Use the graph , Help needed 10 points.

Answer:

Option A.

Step-by-step explanation:

Let A represents have soup and B represents having salad for lunch.

If two events are not dependent on each other, then they are known as independent events.

Probability of having soup is not dependent on Probability of having salad.

[tex]P(A\cap B)=P(A)P(B)[/tex]

Using the formula of conditional probability, we get

[tex]P(A|B)=\frac{P(A\cap B)}{P(B)}\Rightarrow \frac{P(A)P(B)}{P(B)}=P(A)[/tex]

[tex]P(B|A)=\frac{P(A\cap B)}{P(A)}\Rightarrow \frac{P(A)P(B)}{P(A)}=P(B)[/tex]

Having soup or salad for the lunch are two independent event because [tex]P(A|B)=P(A)[/tex] and [tex]P(B|A)=P(B)[/tex].

Therefore, the correct option is A.

The correct answer is:

c) Having soup and salad are not independent events because P(A|B) ≠ P(A) and P(B|A) ≠ P(B).

Given that two events A and B, A represent having soup and B represent having salad for lunch.

We need to determine if the events are independent.

To determine if having soup (A) and salad (B) for lunch are independent events, we need to compare the conditional probabilities with the individual probabilities.

The events A and B are independent if and only if:

P(A|B) = P(A) and P(B|A) = P(B)

where P(A|B) is the probability of having soup given that salad is already chosen, P(A) is the probability of having soup in general, P(B|A) is the probability of having salad given that soup is already chosen, and P(B) is the probability of having salad in general.

Now, let's evaluate each statement:

a) Having soup and salad for lunch are independent events because P(A|B) = P(A) and P(B|A) = P(B).

This statement suggests that both conditional probabilities are equal to the individual probabilities, which would mean the events are independent. However, this contradicts the definition of independent events, where both conditional probabilities should be equal for independence.

b) Having soup and salad for lunch are not independent events because P(A|B) = P(A) and P(B|A) = P(B).

This statement is also incorrect because it states that the conditional probabilities are equal to the individual probabilities, which would indicate independence, but that is not the case.

c) Having soup and salad are not independent events because P(A|B) ≠ P(A) and P(B|A) ≠ P(B).

This statement correctly states that both conditional probabilities are not equal to the individual probabilities, indicating that the events are not independent. This is the correct answer.

d) Having soup and salad for lunch are independent events because P(A|B) ≠ P(A) and P(B|A) ≠ P(B).

This statement is incorrect because it suggests that the events are independent based on the fact that the conditional probabilities are not equal to the individual probabilities. However, this reasoning is flawed, and the correct interpretation for independence is when the conditional probabilities are equal to the individual probabilities.

Therefore, the correct answer is:

c) Having soup and salad are not independent events because P(A|B) ≠ P(A) and P(B|A) ≠ P(B).

Learn more about conditional probability click;

https://brainly.com/question/10567654

#SPJ6

Answer:

x=2, x=-5

Step-by-step explanation:

to work more comfortably, the first thing we need to do is work the equation linearly, for that we take advantage of the property of logarithms that tells me that [tex]log(a^{b})=b*log(a)[/tex]

in this way, the equation remains as:

[tex]log(12^{x^{2} +5x-4 } )=log(12^{5x+6} ) \\ (x^{2} +5x-4 )*log(12)=(5x+6) *log(12)\\x^{2} +5x-4 = 5x+6[/tex]

Now we clear the equation so that it is of the form [tex]ax^{2} +bx+c=0[/tex]

[tex]x^{2} +5x-2x=6+4\\ x^{2} +3x-10=0[/tex]

finally, we apply the equation to solve second degree equations

[tex]x = \frac{-b \pm \sqrt {b^2-4ac}}{2a}[/tex]

[tex]x = \frac{-3 \pm \sqrt {3^2-4*1*(-10)}}{2*1}\\ x = \frac{-3 \pm \sqrt {9+40}}{2}\\ x = \frac{-3 \pm 7}{2}[/tex]

x=2 and x=-5

Done

Answer:

C) x = 2, x = -5

Step-by-step explanation:

took quiz

Answer:

15200cm^2

Step-by-step explanation:

we can separate this into 2 equivalent triangles , 2 equivalent rectangles, and 1 extra rectangle.

