If sine theta equals three over four, what are the values of cos θ and tan θ?

cosine theta equals plus or minus square root of seven over four, tangent theta equals plus or minus two times square root of seven over seven
cosine theta equals plus or minus seven over four, tangent theta equals negative three over seven
cosine theta equals plus or minus square root of seven over 4, tangent theta equals plus or minus three over seven
cosine theta equals plus or minus seven over four, tangent theta equals negative one over seven

Answer with explanation:

For a Lopsided coin ,probability of getting Head is equal to [tex]\frac{1}{3}[/tex] For a Lopsided coin ,probability of getting Tail  is equal to [tex]\frac{1}{3}[/tex].

→Probability of getting Tail > Probability of getting Head

→Coin is heavier from tail side and lighter from Head side.

→→We have to Calculate number of flips of coin that is needed to have both heads and tails appear at least once.

[tex]\rightarrow P(\text{Head})=\frac{1}{3}\\\\ \frac{1}{3} \times x=1\\\\x=3\\\\\rightarrow P(\text{Tail})=\frac{2}{3}\\\\ \frac{2}{3} \times y=1\\\\y=\frac{3}{2}[/tex]

→We need to find common multiple of 3 and [tex]\frac{3}{2}[/tex].

Least common multiple of 3 and [tex]\frac{3}{2}[/tex] is 6.

→So,on Average number of flips of this coin are needed to have both heads and tails appear at least once=6 tosses

Answer:

Radius of the Earth is 3978.8 Miles

Circumference of the Earth is 25000 Miles

Step-by-step explanation:

The angle of the sun shone at an angle of 7.2° to the zenith

This means that the angle of the sector of the circle is 7.2° (θ)

S = Length of the sector of the circle = 500 miles

r = radius of earth

Converting 7.2° to radians

[tex]\theta =7.2\frac{\pi}{180}[/tex]

[tex]S=r\theta\\\Rightarrow r=\frac{S}{\theta}\\\Rightarrow r=\frac{500}{7.2\frac{\pi}{180}}\\\Rightarrow r=3978.8\ Miles[/tex]

∴ Radius of the Earth is 3978.8 Miles

[tex]C=2\pi r\\\Rightarrow C=2\times \pi \frac{500}{7.2\frac{\pi}{180}}\\\Rightarrow C=25000\ Miles[/tex]

∴ Circumference of the Earth is 25000 Miles

The radius and circumference are respectively; r = 3978.86 miles and C = 25000 miles

We are told that the angle of the sun shone at an angle of 7.2° to the zenith. Thus, we can liken this to the angle of a sector and so;

Angle of the sector of the circle; θ = 7.2° = 0.125664 rad

Length of the sector of the circle; S = 500 miles

Formula for length of arc is;

S = rθ

where;

S is length of arc

r is radius

θ is angle of sector in radians

Thus;

r = S/θ = 500/0.125664

r = 3978.86 miles

Formula for circumference is;

C = 2πr

C = 2 * π * 3978.86

C = 25000 miles

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Answer:

Step-by-step explanation:

For principal amount P, the future value of the simple interest account will be ...

  P(1 + rt) = P(1 + .026·20) = 1.52P

The future value of the compound interest account will be ...

  P(1 +r)^t = P(1.026^20) ≈ 1.6708875P

The value of the compound interest account is about 10% greater after 20 years.

I would choose the compound interest account because it has a higher rate of return.

[tex]\bf ~~~~~~ \textit{Continuously Compounding Interest Earned Amount} \\\\ A=Pe^{rt}\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill & \$1000\\ r=rate\to 8\%\to \frac{8}{100}\dotfill &0.08\\ t=years\dotfill &10 \end{cases} \\\\\\ A=1000e^{0.08\cdot 10}\implies A=1000e^{0.8}\implies A=2225.54~\hfill \stackrel{interest = A - P}{1225.54}[/tex]

btw, we could have used the compound formula just the same, by simply using a compounding cycle of 365, namely daily, assuming a year has 365 days.

