Answers
Answer:
C. 57 degrees.
Step-by-step explanation:
It's a line, so it adds to 180 degrees. The interior angle is 180 - 114 = 66 degrees.
A triangle adds up to 180 degrees. Subtract 66 to get 114 degrees. This means the two remaining angles in the triangle add up to 114 degrees. Since they are identical (both are the same because they use the same variable), you can divide 114 by two.
The final answer is 57 degrees.
Let me know if you have any questions.
Explanation:
Since the line is 114 we can divide by 2 to get the answer. So 57+57=114 or 57*2=114
Related Questions
Find the general formula for the following sequence.
300000, 480000, 768000, 1228800, 1966080, ....
Answers
Answer:
3,145,728
Step-by-step explanation:
x1.6
300000 x 1.6 = 4800000
480000 x 1.6 = 7680000
768000 x 1.6 = 1228800
122800 x 1.6 = 1966080
1966080 x 1.6 = 3145728
The shape of the distribution of the time required to get an oil change at a 15-minute oil-change facility is unknown. However, records indicate that the mean time is 16.2 minutes, and the standard deviation is 3.4 minutes.
Requried:
a. What is the probabilty that a random sample of n = 40 oil changes results in a sample mean time less than 15 minutes?
b. Suppose the manager agrees to pay each employee a $50 bonus if they meet a certain goal. On a typical Saturday, the oil-change facility will perform 40 oil changes between 10 A.M. and 12 P.M. Treating this as a random sample, there
would be a 10% chance of the mean oil-change time being at or below what value? This will be the goal established by the manager.
Answers
Answer:
(a) Probability that a random sample of n = 45 oil changes results in a sample mean time < 10 minutes i=0.0001.
(b) The mean oil-change time is 15.55 minutes.
Step-by-step explanation:
Let us denote the sample mean time as x
From the Then x = mean time = 16.2 minutes
The given standard deviation = 3.4 minutes
The value of n sample size = 45
CHECK THE ATTACHMENT FOR DETAILED EXPLANATION
consider a politician discussion group consisting of eight Democrats three Republicans and seven Independents suppose that two group members are randomly selected in succession to attend political convention find the probability of selecting an independent and then a Democrat
Answers
Answer:
(38.8%...7/10), than (47%...8/17) I didnt know if u needrd it in fraction or percent.
Step-by-step explanation:
You want to first add up everyone. So in total there are 18 people.
There is than a 38.8% chance that a independent will be picked first. 7/18.
But since one person was picked already you have to subtract 1 person from the total, so now its out of 17.
There is now a 47% chance that a democrat will be picked next. 8/17.
[10 points] A manufacturer wants to design an open box having a square base and a surface area of 108 square inches. What dimensions will produce a box with maximum volume?
Answers
Answer:
6 inches square by 3 inches high
Step-by-step explanation:
For a given surface area, the volume of an open-top box is maximized when it has the shape of half a cube. If the area were than of the whole cube, it would be 216 in² = 6×36 in².
That is, the bottom is 6 inches square, and the sides are 3 inches high.
_____
Let x and h represent the base edge length and box height, respectively. Then we have ...
x² +4xh = 108 . . . . box surface area
Solving for height, we get ...
h = (108 -x²)/(4x) = 27/x -x/4
The volume is the product of base area and height, so is ...
V = x²h = x²(27/x -x/4) = 27x -x³/4
We want to maximize the volume, so we want to set its derivative to zero.
dV/dx = 0 = 27 -(3/4)x²
x² = (4/3)(27) = 36
x = 6
h = 108/x² = 3
The box is 6 inches square and 3 inches high.
_____
Comment on maximum volume, minimum area
In the general case of an open-top box, the volume is maximized when the cost of the bottom and the cost of each pair of opposite sides is the same. Here, the "cost" is simply the area, so the area of the bottom is 1/3 the total area, 36 in².
If the box has a closed top, then each pair of opposite sides will have the same cost for a maximum-volume box. If costs are uniform, the box is a cube.
A manufacturing company measures the weight of boxes before shipping them to the customers. Assume that the weights of boxes are normally distributed with mean 90 lbs and standard deviation 24 lbs. a) Find the probability that a randomly selected box will exceed 94 lbs. b) If a sample of 36 boxes is randomly selected, find the probability that the average of the boxes exceeds 94 lbs.
Answers
Answer:
24
Step-by-step explanation:
I NEED HELP PLEASE, THANKS! :)
Answers
Answer:
68
Step-by-step explanation:
The number of chips tested is the integral of the rate over the specified time interval: t = 2 to 6.
[tex]\displaysyle n=\int_2^6{-3t^2+16t+5}\,dt=\left.-3\dfrac{t^3}{3}+16\dfrac{t^2}{2}+5t\right|_2^6\\\\=-(6^3-2^3) +8(6^2-2^2)+5(6-2)=-(216-8)+8(32) +5(4)\\\\=-208+256+20=\boxed{68}[/tex]
The technician can test 68 chips in that time period.
32 percent of the customers of a fast food chain order the Whopper, French fries and a drink. A random sample of 10 cash register receipts is selected. What is the probability that eight receipts will show that the above three food items were ordered?
Answers
Answer: 0.0023
Step-by-step explanation:
Let X be the binomial variable that represents the number of receipts will show that the above three food items were ordered.
probability of success p = 32% = 0.32
Sample size : n= 10
Binomial probability function :
[tex]P(X=x)= \ ^nC_xp^x(1-p)^{n-x}[/tex]
Now, the probability that eight receipts will show that the above three food items were ordered :
[tex]P(X=8)=\ ^{10}C_8(0.32)^8(1-0.32)^2\\\\=\dfrac{10!}{8!2!}(0.32)^8(0.68)^2\\\\=5\times9(0.0000508414176684)\\\\=0.00228786379508\approx0.0023[/tex]
hence, the required probability = 0.0023
Would this be correct even though I didn’t use the chain rule to solve?
Answers
Answer:
Dy/Dx=1/√ (2x+3)
Yeah it's correct
Step-by-step explanation:
Applying differential by chain differentiation method.
The differential of y = √(2x+3) with respect to x
y = √(2x+3)
Let y = √u
Y = u^½
U = 2x +3
The formula for chain differentiation is
Dy/Dx = Dy/Du *Du/Dx
So
Dy/Dx = Dy/Du *Du/Dx
Dy/Du= 1/2u^-½
Du/Dx = 2
Dy/Dx =( 1/2u^-½)2
Dy/Dx= u^-½
Dy/Dx=1/√ u
But u = 2x+3
Dy/Dx=1/√ (2x+3)
A takeaway sells 10-inch pizzas and 12-inch pizzas.
Answers
The profit made in week 1 is 0.69 and week 2 is 0.71.
What is Proportion?In general, the term "proportion" refers to a part, share, or amount that is compared to a total.
According to the concept of proportion, two ratios are in proportion when they are equal.
A mathematical comparison of two numbers is called a proportion. According to proportion, two sets of provided numbers are said to be directly proportional to one another if they increase or decrease in the same ratio. "::" or "=" are symbols used to indicate proportions.
Given:
A takeaway sells 10-inch pizzas and 12-inch pizzas.
From the table
For week 1:
Proportion= 509/ 736 = 0.69
and, week 2:
Proportion= 765/ 1076 = 0.71
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Find the slope of the line passing through (6,8) and (-10,3)
Answers
Answer:
5/16
Step-by-step explanation:
Use the formula to find slope when 2 points are given.
m = rise/run
m = y2 - y1 / x2 - x1
m = 3 - 8 / -10 - 6
m = -5 / -16
m = 5/16
The slope of the line is 5/16.
Answer: m=5/16
Step-by-step explanation:
Can someone teach me how to solve this problem please:)
Answers
Answer:
x= -3, y= -5
or x= 5, y=3
Step-by-step explanation:
① Label the 2 equations
x² +y²= 34 -----(1)
3x -3y= 6 -----(2)
From (2):
x -y= 2 -----(3)
Notice that (x-y)²= x² -2xy +y²
Thus, (equation 3)²= (equation 1) -2xy
Squaring (3):
(x -y)²= 2²
(x -y)²= 4
Expand terms in bracket:
x² -2xy +y²= 4
x² +y² -2xy= 4 -----(4)
subst. (1) into (4):
34 -2xy= 4
2xy= 34 -4 (bring constant to 1 side)
2xy= 30 (simplify)
xy= 30 ÷2 (÷2 throughout)
xy= 15 -----(5)
From (3):
x= y +2 -----(6)
I'll rewrite 2 of the equations.
x= y +2 -----(6)
xy= 15 -----(5)
Subst. (6) into (5):
y(y+2)= 15
y² +2y= 15
y² +2y -15= 0
(y +5)(y -3)=0
y+5= 0 or y-3=0
y= -5 or y= 3
Subst. into (6):
x= -5 +2 or x= 3 +2
x= -3 or x= 5
Answer:
y=-5, y=3
x=-3., x=5
Step-by-step explanation:
x^2+y^2=34
3x-3y=6
isolate x in te equation
3x-3y=6
x=3/3 y+6/3
x=y+2
plug the y+2 in the equation:
x^2+y^2=34
(y+2)^2+y^2=34
y^2+4y+4+y^2=34
2y^2+4y=34-4
2y^2+4y=30 divide by 2
y^2+2x-15=0 factorize
(y+5)(y-3)=0 eiter y+5=0 ten y=-5 or y-3=0 then y=3
now plug the solution in the equation
3x-3y=6
3x-3(-5)=6
3x=6-15
x=-9/3=-3
for y=3
3x-3y=6
3x-9=6
3x=15
x=5
Besides the 90° angle measure, what are the other two angle measures of a right triangle with side lengths 5, 12, and 13? Round to the nearest degree.
Answers
Answer:
45
Step-by-step explanation:
I really don't but it seems right
Answer:
b
Step-by-step explanation:
just did it on edge
An integer is 3 less than 5 times another. If the product of the two integers is 36, then find the integers.
Answers
Answer:
3, 12
Step-by-step explanation:
Et x and y be the required integers.
Case 1: x = 5y - 3...(1)
Case 2: xy = 36
Hence, (5y - 3)*y = 36
[tex]5 {y}^{2} - 3y = 36 \\ 5 {y}^{2} - 3y - 36 = 0 \\ 5 {y}^{2} - 15y + 12y - 36 = 0 \\ 5y(y - 3) + 12(y - 3) = 0 \\ (y - 3)(5y + 12) = 0 \\ y - 3 = 0 \: or \: 5y + 12 = 0 \\ y = 3 \: \: or \: \: y = - \frac{12}{5} \\ \because \: y \in \: I \implies \: y \neq - \frac{12}{5} \\ \huge \purple{ \boxed{ \therefore \: y = 3}} \\ \because \: x = 5y - 3..(equation \: 1) \\ \therefore \: x = 5 \times 3 - 3 = 15 - 3 = 12 \\ \huge \red{ \boxed{ x = 12}}[/tex]
Hence, the required integers are 3 and 12.
let
x = one integer
y = another integer
x = 5y - 3
If the product of the two integers is 36, then find the integers.
x * y = 36
(5y - 3) * y = 36
5y² - 3y = 36
5y² - 3y - 36 = 0
Solve the quadratic equation using factorization method
That is, find two numbers whose product will give -180 and sum will give -3
Note: coefficient of y² multiplied by -36 = -180
5y² - 3y - 36 = 0
The numbers are -15 and +12
5y² - 15y + 12y - 36 = 0
5y(y - 3) + 12 (y - 3) = 0
(5y + 12) (y - 3) = 0
5y + 12 = 0 y - 3 = 0
5y = - 12 y = 3
y = -12/5
The value of y can not be negative
Therefore,
y = 3
Substitute y = 3 into x = 5y - 3
x = 5y - 3
x = 5(3) - 3
= 15 - 3
= 12
x = 12
Therefore,
(x, y) = (12, 3)
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Professor Sanchez has been teaching Principles of Economics for over 25 years. He uses the following scale for grading. Grade Numerical Score Probability A 4 0.090 B 3 0.240 C 2 0.360 D 1 0.165 F 0 0.145 a. Convert the above probability distribution to a cumulative probability distribution. (Round your answers to 3 decimal places.)