the area of a triangle is 1/2b*h so 40*60*1/2=1200

we have 2 of these triangles so the area of the triangles in total is 2400.

next, the 2 equivalent rectangles. the area of a rectangle is b*h is 80*50= 4000

we have 2 so the area of these rectangles in total is 8000.

lastly we have one more rectangle 60*80=4800.

then we add all these up 2400+8000+4800= 15200

add unit

15200cm^2

and we're done

Answer:

60 persent of it is dj 105 ]63

Step-by-step explanation:

Answer:

a] 63

Step-by-step explanation:

Of means multiply

60% * 105

Change to decimal form

.60* 105

63

Answer:

the third from the top option

Step-by-step explanation:

Answer:

14x-6y=4 and 14x-28y=1

Step-by-step explanation:

we have

7x-3y=4 ----> equation A

2x-4y=1 ----> equation B

Multiply the equation A by 2 both sides

2*(7x-3y)=4*2

14x-6y=8

Multiply the equation B by 7 both sides

7*(2x-4y)=1*7

14x-28y=7

therefore

The system of equations that is not equal to the system of equations above is

 14x-6y=4 and 14x-28y=1

Answer:

3.5

Step-by-step explanation:

First we use the concept of relative speed.

The rates of the 2 planes are 625 mph & 575 mph. 

Relative speed will be:

(speed of plane A)+(speed of plane B)

=625+575

=1,200 mph

Distance=4200 miles

Thus the time taken for them to meet will be:

Time=distance/speed

=4200/1200

=3.5 hours

We therefore conclude that the planes met after 3.5 hours.

Hope this helps!

Answer:

3.5

Step-by-step explanation:

The correct range for the coefficient of temperature on the crawling age of babies is (0.055, 0.105), indicating a positive impact of temperature on the age at which babies learn to crawl.

A: (0.053, 0.103) The line equation obtained from the least-squares method for the data points indicates that temperature has a positive effect on the age at which babies learn to crawl. The coefficient value of -0.077739 for the temperature variable implies that on average, for every one-degree Fahrenheit increase in temperature, the crawling age increases by 0.077739 weeks. Therefore, the correct range is option B: (0.055, 0.105).

Answer:

c) [tex]x=\frac{y^2\pm\sqrt{y^4-4a}}{2}[/tex]

d) [tex]x= \frac{-3}{p-q^2u}[/tex]

Step-by-step explanation:

c) [tex]y= \frac{\sqrt{x^2 + a} }{x}[/tex]

Solving the question:

[tex]y= \frac{\sqrt{x^2+a}}{x}\\Taking\,\,square\,\,on\,\,both\,\,sides\\(y)^2= (\frac{\sqrt{x^2+a}}{x})^2\\y^2= \frac{x^2+a}{x}\\y^2.x = x^2+a\\x^2 +a - y^2x =0\\Rearranging\\x^2 -y^2x +a =0\\Solving \,\,using\,\,quadratic\,\,equation\,\,\\x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}\\where\,\, a= 1, b= -y^2 and c= a\\x=\frac{-(-y^2)\pm\sqrt{(-y^2)^2-4(1)(a)}}{2(1)}\\x=\frac{y^2\pm\sqrt{y^4-4a}}{2}[/tex]

d) [tex]\sqrt{\frac{px+3}{ux}}=q[/tex]

Solving to find value of x

[tex]\sqrt{\frac{px+3}{ux}}=q\\ Taking\,\, square\,\, on\,\, both\,\, sides\,\,\\(\sqrt{\frac{px+3}{ux}})^2=q^2\\\frac{px+3}{ux} = q^2\\px+3 = q^2.ux\\px = q^2.ux -3\\px - q^2.ux = -3\\x(p-q^2u) = -3\\x= \frac{-3}{p-q^2u}[/tex]

Answer:

Step-by-step explanation:

[tex]x^2-5x-6==\\\\x^2+x-6x-6=0\\\\x(x+1)-6(x+1)=0\\\\(x+1)(x-6)=0\iff x+1=0\ \vee\ x-6=0\\\\x+1=0\qquad\text{subtract 1 from both sides}\\\boxed{x=-1}\\\\x-6=0\qquad\text{add 6 to both sides}\\\boxed{x=6}[/tex]

Answer:

x = -25/13

Step-by-step explanation:

Subtract 41 from 16 and divide the difference by 13

Answer:

[tex]\large\boxed{x=-\dfrac{25}{13}}[/tex]

Step-by-step explanation:

[tex]13x+41=16\qquad\text{subtract 41 from both sides}\\\\13x+41-41=16-41\\\\13x=-25\qquad\text{divide both sides by 13}\\\\\dfrac{13x}{13}=\dfrac{-25}{13}\\\\x=-\dfrac{25}{13}[/tex]

Answer:

The answer is B.