Answer:

c

Step-by-step explanation:

Answer:

answer would be The mean must have a mean of 0 and a standard deviation of 1. hope this helps

Step-by-step explanation:

Answer:

Area=14.22π

Step-by-step explanation:

Area=πr²(C/360)

C  is the central angle in degrees

r  is the radius of the circle of which the sector is part.

Area = π(8)²(80/360)

Area=π(64)(0.2222)

Area=π(14.22)

Area=14.22π....

Answer:

  84 child tickets were sold

Step-by-step explanation:

Had they all been adult tickets, revenue would have been ...

  $9.80 × 147 = $1440.60

It was less by ...

  $1440.60 -1054.20 = $386.40

The child's ticket costs less by ...

  $9.80 -5.20 = $4.60

so there must have been $386.40/$4.60 = 84 child tickets sold.

__

Replacing an adult ticket with a child ticket reduces the revenue by $4.60 without changing the number of tickets sold.

_____

You can let c represent the number of child tickets sold. Then (147 -c) is the number of adult tickets sold, and total revenue is ...

  5.20c + 9.80(147 -c) = 1054.20

  -4.60c +1440.60 = 1054.20 . . . . simplify

  -4.60c = -386.40 . . . . . . . . . . . . . subtract 1440.60

  c = 386.40/4.60 = 84

Answer:

I think its 21.6 or 22 (Mostly 21.6 though) Sorry if its not right but i'm mostly sure of it like this!

Answer:

r = +2√3

Step-by-step explanation:

The equation of a circle with center at (0, 0) and radius r is

x^2 + y^2 = r^2.

Here we have

x^2 + y^2 = 12,

and so we can deduce that r^2 = 12.  Then r = +2√3.

Answer:

The radius is: [tex]2\sqrt{3}[/tex]

Step-by-step explanation:

The equation of a circle in center-radius form is:

[tex](x - h)^2 + (y - k)^2 = r^2[/tex]

Where the center is at the point (h, k) and the radius is "r".

So, given the equation of the circle:

[tex]x^2+y^2=12[/tex]

You can identify that:

[tex]r^2=12[/tex]

Then, solving for "r", you get that the radius of this circle is:

[tex]r=\sqrt{12}\\\\r=2\sqrt{3}[/tex]

Answer:

The probability that the card drawn is a club is 0.25.

The probability that card drawn is a club, when it is given that the card is black is 0.5.

Step-by-step explanation:

In a standard​ deck of cards:

Total number of cards = 52

Total number of cards of each suit (club, spade,heart, diamond) = 13

The probability that the card drawn is a club is

[tex]P=\frac{\text{Favorable outcomes}}{\text{Total outcomes}}[/tex]

[tex]P=\frac{^{13}C_1}{^{52}C_1}=\frac{13}{52}=0.25[/tex]

Therefore the probability that the card drawn is a club is 0.25.

Let A and B represents the following events:

A : Card is black

B : Card is a club

Total number of black cards = 26

[tex]P(A)=\frac{26}{52}=\frac{1}{2}=0.5[/tex]

From the above parts

[tex]P(B)=0.25[/tex]

Total number of black club cards = 13

[tex]P(A\cap B)=\frac{13}{52}=\frac{1}{4}=0.25[/tex]

We need to find the probability that card drawn is a club, when it is given that the card is black.

[tex]P(\frac{B}{A})=\frac{P(A\cap B)}{P(A)}[/tex]

[tex]P(\frac{B}{A})=\frac{0.25}{0.5}=0.5[/tex]

Therefore the probability that card drawn is a club, when it is given that the card is black is 0.5.

Answer:

400,000,000 tons

Step-by-step explanation:

You could reword this sentence to ask the question, "100,000,000 is 25% of how much?"

