Answer:
5/18
Step-by-step explanation:
There are a couple of ways to look at this.
1) If you make a matrix of all possibilities, you find there are 36 possible outcomes from the roll of a die twice. (That is the same number as for rolling two dice once.) Of those 36 outcomes, 10 are outcomes in which a 5 shows exactly once: (5, 1), (5, 2), (5, 3), (5, 4), (5, 6), (1, 5), (2, 5), (3, 5), (4, 5), (6, 5).
The probability of obtaining exactly one 5 is 10/36 = 5/18.
__
2) As listed above, there are two ways to get exactly one 5 in two rolls:
(5 on the first, non-5 on the second) or (non-5 on the first, 5 on the second)
When the rolls are independent, as we assume here, the probability of a certain sequence is the product of the probabilities of the events in that sequence.
P(5, non-5) = (1/6)(5/6) = 5/36
P(non-5, 5) = (5/6)(1/6) = 5/36
The probability of obtaining either event is the sum of their individual probabilities:
P({5, 5'} or {5', 5}) = 5/36 +5/36 = 10/36 = 5/18
__
The probability of obtaining exactly one 5 in two rolls of a die is 5/18.
Answer:
S= (1,1) (1,2) (1,3) (1,4) (1,5) (1,6)
(2,1) (2,2) (2,3) (2,4) (2,5) (2,6)
(3,1) (3,2) (3,3) (3,4) (3,5) (3,6)
(4,1) (4,2) (4,3) (4,4) (4,5) (4,6)
(5,1) (5,2) (5,3) (5,4) (5,5) (5,6)
(6,1) (6,2) (6,3) (6,4) (6,5) (6,6)
For this case the size of the sample space is 36 now we count the number of pairs with exactly one 5 and we have:
(1,5), (2,5), (3,5), (4,5), (6,5), (5,6), (5,4), (5,3), (5,2), (5,1)
And then the probability would be:
[tex] p=\frac{10}{36}= \frac{5}{18}[/tex]
Step-by-step explanation:
For this case w ehave the following sample space:
S= (1,1) (1,2) (1,3) (1,4) (1,5) (1,6)
(2,1) (2,2) (2,3) (2,4) (2,5) (2,6)
(3,1) (3,2) (3,3) (3,4) (3,5) (3,6)
(4,1) (4,2) (4,3) (4,4) (4,5) (4,6)
(5,1) (5,2) (5,3) (5,4) (5,5) (5,6)
(6,1) (6,2) (6,3) (6,4) (6,5) (6,6)
For this case the size of the sample space is 36 now we count the number of pairs with exactly one 5 and we have:
(1,5), (2,5), (3,5), (4,5), (6,5), (5,6), (5,4), (5,3), (5,2), (5,1)
And then the probability would be:
[tex] p=\frac{10}{36}= \frac{5}{18}[/tex]
Please answer this correctly without making a mistake I need a correct answer
Answer: 45.5
Step-by-step explanation:
Im in 6th grade and all you had to do was add 18.3 and 27.2 and you’ll get 45.5
Answer:
The garbage dump is 58.3 miles west of the hotel, and the hotel is 57.1 miles west of the hardware store. The hardware store is 44.8 miles west of the library. The hardware store is 57.9 miles north of the office supply store, and the office supply store is 55.5 miles north of the science lab.
Step-by-step explanation:
Which of the following is the minor arc for the circle shown below?
A. AWR
B. AW
C. RAW
D. RA
Answer:
RA
Step-by-step explanation:
Find the measure of the indicated angle to the nearest degree.
PLEASE HELP ASAP
Answers
A. 26
B. 42
C. 64
D. 48
Answer:
The answer is option C
Step-by-step explanation:
To find the indicated angle we use sine
sin ∅ = opposite / hypotenuse
From the question
The opposite is 37
The hypotenuse is 41
So we have
sin ? = 37/41
? = sin-¹ 37/41
? = 64.4805
? = 64° to the nearest degreeHope this helps you
Answer:
C.) 64
Step-by-step explanation:
I got it correct on founders edtell
Find a solution to the linear equation y=−x+7 by filling in the boxes with a valid value of x and y.
