Answers
Answer:
∛(2b)
Step-by-step explanation:
[tex]\displaystyle\frac{\sqrt[3]{4b^2}}{\sqrt[3]{2b}}=\sqrt[3]{\frac{4b^2}{2b}}=\sqrt[3]{2b}[/tex]
Related Questions
What is the least angle measure by which this figure can be rotated so that it maps onto itself?
45°
90°
180°
360°
Answers
Answer:
The correct answer is 90
Step-by-step explanation:
Mike recently increased the size of his Jeep tires from the original 29 inch diameter to the larger 33.73 inch diameter. If Mike didn't recalibrate his speedometer, how fast is he really going on the new tires when his speedometer shows he is traveling 60 mph?
a. 54.5 mph
b. 62.1 mph
c. 66.1 mph
d. 69.8 mph
Answers
Answer:
d. 69.8 mph
Step-by-step explanation:
Since, the ratio of the diameter of the tyre of a vehicle and its speed must be constant,
Given,
The original diameter of the tyre = 29 inch,
Original speed = 60 mph,
Thus, the ratio of diameter and the speed of the vehicle = [tex]\frac{29}{60}[/tex]
New diameter of the tyre = 33.73 inch,
Let x be the new speed of the vehicle = [tex]\frac{33.73}{x}[/tex]
[tex]\implies \frac{29}{60}=\frac{33.73}{x}[/tex]
[tex]\implies x=\frac{33.73\times 60}{29}=69.79\approx 69.8\text{ mph}[/tex]
Hence, the actual speed of the vehicle would be 69.8 mph.
OPTION D is correct.
A sample of n = 9 college students is used to evaluate the effectiveness of a new Study Skills Workshop. Each student’s grade point average (GPA) is recorded for the semester before the workshop and for the semester after the workshop. The average GPA improved by MD = 0.60 points with s2 = 0.09. The researcher would like to use the sample to estimate how much effect the workshop would have for the entire college population. Which of the following is the 80% confidence interval for these data?
A) μD = 0.60 ± 0.09( 1.860)
B) μD = 0.60 ± 0.10(1.397)
C) μD = 0.60 ± 0.01(1.397)
D) μD = 0.60 ± 0.10( 1.860)
Answers
Answer:
B) μD = 0.60 ± 0.10(1.397)
Step-by-step explanation:
The confidence interval is given by:
[tex]MD±t_{\alpha/2, n-1} \frac{s}{\sqrt{n} }[/tex]
Where
MD=60
n=9
df=n-1=8
[tex]t_{\alpha/2, n-1}=1.397[/tex]
[tex]s=\sqrt{0.09} =0.3[/tex]
Then the confidence interval is
μD=0.60±1.397*(0.3/√9)
μD=0.60±0.10*(1.397)
What are the coordinates of the hole in the graph of the function?
Answers
Answer:
The answer to your question is: (5/2, -6)
Step-by-step explanation:
Given f(x) = (6x - 36) / (2x² - 17x + 30)
Factorize both, numerator and denominator
Numerator = 6(x - 6)
Denominator = 2x² - 12x - 5x + 30
= 2x(x - 6) - 5(x - 6)
= (x - 6) (2x - 5)
Now f(x) = 6(x - 6) / (x - 6) (2x - 5) Cancel (x - 6)
f(x) = 6 / 2x - 5
Find the hole 2x - 5 = 0
2x = 5
x = 5/2
In 5/2 there is a hole, in y is approximately -6
Billy estimates that they will sell approximately 250 burgers thisweekend how much burger meat and fries (in pounds) should he order to be prepared for this weekend
Answers
Answer:
300 Burgers
Step-by-step explanation:
Since the question gives us an approximation of 250 burgers, we can round the number to 300. This is only because they had a estimation of 250 and would like to be prepared for the weekend. Being prepared would consist of ordering more than expected to make sure the burgers do not run out.
