Answer:
A sample size of 3 is required.
Step-by-step explanation:
We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:
[tex]\alpha = \frac{1 - 0.96}{2} = 0.02[/tex]
Now, we have to find z in the Z-table as such z has a p-value of [tex]1 - \alpha[/tex].
That is z with a pvalue of [tex]1 - 0.02 = 0.98[/tex], so Z = 2.054.
Now, find the margin of error M as such
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.
Based on previous evidence, he believes that the standard deviation is approximately 3.6 hours.
This means that [tex]\sigma = 3.6[/tex]
He would like to be 96% confident that his estimate is within 5 hours of the true population mean. Use RStudio to determine how large of a sample size is required without rounding any interim calculations.
The sample size needed is of n, and n is found when M = 5. So
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
[tex]5 = 2.054\frac{3.6}{\sqrt{n}}[/tex]
[tex]5\sqrt{n} = 2.054*3.6[/tex]
[tex]\sqrt{n} = \frac{2.054*3.6}{5}[/tex]
[tex](\sqrt{n})^2 = (\frac{2.054*3.6}{5})^2[/tex]
[tex]n = 2.19[/tex]
Rounding up:
A sample size of 3 is required.
What is an equation of the line that passes through the points (-6, 3) and (-5,2)
Answer:
y=-x-3
Step-by-step explanation:
2) find an equation of the line theough the given
points. Give the final answer in slope-intercept form.
(2,-2) (-1,4)
Answer:
y = -2x + 2
Step-by-step explanation:
Given the following data;
Points on the x-axis (x1, x2) = (2, -1)
Points on the y-axis (y1, y2) = (-2, 4)
To find the equation of line in slope intercept form;
First of all, we would determine the slope of the line.
Mathematically, slope is given by the formula;
[tex] Slope = \frac{Change \; in \; y \; axis}{Change \; in \; x \; axis} [/tex]
[tex] Slope, m = \frac {y_{2} - y_{1}}{x_{2} - x_{1}} [/tex]
Substituting into the equation, we have;
[tex] Slope, m = \frac {4 - (-2)}{-1 -2} [/tex]
[tex] Slope, m = \frac {4 + 2}{-1 -2} [/tex]
[tex] Slope, m = \frac {6}{-3} [/tex]
Slope, m = -2
Next, we would use the following formula to find the equation of the line;
y - y1 = m(x - x1)
Substituting into the formula, we have;
y - (-2) = -2(x - 2)
y + 2 = -2x + 4
y = -2x + 4 - 2
y = -2x + 2 = mx + c
simplify into one fraction 8x/x-8 - 2/x-8
Answer:
- 2+8x/x
Step-by-step explanation:
See image below:)
FYI you can use the app photo math you just take a pic of the problem and it gives you the answer and explains the steps and it is free
Answer:
(8x-2) / (x-8)
Step-by-step explanation:
8x/x-8 - 2/x-8
Since the denominator is the same, we can add the numerators
(8x-2) / (x-8)
The answer and how to find the answer
Answer:
x = 1.9
Step-by-step explanation:
Thanks to a theorem we can use this proportion
10.47 : 4.44 = 4.44 = x
x = (4.44^2)/10.47 = 1,882865 = 1.9
You need to save $1,300 to go overseas in two years. You deposit $800 in a savings account today. The account earns 10% interest. You will make an additional deposit in one year. How much must you deposit in one year in order to have enough to go on the trip?
Answer:
The additional deposit to be made in one year should be $ 301.81.
Step-by-step explanation:
Given that I need to save $ 1,300 to go overseas in two years, and I deposit $ 800 in a savings account today, that earns 10% interest, and I will make an additional deposit in one year, to determine how much must I deposit in one year in order to have enough to go on the trip, the following calculation must be performed:
800 x 1.1 = 880
(880 + X) x 1.1 = 1300
1300 / 1.1 = 1,181.81
1,181.81 - 880 = X
301.81 = X
Therefore, the additional deposit to be made in one year should be $ 301.81.
In a carnival game, there are 8 identical boxes, one of which contains a prize. Contestants guess which box contains the prize. The game is played until one of the contestants guesses it correctly. A contestant with the smaller number of guesses wins the prize. Before each game, a new prize is placed at random in one of the 8 boxes.