Answers
The question is incomplete! Complete question along with answer and step by step explanation is provided below.
Question:
Professor Sanchez has been teaching Principles of Economics for over 25 years. He uses the following scale for grading. Grade Numerical Score Probability A 4 0.090 B 3 0.240 C 2 0.360 D 1 0.165 F 0 0.145
a. Convert the above probability distribution to a cumulative probability distribution. (Round your answers to 3 decimal places.)
b. What is the probability of earning at least a B in Professor Sanchez’s course? (Round your answer to 3 decimal places.)
c. What is the probability of passing Professor Sanchez’s course? (Round your answer to 3 decimal places.)
Answer:
a. Cumulative Probability Distribution
Grade P(X ≤ x)
F 0.145
D 0.310
C 0.670
B 0.910
A 1
b. P(at least B) = 0.330
c. P(pass) = 0.855
Step-by-step explanation:
Professor Sanchez has been teaching Principles of Economics for over 25 years.
He uses the following scale for grading.
Grade Numerical Score Probability
A 4 0.090
B 3 0.240
C 2 0.360
D 1 0.165
F 0 0.145
a. Convert the above probability distribution to a cumulative probability distribution. (Round your answers to 3 decimal places.)
The cumulative probability distribution is given by
Grade = F
P(X ≤ x) = 0.145
Grade = D
P(X ≤ x) = 0.145 + 0.165 = 0.310
Grade = C
P(X ≤ x) = 0.145 + 0.165 + 0.360 = 0.670
Grade = B
P(X ≤ x) = 0.145 + 0.165 + 0.360 + 0.240 = 0.910
Grade = A
P(X ≤ x) = 0.145 + 0.165 + 0.360 + 0.240 + 0.090 = 1
Cumulative Probability Distribution
Grade P(X ≤ x)
F 0.145
D 0.310
C 0.670
B 0.910
A 1
b. What is the probability of earning at least a B in Professor Sanchez’s course? (Round your answer to 3 decimal places.)
At least B means equal to B or greater than B grade.
P(at least B) = P(B) + P(A)
P(at least B) = 0.240 + 0.090
P(at least B) = 0.330
c. What is the probability of passing Professor Sanchez’s course? (Round your answer to 3 decimal places.)
Passing the course means getting a grade of A, B, C or D
P(pass) = P(A) + P(B) + P(C) + P(D)
P(pass) = 0.090 + 0.240 + 0.360 + 0.165
P(pass) = 0.855
Alternatively,
P(pass) = 1 - P(F)
P(pass) = 1 - 0.145
P(pass) = 0.855
The number of degrees of freedom for the appropriate chi-square distribution in a test of independence is a. k – 1. b. A chi-square distribution is not used. c. number of rows minus 1 times number of columns minus 1. d. n – 1.
Answers
Answer:
Option C
Step-by-step explanation:
The chi square test of independence is used to determine if there is a significant association between two categorical variables from a population.
It tests the claim that the row and column variables are independent of each other.
The degrees of freedom for the chi-square are calculated using the following formula: df = (r-1) (c-1) where r is the number of rows and c is the number of columns.
F(x)+6x+11 inverse function
Answers
Answer:
y = x/6 − 11/6
Step-by-step explanation:
y = 6x + 11
To find the inverse, switch x and y, then solve for y.
x = 6y + 11
x − 11 = 6y
y = x/6 − 11/6
The ratio of the areas of two circles is 121/100. What is the ratio of the radii of the two circles
Answers
Answer:
11/10
Step-by-step explanation:
The area ratio is the square of the radius ratio (k):
(121/100) = k²
k = √(121/100) = 11/10
The ratio of radii is 11/10.
At the farm, corn costs $2.50 per pound. How much would 3 1/2 pounds of corn cost? Write your answer in dollars and cents.
Answers
Multiply price per pound by total pounds:
2.50 x 3.5 = 8.75
Total cost = $8.75
Answer:
The cost is $8.75 for 3.5 lbs
Step-by-step explanation:
The rate is 2.50 per pound
Multiply the number of pounds by the rate
3.5 * 2.50 =8.75
The cost is $8.75 for 3.5 lbs
Pls help me help me
Answers
Answer:
C. -4/3
Step-by-step explanation:
Perpendicular lines have negative reciprocal slopes.
We know that line m is perpendicular to line l.
Line l has a slope of 3/4. To find the slope of line m, find the negative reciprocal of 3/4. Negate the fraction and find the reciprocal.
Negative: switch the sign
3/4 --> -3/4
Reciprocal: switch the numerator (top number) and denominator (bottom number)
-3/4 --> -4/3
Line m has a slope of -4/3 and C is correct.
Use matrix operations to solve the following systems of linear equations. Use comments to explain which value is x1, x2, etc
3x1-10 x2- 5x3+30x4 = -1
4x1+7x2+ 5x3- 3x4=0
x2+ x3-3x4 =1
x1-2x2-10x3+6x4 = -1
Answers
Answer:
x⁴ = -0.955939
x³ = 0.206897
x² = -2.07471
x = 2.65517
Step-by-step explanation:
Step 1: Rewrite equations in standard form
30x⁴ - 5x³ - 10x² + 3x = -1
-3x⁴ + 5x³ + 7x² + 4x = 0
-3x⁴ + x³ + x² = 1
6x⁴ - 10x³ - 2x² + x = -1
Step 2: Write in matrix form
Top Row: [30 -5 -10 3 | -1]
2nd Row: [-3 5 7 4 | 0]
3rd Row: [-3 1 1 0 0 | 1]
Bottom Row: [6 -10 -2 1 | -1]
Step 3: Plug in calc with RREF function
Top Row: [1 0 0 0 | -499/522]
2nd Row: [0 1 0 0 | 6/29]
3rd Row: [0 0 1 0 | -361/174]
4th Row: [0 0 0 1 | 77/29]
Determine the area (in units2) of the region between the two curves by integrating over the x-axis. y = x2 − 24 and y = 1
Answers
The area bounded by region between the curve [tex]y = x^2- 24[/tex] and [tex]y = 1[/tex] is
[tex]0[/tex] square units.
To find the Area,
Integrate the difference between the two curves over the interval of intersection.
Find the points of intersection between the curves [tex]y = x^2- 24[/tex] and [tex]y = 1[/tex] .
The point of Intersection is the common point between the two curve.
Value of [tex]x[/tex] and [tex]y[/tex] coordinate will be equal for both curve at point of intersection
In the equation [tex]y = x^2- 24[/tex], Put the value of [tex]y = 1[/tex].
[tex]1 = x^2-24[/tex]
Rearrange, like and unlike terms:
[tex]25 = x^2[/tex]
[tex]x =[/tex] ±5
The point of intersection for two curves are:
[tex]x = +5[/tex] and [tex]x = -5[/tex]
Integrate the difference between the two curve over the interval [-5,5] to calculate the area.
Area = [tex]\int\limits^5_{-5} {x^2-24-1} \, dx[/tex]
Simplify,
[tex]= \int\limits^5_{-5} {x^2-25} \, dx[/tex]
Integrate,
[tex]= [\dfrac{1}{3}x^3 - 25x]^{5} _{-5}[/tex]
Put value of limits in [tex]x[/tex] and subtract upper limit from lower limit.
[tex]= [\dfrac{1}{3}(5)^3 - 25(5)] - [\dfrac{1}{3}(-5)^3 - 25(-5)][/tex]
= [tex]= [\dfrac{125}{3} - 125] - [\dfrac{-125}{3} + 125][/tex]
[tex]= [\dfrac{-250}{3}] - [\dfrac{-250}{3}]\\\\\\= \dfrac{-250}{3} + \dfrac{250}{3}\\\\\\[/tex]
[tex]= 0[/tex]
The Area between the two curves is [tex]0[/tex] square units.
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Calculate the volume of a rectangular prism with a length of 4.4 cm, a width of 3.1 cm, and a height of 6.3 cm. (As before, you do not need to enter the units since they are provided to the right of the answer box.)
Answers
Answer:
85.932 cm³
Step-by-step explanation:
The volume of rectangular prism is obtained as the product of its length (l) by its width (w) and by its height (h):
[tex]V=l*w*h[/tex]
The volume of a prism with a length of 4.4 cm, a width of 3.1 cm, and a height of 6.3 cm is:
[tex]V=4.4*3.1*6.3\\V=85.932\ cm^3[/tex]
The volume of this prism is 85.932 cm³.
You must estimate the mean temperature (in degrees Fahrenheit) with the following sample temperatures: 44 32.8 59.2 31.4 12.7 68.5 84.7 72.5 55.7 Find the 98% confidence interval. Enter your answer as an open-interval (i.e., parentheses) accurate to two decimal places (because the sample data are reported accurate to one decimal place). 98% C.I.
Answers
Answer:
[tex] 51.278 -2.896 \frac{22.979}{\sqrt{9}}= 29.096[/tex]
[tex] 51.278 +2.896 \frac{22.979}{\sqrt{9}}= 73.460[/tex]
And the interval would be:
[tex] (29.10 \leq \mu \leq 73.46)[/tex]
Step-by-step explanation:
For this problem we have the following dataset given:
44 32.8 59.2 31.4 12.7 68.5 84.7 72.5 55.7
We can find the mean and sample deviation with the following formulas:
[tex] \bar X= \frac{\sum_{i=1}^n X_i}{n}[/tex]
[tex] s=\sqrt{\frac{\sum_{i=1}^n (X_i -\bar X)^2}{n-1}}[/tex]
And replacing we got:
[tex]\bar X= 51.278[/tex]
[tex] s= 22.979[/tex]
The confidence interval for the mean is given by:
[tex] \bar X \pm t_{\alpha/2} \frac{s}{\sqrt{n}}[/tex]
The degrees of freedom are:
[tex] df=n-1= 9-1=8[/tex]
The confidence would be 0.98 and the significance [tex]\alpha=0.02[/tex] then the critical value would be:
[tex] t_{\alpha/2}= 2.896[/tex]
Ad replacing we got:
[tex] 51.278 -2.896 \frac{22.979}{\sqrt{9}}= 29.096[/tex]
[tex] 51.278 +2.896 \frac{22.979}{\sqrt{9}}= 73.460[/tex]
And the interval would be:
[tex] (29.10 \leq \mu \leq 73.46)[/tex]
Identify whether the given value is a discrete random variable, a continuous random variable, or if it is not a random variable:
1) A college basketball player's height that is reported in the game-day program
2) The color of a student's car
3) The exact weight of an airline passenger's carry-on bag
Answers
Answer:
1. continuous random variable
2. not a random variable
3. a continuous random variable
Step-by-step explanation:
The classifications are as follow
a) The height of the player reported in the game day program is treated as a continuous random variable as these values could be determined through measuring them
b) The color of student car is not a random variable as it does not contain any quantitative data or we can say numerical data
c) The exact weight of the bag is a continuous variable as it is lie between the range
g A CD player with an original price of $380.00 is on sale at 35% off. What is the discount amount and the CD player sale price?
Answers
Answer:
Cost: $247
Discount: $133
Step-by-step explanation:
Simply multiply 380 and 35% off together to get your answer:
380(1 - 0.35)
380(0.65)
247
To find the discount amount, simply subtract the 2 numbers to get your answer:
380 - 247 = 133
Among 20 golden hamster litters recorded, there was a sample mean of =7.72 baby hamsters, with a sample standard deviation of s=2.5 hamsters per liter. Create a 98% confidence interval for the mean number of baby hamsters per liter.
