prove the identity of
[tex] 4 sin^{2}x + 7sin^{2} = 4 + 3cos^{2} [/tex]

Answers

Answer 1

Answer:

7sin

2

x+3cos

2

x=4

4sin

2

x+3sin

2

x+3cos

2

x=4

4sin

2

x+3=4

4sin

2

x=1

sin

2

x=

4

1

sinx=

2

1

or sinx=−

2

1

Step-by-step explanation:

TAKING THE POSITIVE ROOT x=

6

π

tan(

6

π

)=

3

1


Related Questions

What is the mean of this data set?

A. 84
B. 85
C. 83
D. 88

Answers

Answer:

85

Step-by-step explanation:

Add  to get total. divide by 4.

Answer:

B. 85

Step-by-step explanation:

Sorry for this very late response. But if anyone wasn't sure if 85 is the correct answer, it is. I can confirm this because I just took the test. I hope I could help! (:

Use the ratio of a 45-45-90triangle to solve for the variables. Make sure to simplify radicals. Leave your answers as radicals in simplest form.

Answers

Answer:

Step-by-step explanation:

in this specific case the two legs are congruent:

b = 18

For the Pythagorean theorem

a = √ 2 * 18^2 = 18√2

*20 points*
What is the probability of drawing yellow marble followed by a red marble from a bag containing 12 yellow marbles, 14 red marbles, and 15 green marbles if the first marble is not replaced?

a. 192/1,849
b. 18/43
c. 21/205

Answers

Answer:

c: 21/205

Step-by-step explanation:

The probability of choosing a yellow marble first is 12/41 bc there are 12 yellow marbles and 41 marbles to choose from.

The probability of choosing a red marble is 14/40 bc there are 14 red marbles and 40 marbles to choose from( since you have removed the marble you first chose so there are 40 marbles left).

Multiplying these two together, 12/41 * 14/40 = 168/1640, simplified it's 21/205.

what is the graph of −36≤2x+4(x−3)

Answers

The answer is x ≥ -4

Given the following situation:
A cell phone company offers a data package by charging $20 a month plus $12 per gigabyte of data used. Write a linear equation
that relates the cost C, in dollars, to the amount of data used. Use it to determine the amount of data used if they charge you
$116.

Answers

9514 1404 393

Answer:

C = 20 +12g8 gigabytes

Step-by-step explanation:

At $12 per gigabyte, the data charge will be 12g where g is the number of gigabytes. Then the total charge is ...

  C = 12g +20

__

If C = 116, the value of g is found from ...

  116 = 12g +20

  96 = 12g . . . . . . . subtract 20

  8 = g . . . . . . . . . . divide by 12

The amount of data used is 8 gigabytes if the charge is $116.

Two boats are travelling at 30 miles/hr, the first going north and the second going east. The second crosses the path of the first 10 minutes after the first one was there. At what rate is their distance increasing when the second has gone 10 miles beyond the crossing point

Answers

Answer:

their distance is increasing at the rate of 41.6 miles/hr

Step-by-step explanation:

Given the data in the question;

first we determine the distance travelled by the first boat in 10 min when the second boat was crossing its path;

⇒ ( 30/60 ) × 10 = 5 miles

so as illustrated in the diagram below;

y² = x² + ( x + 5 )²

2y[tex]\frac{dy}{dt}[/tex] = 2x[tex]\frac{dx}{dt}[/tex] + 2(x+5)[tex]\frac{dx}{dt}[/tex]

y[tex]\frac{dy}{dt}[/tex] = ( 2x + 5 ) ][tex]\frac{dx}{dt}[/tex]

[tex]\frac{dy}{dt}[/tex] = [( 2x + 5 )/y ][tex]\frac{dx}{dt}[/tex]   ------ let this be equation 1

Now, given that, [tex]\frac{dx}{dt}[/tex]  = 30 miles/hr, when x = 10

so

y = √( 10² + 15² ) = √325

so from equation 1

[tex]\frac{dy}{dt}[/tex] = [( 2x + 5 )/y ][tex]\frac{dx}{dt}[/tex]

we substitute

[tex]\frac{dy}{dt}[/tex] = [( 2(10) + 5 ) / √325 ]30

[tex]\frac{dy}{dt}[/tex] = [ 25 / √325 ] × 30

[tex]\frac{dy}{dt}[/tex] = 41.6 miles/hr

Therefore, their distance is increasing at the rate of 41.6 miles/hr

8x( 5 x 2 ) Pls give answer

Answers

Answer:

80x

Step-by-step explanation:

Bracket first

5 x 2 = 10

8x x 10 = 80x

(Unless the 'x' next to the 8 is the term for multiplying:

8 x 10 = 80)

Answer:

80

Step-by-step explanation:

8 x (5 x 2)

8 x 10

Answer = 80

Alice and Bob each choose a number uniformly (and independently) from the interval [0, 10]. What is the probability that the absolute value of the difference between their two numbers is less than 1/4

Answers

Answer:

The probability is zero (0)

Step-by-step explanation:

Given;

interval of numbers to be chosen = 0, 1, 2, 3 , 4, 5, 6, 7, 8, 9 , 10

total possible outcome = 11

The possible numbers whose absolute difference is greater than ¹/₄ includes the following;

(0,1), (1,2), (2,3), (3,4), (4,5), (5,6), (6,7), (7,8), (8,9), (9,10), (10,0)

The probability of this = 11 / 11 = 1

The probability that the absolute value of the difference between their two numbers is less than 1/4

[tex]P(less \ than \ \frac{1}{4} ) = 1 - P(greater \ than \ \frac{1}{4} )\\\\P(less \ than \ \frac{1}{4} ) = 1 - 1 \\\\P(less \ than \ \frac{1}{4} ) = 0[/tex]

At the end of March, Jerry bought a plant that was $16.2 inches tall. During April, the plant grew 2] inches,
and during May, the plant grew another 2 inches. How tall was the plant at the beginning of June?
O 18.2 inches
O 19 inches
0 21 inches
21 inches

Answers

Answer:

20.2 inches

Step-by-step explanation:

The plant starts at 16.2 inches

The first month it grows 2 inches

16.2+2 =18.2 inches

Then the next month it grows 2 inches

18.2+2 = 20.2 inches

Companies are starting to use 360-degree surveys to evaluate the performance of their employees. This approach uses annonymous feedback from a variety of people who work closely with the employee. People who fill out the survey could be coworkers, supervisors, subordinates, or even customers. It is different from a traditional performance review, which relies only on feedback from an employee's supervisor. Many prefer the 360-degree approach because it provides a more well-rounded perspective on how the employee performs in their job role. Supervisers can be biased because they do not interact with the employee in the same way that a customer or co-worker might. However, the 360-degree survey approach still relies only on subjective feedback, which does not always give a fair representation of the employee's work?

Answers

Answer:

the study of and knowledge about the physical world and natural lawsthe study of and knowledge about the physical world and natural lawsthe study of and knowledge about the physical world and natural lawsthe study of and knowledge about the physical world and natural laws

Evaluate (657.3÷10)-(94.5÷5)

Answers

Answer:

Ans; (657.3÷10)-(94.5÷5) = 65.73 – 18.9 = 46.83

I hope I helped you^_^

Write a inequality.
Question: twice a number is no more than 14
Please help

Answers

Answer:

2x[tex]\leq[/tex]14

Step-by-step explanation:

Answer:

2x ≤ 14

Step-by-step explanation:

twice a number   is no more than     14

               2x                     ≤                 14

A tortoise is walking in the desert. It walks 7.5 meters in 3 minutes. What is its speed?
meters per minute

Answers

9514 1404 393

Answer:

  2.5 m/min

Step-by-step explanation:

To find meters per minute, divide meters by minutes:

  (7.5 m)/(3 min) = 2.5 m/min

The speed of the tortoise is 2.5 meters per minute.

45%of the total population of a village are males and there are 22000 females Find the male population of the village.​

Answers

Answer:

18000

Step-by-step explanation:

The 22000 females make up 55% of the population. So, we divide 22000 by 0.55 to get the total population.

22000 ÷ 0.55 = 40000

Now we take our total population and subtract 22000 to get the number of males in the population.

40000 - 22000 = 18000

The male population of the village is 18000.

Câu 99: Cho hàm số f x  xác định trên ℝ , bảng biến thiên của hàm số f x   như sau.
x  1 1 3 
f x    |  0  | 
f x  
 
0 0
4
Mệnh đề nào dưới đây đúng?
A. Hàm số f x  đồng biến trên 1;.
B. Hàm số f x  đồng biến trên  ; 1 và 3;.
C. Hàm số f x  nghịch biến trên  ; 1.
D. Hàm số f x  đồng biến trên     ; 1 3;   .

Answers

Answer:

i doesn,t understand this language

Can someone do #8 #9 & #10 for me please?!❤️

Answers

Answer:

8. 72% × 850

= 72/100 × 850

= 72 × 8,5

= 612 ( b )

9. Poin B = 4 ( b )

Answer:

8. B

9. B

10. C

Step-by-step explanation:

8. To find 72% of 850, you would multiply 0.72 x 850. When you do that, it gives you 612.

9. B is on the number 4.

10. The expression is asking, "What is the absolute value of 28?". Absolute value means that the number inside will always be positive. For example, if it was -28, the absolute value would turn to 28. Since the question has 28 already positive, there is no change, so the answer would be 28.

pamela is 8 years older that jiri. the sum of their age is 102. What is jiris age?

Answers

       There are two different ways we can solve this problem. We could use brute force, or we can use some equations to solve the problem. We can start by defining Pamela and Jiri's ages differently. If Jiri is j, and Pamela is p, we can say that p = j + 8, because Jiri + 8 years is Pamela's age.

       Now, using our values for Pamela and Jiri, we can say that (j + 8) + j = 102. Now we just solve like a normal equation, so 2j = 94, and j = 47, so Jiri is 47 years old.

Answer:

J = 47

Step-by-step explanation:

P = Pamela

J = Jiris

P = 8 + J ;- Equation 1

P + J = 102 ;- Equation 2

Substitute equation 1 into 2 to get:

J + 8 + J =102

2J = 102 - 8

2J = 94

J = 47

So Jiris is 47 years old

HELP ASAP!!
If the circle below is cut from the square of plywood below, how many square inches of plywood would be left over?
Use π = 3.14, and round your answer to the nearest hundredth.

Answers

Answer:

13.73 in^2 because the circle's area is 50.27 in^2

Solve the following equation for
f
f. Be sure to take into account whether a letter is capitalized or not.

Answers

Answer:

q + j

Step-by-step explanation:

q = - j + f

f = q + j

q + j is the answer.

Answer:

f = q + j

Step-by-step explanation:

Rewrite the equation:

-j + f = q

Add  j  to both sides of the equation:

f = q + j

In four years,George saved $540. His twin sister, Georgette, saved 10 times as much. How much did Georgette saved?

Answers

5400 dollars

540x10= 5400

plz help me on this question best and right answer gets brainliest

Answers

Answer:

| - 5| 5

| 6 | 6

| - 9 | 9

the numbers will be positive when they come out from the absolute value

Answer and Step-by-step explanation:

The absolute value of a value is the positive version of that value.

| | <- Brackets are used to show that a value is being absolute.

|-5| = 5  The negative 5 with absolute brackets becomes a positive 5.

|6| = 6    A positive 6 with absolute brackets stays a positive 6.

|-9| = 9   A negative 9 with absolute brackets becomes a positive 9.

#teamtrees #PAW (Plant And Water)

Are the two triangles below similar?
U
ВО
56
No because there are not to pairs of congruent corresponding angles
Yes because there are two pairs of congruent corresponding angles
No because the corresponding sides are not proportional
Yes because the corresponding sides are proportional

Answers

Answer:

Yes, because there are two pairs of congruent corresponding angles

Step-by-step explanation:

Two triangles are similar if they have the same angles. For triangle UVT on the left, we know that the sum of angles in a triangle is 180 degrees. There is one missing angle there, so the sum of angles is

80 + 55 + missing angle = 180

subtract 80+55 = 135 from both sides

45 = missing angle

Therefore, the angles in UVT are 45, 55, and 80

Similar, for XWY,

missing angle + 45 + 55 = 180

subtract 45 + 55= 100 from both sides

missing angle = 80

The angles for XWY are 45, 55, and 80. The angles are the same for both triangles, and there are three pairs of congruent corresponding angles (45, 55, and 80). Therefore, the triangles are similar

Suppose that, in the past, 40% of all adults favored capital punishment. Do we have reason to believe that the proportion of adults favoring capital punishment today has increased if, in a random sample of 15 adults, 8 favor capital punishment? Use a 0.05 level of significance.

Answers

Answer:

The p-value of the test is 0.1469 > 0.05, which means that there is no reason to believe that the proportion of adults favoring capital punishment today has increased, using a 0.05 level of significance.

Step-by-step explanation:

Suppose that, in the past, 40% of all adults favored capital punishment. Test if the proportion has increased:

At the null hypothesis, we test if the proportion is still of 40%, that is:

[tex]H_0: p = 0.4[/tex]

At the alternative hypothesis, we test if the proportion has increased, that is, is greater than 40%, so:

[tex]H_1: p > 0.4[/tex]

The test statistic is:

[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, [tex]\sigma[/tex] is the standard deviation and n is the size of the sample.

0.4 is tested at the null hypothesis:

This means that [tex]\mu = 0.4, \sigma = \sqrt{0.4*0.6}[/tex]

Random sample of 15 adults, 8 favor capital punishment.

This means that [tex]n = 15, X = \frac{8}{15} = 0.5333[/tex]

Value of the test statistic:

[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

[tex]z = \frac{0.5333 - 0.4}{\frac{\sqrt{0.4*0.6}}{\sqrt{15}}}[/tex]

[tex]z = 1.05[/tex]

P-value of the test and decision:

The p-value of the test is the probability of finding a sample proportion of 0.5333 or more, which is 1 subtracted by the p-value of z = 1.05.

Looking at the z-table, z = 1.05 has a p-value of 0.8531.

1 - 0.8531 = 0.1469.

The p-value of the test is 0.1469 > 0.05, which means that there is no reason to believe that the proportion of adults favoring capital punishment today has increased, using a 0.05 level of significance.

a swift can fly at 160km/h. what is the speed in m/s? show clearly how you worked out your answer.

Answers

Answer:

[tex]\huge\boxed{\sf Speed = 44.44 \ m/s}[/tex]

Step-by-step explanation:

Speed = 160 km / hr

To convert km/hr to m/s, we multiply it by [tex]\sf \frac{10}{36}[/tex]

Hence,

[tex]\displaystyle Speed = 160 \times \frac{10}{36} \ m/s\\\\Speed = \frac{1600}{36} \ m/s\\\\Speed = 44.44 \ m/s\\\\\rule[225]{225}{2}[/tex]

Hope this helped!

~AH1807Peace!


A car is advertised with a price of $16336. The payment plan to own a car is $474 per month for 8 years. What is the
amount of interest paid?

Answers

The interest rate is about 32.045%.

The side-by-side stemplot below displays the arm spans, in centimeters, for two classes.

A stemplot titled Arm Span (centimeters). For Class A, the values are 148, 151, 153, 155, 156, 159, 161, 162, 164, 165, 169, 169, 170, 171, 175, 176, 179, 179, 180, 182, 183, 186, 186, 190. For Class B, the values are 153, 155, 16, 160, 162, 162, 162, 163, 163, 165, 166, 167, 170, 173, 180, 181, 182, 189, 192, 202.

Which statement correctly compares the variability of the arm spans for Class A to that of Class B?

The arm spans for Class A have more variability than the arm spans for Class B.
The arm spans for Class B have less variability than the arm spans for Class A.
The arm spans for Class A have less variability than the arm spans for Class B.
The arm spans for Class B have about the same variability as the arm spans for Class A.

Answers

Answer:

The answer is in the picture below

Step-by-step explanation:

Sorry just realised the answers were different ;-;

Answer:

The arm spans for Class A are roughly symmetric, while those for Class B are skewed left.

Step-by-step explanation:

Andrew buys 27 identical small cubes, each with two adjacent faces painted red. He then uses all of these cubes to build a large cube. What is the largest number of completely red faces of the large cube that he can make

Answers

Answer:

4

Step-by-step explanation:

Number of Identical small cubes = 27

Determine the largest number of completely red faces of the large cube that he can make

Given that 2 adjacent faces of each cube is painted

and the number of cubes = 27

The number of complete red face Large cube he can make = 4

plz help with this:)

Answers

9514 1404 393

Answer:

  -4

Step-by-step explanation:

The point (x, y) = (0, 0) is on the line, so it represents a proportional relation. Any ratio of y to x will be the slope. The choice that makes this computation easiest is ...

  x = 1, y = -4

  y/x = -4/1 = -4

The slope of the line is -4.

There are 1000 students in a college.Out of 20000 in the whole university in a study of 200 were found to be smokers in the college and 1000 in whole university. Is there any significant difference between the proportion of smokers in college and university​

Answers

Answer:

1000 students in college

2000 students in University

200 out of 2000 are smokers

200 out 1000 are smokers

200 : 2000

1 :10

200 : 1000

1 : 5

Which expression is equivalent to 3/2

Answers

Answer:

C

Step-by-step explanation:

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