Answer:
(0,7) and (7,0)
Step-by-step explanation:
When x = 0, y = 7
When y = 0, x = 7
The solution to this equation is: (0,7) and (7,0) and can be graphed on a cartesian plane like the attached graph.
Factories fully 18x-9
Answer:
Factor 9 out of 18x.
9(2x)−9
Factor 9 out of −9
9(2x)+9(−1)
Factor 9 out of 9(2x)+9(−1)
9(2x−1)
Answer:
9 ( 2x - 1 )
Step-by-step explanation:
→ Look for the HCF of the whole numbers
HCF of 18 and 9 is 9
→ Put 9 outside the brackets
9 ( ? - ? )
→ Perform the calculation 18x ÷ 9 to determine the first question mark
18x ÷ 9 = 2x ⇔ 9 ( 2x - ? )
→ Perform the calculation 9 ÷ 9 to determine the second question mark
9 ÷ 9 = 1 ⇔ 9 ( 2x - 1 )
Enter a range of vaules for x
A range for the values of x:
-2, -1, 0, 1, 2,
Happy to help! You can certainly extend this range
The true average diameter of ball bearings of a certain type is supposed to be 0.5 in. A one-sample t test will be carried out to see whether this is the case. What conclusion is appropriate in each of the following situations?
(a) n = 15, t = 1.66, a = 0.05
a. Reject the null hypothesis. There is sufficient evidence that the true diameter differs from 0.5 in
b. Reject the null hypothesis. There is not sufficient evidence that the true diameter differs from 0.5 in
c. Do not reject the null hypothesis. There is sufficient evidence that the true diameter differs from 0.5 in
d. Do not reject the null hypothesis. There is not sufficient evidence that the true diameter differs from 0.5 in
(b) n = 15, t = 1.66, a = 0.05
a. Reject the null hypothesis. There is sufficient evidence that the true diameter differs from 0.5 in
b. Reject the null hypothesis. There is not sufficient evidence that the true diameter differs from 0.5 in
c. Do not reject the null hypothesis. There is sufficient evidence that the true diameter differs from 0.5 in
d. Do not reject the null hypothesis. There is not sufficient evidence that the true diameter differs from 0.5 in
(c) n = 26, t = 2.55, a = 0.01
a. Reject the null hypothesis. There is sufficient evidence that the true diameter differs from 0.5 in
b. Reject the null hypothesis. There is not sufficient evidence that the true diameter differs from 0.5 in
c. Do not reject the null hypothesis. There is sufficient evidence that the true diameter differs from 0.5 in
d. Do not reject the null hypothesis. There is not sufficient evidence that the true diameter differs from 0.5 in
(d) n = 26, t = 3.95
a. Reject the null hypothesis. There is sufficient evidence that the true diameter differs from 0.5 in
b. Reject the null hypothesis. There is not sufficient evidence that the true diameter differs from 0.5 in
c. Do not reject the null hypothesis. There is not sufficient evidence that the true diameter differs from 0.5 in
d. Do not reject the null hypothesis. There is sufficient evidence that the true diameter differs from 0.5 in
You may need to use the appropriate table in the Appendix of Tables to answer this question.
Answer:
Option C - Do not reject the null hypothesis. There is not sufficient evidence that the true diameter differs from 0.5 in
Step-by-step explanation:
We are given;
n = 15
t-value = 1.66
Significance level;α = 0.05
So, DF = n - 1 = 15 - 1 = 14
From the one-sample t - table attached, we can see that the p - value of 0.06 at a t-value of 1.66 and a DF of 14
Now, since the P-value is 0.06,it is greater than the significance level of 0.05. Thus we do not reject the null hypothesis. We conclude that there is not sufficient evidence that the true diameter differs from 0.5 in.
