5, if r = 3?
what is the answer

Answer:

They are independent events

Step-by-step explanation:

For independent events;

Pr(A & B) = Pr(A) × Pr(B)

Given that:

A = day is Monday or Wednesday

Since we have four weeks and each week will have one Monday and Wednesday each,

Pr(A) = (8/28)

B = day falls in the first or third week

Since, first and the third week has a total of 14 days,

Pr(B) = 14/28

Therefore;

Pr(A) × Pr(B) = 8/28 * 14/28

Pr(A) × Pr(B)  = 1/7

Now, A and B = day is either Monday or Wednesday, and it is in the first or third week

There are four such days, Thus Pr(A and B) = 4/28 = 1/7

Since, Pr(A and B) = Pr(A) * Pr(B),

A and B are independent events

Answer:

A function f is onto if and only if, each element in the codomain of f is the image of at least one element in the domain of f.

Step-by-step explanation:

A function f is onto if and only if, each element in the codomain of f is the image of at least one element in the domain of f.

Let us consider a function f which maps the elements of X to each element in the domain of f, such that

f(1) = D

f(2) = B

f(3) = C

f(4) = C

From here, we can determine the domain and range, so

Domain  X of f = {1, 2, 3, 4}

Domain  Y of f =  {D, B, C}

Therefore, it is clear that every element in the codomain of f is the image of at least one element in the domain of f.

Answer:

[tex]Probability = 0.3131[/tex]

Step-by-step explanation:

Required

Determine the probability of selecting a woman

The given data can be represented to show women distribution as:

-------------------------------------- Women ------------------- Total

Assistant Professors ----------- 108 ----------------------253

Associate Professors ---------97 -------------------------301

Full Professors -----------------78---------------------------350

First, we calculate the number of women

[tex]Women = 108 + 97 + 78[/tex]

[tex]Women = 283[/tex]

Next, we calculate the total number of professors

[tex]Professors = 253 + 301 + 350[/tex]

[tex]Professors = 904[/tex]

Probability of selecting women is then calculated as:

[tex]Probability = \frac{Women}{Professors}[/tex]

[tex]Probability = \frac{283}{904}[/tex]

[tex]Probability = 0.31305309734[/tex]

[tex]Probability = 0.3131[/tex] -- (approximated)

Answer:

effect

Step-by-step explanation:

Answer:

2.5

Step-by-step explanation:

Answer:

5/2

Step-by-step explanation:

To divide fractions, you flip the second fractions and change it to multiplication.

(3/2) / (3/5) =

(3/2) x (5/3)

To multiply them, you just multiply their numerators together to get the new numerator and multiply the denominators together to get the new denominator.

(3/2) x (5/3) =

(3 x 5) / (2 x 3) =

15/6

This can be reduced to:

5/2

Answer:

(130.08, 139.92)

Step-by-step explanation:

Given that:

Mean (m) = 135

Standard deviation (σ) = 30

Sample size (n) = 100

α = 90%

The confidence interval value is obtained using the relation:

Mean ± Zcritical * (standard deviation / sqrt(n))

Zcritical at 90% = 1.64

standard deviation / sqrt(n) = 30 / sqrt(100)

= 30 / 10 = 3

Hence,

135 ± 1.64 * (3)

Lower limit : 135 - (1.64 * 3) = 130.08

Upper limit : 135 + (1.64 * 3) = 139.92

Hence,

Confidence interval = (130.08, 139.92)

Answer:

1.056

Step-by-step explanation:

Because 2 4/5+ 3/5= 3 1/5

3 1/5 as a decimal is, 3.2

3.2× .33= 1.056

Answer:

0.5 ; 0.475 ; 0.689 ; 0.4013

Step-by-step explanation:

Given that:

Rate of production of defective batteries p = 0.05

Number of batteries produced (n) = 10

The expected number of defective batteries = mean = n * p = 10 * 0.05 = 0.5 batteries

Variance of defective batteries :

Var(X) = n * p * q ; q = 1 - p

Hence,

Var(X) = 10 * 0.05 * 0.95 = 0.475

Standard deviation (X) = sqrt(variance) = sqrt(0.475) = 0.689

Probability that atleast 1 battery is defective :

Using the binomial probability function

P(x ≥ 1) = 1 - p(x = 0)

= 1 - q^n

= 1 - 0.95^10

= 1 - 0.59873693923837890625

= 0.40126306076162109375

= 0.4013

Answer:

39 degrees

Step-by-step explanation:

27 + |-12| = 39 to change from -12 to 27 you have to add the distance they are away from each other on a number line by adding the absolute value of -12 to 27 to find their distance

Answer:

Rocco mowed 1 lawn a week.

Step-by-step explanation:

If Carly mowed 18 lawns in six weeks that’s 3 lawns a week and 3-2=1.

Thus Rocco mowed 1 lawn a week.

Answer:

A = 432 ft^2

Step-by-step explanation:

[tex]A=\frac{a+b}{2} *h[/tex]

A = (32+16)/2 * 18

A = 48/2 * 18

A = 24*18

A = 432 ft^2

Answer:

The answer is "0.95 and 0.5271".

Step-by-step explanation:

[tex]p (d) = 0.905 \\\\p( false\ negative) = 0.05\\\\p(false \ positive ) = 0.10 \\\\[/tex]

In point a)  

p ( positive diabetes )[tex]= 1 - 0.05 = 0.95[/tex]

In point b)  

[tex]p(\frac{d}{+ve}) = \frac{0.105 \times 0.95}{0.105 \times 0.95 +0.895 \times 0.10 }[/tex]

           [tex]=\frac{0.09975}{0.09975+0.0895}\\\\=\frac{0.09975}{0.18925}\\\\= 0.5271[/tex]

Answer:

Step-by-step explanation:

First of all, we will sort the data.

185 227 234 245 278 278 279 281 281 291 299

Mean:

Mean is defined as the sum of values divided by the number of values.

n = 11

[tex]Mean = \frac{sum}{n}\\= \frac{185+227 +234+ 245+ 278+ 278+ 279+ 281+ 281+ 291+ 299}{11}\\=\frac{2878}{11}\\=261.63\ pounds[/tex]

Median:

As the number of values is odd,

The median will be:

[tex]Median = (\frac{n+1}{2})th\ value\\= \frac{11+1}{2}\\=\frac{12}{2}\\=6th\ value[/tex]

The 6th value is 278

Median = 278

Mode:

Mode is the most frequent value in a data set.

In the given dataset,

278 and 281 are modes as both are repeated twice

Mid-range:

Mid-range is the average of maximum and minimum value

So,

Min = 185

Max = 299

So,

[tex]Mid-range = \frac{Max+Min}{2}\\= \frac{185+299}{2}\\= \frac{484}{2}\\= 242[/tex]

Hence,

Answer:

Your answer is 2 2/7

Answer:

use sin to find the angle x

Answer:

We can use the triginotemtric ratio inverse cos to solve this problem.

Cos=adjacent side/hypotenuse

cos(h)=21/69

[tex]cos^-1(21/69)=x\\cos^-1(0.30434782608) \\x=72[/tex]

Step-by-step explanation:

Answer:

3 and 1/2 units

Answer:

3 and 1/2 units

Step-by-step explanation:

hope this helps you lol

E

Answer:

with what

Step-by-step explanation:

I can't really see the question

Answer:

113 degrees Fahrenheit

Step-by-step explanation:

Answer:

C. No, because it's determinant is zero

Step-by-step explanation:

[tex]A= \begin{bmatrix} 16 & - 4\\\\ 8 & - 2\end{bmatrix} [/tex]

[tex] det(A) =\begin{vmatrix} 16 & - 4\\\\ 8 & - 2\end{vmatrix} [/tex]

[tex] det(A) = 16\times (-2)-(-4)\times 8[/tex]

[tex] det(A) = -32+32[/tex]

[tex] det(A) = 0[/tex]

This matrix have no inverse, because it's determinant is zero.

It is given a 2*2 matrix of order 2.

To find this matrix have an inverse or not.

What is determinant?

A quantity obtained by the addition of products of the elements of a square matrix according to a given rule.

The given matrix is

A= [tex]\left[\begin{array}{ccc}16&-4\\8&-2\\\end{array}\right][/tex]

det A=16*(-2)-(-4)*8=0

det A=0

So, this matrix have no inverse, because it's determinant is zero.

Learn more about determinant here:

https://brainly.com/question/20367047

#SPJ5

Answer:

-4539

Step-by-step explanation:

147 + 130 + 113 + 96 +

arithmetic, with

a = 147 and d 130 - 147 = -17

Sn = (n/2)(2a + d(n - 1))

S34 = (34/2)(2*147 - 17(34 - 1))

= 17(294 - 561)

hope it helps!

Answer:

What’s pad let?

Step-by-step explanation:

Answer:

20%

Step-by-step explanation:

4+3+7=14

14÷7=2

2×10=20

If I am wrong please tell me I haven't had to do this me method in 3 years

Answer:

0.66

Step-by-step explanation:

Given:

Let P(Throwing strike) = 0.35

So,

P(S') = 1 - 0.35 = 0.65

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

P(Throwing fastball and thrown strike) = P(F / S) = 40% = 0.4

P(Throwing fastball  not thrown  strike) = P(F / S') = 80%

P(Throwing fastball  not thrown  strike) =0.8

So,

P(F and S) = 0.8 x 0.65

P(F and S) = 0.52

P(F) = [P(F / S) x P(S)] + [P(F / S') x P(S')]

= (0.4 x 0.35) + (0.8  x 0.65)

= 0.14 + 0.52

= 0.66

Answer:2x+6

Step-by-step explanation:

the answer to your problem is 60=x

Answer:

[tex]\sin \theta = \frac{40}{41}[/tex], [tex]\cos \theta = \frac{3}{82}[/tex], [tex]\tan \theta = \frac{80}{3}[/tex], [tex]\cot \theta = \frac{3}{80}[/tex], [tex]\sec \theta = \frac{82}{3}[/tex], [tex]\csc \theta = \frac{41}{40}[/tex]

Step-by-step explanation:

We notice that figure represents a right triangle, the hypotenuse has a length of 164 units and the leg opposite to [tex]\theta[/tex] has a length of 160 units. The sine of [tex]\theta[/tex] is:

[tex]\sin \theta = \frac{160}{164}[/tex]

[tex]\sin \theta = \frac{40}{41}[/tex]

The leg adjacent to [tex]\theta[/tex] is determine by the Pythagorean Theorem:

[tex]r = \sqrt{164^{2}-160^{2}}[/tex]

[tex]r = 6[/tex]

Then, the cosine of [tex]\theta[/tex] is:

[tex]\cos \theta = \frac{6}{164}[/tex]

[tex]\cos \theta = \frac{3}{82}[/tex]

Lastly, we determine the remaining trigonometric ratios by using these identities:

[tex]\tan \theta = \frac{\sin \theta}{\cos \theta}[/tex] (1)

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

[tex]\sec \theta = \frac{1}{\cos \theta}[/tex] (3)

[tex]\csc \theta = \frac{1}{\sin \theta}[/tex] (4)

If we know that [tex]\sin \theta = \frac{40}{41}[/tex] and [tex]\cos \theta = \frac{3}{82}[/tex], then the trigonometric ratios are, respectively:

[tex]\tan \theta = \frac{\frac{40}{41} }{\frac{3}{82} }[/tex]

[tex]\tan \theta = \frac{80}{3}[/tex]

[tex]\cot \theta = \frac{1}{\frac{80}{3} }[/tex]

[tex]\cot \theta = \frac{3}{80}[/tex]

[tex]\sec \theta = \frac{1}{\frac{3}{82} }[/tex]

[tex]\sec \theta = \frac{82}{3}[/tex]

[tex]\csc \theta = \frac{1}{\frac{40}{41} }[/tex]

[tex]\csc \theta = \frac{41}{40}[/tex]

Answer:

if they all have the same angle they r congruent

Step-by-step explanation: