Musah stands at the centre of a rectangular field. He first takes 50 steps north, then 25 steps

west and finally 50 steps on a bearing of 3150

.

i. Sketch Musah’s movement

ii. How far west is Musah’s final point from the centre?
iii. How far north is Musah’s final point from the centre?

iv. Describe how you would guide a JHS student to find the bearing and distance of

Musah’s final point from the centre. ​

Answers

Answer 1

Answer:

ii. 75 steps

iii. 75 steps

iv. 106 steps, and [tex]315^{0}[/tex]

Step-by-step explanation:

Let Musah's starting point be A, his waiting point after taking 50 steps northward and 25 steps westward be B, and his stopping point be C.

ii. From the second attachment, Musah's distance due west from A to C (AD) can be determined as;

bearing at B = [tex]315^{0}[/tex], therefore <BCD = [tex]45^{0}[/tex]

To determine distance AB,

[tex]/AB/^{2}[/tex] = [tex]/50/^{2}[/tex]   +  [tex]/25/^{2}[/tex]

          = 25000 + 625

          = 3125

AB = [tex]\sqrt{3125}[/tex]

     = 55.90

AB ≅ 56 steps

Thus, AC = 50 steps + 56 steps

               = 106 steps

From ΔACD,

Sin [tex]45^{0}[/tex] = [tex]\frac{x}{106}[/tex]

⇒ x = 106 × Sin [tex]45^{0}[/tex]

      = 74.9533

     ≅ 75 steps

Musah's distance west from centre to final point is 75 steps

iii. From the secon attachment, Musah's distance north, y, can be determined by;

Cos [tex]45^{0}[/tex] = [tex]\frac{y}{106}[/tex]

⇒ y = 106 × Cos [tex]45^{0}[/tex]

      = 74.9533

      ≅ 75 steps

Musah's distance north from centre to final point is 75 steps.

iv. Musah's distance from centre to final point is AC = AB + BC

                                     = 50 steps + 56 steps

                                     = 106 steps

From ΔACD,

Tan θ = [tex]\frac{75}{75}[/tex]

          = 1.0

θ = [tex]Tan^{-1}[/tex]  1.0

 = [tex]45^{0}[/tex]

Musah's bearing from centre to final point = [tex]45^{0}[/tex] + [tex]270^{0}[/tex]

                                                           =  [tex]315^{0}[/tex]

Musah Stands At The Centre Of A Rectangular Field. He First Takes 50 Steps North, Then 25 Steps West
Musah Stands At The Centre Of A Rectangular Field. He First Takes 50 Steps North, Then 25 Steps West

Related Questions

Multiple Choice The opposite of –4 is A. 4. B. –4. C. –(–(–4)). D. –|4|.

Answers

Answer:

a. 4

Step-by-step explanation:

-1(-4) = 4

Answer:

A 4

Step-by-step explanation:

opposite of –4 = 4

From a group of 11 people, 4 are randomly selected. What is the probability the 4 oldest people in the group were selected

Answers

The probability that the 4 oldest people in the group were selected is based on combinatorics is 0.00303 or 0.303%.

Given that:

Find how many ways the 4 oldest people can be selected from the group.

Since the 4 oldest people are already determined, there is only 1 way to select them.

n = 11 (total number of people in the group) and k = 4 (number of people to be selected).

To calculate the probability, to determine the total number of ways to select 4 people from the group of 11. This can be found using the combination formula:

Number of ways to choose k items from n items :

C(n,k) = n! / (k!(n-k)!)

Calculate the total number of ways to select 4 people from the group:

Plugging n and k value from given data:

C(11,4 )= 11! / (4!(11-4)!)

On simplifications gives:

C(11, 4) = 330.

Calculate the probability:

Probability = Number of ways 4 oldest people selected / Total number of ways to select 4 people

Plugging the given data:

Probability = 1 / 330

Probability ≈ 0.00303 or 0.303%.

Therefore, the  probability that the 4 oldest people in the group were selected is based on combinatorics is 0.00303 or 0.303%.

Learn more about probabilities here:

https://brainly.com/question/23846068

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PLEASE HELP!! (1/5) -50 POINTS-

Answers

Answer:

[tex]X=\begin{bmatrix}5&3\\ -3&2\end{bmatrix}[/tex]

Step-by-step explanation:

We are given the following matrix equation, from which we have to isolate X and simplify this value.

[tex]\begin{bmatrix}2&4\\ \:\:\:5&4\end{bmatrix}X\:+\:\begin{bmatrix}-8&-8\\ \:\:\:12&1\end{bmatrix}=\:\begin{bmatrix}-10&6\\ \:\:\:25&24\end{bmatrix}[/tex]

To isolate X, let us first subtract the second matrix, as demonstrated below, from either side. Further simplifying this equation we can multiply either side by the inverse of the matrix being the co - efficient of X, isolating it in the doing.

[tex]\begin{bmatrix}2&4\\ 5&4\end{bmatrix}X=\begin{bmatrix}-10&6\\ 25&24\end{bmatrix}-\begin{bmatrix}-8&-8\\ 12&1\end{bmatrix}[/tex] (Simplify second side of equation)

[tex]\begin{bmatrix}-10&6\\ 25&24\end{bmatrix}-\begin{bmatrix}-8&-8\\ 12&1\end{bmatrix}=\begin{bmatrix}\left(-10\right)-\left(-8\right)&6-\left(-8\right)\\ 25-12&24-1\end{bmatrix}=\begin{bmatrix}-2&14\\ 13&23\end{bmatrix}[/tex] ,

[tex]\begin{bmatrix}2&4\\ 5&4\end{bmatrix}X=\begin{bmatrix}-2&14\\ 13&23\end{bmatrix}[/tex] (Multiply either side by inverse of matrix 1)

[tex]X=\begin{bmatrix}2&4\\ 5&4\end{bmatrix}^{-1}\begin{bmatrix}-2&14\\ 13&23\end{bmatrix}=\begin{bmatrix}5&3\\ -3&2\end{bmatrix}[/tex]

Our solution is hence option c

Can somebody please solve this problem for me!

Answers

Answer:

x = 200.674

Step-by-step explanation:

tan∅ = opposite/adjacent

Step 1: Find length of z

tan70° = 119/z

ztan70° = 119

z = 119/tan70°

z = 43.3125

Step 2: Find length z + x (denoted as y)

tan26° = 119/y

ytan26° = 119

y = 119/tan26°

y = 243.986

Step 3: Find x

y - z = x

243.986 - 43.3125 = x

x = 200.674

You work for a pharmacy and monthly sales of asthma inhalers in your pharmacy follows a normal distribution with a mean of 191 inhalers per month and a standard deviation of 21 due to a storm the next shipment of inhalers did not arrive. The pharmacy only has 163 inhalers currently in stock and available to sell for the current month. What is the z score corresponding to selling 163 inhalers?

Answers

Answer: -1.33 .

Step-by-step explanation:

Formula to find the Z-score :

[tex]Z=\dfrac{\text{Expected value - Mean}}{\text{Standard deviation}}[/tex]

Given: Mean = 191  and Standard deviation = 21

Then , the z-score corresponding to the expected value of 163 will be :

[tex]Z=\dfrac{163-191}{21}\\\\=\dfrac{-28}{21}\approx-1.33[/tex]

Hence, the z score corresponding to selling 163 inhalers is -1.33 .

How many ways are there to choose 22 croissants with at least one plain croissant, at least two cherry croissants, at least three chocolate croissants, at least one almond croissant, at least two apple croissants, and no more than three broccoli croissants

Answers

Answer:

There are 6566 ways to choose 22 croissants with at least one plain croissant, at least two cherry croissants, at least three chocolate croissants, at least one almond croissant, at least two apple croissants, and no more than three broccoli croissants.

Step-by-step explanation:

Given:

There are 5 types of croissants:

plain croissants

cherry croissants

chocolate croissants

almond croissant

apple croissants

broccoli croissants

To find:

to choose 22 croissants with:

at least one plain croissant

at least two cherry croissants

at least three chocolate croissants

at least one almond croissant

at least two apple croissants

no more than three broccoli croissants

Solution:

First we select

At least one plain croissant to lets say we first select 1 plain croissant, 2 cherry croissants, 3 chocolate croissants, 1 almond croissant, 2 apple croissants

So

1 + 2 + 3 + 1 + 2  = 9

Total croissants = 22  

So 9 croissants are already selected and 13 remaining croissants are still needed to be selected as 22-9 = 13, without selecting more than three broccoli croissants.

n = 5

r = 13

C(n + r - 1, r)

= C(5 + 13 - 1, 13)

= C(17,13)

[tex]=\frac{17! }{13!(17-13)!}[/tex]

= 355687428096000 / 6227020800 ( 24 )

= 355687428096000 / 149448499200

= 2380

C(17,13) = 2380

C(n + r - 1, r)

= C(5 + 12 - 1, 12)

= C(16,12)

[tex]=\frac{16! }{12!(16-12)!}[/tex]

= 20922789888000 / 479001600 ( 24 )

= 20922789888000  / 11496038400

= 1820

C(16,12) = 1820

C(n + r - 1, r)

