The Colonel spots a campfire at a bearing N 59∘59∘ E from his current position. Sarge, who is positioned 242 feet due east of the Colonel reckons the bearing to the fire to be N 34∘34∘ W from his current position.
Determine the distance from the campfire to each man, rounded to the nearest foot.
Colonel is about............................ feet away from the fire
Sarge is about............................... feet away from the fire

Answers

Answer 1

Answer:

i. Colonel is about 201 feet away from the fire.

ii. Sarge is about 125 feet away from the fire.

Step-by-step explanation:

Let the Colonel's location be represented by A, the Sarge's by B and that of campfire by C.

The total angle at the campfire from both the Colonel and Sarge = [tex]59^{0}[/tex] + [tex]34^{0}[/tex]

                                           = [tex]93^{0}[/tex]

Thus,

<CAB = [tex]90^{0}[/tex] - [tex]59^{0}[/tex] = [tex]31^{0}[/tex]

<CBA = [tex]90^{0}[/tex] - [tex]34^{0}[/tex] = [tex]56^{0}[/tex]

Sine rule states;

[tex]\frac{a}{Sin A}[/tex] = [tex]\frac{b}{Sin B}[/tex] = [tex]\frac{c}{Sin C}[/tex]

i. Colonel's distance from the campfire (b), can be determined by applying the sine rule;

[tex]\frac{b}{Sin B}[/tex] = [tex]\frac{c}{Sin C}[/tex]

[tex]\frac{b}{Sin 56^{0} }[/tex] = [tex]\frac{242}{Sin 93^{0} }[/tex]

[tex]\frac{b}{0.8290}[/tex] = [tex]\frac{242}{0.9986}[/tex]

cross multiply,

b = [tex]\frac{0.8290*242}{0.9986}[/tex]

  = 200.8993

Colonel is about 201 feet away from the fire.

ii. Sarge's distance from the campfire (a), can be determined by applying the sine rule;

[tex]\frac{a}{Sin A}[/tex] = [tex]\frac{c}{Sin C}[/tex]

[tex]\frac{a}{Sin 31^{0} }[/tex] = [tex]\frac{242}{Sin 93^{0} }[/tex]

[tex]\frac{a}{0.5150}[/tex] = [tex]\frac{242}{0.9986}[/tex]

cross multiply,

a = [tex]\frac{0.5150*242}{0.9986}[/tex]

  = 124.8073

Sarge is about 125 feet away from the fire.


Related Questions

Please Help me solve it!

Answers

Answer:

C. $4.12

Step-by-step explanation:

From 9 a.m. to noon, it's 3 hours.

From noon to 4 p.m. it's 4 hours.

Total rental time: 3 hours + 4 hours = 7 hours

Total rental cost: $28.84

rental cost per hour = (rental cost)/(number of hours)

rental cost per hour = $28.84/(7 hours) = $4.12/hour

4.12 because if u read the question carefully it is asking what is the rental cost not the total cost

Hi Maths lovers, if someone can explain me when l want to get NR doing NSR way ( going upwards) where this 3/5 b + 2/5 a or 2/5 a + 3/5 b comes from? Thanks

Answers

Answer:

see explanation

Step-by-step explanation:

SQ = SP + PQ = - b + a

Since SN : NQ = 3 : 2 then SQ = 3 + 2 = 5 parts , thus

SN = [tex]\frac{3}{5}[/tex] SQ = [tex]\frac{3}{5}[/tex] ( - b + a) = - [tex]\frac{3}{5}[/tex]b + [tex]\frac{3}{5}[/tex] a

Thus

NR = NS + SR

     = - (- [tex]\frac{3}{5}[/tex] b + [tex]\frac{3}{5}[/tex] a) + a

     = [tex]\frac{3}{5}[/tex] b - [tex]\frac{3}{5}[/tex] a + a

     = [tex]\frac{2}{5}[/tex] a + [tex]\frac{3}{5}[/tex] b

Answer:

Yeah

Step-by-step explanation:

Very simple

It was said that

SN:NQ=3:2

→2SN = 3NQ

SN=SR-NR

SN=a - NR

NQ = NR - QR

NQ=NR - b

SQ = SN + NQ

Recall that SN=(3NQ)/2

SQ = (3NQ)/2 + NQ

SQ = (5/2)NQ

a - b = (5/2)(NR - b)

After simplification

NR = (2/5)a - (2/5)b +b

Factorize

NR = (2/5)a + (-2/5 + 1)b

NR = (2/5)a + (3/5)b

Problem 1. (1 point) A steel ball weighing 128 pounds is suspended from a spring. This stretches the spring 128101 feet. The ball is started in motion from the equilibrium position with a downward velocity of 2 feet per second. The air resistance (in pounds) of the moving ball numerically equals 4 times its velocity (in feet per second) . Suppose that after t seconds the ball is y feet below its rest position. Find y in terms of t. (Note that this means that the positive direction for y is down.)