A blueprint shows a house with two fences. Fence A is 1 4/5 inches long on the blueprint and is to be 1 1/2 feet long. How long is Fence B on the blueprint?
Answers
The problem is about finding a length on a blueprint using scale factor. A ratio is established between blueprint measurements and real-life measurements. However, information about Fence B's actual size is needed to calculate its blueprint length.
Explanation:The subject of this question is mathematics, more specifically proportionality and scale factor. To solve this problem, you need to establish the ratio or scale represented by the blueprint to the actual size. In the given problem, 1 4/5 inches on the blueprint represents 1 1/2 feet in real life. First, convert the measures to improper fractions to easily manage the computations. Hence, 1 4/5 becomes 9/5 inches and 1 1/2 feet becomes 3/2 feet. The scale becomes 9/5 inches:3/2 feet on blueprint:real life. Now, we need additional information about the actual size of Fence B to calculate its length on the blueprint.
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A school administrator will assign each student in a group of n students to one of m classrooms. If 3 < m < 13 < n, is it possible to assign each of the n students to one of the m classrooms so that each classroom has the same number of students assigned to it?A school administrator will assign each student in a group of n students to one of m classrooms. If 3 < m < 13 < n, is it possible to assign each of the n students to one of the m classrooms so that each classroom has the same number of students assigned to it?
Answers
Answer: So you have n students, where n>13, and m classrooms, where 3>m>13.
the question asked is: is it possible to assign each of the n students to one of the m classrooms so that each classroom has the same number of students assigned to it?
The only situation where it will be possible is when you take the total number of students, divide it by the number of classrooms and the result is a whole number ( because here we are working with students, you can't have a 2/5 of a student, for example)
So n/m must be a natural number.
So now suppose that n is prime, this is : n only can be divided by itself, an example of a prime number is 17.
so if you have n = 17 students, there is no m that divides 17 into a whole number, then in this case, you can't assign the same number of students to each classroom.
And because we find a counterexample, so it is not possible for every n and m, so the statement is false. ( independent of the fact that you actually could do this for some m and n given, the important thing here is that you can't do it for every combination of m and n)
Assume that a procedure yields a binomial distribution with a trial repeated n = 20 times. Use either the binomial probability formula (or technology) to find the probability of k = 14 successes given the probability p = 0.72 of success on a single trial.
Answers
Answer:
the probability is 0.1879
Step-by-step explanation:
If a procedure yields a binomial distribution, the probability of having k successes is given by:
[tex]P(k)=nCk*p^{k} *(1-p)^{n-k}[/tex]
Where nCk is calculated as:
[tex]nCk=\frac{n!}{k!(n-k)!}[/tex]
Additionally, n is the number of trials and p is the probability of success in every trial.
Replacing, k by 14, n by 20 and p by 0.72 we get:
[tex]20C14=\frac{20!}{14!(20-14)!}=38,760[/tex]
[tex]P(k)=20C14*0.72^{14} *(1-0.72)^{20-14}[/tex]
[tex]P(k)=38,760*0.72^{14} *(1-0.72)^{20-14}\\P(k)=0.1879[/tex]
So, the probability is 0.1879
To find the probability of 14 successes given a binomial distribution with a trial repeated 20 times and a probability of success of 0.72 on a single trial, use the binomial probability formula.
Explanation:To find the probability of 14 successes given a binomial distribution with a trial repeated 20 times and a probability of success of 0.72 on a single trial, we can use the binomial probability formula. The formula is:
P(X = k) = C(n, k) * p^k * (1 - p)^(n - k)
Plugging in the values, we get:
P(X = 14) = C(20, 14) * 0.72^14 * (1 - 0.72)^(20 - 14)
Calculating this expression will give you the probability of 14 successes out of 20 trials.
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What is the geometric relationship between u, minusv, and uminusv?