Requried:
Is it appropriate to use the binomial probability distribution to find the probability that a contestant who plays the game that day several times wins exactly 4 times?
Since there is a fixed number of trials and the trials are independent, it is appropriate to use the binomial probability distribution to find the probability that a contestant who plays the game that day several times wins exactly 4 times.
What is the binomial distribution formula?The formula is:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
The parameters are:
x is the number of successes.n is the number of trials.p is the probability of a success on a single trial.In this problem:
The game is played n times.In each game, each of the 8 participants is equally as likely to win the game, hence p = 1/8.Thus, the binomial distribution is appropriate.
You can learn more about the binomial distribution at https://brainly.com/question/24863377
multiply (11x+y)² what is the answer?
Answer:
121x+y²
Your Welcome
BIFFY OUT!!!
If the set of values in the table represents points on a line, what is the value of a?
Answer:
3
Step-by-step explanation:
Answer:
7
Step-by-step explanation:
just did it
What is the length of side a? Round to the nearest tenth of an inch. Enter your answer in the box.
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Answer:
14.4
Step-by-step explanation:
The Pythagorean theorem tells you ...
7² +a² = 16²
a² = 256 -49
a = √207
a ≈ 14.4
Is the answer to this question 13.5
Answer:
i think its 13
Step-by-step explanation:
you are supposed to measure the lowest point of the liquid.
can someone help me with this question
please helpppp!!! it’s timed!!!! thank u for helping!!!!!
Answer:
10π in.
Step-by-step explanation:
circumference of a circle = 2πr
=2*π*5
=10π in.
Casandra wants to buy a dress. She had of the money. Her mom gave her $120.00 but she was still short of the cost of the dress. What is the price of the dress?
I dont think I can be answered with just the given info... is some of the q missing still?
Closest we can do with above is dress cost = 120+ c
In the expansion of (1/ax +2ax^2)^5 the coefficient of x is five. Find the value of the constant a.
Answer:
80x⁴
Step-by-step explanation:
[tex](\frac{1}{ax} + 2ax^2)^5 = 5C_0(\frac{1}{ax})^5(2ax^2)^0 + 5C_1(\frac{1}{ax})^4(2ax^2)^1 + 5C_2(\frac{1}{ax})^3 (2ax^2)^2[/tex]
[tex]+ 5C_3 (\frac{1}{ax})^2(2ax^2)^3 + 5C_4(\frac{1}{ax})^1(2ax^2)^4 + 5C_5(\frac{1}{ax})^0(2ax^2)^5[/tex]
[tex]5C_0(\frac{1}{ax})^5(2ax^2)^0 =1 \times (\frac{1}{ax})^5 \times 1 = \frac{1}{a^5x^5}\\\\5C_1(\frac{1}{ax})^4(2ax^2)^1 = 5 \times (\frac{1}{ax})^4 \times (2ax^2)^1 = 10 ax^2 \times \frac{1}{a^4x^4} = \frac{10}{a^3x^2}\\\\5C_2 (\frac{1}{ax})^3 (2ax^2)^2= 10 \times (\frac{1}{ax})^3 \times (2ax^2)^2 = 10 \times \frac{1}{a^3x^3} \times 4a^2x^4 = \frac{40x}{a}\\\\5C_3 (\frac{1}{ax})^2 (2ax^2)^3 = 10 \times (\frac{1}{ax})^2 \times (2ax^2)^3 = 10 \times \frac{1}{a^2x^2} \times 8a^3 x^6 = 80ax^4\\\\[/tex]
[tex]5C_4(\frac{1}{ax})^1(2ax^2)^4 = 5 \times \frac{1}{ax} \times 16a^4x^8 = 80a^3x^7\\\\5C_5(\frac{1}{ax})^0(2ax^2)^5 = 1 \times 1 \times 32a^5x^{10}[/tex]
The fourth term of the expansion has the constant a,
the coefficient of a is 80x⁴
in the right triangle AB, mc=90, a=4, and sinA=1/2. what is the length of the hypotenuse?
Given:
In a right angle triangle ABC, [tex]m\angle C=90^\circ , a=4[/tex] and [tex]\sin A=\dfrac{1}{2}[/tex].
To find:
The length of the hypotenuse.
Solution:
It is given that [tex]m\angle C[/tex], so opposite side of this angle is the hypotenuse, i.e., c.
In a right angle triangle,
[tex]\sin \theta=\dfrac{Perpendicular}{Hypotenuse}[/tex]
In the given triangle,
[tex]\sin A=\dfrac{a}{c}[/tex]
Substituting the given values, we get
[tex]\dfrac{1}{2}=\dfrac{4}{c}[/tex]
By cross multiplication, we get
[tex]1\times c=4\times 2[/tex]
[tex]c=8[/tex]
Therefore, the length of the hypotenuse is 8 units.
Sima drinks 2.5 litres of water each day.
A full glass holds 125 mililitres of water.
How many full glasses of water does Sima drink each day?
Answer:
20 glasses a day
Step-by-step explanation:
2.5litres equals 2500millilitres
2500÷125=20
Question 20
A transformer has 500 turns in its primary coil and 200 in the secondary coil.
a) If an AC voltage of 220 V and frequency 50 Hz is established in the primary coil, find the voltage
and the frequency induced in the secondary coil. (2)
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Answer:
88 V50 HzStep-by-step explanation:
The secondary voltage is proportional to the primary voltage. The constant of proportionality is the ratio of secondary turns to primary turns.
The secondary voltage is ...
(200/500)(220 V) = 88 V
__
A transformer does not change the frequency.* The voltage in the secondary coil is still 50 Hz.
_____
* Most transformers are designed to operate as linear devices. It is possible to design a transformer (with special core material) that operates non-linearly, and/or that is "tuned" to a frequency other than the one exciting the primary. That is, the secondary voltage may be some harmonic of the primary voltage. This would be a relatively unusual application of a transformer, beyond the apparent scope of the question here.
HELPP ASAP plzzz tyy!!!!
Answer:
The domain of a function is the input numbers that, when plugged into a function, the result is defined. In simple words, we can define the domain of a function as the possible values of x that will make an equation true.
The range of a function is defined as a set of solutions to the equation for a given input. In other words, the range is the output or y value of a function. There is only one range for a given function.
hope this helps!
Step-by-step explanation:
Kristin is saving up money to go on a trip around the world next year. In order to make enough to pay for her trip, Kristin has to work at least 260 days this year.
Which of the following inequalities represents Kristin's possible number of workdays, d
Answer:
A.
D needs to be equal or more to 260
Answer:
The correct option is A
Step-by-step explanation:
I got a 90% on my quiz. Thanks to everyone who helped me!
Also this is a really is question but I'm to lazy to do it. Can someone give me the answer to this? (Question in the picture)
Answer: The answer is A
Step-by-step explanation:
In the picture, model A shows 3 groups and in the 3 groups are 4 lines !
I'm bad explaining but I hope this helps .
The volume of a cube is 448cm3.
Work out the length of its side rounded to 1 DP. Please hellp
Answer:
7.65 or 7.7 rounded to 1 DP
Step-by-step explanation:
To find the length of the side of a cube we do the inverse of finding the volume.
one side= x
If x³ = volume, therefore ∛448 is how to find the length of one side.
∛448= 7.65
I hope this helps you.
AABC has been translated 5 units to the right, as shown in the diagram. What
is the length of AB?
A. 10
B. 6
C. 31
D. 15
Karl set out to Alaska on his truck. The amount of fuel remaining in the truck's tank (in liters) as a function of distance driven (in kilometers) is graphed.
What distance did Karl travel by the time he had 200 liters of fuel?
_____ kilometers
Answer:
500 kilometers
Step-by-step explanation:
The fuel (y) Karl has in his car is a function of the distance (x) Karl travelled. The amount of fuel (y) is dependent on the distance (x) Karl travelled.
On the y-axis, we have amount of fuel.
On the x-axis, we have distance travelled.
At the time Karl travelled when he had 200 liters of fuel (y) remaining in his car, he had travelled a distance (x) of 500 kilometers.
We know this by looking at the graph given. When x (distance) = 500, y (fuel) = 200.
HELP MATH ANSWER QUESTION
Answer:
Last one.
