Let A represent going to the movies on Friday and let B represent going bowling on Friday night. The P(A) = 0.58 and the P(B) = 0.36. The P(A and B) = 94%. Lauren says that both events are independent because P(A) + P(B) = P(A and B) Shawn says that both events are not independent because P(A)P(B) ≠ P(A and B) Which statement is an accurate statement? Lauren is incorrect because the sum of the two events is not equal to the probability of both events occurring. Shawn is incorrect because the product of the two events is equal to the probability of both events occurring. Lauren is correct because two events are independent if the probability of both occurring is equal to the sum of the probabilities of the two events. Shawn is correct because two events are independent if the probability of both occurring is not equal to the product of the probabilities of the two events.

Answer:

[tex]Area=\frac{1}{2} (B\,+\,b)\,h[/tex]

Step-by-step explanation:

The grassy area is that of a trapezoid, so recall the formula for the area of a trapezoid:

[tex]Area=\frac{1}{2} (Base\,+\,base)\,height[/tex]

where:

Base stands for the larger base (in our case the dimension "B" in the attached image)

base stands for the shorter base parallel to the largest Base (in our case the dimension "b" in the attached image)

and

height stands for the distance between bases (in our case the dimension "h" in the attached image.

Therefore the formula for the area of the grassy section becomes:

[tex]Area=\frac{1}{2} (Base\,+\,base)\,height\\Area=\frac{1}{2} (B\,+\,b)\,h[/tex]

Answer:

1/2 (b+b) h

here is the actual picture

Answer:

Step-by-step explanation:

a. tan 30/ sin 30 = (sin 30/cos 30) / sin 30 = 1 / cos 30, no

b. cos 30 = √3/2, yes

c. cos 60 tan 60 = cos 60 (sin 60/cos 60) = sin 60 = cos 30, yes

d. sin 60 = cos (90 - 60) = cos 30, yes

[tex]\bf{b.}\ \ \it cos30^o=\dfrac{\sqrt3}{2}\ \ (True)\\ \\ \bf{d.}\ \ \it sin60^o=cos(90^o-60^o)=cos30^o\ \ (True) \\ \\ \bf{c.}\ \it cos60^o\cdot tan60^o=cos60^o\cdot\dfrac{sin60^o}{cos60^o}=\dfrac{cos60^o}{cos60^o}\cdot sin60^o=1\cdot sin60^o=cos30^o\ (T)\\ \\ \\ \bf{a.}\ \ \it \dfrac{tan30^o}{sin30^o}=tan30^o\cdot\dfrac{1}{sin30^o}=\dfrac{sin30^o}{cos30^o}\cdot\dfrac{1}{sin30^o}=\dfrac{sin30^o}{sin30^o}\cdot\dfrac{1}{cos30^o}=\\ \\ \\ =1\cdot\dfrac{1}{cos30^o}=\dfrac{1}{cos30^o}\ \ne\ cos30^o[/tex]

Answer:

Attachment 1 : Option A,

Attachment 2 : Option C

Step-by-step explanation:

( 1 ) Here we know that " n " is 6. Now remember if n is odd, the number of petals on the graph will be n. However if n is even, the number of petals on the graph will be 2n.

6 is even, and hence the number of petals will be 2(6) = 12 petals. Solution : 12 petals

( 2 ) To solve such problems we tend to use the equation [tex]z = x + y * i = r(cos\theta +isin\theta)[/tex] where [tex]r = \sqrt{x^2+y^2}[/tex] etc. Here I find it simpler to see each option, and convert each into it's standard complex form. It might seem hard, but it is easy if you know the value of (cos(5π / 3)) etc...

The answer here will be option c, but let's prove it,

cos(5π / 3) = 1 / 2,

sin(5π / 3) = [tex]-\frac{\sqrt{3}}{2}[/tex]

Plugging those values in for " [tex]8\left(\cos \left(\frac{5\pi }{3}\right)+i\sin \left(\frac{5\pi }{3}\right)\right)[/tex] "

[tex]8\left(-\frac{\sqrt{3}i}{2}+\frac{1}{2}\right)[/tex]

= [tex]8\cdot \frac{1}{2}-8\cdot \frac{\sqrt{3}i}{2}[/tex] = [tex]4-4\sqrt{3}i[/tex]

Hence proved that your solution is option c.

Answer:

B

Step-by-step explanation:

Option A:

1.50÷18≈0.0833

3.00÷36≈0.0833

4.50÷54≈0.0833

Option B:

0.75÷15=0.05

Option C:

2.20÷15=0.146

Answer:

50ft by 120ft

Step-by-step explanation:

Area of a rectangle = L × W

6000ft² = L × W

L = 6000/W

When a diagonal line divides a rectangle into 2 right angled triangles, the diagonal line = Hypotenuse of either of the triangle and it is the longest side.

The formula for a right angle triangle =

a² + b² = c²( c = hypotenuse)

We are told in the question that:

A diagonal between opposite corners is measured to be 10 ft longer than one side of the parcel

Let us assume the side that the hypotenuse is longer than = Width

Hence, the Diagonal = (W + 10)²

Therefore

L² + W² = (W + 10)²

Since L = 6000/W

W² + (6000/W)² = (W + 10)²

W² + (6000/W)² = (W + 10) (W + 10)

W² + (6000/W)² = W² + 10W + 10W + 100

W² + (6000/W)² = W² + 20W + 100

W² - W² + (6000/W)² = 20W+ 100

6000²/W² = 20W + 100

6000² = W²( 20W + 100)

6000² = 20W³ + 100W²

20W³ + 100W² - 6000² = 0

20W³ + 100W² - 36000000 = 0

20(W³ + 5W² - 1800000) = 0

Factorising the quadratic equation,

20(W − 120)(W² + 125W + 15000) = 0

W - 120 = 0

W = 120

Therefore,

W(Width) = 120feet

Since the Width = 120 feet

We can find the length

6000ft² = L × W

L = 6000/W

L = 6000/120

L = 50 feet

The dimensions of the land, correct to the nearest foot is 50ft by 120ft

Answer:

Questions .(1) 2/m. (2). m-1 . (3) 2 . (4) m

Answer:

2m(m-2)/2(m-2)= m

(m-1)(m-1)/m-1   ⇒ ( m-1/m-1)=1

Answer:

[tex]\large \boxed{\mathrm{34.2}}[/tex]

Step-by-step explanation:

[tex]\sf B= arcsin (\frac{b \times sin(A)}{a} )[/tex]

[tex]\sf B= arcsin (\frac{7 \times sin(40\°)}{8} )[/tex]

[tex]\sf B = 0.59733 \ rad = 34.225\°[/tex]

[tex]\\ \sf\longmapsto 2(3x-7)+4(3x+2)=6(5x+9)+3[/tex]

[tex]\\ \sf\longmapsto 6x-14+12x+8=30x+54+3[/tex]

[tex]\\ \sf\longmapsto 6x+12x-14+8=30x+57[/tex]

[tex]\\ \sf\longmapsto 18x+6=30x+57[/tex]

[tex]\\ \sf\longmapsto 30x-18x=6-57[/tex]

[tex]\\ \sf\longmapsto 12x=51[/tex]

[tex]\\ \sf\longmapsto x=\dfrac{51}{12}[/tex]

Answer:  186.75 million which is the same as saying 186,750,000

Work Shown:

75% = 75/100 = 0.75

75% of 249 million = 0.75*249 million = 186.75 million

186.75 million = 186.75*10^6 = 186,750,000

Answer:

186,750,000

Step-by-step explanation:

Take 75% of 249 million

.75 * 249,000,000

186,750,000

Answer:

85

Step-by-step explanation:

Add  to get total. divide by 4.

Answer:

B. 85

Step-by-step explanation:

Sorry for this very late response. But if anyone wasn't sure if 85 is the correct answer, it is. I can confirm this because I just took the test. I hope I could help! (:

Answer:

answer is

In empty set, n(A) = { }.

Answer:

x is 18, and y is 9 √ 3

Step-by-step explanation:

Since this is a right triangle that contains a 30 degree angle, we know this is a special right triangle, and the missing angle is 60 degrees since a triangle is 180 degrees, and 180 - 90 - 30 = 60.

The relationship is listed below:

The side opposite of the 30 degrees can be represented as a variable, say "p", and the hypotenuse which is x in your question is twice this. The side opposite of the 60 degree angle is x + √3

So x is 18, and y is 9√3

Answer:

66

Step-by-step explanation:

when you plug in 9 for k. you do 6(9) which is 54. then add 12 to 54 and thats ur answer, 66.

Answer:

?

Step-by-step explanation

my 4th person to ask a question

Answer:

z -score = 0.0459

Step-by-step explanation:

Given that:

the number of children with food allergies at a sample of elementary schools: 3, 9, 5, 5, 14, 10, 5, 11, 9, 6, 1, 8, 10, 7, 9, 13, 18, 9, 8, 11, 9, 7, 6, 14, 12.

The objective is to find the z- score , but before we can do that , we need to determine the mean and the standard deviation of the sample.