A. The vectors u, minusv, and uminusv form a right triangle.
B. The vectors u, minusv, and uminusv form a parallelogram whose other vertex is at 0.
C. The vectors u, minusv, and uminusv form an equilateral triangle.
D. The vectors u, minusv, and uminusv form a parallelogram whose other vertex is at uplusv.
Answers
Answer:
C. The vectors u, minusv, and uminusv form a parallelogram whose other vertex is at 0.
Step-by-step explanation:
We draw the vector u=A at the origin of a Cartesian plane. then at the same point, we draw -v = -B. To find the vector that represents u-v = A-B, straight lines are drawn parallel to each vector, forming a parallelogram. The resulting vector will be the diagonal of the parallelogram that begins at the origin of the plane.
An irrational number is a real number and an integer.
True
False
Answers
Answer:
A real number is a number that is somewhere on a number line, so any number on a number line that isn't a rational number is irrational. The square root of 2 is an irrational number because it can't be written as a ratio of two integers
hope it helps!!
Step-by-step explanation:
Britney is going to the candy store to buy 20 pieces of candy. She is going to buy chocolate candy and caramel candy. Each piece of chocolate candy costs 50 cents, and each piece of caramel candy costs 10 cents. You know that Britney spent $6.80 and bought 20 pieces of candy. She bought ______ pieces of chocolate.
Answers
Marc is decorating 60 cupcakes for a school fund-raiser. He starts working at 1:00 P.M. In the afternoon, first setting up his supplies and then starting to decorate. At 1:05 P.M. He has 5 cupcakes decorated. At 1:08 P.M. He has 10 cupcakes decorated. If he decorates cupcakes at a constant rate, at what time that afternoon will he finish decorating the 60 cupcakes?
Answers
Answer:
1.38 pm.
Step-by-step explanation:
After 1.05 PM the rate at which he decorates the cakes is 10 - 5 = 5 cakes per 3 minutes = 5/3 cakes per minute. At 1.08 pm he has made 10 cupcakes.
At 1.08 he has to decorate another 50 cakes so the time he will take to do these is 50 / 5/3 = 50 * 3/5 = 30 minutes.
So the time when he finishes 60 cupcakes is 1.08 + 30
= 1.38 pm.
The 60 cupcakes will be decorated at 1.38 pm.
What is an expression?Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.
After 1.05 PM the rate at which he decorates the cakes is 10 - 5 = 5 cakes per 3 minutes = 5/3 cakes per minute. At 1.08 pm he made 10 cupcakes.
At 1.08 he has to decorate another 50 cakes so the time he will take to do these is 50 / 5/3 = 50 * 3/5 = 30 minutes.
The time when he finishes 60 cupcakes is:-
1.08 + 30 = 1.38 pm.
Therefore, 60 cupcakes will be decorated at 1.38 pm.
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Use the discriminant to describe the roots of each equation. Then select the best description.
x^2 - 4x + 4 = 0
double root
real and rational root
real and irrational root
imaginary root
Answers
Answer:
Hello My Friend! The correct answer its double root.
Step-by-step explanation:
In this equation, if we applie the a, b and c coefficients (a=1, b=4, c=4) ind the Bhaskara, the final result will be 4 for both cases. x'=4 and x''=4. It happens because the number of theta is equal to 0. So, both roots will be the same number.
A local technical school has 856 students. They expect 700 guests for a special speaker. The custodian has set up 1,500 chairs. How many more chairs are needed if all visitors and students are to have seats?
Answers
Answer:
56 chairs
Step-by-step explanation:
856+700=1556 <--- expected count
chairs set up= 1500
1556-1500= 56 more chairs
Answer: A.) 56 more
Step-by-step explanation:
What is the degree of the polynomial 5a6bc2+8d5+7e6f2−10g4h7 ? Enter your answer in the box.+
Answers
Answer:
11
Step-by-step explanation:
The degree of a polynomial is he highest of the degrees of its monomials (individual terms) with non-zero coefficients.
