if right triangle RST, ST = 5, RT = 12, and RS = 13. Find tan (S).

[tex]\text{Given that,}\\\\\tan x = \dfrac 3{10}\\\\\text{Now,}\\\\\sin 2x = \dfrac{2\tan x}{1+ \tan^2 x}\\\\\\~~~~~~~~=\dfrac{2 \cdot \tfrac 3{10}}{1+ \left(\tfrac 3{10} \right)^2}\\\\\\~~~~~~~~=\dfrac{\tfrac 35}{1+ \tfrac 9{100}}\\\\\\~~~~~~~~=\dfrac{ \tfrac 35}{\tfrac{109}{100}}\\\\\\~~~~~~~~=\dfrac 35 \times \dfrac{100}{109}\\\\\\~~~~~~~~=\dfrac{60}{109}\\\\\\~~~~~~~~=0.5505[/tex]

Answer: the answer is b

Step-by-step explanation:

Domain and ranges of inverse functions are swapped.

Domain of the original is the range of the inverse and vice versa.

Answer:

random sampling

Step-by-step explanation:

There are no rules or criteria that are set to choose which Starbucks are chosen to be surveyed.

Answer:

[tex]\frac{3}{6}=\frac{3*4}{6*4}=\frac{12}{24}[/tex]

Step-by-step explanation:

How may twenty-fourths equal 3/6

Well, we know that 6 * 4 = 24

So, we will be multipying the numerator and denominator with 4/4:

[tex]\frac{3}{6}=\frac{3*4}{6*4}=\frac{12}{24}[/tex]

Therefore, twelve twenty-fourths (12/24) is equivalent to three-sixths (3/6)

Hope this helps!

Using the graph of the function, it is found that the lateral limits of the function are as follows:

For [tex]x \rightarrow 1^{+}[/tex], we look at the values slightly greater than 1, that is, to the right of x = 1, for which the function goes to negative infinity, hence [tex]f(x) \rightarrow -\infty[/tex].

For [tex]x \rightarrow 1^{-}[/tex], we look at the values slightly less than 1, that is, to the left of x = 1, for which the function goes to infinity, hence [tex]f(x) \rightarrow \infty[/tex].

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Answer:

7.014m

Step-by-step explanation:

[tex] \frac{11.3}{2.9} = \frac{h}{1.8} \\ h = \frac{11.3 \times 1.8}{2.9} \\ h = 7.013793103448275 \\ h = 7.014m[/tex]

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Jorge's momentum given his mass and the velocity while skateboarding is 135kg-m/s north.

Momentum can be described as the impetus that is gained by an object that is motion. Momentum is velocity multiplied by mass. When put simply, momentum can be described as mass in motion. Thus, when an object is moving, it has momentum.

Momentum velocity x mass

45 x 3 = 135kg-m/s north.

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Answer:

using quadratic formula check the attachment

Answer:

  0.34

Step-by-step explanation:

You know from the empirical rule that 68% of the area of the normal distribution lies in the range z=-1 to z=1. The distribution is symmetrical, so half that area lies in the range z = -1 to z = 0.

  area = 68%/2 = 34% = 0.34

__

Your calculator can tell you the same thing.

The number of different collections of 6 books which can be taken on vacation of 11 possible books is 462.

Combination is the way of arrangement or the collection of items in the particular order. The order of this group of items does not matter in the combination type of arrangement.

Here, in the original problem, the number of book selection is6.

Of 11 possible books, one plans to take 6 with on vacation. The number of different collections of 6 books can be taken has to be found out.

Thus, the number of combination to select 6 books collection from 11 is,

[tex]^{11}C_6=\dfrac{11!}{(11-6)!6!}\\^{11}C_6=\dfrac{11\times10\times9\times8\times7\times6!}{5\times4\times3\times2\times1\times6!}\\^{11}C_6=462[/tex]

Thus, the number of different collections of 6 books which can be taken on vacation of 11 possible books is 462.

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Answer:

I think C and D options can be correct

Step-by-step explanation:

PLEASE MARK ME BRAINLIEST IF MY ANSWER IS CORRECT PLEASE

Answer:

I think C and D options can be correct

Step-by-step explanation:

Answer:

9

Step-by-step explanation:

So,

2 is in the units,

4 is in the tens,

1 is in the hundreds,

6 is in the thousands,

9 is in the ten thousands, and

7 is in the hundred thousands.

I hope this is helpful xx

Answer:

9 is in the ten thousands place.

Answer:

$38.1 billion

Step-by-step explanation:

S - 1.5x = 5.1

x = 2020 - 1998

x = 22 years

S - 1.5(22) = 5.1

S = 5.1 + 33

S = 38.1

I hope this helps!

Answer:

38.1 billion dollars.

Step-by-step explanation:

2020 - 1998 = 22 years, so

S  - 1.5(22) = 5.1

S = 5.1 + 1.5(22)

S = 5.1 + 33

= 38.1.

Answer:

4 were broken

Step-by-step explanation:

[tex]\frac{1}{3}[/tex] × 12 = [tex]\frac{12}{3}[/tex] = 4 ← number of broken eggs

Answer:

Large - PR - 15 and QR - 9 Missing degrees is P - 37

Small - Missing degree is 53

They are similar because they have the exca same degrees and if you divided by 3 on each side of the larger triangle you get the small triangle.

Step-by-step explanation:

Pythagorean theorem

Answer:

first blank:center

second blank: equal to

Step-by-step explanation:

A central angle has its vertex (the point or corner of the angle) at the center of a circle. The arc (curved piece of the circle) that is cut off by the angle (intercepted arc) has the same measure as the angle. see image

First of all, subtract 5 from both sides:-

13-5<z+5-5

13-5<z

8<z

Since 8 is less than z, z is greater than 8:-

[tex]\bigstar{\boxed{\pmb{z > 8}}[/tex]

Hence, all the numbers greater than 8 will make this inequality true.

