According to a survey, 67.5% of Californians prefer hot weather over cold weather. Let X = number of Californians in a sample of 19 who prefer hot weather over cold weather. What is the probability that at least 16 Californians prefer hot weather over cold weather? O 0.9098 O 0.0902 0.0284 0.0618

Answers

Answer 1

Answer:

The correct option is 0.9098. The probability that at least 16 Californians prefer hot weather over cold weather is 0.9098.

According to a survey, 67.5% of Californians prefer hot weather over cold weather. Let X = number of Californians in a sample of 19 who prefer hot weather over cold weather. Then, the probability that at least 16 Californians prefer hot weather over cold weather can be calculated by using the cumulative binomial probability formula. Let X = the number of Californians in a sample of 19 who prefer hot weather over cold weather.

The formula for calculating the cumulative binomial probability is: P(X≥k) = ∑i=kn P(X=i)

In this example, k = 16, n = 19, and P(X=i) = 0.675

Therefore, P(X≥16) = ∑i=1619 P(X=i) = 0.9098

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What is the slope and y-intercept of this line?y = –3x + 9
A. slope: 3, y-intercept: –9
B. slope: –3, y-intercept: 9
C. slope: 1, y-intercept: –3
D. slope: 9, y-intercept: –3

Answers

The slope and y-intercept of the given line are -3 and 9 respectively.

What is equation of a line?

The general equation of a line in two variables of the first degree is represented as Ax + By +C = 0, A, B ≠ 0 where A, B and C are constants which belong to real numbers.

When we represent the equation geometrically, we always get a straight line.

Given that, an equation of a line y = -3x+9, we need to determine the slope and the y-intercept of this line,

The slope of a line tell about the steepness and the y-intercept tells the point where it intersects the y-axis,

The slope-intercept form of the equation of a line is given by ;

y = mx+c

Here, m is the slope and c is the y-intercept,

So, the given equation is y = -3x+9

Comparing with the slope-intercept form,

m = -3 and y-intercept = 9

Hence, the slope and y-intercept of the given line are -3 and 9 respectively.

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Slope is -3
Y-intercept is 9

How to solve for 40! / 10!30!

Answers

40! / 30! = 40*39*38*37*36*35*34*33*32*31

dividing this by 10! 10*9*8*7*6*5*4*3*2*1

= 4*13*19*37*17*11*4*31

= 847,660,528

What is the simplified form of the quantity 4 z squared minus 4z minus 15 over the quantity 2 z squared plus z minus 15? (6 points)

Answers

Answer: The simplified form of the given equation is $(2z+3)/(z+3)$

Step-by-step explanation:

From the given information, the numerator of the given fraction is: $4z^2-4z-15$

and denominator of the given fraction is $2z^2+z-15$

The fraction becomes:

$(4z^2-4z-15)/(2z^2+z-15)$

Applying middle term factorization in the numerator and denominator term, we get:

= $(4z^2-10z+6z-15)/(2z^2+6z-5z-15)$

= $(2z(2z-5)+3(2z-5))/(2z(z+3)-5(z+3))$

= $((2z+3)(2z-5))/((2z-5)(z+3))$

Cancelling (2z-5) factor from numerator an denominator, we get:

= $(2z+3)/(z+3)$

The above fraction is the simplified form of the equation formed in the question.

First you simplify it down to (2z+3)(2z-5)/(2z-5)(z+3)
Both of the brackets containing (2z-5) can now be cancelled out leaving you with a final answer of (2z+3)/(z+3)

Solve for x₁ and x₂
6x₁+3x₂=60
6x₁-2x₂=80

Answers

$\left \{ {\big{6x_1+3x_2=60\ \ \ \ \ \ \ \ \ \ \ } \atop \big{6x_1-2x_2=80\ /\cdot(-1)}} \right. \n\n \left \{ {\big{6x_1+3x_2=60\ \ \ \ } \atop \big{-6x_1+2x_2=-80}} \right. \n-----------\n3x_2+2x_2=60-80\n5x_2=-20\ /:5\n\nx_2=-4\n\n6x_1+3x_2=60\ /:3\n2x_1+x_2=20\ \ \ \Rightarrow\ \ \ 2x_1+(-4)=20\ \ \ \Rightarrow\ \ \ 2x_1=24\ /:2\n\nx_1=12\n\n \left \{ {\big{x+1=12} \atop\big {x_2=-4}} \right.$

first let's change the "x1" to "A" Nd the "x2" to "B" __ so now the problem reads "6A + 3B = 60" And "6A - 2B= 80" we want to isolate variable. and the easiest one is the "B" by getting rid of the "A". set up a subtraction problem where you take one equation away from the other. 6a-6a=0. 3b - (-2b) = 5b and 60-80=-20. so your new equation reads 5B= -20. you wanna get B on one side so yu divide 5 on both sides giving you b= -4 or "x2"=-4. from there you can plug -4 into any one of the original equations. ex: 6A -2(-4)=80 then 6A + 8=80 then you subtract 8 from both sides because you're trying to isolate the "A" variable. which leaves you with 6A = 72. and now you wanna get"A" on one side so yu divide 6 from both sides and get A=12 or "x1"=12. do a quick check and plug in these numbers into any one of the equation.

Solve
7 + x - 15 = 2 2/3

Answers

Get x on its own side

7+x-15=2 2/3
+15 +15
7+x=17 2/3
-7 -7
x= 10 2/3
Hope I helped

Let's solve your equation step-by-step.7+x−15=223
Step 1: Simplify both sides of the equation.
x−8=8/3
Step 2: Add 8 to both sides
.x−8+8=8/3+8x=32/3
Answer:x=10 2/3

Ellen Saver went to her bank. She had a balance of $2,447.67 in her savings account. She withdrew $231.49 and the teller credited her account with $36.61. What is her new balance?