What is the initial value of the equation shown? y = −7x − 6 −13 −7 −6 −1
Answer:
-6.
Step-by-step explanation:
The equation is y = -7x - 6.
The initial value is found when x = 0.
y = -7(0) - 6
y = 0 - 6
y = -6
Hope this helps!
Rewriting the Equation:
Answer:
7x+y=-33
Step-by-step explanation:
1.) Combine Like Terms: y=-7x-33
2.) Move the variable to the left side and use the inverse operation:
y+7x=-33
3.) Reorder terms using commutative property since x comes before y:
7x+y=-33
If you want to find the function then tell me.
Help please someone I have solved this multiple times factoring out the quadratic equations and I keep getting m as -1. But the correct answer says m is -5.
Answer: m = -5
Step-by-step explanation:
[tex]\dfrac{m+3}{m^2+4m+3}-\dfrac{3}{m^2+6m+9}=\dfrac{m-3}{m^2+4m+3}\\\\\\\dfrac{m+3}{(m+3)(m+1)}-\dfrac{3}{(m+3)(m+3)}=\dfrac{m-3}{(m+3)(m+1)}\quad \rightarrow m\neq-3, m\neq-1[/tex]
Multiply by the LCD (m+3)(m+3)(m+1) to eliminate the denominator. The result is:
(m + 3)(m + 3) - 3(m + 1) = (m - 3)(m - 3)
Multiply binomials, add like terms, and solve for m:
(m² + 6m + 9) - (3m + 3) = m² - 9
m² + 6m + 9 - 3m - 3 = m² - 9
m² + 3m + 6 = m² - 9
3m + 6 = -9
3m = -15
m = -5
find the product 8x(2x^2+8x-5)
Answer:
16x^3 +64x^2 -40x
Step-by-step explanation:
Use the distributive property. The factor outside parentheses multiplies each term inside parentheses:
8x(2x^2 +8x -5) = (8x)(2x^2) +(8x)(8x) +(8x)(-5)
= 16x^3 +64x^2 -40x
Use differentials to estimate the amount of material in a closed cylindrical can that is 20 cm high and 8 cm in diameter if the metal in the top and bottom is 0.1 cm thick, and the metal in the sides is 0.1 cm thick. Note, you are approximating the volume of metal which makes up the can (i.e. melt the can into a blob and measure its volume), not the volume it encloses
Answer:
The volume is [tex]dV = 19.2 \pi \ cm^3[/tex]
Step-by-step explanation:
From the question we are told that
The height is h = 20 cm
The diameter is d = 8 cm
The thickness of both top and bottom is dh = 2 * 0.1 = 0.2 m
The thickness of one the side is dr = 0.1 cm
The radius is mathematically represented as
[tex]r = \frac{d}{2}[/tex]
substituting values
[tex]r = \frac{8}{2}[/tex]
[tex]r = 4 \ cm[/tex]
Generally the volume of a cylinder is mathematically represented as
[tex]V_c = \pi r^2 h[/tex]
Now the partial differentiation with respect to h is
[tex]\frac{\delta V_v}{\delta h} = \pi r^2[/tex]
Now the partial differentiation with respect to r is
[tex]\frac{\delta V_v}{\delta r} = 2 \pi r h[/tex]
Now the Total differential of [tex]V_c[/tex] is mathematically represented as
[tex]dV = \frac{\delta V_c }{\delta h} * dh + \frac{\delta V_c }{\delta r} * dr[/tex]
[tex]dV = \pi *r^2 * dh + 2\pi r h * dr[/tex]
substituting values
[tex]dV = \pi (4)^2 * (0.2) + (2 * \pi (4) * 20) * 0.1[/tex]
[tex]dV = 19.2 \pi \ cm^3[/tex]
(I deleted my answer because it was incorrect)
Find the surface area of this triangular prism. Be sure to include the correct unit in your answer.
Answer
240cm^2 (i think)
Step-by-step explanation:
find the area of each side then add
The first and last term of an AP are 1 and 121 respectively. If the sum of the series is 671,find a) the number of terms (n) in the AP b) the common
difference between them
Answer:
(a)11
(b)12
Step-by-step explanation:
The first term, a = 1
The last term, l=121
Sum of the series, [tex]S_n=671[/tex]
Given an arithmetic series where the first and last term is known, its sum is calculated using the formula:
[tex]S_n=\dfrac{n}{2}(a+l)[/tex]
Substituting the given values, we have:
[tex]671=\dfrac{n}{2}(1+121)\\671=\dfrac{n}{2} \times 122\\671=61n\\$Divide both sides by 61\\n=11[/tex]
(a)There are 11 terms in the arithmetic progression.
(b)We know that the 11th term is 121
The nth term of an arithmetic progression is derived using the formula:
[tex]a_n=a+(n-1)d[/tex]
[tex]a_{11}=121\\a=1\\n=11[/tex]
Therefore:
121=1+(11-1)d
121-1=10d
120=10d
d=12
The common difference between them is 12.
What are the next three terms in the sequence -27, -19, -11, -3, 5, ...?
Answer:
13, 21
Step-by-step explanation:
Add 8 to the next number from the left to the right.
Answer:
The next three numbers in the sequence are: 13, 21, 29.
Step-by-step explanation:
Common Pattern: +8
-27 +8 = -19
-19 + 8 = -11
-3 + 8 = 5
5 + 8 = 13
13 + 8 = 21
21 + 8 = 29
A satellite dish is being designed so that it can pick up radio waves coming from space. The satellite dish will be in the shape of a parabola and will be positioned above the ground such that its focus is 50 ft above the ground. Using the ground as the x-axis, where should the base of the satellite be positioned? Which equation best describes the equation of the satellite?
Answer:
[tex]y=\frac{x^2}{100}+2500[/tex]
Step-by-step explanation:
Given that the satellite is in the shape of parabola and will be positioned above the ground such that its focus is 50 ft, above ground.
let the point at the ground be (0,0) and focus (0,50). Thus, The base is at equal distance from the ground and focus that the vertex is at
(h,k) =(0,25).
Obtain the equation that describes the equation of the satellite as,
[tex](x-h)^2 =4a(y-k)\\
\Rightarrow (x-0)^2=4(25)(y-25)\\
\Rightarrow x^2=100(y-25)\\
\Rightarrow x^2 =100y-2500\\
\Rightarrow y=\frac{x^2}{100}+2500[/tex]
Thus, the equation of satellite is [tex]y=\frac{x^2}{100}+2500[/tex]
Answer:
(0, 25); y = one over one hundred x2 + 25
Step-by-step explanation:
If your on question 7 of (04.04 MC)
It should be the third option. (C)
Find the area of the triangle. Round the answer to the nearest tenth. A. 4.4 square units B. 5.2 square units C. 6.8 square units D. 8.8 square units
Answer:
A. 4.4 units²
Step-by-step explanation:
Area of a Triangle: A = 1/2bh
sin∅ = opposite/hypotenuse
cos∅ = adjacent/hypotenuse
Step 1: Draw the altitude down the center of the triangle
- We should get a perpendicular bisector that creates 90° ∠ and JM = KM
- We should also see that we use sin∅ to find the h height of the triangle and that we use cos∅ to find length of JM to find b base of the triangle
Step 2: Find h
sin70° = h/3.7
3.7sin70° = h
h = 3.47686
Step 3: Find b
cos70° = JM/3.7
3.7cos70° = JM
JM = 1.26547
Step 4: Find entire length base JK
JM + KM = JK
JM = KM (Definition of Perpendicular bisector)
2(JM) = JK
2(1.26547) = 2.53095
b = 2.53095
Step 5: Find area
A = 1/2(3.47686)(2.53095)
A = 4.39988
A ≈ 4.4
A circle has a radius of 8ft. Find the length s of the arc intercepted by a central angle of π3 radians. Do not round any intermediate computations, and round your answer to the nearest tenth.
