Erin uses a spinner divided into four equal sections to decide which drink she’ll have with her lunch. The sections represent water, milk, lemonade, and tea. If she spins the spinner three days in a row, what is the probability that she drinks lemonade one day, tea one day, and water one day? Complete the steps below to find the sample space and solve the problem. PART A - Create a list of all the possible outcomes for three days of drink selections. Use the abbreviations W, M, T, and L to represent water, milk, tea, and lemonade. PART B - Based on the list you created in part A, how many possible outcomes are there? PART C - What is the probability that Erin drinks lemonade one day, tea one day, and water one day? PART D - What is the probability that Erin drinks water two days and lemonade one day?
Answer:
Part A
W W W M W W T W W L W W
W W M M W M T W M L W M
W W T M W T T W T L W T
W W L M W L T W L L W L
W M W M M W T M W L M W
W M M M M M T M M L M M
W M T M M T T M T L M T
W M L M M L T M L L M L
W T W M T W T T W L T W
W T M M T M T T M L T M
W T T M T T T T T L T T
W T L M T L T T L L T L
W L W M L W T L W L L W
W L M M L M T L M L L M
W L T M L T T L T L L T
W L L M L L T L L L L L
Part B
There are 64 possible outcomes. The sample size is 64.
Part C
To find the probability that Erin drinks lemonade one day, tea one day, and water one day, consider all the cases in which L, T, and W occur one time. Because the order doesn't matter in this scenario, these six outcomes from the list represent the desired event: W T L, T W L, T L W, W L T, L W T, and L T W.
The size of the sample space is 64. So, the probability that Erin drinks lemonade one day, tea one day, and water one day is 3/32.
Part D
To find the probability that Erin drinks water on two days and lemonade one day, we consider all the cases in which two Ws and one L occur. Because the order doesn't matter in this scenario, these three outcomes from the list represent the event: W W L, W L W, and L W W.
The size of the sample space is 64. So, the probability that Erin drinks water two days and lemonade one day is 3/64
Step-by-step explanation:
25) Margie needs to borrow $9,000 from a local bank. The
loan has a 8.5% interest rate for 4 years. What will
Margie's monthly payment be?
A) $ 221,850.00
B) $3060.00
C) $250.0
D) $ 221.85
Answer:
B) $3060.00
Step-by-step explanation:
8.5% of 9,000 equals 765, then 765 multiplied by 4 equals 3060.
I think that it will take Margie 4 years to pay back the bank. And the interest rate that the bank charges is 8.5% per month.
I'm not sure if this is correct
Ms. Wilson's class is choosing a fiction book to read together. The students voted for their
favorite type of fiction book.
Favorite type of fiction book
Type Frequency
Fantasy
6
Mystery
3
Realistic
7
Historical
2.
Adventure
7
Historical fiction received the fewest votes. What percent of students voted for historical
fiction?
%
Answer:
[tex]\%H = 8\%[/tex]
Step-by-step explanation:
Given
See attachment for table
Required
The percentage of historical
From the table, we have:
[tex]Historical = 2[/tex]
and
[tex]Total = 6+3+7+2+7[/tex]
[tex]Total = 25[/tex]
So, the percentage of historical is:
[tex]\%H = \frac{Historical}{Total} * 100\%[/tex]
This gives:
[tex]\%H = \frac{2}{25} * 100\%[/tex]
[tex]\%H = \frac{200\%}{25}[/tex]
[tex]\%H = 8\%[/tex]
Answer:
8%
Step-by-step explanation:
15. If 8x + 6x + 5x + 3x = 440, then
2x + 5.8=
Answer:
2x + 5.8= 45.8
Step-by-step explanation:
8x + 6x + 5x + 3x = 440
combine like terms:
22x = 440
divide both sides of the equation by 22:
x = 20
2x + 5.8= 40 + 5.8 = 45.8
Is there a pattern behind prime numbers?
Answer:
There is a rule on how we find prime numbers.
Step-by-step explanation:
A clear rule determines exactly what makes a prime: it's a whole number that can't be exactly divided by anything except 1 and itself. But there's no discernible pattern in the occurrence of the primes.That's because, after the number 5, there are only four possibilities — 1, 3, 7, and 9 — for prime last digits
Find the area of the shaded figure in the diagram below. Use 3.14 for π and round your answer to the nearest hundredth.
A. 39.57in^2
B. 66.89 in^2
C. 200.67 in^2
D. 118.72 in^2
Answer:
D
Step-by-step explanation:
diameter of 1 circle = 21.3/3= 7.1
radius of 1 circle= 7.1/3=3.55
area of 1 circle =πr^2=3.14× (3.55)^2=39.57
area of 3 circle= 39.57×3=118.72
therefore,area of shaded portion= area of 3 circle =118.72
PLEASE HELP
On the graph below, Point A is located at the intersection of angle θ and the unit circle.
What are the exact coordinates of point A?
Use the on-screen keyboard to type the answer in the box below.
https://imgur.com/a/UwbnsCV
Answer:
1/2,
Step-by-step explanation: Please find the attached image of unit circle.
We have been given that the measure of angle t is 60 degrees. We are asked to find the x-coordinate of the point where the terminal side intersects the unit circle.
We know that x-coordinate on unit circle represents cosine and y-coordinate represents sine of a given angle.
We can see from our attachment that x-coordinate of the point at angle 60 degrees is , therefore, x-coordinate of the angle of 60 degrees, where the terminal side intersects the unit circle is .
Four students used a stopwatch to see how fast they could run around the perimeter of the playground they recorded their times in the chart below
Answer:
C : Duane
Step-by-step explanation:
Your welcome
expand : log3(x^3/81y^2)
Answer:
Use rules of logarithms to expand.
2
log
3
(
x
)
−
4
−
4
log
3
(
y
)
Step-by-step explanation:
A pet store sold 274 cans of cat food last weekend for a total of $216.46. What was the price per can?
Answer:
Compare them ➗That's the answer
What number must you add to the polynomial below to complete the square?
x2 + 15x
Answer:
The number [tex]\frac{225}{4}[/tex] is added to the polynomial below to complete the square.
Step-by-step explanation:
Perfect square binomial:
A perfect square binomial is given by:
[tex](a + b)^2 = a^2 + 2ab + b^2[/tex]
In this question:
We have that:
[tex]a^2 + 2ab + b^2 = x^2 + 15x + ?[/tex]
Since [tex]a = x[/tex], we have that:
[tex]2ab = 15x[/tex]
[tex]2b = 15[/tex]
[tex]b = \frac{15}{2}[/tex]
Completing the square:
The term that completes the square is [tex]b^2[/tex]. So
[tex]b^2 = (\frac{15}{2})^2 = \frac{225}{4}[/tex]
The number [tex]\frac{225}{4}[/tex] is added to the polynomial below to complete the square.
Which statement is true?
Group of answer choices
An equilateral triangle is never an acute triangle.
An isosceles triangle is sometimes a scalene triangle.
An acute triangle is always an equilateral triangle.
A equilateral triangle is always an isosceles triangle.
Answer:
An equilateral is always an isosceles triangle.
Step-by-step explanation:
Use the figure to find the measures.
Lateral area =
Total area =
Volume =
Answer:
Lateral area = 2.pi.r.h = 2 x pi x 2 x 3 = 12 pi
Total area = lateral area + pi. r^2 . 2 = 20 pi
Volume = pi . r^2 . 2 . h = 24 pi
Find the percent of change and state whether it was a percent of increase (I) or percent of decrease (D). from $289 to $762
Answer:
163.67 ( I )
Step-by-step explanation:
Which of the following values is NOT a solution to |4x - 6| - 12 > 8?
A. 10
B. 7
C. 4
D. -5
Answer:
Option C
Step-by-step explanation:
Given :-
| 4x -6| -12>8Options :
1074-5We can check the options , as ,
[tex]:\implies[/tex] Option 1 : 10
| 4*10-6|-6>8| 40 - 6| - 6 > 8| 34 | - 6 > 834 - 6 > 8 28 > 8 ( a solution )[tex]:\implies[/tex] Option C : 4
| 4*4 -6 | -6 > 8| 16 - 6 | - 6 > 8| 10| - 6 > 810 - 6 > 84 > 8 ( not a solⁿ )Hence option C is not a solution .
A psychologist would like to examine the effect of fatigue on mental alertness. An attention test is prepared which requires subjects to sit in front of a blank TV screen and press a response button each time a dot appears on the screen. A total of 110 dots are presented during a 90-minute period, and the reach subject. Two groups of subjects are selected. The first group (n 5) is tested after they have been kept awake for 24 hours. The second group (n-10) is tested in the morning after a full night's sleep. The data for these two samples are as follows:
Awake 24 hours rested
x=35 X=24
ss=120 ss =360
On the basis of these data, can psychologist conclude that fatigue significantly increases errors on an attention task? Test with α-05 and report effect size.
Answer:
The calculated value of t= 0.1908 does not lie in the critical region t= 1.77 Therefore we accept our null hypothesis that fatigue does not significantly increase errors on an attention task at 0.05 significance level
Step-by-step explanation:
We formulate null and alternate hypotheses are
H0 : u1 < u2 against Ha: u1 ≥ u 2
Where u1 is the group tested after they were awake for 24 hours.
The Significance level alpha is chosen to be ∝ = 0.05
The critical region t ≥ t (0.05, 13) = 1.77
Degrees of freedom is calculated df = υ= n1+n2- 2= 5+10-2= 13
Here the difference between the sample means is x`1- x`2= 35-24= 11
The pooled estimate for the common variance σ² is
Sp² = 1/n1+n2 -2 [ ∑ (x1i - x1`)² + ∑ (x2j - x`2)²]
= 1/13 [ 120²+360²]
Sp = 105.25
The test statistic is
t = (x`1- x` ) /. Sp √1/n1 + 1/n2
t= 11/ 105.25 √1/5+ 1/10
t= 11/57.65
t= 0.1908
The calculated value of t= 0.1908 does not lie in the critical region t= 1.77 Therefore we accept our null hypothesis that fatigue does not significantly increase errors on an attention task at 0.05 significance level
Find the amount of wood trim needed to frame a circular window with a diameter of 1.75 ft. Use 3.14 for n.
Answer:
2.40 ft I believe
Step-by-step explanation:
divide diameter by two
put 3.14 time diameter divided by two and square it
A researcher is testing a claim that the mean wing span of bald eagles mean wing span is 22ft. He takes a simple random sample of 40 bald eagles and gets a sample mean of 24.6ft and a sample
standard deviation of 3.5ft. Find the test statistic, t=
Which equation has an a-value of 1, a b-value of –3, and a c-value of –5?
0 = –3x – 5 + x2
0 = x – 3 – 5x2
0 = 3x – 5 – x2
0 = –3x + 5 – x2
Answer:
Option (a) is correct.
For given values a = 1 , b = -3 , c = -5 the quadratic equation is
Step-by-step explanation:
Given : a = 1 , b = -3 , c = -5
We have to write the quadratic equation having a = 1 , b = -3 , c = -5 and choose the correct option.
The standard form of quadratic equation is , where a, b, c are constant integers.
Given : a = 1 , b = -3 , c = -5
Then Substitute, we get,
Thus, the obtained quadratic equation is same as option (a)
Thus, For given values a = 1 , b = -3 , c = -5 the quadratic equation is
The equation for which a-value 1, ab-value -3 and ac-value -5 is 0=-3x-5+x².
What is quadratic equation?
Quadratics can be defined as a polynomial equation of a second degree, which implies that it comprises a minimum of one term that is squared. It is also called quadratic equations.
Here, a-value = 1,
ab-value = -3
ac-value = -5
a = 1, b = -3, and c = -5
General Equation,
ax² + bx + c = 0
1x² + (-3)x + (-5) = 0
x² -3x -5 = 0
Thus, the equation for which a-value 1, ab-value -3 and ac-value -5 is 0= -3x -5 + x².
Learn more about Quadratic Equation from:
https://brainly.com/question/1863222
#SPJ2
Question 1 of 9 Write the slope-intercept inequality for the graph below. If necessary, use does anyone know the right answer i keep getting it wrong
Answer:
y >= 4/3 x + 4
Step-by-step explanation:
First, we find the equation of the line.
y = mx + b
The y-intercept is 4, so b = 4,and we have
y = mx + 4
Now we find the slope using 2 points.
slope = m = (0 - 4)/(-3 - 0) = -4/(-3) = 4/3
The equation of the line is
y = 4/3 x + 4
The line is solid, so we will use >= or <=, but not > or <.