Mean = sum of the sample/ total number of the sample

Mean = (3+9+ 5+ 5+ 14+ 10+ 5+ 11+ 9+ 6+ 1+ 8+ 10+ 7+ 9+13+ 18+ 9+ 8+11+ 9+ 7+ 6+ 14+ 12)/25

Mean = 219/25

Mean = 8.76

Standard deviation = [tex]\sqrt{\dfrac {\sum (x_i - \mu)^2}{N}}[/tex]

Mean (in order )= 1, 3,5,5,5,6,6,7,7,8,8,9,9,9,9,9,10,10,11,11,12,13,14,14,18)

Standard deviation = [tex]\sqrt{\dfrac { (8.76 - 1)^2}{25} + \dfrac { (8.76 - 3)^2}{25} +\dfrac { (8.76 - 5)^2}{25} +...+ \dfrac { (8.76 - 18)^2}{25} }[/tex]

Standard deviation = 5.2174

The standard z score formula is:

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

where X = median (13th observation ) = 9

[tex]z = \dfrac{9- 8.76}{5.2174}[/tex]

[tex]z = \dfrac{0.24}{5.2174}[/tex]

z -score = 0.0459

Answer:

6x+36=180

6x=144

x=24

Step-by-step explanation:

this is the correct answer

Answer:

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

Answer:

[tex]\huge\boxed{f(n)=\left\{\begin{array}{ccc}f(1)=20\\f(n)=f(n-1)-4\end{array}\right}[/tex]

Step-by-step explanation:

[tex]f(n)=20-4(n-1)=20+(n-1)(-4)\\\\\text{It's an explicit formula of an arithmetic sequence:}\\\\f(n)=a_1+(n-1)(d)\\\\a_1-\text{first term}\\d-\text{common difference}\\\\\text{Conclusion:}\\\text{Next term}=\text{previous one}\ -4\\\\\text{The recursive formula:}\\\\\huge\boxed{f(n)=\left\{\begin{array}{ccc}f(1)=20\\f(n)=f(n-1)-4\end{array}\right}[/tex]

Answer:

Step-by-step explanation:

someone answered already

Answer:

0.16

Step-by-step explanation:

See the picture attached for reference.

As you see the best points are the green areas which covers 2 out of 5 zones.

Since it is same for both broken points, the probability of  this is:

Answer is 0.16

Answer: 247.92 euros

Step-by-step explanation:

Given, Varia is required pay $3,500 (in US dollars) per year to the university.

If she must pay in euros , then we convert $3,500 into euros.

Current rate : 1 US dollar = 0.85 euro

Then,  $3,500 = ( 0.85 x 3500) euros

= 2975 euros

She can expect 2975 euros to pay per year.

Also, [tex]2975\div 12\approx247.92[/tex]   [ 1 years = 12 months]

Hence, She can expect 247.92 euros to pay per month to the university.

Answer:

7+sqrt(37)

Step-by-step explanation:

7+sqrt(6*(3+4)-2+9-3*2^2)=7+sqrt(6*7+7-3*4)=7+sqrt(42+7-12)=7+sqrt(37)

Answer:

the answer for y is 9 and x is 9✔2( the check is square root symbol)

Answer:

Hello,

The answer would be,

A union B = {3,6,9,12}

and A intersection B= {6,9}

Answer:

[tex]\huge\boxed{ A\ union \ B = \{3,6,8,9,12\}}[/tex]

[tex]\huge\boxed{A\ intersection \ B = \{6,9\}}[/tex]

Step-by-step explanation:

A = {3,6,9,12}

B = {6,8,9}

A∪B = {3,6,9,12} ∪ { 6,8,9}   [Union means all of the elements should be included in the set of A∪B]

=> A∪B = {3,6,8,9,12}

Now,

A∩B = {3,6,9,12} ∩ {6,8,9}  [Intersection means common elements of the set]

=> A∩B = {6,9}

Answer:

A

Step-by-step explanation:

lemme meh knw if it was helpful..

Answer:

43-28= 15 extra hours

normal hourly rate = a

extra hourly rate = 1.1a

28a + 15(1.1a) = 631.90

28a + 16.5a = 631.90

Answer:

2110

Step-by-step explanation:

4100-1990=2110

Answer:

[tex]\boxed{\sqrt{65}}[/tex]

Step-by-step explanation:

Magnitude is solved with the following equation: [tex]\sqrt{x^{2}+y^{2}}[/tex]

Therefore, just plug in your x and y-values and solve.

[tex]\sqrt{4^{2}+7{^{2}}[/tex]

[tex]\sqrt{16 + 49}[/tex]

[tex]\sqrt{65}[/tex]

Because [tex]\bold{\sqrt{65}}[/tex] cannot be simplified further, this is the magnitude of the vector.

Answer:

The value is [tex]T = \$54200[/tex]

Step-by-step explanation:

From the question we are told that

      The  number of shares is  n  =  400

      The rate  of each share is  [tex]k = 135\frac{1}{2} = 135.5[/tex]

Generally the total price is mathematically represented as

     [tex]T = 400 * 135.5[/tex]

      [tex]T = \$54200[/tex]