Answer:
8.4ft
Step-by-step explanation:
Formula for calculating the length of an arc is expressed as [tex]L = \frac{\theta}{360} * 2\pi r\\[/tex]
[tex]\theta[/tex] is the central angle = π/3 rad
r is the radius of the circle = 8ft
Substituting the values into the formula above we have;
[tex]L =[/tex] [tex]\frac{(\frac{\pi}{3} )}{2 \pi} * 2\pi (8)\\\\[/tex]
[tex]L = \frac{\pi}{6 \pi} * 2\pi(8) \\\\L = 1/6 * 16\pi\\\\L = 8\pi/3\\\\L = \frac{8(22/7)}{3} \\\\L = \frac{8*22}{7*3}\\ \\L = 176/21\\\\L = 8.4 ft (to\ the\ nearest\ tenth)[/tex]
Hence, the length of the arc s is approximately 8.4 ft.
The sum of the digits of a two-digit number is 5. If nine is subtracted from the number, the digits will be reversed. Find the Algebraic equation by replacing the tens digit with x.
Let a be the number in the 10s place and b in the 1s place. Then the original two-digit number is 10a + b.
The sum of the digits is 5:
a + b = 5
Subtract 9 from the original number, and we get the same number with its digits reversed:
(10a + b) - 9 = 10b + a
Simplifying this equation gives
9a - 9b = 9
or
a - b = 1
Add this to the first equation above:
(a + b) + (a - b) = 5 + 1
2a = 6
a = 3
Then
3 - b = 1
b = 2
So the original number is 32. Just to check, we have 3 + 2 = 5, and 32 - 9 = 23.
The area of a triangle is 14 square inches. The base is 28 inches. What is the height in inches? Do not include units in your answer.
Answer:
Hey there!
A=1/2bh
14=1/2(28)h
14=14h
h=1
Hope this helps :)
Answer:
the height is 1 inchStep-by-step explanation:
Area of a triangle is
[tex] \frac{1}{2} \times b \times h[/tex]
where b is the base
h is the height
From the question
Area = 14in²
b = 14 inches
So we have
[tex]14 = \frac{1}{2} \times 28 \times h[/tex]
which is
[tex]14 = 14h[/tex]
Divide both sides by 14
That's
[tex] \frac{14}{14} = \frac{14h}{14} [/tex]
We have the final answer as
h = 1
Therefore the height is 1 inch
Hope this helps you
A business tenant has a percentage lease stating rent payment is greater of 2% of the business’s total gross sales volume or a minimum base rental of $1,000.00 per month. In the past year, sales totaled $435,000. How much rent did the business pay?
Answer:
$12,000
Step-by-step explanation:
By paying the minimum rent, the tenant would pay $1000 * 12 = $12,000.
Rent cannot be less than $12,000.
If the 2% of sales is greater than $12,000, then 2% of sales becomes the rent.
Now we calculate 2% of annual sales.
2% * $435,000 = $8,700
Since the minimum rent, $12,000, is greater than 2% of sales, then rent is $12,000.
experts, geniuses, aces and moderators .. need help on the attached. will give brainliest!!! find the derivative of e^x
Please Help!!! Find X for the triangle shown.
Answer:
[tex] x = 2 [/tex]
Step-by-step explanation:
Given a right-angled triangle as shown above,
Included angle = 60°
Opposite side length = 3
Adjacent side length = x
To find x, we would use the following trigonometric ratio as shown below:
[tex] tan(60) = \frac{3}{x} [/tex]
multiply both sides by x
[tex] x*tan(60) = \frac{3}{x}*x [/tex]
[tex] x*tan(60) = 3 [/tex]
Divide both sides by tan(60)
[tex] \frac{x*tan(60)}{tan(60} = \frac{3}{tan(60} [/tex]
[tex] x = \frac{3}{tan(60} [/tex]
[tex] x = 1.73 [/tex]
[tex] x = 2 [/tex] (approximated to whole number)
Find the centroid of the quarter of the unit circle lying in the fourth quadrant.