Answers

Answer:

seeed

Step-by-step] explanation:

ddd~!`

Based on all student records at Camford University, students spend an average of 5.30 hours per week playing organized sports. The population’s standard deviation is 3.20 hours per week. Based on a sample of 64 students, Healthy Lifestyles Incorporated (HLI) would like to apply the central limit theorem to make various estimates. Compute the standard error of the sample mean. (Round your answer to 2 decimal places.)

Answers

Answer:

The standard error of the sample mean is [tex]\sigma_{\= x } = 0.40[/tex]

Step-by-step explanation:

From the question we are told that

     The population mean is  [tex]\mu = 5.30 \ hours[/tex]

     The population standard deviation is [tex]\sigma = 3.20 \ hours[/tex]

      The sample size is  [tex]n = 64[/tex]

Generally the standard error of the sample mean is mathematically represented as

               [tex]\sigma_{\= x } = \frac{\sigma}{\sqrt{n} }[/tex]

substituting values

                [tex]\sigma_{\= x } = \frac{3.20}{\sqrt{64} }[/tex]

                [tex]\sigma_{\= x } = 0.40[/tex]

What is the slope of the line shown below?



A.


B.


C.
-

D.
3

Answers

Answer:

D

Step-by-step explanation:

Option D is correct. Slope of the line shown in the graph is 3.

The slope of the line is the ratio of the rise to the run, or rise divided by the run.

It describes the steepness of line in the coordinate plane.

The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.

The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is

m=(y₂-y₁)/(x₂-x₁)

The line is passing through point (2, 2) and (4, 8).

Lets find the corresponding point values y₂= 8, y₁ = 2, x₂= 4 and x₁ =2.

Plug in the values in slope formula:

Slope = (8-2)/(4-2)  

=6/2

=3

Hence, slope of the line shown in the graph is 3. Option D is correct.

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What do we use mathematical induction for?

Answers

proving statements!

it's the very definition of it

A. or C. May be the answer

Hope this helped ♥︎

Find the solution set of the inequality and what is the number? 16x − 7 ≤ − 71 A. C. ≤ D. ≥ E. =

Answers

x  ≤  −  4

Step-by-step explanation:

Answer:

x ≤ -4

Step-by-step explanation:

16x − 7 ≤ − 71

Add 7 to both sides.

16x ≤ -64

Divide both sides by 16.

x ≤ -4

Suppose that a password for a computer system must have at least 8, but no more than 12, characters, where each character in the password is a lowercase English letter, an uppercase English letter, a digit, or one of the six special characters ∗, >, <, !, +, and =.
a) How many different passwords are available for this computer system?
b) How many of these passwords contain at least one occurrence of at least one of the six special characters?
c) Using your answer to part (a), determine how long it takes a hacker to try every possible password, assuming that it takes one nanosecond for a hacker to check each possible password.

Answers

Part a)

There are 52 letters (26 lowercase and 26 uppercase), 10 digits, and 6 symbols. There are 52+10+6 = 68 different characters to choose from.

If there are 8 characters for this password, then we have 68^8 = 4.5716 * 10^14 different passwords possible.If there are 9 characters, then we have 68^9 = 3.1087 * 10^16 different passwordsIf there are 10 characters, then we have 68^10 = 2.1139 * 10^18 different passwordsIf there are 11 characters, then we have 68^11 = 1.4375 * 10^20 different passwordsIf there are 12 characters, then we have 68^12 = 9.7748 * 10^21 different passwords

Adding up those subtotals gives

68^8+68^9+68^10+68^11+68^12 = 9.9207 * 10^21

different passwords possible.