Step-by-step explanation:

Let us go through each of the points one by one:

The label A represents the radius of the base of the cone.

The label B represents the height of the cone.

The label C represents the origin of the base of the cone.

The label D represents the vertex of the cone (where the cone ends).  

So it is choice B that represents the height of the cone.

P.S: it is tempting to pick label D to represent the height, but since label A already points to a line that is the height of the cone, we don't pick Label D.

Answer:

P = 2l + 2w

x = "a number"

54 = 2(l+w)

27 = l + w

27 = (x+2) + (2x-5)

27 = 3x - 3

27 = 3 (x-1)

9 = x-1

10 = x

Step-by-step explanation:

To solve for the unknown number given the rectangle's dimensions and perimeter, we set up an equation in terms of the unknown number, which represents the width, and solve for it, finding that the number is approximately 8.33.

The question involves finding a specific number given the perimeter of a rectangle and the relationships between its dimensions. First, let's represent the unknown number as x. Given, the length (L) is 2 cm more than x, so L = x + 2. The width (W) is twice x, so W = 2x. The perimeter (P) of a rectangle is given by 2(L + W), and we're told it is 54 cm.

Substituting the expressions for L and W into the perimeter formula gives: 2((x + 2) + 2x) = 54. Simplifying, we get 6x + 4 = 54, and further simplifying results in 6x = 50. Dividing both sides by 6 gives x = 8.33. Therefore, the unknown number is approximately 8.33.

Answer:

r = 16.9 cm

Step-by-step explanation:

We are given the circumference of a circle to be 106.81 cm and with the help of this, we are to find the radius of the circle.

We know that the formula for the circumference is given by:

[tex] 2\pi r [/tex]

so equating the given value to get:

[tex] 2 \pi r = 106.81 [/tex]

[tex] r = \frac { 106.81 } { 2\times \pi } [/tex]

r = 16.9 cm

For this case we have that by definition, the circumference of a circle is given by:

[tex]C = \pi * d[/tex]

Where:

d: It is the diameter of the circle.

[tex]d=2r[/tex]

Clearing we have:

[tex]C=2\pi*r\\r=\frac{C}{2\pi}\\r=\frac{106.81}{2\pi}\\r=17,0079[/tex]

Rounding the amount and [tex]\pi=3.14[/tex]

Then, the radius of the circle is 17 centimeters

ANswer:

[tex]r = 17 \ cm[/tex]

1/2 *30*12=180

The area of the triangle is 180 meters squared

Hope this helped!

Answer:

180 meters

Step-by-step explanation:

Answer:

The standard form of the equation of the ellipse is x² + y²/36 = 1

Step-by-step explanation:

* Lets revise the standard equation of the ellipse

- The standard form of the equation of an ellipse with  

  center (0 , 0) is  x²/b² + y²/a² = 1

, where

* the length of the major axis is 2a

* the coordinates of the vertices are (0 , ±a)

* the length of the minor axis is 2b

* the coordinates of the co-vertices are (±b , 0)

*  the coordinates of the foci are (0 , ± c),  where c² = a² - b²

* Now lets solve the problem

∵ The vertex of the ellipse is (0 , 6)

∴ a = 6

∵ The co-vertex is (1 , 0)

∴ b = 1

∵ the center is the origin (0 , 0)

∵ The standard form equation is x²/b² + y²/a² = 1

∴ x²/(1)² + y²/(6)² = 1 ⇒ simplify

∴ x² + y²/36 = 1

* The standard form of the equation of the ellipse is x² + y²/36 = 1

ANSWER

[tex]\frac{ {y}^{2} }{ 36 } + \frac{ {x}^{2} }{ 1} = 1[/tex]

EXPLANATION

The equation of an ellipse in standard form with vertices on the y-axis and center at the origin is given by:

[tex] \frac{ {y}^{2} }{ {a}^{2} } + \frac{ {x}^{2} }{ {b}^{2} } = 1[/tex]

where

a=6 and b=1

We plug in these value into the formula to get:

[tex]\frac{ {y}^{2} }{ {6}^{2} } + \frac{ {x}^{2} }{ {1}^{2} } = 1[/tex]

[tex]\frac{ {y}^{2} }{ 36 } + \frac{ {x}^{2} }{ 1} = 1[/tex]

Answer:

1 + 1 = 2

Other people say 1 +1 = window.

Answer:

Option b 18x-8 is correct answer.

Step-by-step explanation:

We need to simplify the expression 4(3x – 2) + 6x(2 – 1) and find the result.

Solving:

= 4(3x – 2) + 6x(2 – 1)

Multiplying terms with values in the bracket.

= 12x - 8 + 12x -6x

Adding like terms

= 12x + 12x - 6x -8

= 24x -6x -8

= 18x -8

So, Option b 18x-8 is correct answer.

You simplify expressions by distributing where possible and combining like terms where possible.

4(3x - 2) + 6x(2 - 1)

12x - 8 + 12x - 6x <--- Used the distributive property for both parentheses.

18x - 8                  <--- Combined like terms.

So, B. 18x - 8 is the answer.

Answer:

Total area equation = tex]w(w+6)=91[/tex]

b/2 = 3

Dimensions of the patio: width = 7 feet, length = 13 feet

Step-by-step explanation:

The area of a rectangle is given the formula:

[tex]A=wl[/tex]

where

[tex]w[/tex] is the width

[tex]l[/tex] is the length

We know from our problem that the area of the patio is 91 square feet, so [tex]A=91[/tex]. We also know that the length is 6 feet longer then the width, so [tex]l=w+6[/tex].

Replacing values in our area equation

[tex]A=wl[/tex]

[tex]91=w(w+6)[/tex]

[tex]w(w+6)=91[/tex]

Expanding the left side:

[tex]w*w+6w=91[/tex]

[tex]w^2+6w=91[/tex]

Remember that to complete the square we need to add half the coefficient of the linear term squared. The lineal term is [tex]w[/tex], so its coefficient is 6. Now, half its coefficient or [tex]\frac{b}{2} =\frac{6}{2} =3[/tex]. Finally, [tex]3^2=9[/tex].

To complete the square we need to add 9 to both sides of the equation:

[tex]w^2+6w+9=91+9[/tex]

[tex]w^2+6w+9=100[/tex]

Notice that the left side is a perfect square trinomial (both [tex]w^2[/tex] and 9 are perfect squares), so we can express it as:

[tex](w+3)^2=100[/tex]

Now that we completed the square, we can solve our equation

- Take square root to both sides

[tex]\sqrt{(w+3)^2} =\pm\sqrt{100}[/tex]

[tex]w+3=\pm10[/tex]

- Subtract 3 from both results

[tex]w=10-3,w=-10-3[/tex]

[tex]w=7,w=13[/tex]

Since length cannot be negative, [tex]w=7[/tex] is the solution of our equation.

We now know that the width of our rectangular patio is 7 feet, so we can find its length:

[tex]l=w+6[/tex]

[tex]l=7+6[/tex]

[tex]l=13[/tex]

We can conclude that half the coefficient of the width is [tex]\frac{b}{2}=3[/tex], the width of the patio is 7 feet, and its length is 13 feet.

Answer:

x = 9

Step-by-step explanation:

All 3 sides of the triangle are congruent making it an equilateral triangle with all 3 angles being congruent.

Each angle is therefore 180° ÷ 3 = 60°

Hence

7x - 3 = 60 ( add 3 to both sides )

7x = 63 ( divide both sides by 7 )

x = 9

ANSWER

x=9

y=5

EXPLANATION

The y triangle is an equilateral triangle.

Each measure of an equilateral triangle is 60°

This implies that:

(7x-3)°=60°

Add 3 to both sides

7x=60+3

7x =63

Divide both sides by 7

[tex]x = \frac{63}{7} [/tex]

[tex]x = 9[/tex]

Also,

11y+5=60°

Subtract 5: from both sides of the equation

11y=60-5

11y=55

Divide both sides by 11

y=5

The value of nine is 5

Answer: second one

Step-by-step explanation:

Y=2 and X=2.5 You do this by doing scale factor!!

X = 2.5

Y= 5

To find these numbers, I First compared the first triangle to the second triangle.

