Answer:
0.294 = 29.4% probability that none of the chosen entrees contain spinach.
Step-by-step explanation:
The choices of entrees are chosen without replacement, which means that the hypergeomtric distribution is used to solve this question.
Hypergeometric distribution:
The probability of x sucesses is given by the following formula:
[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}[/tex]
In which:
x is the number of sucesses.
N is the size of the population.
n is the size of the sample.
k is the total number of desired outcomes.
Combinations formula:
[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
13 different entrees for an important banquet
This means that [tex]N = 13[/tex]
3 of which contain spinach.
This means that [tex]k = 3[/tex]
The guests will have a choice of 4 entrees.
This means that [tex]n = 4[/tex]
What is the probability that none of the chosen entrees contain spinach?
This is P(X = 0). So
[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}[/tex]
[tex]P(X = 0) = h(0,13,4,3) = \frac{C_{3,0}*C_{10,4}}{C_{13,4}} = 0.294[/tex]
0.294 = 29.4% probability that none of the chosen entrees contain spinach.
name the property that justifies each statement -3(m+8)=-3m-24
Answer: Distributive Property
Explanation: The distributive property tells us that if we're given an expression such as -3(m + 8), we can multiply the -3 by both the m and the 8.
Consider this absolute value function.
f(x) = |1 + 3|
How can function fbe rewritten as a piecewise function?
Answer:
The function [tex]f(x) = |x+3|[/tex] can be rewritten in the following form:
[tex]f(x) = \left\{\,\begin{array}{ccc}x+3\,\,\,x\ge -3\\-x-3\,\,\,x < -3\end{array}[/tex]
Step-by-step explanation:
According to the definition of absolute value, we know that:
[tex]f(a) = \left\{\,\begin{array}{ccc}a\,\,\,a\ge 0\\-a\,\,\,a < 0\end{array}[/tex]
According to this, we can define [tex]f(x) = |x+3|[/tex] in the following form:
[tex]f(x) = \left\{\,\begin{array}{ccc}x+3\,\,\,x\ge -3\\-x-3\,\,\,x < -3\end{array}[/tex]
Answer:
The correct order is in the picture i attatched:)
Step-by-step explanation:
Hope this helps explain a little better:)
PLS HELP!! :))
Find the surface area of a sphere with a diameter of 8 ft. Round your answer to the
nearest tenth.
Clear selection
1 point
The possible outcomes of flipping two coins is shown below.
Flipping Two Coins
First Coin Second Coin
Heads
Tails
Heads
Heads
Tails
Tails
Tails
Heads
What is the probability the coins will land with different sides showing?
The probability the coins will land with different sides showing should be 1/2.
pls help
When you multiply a fraction by a whole number, you can use the property to regroup factors to make it easier to multiply since the product
remains true. 3/4 * 7= 7 * 3/4.*
A. Communitive Property
B. Associative Property
C. Distributive Property
A study is conducted to determine how long a person will wait on hold on a telephone call before hanging up. A sample of 1000 people found that 569 hung up the phone in the first minute of waiting. It is of interest to estimate a range of plausible values for the true proportion of people that will not wait more than one minute on hold. Round all answers to three decimal places.(a) Construct a two-sided 95% confidence interval for p, the true proportion of people that will not wait on hold more than one minute. This confidence interval is ______
Answer:
CI = ( 0,539 ; 0,599)
Step-by-step explanation:
The proportion p₀ of person that hung up the phone in the first minute of waiting is:
p₀ = 569/1000 p₀ = 0,569 p₀ = 56,9 %
Then q₀ = 1 - 0,569 q₀ = 0,431 q₀ = 43,1 %
Sample size is n = 1000
A 95 % CI is: α = 5 % α = 0,05 a/2 = 0,025
In z-table we look z ( score ) for 0,025 z = ± 1,96
Now CI for proportion is:
p₀ - z (α/2) * √ (p₀*q₀ )/n < p < p₀ + z (α/2) * √ (p₀*q₀ )/n
we need to find out
z(α/2) * √ (p₀*q₀ )/n = 1,96*√ ( 0,569*0,431)/1000 = 1,96 *0,01566 =0,03
Then
CI ( 95%) = 0,569 ± 0,03 = ( 0,569 - 0,03 ; 0,569 + 0,03)
CI = ( 0,539 ; 0,599)
The length of a rectangle is 12 miles less than twice the width. The perimeter of the rectangle is 96 miles. Find the dimensions of the rectangle.
