given that sin theta= 1/4, 0 is less than theta but less than pi/2, what is the exact value of cos theta

Answers

Answer 1

Answer:

[tex]\cos{\theta} = \frac{\sqrt{15}}{4}[/tex]

Step-by-step explanation:

For any angle [tex]\theta[/tex], we have that:

[tex](\sin{\theta})^{2} + (\cos{\theta})^{2} = 1[/tex]

Quadrant:

[tex]0 \leq \theta \leq \frac{\pi}{2}[/tex] means that [tex]\theta[/tex] is in the first quadrant. This means that both the sine and the cosine have positive values.

Find the cosine:

[tex](\sin{\theta})^{2} + (\cos{\theta})^{2} = 1[/tex]

[tex](\frac{1}{4})^{2} + (\cos{\theta})^{2} = 1[/tex]

[tex]\frac{1}{16} + (\cos{\theta})^{2} = 1[/tex]

[tex](\cos{\theta})^{2} = 1 - \frac{1}{16}[/tex]

[tex](\cos{\theta})^{2} = \frac{16-1}{16}[/tex]

[tex](\cos{\theta})^{2} = \frac{15}{16}[/tex]

[tex]\cos{\theta} = \pm \sqrt{\frac{15}{16}}[/tex]

Since the angle is in the first quadrant, the cosine is positive.

[tex]\cos{\theta} = \frac{\sqrt{15}}{4}[/tex]

Answer 2

Answer:

b.[tex]\frac{\sqrt{15} }{4}[/tex]

Step-by-step explanation:


Related Questions

Which point lies on the Y axis been on the X axis (0,0) (0,-3) (1,3) (3,0)

Answers

Answer:

(0,-3)

Step-by-step explanation:

Answer: The second number goes on your X axis and the first number goes on your Y axis .

Step-by-step explanation:

(0,0)=Y,X

Mr. Otsuki has 25 bills worth $300. He has $5, $10, and $20 bills. How many of each type of bill could he have if he has exactly ten $20 bills and at least nine $5 ...

Answers

Answer:

Mr. Otsuki could have:

10 $20 bills

5 $10 bills

10 $5 bills

but there are many other ways.

Step-by-step explanation:

We already know that Mr. Otsuki already has at least $245.

10 $20 bills - $200

at least 9 $5 bills - $45

300 - 245 = 55

55 can be made up in many different ways

5 tens + 1 five

9 fives+ 1 tens

4 tens + 3 fives

5 fives+ 3 tens

2 tens + 7 fives

So there are like five answers to this question:

A.

10 $20 bills

5 $10 bills

10 $5 bills

B.

10 $20 bills

1 $10 bills

9 $5 bills

C.

10 $20 bills

4 $10 bills

3 $5 bills

D.

10 $20 bills

3 $10 bills

5 $5 bills

10 $20 bills

2 $10 bills

7 $5 bills

I need help with this problem

Answers

Answer:

Step-by-step explanation:

ill help

Which best describes the range of numbers that satisfy the inequality x> 124?
The range of numbers has an upper limit but no lower limít.
The range of numbers has a lower limit but no upper limit.
The range of numbers has a lower limit and an upper limit.
The range of numbers has neither a lower limit nor an upper limit.

Answers

Answer:

Answer shown below

Step-by-step explanation:

The range has a lower limit but no upper band limit

(124, infinity)

Answer:

B: The range of numbers has a lower limit but no upper limit.

Step-by-step explanation:

Trust me on this, also can I have brainiest please?

Hope you do well! :D

I took the test and I got 100%.

Helpppp plzzzz what is the measure of /_x

Answers

Answer:

100

Step-by-step explanation:

Please can someone help?
I will give you brainliest and points :)

Answers

Answer:

216 ft³

Step-by-step explanation:

A cone has 3 sides

72ft³ times 3 is 216 ft³

Answer:

216 ft by 3

Step-by-step explanation:

This is my alt account btw so don’t brainliest this account, the other one.