Step-by-step explanation:
In the fourth quadrant, the equation of the unit circle is:
y = -√(1 − x²), 0 ≤ x ≤ 1
The x and y coordinates of the centroid are:
cₓ = (∫ x dA) / A = (∫ xy dx) / A
cᵧ = (∫ y dA) / A = (∫ ½ y² dx) / A
For a quarter circle in the fourth quadrant, A = -π/4.
Solving each integral:
∫₀¹ xy dx
= ∫₀¹ -x √(1 − x²) dx
= ½ ∫₀¹ -2x √(1 − x²) dx
If u = 1 − x², then du = -2x dx.
When x = 0, u = 1. When x = 1, u = 0.
= ½ ∫₁⁰ √u du
= ½ ∫₁⁰ u^½ du
= ½ (⅔ u^³/₂) |₁⁰
= (⅓ u√u) |₁⁰
= 0 − ⅓
= -⅓
∫₀¹ ½ y² dx
= ½ ∫₀¹ (1 − x²) dx
= ½ (x − ⅓ x³) |₀¹
= ½ [(1 − ⅓) − (0 − 0)]
= ⅓
Therefore, the x and y coordinates of the centroid are:
cₓ = (-⅓) / (-π/4) = 4/(3π)
cᵧ = (⅓) / (-π/4) = -4/(3π)
6th grade math, help me please.
Answer:
1:3
Step-by-step explanation:
3/3=1
9/3=6
Answer:
1 : 3Option A is the correct option.
Step-by-step explanation:
Given,
Number of pears = 3
Number of apples = 9
Find : Ratio of the number of pears to the number of apples on the fruit salad
Now,
[tex] \frac{pear}{apples} [/tex]
Plug the values
[tex] = \frac{3}{9} [/tex]
Divide the numerator and denominator by 3
[tex] = \frac{3 \div 3}{9 \div 3} [/tex]
Divide the numbers
[tex] = \frac{1}{3} [/tex]
It can be written as :
1 : 3
Hope this helps..
Best regards!!!
Find the maximum and minimum values by evaluating the equation
Answer:
min = -9
max =3
Step-by-step explanation:
C = x-3y
x ≥0
x≤3
y≥0
y≤3
The minimum will be be when x is smallest and y is at its max
x =0 and y = 3
C = 0 - 3(3)
C = 0-9 = -9
The minimum is -9
The maximum occurs when x is largest and y is smallest
x =3 and y = 0
C = 3 - 3(0)
C = 3-0 = 3
The max is 3
Write the equation of the line, in point-slope form. Identify (x, y) as the point (-2, 2). Use the box provided or the upload
option to submit all of your calculations and final answers.
Answer:
y = -x + 0
Step-by-step explanation:
well the equation of a line is y = mx + b
m = the slope , b = the y-intercept
m = y2 - y1 / x2 - x1
m = -1
and b is the y-intercept of the line.
finally:
y = -1x + 0
The graph shows how the length of time a boat is rented is related to the
rental cost. What is the rate of change shown in the graph?
Boat Rental
AY
440
400
380
320
Cost (dollars)
240
200
100
120
80
40
0
Time (hours)
A. $40/hour
B. $80/hour
C. 80 hours/dollar
D. 40 hours/dollar
A slope is also known as the gradient of a line is a number. The correct option is B.
What is Slope?A slope is also known as the gradient of a line is a number that helps to know both the direction and the steepness of the line.
slope = (y₂-y₁)/(x₂-x₁)
The rate of change shown in the graph is the slope of the given line.
Now, to know the slope of the line consider any two points on the line, such as (0,0) and (5,400).