The word "is" means equals, the percent will be .25 in decimal form, the word "of" means to multiply, and "how much" is x, our unknown.  In equation form, then, this looks like

100,000,000 = .25 × x

We will divide both sides by .25 to get that

x = 400,000,000

That's how much grain was grown in 2008

Answer: 400 million tons

Step-by-step explanation:

100 millions is 1/4 of 400 million

Answer:

quarters = 6+x

dimes = x

Total value = 325

Dime value = 10

Quarter value = 25

Step-by-step explanation:

25x+150+10x=325 (simplify)

35x=175

x=5  

6+5 = 11  

Hence Zoe has 5 dimes and 11 quarters.

Hope this helps!!❤

The expression that shows the total attendance is 7 x 40 + 7 x 2.

An algebraic expression is consists of variables, numbers with various mathematical operations,

Given that,

Total number of rows = 8.

Number of seats in each row = 42.

Total number of seats = 42 x 8 = 336.

Since, an act needs to keep first row empty, but rest of the seats sold.

So the remaining seats = 336 - 42 = 294.

So, the expression for the total attendance can be given as,

7 x 40 + 7 x 2 = 280 + 14 = 294.

The required expression is 7 x 40 + 7 x 2.

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The base is a right triangle with side lengths of 6 and 8 ft.

The area of a triangle is 1/2 x base x height = 1/2 x 6 x 8 = 24 square feet.

Now to find the volume, multiply the area by the height:

24 square ft x 12 ft = 288 ft^3

Answer:

i think it is 288 ft^3

Step-by-step explanation:

Answer:

264 transistors.

Step-by-step explanation:

By proportion the total number made if  16 are faulty is (35/2) * 16

=  280.

The number of good ones is 280 - 16

= 264 transistors.

Answer:

264 good ones

Step-by-step explanation:

2 in 35 are faulty = in a batch of 35, 2 will be faulty = there are 33 good for every 2 faulty ones there are

16 faulty have been made - to figure out how many batches there have been do 16/2=8

8 batches of 35, 8 × 35 = 280 total

280 total - 16 faulty = 264 good

OR do 8 batches × 33 good per batch = 264 good

at least thats how i interpreted it!

Finding the slope using two points:

The formula for slope is

[tex]\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]

In this case...

[tex]y_{2} =7\\y_{1} =6\\x_{2} =8\\x_{1} =4[/tex]

^^^Plug these numbers into the formula for slope...

[tex]\frac{7 - 6}{8 - 4}[/tex]

C) [tex]\frac{1}{4}[/tex]

^^^This is your slope

Hope this helped!

~Just a girl in love with Shawn Mendes

Answer:

5.779 x 10^-8 =0.00000005779

Step-by-step explanation:

The E-8 at the end means the number is multiplied by 10^-8.

So 5.779E-8=5.779 x 10^-8

A negative power means move the decimal place that many places to the left

So 5.779 x 10^-8 =0.00000005779

Answer:

Sample response: The E indicates scientific notation. The first number is the coefficient of the number in scientific notation. This number is multiplied by a power of 10. The number following the E, which is –8, is the exponent, and the base is 10.

Step-by-step explanation:

2020

Answer:

Option 2: (x-4)^2 + (x-5)^2 = 4

Step-by-step explanation:

The given circle's center is: (4,5)

And the radius is 4 units.

We are told in the question that the center will remain same only the radius will be changed.

The center is denoted by (h,k) = (4,5) and radius is 2

Standard equation of circle is:

(x-h)^2 + (y-k)^2 = r^2

So the equation of another circle with same center and radius of 2 units will be:

(x-4)^2 + (x-5)^2 = 2^2

(x-4)^2 + (x-5)^2 = 4  

Hence option 2 is correct ..

Answer:

  5y = 5

Step-by-step explanation:

When the second equation is multiplied by -2, it becomes ...

  -2(x -2y) = -2(-1)

  -2x +4y = 2

Adding this to the first equation gives ...