Answers
Answer:
[tex] 7.72 -2.539 \frac{2.5}{\sqrt{20}} =6.30[/tex]
[tex] 7.72 +2.539 \frac{2.5}{\sqrt{20}} =9.14[/tex]
Step-by-step explanation:
For this case we have the following info given:
[tex]\bar X= 7.72[/tex] represent the sample mean
[tex]s= 2.5[/tex] represent the sample deviation
[tex] n=20[/tex] represent the sample size
The confidence interval is given by:
[tex] \bar X \pm t_{\alpha/2} \frac{s}{\sqrt{n}}[/tex]
The confidence interval is 98% and the significance level is [tex]\alpha=0.02[/tex] the degrees of freedom are given by:
[tex] df= n-1 = 20-1=19[/tex]
And the critical value would be:
[tex] t_{\alpha/2}= 2.539[/tex]
And replacing we got:
[tex] 7.72 -2.539 \frac{2.5}{\sqrt{20}} =6.30[/tex]
[tex] 7.72 +2.539 \frac{2.5}{\sqrt{20}} =9.14[/tex]
The 98% confidence interval is between 6.42 hamsters per liter to 9.02 hamsters per liter
Mean (μ) = 7.72, standard deviation (σ) = 2.5, sample size (n) = 20, Confidence (C) = 98% = 0.98
α = 1 - C = 0.02
α/2 = 0.01
The z score of α/2 is the same as the z score of 0.49 (0.5 - 0.01) which is equal to 2.326.
The margin of error E is:
[tex]E = Z_\frac{\alpha }{2} *\frac{\sigma}{\sqrt{n} } \\\\E=2.326*\frac{2.5}{\sqrt{20} } =1.3[/tex]
The confidence interval = (μ ± E) = (7.72 ± 1.3) = (6.42, 9.02)
Hence the 98% confidence interval is between 6.42 hamsters per liter to 9.02 hamsters per liter
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Consider rolling dice and getting a total of 8. Find the probability if two dice are rolled. (Enter the value of probability in decimals. Round the answer to three decimal places.)
Answers
Answer:
13.89%
Step-by-step explanation:
The probability when two dices are rolled and their sum is 8 is shown below:
But before that we need to see the probabilities of the sum i.e 8
2 + 6 = 8
3 + 5 = 8
4 + 4 = 8
5 + 3 = 8
6 + 2 = 8
There are 5 outcomes
And, the two dice is 36 i.e square of 6
So, the probability of two dices are rolled and their sum is 8 is
= [tex]\frac{5}{36}[/tex]
= 13.89%
help with this I don't know how to solve please and thanks
Answers
Answer:
6.5 ft
Step-by-step explanation:
When we draw out our picture of our triangle and label our givens, we should see that we need to use cos∅:
cos57° = x/12
12cos57° = x
x = 6.53567 ft
whats the answer ?? ill mark brainliest
Answers
Answer:
[tex]\boxed{Option A ,D}[/tex]
Step-by-step explanation:
The remote (non-adjacent) interior angles of the exterior angle 1 are <4 and <6
In a large city, the city supervisor wants to find the average number of aluminum cans that each family recycles per month. So, she surveys 18 families and finds that these 18 families recycle an average of 140 cans per month with a standard deviation of 26 cans per month. Find the 90 % confidence interval for the mean number of cans that all of the families in the city recycle per month.
Answers
Answer:
The 90% onfidence interval for the mean number of cans that all of the families in the city recycle per month is between 129.34 and 150.66 cans per month
Step-by-step explanation:
We have the standard deviation of the sample, so we use the t-distribution to solve this question.
The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So
df = 18 - 1 = 17
90% confidence interval
Now, we have to find a value of T, which is found looking at the t table, with 17 degrees of freedom(y-axis) and a confidence level of [tex]1 - \frac{1 - 0.9}{2} = 0.95[/tex]. So we have T = 1.74
The margin of error is:
[tex]M = T\frac{s}{\sqrt{n}} = 1.74\frac{26}{\sqrt{18}} = 10.66[/tex]
In which s is the standard deviation of the sample and n is the size of the sample.
The lower end of the interval is the sample mean subtracted by M. So it is 140 - 10.66 = 129.34 cans per month
The upper end of the interval is the sample mean added to M. So it is 140 + 10.66 = 150.66 cans per month.
The 90% onfidence interval for the mean number of cans that all of the families in the city recycle per month is between 129.34 and 150.66 cans per month