= C(5 + 11 - 1, 11)

= C(15,11)

[tex]=\frac{15! }{11!(15-11)!}[/tex]

= 1307674368000 / 39916800 (24)

= 1307674368000 / 958003200

= 1307674368000 / 958003200

= 1365

C(15,11) = 1365

C(n + r - 1, r)

= C(5 + 10 - 1, 10)

= C(14,10)

[tex]=\frac{14! }{10!(14-10)!}[/tex]

= 87178291200 / 3628800 ( 24 )

= 87178291200 / 87091200

= 1001

C(14,10) = 1001

Adding them:

2380 + 1820 + 1365 + 1001 = 6566 ways

A middle school has 470 students. Regina surveys a random sample of 40 students and finds that 28 have cell phones. How many students at the school are likely to have cell phones? A. 132 students B. 188 students C. 329 students D. 338 students Please include ALL work! <3

Answers

Answer:

C. 329

Step-by-step explanation:

So 28 is 70% of 40

so we know that 70% percent of students have phones

70% of 470

329

Thats how I solved it have a great day :)

Which table represents a linear function?
x y
1 5
2 10
3 15
4 20
5 25

x y
1 5
2 20
3 45
4 80
5 125

x y
1 5
2 25
3 125
4 625
5 3125

x y
1 2
2 4
3 7
4 16
5 32​

Answers

Answer:

The first table on the list:

x 1   2  3  4    5

y 5 10 15 20 25

Step-by-step explanation:

A linear equation is when the slope is the exact same between each point.  The way we find slope is by finding the change in "y" over the change in "x".

x-values: 1, 2/y-values: 5, 10---[tex]\frac{10-5}{2-1}[/tex]=5/1=5

x-values: 2, 3/y-values: 10, 15---[tex]\frac{15-10}{3-2}[/tex]=5/1=5

x-values: 3, 4/y-vaues: 15, 20---[tex]\frac{20-15}{4-3}[/tex]=5/1=5

x-values: 4, 5/y-values: 20, 25---[tex]\frac{25-20}{5-4}[/tex]=5/1=5

The slope for each change in points is 5, which means that this table represents a linear function.

The only table that represents a linear function is; Table 1

Linear function

A linear function is one that has the same slope for every coordinate point.

Looking at the tables, the one with same slope for all points is table 1 and we will prove that as follows;

At x = 1, y = 5 and;

Slope = 5/1 = 5

At x = 2; y = 10 and;

Slope = 10/2 = 5

At x = 3, y = 15 and;

Slope = 15/3 = 5

At x = 4, y = 20 and;

Slope = 20/4 = 5

At x = 5, y = 25 and;

slope = 25/5 = 5

In conclusion, only table 1 represents a linear function.

Read more about Linear function at; https://brainly.com/question/15602982

32 to 34 Directions: Given the following set of
numbers find the mean, median, and mode.
12, 13, 15, 15, 16, 19, 19, 19, 20, 21, 25
39.
32. Mean =
a. 17.64
b. 19
c. 15
40. 1
33. Median
a. 17.64
b. 19
c. 15

Answers

Answer:

32. A

33. B

Step-by-step explanation:

32. Mean: In order to find the mean, add all of the #up which is 194 then divide by how many # there is

33. Start by crossing out the beginning # and the end # all the way till you get the # without another pair in the end

Which choice shows the product of 22 and 49 ?

Answers

Answer:

1078

Step-by-step explanation:

The product of 22 and 49 is 1078.

Answer:

1078 is the product

Step-by-step explanation:

Help someone please!!

Answers

Answer:

A. 5:4

Step-by-step explanation:

Since the question mentions twelfths of a pie, it is easier to say each pie has 12 pieces or 36 total pieces ordered from the 3 pies. Ty ate 5 and Rob ate 15 which is 3 times more than Ty. A total of 20 pieces have been eaten from the 36 you started with. Eaten = 20 and Remaining = 16. So the ratio is 20:16 which is simplified to 5:4.

the answer is A. 5:4

Let E and F be two events of an experiment with sample space S. Suppose P(E) = 0.6, P(F) = 0.3, and P(E ∩ F) = 0.1. Compute the values below.

(a) P(E ∪ F) =



(b) P(Ec) =



(c) P(Fc ) =



(d) P(Ec ∩ F) =

Answers

Answer:

(a) P(E∪F)= 0.8

(b) P(Ec)= 0.4

(c) P(Fc)= 0.7

(d) P(Ec∩F)= 0.8

Step-by-step explanation:

(a) It is called a union of two events A and B, and A ∪ B (read as "A union B") is designated to the event formed by all the elements of A and all of B. The event A∪B occurs when they do A or B or both.

If the events are not mutually exclusive, the union of A and B is the sum of the probabilities of the events together, from which the probability of the intersection of the events will be subtracted:

P(A∪B) = P(A) + P(B) - P(A∩B)

In this case:

P(E∪F)= P(E) + P(F) - P(E∩F)

Being P(E) = 0.6, P(F) = 0.3 and P(E ∩ F) = 0.1

P(E∪F)= 0.6 + 0.3 - 0.1

P(E∪F)= 0.8

(b)  The complement of an event A is defined as the set that contains all the elements of the sample space that do not belong to A.  The Complementary Rule establishes that the sum of the probabilities of an event and its complement must be equal to 1. So, if P (A) is the probability that an event A occurs, then the probability that A does NOT occur is  P (Ac) = 1- P (A)

In this case: P(Ec)= 1 - P(E)

Then: P(Ec)= 1 - 0.6

P(Ec)= 0.4

(c) In this case: P(Fc)= 1 - P(F)

Then: P(Fc)= 1 - 0.3

P(Fc)= 0.7

(d)  The intersection of two events A and B, designated as A ∩ B (read as "A intersection B") is the event formed by the elements that belong simultaneously to A and B. The event A ∩ B occurs when A and B do at once.

As mentioned, the complementary rule states that the sum of the probabilities of an event and its complement must equal 1. Then:

P(Ec intersection F) + P(E intersection F) = P(F)

P(Ec intersection F) + 0.1 = 0.3

P(Ec intersection F)= 0.2

Being:

P(Ec∪F)= P(Ec) + P(F) - P(Ec∩F)

you get:

P(Ec∩F)= P(Ec) + P(F) - P(Ec∪F)

So:

P(Ec∩F)= 0.4 + 0.3 - 0.2

P(Ec∩F)= 0.8

Mark each of the following as true or false and explain how you know.

Answers

true false false true...is the quick answer

Remember that negatives are always less than positive numbers.

This test statistic leads to a decision to...

reject the null

accept the null

fail to reject the null



As such, the final conclusion is that...

There is sufficient evidence to warrant rejection of the claim that the population mean is not equal to 88.9.

There is not sufficient evidence to warrant rejection of the claim that the population mean is not equal to 88.9.

The sample data support the claim that the population mean is not equal to 88.9.

There is not sufficient sample evidence to support the claim that the population mean is not equal to 88.9.

Answers

Answer:

There is not sufficient sample evidence to support the claim that the population mean is not equal to 88.9.

Step-by-step explanation:

We are given the following hypothesis below;

Let [tex]\mu[/tex] = population mean.

So, Null Hypothesis, [tex]H_0[/tex] : [tex]\mu[/tex] = 88.9      {means that the population mean is equal to 88.9}

Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu\neq[/tex] 88.9     {means that the population mean is different from 88.9}

The test statistics that will be used here is One-sample t-test statistics because we don't know about population standard deviation;

                             T.S.  =  [tex]\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }[/tex]  ~  [tex]t_n_-_1[/tex]

where, [tex]\bar X[/tex] = sample mean = 81.3

             s = sample standard deviation = 13.4

            n = sample size = 7

So, the test statistics =  [tex]\frac{81.3-88.9}{\frac{13.4}{\sqrt{7} } }[/tex]   ~ [tex]t_6[/tex]

                                     =  -1.501

The value of t-test statistics is -1.501.

Also, the P-value of the test statistics is given by;

                    P-value = P([tex]t_6[/tex] < -1.501) = 0.094

Since the P-value of our test statistics is more than the level of significance as 0.094 > 0.01, so we have insufficient evidence to reject our null hypothesis as the test statistics will not fall in the rejection region.

Therefore, we conclude that the population mean is equal to 88.9.

“Type ‘equal, supplementary, complementary, or vertical in the space provided’”

Answers

Answer:

Supplementary

Step-by-step explanation:

When the sum of 2 angles equal 180°, they are called supplementary angles. And they also form a straight line together.

<AOB (40°) and <BOC (140°) are not equal angles.

<AOB (40°) and <BOC (140°) are not complementary angles. Complementary angles add up to equal 90°.

<AOB (40°) and <BOC (140°) are not vertical angles. Vertical angles are opposite angles formed when two lines intersect.

<AOB (40°) and <BOC (140°) are supplementary angles. They add up to equal 180°.

Ben and Cam are scuba diving. Ben is 15.8 meters below the
surface of the water. Cam is 4.2 meters above Ben. What is Cam's
position relative to the surface of the water?