Answer:
Length= 68 miles
Width=28 miles.
Step-by-step explanation:
Length=2x+12
Width=x
2x+12+x=96
3x+12=96
3x=96-12
3x=84
X=28
Width=28
Length=(2×28)+12=68
A water balloon was launched into the top of the hill 38 feet above the ground
Answer: -71.104 ft/sec
Step-by-step explanation:So you need to know how fast the balloon is moving when it hits this person's head. velocity is based on time. So you need the time that it hits this person's head. You can get time from the position equation. Because the balloon hits this person's head 6 feet from the ground, you know that the final position is at 6 so you plug that into the position equation and solve for t. You look and see what the appropriate t value is and plug it into the velocity equation and see what the answer is.
6=-16t^2+40t+60
0=-16t^2+40t+54
plug in those values into the quadratic formula or your calculator and you get:
t = -.972
or
t = 3.472
since you can't have negative time, the other answer must be it.
So you then plug it in and solve.
v(3.472) = -32(3.472) + 40
which is approximately -71.104 ft/sec
or if they just want speed, 71.104 ft/sec. (remember, speed is velocity without direction)
c. Debbie and Jan are both in the 28% tax bracket. Since the interest is deductible, how much would Debbie and Jan each save in taxes? (Round your answers to the nearest cent.)
Step-by-step explanation:
Let's assume Debbie paid $1700 in interest, while Jan paid $9000.
Debbie Saves = $1700* 0.28
Jan Saves = $9000 * 0.28
Debbie Saves $476 in taxes
Jan Saves $2520 in taxes
I need this fast pls
Answer:
D
Step-by-step explanation
-2 1/2 is less than -1 1/2, s -2 1/2<-1 1/2
Consider the exponential function of f(x) =10(2)x. Find the value of f (0). What point does this represent on the graph of y=f (x)? Is this an increasing or decresasing function? How can you tell based on its equation.
Answer:
la respuesta que buscas es bastante simple pero no lo sé
Step-by-step explanation:
Following are weights, in pounds, of two-month-old baby girls. It is reasonable to assume that the population is approximately normal.
12.32 11.87 12.34 11.48 12.66
8.51 14.13 12.95 9.34 8.63
Required:
a. Construct a interval for the mean weight of two-month-old baby girls.
b. According to the National Health Statistics Reports, the mean weight of two—month-old baby boys is 13.9 pounds. Based on the confidence interval, is it reasonable to believe that the mean weight of two-month—old baby girls may be the same as that of two-month-old baby boys? Explain.
Answer:
10.224 < μ < 12.622 ;
Since the mean weight of 2-montj old baby boys (13.9) falls outside the confidence interval, we can conclude that it is not reasonable to believe that the mean weight of two-month-old baby girls may be the same as that of two-month-old baby boys.
Step-by-step explanation:
The confidence interval is given as :
Mean ± Margin of Error
margin of error = Zcritical * standard deviation /sqrt(n)
n = sample size
From the data:
12.32, 11.87, 12.34, 11.48, 12.66, 8.51, 14.13, 12.95, 9.34, 8.63
From the data:
Using calculator :
Mean, = 11.423
Standard deviation, s = 1.934
Zcritical at 95% confidence interval = 1.96
Sample size, n = 10
Margin of Error = 1.96* 1.934/sqrt(10) = 1.199
Lower boundary = 11.423 - 1.199 = 10.224
Upper boundary = 11.423 + 1.199 = 12.622
10.224 < μ < 12.622
Since the mean weight of 2-montj old baby boys (13.9) falls outside the confidence interval, we can conclude that it is not reasonable to believe that the mean weight of two-month-old baby girls may be the same as that of two-month-old baby boys.
Malik purchased a pair of roller blades that were originally priced at $250 for a sale price of
$180. He charged the roller blades on his credit card and made the minimum monthly
payment of $20. When he received his first statement, he read that the minimum finance
charge for each month that there was a balance on the card would be $15. How many
months will Malik need to pay off the roller blades? (Assume that a minimum finance
charge of $15 will apply to all balances of $250 or less.)
Answer:f he made a first payment of $20 shortly after the purchase, he would have a balance of $180-$20=$160, before they applied the first $15 finance charge, but he will see a balance of $180-$20+$15=$175 (with the finance charge) in that first statement.
Each month, his balance will change by -$20+$15=-$5, so it will take him, another 32 payments to reduce that $160 to $0. That month, he will pay the $20 balance to get a balance of zero, and hopefully see no more finance charges.
In all, paying the minimum $20 payment each month, Malik will make 33 such payments for a total of $660. If he saved $20 per month, he could have saved $180 in 9 months, or $260 in 13 months, and he would have saved a lot of money. He would probably have to pay the $250 regular price, and would have missed about a year of roller blading, but he would have saved $660-250=$410.
Step-by-step explanation:
PLZ HELP ME DO THIS ITS DUE RN
Answer:
least to greatest: -5 and 1
Step-by-step explanation:
they represent the zeroes of the function and are sorted from least to greatest
help me please thanks
Answer:
325m = c
Step-by-step explanation:
Each meeting room has 325 chairs.
Since we don't know how many meeting rooms there are, the number is replaced with the variable, m.
An equation is a problem with an equals sign so you need to put what it would equal.
Since you don't know how many meeting rooms there are you use the variable, c which represents the total number of chairs.
pleaase help!
Find h. 11 in. h = ✓ [?] in. 14 in Enter
Answer:
[tex]h=8.48\ \text{inches}[/tex]
Step-by-step explanation:
Given that,
Radius of cone, r = 7 inches
Slant height of the cone, l = 11 inches
We need to find the height of the cone. Let the height be h. Using trigonometry to find it as follows :
[tex]h^2+r^2=l^2\\\\h=\sqrt{l^2-r^2}\\\\h=\sqrt{11^2-7^2}\\\\h=8.48\ \text{inches}[/tex]
So, the height of the cone is equal to [tex]8.48\ \text{inches}[/tex].
Heya!
Answer:
√72
Step-by-step explanation:
Use Pythagorean:
h² + (14/2)² = 11²
h² + 49 = 121
h² = 121 - 49
h² = 72
h = √72 in
Hope this helps <33
Melanie moved to Toledo on September 14 and returned home for a visit fifteen months later. When did she return home?
A. November 13th
B. December 13th
C. November 14th
D. December 14th
Answer:
D. December 14th.
Answer:
Dec 14 next year
Step-by-step explanation:
just add 15 months lol
Write an equation for the polynomial graphed below
y(x) =
The Smith family went out for pizza. Their bill was $37.85. They left a tip of 15%. What was the approximate amount of the tip? pls help me!
Answer:
$5.7
Step-by-step explanation:
Given data
Bill= $37.85
Tip= 15%
Required
The amount of the tip
let us find 15% of $37.85
=15/100*37.85
=0.15*37.85
=$5.6775
Hence the amount of the tip is
=$5.7
If x = 5, then which of the following equations makes a true statement?
Can someone help please
Answer:right scalene
Step-by-step explanation:
The store sells a 9 ounce jar of mustard for $1.53 and a 15 ounce for $2.55 explain whether the cost of the mustards have the same unit rate per ounce
Answer:
same amount of money
Step-by-step explanation:
The unit rate for a 9-ounce jar is $0.17.
The unit rate for a 15-ounce jar is $0.17.
What is a unit rate?It is the quantity of an amount of something at a rate of one of another quantity.
In 2 hours, a man can walk for 6 miles
In 1 hour, a man will walk for 3 miles.
We have,
The store sells a 9-ounce jar of mustard for $1.53.
The unit rate.
= 1.53/9
= 0.17 _____(1)
The store sells a 15-ounce for $2.55.
The unit rate.
= 2.55/15
= 0.17 ______(2)
From (1) and (2) we see that,
The unit rate is the same.
Thus,
The unit rate is the same.
Learn more about unit rates here:
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don’t send links; PLEASE HELP FAST I WILL DO ANYTHING, I’LL GIVE U 2K ON BLOXBURG
Answer:
i think its 90
Step-by-step explanation:
you would multiply the right box which is 2 x 3 ( i got 3 because its half of 6 which is at the top) then you would multiply the left box which is 3 x 5
2 x 3 = 6
3 x 5 = 15
15 x 6 = 90
i dont need the 2k on bloxburg
if its right could i get brainliest?
Use a half-angle formula to find the exact value of the expression.
Step-by-step explanation:
The answer is
[tex] \sqrt{2} - 1[/tex]
If you need any explanation in it or anything on math you can communicate with me on Whats on this number +201557831028 or in email or face or anything.
I can help you solve what you want in mathematics in exchange for some money. If you want to, you can inform me about it and I will help you.
flocabulary rates vocab game
Answer:
Rate.
Step-by-step explanation:
HELP! 50 POINTS!
A system of equations consists of a line s of the equation y = x - 5 that is graphed in orange, and a line t that passes through the points (0, 2) and (8, -4). The equation of line t is y = −3/4 x + 2.
What is the solution to this system of linear equations?
Answer form: ( __ , __ )
(4, -1) ---> x = 4 and y = -1
If you look at the graph you can se this
Mark points (0, 2) and (8, -4) in the coordinate plane
Plot the line going through both of these points.
Read the coordinates of the intersection of the line so you can see the solution!
what the total area of a rectangular prism with a hight of 17feet a width of 12 feet and a thickness of 10 feet ?
Answer:
[tex]A=988\ \text{feet}^2[/tex]
Step-by-step explanation:
Given that,
The height, width and the thickness of a rectangular prism are 17 feet, 12 feet and 10 feet.
We need to find the area of a rectangular prism. The formula for the ara of rectangular prism is given by :
[tex]A=2(lb+bh+hl)[/tex]
Substitute all the values,
[tex]A=2(17\times 12+12\times 10+10\times 17)\\\\A=2\times 494\\\\A=988\ \text{feet}^2[/tex]
So, the area of the rectangular prism is equal to [tex]988\ \text{feet}^2[/tex].
What is 39.3766 to the nearest degree
Answer:39
Step-by-step explanation:
Graph the line with slope
4/3
and y-intercept -9.
The graph is shown in the attached image.
The graph of the line is a straight line with points on are: (0, -9), (3, -5) and (6, -1).
Given that a line has a slope of 4/3 and the y-intercept is -9, we need to graph the line,
To graph the line with a slope of 4/3 and a y-intercept of -9, we can use the slope-intercept form of a linear equation, which is y = mx + b.
Here, the slope (m) is 4/3, and the y-intercept (b) is -9.
Start by plotting the y-intercept, which is the point (0, -9).
Next, use the slope to determine the direction of the line. The slope 4/3 means that for every 4 units you move up, you need to move 3 units to the right.
So, from the y-intercept (0, -9), move up 4 units and then move to the right 3 units to find the next point on the line. This point would be (3, -5).
Repeat this process to find more points on the line. Move up 4 units and to the right 3 units from the previous point (3, -5) to get (6, -1).
You can continue this process to find more points if desired.
Once you have a few points, connect them with a straight line to graph the line.
The graph of the line with a slope of 4/3 and a y-intercept of -9 is attached in the solution.
Learn more about Linear equations click;
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10
Gary, Nancy, and Jamal are trying to write an inequality where all values in the set of numbers below make the inequality true.
{0, 1, 3, 4, 6, 12}
Consider their inequalities.
Gary: 6 > 0.50
Nancy: 30 -t < 18
Jamal: 12
Which student(s) wrote an inequality that is true for all values in the set of numbers? Select your answer from the drop-down list
Only Gary as the
Only Gary
Only Nancy
Only Jamal
Only Gary and
Nancy
Only Gary and
Jamal
Only Nancy and
Jamal
Answer:
Jamal's inequality is correct
Step-by-step explanation:
Given
[tex]Sets:\{0,1,3,4,6,12\}[/tex]
Gary: [tex]6>0.5t[/tex]
Nancy: [tex]30 -t \le 18[/tex]
Jamal: [tex]12 \le t+12[/tex]
Required
Which of the inequalities is/are true
Gary: [tex]6>0.5t[/tex]
[tex]6>0.5t[/tex]
Divide both sides by 0.5
[tex]\frac{6}{0.5} > \frac{0.5t}{0.5}[/tex]
[tex]12 > t[/tex]
Rewrite as:
[tex]t < 12[/tex]
Gary's inequality is false because: [tex]12 = 12[/tex]
Nancy: [tex]30 -t \le 18[/tex]
[tex]30 -t \le 18[/tex]
Collect like terms
[tex]-t \le 18 - 30[/tex]
[tex]-t \le -12[/tex]
Divide both sides by -1
[tex]t \ge 12[/tex]
Nancy's inequality is incorrect because: 0,1,3,4 and 6 are less than 12
Jamal: [tex]12 \le t+12[/tex]
[tex]12 \le t+12[/tex]
[tex]12 - 12 \le t[/tex]
[tex]0 \le t[/tex]
Rewrite as:
[tex]t \ge 0[/tex]
Jamal's inequality is correct because: 0,1,3,4,6 and 12 [tex]\ge 0[/tex]