Hope everything is clear; if you need any explanation/clarification, kindly let me know, and I will comment and/or edit my answer :)

Answer:

Let's solve your inequality step-by-step.

13<z+5

Step 1: Flip the equation.

z+5>13

Step 2: Subtract 5 from both sides.

z+5−5>13−5

z>8

Answer:

z>8

Step-by-step explanation:

Using the normal approximation to the binomial distribution, it is found since np = 0.5 < 10, we cannot find the probability.

In a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

In this problem, we have that:

Then:

np = 50 x 0.01 = 0.5 < 10.

Thus we cannot find the probability.

More can be learned about the normal approximation to the binomial distribution at https://brainly.com/question/14424710

Answer:

1) 69/81 (indirect probability)

2) not asked a question (indirect probability)

3) 1/4 (indirect)

4) 75% (indirect)

Step-by-step explanation:

1) 45+24/12

2) Doesn't ask a question

3) 2 are white females so 2/8=1/4

4) 45%+30%

I hope this okay and correct

The internal angles of 64.801° (2 in total) and 115.199° (2 in total) lead to a maximum area of 27.88 square units.

Quadrilaterals are figures formed by four line segments and whose sum of internal angles equals 360°. By geometry we know that the area of a trapezoid is the average of the length of the two bases (B, b), in inches, multiplied by the height of the quadrilateral.

A = 0.5 · (B + b) · h   (1)

By trigonometry the measure of the longer base and the height of the isosceles trapezoid are, respectively:

B = b + 2 · l · cos θ   (2)

h = l · sin θ   (3)

Where θ is an internal angle, in degrees.

By (2) and (3) in (1):

A = 0.5 · (2 · b + 2 · l · cos θ) · (l · sin θ)

A = (b + l · cos θ) · (l · sin θ)

A = b · l · sin θ + l² · sin θ · cos θ

A = b · l · sin θ + 0.5 · l² · sin 2θ  (4)

If we know that b = 6 in and l = 4 in, then the area of the isosceles trapezoid is represented by the following function:

A = 24 · sin θ + 8 · sin 2θ   (5)

Now we determine the angle associated to the maximum area by graphic approach.

According to this approach, the internal angles of 64.801° (2 in total) and 115.199° (2 in total) lead to a maximum area of 27.88 square units. [tex]\blacksquare[/tex]

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Answer:

BC = FE

Step-by-step explanation:

given ,

BA = FD and the measure of angle ABC = the measure of angle DFE

If we have BC = FE then according to the SAS criterion the two triangles are congruent

Answer:

one hour have 60 minutes and the plane took one hour and 20 minutes so total it used 80 minutes

Answer: C.

Step-by-step explanation:Parallel lines never touch so they cant be intersecting.

Answer:

The first can.

Step-by-step explanation:
formula: Pi x diameter x height

1st can has a volume of 113.10
2nd can has a volume of 75.40

Answer:

28%

Step-by-step explanation:

Divide 14 by 50. 50 is the total and 14 is the amount she thought was good so it would be 14/50 and then divide it and you get .28 which is 28%

Answer:

Hope the pictures will help you..

Step-by-step explanation:

-10(y-4)+3y=5

-10y +40+3y =5

-7y = -40 +5

-7y=-35

7y = 35

{y= 5}

--------------

y=5

x=y-4

x=5-4

{x=1}

Answer:

68

Step-by-step explanation:21+6+6+14+21=68

Answer:

82

Step-by-step explanation:

Calculate the area of each part and sum them up

S= 7x3+7x2+7x3+2x3+2x3+7x2

42+28+12

=82

hope this helps!

Answer:

20 Units

Step-by-step explanation:

The question wants us to find the area of the shape.

From looking at the shape, we can easily infer that it is made of 1 square and 1 triangle.

Area of a Square/Rectangle Formula: A = W(L)

Area of a Trangle Formula: A = (1/2)(b)h

A = W(L)+(1/2)(b)h

The base of the traingle can be found by subtracting the longer length (6) from the smaller length (4).

A = 4(4)+(1/2)(2)4

A = 16+(1)4

A = 16+4

A = 20 Units

The amount $4,000 deposited by Sam into an IRA account where it earns 9.8% interest, compounded monthly, will be $12903.8  when Sam is 33.

Compound interest is the amount charged on the principal amount and the accumulated interest with a fixed rate of interest for a time period.

The formula for the final amount with the compound interest formula can be given as,

[tex]A=P\times\left(1+\dfrac{r}{n\times100}\right)^{nt}\\[/tex]

Here, A is the final amount (principal plus interest amount) on the principal amount P of with the rate r of in the time period of t.

At age 25, Sam deposited $4,000 into an IRA account where it earns 9.8% interest, compounded monthly. Thus,

[tex]P=4000\\r=9.8\%[/tex]

Now the worth has to be found out when Sam is 33. Thus, the total time period in year is,

[tex]t=33-25\\t=12\rm\; years[/tex]

Put the values in the formula,

[tex]A=4000\times\left(1+\dfrac{9.8}{12\times100}\right)^{12\times12}\\A\approx12903.8[/tex]

Thus, the amount $4,000 deposited by Sam into an IRA account where it earns 9.8% interest, compounded monthly, will be $12903.8  when Sam is 33.

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Answer: $8733.01

Step-by-step explanation: I got it right on my quiz