Find sin 2x, cos 2x, and tan 2x from the given information.
cos x = 15/17
csc x < 0

Answer:

The value of 55th term a₅₅  = 161

Step-by-step explanation:

It is given that,

aₙ = −1 + 3(n − 1)

To find 55th term

To find the 55th term we have to substitute 55 instead of n in the expression of an.

aₙ = −1 + 3(n − 1)

a₅₅ = −1 + 3(n − 1) = -1 + 3( 55 - 1)

  = -1 + 3 * 54 = -1 + 162

  = 161

Therefore the value of 55th term a₅₅  = 161

Answer:

2.  22/35

3a. 0.24

3b. 0.84

3c. 0.54

3d. 0.73

Step-by-step explanation:

2. There are 22 songs on albums 1 and 2, and 35 total songs. Thus the probability of randomly choosing a song from albums 1 or 2 is 22/35.

__

3. The sum of the probabilities of all possible mutually exclusive events is 1, so ...

a. p(blue) = 1 - p(any other color) = 1 - 0.76 = 0.24

b. p(not green) = 1 - p(green) = 1 - 0.16 = 0.84

c. p(green+yellow+blue) = p(green) +p(yellow) +p(blue) = 0.16 +0.14 +0.24 = 0.54

d. p(not(yellow+red)) = 1 - p(yellow+red) = 1 - 0.27 = 0.73

Answer:

Equation:  (1 2/3)(2 1/3) = x

Answer:  3 8/9 cups

Step-by-step explanation:

x represents the amount of flour she will need in cups.

To solve, convert the mixed numbers to improper fractions and multiply...

1 2/3 becomes 5/3

2 1/3 becomes 7/3

Now we have

(5/3)(7/3) = x

  35/9 = x

35/9 is 3 8/9 as a mixed number

An equation that represents the number of cups of flour Genise will need​ is (1 2/3 ) × (2 1/3) which gives the value 3 8/9 cups.

An equation is the statement of two expressions located on two sides connected with an equal to sign. The two sides of an equation is usually called as left hand side and right hand side.

Given that,

Number of cups of flour needed to make 1 batch of cookies = 1 2/3 cups

                                                                                                    = 5/3 cups

We have to calculate the number of cups of flour for 2 1/3 batches.

Number of cups of flour needed to make 2 1/3 batches of cookies is,

(5/3) × (2 1/3)

= (5/3) × (7/3)

= (35/9)

= 3 8/9

Hence the number of cups of flour needed is 3 8/9 cups.

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Answer:

60 m/h

Step-by-step explanation:

1. the basic formula is Time=Distance/Speed;

2. total time is time1 (for 84 miles)+time2 (for 130 miles)=time (4 hours);

3. the time for the first 84 mi. is time1=84/S;

4. the time for the rest 130 mi. is time2=130/(S-10);

5. using all the data of items 2-4, it is possible to substitute into the basic formula and resolve an equation:

[tex]\frac{84}{s} +\frac{130}{s-10} =4; \ => \ 2s^2-127s+420=0;[/tex]

[tex]\left[\begin{array}{ccc}s=60\\s=3.5\end{array}[/tex]

note, that the value of speed has one condition: s>10. It means, the only value is true: 60 miles per hour.

Answer:

1,080 Pennies

Step-by-step explanation:

This question is fairly simple, you just have to simplify it. You are starting at already half-full, so you can keep that 1/2 in mind. Then, she adds 360 pennies to get 5/6. If you convert 1/2 into 3/6, you can see that 360 pennies fills 2/6 of the piggy bank. So now you can solve two different ways. The first, you can take 360 and multiply it by 3 to get the amount that can fit in the piggy bank, because 2 * 3 = 6 and that would make it 6/6, or 1. The other way would be to divide 360 by 2 to get 1/6 of the piggy bank, or 180. Then you can multiply 180 by 6 to get the entire amount.

Hope this helped ^-^

By setting up a proportion, we can find that the total capacity of Amy's penny bank is 1440 pennies.

The subject of this problem is mathematics. We know that after adding 360 pennies, Amy's penny bank was 5/6 full. Before she added those pennies, it was 1/2 full. So, those 360 pennies represent the difference between 5/6 and 1/2 of the capacity of the penny bank.

To find the total capacity of the penny bank, we can set up a proportion as follows:

360 pennies / (5/6 - 1/2) = x pennies / 1

Therefore, x = 360 * (1 / (5/6 - 1/2))

By simplifying this, we find that the total capacity of Amy's penny bank is 1440 pennies.

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1/3

7/12

9/12

1/4

and more

The fraction that is not equivalent to [tex]\( \frac{8}{12} \) is \( \frac{6}{10} \), option D, as it simplifies to \( \frac{3}{5} \), while the others simplify to \( \frac{2}{3} \), which is equivalent to \( \frac{8}{12} \).[/tex]

To find the fraction that is not equivalent to [tex]\( \frac{8}{12} \), we need to simplify each option and compare it with \( \frac{8}{12} \).[/tex]

We simplify each option:

A) [tex]\( \frac{2}{3} \)[/tex]

B) [tex]\( \frac{24}{36} = \frac{2}{3} \) (Equivalent to \( \frac{8}{12} \))[/tex]

C) [tex]\( \frac{4}{6} = \frac{2}{3} \) (Equivalent to \( \frac{8}{12} \))[/tex]

D)[tex]\( \frac{6}{10} = \frac{3}{5} \)[/tex]

So, the fraction that is not equivalent to [tex]\( \frac{8}{12} \) is \( \frac{6}{10} \),[/tex]option D.

Answer:

46 packages

Step-by-step explanation:

2 7/8= 23/8= 46/16...THUS SINCE SHE IS MAKING 1/16 POUND PACKAGES, SHE CAN MAKE 46 PACKAGES

Answer:

• 2/3|2 -x| = 1/15

• |2 -x| = 1/10

• 1/5 +|4/3 -2/3x| = 4/15

Step-by-step explanation:

Starting with the given equation, subtract 1/5 = 3/15.

(2/3)|2 -x| = 4/15 - 3/15

(2/3)|2 -x| = 1/15 . . . . . . . . matches the first choice

Now, multiply by 3/2.

|2 -x| = 3/30

|2 -x| = 1/10 . . . . . . . . . . . . matches the third choice

___

If you decide to distribute the coefficient 2/3 instead, you have

1/5 + |2·2/3 -x·2/3| = 4/15

1/5 + |4/3 -2/3x| = 4/15 . . . . matches the selected choice

Answer:

The answer is A and C

Step-by-step explanation:

I just did the work

Good luck

Answer:

1. g

2. a

3. d

4. b

Step-by-step explanation:

If you can't do these in you head or on a graph, you can always let your calculator do it.

When adding vectors put the tail of one at the nose of the other. When subtracting, add the opposite. When adding or subtracting a multiple, just do the repeated addition or subtraction.

Answer:

  -2 < x < 4/3

Step-by-step explanation:

A graphing calculator can show you the solution. I like to recast the equation as a comparison to zero, since a graphing calculator often can display zeros of a function easily. Here that means ...

  |6x +2| -10 < 0

___

If you want to solve this by hand, you can "unfold" the absolute value to get ...

  -10 < 6x +2 < 10

  -12 < 6x < 8 . . . . . . subtract 2

  -12/6 < x < 8/6 . . . . divide by 6

  -2 < x < 4/3 . . . . . . simplify

This graphs on the number line as a solid line between open circles at -2 and 4/3. On the attached graph, the boundary values are shown as dotted blue lines, and the solution space is shown in blue.

I already did this question once so I'm just gonna include the answer

Answer: The value of KP = 12 units.

Step-by-step explanation:

Since we have given that

KE is a tangent with KE = 18

KPL is a secant with PL = 15

Let KP = x

Since we know that The product of segments of secants is square of the tangents.

Mathematically, it is expressed as ,

[tex]KE^2=KP.KL\\\\18^2=x(x+15)\\\\324=x^2+15x\\\\x^2+15x-324=0\\\\x^2+27x-12x-324=0\\\\x(x+27)-12(x+27)=0\\\\(x+27)(x-12)=0\\\\x=-27,x=12[/tex]

Measure of secant can't be negative.

So, KP = 12

The distance from the center of the circle at (-1,2) to the point (2,-2) is 5 units and he did not calculate the distance correctly

The distance of a line between 2 points is always positive and given by the formula

Let the first point be A ( x₁ , y₁ ) and the second point be B ( x₂ , y₂ )

The distance between A and B is D , and the distance D is

Distance D = √ ( x₂ - x₁ )² + ( y₂ - y₁ )²

Given data ,

Let the first point be P = P ( -1 , 2 )

Let the second point be Q = Q ( 2 , -2 )

To find the distance from the center of the circle at (-1,2) to the point (2,-2), we can use the distance formula:

Distance D = √ ( x₂ - x₁ )² + ( y₂ - y₁ )²

Distance D = √[(2 - (-1))² + (-2 - 2)²]

Distance D = √[3² + (-4)²]

D = √[9 + 16]

D = √25 = 5 units

Therefore, the point (2,-2) does lie on the circle.

However, Amit's work does not account for the fact that the center of the circle is not at the origin, but rather at (-1,2). This means that the distance from (-1,2) to (2,-2) must be used to determine if the point is on the circle, not the radius of the circle.

No, he should have used the center of the circle at (-1,2) to calculate the distance.

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Answer:

Step-by-step explanation:

The graph a.) is the best draw that represents a line with positive rate of change.