The shading is "above" the line, so the correct sign is >=.
Answer: y >= 4/3 x + 4
When Elijah left his house in the morning, his cell phone battery was partially
charged. The charge remaining in Elijah's battery, as a percentage, can be modeled by
the equation B = 27 – 4.5t, where t is the number of hours since Elijah left his
house. What is the slope of the equation and what is its interpretation in the context
nf the problem?
Answer:
The slope is -4.5
The slope means that Elijah's phone battery will decrease by 4.5 percent each hour.
Step-by-step explanation:
In the equation y = mx + b, m is the slope.
The coefficient in the equation B = 27 – 4.5t is -4.5. This means that -4.5 is the slope of the equation.
In the context of this problem, the slope will represent the percent that Elijah's phone battery will decrease per hour.
So, the slope means that Elijah's phone battery will decrease by 4.5 percent each hour.
5.
Multiply.
(3x + 2)(x - 3)
Answer: 3x^2 - 7x - 6
Step-by-step explanation:
Answer:
3x^2-7x-6
Step-by-step explanation:
(3x+2)(x-3)
3x^2-9x+2x-6
3x^2-7x-6
Hope this helps.
Does anyone know the answer
Answer:
d = 126, z = 28
Step-by-step explanation:
The angle with the variable is diagonal from the 105 degree angle. In this case, that means that they are equivalent. So, 105+21 = 126. d = 126 :)
A machine produces 3-inch nails. A sample of 10 nails is obtained and the lengths determined. After some calculation, the sample mean is 2.98 and the sample standard deviation is 0.09. Find a 90% confidence interval for the population mean length of nails produce by the machine. Please input the upper limit of the confidence interval
Answer:
The 90% confidence interval for the population mean length of nails produced by the machine.
(2.91562, 3.04438)
Step-by-step explanation:
Step:1
Given that the size of the sample 'n' = 10
Given that the mean of the sample (x⁻) = 2.98
Given that the standard deviation of the sample (s) = 0.09
Degrees of freedom = n-1 = 10 -1 = 9
t₀.₁₀ = 2.2621
Step:2
The 90% confidence interval for the population mean length of nails produced by the machine.
[tex](x^{-} - t_{9 , 0.10} \frac{S}{\sqrt{n} } , x^{-} + t_{9,0.10} \frac{S}{\sqrt{n} } )[/tex]
[tex](2.98 - 2.2621(\frac{0.09}{\sqrt{10} } , 2.98 + 2.262 \frac{0.09}{\sqrt{10} } )[/tex]
(2.98 - 0.06438 , 2.98 + 0.06438)
(2.91562 , 3.04438)
Final answer:-
The 90% confidence interval for the population mean length of nails produced by the machine.
(2.91562, 3.04438)
Determine the equation of this circle Assume the radius is a whole number (3,-2)
Answer:
1 1/2
Step-by-step explanation:
Please help me. Image below.
Answer:
10 cubes
Step-by-step explanation:
2.5 × 1 × 2 = 5 cm³
5 ÷ 0.5
10 cubes
Answer:
10 cubes
Step-by-step explanation:
1 × 2 × 2.5 = 5cm^3
5 ×× .5 = 10
so 10 cubes would fit
Simplify to a single power of 2
Answer:
2^7
Explanation:
You can add up the square of two and the square of five. This is the easiest way.
In the map below, Side P Q is parallel to Side S T.
Triangle P Q R. Side P Q is 48 kilometers and side P R is 36 kilometers. Triangle S R T. Side R T is 81 kilometers.
What is the distance between S and T? If necessary, round to the nearest tenth.
21.3 km
60.8 km
108 km
117 km
answer C.
Answer:
C.
Step-by-step explanation:
The perimeter of a square is 36 feet. If you increase the length by 3 feet and decrease the width
by 2 feet, what is the area of the new figure?
Answer:
84 feet
Step-by-step explanation:
If the perimeter is 36 feet, and all the sides are the same length, then all the sides are 9. if we increase the length by 3 feet and decrease the width by 2 feet then we are left with 12 * 7 = 84
In London today, twice the low temperature was less than three times
the low temperature minus ten. In interval form, what are the possible
temperatures?