[tex]\cot(\frac{\pi}{2} - \theta) = 9[/tex]

Solving (d):

[tex]\csc^2(\theta)[/tex]

This is calculated as:

[tex]\csc^2(\theta) = (\csc(\theta))^2[/tex]

[tex]\csc^2(\theta) = (\frac{1}{\sin(\theta)})^2[/tex]

Where:

[tex]\sin(\theta) = \frac{Opposite}{Hypotenuse}[/tex]

[tex]\sin(\theta) = \frac{9}{\sqrt{82}}[/tex]

So:

[tex]\csc^2(\theta) = (\frac{1}{\frac{9}{\sqrt{82}}})^2[/tex]

[tex]\csc^2(\theta) = (\frac{\sqrt{82}}{9})^2[/tex]

[tex]\csc^2(\theta) = \frac{82}{81}[/tex]

Answer:

lx-3l

Step-by-step explanation:

negative in the abs means moving to the right

=========================================================

Explanation:

We start with the parent function y = |x|

Shifting it 3 units to the right will make the equation y = |x-3| and that's the equation of the green curve shown.

The x-3 is because each input is 3 units smaller than it used to be. Imagine the xy axis moved 3 units to the left while the V shaped graph stayed fixed in place. It would give the illusion the V shape moved while the xy axis stay fixed.

The graph doesn't shift up or down, so k = 0

The value of 'a' stays the same at a = 1.

Answer:

Average rate of change = 5

Step-by-step explanation:

Average rate of change of a function is defined by the expression over the interval a ≤ x ≤ b,

Average rate of change = [tex]\frac{f(b)-f(a)}{b-a}[/tex]

Using this rule for the average rate of change of the function (defined by the table) over the interval 4 ≤ x ≤ 5,

Average rate of change = [tex]\frac{f(5)-f(4)}{5-4}[/tex]

From the table,

f(5) = 10

f(4) = 5

Therefore, average rate of change of the function = [tex]\frac{10-5}{5-4}[/tex]

                                                                                    = 5

Answer:

=5

Step-by-step explanation:

Answer:

18 L

Step-by-step explanation:

a = 36,864 * (1/2)^(11)

a = 18

36 L of water will be left after 11 days

GP is a type of sequence where each succeeding term is produced by multiplying each preceding term by a fixed number .

Constituting an GP according to the question

36,864 , 18432 , 9216 , ...........

In order to find nth term  of an GP, formula used will be :

a(n) = a (r^(n-1))

considering above GP ,

a(n) = ? water left after 11 days

a = 36864

r= 18432 /36864 = 1/2

n = 11

a(n) = 36864 ((1/2)^(11-1))

  a(n) =   36

Hence 36 L of water will be left after 11 days

Learn more about GP:

https://brainly.com/question/4853032?referrer=searchResults

#SPJ2

Answer:

225cc

Step-by-step explanation:

the solution is attached to the picture.

The amount of the 10% solution should he use if the nurse mixes 90 cc of a 45% saline solution with a 10% saline solution is 225cc

Let the amount of 10% solution she should use be x.

If a nurse mixes 90 cc of a 45% saline solution with a 10% saline solution to produce a 20% saline solution, the equivalent equation will be:

90(0.45) + 0.1x = 0.2(90+x)

Simplify the resulting equation for "x"

40.5 + 0.1x = 18 + 0.2x
0.1x = 40.5 - 18
0.1x = 22.5
x = 225cc

Hence the amount of the 10% solution should he use if the nurse mixes 90 cc of a 45% saline solution with a 10% saline solution is 225cc

Learn more on proportion here: https://brainly.com/question/19994681

Answer:

Step-by-step explanation:

a)

The mean for ground floor is 20.67

The mean for balcony is 15.8

b)

the difference between the means is ground floor - balcony

20.67 - 15.8 = 4.87

You can talk about it yourself for part c

Answer and Step-by-step explanation:

Angle B' is congruent to Angle B.

The measure of an angle stays the same when dilating, translating, and other transformations.

#teamtrees #PAW (Plant And Water)

Answer:c

Step-by-step explanation:

c

Answer:

The margin of error is of 20, option B.

Step-by-step explanation:

Confidence interval concepts:

A confidence interval has two bounds, a lower bound and an upper bound.

A confidence interval is symmetric, which means that the point estimate used is the mid point between these two bounds, that is, the mean of the two bounds.

The margin of error is the subtraction between the bounds, divided by 2.

In this question:

Lower bound: 200

Upper bound: 240

Margin of error:

(240 - 200)/2 = 40/2 = 20

The margin of error is of 20, option B.