  (2x +y) +(-2x +4y) = (3) +(2)

  2x +y -2x +4y = 5 . . . . . . . . . eliminate parentheses

  5y = 5 . . . . . . . . . . . . . . . . . . .collect terms

Answer:

210 is the only choice I see listed that works.

Step-by-step explanation:

I don't know if you know this but you can apply a co-function identity here giving you the equation:

[tex]cos(x)=-\frac{\sqrt{3}}{2}[/tex].

If you are unsure of the identity sin(90-x)=cos(x) then I can show you another identity that leads to this one.

The difference identity for sine is sin(a-b)=sin(a)cos(b)-sin(b)cos(a).

Applying this to sin(90-x) gives you sin(90)cos(x)-sin(x)cos(90).

Let's simplify that using that sin(90)=1 while cos(90)=0:

sin(90-x)=sin(90)cos(x)-sin(x)cos(90)

sin(90-x)=1cos(x)-sin(x)(0)

sin(90-x)=cos(x)

You can also prove this identity using a right triangle like the one in this picture:  

That missing angle is 90-x since we need the angles in this triangle to add up to 180 which it does:

(x)+(90)+(90-x)

x+90+90-x

x-x+90+90

0+180

180

Anyways you should see that sin(90-x)=b/c while cos(x)=b/c.

Since they are equal to the same ratio, then you can say sin(90-x)=cos(x).

There are other co-function identities you can get from using this idea.

Anyways back to the problem.

We are solving:

[tex]cos(x)=-\frac{\sqrt{3}}{2}[/tex].

It looks like you have a drop-down menu with answers ranging from 0 to 360.

So I'm going to answer in degrees using the unit circle.

cosine value refers to the x-coordinate.

We are looking for when the x-coordinate is [tex]-\frac{\sqrt{3}}{2}[/tex] which is at [tex]\theta=150^\circ , 210^\circ[/tex].

Answer:

For [tex]3,604\ books[/tex] the cost for both methods will be the same

Step-by-step explanation:

Let

y ------> the production cost

x ------> the number of books

we know that

First production Method

[tex]y=19.25x+22,427[/tex] -------> equation A

Second production Method

[tex]y=10.50x+53,962[/tex] -------> equation B

Solve the system of equations

Equate equation A and equation B and solve for x

[tex]19.25x+22,427=10.50x+53,962[/tex]

[tex]19.25x-10.50x=53,962-22,427[/tex]

[tex]8.75x=31,535[/tex]

[tex]x=3,604\ books[/tex]

Answer:

Explanation:

1) Set the algebraigic expression that represents the combinations of sofa and pillow orders:

2) Predict the graph of the inequality x + 2y ≥ 4

        x = 0 ⇒ 2y = 4 ⇒ y =4/2 ⇒ y = 2 ⇒ point (0,2)

        y = 0 ⇒ x = 4 ⇒ point (4,0)

        Then the lines goes through (0,2) and (4,0) ... [the four graphs meet this]

3) Conclusion:

That means that the correct graph is the last one: solid line, shaded area over the line y = 2 - x/2.

Note: a more detailed graph would include the fact that the items cannot be negative, i.e. x ≥ 0 and y ≥ 0, which would result in that the shaded area would be on the first quadrant.

Answer: D

Step-by-step explanation:

6x + y = 28.  The standard form of the equation that is parallel to y = -6x + 5 and goes through point (4, 4) is 6x + y = 28.

The equation is written in the slope-intercept form y = mx +b. So:

y = -6x + 5

The slope m = -6

Since the slopes of parallel lines are the same, we are looking for a slope line m = -6 and goes through point (4, 4).

