Paul is filling the rectangular prism shown with cubes that measure 14 inch along each edge.

Answer:

Gretchen charges $12 dollars per hour

Step-by-step explanation:

$18/1.5=$12

Answer:

30ft.

your welcome. ...................

Answer:

slope=-9/2

y int- 6

Step-by-step explanation:

okay lets take two points

-2,15 and -6,33

the slope is 33-15/ -6-(-2)= 18/-4=-9/2

equation is y=mx+b where m is slope and b is y intercept

so plugging values in we get

15=-2(-9/2)+b

15=9+b

b=6

sin

(

2

θ

)

=

2

(

3

5

)

(

−

4

5

)

=

−

24

25

Write the double-angle formula for cosine.

\displaystyle \cos \left(2\theta \right)={\cos }^{2}\theta -{\sin }^{2}\thetacos(2θ)=cos

​2

​​ θ−sin

​2

​​ θ

Again, substitute the values of the sine and cosine into the equation, and simplify.

)Answer:

In the previous section, we used addition and subtraction formulas for trigonometric functions. Now, we take another look at those same formulas. The double-angle formulas are a special case of the sum formulas, where \displaystyle \alpha =\betaα=β. Deriving the double-angle formula for sine begins with the sum formula,

\displaystyle \sin \left(\alpha +\beta \right)=\sin \alpha \cos \beta +\cos \alpha \sin \betasin(α+β)=sinαcosβ+cosαsinβ

If we let \displaystyle \alpha =\beta =\thetaα=β=θ, then we have

Deriving the double-angle for cosine gives us three options. First, starting from the sum formula, \displaystyle \cos \left(\alpha +\beta \right)=\cos \alpha \cos \beta -\sin \alpha \sin \betacos(α+β)=cosαcosβ−sinαsinβ, and letting \displaystyle \alpha =\beta =\thetaα=β=θ, we have

Using the Pythagorean properties, we can expand this double-angle formula for cosine and get two more interpretations. The first one is:

Similarly, to derive the double-angle formula for tangent, replacing \displaystyle \alpha =\beta =\thetaα=β=θ in the sum formula gives

\displaystyle \begin{array}{c}\tan \left(\alpha +\beta \right)=\frac{\tan \alpha +\tan \beta }{1-\tan \alpha \tan \beta }\\ \tan \left(\theta +\theta \right)=\frac{\tan \theta +\tan \theta }{1-\tan \theta \tan \theta }\\ \tan \left(2\theta \right)=\frac{2\tan \theta }{1-{\tan }^{2}\theta }\end{array}

​tan(α+β)=

​1−tanαtanβ

​

​tanα+tanβ

​​

​tan(θ+θ)=

​1−tanθtanθ

​

​tanθ+tanθ

​​

​tan(2θ)=

​1−tan

​2

​​ θ

​

​2tanθ

​​

​​

A GENERAL NOTE: DOUBLE-ANGLE FORMULAS

The double-angle formulas are summarized as follows:

\displaystyle \sin \left(2\theta \right)=2\sin \theta \cos \thetasin(2θ)=2sinθcosθ

\displaystyle \tan \left(2\theta \right)=\frac{2\tan \theta }{1-{\tan }^{2}\theta }tan(2θ)=

​1−tan

​2

​​ θ

​

​2tanθ

​​

HOW TO: GIVEN THE TANGENT OF AN ANGLE AND THE QUADRANT IN WHICH IT IS LOCATED, USE THE DOUBLE-ANGLE FORMULAS TO FIND THE EXACT VALUE.

Draw a triangle to reflect the given information.

Determine the correct double-angle formula.

Substitute values into the formula based on the triangle.

Simplify.

EXAMPLE 1: USING A DOUBLE-ANGLE FORMULA TO FIND THE EXACT VALUE INVOLVING TANGENT

Given that

and \displaystyle \thetaθ is in quadrant II, find the following:

\displaystyle \sin \left(2\theta \right)sin(2θ)

\displaystyle \cos \left(2\theta \right)cos(2θ)

\displaystyle \tan \left(2\theta \right)tan(2θ)

SOLUTION

If we draw a triangle to reflect the information given, we can find the values needed to solve the problems on the image. We are given \displaystyle \tan \theta =-\frac{3}{4}tanθ=−

​4

​

​3

​​ , such that \displaystyle \thetaθ is in quadrant II. The tangent of an angle is equal to the opposite side over the adjacent side, and because \displaystyle \thetaθ is in the second quadrant, the adjacent side is on the x-axis and is negative. Use the Pythagorean Theorem to find the length of the hypotenuse:

Now we can draw a triangle similar to the one shown in Figure 2.

Diagram of a triangle in the x,y-plane. The vertices are at the origin, (-4,0), and (-4,3). The angle at the origin is theta. The angle formed by the side (-4,3) to (-4,0) forms a right angle with the x axis. The hypotenuse across from the right angle is length 5.

Figure 2

Let’s begin by writing the double-angle formula for sine.

\displaystyle \sin \left(2\theta \right)=2\sin \theta \cos \thetasin(2θ)=2sinθcosθ

We see that we to need to find \displaystyle \sin \thetasinθ and \displaystyle \cos \thetacosθ. Based on Figure 2, we see that the hypotenuse equals 5, so \displaystyle \sin \theta =\frac{3}{5}sinθ=

. Substitute these values into the equation, and simplify.

Thus,

​​

Solution

EXAMPLE 2: USING THE DOUBLE-ANGLE FORMULA FOR COSINE WITHOUT EXACT VALUES

Use the double-angle formula for cosine to write \displaystyle \cos \left(6x\right)cos(6x) in terms of \displaystyle \cos \left(3x\right)cos(3x).

SOLUTION

c

Analysis of the Solution

This example illustrates that we can use the double-angle formula without having exact values. It emphasizes that the pattern is what we need to remember and that identities are true for all values in the domain of the trigonometric function.

Using Double-Angle Formulas to Verify Identities

Establishing identities using the double-angle formulas is performed using the same steps we used to derive the sum and difference formulas. Choose the more complicated side of the equation and rewrite it until it matches the other side.

EXAMPLE 3: USING THE DOUBLE-ANGLE FORMULAS TO ESTABLISH AN IDENTITY

Establish the following identity using double-angle formulas:

\displaystyle 1+\sin \left(2\theta \right)={\left(\sin \theta +\cos \theta \right)}^{2}1+sin(2θ)=(sinθ+cosθ)

​2

​​

θ

)

Step-by-step explanation:

Answer: i think true

Step-by-step explanation:

Answer:

6m + 2n

Step-by-step explanation:

we have to added up the like therms

like therms are therms that have the same literal part

6m + 2n

Answer:

7m-m+4n-2n

m(7-1)+2n(2-1)

m(6)+2n(1)

6m+2n

Answer:

Hello! answer: x = 20

Step-by-step explanation:

Because 3 multiplied by x which equals 20 gets us 60 then we just add the 2 and get 62 these are vertical angles so they will have the same measure hope that helps!

Answer:

189 components must be sampled.

Step-by-step explanation:

We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:

[tex]\alpha = \frac{1 - 0.99}{2} = 0.005[/tex]

Now, we have to find z in the Ztable as such z has a pvalue of [tex]1 - \alpha[/tex].

That is z with a pvalue of [tex]1 - 0.005 = 0.995[/tex], so Z = 2.575.

Now, find the margin of error M as such

[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]

Assume that component lifetimes are normally distributed with population standard deviation of 16 hours.

This means that [tex]\sigma = 16[/tex]

How many components must be sampled so that a 99% confidence interval will have margin of error of 3 hours?

n components must be sampled.

n is found when M = 3. So

[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]

[tex]3 = 2.575\frac{16}{\sqrt{n}}[/tex]

[tex]3\sqrt{n} = 2.575*16[/tex]

[tex]\sqrt{n} = \frac{2.575*16}{3}[/tex]

[tex](\sqrt{n})^2 = (\frac{2.575*16}{3})^2[/tex]

[tex]n = 188.6[/tex]

Rounding up:

189 components must be sampled.

Answer:

If a coin is tossed 12 times, the maximum probability of getting heads is 12. But, 12 coin tosses leads to 212 , i.e. 4096 number of possible sequences of heads & tails.

Step-by-step explanation:

Answer:

8/13

Step-by-step explanation:

Pam flips a coin 12 times. The coin lands on heads 8 times. What is the theoretical

probability of landing on heads on the next flip?

well it would be 8 and 13

Answer: A=144

Step-by-step explanation:

A=a^2=12^2=144 I hope this helps sorry if it doesn't. :)  

Answer:

the second angle

sorry if wrong

Step-by-step explanation:

Answer:

c

Step-by-step explanation:

right on plato

Answer:

(-4, 16)

Step-by-step explanation:

Answer:

False because 1/2 would be half the number 2/2 or 1 would be the whole number so 3/2 would be a whole and half or 1 1/2

Answer:

false

if the number is X

3/2 of X= X 1/2

[tex]x \frac{1}{2} > x[/tex]

Answer:

I think it would be B.

Step-by-step explanation:

Since you aready have a 50% chance of landing on both heads or tails once. To land it on heads twice you would have a twenty five percent chance if you look at logic.  in which my dad would often say. Please mark the brainliest

Answer:

≠

Step-by-step explanation:

Sorry I just need 20 Characters

Answer:

≠

Step-by-step explanation:

Because 3/8 is 0.375, 8/15 is 0.53( with the 3 repeated). The decimal values aren't the same so the answer is that these 2 fractions are not equivalent.

Answer:

4,261

Step-by-step explanation:

after 23 hours, the number of bacteria =

4,000.

so, after 26 hours = 4,000+ (3/23 ×4000)

= 4,000 + 261 = 4,261

9514 1404 393

Answer:

  C.  (-1, 2) and (4, 7)

Step-by-step explanation:

It may be simplest just to try the answer choices.

We notice that y = x+3 is not satisfied by the points in choices A or D, so those can be eliminated.

__

The second equation can be written in vertex form as ...

  y = (x -1)^2 -2

This equation is not satisfied by the points of choice B.

  Using (-1, 4) (from choice B), we get 4 = (-1-1)^2 -2 = 4-2 = 2 . . . FALSE.

However it is a good match for the points of choice C.

  Using (-1, 2) (from choice C), we get 2 = (-1-1)^2 -2 = 4 -2 = 2 . . . True

The appropriate choice is ...

  (-1, 2) and (4, 7)

Find the actual Dimensions of the triangle.

Multiply the size of the triangle on paper by 1.5 feet per inch:

Width = 5 x 1.5 = 7.5 feet.

Height= 7 x 1.5 =10.5 feet

Area of a triangle is 1/2 x base x height:

Area = 1/2 x 7.5 x 10.5 = 39.375 square feet.

Answer: 39.375 square feet.

The area of the actual banner is 39.375 feet²

Scaling is used to increase or decrease the size of a figure so as to create an image.

Given that 1 inch on the drawing Is equivalent to 1.5 feet on the actual banner, hence:

Base = 5 in * 1.5 feet per in = 7.5 feet

Height = 7 in * 1.5 feet per in = 10.5 feet

Area of the actual banner = (1/2) * 7.5 * 10.5 = 39.375 feet²

The area of the actual banner is 39.375 feet²

Find out more on scaling at: https://brainly.com/question/25324744

Answer:

area of a trapezoidal base  of each prism with heights  6 and 8 units are 4 square units and 3 square units respectively

Step-by-step explanation:

Let us first be aware of formula of volume for any regular geometrical figure.

Fundamental formula for  volume for any regular geometrical figure is.

volume = area of cross section of object*  height of object (A)

In the problem stated area of cross section of object will be  area of a trapezoidal base.

Given in the question is

Volume of both the trapezoidal prisms = 24 cubic units

*************************************************************************************

For prism with height 6 unit

Substituting the value of height and volume in formula for trapezoidal prisms

24 = 6 * area of a trapezoidal base

=> area of a trapezoidal base = 24/6 = 4 square units

*************************************************************************************

For prism with height 8 unit

Substituting the value of height and volume in formula for trapezoidal prisms

24 = 8 * area of a trapezoidal base

=> area of a trapezoidal base = 24/8 = 3 square units

*************************************************************************************

Therefore area of a trapezoidal base  of each prism with heights  6 and 8 units are 4 square units and 3 square units respectively.

Answer:

3 1/3 gallons

Step-by-step explanation:

Answer:

[tex]f + e + d = 360^o[/tex]

Step-by-step explanation:

The question is incomplete, as what is required is not stated and the triangle is not given.

So, I will solve generally.

The proof is as follows (see attachment for triangle)

From the attachment, we have:

[tex]a + f = 180[/tex]

[tex]b + e = 180[/tex]

[tex]c + d = 180[/tex]

Make f, e and d the subject

[tex]f = 180 - a[/tex]

[tex]e = 180 - b[/tex]

[tex]d = 180 - c[/tex]

Add up the equations

[tex]f + e + d = 180 -a + 180 - b + 180- c[/tex]

Collect like terms

[tex]f + e + d = 180 + 180+ 180-a- b - c[/tex]

[tex]f + e + d = 540-a- b - c[/tex]

We have:

[tex]f + e + d = 540-(a+ b + c)[/tex]

[tex]a + b + c \to 180[/tex] --- angles in a triangle

So, we have:

[tex]f + e + d = 540-180[/tex]

[tex]f + e + d = 360^o[/tex] --- proved

9514 1404 393

Answer:

  (a)  6

Step-by-step explanation:

The median is the middle number when they are sorted into order. If one of the numbers is 10, the remaining number must be any number less than 7. Of the offered choices, the only one less than 7 is 6.

__

The three numbers are 6, 7, 10.

Answer:

Step-by-step explanation:

Hope it helps u!!

Trapezoid Area =

[ ( Sum of the rules ) × ( height ) ] ÷ 2

_________________________________

Area = [ ( 2 + 3 ) × 3 ] ÷ 2

Area = [ 5 × 3 ] ÷ 2

Area = 15 ÷ 2

Area = 7.5 m^2

Answer:

-18

Step-by-step explanation:

y=6x-3

6x-3=-18

-18=6x-3

Answer:

intercept: -3

slope: 6

Step-by-step explanation:

The number in the back and the operations are the y-intercept and the number multiplied by x is the slope.

Answer:

16.73 I THINK

Step-by-step explanation:

my guess is n1 is relating to the 4.9, and if it then you would do the Pythagorean theorem. because the degrees are there to let you know it's a right angle and you are able to use the theorem..... so -

4.9^2 + 4.9^2 =C^2

48.02 =C

√48 = 6.93 (rounded to nearest hundredth)

then you add them all together

4.9+4.9+6.93=16.73

Answer:

A. She will have $2 left over

Step-by-step explanation:

I know this because 3 yards of fabric cost $18 dollars so there would be $2 left