Answer: Approximately 9.9207 * 10^21

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

Part b)

Let's find the number of passwords where we don't have a special symbol

There are 52+10 = 62 different characters to pick from

If there are 8 characters for this password, then we have 62^8 = 2.1834 * 10^14 different passwords possible. If there are 9 characters, then we have 62^9 = 1.3537 * 10^16 different passwords If there are 10 characters, then we have 62^10 = 8.3930 * 10^17 different passwords If there are 11 characters, then we have 62^11 = 5.2037 * 10^19 different passwords If there are 12 characters, then we have 62^12 = 3.2263 * 10^21 different passwords

Adding those subtotals gives

62^8+62^9+62^10+62^11+62^12 = 3.2792 * 10^21

different passwords where we do not have a special character. Subtract this from the answer in part a) above

( 9.9207 * 10^21)  - (3.2792 * 10^21) = 6.6415 * 10^21

which represents the number of passwords where we have one or more character that is a special symbol. I'm using the idea that we either have a password with no symbols, or we have a password with at least one symbol. Adding up those two cases leads to the total number of passwords possible.

Answer: Approximately 6.6415 * 10^21

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

Part c)

The answer from part a) was roughly 9.9207 * 10^21

It will take about 9.9207 * 10^21  nanoseconds to try every possible password from part a).

Divide 9.9207 * 10^21  over 1*10^9 to convert to seconds

(9.9207 * 10^21 )/(1*10^9) = 9,920,700,000,000

This number is 9.9 trillion roughly.

It will take about 9.9 trillion seconds to try every password, if you try a password per second.

------

To convert to hours, divide by 3600 and you should get

(9,920,700,000,000)/3600 = 2,755,750,000

So it will take about 2,755,750,000 hours to try all the passwords.

------

Divide by 24 to convert to days

(2,755,750,000)/24= 114,822,916.666667

which rounds to 114,822,917

So it will take roughly 114,822,917 days to try all the passwords.

------

Then divide that over 365 to convert to years

314,583.334246576

which rounds to 314,583

It will take roughly 314,583 years to try all the passwords

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

Answers:9.9 trillion seconds2,755,750,000 hours114,822,917 days314,583 years

All values are approximate, and are roughly equivalent to one another.

A) 9,920,671,339,261,325,541,376 different passwords are available for this computer system.

B) 875,353,353,464,234,606,592 of these passwords contain at least one occurrence of at least one of the six special characters.

C) It would take 314,582.42 years for a hacker to try every possible password.

To determine how many different passwords are available for this computer system; how many of these passwords contain at least one occurrence of at least one of the six special characters; and how long it takes a hacker to try every possible password, assuming that it takes one nanosecond for a hacker to check each possible password, the following calculations must be performed:

26 + 26 + 10 + 6 = 68 A) 68 ^ 12 + 68 ^ 11 + 68 ^ 10 + 68 ^ 9 + 68 ^ 8 = X 9,920,671,339,261,325,541,376 = XB)6 x (68^11) + 6 x (68^10) + 6 x (68^9) + 6 x (68^8) + 6 x (68^7) = X875,353,353,464,234,606,592 = XC)1 nanosecond = 1,66667e-11 minutes9,920,671,339,261,325,541,376 nanoseconds = 165344522321.02209473 minutes165344522321.02209473 minutes = 2755742038.6837015152 hours2755742038.6837015152 hours = 114822584.94515423477 days114822584.94515423477 days = 314582.4245072719059 years

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in need of assistance answers are greatly appreciated thank you for your time and effort

Answers

Answer:

x = (h+g)/-f

Step-by-step explanation:

-fx-g = h

Add g to each side

-fx-g+g = h+g

-fx = h+g

Divide each side by -f

-fx/-f = (h+g)/-f

x = (h+g)/-f

as
8
3) The volume of
a wall, 5 times
high as it is board and 8
times as long as it is high, 12.8
(a.metors) Find The Breadth of the
Wall​

Answers

Answer:

  0.4 meters

Step-by-step explanation:

The volume is ...

  V = LHB

  12.8 m³ = (8(5B))(5B)(B) = 200B³ . . . fill in given values

  0.064 m³ = B³ . . . . . simplify

  ∛0.064 m = B = 0.4 m

The breadth of the wall is 0.4 meters.

Find an exact value of sin(17pi/12)

Answers

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   Hi my lil bunny!

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[tex]\frac{(17)(3.141593)}{12}[/tex]

= [tex]\frac{53.407075}{12}[/tex]

= [tex]4.45059[/tex]

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If this helped you, could you maybe give brainliest..?

Also Have a great day/night!

❀*May*❀

I have an answer and explanation but I can't type so search up the question you asked and you should get an answer and explanation from s0cratic.

Given the exponential function f(x) = 16(0.75)", classify the function as exponential growth or decay and determine the percent rate of growth or decay.
Exponential growth, 75% increase
O Exponential decay, 75% decrease
O Exponential growth, 25% increase
Exponential decay, 25% decrease​

Answers

Answer:

D

Step-by-step explanation:

To determine if a function is exponential decay or growth, simply look at the rate. If the rate is less than one, it is decay. It it's greater than one, it's growth.

The rate in the given function is 0.75 or 75%. 0.75 is less than one so it's exponential decay.

To determine the percent decrease, simply subtract the rate into 1 or 100%. Thus:

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

Therefore, it is a 0.25 or 25% decrease.

The answer is D.

Answer: D

Step-by-step explanation:

1-0.75=0.25

Therefore, it decreases Exponential decay,25 percent decrease  

Paisley is playing with a yo-yo. The following graph traces the path of the yo-yo while it is in the air, where y is the height of the yo-yo above the
ground, and x is the time, in seconds, from when the yo-yo leaves Paisley's hand Five stages of the yo-yo's path are marked on the graph.
Which of the five stages shows the slowest rate of change in the yo-yo's height above the ground?
А
В
C
D​

Answers

Answer:

C

Step-by-step explanation:

From the graph we can notice that the yo-yo crosses five positions: A,B,C,D and E.

The path created by the yo-yo has a parabolic form.

● In the area C, the yoyo crosses the vertex in wich the rate of change equals 0.

●In A the parabola decreases dramatically

● In B, the parabola is decreasing but slower than A.

● In D, the parabola is increasing in a fast way

● In E, the parabola is increasing faster than D.

● In the first half of C, the parabola is decreasing slower than B and A.

● At the vertex, the parabola has a null rate of change.

● In the second half of C, the parabola is increasing but slower than D and E.

So we deduce that C has the slowest rate of change.

Answer:

The answer is C i took the test

Step-by-step explanation:

Complete the square to make a perfect square trinomial. Then, write the result as a binomial squared. n^2+5/2n

Answers

Answer:  [tex]\bigg(n+\dfrac{5}{4}\bigg)^2[/tex]

Step-by-step explanation:

[tex]n^2+\dfrac{5}{2}n+\underline{\qquad}\\\\\\n^2+\dfrac{5}{2}n+\bigg(\dfrac{5}{2\cdot 2}\bigg)^2\\\\\\n^2+\dfrac{5}{2}n+\bigg(\dfrac{5}{4}\bigg)^2\\\\\\=\bigg(n+\dfrac{5}{4}\bigg)^2[/tex]

Mark has a collection of 80 coins. There are only nickels and dimes in the collection. The total value of the coins is $5.00. How many dimes does Mark have?

Answers

Answer:

number of nickel = 60

number of dimes  = 20

Step-by-step explanation:

1 nickel = 5 cents

1 dimes = 10 cents

$1 = 100 cents

we will use these value to solve the questions

_______________________________

Total no of coins = 80

let the number of nickels be x

let the number of dimes be y

thus,

x+y = 80

y = 80-x   equation 2

value of x nickels = 5x

value of y dimes = 10y

Total value of x nickels and y dimes = 5x+10y

The total value of the coins is $5.00

total value of the coins in cents = 5*100 = 500

thus

5x+10y = 500

using y = 80-x   from equation 2

5x + 10(80 - x) = 500

5x + 800 - 10x = 500

-5x = 500 - 800 = -300

x = -300/-5 = 60

Thus,

number of nickel = 60

number of dimes = 80-60 = 20

solve for x: 7^2x+3 =2401 . show substitution of your solution to verify the equation. show steps. show work.

Answers

Answer:

X= 1/2

Step-by-step explanation:

7^2x+3 =2401

7^(2x+3 )=2401

7^(2x+3 )= 7^4

Taking away the base because its equal to 7

Then solving the power as an equation

2x+3= 4

2x= 4-3

2x= 1

X=1/2

Now substituting x into the equation to know if we are correct

7^(2x+3 )=2401

Where x= 1/2

7^(2*(1/2) +3)= 7^4

7^(1+3)= 7^4

7^4= 7^4

7^4= 2401

Evaluate the double integral ∬Ry2x2+y2dA, where R is the region that lies between the circles x2+y2=16 and x2+y2=121, by changing to polar coordinates.