Answers

Answer: Cam is 11.6 meters below the surface of the water

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

Explanation:

Check out the diagram below.

Draw a vertical number line with 0 at the center. The positive values are above it, while the negative values are below it.

Between -15 and -16, closer to -16, plot the value -15.8 to indicate Ben's position. I have done so as the point B.

We move 4.2 units up to arrive at Cam's position

-15.8 + 4.2 = -11.6

So Cam is 11.6 meters below the surface of the water.

Evaluate 3h(2) + 2k(3) =

Answers

Answer:

6h + 6k

Step-by-step explanation:

[tex]3h\left(2\right)+2k\left(3\right)\\\\\mathrm{Remove\:parentheses}:\quad \left(a\right)=a\\\\=3h\times \:2+2k\times \:3\\\\\mathrm{Multiply\:the\:numbers:}\:3\times \:2=6\\\\=6h+2\times \:3k\\\\\mathrm{Multiply\:the\:numbers:}\:2\times \:3=6\\\\=6h+6k[/tex]

Answer:

Answers for E-dge-nuityyy

Step-by-step explanation:

(h + k)(2) = 5

(h – k)(3) = 9

Evaluate 3h(2) + 2k(3) = 17

How to convert 2cm to feet?

Answers

Answer:

Divide by 30.48: It would be 0.0656168 feet.

Step-by-step explanation:

Answer:

0.0656

Step-by-step explanation:

2.54 cm = 1 in

12 in = 1 ft

2.54 * 12 = 30.48

2/30.48 = 0.0656167979

What is credit?
an arrangement in which you receive money, goods, or services now in exchange for the promise of payment later
an arrangement in which you receive goods or services in exchange for other goods and services
an arrangement in which you receive money now and pay it bulk later with fees?

Answers

An arrangement in which you receive money more and pay it back later with fees

Change each of the following points from rectangular coordinates to spherical coordinates and to cylindrical coordinates.
a. (4,2,−4)
b. (0,8,15)
c. (√2,1,1)
d. (−2√3,−2,3)

Answers

Answer and Step-by-step explanation: Spherical coordinate describes a location of a point in space: one distance (ρ) and two angles (Ф,θ).To transform cartesian coordinates into spherical coordinates:

[tex]\rho = \sqrt{x^{2}+y^{2}+z^{2}}[/tex]

[tex]\phi = cos^{-1}\frac{z}{\rho}[/tex]

For angle θ:

If x > 0 and y > 0: [tex]\theta = tan^{-1}\frac{y}{x}[/tex];If x < 0: [tex]\theta = \pi + tan^{-1}\frac{y}{x}[/tex];If x > 0 and y < 0: [tex]\theta = 2\pi + tan^{-1}\frac{y}{x}[/tex];

Calculating:

a) (4,2,-4)

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

[tex]\phi = cos^{-1}(\frac{-4}{6})[/tex]

[tex]\phi = cos^{-1}(\frac{-2}{3})[/tex]

For θ, choose 1st option:

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

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

b) (0,8,15)

[tex]\rho = \sqrt{0^{2}+8^{2}+(15)^{2}}[/tex] = 17

[tex]\phi = cos^{-1}(\frac{15}{17})[/tex]

[tex]\theta = tan^{-1}\frac{y}{x}[/tex]

The angle θ gives a tangent that doesn't exist. Analysing table of sine, cosine and tangent: θ = [tex]\frac{\pi}{2}[/tex]

c) (√2,1,1)

[tex]\rho = \sqrt{(\sqrt{2} )^{2}+1^{2}+1^{2}}[/tex] = 2

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

[tex]\phi[/tex] = [tex]\frac{\pi}{3}[/tex]

[tex]\theta = tan^{-1}\frac{1}{\sqrt{2} }[/tex]

d) (−2√3,−2,3)

[tex]\rho = \sqrt{(-2\sqrt{3} )^{2}+(-2)^{2}+3^{2}}[/tex] = 5

[tex]\phi = cos^{-1}(\frac{3}{5})[/tex]

Since x < 0, use 2nd option:

[tex]\theta = \pi + tan^{-1}\frac{1}{\sqrt{3} }[/tex]

[tex]\theta = \pi + \frac{\pi}{6}[/tex]

[tex]\theta = \frac{7\pi}{6}[/tex]

Cilindrical coordinate describes a 3 dimension space: 2 distances (r and z) and 1 angle (θ). To express cartesian coordinates into cilindrical:

[tex]r=\sqrt{x^{2}+y^{2}}[/tex]

Angle θ is the same as spherical coordinate;

z = z

Calculating:

a) (4,2,-4)

[tex]r=\sqrt{4^{2}+2^{2}}[/tex] = [tex]\sqrt{20}[/tex]

[tex]\theta = tan^{-1}\frac{1}{2}[/tex]

z = -4

b) (0, 8, 15)

[tex]r=\sqrt{0^{2}+8^{2}}[/tex] = 8

[tex]\theta = \frac{\pi}{2}[/tex]

z = 15

c) (√2,1,1)

[tex]r=\sqrt{(\sqrt{2} )^{2}+1^{2}}[/tex] = [tex]\sqrt{3}[/tex]

[tex]\theta = \frac{\pi}{3}[/tex]

z = 1

d) (−2√3,−2,3)

[tex]r=\sqrt{(-2\sqrt{3} )^{2}+(-2)^{2}}[/tex] = 4

[tex]\theta = \frac{7\pi}{6}[/tex]

z = 3

Which is an infinite arithmetic sequence? a{10, 30, 90, 270, …} b{100, 200, 300, 400} c{150, 300, 450, 600, …} d{1, 2, 4, 8}

Answers

Answer:

C

Step-by-step explanation:

An arithmetic sequence has a common difference d between consecutive terms.

Sequence a

30 - 10 = 20

90 - 30 = 60

270 - 90 = 180

This sequence is not arithmetic

Sequence b

200 - 100 = 100

300 - 200 = 100

400 - 300 = 100

This sequence is arithmetic but is finite, that is last term is 400

Sequence c

300 - 150 = 150

450 - 300 = 150

600 - 450 = 150

This sequence is arithmetic and infinite, indicated by ........ within set

Sequence d

2 - 1 = 1

4 - 2 = 2

8 - 4 = 4

This sequence is not arithmetic

Thus the infinite arithmetic sequence is sequence c

Carl recorded the number of customers who visited his new store during the week:


Day Customers

Monday 17

Tuesday 13

Wednesday 14

Thursday 16


He expected to have 15 customers each day. To answer whether the number of customers follows a uniform distribution, a chi-square test for goodness of fit should be performed. (alpha = 0.10)


What is the chi-squared test statistic? Answers are rounded to the nearest hundredth.

Answers

Answer:

The chi - square test can be [tex]\approx[/tex] 0.667

Step-by-step explanation:

From the given data :

The null hypothesis and the alternative hypothesis can be computed as:

Null hypothesis: The number of customers does  follow  a uniform distribution

Alternative hypothesis: The number of customers does not  follow  a uniform distribution

We learnt that: Carl recorded the number of customers who visited his new store during the week:

Day              Customers

Monday               17

Tuesday              13

Wednesday         14

Thursday              16

The above given data was the observed value.

However, the question progress by stating that : He expected to have 15 customers each day.

Now; we can have an expected value for each customer  as:

                      Observed Value                   Expected Value

Day                 Customers                        

Monday                17                                          15

Tuesday               13                                          15

Wednesday          14                                          15

Thursday               16                                         15

The Chi square corresponding to each data can be determined by using the formula:

[tex]Chi -square = \dfrac{(observed \ value - expected \ value )^2}{expected \ value}[/tex]

For Monday:

[tex]Chi -square = \dfrac{(17 - 15 )^2}{15}[/tex]

[tex]Chi -square = \dfrac{(2)^2}{15}[/tex]

[tex]Chi - square = \dfrac{4}{15}[/tex]

chi - square = 0.2666666667

For Tuesday :

[tex]Chi -square = \dfrac{(13- 15 )^2}{15}[/tex]

[tex]Chi -square = \dfrac{(-2)^2}{15}[/tex]

[tex]Chi - square = \dfrac{4}{15}[/tex]

chi - square = 0.2666666667

For Wednesday :

[tex]Chi -square = \dfrac{(14- 15 )^2}{15}[/tex]

[tex]Chi -square = \dfrac{(-1 )^2}{15}[/tex]

[tex]Chi -square = \dfrac{(1 )}{15}[/tex]

chi - square = 0.06666666667

For Thursday:

[tex]Chi -square = \dfrac{(16- 15 )^2}{15}[/tex]

[tex]Chi -square = \dfrac{(1 )^2}{15}[/tex]

[tex]Chi -square = \dfrac{(1 )}{15}[/tex]

chi - square = 0.06666666667

                   Observed Value   Expected Value    chi - square

Day                 Customers                        

Monday                17                     15                       0.2666666667

Tuesday               13                     15                       0.2666666667

Wednesday          14                     15                       0.06666666667

Thursday               16                    15                       0.06666666667

Total :                                                                        0.6666666668

The chi - square test can be [tex]\approx[/tex] 0.667

At level of significance ∝ = 0.10

degree of freedom = n - 1

degree of freedom = 4 - 1

degree of freedom = 3

At ∝ = 0.10 and df = 3

The p - value for the chi - square test statistics is 0.880937

Decision rule: If the p - value is greater than the level of significance , we fail to reject the null hypothesis

Conclusion: Since the p - value is greater than the level of significance , we fail to reject the null hypothesis and conclude that there is insufficient evidence to show that the number of customers does not follows a uniform distribution.

Answer:.67

Step-by-step explanation:

Lori buys a $586 certificate of deposit (CD) that earns 6.6% interest that compounds monthly. How much will the CD be worth in 13 years? Express your answer rounded correctly to the nearest cent. Do not include units on your answer.

Answers

Answer:

$1344.9

Step-by-step explanation:

This problem can be solved using the compound interest formula

[tex]A= P(1+r)^t[/tex]

Given data

A, final amount =?

P, principal = $586

rate, r= 6.6% = 0.066

Time, t= 13 years

Substituting our values into the expression we have

[tex]A= 586(1+0.066)^1^3\\\ A= 586*(1.066)^13\\\ A= 586*2.295\\\ A= 1344.87[/tex]

To the nearest cent the in 13 years the CD will be worth $1344.9

The data represents the daily rainfall​ (in inches) for one month. Construct a frequency distribution beginning with a lower class limit of and use a class width of . Does the frequency distribution appear to be roughly a normal​ distribution?

Answers

Answer:

The frequency distribution does not appear to be normal.

Step-by-step explanation:

The data provided is as follows:

S = {0.38 , 0 , 0.22 , 0.06 , 0 , 0 , 0.21 , 0 , 0.53 , 0.18 , 0 , 0 , 0.02 , 0 , 0 , 0.24 , 0 , 0 , 0.01 , 0 , 0 , 1.28 , 0.24 , 0 , 0.19 , 0.53 , 0 , 0, 0.24 , 0}

It is provided that the first lower class limit should be 0.00 and the class width should be 0.20.

The frequency distribution table is as follows:

Class Interval  Count

 0.00 - 0.19            21

 0.20 - 0.39             6

 0.40 - 0.59             2

 0.60 - 0.79             0

 0.80 - 0.99             0

  1.00 - 1 . 19             0

  1.20 - 1. 39             1

The frequency distribution does not appear to be normal. This is because the frequencies does not start and end at almost equivalent points and the mid-distribution does not consist of the highest frequency.

Thus, the frequency distribution does not appear to be normal.

Can someone help? This hard

Answers

Answer:

The expression = [tex] \frac{40}{y - 16} [/tex]

Value of the expression = 4 (when y is 20)

Step-by-step explanation:

Quotient simply means the result you get when you divide two numbers. Thus, dividend (the numerator) ÷ divisor (the denominator) = quotient.

From the information given to us here,

the dividend = 40

the divisor = y - 16

The quotient = [tex] \frac{40}{y - 16} [/tex]

There, the expression would be [tex] \frac{40}{y - 16} [/tex]

Find the value of the expression when y = 20.

Plug in 20 for y in the expression and evaluate.

[tex] \frac{40}{y - 16} [/tex]

[tex] = \frac{40}{20 - 16} [/tex]

[tex] = \frac{40}{4} = 10 [/tex]

The value of the expression, when y is 20, is 4.

Pennsylvania Refining Company is studying the relationship between the pump price of gasoline and the number of gallons sold. For a sample of 14 stations last Tuesday, the correlation was 0.65. Can the company conclude that the correlation is positive

Answers

Complete Question

Pennsylvania Refining Company is studying the relationship between the pump price of gasoline and the number of gallons sold. For a sample of 14 stations last Tuesday, the correlation was 0.65.At the 0.01 significance level Can the company conclude that the correlation is positive

Answer:

Yes the company conclude that the correlation is positive

Step-by-step explanation:

From the question we are told that

   The  sample size is  n =  14

    The correlation is  r =  0.65

     

The  null hypothesis is  [tex]H_o : r < 0[/tex]

The  alternative hypothesis is  [tex]H_1 : r > 0[/tex]

Generally the standard deviation is mathematically evaluated as

       [tex]Sr = \sqrt{1- r}[/tex]

       [tex]Sr = \sqrt{1- 0.65}[/tex]

       [tex]Sr = 0.616[/tex]

The  degree of freedom for the one-tail test is

       [tex]df = n- 2[/tex]

        [tex]df = 14- 2[/tex]

        [tex]df = 12[/tex]

The standard error is evaluated as

        [tex]SE = \frac{0.616}{ \sqrt{12} }[/tex]

        [tex]SE =0.1779[/tex]

The test statistics  is evaluated as

      [tex]t = \frac{r }{SE}[/tex]

       [tex]t = \frac{0.65 }{0.1779}[/tex]

        [tex]t = 3.654[/tex]

The p-value of of  t is obtained from the z table, the value is  

        [tex]p-value = P(t < 3.654) = 0.00012909[/tex]

Given that [tex]p-value < \alpha[/tex]  then we reject the null hypothesis

           Hence the company can conclude that the correlation is positive

     

10-
What is the equation of the line that is perpendicular to
the given line and passes through the point (2, 6)?
8-
(2,6)
-6
O x = 2
4
O x = 6
-2
-10 -3 -6 -22
2
4
B
8
10
X
O y = 2
O y = 6
(-34)
(814)
8
WO

Answers

Answer:

x = 2

Step-by-step explanation:

This blue line seems to be horizontal, and so a line perpendicular would have to be vertical. The only vertical line that passes through (2, 6) would be x = 2.

The equation of the line perpendicular to the given line and passes through the point (2, 6) is x = 2.

What is the Equation of line in Slope Intercept form?

Equation of a line in slope intercept form is y = mx + b, where m is the slope of the line and b is the y intercept, which is the y coordinate of the point where it touches the Y axis.

Given is a line that passes through the points (-8, -4) and (8, -4).

This line is parallel to the X axis.

A line parallel to X axis has the equation y = b.

The y coordinate is -4 throughout the line.

So equation of the line is y = -4.

A line perpendicular to the given line will be parallel to Y axis.

Parallel lines to Y axis has the equation of the form x = a.

Line passes through the point (2, 6).

x coordinate will be 2 throughout.

So the equation of the perpendicular line is x = 2.

Hence the required equation is x = 2.

Learn more about Equations of Lines here :

https://brainly.com/question/21511618

#SPJ7

Evaluate S_5 for 600 + 300 + 150 + … and select the correct answer below. A. 1,162.5 B. 581.25 C. 37.5 D. 18,600

Answers

Answer:

  A.  1,162.5

Step-by-step explanation:

Write the next two terms and add them up:

  S5 = 600 +300 +150 +75 +37.5 = 1162.5 . . . . matches choice A

Answer: Choice A 1,162.5

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

Explanation:

{600, 300, 150, ...} is a geometric sequence starting at a = 600 and has common ratio r = 1/2 = 0.5, this means we cut each term in half to get the next term. We could do this to generate five terms and then add them up. Or we could use the formula below with n = 5

Sn = a*(1-r^n)/(1-r)

S5 = 600*(1-0.5^5)/(1-0.5)

S5 = 1,162.5

-----------

Check:

first five terms = {600, 300, 150, 75, 37.5}

S5 = sum of the first five terms

S5 = 600+300+150+75+37.5

S5 = 1,162.5

Because n = 5 is relatively small, we can quickly confirm the answer. With larger values of n, a spreadsheet is the better option.

The manager of the video department at a department store plans to purchase a large number of DVDs of a recent movie. One supplier is selling boxes of 20 DVD movies for $240, and a second supplier is selling boxes of 14 DVD movies for $170. Only complete boxes of DVD movies can be purchased. Complete part a) and b) below. ​a)

a) If the manager can purchase boxes of DVD movies from either or both​ suppliers, determine the maximum number of DVD movies that can be purchased for ​$415. Indicate how many boxes of 20 and how many boxes of 14 will be purchased.
— box(es) of 20 and — box(es) of 14

b) How much will the DVD movies​ cost?
They will cost​ $—

Answers

Answer:

1 box of 20 and 1 box of 14

They will cost $410

Step-by-step explanation:

1. Find how many boxes of 20 DVD movies can be bought

415 - 240 = 175

1 box of 20 DVD movies can be sold

2. Find how many boxes of 14 DVD movies can be bought from $175

175 - 170 = 5

1 box of 14 DVD movies can be bought

3. Find the cost

240 + 170 = 410

find the slope of the line that passes through the two points (0,1) and (-8, -7)

Answers

Answer:

The slope of the line is 1

Step-by-step explanation:

The slope of a line is found by using the formula

[tex]m = \frac{y2 - y1}{x2 - x1} [/tex]

where

m is the slope and

(x1 , y1) and ( x2 , y2) are the points

Substituting the above values into the above formula we have

Slope of the line that passes through

(0,1) and (-8, -7) is

[tex]m = \frac{ - 7 - 1}{ - 8 - 0} = \frac{ - 8}{ - 8} = 1[/tex]

The slope of the line is 1

Hope this helps you

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