Find the area of the sector in
terms of pi.
270°
12
Area = [?]

9514 1404 393

Answer:

  (3)  35·cos(57°)

Step-by-step explanation:

The relevant trig relation is ...

  Cos = Adjacent/Hypotenuse

For the given triangle, this is ...

  cos(57°) = QR/QS

Multiplying by QS gives ...

  QS·cos(57°) = QR

Filling in the value of QS, we have ...

  QR = 35·cos(57°)

Answer:

b. (4,14)

Step-by-step explanation:

Juan earns $7 per hour at his job.

This means that the ordered pairs showing his earnings y in x hours, (x,y), have the following format:

(x,7x).

Then, the ordered pairs are:

(1,7)

(2,14)

(3,21)

(4,28)

...

Thus, the ordered pair (4,14) would not appear on the graphic.

Answer:

[tex]\frac{\sqrt{3} }{3} }(cos(\frac{19\pi}{12})+isin(\frac{19\pi}{12}))[/tex]

Step-by-step explanation:

Division of complex numbers in polar form is [tex]z_1/z_2=\frac{r_1}{r_2}cis(\theta_1-\theta_2)[/tex] where [tex]z_1[/tex] and [tex]z_2[/tex] are the complex numbers being divided, [tex]r_1[/tex] and [tex]r_2[/tex] are the moduli, [tex]\theta_1[/tex] and [tex]\theta_2[/tex] are the arguments, and [tex]cis[/tex] is shorthand for [tex]cos\theta+isin\theta[/tex]. Therefore:

[tex]\frac{9(cos(\frac{11\pi}{6})+isin(\frac{11\pi}{6})) }{3\sqrt{3}((cos\frac{\pi}{4})+isin(\frac{\pi}{4})) }[/tex]

[tex]\frac{9}{3\sqrt{3} }cis(\frac{11\pi}{6}-\frac{\pi}{4})[/tex]

[tex]\frac{\sqrt{3} }{3} }cis(\frac{19\pi}{12})[/tex]

[tex]\frac{\sqrt{3} }{3} }(cos(\frac{19\pi}{12})+isin(\frac{19\pi}{12}))[/tex]

Answer:

A. Qualitative - Column chart

Step-by-step explanation:

Data could either be qualitative or quantitative. Quantitative data are usually given in a definite number, i.e it can be counted. While qualitative deals with characteristics, i.e it can be collected either by the use of questionnaires, or any similar method.

Therefore for the given question, the data survey is qualitative. And since the result would be presented as a graph showing the percentage users for each application, a column chart would be appropriate.

Thus for the data and its presentation, the answer is A. Quantitative - Column chart

Answer:

5

Step-by-step explanation:

jnjknmnj

Answer:

1/4= 3/12 & 2/6 = 4/12

Step-by-step explanation:

Answer:

Its simply B

Step-by-step explanation:

If we are to express both ratios in their simplest form, we will have the ratio of Michael’s lemonade is 1:4 and that of Sondra is 1:3. The denominator that can be used in order to compare the ratios is that which can be divided by both ratios. For example, we have 12 as a denominator. The ratios can be expressed as 3/12 and 4/12. Also, the denominator can be 24 such that the ratios can be expressed as 6/24 and 8/24.

Answer:

Mike made $ 200.63 last Friday.

Step-by-step explanation:

Since Ms. Peralta's friend Mike is a construction worker who gets paid $ 15 an hour, and after working 9 hours he gets paid 1.25 times his hourly rate, and last Friday Mike worked for 5 hours - took an 1 hr and 15 minute break for lunch (does not count toward his work hours) - and worked for an additional 7.5 hours, to determine how much money did Mike make last Friday the following calculation must be performed:

5 + 7.5 = 12.5

12.5 - 9 = 3.5

9 x 15 + (3.5 x (15 x 1.25)) = X

135 + 3.5 x 18.75 = X

135 + 65.625 = X

200.63 = X

Therefore, Mike made $ 200.63 last Friday.

Answer:

Triangles have two meanings depending on their position. When pointing up, they represent stability and power, when pointing down they become unstable. The triangle is primarily a masculine shape, but when inverted it also represents female reproduction. Triangles possess a number of key advantages that make them ideal for both architects and curious students. The strength of a triangle derives from its shape, which spreads forces equally between its three sides.