Answers

Answer:

See answer and graph below

Step-by-step explanation:

∬Ry2x2+y2dA

=∫Ry.2x.2+y.2dA

=A(2y+4Ryx)+c

=∫Ry.2x.2+y.2dA

Integral of a constant ∫pdx=px

=(2x+2.2Ryx)A

=A(2y+4Ryx)

=A(2y+4Ryx)+c

The graph of y=A(2y+4Ryx)+c assuming A=1 and c=2

The evaluation of the double integral is [tex]\mathbf{ \dfrac{105}{2}\pi }[/tex]

The double integral [tex]\mathbf{\int \int _R\ \dfrac{y^2}{x^2+y^2} \ dA}[/tex], where R is the region that lies between

the circles [tex]\mathbf{x^2 +y^2 = 16 \ and \ x^2 + y^2 = 121}[/tex].

Let consider x = rcosθ and y = rsinθ because x² + y² = r²;

Now, the double integral can be written in polar coordinates as:

[tex]\mathbf{\implies \int \int _R\ \dfrac{y^2}{x^2+y^2} \ dxdy}[/tex]

[tex]\mathbf{\implies \int \int _R\ \dfrac{r^2 \ sin^2 \theta}{r^2} \ rdrd\theta}[/tex]

[tex]\mathbf{\implies \int \int _R\ \ sin^2 \theta \ r \ drd\theta}[/tex]

Thus, the integral becomes:

[tex]\mathbf{=\int^{2 \pi}_{0} sin^2 \theta d\theta \int ^{11}_{4} rdr }[/tex]

since 2sin² = 1 - cos2θ

[tex]\mathbf{=\int^{2 \pi}_{0} \dfrac{1-cos 2 \theta }{2} \ \theta \ d\theta\dfrac{r}{2} \Big|^{11}_{4}dr }[/tex]  

[tex]\mathbf{\implies \dfrac{1}{2} \Big[\theta - \dfrac{sin \ 2 \theta}{2}\Big]^{2 \pi}_{0} \ \times\Big[ \dfrac{11^2-4^2}{2}\Big]}[/tex]

[tex]\mathbf{\implies \dfrac{\pi}{2} \times\Big[ 121-16\Big]}[/tex]

[tex]\mathbf{\implies \dfrac{105}{2}\pi }[/tex]

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The ball bearing have volumes of 1.6cm cube and 5.4cm cube . Find the ratio of their surface area.

Answers

Answer:

  4/9

Step-by-step explanation:

The scale factor for the linear dimensions of the ball bearings will be the cube root of the volume scale factor:

  k = ∛(1.6/5.4) = 2/3

Then the scale factor for the areas will be the square of this scale factor:

  ratio of surface area = (2/3)² = 4/9

_____

The area is the product of two linear dimensions, so its scale factor is the product of the linear dimension scale factors. That is, the scale factor for area is the square of the linear dimension scale factor.

Similarly, volume is the product of three linear dimensions, so its scale factor is the cube of the linear dimension scale factor.

QUESTION TWO [25 MARKS] a) Your task is to interview a representative sample of attendees for the large concert venue where you work. The new season schedule includes 200 live concerts featuring all types of musicians and musical groups. Since neither the number of attendees nor their descriptive characteristics are known in advance you decide on nonprobability sampling. Based on past seating configurations, you can calculate the number of tickets that will be available for each of the 200 concerts. Thus, collectively, you will know the number of possible attendees for each type of music From attendance research conducted at concerts held by the Glacier Symphony during the previous two years, you can obtain gender data on attendees by type of music. How would you conduct a reasonably reliable nonprobability sampling? T5 marks] (b) A recent article in Nairobi Post Weekly Edition indicated that about 80% of the​

Answers

Answer:

The answer to this question depends, in part, on the kinds of questions that you want to ask them. If the purpose of the survey is to try and figure out what concert patrons are thinking, then you want to try to get a good variety of ideas. In that case, you're no so interested in having a sample of individuals that's exactly representative of the population of concert goers. You only want to get a wide variety of the ideas that are out there. This is called heterogeneity sampling. That is, in this case, we'll be trying to get a sample not of people, but of ideas. In this case, we'd use brainstorming groups, panel sessions, and other group discussion methods to get all the ideas out there.

This approach is not an appropriate one if the purpose of the questions is to determine the preferences of the population of theater goers. That's because it doesn't communicate the popularity or prevalence of ideas in the sample. If this is a problem, and it likely is, it seems more appropriate to use some sort of purposive sampling method like modal interest sampling. This approach requires determining what the typical concert goer is like . If the company determines that the typical (or modal) attender is a young single person in college, then those people are sought out and interviewed. This is the sort of polling that is used in election polls where they interview "typical voters." For different genres of music and concert, a different typical concert goer could be postulated and different surveys and interview styles determined.

Probably most appropriate to this problem, though, is quota sampling. This form of purposive sampling uses demographic and other information to determine how many of different kinds of people to interview. For instance, if it is determined that only 20% of concert goers for a particular concert were women, then only 20% of the nonprobability sample should be made up of women. As long as these quotas are met, the sample can be sufficiently random.

I recommend using a combination of quota sampling and modal instance sampling. It seems to me that the kinds of people who attend concerts are idiosyncratic in some ways. Inasmuch as we can define universal characteristics of concert goers, we should seek to include only those people in the sample, but since we have demographic data as well, we should use these proportions as quotas as we select typical concert goers. For example, suppose we determine that the vast majority of people who attend operas make over $80,000/year, then we should limit our sample to people with that income level, but if we also know that 80% of opera attenders are women, we should work to insure that not more than 20% of our sample is men.

MY
A circle with radius of 5 cm sits inside a 11 cm x 11 cm rectangle.
Col
What is the area of the shaded region?
Round your final answer to the nearest hundredth.
MY
11 cm
Pro
Pro
Теа
5 cm
11 cm
cm2
2 of 4 OOO


Help

Answers

Step-by-step explanation:

Hi, there!!!

According to the question we must find the area of shaded region, but we must find area of circle and rectangle to find area of shaded region,

So, let's simply work with it,

Firstly, finding the area of rectangle,

length = 11cm.

breadth = 11cm.

now, area= length× breadth.

or, a = 11cm× 11cm.

a= 121cm^2

Now, let's work out the area of circle.

radius= 5cm

and pi. = 3.14 {using pi value as 3.14}

now,

area of a circle = pi× r^2

or, a= 3.14×5^2

or, a = 78.5 cm^2.

Therefore, The area of a circle is 78.5cm^2.

Now lastly finding the area of shadedregion,

area of shaded region = area of rectangle - area of circle.

or, area of shaded region = 121cm^2 - 78.5cm^2

Therefore, the area of shaded region is 42.5 cm^2.

Hope it helps...

A United Nations report shows the mean family income for Mexican migrants to the United States is $26,500 per year. A FLOC (Farm Labor Organizing Committee) evaluation of 24 Mexican family units reveals a mean to be $30,150 with a sample standard deviation of $10,560. State the null hypothesis and the alternate hypothesis.

Answers

Answer:

The null hypothesis [tex]\mathtt{H_0 : \mu = 26500}[/tex]

The alternative hypothesis [tex]\mathtt{H_1 : \mu \neq 26500}[/tex]

Step-by-step explanation:

The summary of the given statistics is:

Population Mean = 26,500

Sample Mean = 30,150

Standard deviation = 10560

sample size = 24

The objective is to state the null hypothesis and the alternate hypothesis.

An hypothesis is a claim with  insufficient information which tends to be challenged into  further testing and experimentation in order to determine if such claim is significant or not.

The null hypothesis is a default hypothesis where there is no statistical significance between the two variables in the hypothesis.

The alternative hypothesis is the research hypothesis that the  researcher is trying to prove.

The null hypothesis [tex]\mathtt{H_0 : \mu = 26500}[/tex]

The alternative hypothesis [tex]\mathtt{H_1 : \mu \neq 26500}[/tex]

The test statistic can be  computed as follows:

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

[tex]z = \dfrac{30150 - 26500}{\dfrac{10560}{\sqrt{24}}}[/tex]

[tex]z = \dfrac{3650}{\dfrac{10560}{4.8989}}[/tex]

[tex]z = \dfrac{3650 \times 4.8989 }{{10560}}[/tex]

z = 1.6933

A manufacturer of chocolate chips would like to know whether its bag filling machine works correctly at the 445 gram setting. It is believed that the machine is underfilling the bags. A 12 bag sample had a mean of 442 grams with a standard deviation of 20. A level of significance of 0.05 will be used. Assume the population distribution is approximately normal. State the null and alternative hypotheses.

Answers

Answer:

The  null hypothesis is  [tex]H_o : \mu = 445[/tex]

The  alternative hypothesis  [tex]H_a : \mu < 445[/tex]  (This is the original claim[ It is believed that the machine is under filling the bags] )

Step-by-step explanation:

From the question we are told that  

    The population mean is   [tex]\mu = 445 \ g[/tex]

    The  sample size is  [tex]n = 12[/tex]

    The  sample mean is  [tex]\= x = 442 \ g[/tex]

     The  standard deviation is  [tex]\sigma = 20[/tex]

     The  level of significance is  [tex]\alpha = 0.05[/tex]

The  null hypothesis is  [tex]H_o : \mu = 445[/tex]

The  alternative hypothesis  [tex]H_a : \mu < 445[/tex]  (This is the original claim )

Reduce 18/24 to its lowest terms

Answers

Answer:

3/4

Step-by-step explanation:

find a common number that 18 and 24 are both divisible by. I chose 6. So when i divide 6 by 18, I got 3. Which I put on my numerator, when I divided 24 by 6 I got 4 which I put on my denominator. My end result was 3/4

Answer:

3/4

Step-by-step explanation:

18/24

=2*9=18

=2*12=24

=9/12

=3/4

For f(x) = 3х – 5 and g(x) = х2+ 2, find (f+ g)(x).
ОА. ? + 3х – 7
ОВ. 3х2 – 30
Ос. 3х3 – 3
OD. х2 + 3х - з

Answers

Answer:

x^2 +3x -3

Step-by-step explanation:

f(x) = 3х – 5

g(x) = х^2+ 2,

(f+g)(x) = 3х – 5 +х^2+ 2

Combine like terms

         = x^2 +3x -3

g If two events are mutually exclusive, what is the probability that both occur at the same time? a. 1.00 b. 0.00 c. Cannot be determined from the information given. d. 0.50

Answers

The correct answer is B. 0.00

Explanation:

In statistics, two events are mutually exclusive if only one event can occur at one time. For example, if you have a deck of cards with Hearts and Spades, every time you choose a card you will have either Hearts or Spades but not both at the same time as there is not any card that combines Hearts and Spades in the same card. This means it is statistically impossible for two mutually exclusive events to occur at the same time, which means the probability is 0.00.

Which of the following is NOT a property of a paralleogram? * The opposite sides are equal. The opposite angles are equal. Each diagonal bisects the parallogram. The diagonals of all parallograms bisect each other at 90 degree angles. I will give brainliest

Answers

Answer:

The diagonals of all parallelograms do not bisect each other at 90 degree angles.

Step-by-step explanation:

Suppose that you begin with 10 grams of magic crystals, and your crystals grow at a
continuous rate of 25% every day (that's why they're magic). How many grams of
crystals will you have after one week (7 days)?!
ANSWER IS BRAINLEIST

Answers

Answer:

After 7 days the crystals will be 57.57 grams.

Step-by-step explanation:

In this the continuous exponential growth formula will be used.

y = A e ^rt

Where A = original amount = 10 grams

y is the growth after 7 days

e is Euler's number= 2.719

t is the time in hours , weeks, years etc.= 7 days

r  is the rate in decimals = 25% = 0.25

Putting the values in the formula:

y = A e ^rt

y = 10 e ^0.25 (7)

Calculating with the calculator

y = 10* 2.719^1.75

y= 57.57 grams.

After 7 days the crystals will be 57.57 grams.

 

Answer:

57.55g

Step-by-step explanation:

Use the formula f(t) = aert, where a = 10, r = 0.25, and t = 7. This gives f(7) = 10e(0.25)(7) = 10e1.75 ≈ 10(5.755) ≈ 57.55.

Help Please. I will Give Brainliest.

Answers

Answer:

1/2

Step-by-step explanation:

● 1/4 + 4(1/2 - 3/4 )^2

To make it easier convert the fractions to decimal numbers.

● 1/4 = 0.25

● 1/2 = 0.5

● 3/4 = 0.75

So the expression will be:

● 0.25 + 4(0.5 - 0.75)^2

Calculte first 0.5-0.75 (0.5-0.75= -0.25)

● 0.25 + 4 × (-0.25)^2

-0.25^2 is the same as 0.25^2

● 0.25 + 4 × (0.25)^2

0.25^2 is 0.0625

● 0.25 + 4×0.0625

Multiplication has the priority (4 ×0.0625) wich is 0.25

● 0.25 + 0.25

● 0.5

0.5 is 1/2

So the answer 1/2

Answer:

[tex]\frac{1}{2}[/tex]

Step-by-step explanation:

[tex]\frac{1}{4}+4(\frac{1}{2}-\frac{3}{4})^2\\\frac{1}{4}+4(\frac{2-3}{4})^2\\\frac{1}{4}+4(\frac{-1}{4})^2\\\frac{1}{4}+4(\frac{1}{16})\\\frac{1}{4}+\frac{1}{4}=\frac{2}{4}=\frac{1}{2}[/tex]

You might need:
Calculator
Astrid is in charge of building a new fleet of ships. Each ship requires 40 tons of w
sailors. She receives a delivery of 4 tons of wood each day. The deliveries can con
afterwards the weather is too bad to allow them. Overall, she wants to build enou
least 2100 sailors.
How much wood does Astrid need to accommodate 2100 sailors?
tons
Show Calculator​

Answers

This question is incomplete.

Complete Question

Astrid is in charge of building a new fleet of ships. Each ship requires 40 tons of wood, and accommodates 300 sailors. She receives a delivery of 4 tons of wood each day. The deliveries can continue for 100 days at most, afterwards the weather is too bad to allow them. Overall, she wants to build enough ships to accommodate at least 2100 sailors. How much wood does Astrid need to accommodate 2100 sailors?

Answer:

280 tons of wood.

Step-by-step explanation:

From the above question:

To make 1 ship = we require 40 tons of wood.

1 ship = can accommodate 300 sailors.

Step 1

If :

300 sailors = 1 ship

2100 sailors = y ships

Cross Multiply

300 × y ships = 1 ship × 2100 sailors

y ships = 2100 / 300

y ships = 7

Hence, 2100 sailors can occupy 7 ships.

Step 2

We are told in the question that:

Astrid wants to build enough ships to accommodate at least 2100 sailors. How much wood does Astrid need to accommodate 2100 sailors?

If:

1 ship = 40 tons of wood

Since 7 ships can accommodate 2100 sailors,

7 ships =

7 × 40 tons of wood = 280 tons of wood.

Therefore , Astrid needs 280 tons of wood to accommodate 2100 sailors.

List the sides in order from the largest to the smallest. A. XY, YW, WX B. XY, WX, YW C. WX, YW, XY D. WX, XY, YW

Answers

Answer:

Option (D)

Step-by-step explanation:

By applying Sine rule in the given triangle WXY,

[tex]\frac{\text{SinW}}{\text{XY}}=\frac{\text{SinY}}{\text{XW}}=\frac{\text{SinX}}{\text{WY}}[/tex]

[tex]\frac{\text{Sin59}}{\text{XY}}=\frac{\text{Sin82}}{\text{XW}}=\frac{\text{Sin39}}{\text{WY}}[/tex]

[tex]\frac{\text{Sin59}}{\text{XY}}=\frac{\text{Sin82}}{\text{XW}}[/tex]

[tex]\frac{\text{XW}}{\text{XY}}=\frac{\text{Sin82}}{\text{Sin59}}[/tex]

      = 1.1489

XW : XY ≈ 1.15 : 1

[tex]\frac{\text{Sin59}}{\text{XY}}=\frac{\text{Sin39}}{\text{WY}}[/tex]

[tex]\frac{\text{XY}}{\text{WY}}=\frac{\text{Sin59}}{\text{Sin39}}[/tex]

[tex]\frac{\text{XY}}{\text{WY}}=\frac{1.36}{1}[/tex]

[tex]\frac{\text{XY}}{\text{WY}}=\frac{\frac{1}{1}}{\frac{1}{1.36} }[/tex]

[tex]\frac{\text{XY}}{\text{WY}}=\frac{1}{0.7342}[/tex]

XY : WY = 1 : 0.7342

XW : XY : WY = 1.15 : 1 : 0.7342

Therefore, WX > XY > WY

Option (D). will be the correct option.

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