You are given the polynomial
[tex]5a^6bc^2+8d^5+7e^6f^2-10g^4h^7[/tex]
It consists of 4 terms:
[tex]5a^6bc^2[/tex][tex]8d^5[/tex][tex]7e^6f^2[/tex][tex]-10g^4h^7[/tex]The degrees are:
of the first term is [tex]6+1+2=9[/tex]of the second term is [tex]5[/tex]of the third term is [tex]6+2=8[/tex]of the fourth term is [tex]4+7=11[/tex]The greatest degree is 11.
Answer:
11
Step-by-step explanation:
I did the quiz
Circle the function types that are both increasing & decreasing for the same function. Choose all that apply.
A. Linear functions
B. Constant functions
C. Quadratic functions
D. Exponential functions
E. Linear absolute value functions
Answers
Quadratic functions and linear absolute value functions can be both increasing and decreasing within the same function. Linear, constant and exponential functions do not exhibit this behaviour.
Explanation:In mathematics, a function can be both increasing and decreasing at different parts of its graph. This means that the function's value increases for some parts of the domain (the x-values) and decreases for others. Not every function type can show this behavior. Let's consider the options:
A. Linear functions: These are either increasing or decreasing over their entire domain, so they are not both.B. Constant functions: These do not increase or decrease; their value remains constant.C. Quadratic functions: Depending on the shape of the parabola (opens upward or downward), quadratic functions can be both increasing and decreasing.D. Exponential functions: These are typically either entirely increasing or entirely decreasing, not both.E. Linear absolute value functions: These functions increase or decrease until they reach the vertex (the point of absolute value), then change direction. So they can be both increasing and decreasing as well.Therefore, the function types that can be both increasing and decreasing within the same function are quadratic functions and linear absolute value functions.
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-7y-4x=1
7y-2x=53
solve for system of equations
Answers
Answer:
x = -9
y = 35/7
Step-by-step explanation:
Given equations :-
-7y - 4x = 1 ....... ( i )
7y - 2x = 53 ........ ( ii )
From ( i )
-7y = 1 + 4x
[tex]y = \frac{ - (1 + 4x)}{7} [/tex]
..........( iii )
From ( ii )
7y - 2x = 53
7y = 53 + 2x
[tex]y = \frac{53 + 2x}{7} [/tex]
.......( iv )
Equating both ( iii ) & ( iv )
y = y
[tex] \frac{ - (1 + 4x)}{7} = \frac{53 + 2x}{7} [/tex]
-(1 + 4x ) = 53 + 2x
-1 -4x = 53 + 2x
-1 - 53 = 2x + 4x
-54 = 6x
-54/6 = x
-9 = x
Also,
[tex]y = \frac{ - (1 + 4x)}{7 } \\ \\ y = - \frac{(1 + 4( - 9))}{7} [/tex]
[tex]y = - \frac{ (1 - 36)}{7} \\ \\ y = - \frac{( - 35)}{7} \\ \\ y = \frac{35}{7} [/tex]
PLEASE HELP What is the equation in standard form of a parabola with a focus of (-3,2) and a directrix of y=4.
Answers
Graphing y = 4 and the focus, we clearly see that the equation we need has the form (x - h)^2 = 4a(y - k).
We need to find a, h and k.
The focus is half way between the vertex and directrix.
You know that y = 4 is 2 units away from the focus and the focus is 2 units down from the focus. So, our vertex is (-3, 0).
From the vertex to the directrix, there are 4 units. Half that distance is the value of a. So, a = 2.
We have all that is needed to form our equation.
(x - (-3))^2 = 4(2)(y - 0)
(x + 3)^2 = 8y
Done.
Answer:
i think this will help (x - (-3))^2 = 4(2)(y - 0)
(x + 3)^2 = 8y
Step-by-step explanation:
PLEASE HELP!!!!
WILL GIVE BRAINLY
Which statements are true?
Select each correct answer.