Step-by-step explanation:
[tex]\sqrt{3}[/tex] is used in 30-60-90 triangles
[tex]\sqrt{2}[/tex] is used in 45-45-90 triangles
Base is x, leg is x[tex]\sqrt{3}[/tex], hypotenuse is 2x
Answer:
x = 20 ; y= 10√3
Step-by-step explanation:
30, 60 , 90 triangle ratio is
Side opposite to 30 is a
a = AC = 10
Side opposite to 60 is a[tex]\sqrt{3}[/tex]
AB = a[tex]\sqrt{3}[/tex] = 10√3
Side opposite to 90 is 2a
BC = 2a = 2* 10 = 20
7[tex]\sqrt -9[/tex]
Answer:
= 21i
Step-by-step explanation:
√-9 = 3i
= 7 . 3i
Multiply the numbers: 7 . 3 = 21
= 21i
Hope this helps!
NO LINKS OR ANSWERING QUESTIONS YOU DON'T KNOW. Please help me with #29 and 30.
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Answer:
29) 1/5
30) independent; 64/225 ≈ 0.284
Step-by-step explanation:
In general, a "spinner" is considered to be a (mathematically ideal) device that returns one of the values with which it is marked, with a probability according to the area of the sector in which the mark resides. Usually, sectors are presumed to have equal areas. The result of one spin is generally considered to be independent of the result from any other spin. In the real world, an operator familiar with a given spinner can often ensure that the results do not have equal probability and are not independent. We ignore that possibility in math problems.
__
29) Of the numbers 1 to 15, there are three numbers less than 4. The probability of spinning one of them is 3/15 = 1/5.
__
30a) We have defined our spinner so that the events are independent. (See above.)
30b) In the set of numbers 1 to 15, 8 are odd and 7 are even. The probability of getting an odd number on any spin is 8/15. Because the results of successive spins are independent, the probability of any given sequence is the product of the probabilities of the numbers in that sequence.
P(2 odd) = P(odd)×P(odd) = (8/15)(8/15) = 64/225 ≈ 0.284
Q22. Solve the equation x – 25 = 25 and state which axiom do you use here.
Answer:
x=50
Step-by-step explanation:
The solution to the equation x – 25 = 25 is x = 50. The axiom used to solve the equation is the addition property of equality.
To solve the equation x - 25 = 25, we want to isolate the variable x to find its value.
Adding 25 to both sides of the equation, we get:
x - 25 + 25 = 25 + 25
Simplifying, we have:
x = 50
Therefore, the solution to the equation is x = 50.
In this case, the axiom used to solve the equation is the addition property of equality. According to this axiom, if two expressions are equal, adding the same value to both sides of the equation preserves the equality.
In the given equation, we add 25 to both sides of the equation to maintain equality and obtain the solution x = 50. The addition property of equality allows us to perform this operation and determine the value of x.
To learn more about axioms click on,
https://brainly.com/question/33725824
#SPJ2
Triangle A B C is cut by line segment D E. Line segment D E goes from side A C to line A B. The length of A E is 12, the length of E B is 4, and the length of A D is 9. What is the length of Line segment D C? 2 units 3 units 6 units
Answer: The length of DC is 3 units
Step-by-step explanation:
The Basic proportionality theorem states that if a line is parallel to one side of a triangle and intersects the other two at different points, then the other two sides are divided in the same ratio.
The given image is attached below.
From the BPT theorem, we can say that:
[tex]\Rightarrow \frac{AE}{EB}=\frac{AD}{DC}[/tex]
We are given:
AE = 12 units
EB = 4 units
AD = 9 units
Putting values in above equation, we get:
[tex]\Rightarrow \frac{12}{4}=\frac{9}{DC}\\\\\Rightarrow DC=\frac{9\times 4}{12}\\\\\Rightarrow DC=3 units[/tex]
Hence, the length of DC is 3 units
Answer:
The answer is 3 units
Step-by-step explanation:
What is the perimeter of a triangle with the side lengths 4 cm, 6 cm, and (3y-2) cm?
Answer:
Step-by-step explanation:
P = 4 + 6 + (3y - 2) Remove the brackets
P = 10 + 3y - 2 Combine
P = 8 + 3y
Note 3y must be less than 8. That's because 2 sides of any triangle must be larger than the 3rd side or else you don't have a triangle.
6+t=1 pls help.............
6+T=1
Try T=-5
6+(-5) = 1
Correct, So...
T=-5