The angles on the right side were 2x bigger than the angle on left.

Answer:

D

Step-by-step explanation:

The average profit from the sale of 1 piece of furniture = x+4

The average number of pieces of furniture that can be made using the current supply of raw materials = x - 4

The average profit = The average profit from the sale of 1 piece × The average number of pices that can be made

Hence,

[tex]F(x)=(x+4)(x-4)[/tex]

Use the difference of squares formula:

[tex]F(x)=x^2-4^2\\ \\F(x)=x^2-16[/tex]

the square root is 2

Answer:

2

Step-by-step explanation:

2 times 2 equals 4

Answer:

f(- 1) = 3

Step-by-step explanation:

Locate x = - 1 on the x- axis, then moving vertically up until you meet f(x)

The corresponding value on the y- axis is y = 3, thus

f(- 1) = 3

Step-by-step explanation:

[tex]A=\left[\begin{array}{ccc}3&1\\5&7\end{array}\right][/tex]

[tex]B=\left[\begin{array}{ccc}4&1\\6&0\end{array}\right][/tex]

[tex]C=\left[\begin{array}{ccc}-2&3&1\\-1&0&4\end{array}\right][/tex]

[tex]D=\left[\begin{array}{ccc}-2&3&4\\0&-2&1\\3&4&-1\end{array}\right][/tex]

[tex]1.\\A+B=\left[\begin{array}{ccc}3&1\\5&7\end{array}\right]+\left[\begin{array}{ccc}4&1\\6&0\end{array}\right]=\left[\begin{array}{ccc}3+4&1+1\\5+6&7+0\end{array}\right]=\left[\begin{array}{ccc}7&2\\11&7\end{array}\right][/tex]

[tex]2.\\B-A=\left[\begin{array}{ccc}4&1\\6&0\end{array}\right]-\left[\begin{array}{ccc}3&1\\5&7\end{array}\right]=\left[\begin{array}{ccc}4-3&1-1\\6-5&0-7\end{array}\right]=\left[\begin{array}{ccc}1&0\\1&-7\end{array}\right][/tex]

[tex]3.\\3C=3\left[\begin{array}{ccc}-2&3&1\\-1&0&4\end{array}\right]=\left[\begin{array}{ccc}(3)(-2)&(3)(3)&(3)(1)\\(3)(-1)&(3)(0)&(3)(4)\end{array}\right]=\left[\begin{array}{ccc}-6&9&3\\-3&0&12\end{array}\right][/tex]

[tex]4.\\C\cdot D=\left[\begin{array}{ccc}-2&3&1\\-1&0&4\end{array}\right]\cdot\left[\begin{array}{ccc}-2&3&4\\0&-2&1\\3&4&-1\end{array}\right]\\\\=\left[\begin{array}{ccc}(-2)(-2)+(3)(0)+(1)(3)&(-2)(3)+(3)(-2)+(1)(4)&(-2)(4)+(3)(1)+(1)(-1)\\(-1)(-2)+(0)(0)+(4)(3)&(-1)(3)+(0)(-2)+(4)(4)&(-1)(4)+(0)(1)+(4)(-1)\end{array}\right]\\=\left[\begin{array}{ccc}7&-8&-6\\14&13&-8\end{array}\right][/tex]

[tex]5.\\2D+3C\\\text{This operation can't be performed because the matrices}\\\text{ are of different dimensions.}[/tex]

Answer:

The x-intercepts are (4,0) and (-9,0)

Step-by-step explanation:

We want to find the x-intercepts of the function: [tex]f(x)=x^2+5x-36[/tex]

At x-intercept, [tex]f(x)=0[/tex]

[tex]\implies x^2+5x-36=0[/tex]

We split the middle term to obtain;

[tex]x^2+9x-4x-36=0[/tex]

Factor by grouping:

[tex]x(x+9)-4(x+9)=0[/tex]

[tex](x-4)(x+9)=0[/tex]

Apply the zero product principle.

[tex](x-4)=0,(x+9)=0[/tex]

[tex]x=4,x=-9[/tex]

Hence the x-intercepts are (4,0) and (-9,0)

Answer:

it is -1

Step-by-step explanation:

m= - (4 = m ) + 2

m= -4−m+2

m = −2 −m

m + m = -2 - m + m

2m = -2

2m/2 = -2/2

m= - 1

Answer:

2

Step-by-step explanation: