A detective knows what time of day it is based on the angle at which the sun is hitting a man. Suppose a detective is looking at a photograph of a 6-foot tall man with a shadow that is 3.5 feet. Find the angle at which the sun is hitting the ground.

Answer:

Step-by-step explanation:

If I choose a number from the integers 1 to 25, the total number of integers I can pick is the total outcome which is 25. n(U) = 25

Let the probability that the number chosen at random is a multiple of  6 be P(A) and the probability that the number chosen at random is is larger than 18 be P(B)

P(A) = P(multiple of 6)

P(B) = P(number larger than 18)

A = {6, 12, 18, 24}

B = {19, 20, 21, 22, 23, 24, 25}

The conditional probability that the number is a multiple of 6 (including 6) given that it is larger than 18 is expressed as P(A|B).

P(A|B) = P(A∩B)/P(B)

Since probability = expected outcome/total outcome

A∩B = {24}

n(A∩B) = 1

P(A∩B) = n(A∩B)/n(U)

P(A∩B) = 1/25

Given B = {19, 20, 21, 22, 23, 24, 25}.

n(B) = 7

p(B) = n(B)/n(U)

p(B) = 7/25

Since P(A|B) = P(A∩B)/P(B)

P(A|B) = (1/25)/(7/24)

P(A|B) = 1/25*25/7

P(A|B) = 1/7

Hence the conditional probability that the number is a multiple of 6 (including 6) given that it is larger than 18 is 1/7

Answer:

0.03 square meters

Step-by-step explanation:

1. convert 20 cm, 15 cm into m by dividing the number by 100 then you got 0.2 m and 0.15 m respectively

2. calculate the area by multiply 2 numbers together

0.2 × 0.15 = 0.03 square meter

Answer:

The critical value is 6.26.

Step-by-step explanation:

It is provided that there are 5 independent variables involved in a multiple regression model and the sample consist of 10 data points.

The critical value of F to test the significance of the model is:

[tex]\text{Critical Value}=F_{\alpha, (k, n-k-1)}[/tex]

Here,

k = number of independent variables

n = number of observations.

Then the critical value is:

[tex]\text{Critical Value}=F_{\alpha, (k, n-k-1)}[/tex]

                      [tex]=F_{\alpha, (5, 10-5-1)}\\=F_{0.05,(5, 4)}\\=6.2561\\\approx 6.26[/tex]

*Use a F-table.

Thus, the critical value is 6.26.

Answer:

Option (4)

Step-by-step explanation:

By the property of exterior angle of a triangle,

"Exterior angle of a triangle is equal to the sum of two opposite interior angles."

In the triangle ABC,

∠ACD is an exterior angle and ∠BAC and ∠ABC are the opposite interior angles.

m∠ACD = m∠BAC + m∠ABC

95° = m∠BAC + m∠ABC

Therefore, Option (4) will be the correct option.

Answer:

this is an inconsistent because no solutions

Complete Question

The complete question is shown on the first uploaded image

Answer:

the null hypothesis is  [tex]H_o : \mu = 122[/tex]

the alternative hypothesis is [tex]H_a : \mu \ne 122[/tex]

The test statistics is  [tex]t = - 1.761[/tex]

The p-value is  [tex]p = P(Z < t ) = 0.039119[/tex]

so

    [tex]p \ge 0.01[/tex]

Step-by-step explanation:

From the question we are told that

   The population mean is  [tex]\mu = 122[/tex]

     The sample size is  n=  38

    The sample mean is  [tex]\= x = 116 \ feet[/tex]

     The standard deviation is [tex]\sigma = 21[/tex]

Generally the null hypothesis is  [tex]H_o : \mu = 122[/tex]

                the alternative hypothesis is [tex]H_a : \mu \ne 122[/tex]

Generally the test statistics is mathematically evaluated as

         [tex]t = \frac { \= x - \mu }{\frac{ \sigma }{ \sqrt{n} } }[/tex]

substituting values

         [tex]t = \frac { 116 - 122 }{\frac{ 21 }{ \sqrt{ 38} } }[/tex]

         [tex]t = - 1.761[/tex]

The p-value is mathematically represented as

      [tex]p = P(Z < t )[/tex]

From the z- table  

     [tex]p = P(Z < t ) = 0.039119[/tex]

So  

     [tex]p \ge 0.01[/tex]

Answer:

Segment LM Corresponds to RQ    

Segment R corresponds to angle M

Answer:

Step-by-step explanation:

six hundred men,six hundred men with big mouths to feed

Answer:

Yes it is reasonable to conclude the mean rate charged is greater than 14%

Step-by-step explanation:

From the question we are told that

    The  population mean is  [tex]\mu = 0.14[/tex]

    The sample size is  [tex]n = 10[/tex]

    The  sample mean is  [tex]\= x = 0.1564[/tex]

     The  standard deviation is  [tex]\sigma = 0.01561[/tex]

     The level of significance is  [tex]\alpha = 0.01[/tex]

The null hypothesis is    [tex]H_o: \mu = 0.14[/tex]

The  alternative hypothesis is  [tex]H_a : \mu > 0.14[/tex]

 Generally the test statistic is mathematically represented as

              [tex]t = \frac{ \= x - \mu }{ \frac{\sigma }{\sqrt{n} } }[/tex]

substituting values

              [tex]t = \frac{ 0.1564 - 0.14 }{ \frac{0.01561 }{\sqrt{10} } }[/tex]

              [tex]t = 3.322[/tex]

Now the p-value obtained from the z-table is

        [tex]p-value = P(t > 3.322) = 0.00044687[/tex]

Since the [tex]p-value < \alpha[/tex] then we reject the null hypothesis, hence we can conclude that  the mean rate charged is greater than 14%

Answer:

Rounded: -5.5

Step-by-step explanation:

Work above :)

Answer:

$3.60

Step-by-step explanation:

2.40/8=.30

$.30 per bar

.3 x 12= $3.60

Answer:

$3.60

Step-by-step explanation:

Proportions

8 bars ⇔ $2.4

12 bars ⇔ $W

W = 12*2.4/8

W = $3.6

Answer:

0.0319

Step-by-step explanation:

To approximate this probability, we shall be using the Bernoulli approximation of the Binomial distribution.

Let p = probability of selecting a reference book = 65% = 0.65

Let q = probability of selecting other books= 1-p = 1-0.65 = 0.35

Now, we want to find the probability that all of these 8 books to be re-shelved are reference book.

We set up the probability as follows;

P(X = 8) = 8C8 •p^8•q^0

P(X = 8) = 1 * (0.65)^8 * (0.35)^0

P(X = 8) = 0.031864481289 which is 0.0319 to 4 decimal places

Answer:

6.02

six point zero two

Step-by-step explanation:

Answer:

602 / 100= 6,02

Step-by-step explanation:

602 to divide 100 = 6,02

Answer:

NOT SURE

Step-by-step explanation:

Answer:

wat do u want me to do

Step-by-step explanation:

Step-by-step explanation:

When you have a ratio, you put one number as the numerator and than one number as the denominator.

so it would be (12/34)=(x/68)

In this example I made the ratio you are comparing it to have 68 dollars, so when you solve for the amount of quarters you need it should be 24, since all of the numbers in this example are just being doubled.

To solve for x, you multiply 68 on both sides of the equation, 68×(12/34)=x

24=x

So this proves that this is how ratios, are used. It also does not matter what number you place on the numerator or denominator.

Hi there! :)

Answer:

The lines are the same.

Step-by-step explanation:

Begin by converting each equation into its simplest form in slope-intercept form:

-36x + 8y = 16

Move the "x" variable to the right side of the equation:

8y = 36x + 16

Divide all terms by 8:

y = 36/8x + 16/8

y = 9/2x + 2

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

-9x + 2y = 4

Move "x" variable:

2y = 9x + 4

Divide both sides by 2:

y = 9/2x + 2

Both of the equations are equivalent, meaning both of the lines are the same.

In a preliminary study, he observed one of his workers perform this task five times, with the following results:

Observation: Time (secs):

1 27

2 19

3 20

4 21

5 13

Answer:

100 Observations

Step-by-step explanation:

Z value = 2 (due to confidence percentage of 95.44)

S = 5

A = 1

N equals to square of (ZxS/A)

N = (ZxS/A)^2

N = (2x5/1)^2

N = 10^2 = 100

Answer:

170 m³

Step-by-step explanation:

To solve this type of problem, assume you have two solids joined together to make the shape you have up there. This will enable you find the volume of each, then sum both volume together to get your answer.

Let's solve for the volume as follows.

If we divide the solid into 2, what we have is 2 cuboid: the first having dimensions of:

length (l) = 6m,

width (w) = 2m,

height (h) = 8m

Volume of the first cuboid = [tex] l*w*h = 6*2*8 = 86 m^3 [/tex]

The second cuboid:

length (l) = 7m,

width (w) = 6m,

height (h) = 2m

Volume of the first cuboid = [tex] l*w*h = 7*6*2 = 84 m^3 [/tex]

Volume of the figure = 86 + 84 = 170 m³

Answer:

100,000

You take 1,000 because it's in the thousandths place of 1,255. The value of that one is 1,000 so you multiply that times 100, which is the value of 1 in 82,175.

Answer:

Step-by-step explanation:

There are many examples to pick from, one is

point = location on map

line = straight road between two locations (aka two points)

plane = flat ground (the ground cannot have any hills or valleys)

First, let's write some useful definitions:

Point: it is an entity that has a location in a given space or plane, and do not have any surface nor measure.

Line: if we have two points, we can define a line as a straight, infinite ray that connects them. Still does not have a surface

Plane: We can define a plane as a line and a point outside of it, here appears the concept of the surface.

So, the easier one is a plane, a sheet of paper could be a good representation of a plane. And in the same way that a sheet of paper can bend in different ways, also do the planes.

For the line, we could use a really straight wire.

Finally, the point, which is the hardest one to describe (notice that we used points to describe the other two, lines, and planes) so here we could choose something small, that has near to no surface and that also has a location in the space. An example of this could be an electron or any other elemental particle.

If you want to learn more, you can read:

https://brainly.com/question/17213603

Answer:

k = -2

Step-by-step explanation:

83=4k-7(1+7k)

Distribute

83=4k-7-49k

Combine like terms

83 = -45k -7

Add 7 to each side

83+7 = -45k-7+7

90 = -45k

Divide each side by -45

90/-45 = -45k/-45

-2 = k

Answer:

Step-by-step explanation:

Step 1: Use 7 to open the bracket :

-7(1+7k)=-7-49k

Step 2: Collect like terms

Step 3 : Divide both sides of the equation by -45

[tex]83=4k-7(1+7k) \\ \\83 = 4k-7-49k\\\\ 83+7=4k-49k\\\\90 = -45k\\\\\frac{90}{-45} = \frac{-45k}{-45} \\\\k = -2[/tex]

Answer:

Diagnostic

Step-by-step explanation:

The teacher made a diagnostic decision relative to Roberts skill level. Before she made this decision, she first started with the process of evaluation to know his strength and also establish his weakness. With the knowledge she has gotten she now plans to him with meaningful learning and an efficient curriculum that would help him in mastering multiplication first before division.

true false false true...is the quick answer

Remember that negatives are always less than positive numbers.

Here is the complete question:

a. Statistically significant at 0.01

b. Not statistically significant

Answer:

The test is significant

Step-by-step explanation:

When a p value is smaller than or less than alpha we say it is statistically significant.

We are testing the p value or likelihood of 0005 against a significant level of 0.01

P value = 0.005 < 0.01

0.005 is less than 0.01 which shows the test to be significant.

The decision rule would be to reject the null hypothesis and say the result is statistically significant.

Answer:

x = 32

but

I would say anything from 30 to 33

but truly i have no clue about the range

Step-by-step explanation:

3x-9=87 (because 180 -93 =87)

3x = 96

x = 32

Answer:

it is 32

Step-by-step explanation:

Answer:

70%

Step-by-step explanation:

Given

Number of Siblings:   ||    0  ||    1    ||      2     ||       3

Number of Students: ||    4  ||    18    ||    10     ||       8

Required

Determine the probability of a student having at least one but not more than 2 siblings

First, we have to determine the total number of 10th grade students

[tex]Total = 4 + 18 + 10 + 8[/tex]

[tex]Total = 40[/tex]

The probability of a student having at least one but not more than 2 siblings = P(1) + P(2)

Solving for P(1)

P(1) = number of students with 1 sibling / total number of students

From the given parameters, we have that:

Number of students with 1 sibling = 18

So:

[tex]P(1) = \frac{18}{40}[/tex]

Solving for P(2)

P(2) = number of students with 2 siblings / total number of students

From the given parameters, we have that:

Number of students with 2 siblings = 10

So:

[tex]P(2) = \frac{10}{40}[/tex]

[tex]P(1) + P(2) = \frac{18}{40} + \frac{10}{40}[/tex]

Take LCM

[tex]P(1) + P(2) = \frac{18 + 10}{40}[/tex]

[tex]P(1) + P(2) = \frac{28}{40}[/tex]

Divide numerator and denominator by 4

[tex]P(1) + P(2) = \frac{7}{10}[/tex]

[tex]P(1) + P(2) = 0.7[/tex]

Convert to percentage

[tex]P(1) + P(2) = 70\%[/tex]

Hence, the required probability is 70%

Answer:

Step-by-step explanation:

bB

Answer:

85.36 far north from the center

10.36 far east from the center

Step-by-step explanation:

The extra direction taken in the north side is x

X/sin(360-315)=50/sin 90

Sin 90= 1

X/sin 45= 50

X= sin45 *50

X= 0.7071*50

X= 35.355 steps

X= 35.36

Then the west direction traveled

West =√(50² - 35.355²)

West = √(2500-1249.6225)

West= √1250.3775

West= 35.36 steps

But this was taken in an opposite west direction

From the center

He is 35.36 +50

= 85.36 far north from the center

And

25-35.36=-10.36

10.36 far east from the center

Answer:

Step-by-step explanation:

Given that

sin(2θ)+sinθ=0

We know that

sin(2θ)=2 sinθ x cosθ

Therefore

2 sinθ x cosθ + sinθ=0

sinθ(2 cosθ+1)=0

sinθ= 0

θ=0

2 cosθ+1=0

cosθ= - 1/2

θ=120°

_______________________________________________________

[tex]sin 2\theta=\sqrt{3cos\theta}[/tex]

By squaring both sides

[tex]sin^2 2\theta={3cos\theta}[/tex]

4 sin²θ x cos²θ=3 cosθ

4 sin²θ x cos²θ - 3 cosθ=0

cos θ = 0

θ= 90°

4 sin²θ=3

θ=60°

Answer:

Lower quartile= 4.75

Middle quartile= 9.5

Upper quartile= 14.25

Step-by-step explanation:

The given date set is 24, 43, 65, 12, 31, 78, 43, 24, 25, 18, 29, 53, 18, 23, 20, 43, 53, 25

On counting them we notice that it's number of element is 18

So N = 18

Arranging them in ascending order gives

12,18,18,20,23,24,24,25,25,29,31,43,43,43,53,53,65,78

Lower quartile= (N+1)*1/4

Lower quartile= (18+1)/4

Lower quartile= 19/4

Lower quartile= 4.75

Middle quartile= (N+1)*2/4

Middle quartile= (18+1)*2/4

Middle quartile= (19)*2/4

Middle quartile= 9.5

Upper quartile= (N+1)*3/4

Upper quartile= (18+1)*3/4

Upper quartile= (19)*3/4

Upper quartile= 14.25

Inter quartile range = upper quartile- minutes lower quartile

= 14.25-4.75

= 9.5