Answer:

The two minimum numbers = 5, 5

Step-by-step explanation:

Let the first number = x

let the second number = y

Their sum: x + y = 10

Sum of their squares:  = x² + y²

y = 10 - x

f(x) = x² + (10 - x)²

f(x) = x² + 100 - 20x  + x²

f(x) = 2x² - 20x  +  100

Find the derivative of f(x), to obtain the critical points;

f'(x) = 4x - 20

4x - 20 = 0

4x = 20

x = 5

The value of y is calculated as;

y = 10 - x

y = 10 - 5

y = 5

The two minimum numbers = 5, 5

Answer:

A

Step-by-step explanation:

t-3.2 ≤ 7.5

"at most" means less than or equal to

Answer:

B

Step-by-step explanation:

Hi there!

We are given the points (-1,2) and (3,3) and we need to find the slope.

The formula for slope calculated from two points is [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1}}[/tex], where ([tex]x_{1}[/tex],[tex]y_{1}[/tex]) and ([tex]x_{2}[/tex],[tex]y_{2}[/tex]) are points

since we have two points, we can substitute them into the formula, but let's label their values to avoid any confusion

[tex]x_{1}[/tex]=-1

[tex]y_{1}[/tex]=2

[tex]x_{2}[/tex]=3

[tex]y_{2}[/tex]=3

now substitute into the formula (m is the slope); remember: we have a negative number in this, so we'll be subtracting a negative.

m=[tex]\frac{3-2}{3--1}[/tex]

simplify

m=[tex]\frac{3-2}{3+1}[/tex]

m=[tex]\frac{1}{4}[/tex]

so B is your answer

Hope this helps! :)

Answer:

Question 4 is B and Question 5 is C

Step-by-step explanation:

Question 4 is B because the DIFFERENCE between the two terms is 15 therefore when you subtract the terms it must equal 15 so B could no be an answer. Also since they both equal 24 they both add up to 24

Answer:

150

Step-by-step explanation:

35÷7=5 therefore each 5 apples is equal to 1 orange

Answer:

150

Step-by-step explanation:

we're gonna compare ratios. if the initial ratio is 35/7, then we will need to make a similar one for this question. with apples on top, we'll write 'x/30' and cross multiply and solve to get 150

Answer:

let the number of adult tickets = x

Then the number of student tickets = 3x

Total tickets x+3x = 416

4x = 416

x = 416/4

x = 104

Therefore the number of adult tickets sold is 104

Step-by-step explanation:

Answer:

The 90% confidence interval for the mean is (170.87 , 189.13)

Step-by-step explanation:

Using the calculator we can easily calculate   the 90% confidence interval for the mean, the given values are:

mean=180

sx : 38.5

n : 50

c - Level : 0.90

Then the output will be [170.87 , 189.13]

Answer:

72 crayons

Step-by-step explanation:

8/3 × 27 = 72 crayons

Answer:

ur dog water kid *take the L dance

Step-by-step explanation:

cheese

Answer:

55%

Step-by-step explanation:

Just do 33/60 and multiply by 100

Answer:

Step-by-step explanation:

430

x4%

_________

$17.20+ $430= $447.20

9514 1404 393

Answer:

  D.  32 square units

Step-by-step explanation:

At 40% scale, the length is ...

  (20 units)×40% = 8 units

and the width is ...

  (10 units)×40% = 4 units

The area is the product of length and width, so is ...

  A = (8 units)(4 units) = 32 square units

Answer:

Step-by-step explanation:

If the radius of the circle is equal to

[tex]\sqrt{\frac{A}{3} }[/tex] and the area is given as 45, then

[tex]r=\sqrt{\frac{45}{3} }[/tex] which simplifies to

[tex]r=\sqrt{15}[/tex] and to the nearest tenth,

r = 3.9

Answer:

A 95% prediction interval for the drying time for the next trial of the paint is between 3.25 and 4.33 hours.

Step-by-step explanation:

First we have to find the sample mean and the sample standard deviation.

We have 15 measurements. Using a calculator, the mean is [tex]\overline{x} = 3.79[/tex] and the standard deviation is of [tex]s = 0.97[/tex].

Now, we have the standard deviation for the sample, which means that the t-distribution is used to solve this question.

T interval

The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So

df = 15 - 1 = 14

95% confidence interval

Now, we have to find a value of T, which is found looking at the t table, with 14 degrees of freedom(y-axis) and a confidence level of [tex]1 - \frac{1 - 0.95}{2} = 0.975[/tex]. So we have T = 2.1448

The margin of error is:

[tex]M = T\frac{s}{\sqrt{n}} = 2.1448\frac{0.97}{\sqrt{15}} = 0.54[/tex]

In which s is the standard deviation of the sample and n is the size of the sample.

The lower end of the interval is the sample mean subtracted by M. So it is 3.79 - 0.54 = 3.25 hours

The upper end of the interval is the sample mean added to M. So it is 3.79 + 0.54 = 4.33 hours

A 95% prediction interval for the drying time for the next trial of the paint is between 3.25 and 4.33 hours.

Answer:

376 inches squared.

Step-by-step explanation: