What is the approximate length of arc s on the circle below? Use 3.14 for Pi. Round your answer to the nearest tenth.

-5.8 ft
-6.3 ft
-27.5 ft
-69.1 ft

Equate whats inside (arguments) [tex]\sin[/tex] with base period of sine function [tex]2\pi[/tex] and solve for x to get period,

[tex]\pi x=2\pi\implies x=2[/tex]

So the period of the graph of the given function is precisely 2.

Hope this helps :)

Answer:

Step-by-step explanation:

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Answer:

a. 9 students

b. 20 students

c. 4 students

The rate of change of R with time in the given equation is 0.004 ohm/s

Given parameters:

[tex]\frac{1}{R} = \frac{1}{R_1} + \frac{1}{R_2} \\\\\frac{dR_1}{dt} = 0.3 \ ohm/s\\\\\frac{dR_2}{dt} = 0.2 \ ohm/s\\\\R_1 = 60 \ ohms\\\\R_2 = 80 \ ohms[/tex]

To find:

First determine the value of R from the given equation;

[tex]\frac{1}{R} = \frac{1}{R_1} + \frac{1}{R_2} \\\\\frac{1}{R} = \frac{1}{60} + \frac{1}{80} \\\\\frac{1}{R} = \frac{4 + 3}{240} \\\\\frac{1}{R} = \frac{7}{240} \\\\R = \frac{240}{7} = 34.286 \ ohms[/tex]

Finally, to determine the rate of change of R, differentiate the given equation.

[tex]\frac{-1}{R^2} \frac{dR}{dt} = \frac{-1}{R_1^2} \frac{dR_1}{dt} - \frac{1}{R_2^2} \frac{dR_2}{dt} \\\\\frac{1}{R^2} \frac{dR}{dt} = \frac{1}{R_1^2} \frac{dR_1}{dt} + \frac{1}{R_2^2} \frac{dR_2}{dt}\\\\\frac{dR}{dt} = R^2(\frac{1}{R_1^2} \frac{dR_1}{dt} + \frac{1}{R_2^2} \frac{dR_2}{dt})[/tex]

[tex]\frac{dR}{dt} = 34.286(\frac{1}{(60)^2} \times 0.3 \ \ \ + \ \ \ \frac{1}{(80)^2} \times 0.2)\\\\\frac{dR}{dt} = 34.286(8.333 \times 10^{-5} \ \ \ + \ \ \ 3.125 \times 10^{-5})\\\\\frac{dR}{dt} = 34.286(11.458 \times 10^{-5})\\\\\frac{dR}{dt} = 0.00393\\\\\frac{dR}{dt} \approx 0.004 \ ohm/s[/tex]

Thus, from the given equation the rate of change of R with time is 0.004 ohm/s

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Answer:

the verified answer is wrong.

Step-by-step explanation:

OP forgot to square R (34.286)

Answer:

26029.26

Step-by-step explanation:

Assuming we are investing the 500 at the end of the period and starting with 500 in the account

[ P(1+r/n)^(nt) ]+PMT × {[(1 + r/n)^(nt) - 1] / (r/n)}

PMT = the monthly payment

r = the annual interest rate (decimal)

n = the number of times that interest is compounded per year

t = the time in years

[ 500(1 + .03/12)^(4*12) ]+500 × {[(1 + .03/12)^(4*12) - 1] / .03/12)}

[ 500(1 + .0025)^(48) ]+500 × {[(1 + .0025)^(48) - 1] / .0025)}

563.66 +25465.60

5/3 is farthest according to me

Answered by Gauthmath must click thanks and mark brainliest

Answer:

0.27, 1.1, - 1/4, 5/3

Change all to decimal:-

0.27, 1.1, -.2.5, 1.67

So, 1.67 is farthest from zero

D) 5/3  is your answer

~OAmalOHopeO

The probability of the event. par or above is 0.74

Using the table in the question as reference, we are to calculate the probability of an event par or above.

This probability is represented as: P(par or above)

The par value from the question is:

[tex]par = 70[/tex]

So, the required probability is:

[tex]P(par\ or\ above) = P(x \ge 70)[/tex]

This mean that we consider scores that are 70 and above

So, the formula to use is:

[tex]P(par\ or\ above) = P(70-74) + P(75 -79) +..... + P(100\ or\ above)[/tex]

Using the data from the question, the equation becomes

[tex]P(par\ or\ above) = 0.28+ 0.20 +0.12+ 0.07+ 0.03+ 0.03+ 0.01​[/tex]

[tex]P(par\ or\ above) = 0.74[/tex]

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Answer:

The probability of Josh scoring par or above is 0.75.

Step-by-step explanation:

Find where par is on the table (70-74). Since it is par or above, you would take the probabilities of par and all numbers higher than par. Add them together, and you have your answer.

(.29) + (.21) + (.11) + (.08) + (.02) + (.03) + (.01) = 0.75

**I attached a screenshot of the table and the correct answer

good luck! <3

Answer:

in five (5) ways a committee can be formed from 7 men and 5 women

Answer:

C - qt = -k

k = - C + qt

V = u + at

V - at = u

u = V - at

Answer:

c=qt-k

c-qt= -k

c-qt/-1=-k/-1

k=c-qt/-1....

v=u+at

v-at=u

u=v-at

I hope this helps

The equation has 2 valid solutions; no extraneous solutions

The given equation is:

[tex]\sqrt{x - 1} - 5= x - 8[/tex]

First, we determine the solutions

[tex]\sqrt{x - 1} - 5= x - 8[/tex]

Add 5 to both sides

[tex]\sqrt{x - 1} = x - 8 + 5[/tex]

[tex]\sqrt{x - 1} = x - 3[/tex]

Square both sides

[tex]x - 1 = (x - 3)^2[/tex]

Expand

[tex]x - 1 = x^2- 3x - 3x + 9[/tex]

[tex]x - 1 = x^2- 6x + 9[/tex]

Collect like terms

[tex]x^2 - 6x - x + 9 + 1 = 0[/tex]

[tex]x^2 - 7x + 10 = 0[/tex]

Expand again

[tex]x^2 - 2x-5x + 10 = 0[/tex]

Factorize

[tex]x(x - 2) -5(x -2)= 0[/tex]

Factor out x - 2

[tex](x - 5)(x -2)= 0[/tex]

Split

[tex]x - 5=0[/tex] or [tex]x - 2 = 0[/tex]

[tex]x= 5[/tex] or [tex]x = 2[/tex]

The above values are valid values of x.

Hence, the equation has 2 valid solutions; no extraneous solutions

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Answer:

That person is wrong, First blank is : one valid solution , Second blank is : one extraneous solution, and I'm not sure what the 3rd blank is but I think It's 4.

Step-by-step explanation:

for plato users

Answer:

98 meters

Step-by-step explanation:

Simplify each side of the equation:

318 = 2(61+x)

318= (2)(61) + (2)(x)

318= 122 + 2x

Flip the equation:

2x + 122 = 318

Subtract 122 from each side:

2x + 122 − 122 = 318 − 122

2x = 196

Divide both sides by 2:

2x/2 = 196/2

x = 98

Answer:

x= -2

y= -1

z= -3

Step-by-step explanation:

x-y= -1 (1)

x+z= -5 (2)

y-z= 2 (3)

(1)+(3)==> x-z= 1 (4)

(4)+(2)==> 2x= -4 ==> x= -2

we replace x by its value in equation (2):

-2+z= -5 ==> z= -3

we replace z by its value in equation (3):

y-(-3)= 2 ==> y+3=2 ==> y= -1

Answer:

16 is answer

Step-by-step explanation:

3(2)^2+4(1)^2= 3(4)+4(1)=12+4=16

Answer:

Following are the complete solution in the attached file.

Step-by-step explanation:

Answer:

Step-by-step explanation:

It asks for the common set of A and B.

There only one element common to both the given sets:

Answer:

Step-by-step explanation:

∩ == this symbol stands for the common element/set

So according to this question you have to find the element which is common for both A and B sets.

So now you can see that only number 2 is common for both.

So, the answer is,

Answer:

There is 10% error in both minimum and extreme values i.e. 120 & 140 , Error in 120 is 10% i.e. = 12, Since value can be more or less in error ∴ Error in 120 is ±12.

Answer:

Casey's monthly charge for making 1,100 minutes of calls is $70.

Step-by-step explanation:

We can write a piecewise function to model the situation.

Since Casey's phone service only charges a monthly fee of $30 for the first 1000 minutes, we can write that for calling t minutes:

[tex]\displaystyle C(t) = 30\text{ if } t\leq 1000[/tex]

In other words, the total cost is only $30 is the total minutes of call is less than  1000 minutes.

However, if the total minutes of calls is greater than 1000, then its $0.40 per minute on top of the 30. Thus:

[tex]\displaystyle C(t) = 30 + 0.4(t-1000)\text{ if } t>1000[/tex]

All together, our piecewise function will be:

[tex]\displaystyle C(t) = \begin{cases} 30 & t\leq 1000 \\ 30 + 0.4(t-1000) & t>1000\end{cases}[/tex]

We want to determine Caseys monthly charge if he makes 1,100 minutes of calls. So, t = 1100. Since 1100 > 1000, we will use the second equation. This yields:

[tex]C(1100)= 30+0.4((1100)-1000)[/tex]

Evaluate:

[tex]\displaystyle C(1100) = 30+0.4(100) = 30+40=\$70[/tex]

Casey's monthly charge for using 1,100 minutes of call is $70.

Since this is a right triangle, we can use one of the three main trigonometric functions: sine, cosine, or tangent.

Remember: SOH-CAH-TOA

Looking from the given angle, we know the opposite side and want to know the adjacent side. Therefore, we should use the tangent function.

tan(54) = 16/BC

BC = 16/tan(54)

BC = 11.62 units

Hope this helps!

Answer:

1(16x²-9y²)

Step-by-step explanation:

1(16x²-9y²) there are no common factors or variables

9514 1404 393

Answer:

  14.3%

Step-by-step explanation:

We assume this question is asking for the annual interest rate for an amortized loan that would produce the same total repayment amount as if 8% simple interest were added to the $4900 loan amount. There is no formula for that, but there are a number of apps and spreadsheets that can calculate it. In the attached, we have use a graphing calculator.

The APR is about 14.3%.

_____

The amount to be repaid is calculated using the simple interest formula:

  A = P(1 +rt) = $4900(1 +0.08·4) = $6468

Then the required monthly payment (for 48 months) is ...

  $6468/48 = $134.75

__

The payment amount for a 48-payment loan at rate r on a principal of $4900 will be ...

  A = 4900(r/12)/(1 -(1 +r/12)^-48)

In the attachment, we show the value of r (in percent) that would make the payment amount A be $134.75. We have done this by casting the problem in the form f(r) = 0 and looking for the x-intercept of f(r).

_____

Additional comment

The second attachment uses a spreadsheet for the same purpose. Here, we have used Go.ogle Sheets with a "Goal Seek" add-on to adjust the value in cell B5 so that the computed payment on the loan (cell B6) is the same as the value we calculated in cell B4.

We found the graphing calculator solution to be much quicker, though in that case we actually had to know the formula to use to calculate the payment. The payment formula is built into the spreadsheet.

Answer:

5880 ways

Step-by-step explanation:

For selections like this, we solve using the combination theory. Recall that

nCr = n!/(n-r)!r!

Hence given to find the number of ways 6 gentleman and 4 ladies can be choosen out of 10 gentleman and 8 ladies,

= 10C6 * 8C4

= 10!/(10-6)!6! * 8!/(8-6)!6!

= 10 * 9 * 8 * 7 * 6!/4 *3 *2 * 6! * 8 * 7 * 6!/2 * 6!

= 210 * 28

= 5880 ways

The arrangement can be done in 5880 ways

Answer:

[tex]x = \frac{log\sqrt{-1/6}}{log2}[/tex]

Step-by-step explanation:

Given the expression

[tex]2^{2x}+3-7(2^{2x}+1)+3=0[/tex]

Let [tex]P=2^x[/tex]

Substituting into the expression, we will have:

[tex]P^2+3-7(P^2+1)+3=0\\Expand\\P^2+3-7P^2-7+3=0\\-6P^2-1=0\\6P^2=-1\\p^2=-1/6\\P=\sqrt{-1/6}[/tex]

Since:

[tex]P=2^x\\2^x=\sqrt{-1/6}\\xlog2=log(\sqrt{-1/6}) \\x = \frac{log\sqrt{-1/6}}{log2}[/tex]

Answer:

2 sinh viên sẽ làm đc 0,452

Answer:

90 ml of the 25 percent mixture and 585 of pure alcohol

Step-by-step explanation:

Firstly, you should find the quantity of alcohol in the desired mixture.

675:100*90= 675*0.9= 607.5

Firstly,  define all the 25 percents mixure as x, the pure alcohol weight is y.

1. x+y= 675 (because the first and the second liquid form a desired liquid).

Then find the equation for spirit

The first mixture contains 25 percents. It is x/100*25= 0.25x

When the second one consists of pure alcohol, it contains 100 percents of spirit,  so it is x.

2. 0.25x+y=607.5

Then you have a system of equations ( 1.x+y= 675 and 2. 0.25x+y= 607.5)

try 2-1 to get rid of y

x+y- (0.25x+y)= 675-607.5

0.75x= 67.5

x= 90

y= 675-x= 675-90= 585

It means that you need90 ml of the 25percents mixture and 585 0f pure alcohol

[tex]\huge\textsf{Hey there!}[/tex]

[tex]\mathsf{= (3^{-1}+4^{-1})^{-2}}\\\\\\\mathsf{3^{-1} = \bf {\dfrac{1}{3}}}\\\\\\\mathsf{4^{-1} = \bf \dfrac{1}{4}}\\\\\\\mathsf{= (\dfrac{1}{3}+\dfrac{1}{4})^{-2}}\\\\\\\mathsf{\dfrac{1}{3} + \dfrac{1}{4} = \bf \dfrac{7}{12}}\\\\\\\mathsf{= (\dfrac{7}{12})^{-2}}\\\\\large\text{Simplify above and you have your overall answer...}\\\\\\\boxed{\boxed{\large\textsf{Answer: }\mathsf{\bf \dfrac{144}{49}}}}\huge\checkmark[/tex]

[tex]\huge\textsf{Good luck on your assignment \& enjoy your day!}\\\\\\\\\frak{Amphitrite1040:)}[/tex]

Answer:

C

Step-by-step explanation:

Answer:

$16186.20

Step-by-step explanation:

Assuming that P represents the initial amount, A represents the end amount, r represents the annual interest rate, m represents the amount of times compounded per year, and t represents the amount of years, we can write this as

A = P(1+r/m)^(mt)

Since 12,000 is invested, that is the initial amount. To find the interest rate as a decimal from a percent (as we need it in decimal form for this formula), we can divide the percent by 100 to get 6%/100 = 0.06 as our interest rate. Because there are 12 months in a year, the interest is compounded 12 times a year, and since it takes 5 years, t=5. Our formula is now

A = 12000 * (1+0.06/12)^(12 * 5)

A = 12000 * (1+0.06/12) ^(60)

A = 16186.20 rounded to the nearest cent

Option D is correct. 95% of the distribution lies between 1.9975inches and 3.4025inches.

To get the required range of values, we will have to first get the z-score for the two-tailed probability at a 95% confidence interval. According to the normal table, the required range is between -2.81 and 2.81

The formula for calculating the z-score is expressed as;

[tex]z=\frac{x-\overline x}{s}[/tex] where:

[tex]\overline x[/tex] is the mean

s is the standard deviation

z is the z-scores

Given the following

[tex]\overline x[/tex]=2.7 in

s = 0.25

if z = -2.81

[tex]-2.81=\frac{x-2.7}{0.25}\\x-2.7=-2.81*0.25\\x-2.7=-0.7025\\x=-0.7025+2.7\\x=1.9975[/tex]

Similarly:

[tex]2.81=\frac{x_2-2.7}{0.25}\\x_2-2.7=2.81*0.25\\x_2-2.7=0.7025\\x_2=0.7025+2.7\\x_2=3.4025[/tex]

Hence the 95% of the distribution lies between 1.9975inches and 3.4025inches.

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Answer:

Bayes’ Theorem describes the probability of occurrence of an event related to any condition. It is also considered for the case of conditional probability.

For prove refer to the attachment.

Hope this helps you^_^

Answer:

See below.

Step-by-step explanation:

Sleeping:

8/24 * 365 = 121.76 days

Eating:

3/24 * 365 = 45.63 days

Total sleeping and eating: 167 days

Summer Vacation & Holidays:

90 + 21 = 111 days

Saturdays and Sundays: 52 + 52 = 104 days

Vacation + Holidays Saturdays + Sundays = 111 + 104 = 215 days

It may be true that all days of vacation, holiday, Saturdays, and Sundays combined are a total of 215 days, but these 215 days cannot be added to the 167 days above because these 215 days include time for sleeping and eating which was already included in the sleeping and eating times for the entire year. The mistake in the reasoning is counting twice the time of sleeping and eating on the 215 days in which there is no school.

Answer:

B

Step-by-step explanation:

The domain goes from -4 to 9. It would not be brackets since the actual points are not on the graph so it would be parentheses.