Best regards

Answer:

Fiona has 6 quarters

Step-by-step explanation:

If Fiona were to have 1 quarter and 1+6 dimes she would have 8 coins

If she were to have 2 quarters and 2+6 dimes she would have 10 coins

If she were to have 3 quarters and 3+6 dimes she would have 12 coins

If she were to have 4 quarters and 4+6 dimes she would have 14 coins

If she were to have 5 quarters and 5+6 dimes she would have 16 coins

If she were to have 6 quarters and 6+6 dimes she would have 18 coins

Therefore, she has to have 6 quarters in order to have 6 more dimes and a total of 18 coins

I hope this helps, and I'm sorry it took so long for me to write this out

Answer:

-3x^2 -6x -7

Step-by-step explanation:

See the attachment for the synthetic division. Of course, polynomial long division will give the same result. Make sure you deal with the signs and the powers of x properly.

Answer:

  A.) 0.9cm, 1.2cm, 1.5cm

Step-by-step explanation:

The side ratios of the offered answers are ...

  A — 3:4:5 . . . . . . obviously a right triangle

  B — 3:5:5 . . . . . . isosceles, but not a right triangle

  C — 3:4:6 . . . . . . an obtuse triangle

  D — 3:2:5 . . . . . . not even a triangle (just a line segment)

_____

Comment on 3:4:5

This set of small integers appears often in problems involving right triangles. It is the smallest "Pythagorean triple" — a set of integers that satisfies the relationship of the Pythagorean theorem — and it is the only Pythagorean triple that is an arithmetic sequence (differences between the numbers are the same).

When you see a triangle with sides in these ratios, you know it is a right triangle. When you see a right triangle with two of the sides having a ratio of 3:4, 3:5, or 4:5 (where "5" is the hypotenuse), then you know the length of the remaining side.

Answer:

This is the simplified number for Pi, which is 3.14

Step-by-step explanation:

Answer:

8. (10/7)x^(0.7) +C

10. (x^-2)/2 -x^-1 +C

Step-by-step explanation:

The integral of x^a is x^(a+1)/(a+1).

8. a = -.3, so the integral is x^0.7/0.7

___

10. This is the difference of two integrals, one with a=-2; the other with a=-3, so ...

the integral is (x^-1)/(-1) -(x^-2)/(-2)

_____

Of course, an arbitrary constant is added to each result to complete the indefinite integral.

Answer:

Parallel line = Same m value (same slope)

Perpendicular line = The reciprocal m value (x/y = y/x).

Going through a point = First, find the slope of the line (perpendicular or parallel), then plug in the point (4,10) to find the y intercept.

Answer:

See below.

Step-by-step explanation:

Parallel

y = -1/2x + b

The slope is the same for any set of parallel lines. The point determines the y intercept.

x = 4

y = 10

Solve for b

10 = -1/2(4) + b

10 = - 2 + b

b = 10 + 2

b = 12

Equation: y = - 1/2 x + 12

Perpendicular

Here you actually have to solve for the slope.

Equation

m1 * m2 = - 1

m1 is the given slope of - 1/2 which I will chance to -0.5. Substitute for m1.

-0.5 * m2 = - 1                          Divide by -0.5

m2 = -1/-0.5

m2 = 2

Now what you have is

y = 2x + b

x = 4

y = 10

10 = 2*4 + b

10 = 8 + b

10 - 8 = b

b = 2

Equation: y = 2x + 2

(x + 3) divided by 2

third option

Answer:

(x + 3) divided by 2

third optionStep-by-step explanation:

Answer:

either of Step 3 or Step 4

Step-by-step explanation:

At Step 3, -1 is added to both sides of the equation. Technically, this is correct (not an error), but it does not lead to a solution to the equation (so, could be considered to be an error). Adding +1 to both sides of the equation would lead more directly to a solution.

__

At Step 4, x -1 -1 is simplified to x. This is an error, as the correct simplification is x-2, so the equation after this step should read x-2 = 5. If Step 3 had been executed by adding +1 to both sides of the equation, then the simplification here would be x=7.

_____

Answering "why" someone does something is always tricky. One can project one's own interpretation onto the actions of others, but one never really knows whether that is accurate or not.

The "why" in this case could go back to the motivation of the problem's author, which may be to see if the student can recognize that the opposite of -1 is +1, or that the sum -1-1 is not zero.

___

My guess is that Step 3 is considered to be the erroneous step, and that choosing Step 4 will get you into a losing argument with your grader.

The answer is C. His gross pay is $974.00.

Answer:

Step-by-step explanation:

Weekly Salary = 844 dollars.

Commision Rate = 4% = 0.04

Last week Sales = 3250 dollars.

Last week commission on sales = 0.04 x 3250 = 130 dollars.

Gross pay = Weekly Salary + Commission amount.

Gross pay = 844 + 130 = 974 dollars.

Hence, option C is correct i.e. 974.00 dollars.

Answer:

The area is multiplied by 0.84 (decreased 16%)

Step-by-step explanation:

The length is multiplied by (1 +0.40) = 1.4.

The width is multiplied by (1 -0.40) = 0.6

So, the new area is ...

A = (L·1.4)·(W·0.6) = LW·0.84

The original area was the product of the original length and width, so was LW. This means the new area is 0.84 times the original area.

0.84 = 1 - 0.16

so, another way to describe the change is to say the area decreased 16%.

We want to see how some changes in the measures of a rectangle affect the area of the given rectangle.

We will see that the new area is 0.84 times the original area (meaning that the area decreases by 16%).

We will have.

First, we know that for a rectangle of length L and width W the area is given by:

A = L*W

Now, if we increase the length bt 40%, the new length will be:

L' = L +  (40%/100%)*L = L*1.4

And if the width is decreased by 40%, the new width will be:

W' = W - (40%/100%)*W = W*0.6

The new area is given by:

A' = L'*W' = (L*1.4)*(W*0.6) = (L*W)*(1.4*0.6) = 0.84*(L*W)

Where L*W is the area of the original rectangle, so we can write:

A' = 0.84*A

Meaning that the area decreased, the new area is 0.84 times the original area (we can actually see that the area decreased by 16%).

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Answer:

200 Boxes of Popcorn

Step-by-step explanation:

To find the total amount of popcorn boxes there are in the store, we need to consider the amount of boxes displayed at the front of the store.

We have:

60 boxes = Cinnamon + Cheese

60 boxes = 15% + 15%

60 = 30% of the total boxes in the store.

Now we know that 60 boxes is equivalent to 30%, we can use this to find the number of kettle corn.

60 + 60 = 120

30% + 30% = 60%

This means that we have 120 Kettle Korn boxes.

We can also use the amount of 60 boxes to find what 10% will be equivalent to.

60 boxes = 30%

So if we divide the number of boxes by 3, we'll get the 10% of the total number of boxes.

60/3 = 30%/3

20 = 10%

So all in all we have:

120 Kettle Korn

60 Cinnamon + Cheese

20 Caramel

120 + 60 + 20 = 200

There are 200 popcorn boxes in the store.

Answer:  [tex]\bold{\dfrac{7w^2y^3}{32}}[/tex]

Step-by-step explanation:

[tex]\dfrac{3w^9y^4}{8w^5}\cdot \dfrac{7y^4}{12w^2y^5}\\\\\\\text{Multiply across. ADD exponents when like bases are being multiplied}\\=\dfrac{21w^9y^8}{96w^7y^5}\\\\\\\text{Cancel out common factors. SUBTRACT exponents when dividing}\\=\dfrac{7w^2y^3}{32}[/tex]

See the image for solution

Answer:

  y ≈ 240.3 ft

Step-by-step explanation:

The mnemonic SOH CAH TOA reminds you that the relation between an angle and the sides adjacent and opposite is ...

  Tan = Opposite/Adjacent

In this triangle, the interior angle at lower right is the same as the one marked at upper left: 31°. y is the side opposite that angle, and 400 ft is the side adjacent. Then the relation is ...

  tan(31°) = y/(400 ft)

Multiplying by 400 ft gives ...

  y = (400 ft)·tan(31°) ≈ 240.3 ft

_____

The triangle interior angle at lower right and the angle marked 31° are "alternate interior angles" relative to the transversal marked x and the (parallel) horizontal lines in the figure. Alternate interior angles always have the same measure.

In geometry problems like this one, it means the angle of elevation (above the horizontal) is equal to the angle of depression (below the horizontal).

Answer:

  [550, 1250] miles ([minimum, maximum] miles)

  700 miles (difference between minimum and maximum)

Step-by-step explanation:

"Range" has different meanings in different contexts with respect to a list of numbers and/or ordered pairs.

For a function, characterized by ordered pairs, the range is often specified by the interval between the minimum and the maximum. That is, the range of the function ...

  (Jan, 914), (Feb, 740), (Mar, 815), (Apr, 550), (May, 815), (Jun, 1250), (Jul, 740)

can be specified either as the list of dependent variable values:

  {550, 740, 815, 914, 1250}

or as the interval between the minimum and the maximum:

  [550, 1250]

___

If you're plotting these values or creating a histogram, the "range" you're interested in is often the difference between the minimum and maximum:

  1250 -550 = 700

The widths of bins of a histogram are defined by dividing this range into a suitable number of smaller intervals.

Answer:

  25 in

Step-by-step explanation:

The diameter is shown to be 10/4 times the height, so the diameter of the smaller solid is ...

  (10/4)×(10 in) = (100/4) in = 25 in

Answer:

25 in.

Step-by-step explanation: