Answer:
The 90% confidence interval is [tex] 2.47<\mu < 2.59 [/tex]
Step-by-step explanation:
From the question we are told that
The sample size is n = 6
The sample mean is [tex]\= x = 2.53 \ mm[/tex]
The standard deviation is [tex]\sigma = 0.090\ mm[/tex]
Given that the confidence level is 90% then the level of significance is
[tex]\alpha = (100 - 90)\%[/tex]
=> [tex]\alpha = 0.10 [/tex]
Generally from the normal distribution table the critical value of [tex]\frac{\alpha }{2}[/tex] is
[tex]Z_{\frac{\alpha }{2} } = 1.645 [/tex]
Generally the margin of error is mathematically represented as
[tex]E =1.645 * \frac{0.090 }{\sqrt{6} }[/tex]
=> [tex]E = 0.060 [/tex]
Generally 90% confidence interval is mathematically represented as
[tex]\= x -E < \mu < \=x +E[/tex]
[tex]2.53 -0.060 <\mu < 2.53 + 0.060[/tex]
=> [tex] 2.47<\mu < 2.59 [/tex]
The terminal side of angle θ intersects the unit circle in the first quadrant at (925,y). What are the exact values of sinθ and cosθ?
Correct question is;
The terminal side of angle θ intersects the unit circle in the first quadrant at (9/25,y). What are the exact values of sinθ and cosθ?
Answer:
sinθ = (√544)/25) and cosθ = 9/25
Step-by-step explanation:
We are given that (9/25,y) lies on the unit circle. Thus, from general representation of equation of a circle, we can write that;
(9/25)² + y² = 1²
y² = 1 - (9/25)²
y² = (625 - 81)/25²
y² = 544/25²
y = ±(√544)/25
We are told the point is in the first quadrant and so we will choose the positive value of y = (√544)/25.
Therefore, the terminal side of the angle θ intersects the unit circle at [9/25, (√544)/25)]
In unit circle geometry, cosθ = x, while sinθ = y.
Thus; sinθ = (√544)/25) and cosθ = 9/25
The exact value of [tex]sin\theta[/tex] and [tex]cos\theta[/tex] is [tex]cos\theta = \frac{9}{25} , sin\theta = \frac{\sqrt{544} }{25}[/tex] and this can be determined by forming the equation of circle.
Given :
The terminal side of angle [tex]\theta[/tex] intersect at unit circle ([tex]\frac{9}{25}, y[/tex]).
From general representation of equation of circle , we can write
[tex]x^{2} + y^{2} = a^{2}\\[/tex]
[tex](\frac{9^{2} }{25^{2} })[/tex] + [tex]y^{2} = 1^{2}[/tex]
[tex]y^{2} = 1 - \frac{81}{625}[/tex]
[tex]y^{2} = \frac{625-81}{625}[/tex]
[tex]y^{2}=\frac{544}{625}[/tex]
Taking square root both sides
[tex]y= \frac{\sqrt{544} }{\sqrt{625} }[/tex]
[tex]y = \frac{\sqrt{544} }{25}[/tex]
We are taking only because point lies in first quadrant.
The terminal side of angel [tex]\theta[/tex] unit circle in first quadrant at [tex](\frac{9}{25} , \frac{\sqrt{544} }{25})[/tex]
In unit circle
[tex]x = cos\theta , y = sin\theta[/tex]
[tex]\rm cos\theta = \frac{9}{25} , sin\theta = \frac{\sqrt{544} }{25}[/tex].
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Real Numbers Quiz Active 1 2 3 4 Which answer describes the type of numbers that are dense? whole numbers and integers O whole numbers but not integers rational numbers and irrational numbers rational numbers but not irrational numbers
Answer:
C. rational numbers and irrational numbers
Step-by-step explanation:
Rational numbers are those numbers that can be used to express the ratio of two whole numbers. An example is the figure 2. It can be expressed as a fraction of another number like when we write 2/8. Both figures are rational. Irrational numbers cannot be used to express the ratio of two whole numbers or integers. An example is a digit like 0.666666... Rational and irrational numbers are real numbers because real numbers encompass all the types of numbers we can think of, positive, negative, decimals, whole, etc.
The density of numbers is seen in the fact that there is no vacuum created between real numbers when plotted on the number line.
Subtract -2x^2+4x-1−2x
2
+4x−1minus, 2, x, squared, plus, 4, x, minus, 1 from 6x^2+3x-96x
2
+3x−96, x, squared, plus, 3, x, minus, 9.
Your answer should be a polynomial in standard form.
Answer:
8x²- x -8
Step-by-step explanation:
The question is not well written. I guess what you mean is:
Subtract -2x^2+4x-1 ( minus 2x squared plus 4x minus 1) from 6x^2+3x-9 (6x squared plus 3x minus 9).
To subtract -2x^2+4x-1 from 6x^2+3x-9, that is
6x^2+3x-9 - (-2x^2+4x-1). This can be written as
6x²+3x-9 - (-2x²+4x-1)
Now, opening the bracket, we will get
6x²+3x-9 +2x²-4x+1
Then, collecting like terms, we get
6x²+2x²+3x-4x-9+1
6x²+2x² = 8x²
3x-4x = -x
-9+1 = -8
∴6x²+2x²+3x-4x-9+1 becomes
8x²-x -8
The answer is 8x²-x -8.
Simplified form of the polynomial :
8x²- x -8
Given(correct form of question):
Subtract -2x²+4x-1 ( minus 2x squared plus 4x minus 1) from 6x²+3x-9 (6x squared plus 3x minus 9).
Now,
To subtract -2x²+4x-1 from 6x²+3x-9, that is
6x²+3x-9 - (-2x²+4x-1). This can be written as
6x²+3x-9 - (-2x²+4x-1)
Now, opening the bracket, we will get
6x²+3x-9 +2x²-4x+1
Then, collecting like terms, we get
6x²+2x²+3x-4x-9+1
6x²+2x² = 8x²
3x-4x = -x
-9+1 = -8
∴6x²+2x²+3x-4x-9+1 becomes 8x²-x -8
Thus,
The answer is 8x²-x -8.
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Alex has to fill his 10 gallon fish tank with water. He only has a 1 pint bucket. How many times will he have to fill his bucket to fill the tank?????W
Answer:
80
Step-by-step explanation:
8 pints in a gallon so then you multiply 8 x 10 and get 80
Answer:
80
Step-by-step explanation:
1 gallon = 8 pints8 × 10 = 80I hope this helps!
g What is the max number of 4-element-subsets of we can select, such that intersection of any 3 of them is empty?
Answer:
16Step-by-step explanation:
In order to get the max number of 4-element-subsets of we can select, such that intersection of any 3 of them is empty, we need to calculate the power of the set having four elements. Let the set containing the element be A as shown;
Let set A = {a, b, c, d}
Power of the set P(A) = [tex]2^n[/tex] where:
n is the total number of element in the set. Since we have four elements in the set, n = 4
[tex]P(A) = 2^4\\P(A) = 16[/tex]
This means that the set A have 16 subsets. The subsets of the set are:
{}, {a}, {b}, {c}, {d}, {a, b}, {a, c}, {a, d}, {b, c}, {b, d}, {c, d}, {a, b, c}, {a, b, d}, {b, c, d}. {a, c, d}, {a, b, c, d}.
From all the subsets, it can be seen that intersection of set {a} and {b}, {a} and {c}, {c} and {d} are empty.
Hence the max number of 4-element-subsets of we can select, such that intersection of any 3 of them is empty is 16
Looking around in your own country, discuss two practical applications in which “piecewise functions” are used either explicitly or implicitly
Answer:
Piecewise functions are functions that behave differently in different regions of the domain.
One example that you may see in your city is the case of the street illumination, such that can be modeled as:
x = time
Suppose that the lights are turned on at a given hour x0 and then turn off at the hour x1, we can define:
f(x) = 0 if x1 < x < x0
f(x) = 1 if x0 ≤ x ≤ x1
Where f(x) represents the intensity of the light at the time x.
Between x1 and x0, the lights are not working, so the illumination that they provide is zero.
Between x0 and x1 the lights are turned on, so the illumination is 1.
Another example can be the accurate description of the velocity of a car as a function of time.
For some pieces, the car will be stopped (maybe in a red light)
For some pieces, the car will be moving slow (maybe there is a lot of traffic)
For some pieces, the car will be moving fast or accelerating (in an empty street).
So we can define this motion as a piecewise function that obviously will depend on how the car moves.
PLEASE HELP
Select the correct answer from each drop-down menu. Options are (equal to, not equal to)
Answer:
Not equal to.
Step-by-step explanation:
2) Chicken soup is 3 cans for $0.55. How much would a
dozen soup cans cost?
Answer:
It would cost $2.20
Step-by-step explanation:
If 3 cans = $.55
then 3*4 = 12
soooo 4*.55 = 2.20
Hope this helps!!!
The mayor of a town has proposed a plan for the annexation of a new bridge. A political study took a sample of 1100 voters in the town and found that 54% of the residents favored annexation. Using the data, a political strategist wants to test the claim that the percentage of residents who favor annexation is more than 50%. Determine the P-value of the test statistic. Round your answer to four decimal places.
Answer:
The p-value is [tex]p-value = 0.0039854[/tex]
Step-by-step explanation:
From the question we are told that
The sample size is n = 1100
The population proportion is p = 0.50
The sample proportion is [tex]\^ p = 0.54[/tex]
The null hypothesis is [tex]H_o : p = 0.50[/tex]
The alternative hypothesis is [tex]H_a : p > 0.50[/tex]
Generally the test statistics is mathematically represented as
[tex]z = \frac{\^ p - p }{ \sqrt{\frac{ p(1 - p)}{n} } }[/tex]
=> [tex]z = \frac{ 0.54 - 0.54 }{ \sqrt{\frac{ 0.50 (1 - 0.50)}{1100} } }[/tex]
=> [tex]z = 2.6533[/tex]
Generally from the z-table the probability of 2.6533 for a right tailed test is
[tex]p-value = 0.0039854[/tex]
Unpredictable numbers that are distributed over a certain range are ____.
A. Random numbers
B. Random equations
C. Random formulas
D. Tables of formulas
Answer:
random numbers
Step-by-step explanation:
because they are randomly picked
Unpredictable numbers that are distributed over a certain range are _Random numbers_.
What is random experiment?Random experiments are repeated multiple times to determine its likelihood.
The number of times an experiment is repeated is better described as number of trials.
The range of a function is defined as the set of all the possible output values that are valid for the given function.
Now, Unpredictable numbers that are distributed over a certain range are random numbers because they are randomly picked.
Unpredictable numbers that are distributed over a certain range are _Random numbers_.
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Rosanne makes 1 1/2 liters of strawberry lemonade. She pours 1/4 of a liter of lemonade into a thermos to take to the park. Her brother drinks 2/5 of the remaining lemonade. How much lemonade does rosanne’s brother drink?
Answer:
1/2 liters
Step-by-step explanation:
Rosanne makes 1 1/2 liters of strawberry lemonade
She pours 1/4 of the lemonade into a thermos
The quantity left is
= 1 1/2 - 1/4
= 3/2 - 1/4
= 5/4
Her brother drinks 2/5 of the remaining lemonade
Therefore the quantity of lemonade that Rosanne brother drinks can be calculated as follows
= 2/5 × 5/4
=1/2
Hence the quantity of lemonade that Rosanne brother drinks is 1/2 liters
Answer:
1/2 liters
Step-by-step explanation: Rosanne makes 1 1/2 liters of strawberry lemonade
She pours 1/4 of the lemonade into a thermos
The quantity left is
= 1 1/2 - 1/4
= 3/2 - 1/4
= 5/4
Her brother drinks 2/5 of the remaining lemonade
Therefore the quantity of lemonade that Rosanne brother drinks can be calculated as follows
= 2/5 × 5/4
=1/2
A short quiz has two true-false questions and one multiple-choice question with four possible answers. A student guesses at each question. Assuming the choices are all equally likely and the questions are independent of each other, the following is the probability distribution of the number of answers guessed correctly. What is the Probability of two or more questions right? X 0 1 2 3 P(X) .1875 .4375 .3125 .0625
Answer:
[tex]P(X\geq 2) = 0.375[/tex]
Step-by-step explanation:
Given
X ------0 --------1 -------- 2--------- 3
P(X) --.1875 -.4375 ---.3125 --- .0625
Required
Determine [tex]P(X\geq 2)[/tex]
This is calculated as:
[tex]P(X\geq 2) = P(X = 2) + P(X = 3)[/tex]
[tex]P(X\geq 2) = 0.3125 + 0.0625[/tex]
[tex]P(X\geq 2) = 0.375[/tex]
Solve for x: x + 4 = 10 *
Your answer
Answer:
6
Step-by-step explanation:
A way to answer these questions like I usually do is to subtract the result by the number you already know, like this; 10-4=6, so 6 would be what X equals, or you can just take the long way and keep guessing what the answer would be and keep doing the problems, but that would be very time consuming so I would recommend just doing the subtraction method!
Hope this helps!
Answer:
x = 6
Step-by-step explanation:
x + 4 = 10
=> x = 10 - 4
=> x = 6
What is the best estimate of 49.13 + 0.58?
A: 80
B: 40
C: 25
D: 50
Answer:
D.50
Step-by-step explanation:
its the closes whole number to 49.13
POSSIBLE POINTS: 3.33
Tracy wants to buy some pies for her sisters and she has a budget of $82 to spend on $5
apple pies, $4.5 banana pies, and $5.5 chocolate pies. She wants to buy 16 pies for her
sisters and must buy as many chocolate pies as apple pies and banana pies combined.
How many of each item should she buy? Write a system of equations to help you solve
this problem.
# of applie pies =
# of banana pies =
# of chocolate piles =
1
2 3
Answer:
From the information given, you can write the following system of equations:
x+y+z=16 (1)
5x+4.5y+5.5z=82 (2)
z=x+y (3)
You can replace (3) in (1) and (2):
x+y+x+y=16
2x+2y=16 (4)
5x+4.5y+5.5(x+y)=82
5x+4.5y+5.5x+5.5y=82
10.5x+10y=82 (5)
Now, you have the following equations:
2x+2y=16 (4)
10.5x+10y=82 (5)
You can isolate x in (4):
2x=16-2y
x=8-y (6)
Then, you have to replace (6) in (5):
10.5(8-y)+10y=82
84-10.5y+10y=82
84-82=10.5y-10y
2=0.5y
y=2/0.5
y=4
Now, you can replace the value of y in (6) to find x:
x=8-4
x=4
Finally, you can replace the vaue of x and y in (3) to find z:
z=4+4
z=8
According to this, she should buy 4 apple pies, 4 banana pies and 8 chocolate pies.
Which expression is equivalent to Y.Y.Y.Z.Z.Z.Z?
O y 24
O 12xy
o (yz)
07xy
HURRYPLEASEEEE
By definition, two rays labeled Ab and AC must exist with which of the following conditions?
Answer:
A. The two rays form angle CAB.
C. The two rays make a line AC.
D. The two rays intersect at point A.
E. The two rays are perpendicular.
This is shown in figure 1 in the attachment provided.
Step-by-step explanation:
The given rays, [tex] \overrightarrow{AB} [/tex] and [tex] \overrightarrow{AC} [/tex] shows that both rays have a common endpoint A.
Therefore, the following conditions exists:
A. "The two rays form angle CAB."
Take a look at figure 1 in the attachment provided below. The two rays meet at point A to form angle CAB.
C. "The two rays make a line AC."
As shown in figure 2 in the attachment provided below, [[tex] \overrightarrow{AB} [/tex] and [tex] \overrightarrow{AC} [/tex] have a common end point, A, and they extend in opposite directions to form a straight line AC. [tex] (\overline{AC}) [/tex]
D. "The two rays intersect at point A."
This is shown in figure 1 in the attachment provided.
E. "The two rays are perpendicular."
Since [tex] \overrightarrow{AB} [/tex] and [tex] \overrightarrow{AC} [/tex] intersect at point A, they are perpendicular to each other, forming a right angle at point A. This we can see in figure 2 provided in the attachment.
Ronald has a 10% solution of the fertilizer Super Grow. How much pure Super Grow should he add to the mixture to get 36 oz of a 12.5% concentration?
Answer:
1 oz
Step-by-step explanation:
Given that:
% solution of super grow fertilizer = 10%
To obtain mixture of 36oz of a 12.5% concentration
Let oz of pure supergrowth to be added = s
(Initial % * (36 - s) + s) / 36 = target concentration
(10% * (36 - s) + s) / 36 = 12.5%
(0.1(36 - s) + s) / 36 = 0.125
Cross multiply:
0.1(36 - s) + s =. 0.125 * 36
3.6 - 0.1s + s = 4.5
3.6 + 0.9s = 4.5
0.9s = 4.5 - 3.6
0.9s = 0.9
s =. 0.9/0.9
s = 1
Hence, 1 oz of pure supergrowth should be added to the 10% solution to get 36 oz of a 12.5% concentration.
What is 2+2-2X2 divided by 2??
Answer:
0
Step-by-step explanation:
cause 2+2 is 4 and 2x2 is four and since u put - it take it away a then divide 0 by 2 u get 0
you must have a common denominator when ? fractions
Step-by-step explanation:
ADD::If the denominators are not the same, you must find the common denominator by finding the least common multiple of the 2.
SUBTRACT::If the denominators are not the same, you must find the common denominator by finding the least common multiple of the 2.
The sum of three consecutive odd integers is 18 less than five times the middle number fimd the three integers
Answer:
7, 9, 11
Step-by-step explanation:
x+x+2+x+4=5(x+2)-18
3x+6=5x+10-18
3x+6=5x+-8
3x=5x+-14
-2x=-14
x=7
the answer to the universe, life, and everything
Answer:
my life hurts now
Step-by-step explanation:
Answer:
42
Step-by-step explanation:
GET A BOOK U MORON
Which expression is equivalent to 27 + 15?
1) 3(24 + 12)
2) 319 + 5)
3) 9(3 + 15)
4) 9(18+ 6)
Which is the better deal 8 ounces of shampoo for $0.99 or 12 ounces for $1.47?
Answer:
12 ounces for $1.47.
Step-by-step explanation:
:) ello
Please help me solve What is m
Answer:
a=60
b=85
c=35
Step-by-step explanation:
a is shown to be 60 in the text along with c being 85 with its angle so just add 60 and 85 to get 145 and fill in the remaining to get 180 which gives you c as 35
On a lunch counter, there are 3 oranges, 5 apples, and 2 bananas. If 3 pieces of fruit are selected, find the probability that 1 orange, 1 apple, and 1 banana are selected (does not have to be in that order).
Answer:
[tex]Probability = \frac{1}{24}[/tex]
Step-by-step explanation:
Given
[tex]Oranges = 3[/tex]
[tex]Apples = 5[/tex]
[tex]Banana = 2[/tex]
[tex]Total = 10[/tex]
Required
Determine the probability of 1 orange, 1 apple and 1 banana
Since, order is not important:
[tex]Probability = P(Orange) * P(Apple) * P(Banana)[/tex]
[tex]Probability = \frac{3}{10} * \frac{5}{9} * \frac{2}{8}[/tex]
The difference in the numerator is as a result of picking the fruit without replacement
[tex]Probability = \frac{30}{720}[/tex]
[tex]Probability = \frac{1}{24}[/tex]
Probability is simply how likely something is to happen.
The probability of 1 orange, 1 apple, and 1 banana are [tex]\frac{1}{24}[/tex]
On lunch counter,
Number of oranges = 3
Number of apples = 5
Number of bananas = 2
If 3 piece of fruit is selected then, probability of 1 orange, 1 apple and 1 banana
[tex]=\frac{3}{10}*\frac{5}{9} *\frac{2}{8} \\\\=\frac{30}{720}\\\\=\frac{1}{24}[/tex]
Therefore, the probability of selecting 1 orange, 1 apple, and 1 banana are [tex]\frac{1}{24}[/tex]
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Describe the similarities and differences between a bar graph and a histogram.
Answer:
Bar graphs are used with nominal or ordinal scores; histograms are used with interval or ratio scores.
Step-by-step explanation:
Walter is helping to make cookies for a basketball tournament. He's made 15 cookies so far. His coach asked him to make at least 20 cookies but no more than 55. Solve the inequality and interpret the solution.
Answer:
[tex]5\leq x\leq 40[/tex]
Here, [tex]x[/tex] denotes the additional cookies that need to be made by Walter besides 15 cookies made by him so far
Step-by-step explanation:
Number of cookies made by Walter so far = 15
He is asked by his coach to make at least 20 cookies but no more than 55.
Let [tex]x[/tex] denotes the additional cookies that need to be made by Walter besides 15 cookies made by him so far.
The inequality is [tex]20\leq x+15\leq 55[/tex]
Now solve this inequality.
[tex]20\leq x+15\leq 55\\20-15\leq x\leq 55-15\\5\leq x\leq 40[/tex]
Answer: a
Step-by-step explanation: because its right
I will give brainliest! 2(6x+3)
Answer: 12x+6
Step-by-step explanation:
distributive property
Answer:
=12x + 6
Step-by-step explanation:
(2fg)7 simplify the expression
Answer:
14 f g
Step-by-step explanation:
Multiply 7 by 2 .