Quickly Please!
Which equation has the solutions x = StartFraction 5 plus-or-minus 2 StartRoot 7 EndRoot Over 3 EndFraction?
3x2 – 5x + 7 = 0
3x2 – 5x – 1 = 0
3x2 – 10x + 6 = 0
3x2 – 10x – 1 = 0

Answers

Answer:

3x^2-10x+6=0

Step-by-step explanation:

3x^2-10x+6=0

Δ=10^2-4*3*6=100-72=28

V28=V4*7=2V7

x1=(10+2V7)/6=2(5+V7)/6=(5+V7)/3

x2=(5-V7)/3

Answer:

d

Step-by-step explanation:

edge

please help me to find the correct answer

Answers

Answer:

Step-by-step explanation:

1) Your calculator can evaluate f(-5) for you. It will be ...

  f(-5) = (1/3)^(-5) -3 = 243 -3

  f(-5) = 240

So, a point on the graph is (-5, 240).

Other points on the graph will be (1, -8/3), (0, -2), (-1, 0), (-2, 6).

__

2) The given function f(x) can be written as ...

  f(x) = (1/3)^x -3 = (3^-1)^x -3 = 3^-x -3

So, the transformed function is transformed by adding 1, changing the horizontal asymptote from -3 to -2. The whole graph is translated upward one unit. Each of the above-listed points will have 1 added to its y-value.

Jake received $300 for his birthday. He must decide how much of it to save and how much to spend. His bank has a 5% interest rate. How much more would be in his account after 5 years if he saved $300 than if he saved $250?

Answers

Answer:

Assuming no compounding, given an interest rate of 5%, after 5 years the $300 dollars become:

300*(1+5%)^5= $382.884469

By saving $250 instead,

250*(1.05)^5=319.07039

The difference is 382.8845-319.0704= 63.8141

Step-by-step explanation:

The formula is FV=PV*(1+r%)^T

Where:

FV- future value

PV- present value

r%- interest rate

T- Time (usually in years)

A 100 gallon tank initially contains 100 gallons of sugar water at a concentration of 0.25 pounds of sugar per gallon suppose that sugar is added to the tank at a rate of p pounds per minute that sugar water is removed at a rate of 1 gallon per minute and that water in the tank is kept well mixed. What value of P should we pick so that that when 5 gallons of sugar solution is left in the tank the concentration is .5lbs of sugar/gallon?

Answers

At the start, the tank contains

(0.25 lb/gal) * (100 gal) = 25 lb

of sugar. Let [tex]S(t)[/tex] be the amount of sugar in the tank at time [tex]t[/tex]. Then [tex]S(0)=25[/tex].

Sugar is added to the tank at a rate of P lb/min, and removed at a rate of

[tex]\left(1\frac{\rm gal}{\rm min}\right)\left(\dfrac{S(t)}{100}\dfrac{\rm lb}{\rm gal}\right)=\dfrac{S(t)}{100}\dfrac{\rm lb}{\rm min}[/tex]

and so the amount of sugar in the tank changes at a net rate according to the separable differential equation,

[tex]\dfrac{\mathrm dS}{\mathrm dt}=P-\dfrac S{100}[/tex]

Separate variables, integrate, and solve for S.

[tex]\dfrac{\mathrm dS}{P-\frac S{100}}=\mathrm dt[/tex]

[tex]\displaystyle\int\dfrac{\mathrm dS}{P-\frac S{100}}=\int\mathrm dt[/tex]

[tex]-100\ln\left|P-\dfrac S{100}\right|=t+C[/tex]

[tex]\ln\left|P-\dfrac S{100}\right|=-100t-100C=C-100t[/tex]

[tex]P-\dfrac S{100}=e^{C-100t}=e^Ce^{-100t}=Ce^{-100t}[/tex]

[tex]\dfrac S{100}=P-Ce^{-100t}[/tex]

[tex]S(t)=100P-100Ce^{-100t}=100P-Ce^{-100t}[/tex]

Use the initial value to solve for C :

[tex]S(0)=25\implies 25=100P-C\implies C=100P-25[/tex]

[tex]\implies S(t)=100P-(100P-25)e^{-100t}[/tex]

The solution is being drained at a constant rate of 1 gal/min; there will be 5 gal of solution remaining after time

[tex]1000\,\mathrm{gal}+\left(-1\dfrac{\rm gal}{\rm min}\right)t=5\,\mathrm{gal}\implies t=995\,\mathrm{min}[/tex]

has passed. At this time, we want the tank to contain

(0.5 lb/gal) * (5 gal) = 2.5 lb

of sugar, so we pick P such that

[tex]S(995)=100P-(100P-25)e^{-99,500}=2.5\implies\boxed{P\approx0.025}[/tex]

What is 50% of 30 and what is 30% of 10

Answers

Answer:

50% of 30 is 15.

30% of 10 is 3

What does X equal please help I don’t want to do summer school!!!

Answers

Answer:

180-165 = 15 (remember how a line is always 180 degrees)

Answer:

15

Step-by-step explanation:

Since 180-165=15. That is the answer for x.

PLZ MARK BRAINLIEST!!!

To solve the equation, -6(x + 2) = 30, you can distribute the negative number and then use the

Answers

-6(x+2)=30
-6x-12=30
-6x=18
x=-3

Female athletes receive 25

Answers

okay and? what’s next

$56 they are 25% off wants to know what is the discount price

Answers

Answer:

$42

Step-by-step explanation:

This is an example of a percentage decrease.

To work out the percentage decrease you would first need to convert the percentage of 25% into a decimal. You can do this by dividing the percentage  of 25 by 100, this gives you 0.25. This is because percentages are out of 100.

The next step is to minus 0.25 from 1, this gives you 0.75. This is because we are working out the percentage decrease.

To work out the discounted price you would multiply the amount of $56 by 0.75, this gives you $42.

1) Divide 25 by 100.

[tex]25/100=0.25[/tex]

2) Minus 0.25 from 1.

[tex]1-0.25=0.75[/tex]

3) Multiply $56 by 0.75.

[tex]56*0.75=42[/tex]

What is the square root of -1?

Answers

Answer:

i

Step-by-step explanation:

i means imaginary because whatever you try you can't get a number which squared gets a negative number.

Determine which of the following relations is a function.

Answers

Answer:

The farthest left box.

Step-by-step explanation:

In order for a relation to be a function, the order of numbers must be constant from the input to the output. The other numbers do not have a consistent value, but the one on the far left is x=+5 and y=-5, and it continues this way throughout the relation.

Hopefully this helped!

Answer: Hi! I am doing the same school program and the answer is A and C! Hope this helps.

The base of a prism is never a

Answers

Answer:

circle,oval overall its never round or with curves

Step-by-step explanation:

The base of a prism is never a ''Circle''. Because by definition Circular prism is not a prism.

What is mean by Triangle?

A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.

Given that;

To find the never possible shape of base of prism.

Now, We know that;

A prism is a solid that has two faces that are parallel and congruent.

Hence, If you take any cross section of a prism parallel to those bases by making a cut through it parallel to the bases, the cross section will look just like the bases.

Hence, Circular prism is not a prism according to definition.

Learn more about the triangle visit;

brainly.com/question/1058720

#SPJ6

Unknown cultural affiliations and loss of identity at high elevations." These are words used to propose the hypothesis that archaeological sites tend to lose their identity as altitude extremes are reached. This idea is based on the notion that prehistoric people tended not to take trade wares to temporary settings and/or isolated areas. As elevation zones of prehistoric people (in what is now the state of New Mexico) increased, there seemed to be a loss of artifact identification. Consider the following information.Elevation Zone Number of Artifacts Number Unidentified7000-7500 ft 114 715000-5500 ft 142 23Let p1 be the population proportion of unidentified archaeological artifacts at the elevation zone 7000-7500 feet in the given archaeological area. Let p2 be the population proportion of unidentified archaeological artifacts at the elevation zone 5000-5500 feet in the given archaeological area.(a) Find a 95% confidence interval for p1 − p2. (Round your answers to three decimal places.)lower limit: upper limit:

Answers

Answer:

Step-by-step explanation:

Express 30p as a fraction of £3.00

Answers

Answer:

[tex]\frac{1}{10} \£[/tex]

Step-by-step explanation:

We know that £1 equals 100p.

Knowing this relation, we can use the rule of three

[tex]30p \times \frac{ \£1}{100p} =0.3 \£[/tex]

Then, we form the fraction

[tex]\frac{0.3 \£}{\£ 3.00} =\frac{3}{30} =\frac{1}{10} \£[/tex]

Therefore, the fraction of of £3.00 is

[tex]\frac{1}{10} \£[/tex]

Max and Leah each have a lemonade stand . Max sold 12 glasses the first hour and 10 glasses each hour after that . Leah sold 8 glasses the first hour and 10 glasses each hour after that . How many glasses will each person have sold after 5 hours?

Answers

Answer:

max wil sell 52 because the first hour he sold 12 5hours -1 hour = 4 hour

4 hour × 10 p/h= 40

max sold 12+40 =52

leah will sell 58 because the first hour she sold 8

5hours - 1hour = 4 hours

4hours× 10 glasses p/h = 40

leah sold 40+8 =48 glasses

If Max and Leach sold 10 glasses each hour then after Max sold 52 glasses after 5 hours and Leach sold 48 glasses after 5 hours because it forms arithmetic progression.

What is an arithmetic progression?

It is a type of sequence in which each number have a common difference from the other number. The nth term of an arithmetic progression can be calculated as a+(n-1)d.

How to calculate nth term of an A.P.?

For Max we have been given that the first term is 12 and the common difference is 10.

After 10 hours the glasses which Max will sell as 12+(5-1)*10

=12+40=52 glasses

For Leach we have been given that the first term is 8 and the common difference is 10.

After 5 hours the glasses which Leach will sell as 8+(5-1)*10

=48 glasses.

Hence the number of glasses will be 52 and 48 glasses for Max and Leach.

Learn more about arithmetic progression at https://brainly.com/question/13989292

#SPJ2

Given the table of candy distributions below, find P(Not green), the probability
of selecting anything but a green candy at random from a large bag.
Above or below is the list of possible answers

Answers

Answer:

C

Step-by-step explanation:

Find the area of the shaded region. The graph depicts the standard normal distribution with mean 0 and standard deviation 1

Answers

Answer:

[tex] P(z<1.13) = 0.8708[/tex]

And the best option would be:

[tex] 0.8708[/tex]

Step-by-step explanation:

We assume that the distribution for the random variable is:

[tex] X \sim N (\mu=0 , \sigma=1) [/tex]

For this case we want to calculate the following probability:

[tex] P(z<1.13)[/tex]

And we can use the normal standard distribution or excel and we got:

[tex] P(z<1.13) = 0.8708[/tex]

And the best option would be:

[tex] 0.8708[/tex]

What is the square root of -1?
-j.
-1

Answers

Answer:

Its not a real number for the square roots of negative number

its not possible... [tex]\sqrt{-4}[/tex] = -2 x -2   no...   2 x 2   no..... -2 x 2 yea but thats not square root anymore...

Step-by-step explanation:

Give me brainliest!!!

Solve for yyy.
6=2(y+2)
y=

Answers

y = 1, hope this helps!

5. Garrett and Jeffrey are planning a treasure hunt. They decide to place a treasure at a point that is a
distance of 5 units from the x-axis and 3 units from the y-axis. Jeffrey places a treasure at point J, and
Garrett places one at point G. Who put the treasure in the right place? Explain how you know.

Answers

Answer:

Garret placed the treasure at the right place.

Step-by-step explanation:

The Cartesian plane can be used to locate the position of any given point with a coordinate. It consists of two numbered lines perpendicular to each other and intersecting at point zero of the lines.

From the statements given, 5 units from x-axis is not the same as 5 units on x-axis. Also, 3 units from y-axis is not the same as 3 units on y-axis.

So, distance 5 units from x-axis implies that a point 5 units after the x-axis. And also, distance 3 units from y-axis means 3 units after the y-axis.

With these conditions of the coordinate of the treasure, Garrett placed the treasure at the right place.

Answer:

carl amd melly was so kind

Need help with Math.

Answers

Answer:

  4^(11/20)

Step-by-step explanation:

The applicable rule of exponents is ...

  (a^b)/(a^c) = a^(b-c)

Using that here, we have ...

  4^(3/4)/4^(1/5) = 4^(3/4 -1/5)

  = 4^(15/20 -4/20) = 4^(11/20)

A fire hydrant with a blue cap provides water at a rate of 1,500 gallons per minute. A fire hydrant with a green cap provides water at a rate of 1,000 gallons per minute. A fire hydrant with a purple cap provides water at half the rate of a fire hydrant with a green cap.

Part A
Which equation relates the flow of water from the blue hydrant, b, to the flow from the green hydrant, g.
A. b = 13g
B. b = 12g
C. b = 23g
D. b = 32g

Part B
Which equation relates the flow of water from the purple hydrant, p, to the flow from the blue hydrant, b.
A. p = 13b
B. p = 12b
C. p = 23b
D. p = 34b

Answers

Answer:

Part A = B.

Part B = A.

Step-by-step explanation:

For the given​ data, (a) find the test​ statistic, (b) find the standardized test​ statistic, (c) decide whether the standardized test statistic is in the rejection​ region, and​ (d) decide whether you should reject or fail to reject the null hypothesis. The samples are random and independent. ​
Claim: μ1 < μ2​, α = 0.01. Sample​ statistics: x^-1 = 1240, n1 = 40, x^-2 = 1200 and n2 = 80. Population​ statistics: σ1 = 65 and σ2 = 110.
(a) The test statistic for μ1 - μ2 is _________.
(b) The standardized test statistic for μ1 - μ2 is __________. (Round to two decimal places as needed.)
(c) Is the standardized test statistic in the rejection region?
O Yes Ο Nο
(d) Should you reject or fail to reject the null hypothesis?

Answers

Complete Question

The complete question is shown on the first uploaded image  

Answer:

a

  The test statistic for μ1 - μ2 is   [tex]\= x_1 - \= x_2 = 40[/tex]

b

  The standardized test statistic for μ1 - μ2 is   [tex]z = 2.5[/tex]

c

  No

d

    Fail to reject null hypothesis  [tex]H_O : \mu_1 \ge \mu_2 ; H_a : \mu_1 < \mu_2[/tex] At the 1% significance level , there is insufficient evidence to support the claim

Step-by-step explanation:

From the question we are told that

The given data is  

         [tex]\= x_1 = 1240[/tex]

          [tex]\= x_2 = 1200[/tex]

           [tex]n_1 = 40[/tex]

           [tex]\alpha = 0.01.[/tex]

          [tex]n_2 = 80.[/tex]

           [tex]\sigma 1 = 65 \ and\ \sigma2 = 110.[/tex]

Now the test statistic is mathematically evaluated as

           [tex]\= x_1 - \= x_2 = 1240 -1200[/tex]

          [tex]\= x_1 - \= x_2 = 40[/tex]

 The standardized test​ statistic is mathematically represented as

        [tex]z = \frac{\= x_1 - \= x_2}{\sqrt{\frac{\sigma_1^2}{n_1} } + \frac{\sigma_2^2}{n_2} }[/tex]

substituting values

     [tex]z = \frac{\= 1240 - \= 1200}{\sqrt{\frac{65^2}{40} } + \frac{110^2}{80} }[/tex]

     [tex]z = 2.5[/tex]

Now  the standardized test​ statistic is not in the rejection region because the z value of  [tex]\alpha[/tex]  is  2.33 and  the standardized test​ statistic  is greater than that hence it is not in the rejection region

This implies that the test statisties failed to reject the null hypothesis at significance level of 0.01 , there insufficient evidence to support the claim

In a large population, 69% of the people have been vaccinated. If 4 people are randomly selected, what is the probability that At least one of them has been vaccinated?

Answers

Answer:

0.991

Step-by-step explanation:

Let Q be probability none of the 4 are vaccinated.

Let P be probability that at least 1 is vaccinated.

P = 1 - Q

Now if 69% are vaccinated, then 31% are not vaccinated.

Thus any given person has a probability of 0.31 of not being vaccinated.

Q = (0.31)^4 = 0.00924

P = 1 - 0.00924 = 0.991

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