With the slope-intercept form:

y = mx + b

Introducing the slope m = -6:

y = -6x + b

Introducing the point (4, 4):

4 = -6(4) + b

b = 4 + 6(4)

b= 24 + 4

b = 28

Then

y = -6x + 28

write the equation in standard form ax + by = c:

y = -6x + 28

6x + y = 28

Answer:

  A ≈ 32°

Step-by-step explanation:

You are given two sides and the angle between them, so the law of cosines applies. The measure of side b can be found to be ...

  b² = a² + c² -2ac·cos(B)

  b² = 2² +3² -2·2·3·cos(95°) ≈ 14.0459

  b ≈ 3.74778

Then the law of sines can help you find angle A, the angle opposite the shortest side.

  sin(A)/a = sin(B)/b

  A = arcsin(a/b·sin(B)) = arcsin(2/3.74778·sin(95°)) ≈ 32.11°

  A ≈ 32°

The smallest angle is about 32°.

Answer:

142.4 cubic units

Step-by-step explanation:

Formula: π * r²

Radius = 4

Height = 8.5

Volume = 1/3 x 3.14 x (4)^2 x 8.5 =

The volume of an oblique cone is given in cubic units. The two options presented as cubic units are 142.4 and 196.0. Without additional measurements, we cannot calculate the exact volume, but we know that the volume must be one of these two options.

The question is asking to determine which of the provided values represents the volume of an oblique cone. Volume is the measure of space occupied by a three-dimensional object and is expressed in cubic units. In general, the volume of a cone can be calculated using the formula V = (1/3)πr²h, where 'r' is the radius of the base, 'h' is the height, and π is Pi, approximately 3.14159. Since an oblique cone has a circular base but is tilted, the formula for its volume is the same as that of a right cone.

Looking at the options provided, we need to determine which value most likely represents the volume of a cone. Since volume is expressed in cubic units, the correct answer will be in cubic units, not square units. Therefore, we can immediately eliminate the options with 'square units' as they represent an area measure instead of volume.

Thus the potential answers could either be 142.4 cubic units or 196.0 cubic units. Without additional information, such as the dimensions of the base and the height, we cannot perform the calculation to further refine the answer. However, the question might be simplifying the process by providing the answer directly, and it is up to the student to choose between the given cubic unit options based on an understanding of volumes rounding procedures, if applicable.

Answer:

Step-by-step explanation:

The dot product is the sum of products of the corresponding coordinate values:

[tex]\text{\bf{a}$\cdot$\bf{b}}=a_{x}b_{x}+a_{y}b_{y}[/tex]

The value of this can also be written in terms of the magnitudes of the vectors and the angle θ between them:

  |a|·|b|·cos(θ)

But the angle between the vectors is the same as the difference of their individual angles, θ = α - β, so this can also be written as ...

  |a|·|b|·cos(α-β)

And the trig identity for the cosine of the difference of angles lets us write the above as ...

  = |a|·|b|·(cos(α)cos(β) +sin(α)sin(β))

Answer:

  remaining zeros: negative i comma 5 minus i

Step-by-step explanation:

The remaining two zeros are the conjugates of the two zeros given. That brings the total number to 4 zeros, consistent with the number of zeros expected for a 4th-degree polynomial.

The conjugate of a complex number has the same real part and the opposite imaginary part.

Answer:

-i, 5-i

Step-by-step explanation:

Given that a function f(x) has only real coefficients and also of degree 4.

Since any polynomial with real roots have imaginary roots only with conjugate pairs, we can find other two roots easily

Degree of polynomial = 4

No of roots = 4

GIven roots are i, 5+i

Conjugate of the given roots are -i, 5-i

Hence remaining zeroes of f are -i, 5-i

Answer:

Choice A. 3.

Step-by-step explanation:

The triangle in question is a right triangle.

As a result, the length of both legs can be found directly using the sine function and the cosine function.

Let [tex]\text{Opposite}[/tex] denotes the length of the side opposite to the [tex]30^{\circ}[/tex] acute angle, and [tex]\text{Adjacent}[/tex] be the length of the side next to this [tex]30^{\circ}[/tex] acute angle.

[tex]\displaystyle \begin{aligned}\text{Opposite} &= \text{Hypotenuse} \times \sin{30^{\circ}}\\ &=2\sqrt{3}\times \frac{1}{2} \\&= \sqrt{3}\end{aligned}[/tex].

Similarly,

[tex]\displaystyle \begin{aligned}\text{Adjacent} &= \text{Hypotenuse} \times \cos{30^{\circ}}\\ &=2\sqrt{3}\times \frac{\sqrt{3}}{2} \\&= 3\end{aligned}[/tex].

The longer leg in this case is the one adjacent to the [tex]30^{\circ}[/tex] acute angle. The answer will be [tex]3[/tex].

There's a shortcut to the answer. Notice that [tex]\sin{30^{\circ}} < \cos{30^{\circ}}[/tex]. The cosine of an acute angle is directly related to the adjacent leg. In other words, the leg adjacent to the [tex]30^{\circ}[/tex] angle will be the longer leg. There will be no need to find the length of the opposite leg.

Does this relationship [tex]\sin{\theta} < \cos{\theta}[/tex] holds for all acute angles? (That is, [tex]0^{\circ} < \theta <90^{\circ}[/tex]?) It turns out that:

Answer:

A

Step-by-step explanation:

Since the triangle is right use the cosine ratio

cos30° = [tex]\frac{adjacent }{hypotenuse}[/tex] = [tex]\frac{adj}{2\sqrt{3} }[/tex], so

[tex]\frac{\sqrt{3} }{2}[/tex] = [tex]\frac{adj}{2\sqrt{3} }[/tex]

Multiply both sides by 2[tex]\sqrt{3}[/tex]

adj = [tex]\frac{\sqrt{3} }{2}[/tex] × 2[tex]\sqrt{3}[/tex] = 3

Answer:

It would take Tom 8 hours alone

Step-by-step explanation:

We are looking at this basic equation:

Tom + Shirley = 8 hours

Tom takes x hours to cut the grass; this means that 1/x of the job gets done in 1 hour

It takes Shirley 3 times as long as Tom, so it takes her 3x hours to cut the grass; this means that 1/3x of the job gets done in 1 hour

If the total number of hours it takes them to do the job is 6 hours; this means that 1/6  of the job gets done in 1 hour

Looking back at the original basic equation, we will fill in our info:

[tex]\frac{1}{x}+\frac{1}{3x}=\frac{1}{6}[/tex]

We can solve for x by first finding the LCD and eliminating the denominators.  The LCD is 6x, since all the denominators go into 6x evenly.

We will multiply the rational equation through by the LCD:

[tex]6x[\frac{1}{x}+\frac{1}{3x}=\frac{1}{6}][/tex]

Dividing each denominator into the LCD gives us:

6 + 2 = x so

x = 8

This means that it takes Tom 8 hours to do the job alone.  It would take Shirley 24 hours alone.  Ugh.

The time it would take Tom to mow the lawn alone is 3 hours

From the information given;

Let Tom's working hours be x.

Let Shirley's working hours be y.

We have  that;

Shirley and Tom work 6 hours together, this is expressed as;

x + y = 6

Given that Shirley work 3 hours alone, we have;

y = 3

Substitute the value of y as 3 in the equation

x + 3 = 6

x = 6 - 3

x = 3

Thus, the time it would take Tom  to mow the lawn alone is 3 hours

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There are 511 positive integers whose digits strictly increase from left to right.

To determine how many positive integers have digits that strictly increase from left to right, we need to consider combinations of digits. Since the digits must strictly increase, we cannot repeat any digit, and we can only use digits from 1 to 9.

Each number can be considered a unique combination of these digits, where the order of digits matters. For example, the digits {1, 2, 3} can only form the number 123. The total number of such combinations is given by the binomial coefficient C(9, k), where k is the number of digits.