9g3+12=3(3g3+4)
35g5−25g2=5g2(7g3−5)
24g4+18g2=6g2(4g2+3g)
4g2−g=g2(4−g)
Answers
During the year, FastDry Corporation has $ 340,000 in revenues, $ 155,000 in expenses, and $ 12,000 in dividend declarations and payments. Net income for the year was:
Answers
Answer:
$185,000
Step-by-step explanation:
We have been been given that during the year, Fast Dry Corporation has $ 340,000 in revenues, $ 155,000 in expenses, and $ 12,000 in dividend declarations and payments.
We will use following formula to solve our given problem.
[tex]\text{Net income}=\text{Revenues}-\text{Expenses}[/tex]
[tex]\text{Net income}=\$340,000-\$155,000[/tex]
[tex]\text{Net income}=\$185,000[/tex]
Therefore, the net income for the year was $185,000.
Write the equation of the line perpindicular to the graph of 2x-5y=0 that passes through the point (-2,3)
Answers
Answer:
5x-2y=-4
Step-by-step explanation:
2x-5y=0
eq. of line perpendicular to ax+by=c is bx-ay=d,d is calculated by the given condition.
line perpendicular to 2x-5y=0 is 5x+2y=c
if it passes through (-2,3) ,then
5*-2+2*3=c
c=-10+6=-4
reqd. eq. is 5x+2y=-4
Three parking attendants are required to park cars for each blue lot , while two can handle each red lot. Of the 15 lots that will be used for tonight, 60% are blue and 40% are red. How many parking attendants are required for tonight's event
Answers
Answer:
[tex]39\ parking\ attendants[/tex]
Step-by-step explanation:
Let
x -----> the number of blue lots
y-----> the number of red lots
we know that
[tex]x+y=15[/tex] ------> equation A
we have that
[tex]x=0.60(15)=9\ blue\ lots[/tex]
[tex]y=0.40(15)=6\ red\ lots[/tex]
The total parking attendants required for tonight's event is equal to the product of the number of blue lots by three plus the product of the number of red lots by two
so
[tex]9(3)+6(2)=39\ parking\ attendants[/tex]
Answer:
39
Step-by-step explanation:
Please Help! I don't know where to start with this, please show all work!
What is the vertex form of the equation?
y = -x^2 + 12x - 4
Answers
Hey!
-------------------------------------
Formula's:
x_v = -b/2a
y_v = ax² + bx + c
-------------------------------------
Parabola Params:
a = -1
b = 12
c = 4
-------------------------------------
Solve for [tex]x_{v}[/tex]
[tex]x_{v} = \frac{-b}{2a}[/tex]
[tex]x_{v} = \frac{-12}{2(-1)}[/tex]
[tex]x_{v} = -6[/tex]
-------------------------------------
Solve for [tex]y_{v}[/tex]
Use -6 for [tex]x_{v}[/tex]
[tex]y_{v} = -6^2 + 12(6) - 4\\[/tex]
[tex]y_{v} = -36 + 72 - 4[/tex]
[tex]y_{v} = 32[/tex]
-------------------------------------
Answer:
(6, 32)
-------------------------------------
Hope This Helped! Good Luck!
A bag contains 99 red marbles and 99 blue marbles. Taking two marbles out of the bag, you:
• put a red marble in the bag if the two marbles you drew are the same color (both red or both
blue), and
• put a blue marble in the bag if the two marbles you drew are different colors.
Repeat this step (reducing the number of marbles in the bag by one each time) until only one
marble is left in the bag. What is the color of that marble?
Answers
The final marble left in the bag will be red.
Let, analyze the process step by step:
Initially, the bag contains 99 red marbles and 99 blue marbles.
When you take two marbles out of the bag, there are two possibilities: either you get two red marbles or two blue marbles, or you get one red and one blue marble.
a. If you get two marbles of the same color (both red or both blue), you put a red marble in the bag.
b. If you get one red and one blue marble, you put a blue marble in the bag.
After putting a marble back in the bag, you have one less marble in the bag.
You repeat this process, reducing the number of marbles in the bag by one each time, until only one marble is left in the bag.