Therefore, the slope of the line can be written as,
Slope, m = ($400 - $0)/(5-0) hour
= $400/5 hour
= $80/hour
Learn more about Slope of Line:
https://brainly.com/question/14511992
#SPJ2
Please amswere my school is due tommorow and i meed some help
Answer:
88
Step-by-step explanation:
M : R
3 : 7
R : E
1 : 2
So make Ryan equal
1×7=7
2×7=14
tfo R : E
7 : 14
then add all 3forM+7forR+14forE = 24
192/24=8
so for Ethan, 8×14=112and for Marc, 8×3=24
therefore Ethan has 112-24=88 more stickers than Marc
Heights for teenage boys and girls were calculated. The mean height for the sample of 46 boys was 195 cm and the variance was 58. For the sample of 66 girls, the mean was 165 cm and the variance was 75. Estimate how much taller teenage boys are using a 85% confidence level. Round answers to the nearest hundredth and provide the point estimate together with the margin of error.
Answer:
With a 85% confidence level you'd expect the teenage boys to be on average between [29.217; 30.783]cm taller than the girls.
Step-by-step explanation:
Hello!
Given the variables:
X₁: height of a teenage boy.
n₁= 46
[tex]\frac{}{X}[/tex]₁= 195cm
S₁²= 58cm²
X₂= height of a teenage girl
n₂= 66
[tex]\frac{}{X}[/tex]₂= 165cm
S₂²= 75cm²
If the boys are taller than the girls then you'd expect μ₁ > μ₂ or expressed as a difference between the two population means: μ₁ - μ₂ > 0
To estimate the difference between both populations you have to calculate the following interval:
([tex]\frac{}{X}[/tex]₁- [tex]\frac{}{X}[/tex]₂) + [tex]t_{n_1+n_2-2; 1-\alpha /2}[/tex] * [tex]\sqrt{\frac{S_1}{n_1} +\frac{S_2}{n_2} }[/tex]
[tex]t_{n_1+n_2-2; 1-\alpha /2}= t_{110; 0.925}= 1.450[/tex]
Point estimate: ([tex]\frac{}{X}[/tex]₁- [tex]\frac{}{X}[/tex]₂) = (195-165)= 30
Margin of error:[tex]t_{n_1+n_2-2; 1-\alpha /2}[/tex] * [tex]\sqrt{\frac{S_1}{n_1} +\frac{S_2}{n_2} }[/tex]= 1.450*0.54= 0.783
30 ± 0.783
[29.217; 30.783]
With a 85% confidence level you'd expect the teenage boys to be on average between [29.217; 30.783]cm taller than the girls.
I hope this helps!
Miguel is playing a game in which a box contains four chips with numbers written on them. Two of the chips have the number 1, one chip has the number 3, and the other chip has the number 5. Miguel must choose two chips, and if both chips have the same number, he wins $2. If the two chips he chooses have different numbers, he loses $1 (–$1). • Let X = the amount of money Miguel will receive or owe. Fill out the missing values in the table. (Hint: The total possible outcomes are six because there are four chips and you are choosing two of them.) Xi 2 –1 P(xi) • What is Miguel’s expected value from playing the game? • Based on the expected value in the previous step, how much money should Miguel expect to win or lose each time he plays? • What value should be assigned to choosing two chips with the number 1 to make the game fair? Explain your answer using a complete sentence and/or an equation.
Answer:
See explanation
Step-by-step explanation:
Step 1Miguel wins $2 is if he pulls two chips with the number 1.
Probability of winning is:
2/4 * 1/3 = 1/6 as there are 4 chips in totalProbability of loosing is:
1- 1/6 = 5/6Step 2Missing values we found in the step 1, can be populated in the table:
Xi === 2 === -1P(Xi) === 1/6 === 5/6Expected Value as per table data:
1/6*2 + 5/6*(-1) = -1/2Expected value is $1/2 loss each time he plays
Step 3To make the game fair, the expected value should be zero.
Then as per the calculation above, let's replace 2, with x, and find its value.
1/6x + 5/6*(-1) = 0 1/6x = 5/6 x= 5So the amount should be $5 to make the game fair.