If the angles are represented in degrees, find both angles: \cos(3x+13)=\sin(2x+42) cos(3x+13)=sin(2x+42)

Answer: 181 degrees.

Step-by-step explanation:

If we have an angle A, between, then the angle B is coterminal to A if:

B = A + n*360°

where n can be any whole number (if n = 0, we have B = A)

Then, if we take our angle as A = 541°

we can take n = -1 and get:

B = 541° - 1*360° = 181°

Now, if we subtract again 360°, we will end with an angle of negative measure, so 181° is the least positive measure angle that is coterminal with 541°

Answer:

D) is directly related to the risk of the company's assets.

Step-by-step explanation:

Equity which may be defined as what the difference between what your business worth minus what you owe in it.

It can also be put in a way as the remaining value of an owners interest in a particular company after all debt might have been cleared.

Equity= assets - liability

So equity has a lot to do in the risk management of a business or a particular company.

Answer:

20/40

Step-by-step explanation:

1/5=40/100*x

x=1/5*100/40

x=20/40 or 10/20 or 0.5

Answer:

14.13 in³

Step-by-step explanation:

Volume of a ball (sphere) is:

V = ⁴/₃ π r³

Circumference of a ball (circle) is:

C = 2π r

Use the circumference to find the radius.

9.42 in = 2π r

r = 1.50 in

Use the radius to find the volume:

V = ⁴/₃ π (1.50 in)³

V = 14.13 in³

Step-by-step explanation:

The probability of success = 8/(8 + 17) = 8/25 = 0.32.

Let X be the random variable denoting the number of successes (number of times the individual won a prize) in four picks.

Hence, X ~ Bin(4, 0.32).

Thus, P(X = 1) = [tex]4C_1=(0.32)(1-0.68)^{4-1}=4C_1(0.32)(0.68)^3[/tex]

The probability the individual will win a prize exactly one time is

C(4, 1)(0.32)¹ (0.68)³ if the total of eight ducks with “Win” written on the underside of the duck.

It is defined as the ratio of the number of favourable outcomes to the total number of outcomes, in other words, the probability is the number that shows the happening of the event.

We have:

There are a total of eight ducks with “Win” written on the underside of the duck, and there are 17 ducks with “Lose” written on the underside of the duck.

The probability of success

P = 8/(8 + 17)

P = 8/25

P = 0.32

Let's suppose the X is the random variable denoting the number of the individual won a prize in four picks.

So,

X ~ Bin(4, 0.32).

Thus, P(X = 1) = C(4, 1)(0.32)(1 0.32)⁴⁻¹

= C(4, 1)(0.32)¹ (0.68)³

Thus, the probability the individual will win a prize exactly one time is

C(4, 1)(0.32)¹ (0.68)³ if the total of eight ducks with “Win” written on the underside of the duck.

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Answer:

D.

Step-by-step explanation:

For independent events

P(A and B) = P(A) × P(B)

FINDING P(B)

P(B) = P(A and B) /P(A)

P(B) = 0.6/0.8

P(B) = 0.75

Answer:

6 / 51

Step-by-step explanation:

It is false.

Reason:

The probability of picking a black card at first is:

26 / 52 = 1/2

There are now 25 black cards and 51 cards in total.

The probability of picking another black card, if there's no replacement is now:

25 / 51

Now, there are 24 black cards and 50 cards left in total.

The probability of picking a black card without replacement now becomes:

24 / 50 = 12 / 25

Hence, the probability of picking three black cards without replacement is:

1/2 * 25/51 * 12 / 25 = 300 / 2550

In simplest form, it is 6 / 51

Answer:

the answer to the problem is 35.

Answer:

he horizontal value in a pair of coordinates: how far along the point is. The X Coordinate is always written first in an ordered pair of coordinates (x,y), such as (12,5). In this example, the value "12" is the X Coordinate. Also called "Abscissa"

Step-by-step explanation:

Answer:

1

Step-by-step explanation:

coz  1 x 1 x 1=1

Step-by-step explanation:

5x3 + 20x2 + 2x + 8

5x2 (x + 4) + 2(x + 4)

(5x2 + 2) (x + 4)

Answer:

  (f+g)(x) = 5x +3

Step-by-step explanation:

(f+g)(x) = f(x) +g(x)

  = (2x -6) +(3x +9)

  = 2x +3x -6 +9

(f+g)(x) = 5x +3

Answer:

8(3x + 2)

Step-by-step explanation:

→To factorize this expression, you must take out the GCF (Greatest Common Factor). The GCF is the biggest number that you can take out of all the terms in the expression, meaning the number has to be able to be divide by 24x and 16.

→The GCF is 8:

8(3x + 2)

Answer:

8(3x+2)

Step-by-step explanation:

24x+16

8*3*x + 8*2

Factor out an 8

8(3x+2)

It reheats the gas from the fuel and releases it more rapidly.

The answer is option A.

In full afterburner at low altitudes, the F-16 can burn in excess of 64,000 pounds an hour. At full throttle, a U.S.-variant F-16 with maximum external fuel stores has about 20 minutes until it's on emergency reserves (which would only last an extra minute or so at full afterburner).

Since the exhaust gas already has a reduced oxygen content, owing to the previous combustion, and since the fuel is not burning in a highly compressed air column, the afterburner is generally inefficient in comparison to the main combustion process.

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Answer:

[tex]22+2\sqrt{2}[/tex]

Step-by-step explanation:

[tex](4+\sqrt{2} )(6-\sqrt{2} )[/tex]

[tex]4(6)-4\sqrt{2} +6\sqrt{2} -2[/tex]

[tex]24+2\sqrt{2} -2[/tex]

[tex]22+2\sqrt{2}[/tex]

Answer: 135 soccer balls

Step-by-step explanation:

In this equation, let x represent the number of soccer balls, and 7x represent the number of volley balls.

7x + x = 1,080

8x = 1,080

Now divide 1,080 by 8 to get the number of soccer balls.

1,080 / 8 = 135

In case you’re wondering how to find the number of volley balls, just multiply 135 by 7

135 * 7 = 945

Answer:

Step-by-step explanation:

Given that

n = 25

mean = 3100

standard deviation = 500

[tex]\bar x = \frac{500}{\sqrt{25} }[/tex]

= 500 / 5

= 100

N ( μ = 3500, (500)² / 25)

N = (3500,(100)² )

b) P ( x < 3100)

c) Z score

[tex]z = \frac{x - u _{\bar x}}{\sigma \_ {\bar x}}[/tex]

[tex]u_{\bar x}= 3500[/tex]

[tex]\sigma _{\bar x}= 100[/tex]

[tex]z = \frac{3100-3500}{100} \\\\= -4[/tex]

d)

probability=

P ( x < 3100) = P < -4 = 0

Answer:

a) The parameters for the sampling distribution include

Mean = μₓ = 3500 g

Standard deviation = σₓ = 100 g

Required probability = P(x < 3100)

b) The image of the probability density curve is presented in the attached image.

c) The z-score for 3100 g in the sampling distribution = -4.00

d) The probability that the 25 babies that are born that their mean weigh less than 3100 g = 0.00003

Step-by-step explanation:

Complete Question

Suppose we know the birth weights of babies is normally distributed, with mean of 3500 g and standard deviation 500g.

If 25 new born babies are randomly selected, what is the probability that the 25 babies are born that their mean weigh less than 3100g?

a) What are the parameters?

b) Draw a probability density curve for the problem.

c) What is the z-score of the weight?

d) What is the required probability?

Solution

The Central limit theorem explains that for a random sample of adequate size obtained from a normal distribution with independent variables, the mean of the sampling distribution is approximately equal to the population mean and the sampling distribution is approximately of the nature of the population distribution (normal) with the standard deviation of the sampling distribution given as

Standard deviation of the sampling distribution = [(Population Standard deviation)/√n]

σₓ = (σ/√n)

Mean of Sampling distribution = Population mean

μₓ = μ = 3500 g

σₓ = (σ/√n) = (500/√25) = 100 g

a) The parameters for the sampling distribution include

Mean = μₓ = 3500 g

Standard deviation = σₓ = 100 g

Required probability = P(x < 3100)

b) The image of the probability density curve is presented in the attached image.

c and d) To obtain the required probability, we need the z-score for 3100 g, so we standardize 3100g

The standardized score for any value is the value minus the mean then divided by the standard deviation.

z = (x - μ)/σ = (3100 - 3500)/100 = - 4.00

To determine the required probability 45mg/L, P(x < 3100) = P(z < -4.00)

We'll use data from the normal probability table for these probabilities

P(x < 3100) = P(z < -4.00) = 0.00003

Hence, the probability that the 25 babies that are born that their mean weigh less than 3100 g = 0.00003

Hope this Helps!!!!

Step-by-step explanation:

Let the number is x. Its reciprocal will be 1/x. According to given condition, we get :

[tex]x+\dfrac{1}{x}=\dfrac{41}{20}\\\\\dfrac{x^2+1}{x}=\dfrac{41}{20}\\\\20x^2+20=41x\\\\20x^2-41x+20=0[/tex]

It is a quadratic equation. The values of x are :

[tex]20x^2-25x - 16x+ 20 =0\\\\5x(4x - 5) -4( 4x - 5) = 0\\\\(5x-4)(4x-5)=0\\\\5x-4=0\ \text{and}\ (4x-5)=0\\\\x=\dfrac{4}{5}\ \text{and}\ x=\dfrac{5}{4}[/tex]

The smaller number is 4/5 and the larger number is 5/4.

Answer: 150

Step-by-step explanation: K is constant

250= K (8+2)2

250= K (10)2

250= K (20)

250= K20

divide both sides by 20

250/20= K

12.5= K

THEREFORE

Y= K (4+2)2

Y= 12.5 (6)2

Y= 12.5 × 12

Y= 150

At x = 4 the value of the variable y will be 90 as per the proportionality given.

The property of having suitable proportions in terms of size, number, degree, harshness, etc.: If a defensive action against an unfair attack results in destruction that contravenes the proportionality criterion, it may even go far beyond a justifiable defense.

Given, Y is directly proportional to (x+2)2 when x=8 y = 250

Since Y ∝ (x + 2)²

Y = k (x + 2)²

Where k is constant

For x = 8 y = 250

Substituting the values

250 = k(8 + 2)²

k = 2.5

Thus for x= 4

y = 2.5 (4 + 2)²

y = 90

therefore, According to the proportionality, the variable y will have a value of 90 at x = 4.

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Answer:

The work done in stretching it from its natural length to 14 in. beyond its natural length is W=8.17 ft-lb.

Step-by-step explanation:

We know that a force of 8 lb is required to hold a spring stretched 8 in. beyond its natural length.

This let us calculate the spring constant k as:

[tex]F=kx\\\\k=F/x=(8 \;lb)/(8\;in)=1\;lb/in[/tex]

We know that work is, in an scalar form, the product of force and distance.

The force F is equal to the spring constant multiplied by the distance from the natural length.

Then, as the force changes with the distance from the natural length, we have to calculate integrating:

[tex]W=\int_0^{14}F\,dx=\int_0^{14}kx\,dx\\\\\\W=\dfrac{1}{2}kx^2\left|^{14}_0=\dfrac{1}{2}(1\,lb/in)(14 \,in)^2-\dfrac{1}{2}(1\,lb/in)(0 \,in)^2[/tex]

[tex]W=98lb\cdot in-0lb-in\\\\W=98(lb\cdot in)\cdot \dfrac{1 \,ft}{12\,in}=8.17\;lb\cdot ft[/tex]

Answer:

Slow = 30

Fast = 50

Step-by-step explanation:

So make variables for the speed.

Slow wanderer = x

Faster wanderer = x + 20

The time it took was 2.5 hours.

2.5x + 2.5x + 50 = 200

5x + 50 = 200

x = 30

Answer:

Step-by-step explanation:

For n=129 and with leaf unit = 0.1, the stem and leaf chart of the given data on Shower-flow rate (L/min) is as follows:

2 28

Stem        leaves

3----------1344567789

4----------01356889

5----------00001114455666789

6----------0000122223344456667789999

7----------00012233455555668

8----------02233448

9----------012233335666788

10----------2344455688

11--------- 2335999

12---------- 17

13-------- 9

14--------36

15---------- 0035

16---------None

17---------None

18 ----------3

* From steam and leaf chart we note that minimum Shower flow rate is 2.2 whereas maximum is 18.3 L/mim. Further typical or representative rate is 7.0 L/min.

* The display of data on steam and leaf chart shows that data is positively skewed means concentration of data on left side or lower value side is high as compared to other side.

* Distribution is not symmetric rather very clear positive skew ness is observed through steam and leaf chart. Even distribution is Unimodal.

* From steam and leaf chart is indicative to conclude that the highest observation 18.3 is outlier.

Answer:

The best prediction for  the number of years it will take for the population to reach 200,000 is 9.41

Step-by-step explanation:

Year     Population

1              11,920

2              16,800

3              23,300

4              33,000

5             45,750

6             64,000

[tex]y_1 =A _0 e ^{kt _1}\\y_2 = A_0 e^{k t_2}\\(t_1,y_1)=(1,11920)\\(t_2,y_2)=(2,16800)[/tex]

Substitute the values

[tex]11920=A _0 e ^{k} ---1\\16800 = A_0 e^{2k} ---2[/tex]

Divide 1 and 2

[tex]\frac{11920}{16800}=\frac{e^k}{e^{2k}}\\\frac{11920}{16800}=e^{k-2k}\\ln(\frac{11920}{16800})=-k\\k=-1 ln(\frac{11920}{16800})\\k=0.3432\\A_0=y_1 e^{-k t_1}\\A_0=11920 e^{-0.3432}\\A_0=8457.5238[/tex]

The exponential function that passes through the points (1, 11920) and (2, 16800) is[tex]y=8457.5238 e^{0.3432t}[/tex]

Now we are supposed to find  the best prediction for  the number of years it will take for the population to reach 200,000

[tex]200000=8457.5238 e^{0.3432t}[/tex]

[tex]\frac{200000}{8457.5238}=e^{0.3432t}[/tex]

[tex]ln(\frac{200000}{8457.5238})=0.3432t[/tex]

t = 9.41

Hence the best prediction for  the number of years it will take for the population to reach 200,000 is 9.41

Answer:

With this P-value, we have statistical evidence to support the claim that there is a relationship between the average number of putts per hole and the player's total winnings.

Step-by-step explanation:

In this case, the hypothesis test has the following hypothesis:

Null hypothesis: there is no relationship between the average number of putts per hole and the player's total winnings.

Alternative hypothesis: there is relationship between the average number of putts per hole and the player's total winnings.

Then, a P-value of 0.0087 is, without doubt, a strong evidence that the null hypothesis is false.

With this P-value, we have statistical evidence to support the claim that there is a relationship between the average number of putts per hole and the player's total winnings.

Answer:

7.0422  is the correct answer to the given question .

Step-by-step explanation:

Given

R1 = 7.21 + 0.55t

R2 = 7.21 + 0.44t

Decrease in the revenue  can be determined by the formula

[tex]= Reduction\ in\ R1\ -\ Reduction\ in\ R2[/tex]

[tex]= (7.21 + 0.55t ) - (7.21 + 0.44t)[/tex]

=0.11 t

Now overall Reduction can be determined by the interval from t=8 to t=15

Consider c=0.11 t

[tex]\frac{dc}{dt}[/tex]=0.11

Now integrated the equation from t=8 to t=15 to determine total reduction in revenue

[tex]=\int_{8}^{15}\sqrt{1+0.11^2}\ dL[/tex]

[tex]=7.0422[/tex]

Answer:

A.

Step-by-step explanation:

Circle with centre (0,2) will have the equation

(x)²+(y-2)² = r²

Finding r² by distance formula using P(-7,2)

r² = (-7-0)²+(2-2)²

r² = (-7)²

r² = 49

So substituting in the equation

x²+(y-2)² = 49

Answer: There are 6 different ways in which they can share the work.

Step-by-step explanation:

Suppose that Terry selects first the place where he goes, in the selection he has 3 options at random to chose.

Then Edin selects, Edin has two options (because one is already taken)

Then Gordon selects, he has only one options.

The number of combinations is equal to the product of the number of options for each selection, this is:

Combinations = 3*2*1 = 6

There are 6 different ways in which they can share the work.

Answer:

36

Step-by-step explanation:

Diameter AB bisects the chord

MO = NO

5x+3=6x

3 = 6x-5x

x = 3

Now

MN = 5x+3+6x

MN = 5(3)+3+6(3)

MN = 15+3+18

MN = 36

Answer:

A.

Step-by-step explanation:

98%

The probability of not winning the raffle is 100% - 2% = 98%