Now, let's think about the outcomes at each step:
If the bag contains an odd number of marbles (99 red + 99 blue = 198), the final marble will be red because at each step, you are adding a red marble back to the bag.
If the bag contains an even number of marbles (e.g., 100 red + 100 blue = 200), the final marble will be blue because at each step, you are adding a blue marble back to the bag.
In this case, the bag contains 99 red marbles and 99 blue marbles, which is an odd number (198 marbles).
Therefore, the final marble left in the bag will be red.
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| A retiree invests $8,000 in a savings plan that pays
4% per year. What will the account balance be at
the end of the first year?
Answers
Answer:
8320
Step-by-step explanation:
(100%+4%)8000=8320
The balance at the end of the first year of the investment will be $8320, which includes the initial investment of $8000 and the interest earned, calculated as 4% of the initial investment.
Explanation:This is a basic interest problem in mathematics. To calculate the balance at the end of the first year, we need to add the initial investment to the amount earned through interest. The interest earned is the product of the initial investment and the interest rate.
In this case, the initial investment is $8000 and the interest rate is 4% per year or 0.04 in decimal form. So, the interest earned would be the product of $8000 and 0.04, which equals $320.
Therefore, the balance at the end of the first year would be the initial investment plus the interest earned, which is $8000 + $320 = $8320.
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Given the coordinates of the vertices of a quadrilateral, determine whether it is a square, a rectangle, or a parallelogram. Then find the perimeter of the quadrilateral. A(6, –4), B(11, –4), C(11, 6), D(6, 6)
Answers
Answer:
The answer to your question is: it's a rectangle
perimeter = 30 u
Step-by-step explanation:
d = √((x2.x1)² + (y2-y1)²)
Now, calculate the distances AB, BC, CD, AD
dAB = √((11-6)² + (-4+4)² = √5² = 5
dBC = √((11-11)² + (-4-6)² =√10 = 10
dCD = √((6-11)² + (6-6)² = √5² = 5
dAD = √((6-6)² + (6+4)² = √10² = 10
From the results we conclude that is a rectangle because two sides have the same length and the other two also measure the same. We can draw it to confirm this.
Perimeter = dAB + dBC + dCD + dAD
= 5 + 10+ 5 + 10 = 30 units
To determine the shape of the quadrilateral, calculate the distances between the vertices and check for equal side lengths and 90-degree angles. The given quadrilateral is a parallelogram since the opposite sides are parallel and equal. The perimeter of the quadrilateral is 30 units.
Explanation:To determine whether the given quadrilateral is a square, a rectangle, or a parallelogram, we can use the properties of each shape. A square is a quadrilateral with all sides equal in length and all angles equal to 90 degrees. A rectangle is a quadrilateral with opposite sides equal in length and all angles equal to 90 degrees. A parallelogram is a quadrilateral with opposite sides parallel and equal in length. To find the perimeter of the quadrilateral, we can calculate the sum of the lengths of all four sides.
Calculating the distances between each pair of given points:
Distance between A and B: √[(11-6)² + (-4-(-4))²] = √(5² + 0) = √25 = 5Distance between B and C: √[(11-11)² + (6-(-4))²] = √(0 + 100) = 10Distance between C and D: √[(6-11)² + (6-6)²] = √((-5)² + 0) = √25 = 5Distance between D and A: √[(6-6)² + (6-(-4))²] = √(0 + 100) = 10The distances between the vertices are: AB = 5, BC = 10, CD = 5, and DA = 10. Therefore, the perimeter of the quadrilateral is 5 + 10 + 5 + 10 = 30 units.
At the end of year X, automobile installment credit accounted for 36 percent of all outstanding consumer installment credit. At that time automobile finance companies extended $57 billion of credit, or \small \frac{1}{3} of the automobile installment credit. How many billion dollars of consumer installment credit was outstanding at that time?A. 62B. 171C. 475D. 513E. 684
Answers
Answer:
option (c) 475
Step-by-step explanation:
let the automobile installment credit be 'C'
Given:.
Automobile installment credit accounted for 36 percent of all outstanding consumer installment credit
Now,
57 billion is [tex]\frac{1}{3}[/tex] of automobile installment credit
or
57 billion = [tex]\frac{1}{3}[/tex] × C
or
C = 57 × 3
or
C = 171 billion
now,
installment credit accounted = 36% of all outstanding consumer installment credit
or
171 billion = 0.36 × all outstanding consumer installment credit
or
All outstanding consumer installment credit = $475 billion
Hence, the correct answer is option (c) 475
Suppose you have two 100 mL graduated cylinders. In each cylinder, there is 40.0 mL of water. You also have two cubes: one is lead, and the other is aluminum. Each cube measures 2.90 cm on each side. After you carefully lower each cube into the water of its own cylinder, what will the new water level be in each of the cylinders?
Answers
Answer:64.389
Step-by-step explanationthe new volume in each cylinder will be the volume of water + volume 1 cube (assuming the cubes does not float on water)
then volume of a cube =side^3=(2.90 cm)^3= 24.389cm^3=24.389mL
(considering that 1 ml= 1 cm^3)
Finally the new level of each cylinder is=40 mL+24.389mL=64.389 mL
(if the cube float we need to consider the volume under water (with densities which are not given)
The fraction of defective integrated circuits produced in a photolithography process is being studied. A random sample of 300 circuits is tested, revealing 14 defectives. Calculate a 95% two-sided confidence interval on the fraction of defective circuits produced by this particular tool. Round the answers to 4 decimal places.
Answers
Answer: [tex](0.0228\ ,0.0706)[/tex]
Step-by-step explanation:
Given : Sample size : n= 300
The sample proportion of defectives : [tex]\hat{p}=\dfrac{14}{300}=0.0467[/tex]
Significance level for 95% confidence level =[tex]\alpha=1-0.95=0.05[/tex]
Critical z-value:[tex]z_{\alpha/2}=\pm1.96[/tex]
Confidence interval for population proportion :
[tex]\hat{p}\pm z_{\alpha/2}\sqrt{\dfrac{\hat{p}(1-\hat{p})}{n}}[/tex]
[tex]= 0.0467\pm (1.96)\sqrt{\dfrac{0.0467(1-0.0467)}{300}}[/tex]
[tex]\approx\ 0.0467\pm 0.0239\\\\=(0.0467-0.0239\ , \ 0.0467-0.0239)\\\\=(0.0228\ ,0.0706)[/tex]
Hence, a 95% two-sided confidence interval on the fraction of defective circuits produced by this particular tool= [tex](0.0228\ ,0.0706)[/tex]
12. The geographic grid apportions the globe into hemispheres of 180 lines of longitude. Based on your knowledge of basic geometry, what portion of a sphere does 180 degrees equal? __________________ The grid also defines so-called "central meridians" centered on every 15 degrees of longitude. How many central meridians would there be for a complete sphere? ________________________ Compare this answer to the number of hours in a day. How does it compare?
Answers
Answer:
For the first question, 180 degrees equals to a half of the sphere. For the second question, you need 24 central meridians for a complete sphere, which are exactly the hours in a day.
Step-by-step explanation:
A sphere is basically a 3D circle. As a circle has 360 degrees, 180 degrees would be half of a circle. Imagine you are on a satellite over the north pole or the south pole and you have a way to cut the earth by the middle. You will get two halves of sphere.
About the second question, you may need to have in mind that a day is the time spent for the earth to rotate all 360 degrees over its own axis. British fellow, on XIX century, decided they were the center of the world. As previously, back in the days, some other people decided a day had 24 hours, they decided to draw this lines and divide the earth in 24 pieces, so they could knew which time was on every point their extense kingdom had. As I said, a circle has 360 degrees, (360 degrees)/(24 hours) equals to 15 degrees.