Step-by-step explanation:

Answer:

- 30 is the answer

Step-by-step explanation:

5 multiply 6 - 60​

5 × 6 - 60

= 30 - 60

= - 30

Answer: yes yes no yes yes no

Step-by-step explanation:

Answer:

See below for answers and explanations (as well as a graph attached)

Step-by-step explanation:

The function [tex]f(x)=\frac{x-5}{x^2-1}[/tex] can be written as [tex]\frac{x-5}{(x+1)(x-1)}[/tex], showing that there are 2 vertical asymptotes, which are at [tex]x=-1[/tex] and [tex]x=1[/tex] as they both make the denominator equal to 0.

Additionally, there would be a horizontal asymptote at [tex]y=0[/tex] since the degree of the numerator is less than the degree of the denominator.

See the attached graph.

Answer:

The number of vials of type A insulin sold were _21__ and the number of vials of type B insulin sold were __29__.

Step-by-step explanation:

Let a = number of type A vials.

Let b = number of type B vials.

38.85a + 30.34b = 1695.71

a + b = 50

            38.85a + 30.34b = 1695.71

(+)        -38.85a - 38.85b = -1942.50

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

                               -8.51b = -246.79

b = 29

a + b = 50

a + 29 = 50

a = 21

Answer: The number of vials of type A insulin sold were _21__ and the number of vials of type B insulin sold were __29__.

Answer:

Step-by-step explanation:

Mp=$1200

Let sp be x

SP=MP-discount% of MP

x=1200-15/100 * 1200

x=120000-18000/100

x=102000/100

x=1020

the amount of money person saves=MP-SP

=$1200-$1020

=$180

therefore he saves $180

Answer:

Step-by-step explanation:

A = P(1+r/n)^ nt

A = 2000(1+.04/2)^(5*2)

A = [tex]2000(1.02)^{10}[/tex] = $2437.99

f(x) = 3/x+2 - √x - 3

f(3) = 3/3 + 2 - √3 - 3

f(3) = 3/3 + 2 - √0

f(3) = 3/5 - 0

f(3) = 3/5

You can let x be any value of your choice.

Answer:

x=15 degree

Step-by-step explanation:

5x +5+6x -1+3x+5x+3+4x+8 =360 degree (exterior angles of pentagon is 360 degree)

23x +15 =360

23x=360-15

x=345

x=345/23

x=15 degree

Answer:

(E) 9

Step-by-step explanation:

[tex]\frac{(3^{2008})^2-(3^{2006})^2}{(3^{2007})^2-(3^{2005})^2} = \\\frac{(3^{2007+1})^2-(3^{2007-1})^2}{(3^{2007})^2-(3^{2007-2})^2} = \\\frac{(3^{2007})^2(3^{2}-3^{-2} )}{(3^{2007})^2(1-3^{-4} )} =\\\frac{9-\frac{1}{9} }{1-\frac{1}{81} }=\\\frac{80}{9}:\frac{80}{81} = \\\frac{80}{9}*\frac{81}{80} = \frac{81}{9} = 9[/tex]

Answer:

b

Step-by-step explanation:

glad I helped..............

Answer:

B

Step-by-step explanation:

792 is a bigger number than 456

Answer: B

Step-by-step explanation: 792 is larger than 456

Answer:

202 m

Step-by-step explanation:

Given :

Angle of depression, θ = 36°45' ; 45/60 = 0.75 = 36 + 0.75 = 36.75°

The height, h = 270

The distance of park bench from the building, d is given by :

Tan θ = opposite / Adjacent

Tan 36.75 = d / 270

d = 270 * Tan 36.75

d = 201.61856

d, distance of Park bench from building is 202 m

9514 1404 393

Answer:

  (b)  $1,393.88

Step-by-step explanation:

For each overtime hour, Michelle is paid for 1.5 hours. That is we can figure her pay as though she worked straight time for ...

  47.75 hours + (7.75 hours)/2 = 51.625 hours

That pay is ...

  (51.625 h)($27/h) = $1393.88

Answer:

41.6

Step-by-step explanation:

got it wrong and it showed me the right answer

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

Explanation:

The diagram is shown below. We know the vertical part of the triangle is 13 inches, which is the side opposite the reference angle 13 degrees. The adjacent side is unknown. We'll call it x. This is how long the base of the ramp is, which is the horizontal distance along the entire ramp. This distance is on the ground. The ramp itself is the hypotenuse but it seems like your teacher isn't wanting to know this value. So we'll ignore the hypotenuse.

We'll use the tangent rule to connect the opposite and adjacent sides.

tan(angle) = opposite/adjacent

tan(13) = 13/x

x*tan(13) = 13

x = 13/tan(13)

x = 56.309186365694

x = 56 inches is the approximate horizontal distance underneath the ramp

The base of the ramp is 57 inches long.

Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.

The tangent function relates the opposite side (height) and adjacent side (base) of a right triangle to the angle of elevation.

We know the opposite side is the height of the ramp, which is 13 inches, and the angle of elevation is 13 degrees.

Let the adjacent side (the base of the ramp) be "x".

The tangent of 13 degrees is equal to the opposite side divided by the adjacent side:

tan(13) = 13/x

To solve for x, we can multiply both sides by x:

x × tan(13) = 13

Then, we can divide both sides by tan(13):

x = 13 / tan(13)

x = 13 / 0.228

x= 56.99

Therefore, the base of the ramp is 57 inches long.

To learn more on trigonometry click:

https://brainly.com/question/25122835

#SPJ2

Answer:

10.7

Step-by-step explanation:

17.445 - 6.76= 10.685

10.685 is 10.7 when rounded to the nearest tenth!

Answer:

17.5 cards

Step-by-step explanation:

11 x 1.5 = 16.5

16.5 + 11 = 17.5 cards

Answer:

110

Step-by-step explanation:

Let us take Jack cards as x

Then Mark cards will be 1.5 * x

Mark gives 11 cards to Jack...the equation is

1.5 * x  - 11 = x + 11

Adding +11 on both sides

1.5*x -11 + 11 = x + 11 + 11

1.5*x = x + 22

Subtracting x on both sides

1.5*x - x = x + 22 - x

.5*x = 22

x = 22 * 1/.5 = 220/5 = 44

Now go back to the initial equation

Mark >> 1.5  * x = 66

Jack  >> 1 * x = 44

Total >> 110.

Step-by-step explanation:

1) 6s^2

(s mean the length of each side, s=7)

= 6x7^2

= 294

2) 2(3)(2)+2(1)(2)+2(3)(1)

（l=length, w=wide, h=height)

= 12+4+6

= 22

3) 4(π)12^2

(r=radius)

= 576

Compare to the divergent series,

[tex]\displaystyle\sum_{n=1}^\infty\frac1n[/tex]

Then by the limit comparison test, the given series also diverges, since the limit

[tex]\displaystyle\lim_{n\to\infty}\frac{\frac{2n^5-1}{n^6+1}}{\frac1n} = \lim_{n\to\infty}\frac{2n^6-n}{n^6+1}=\lim_{n\to\infty}\frac{2-\frac1{n^5}}{1+\frac1{n^6}}=2[/tex]

is positive and finite.

Answer:

[tex]\sin(G) = \frac{8}{17}[/tex]

Step-by-step explanation:

Given

[tex]\angle H = 90^o[/tex]

[tex]FH = 8[/tex]

[tex]GF = 17[/tex]

[tex]HG = 15[/tex]

See attachment for illustration

Required

The ratio of [tex]\sin(G)[/tex]

[tex]\sin(G)[/tex] is calculated as:

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

From the attachment, we have:

[tex]\sin(G) = \frac{FH}{GF}[/tex]

This gives:

[tex]\sin(G) = \frac{8}{17}[/tex]

Answer:

False

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set 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]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

Population:

[tex]\mu = 30, \sigma = 8[/tex]

Sample of 4

This means that [tex]n = 4, s = \frac{8}{\sqrt{4}} = 4[/tex]

Probability of obtaining a sample mean greater than 34:

This is 1 subtracted by the p-value of Z when X = 34. So

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

By the Central Limit Theorem

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

[tex]Z = \frac{34 - 30}{4}[/tex]

[tex]Z = 1[/tex]

Thus, the probability of obtaining a sample mean greater than 34 is equal to the probability of obtaining a z-score greater than z = 1.00, and the statement in this question is false.