The critical value is 2.65
Given,
The confidence interval = 99%
Sample size, n = 12
We have to find the critical value;-
Critical value;-
A critical value is the test statistic's value that establishes a confidence interval's upper and lower boundaries or the level of statistical significance for a given test.
Here,
The sample size n = 12,
Then, the degrees of freedom is n - 1 = 12 - 1 = 11
The critical value= t₀.₀₀₁/2 = t₀.₀₀₅
Using the t-table and selecting df =12 and since it’s a 2 tail the corresponding t-score is 2.65
Therefore, the critical value is 2.65
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Suppose you have a nickel, two dimes, and a quarter. One of the dimes was minted in 1976, and the other one was minted in 1992. a. Assuming you choose at least one coin, how many different sets of coins can you form? b. Assuming you choose at least one coin, how many different sums of money can you produce? c. Explain why the answers in part a and part b are not the same.
As per the concept of counting problem, the reason that the answers in part (a) and part (b) are not the same is because Q1 and Q2 are treated as two different coins in part (a) whereas they are effectively treated as the same coin in part (b). And the reason they are treated as one coin is because they both contribute the same amount to the sum of money.
Counting Problems
Basically, counting refers the process of finding the number of elements of a finite set of objects.
Given,
Suppose you have a nickel, two dimes, and a quarter. One of the dimes was minted in 1976, and the other one was minted in 1992.
While we looking into the given problem,
For A) states that, If you choose at least one coin, this means you could choose 1, 2, 3 or 4 coins. Let us label the dime as D, the penny as P, the quarter minted in 1976 as Q1 and the quarter minted in 1992 as Q2.
Here in this process if you choose one coin, you could choose either D, P, Q1, or Q2. This gives us 4 possible sets.
And If you choose two coins, you choose the following sets of coins: DP, DQ1, DQ2, PQ1, PQ2, Q1Q2. This gives us 6 possible sets.
Then If you choose three coins, you could the following sets of coins: DPQ1, DPQ2, DQ1Q2, PQ1Q2. This gives us 4 possible sets.
So, If you choose four coins, you can only choose DPQ1Q2. This gives us 1 possible set.
So, the total number of different sets of coins you can form is 4 + 6 + 4 + 1 = 15 different sets of coins can be formed.
Similarly, for b) If you choose at least one coin, this means you could choose 1, 2, 3 or 4 coins.
Then If you choose one coin you could choose either D, P, Q1, or Q2. However, since Q1 and Q2 give us the same sum, they are effectively the same set. This gives us 3 possible sums.
So, If you choose two coins, you could choose the following sets of coins : DP, DQ, PQ, Q1Q2.And this gives us 4 possible sums
Then If you choose three coins, you could choose the following sets of coins: DPQ, DQ1Q2, PQ1Q2. And this gives us 3 possible sums
Then If you choose four coins, you can only choose DPQ1Q2. This gives us 1 possible sum.
So, the total number of different sums of coins you can form is 3 + 4 + 3 + 1 = 11 different sums of money can be produced.
Finally, c) The reason that the answers in part (a) and part (b) are not the same is because Q1 and Q2 are treated as two different coins in part (a) whereas they are effectively treated as the same coin in part (b). And the reason they are treated as one coin is because they both contribute the same amount to the sum of money.
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A store is offering a 25% discount on all electronics during a special weekend sale. Marcia wants to buy a television that regularly costs p dollars. She has written the expression 0. 75p to represent the sale price. Which is the best description for her expression?.
Marcia has written the expression 0. 75p to represent the sale price. The best description for her expression is she multiplied p by 0.25 then subtracted that from p.
How to express the sale price?
The sale price is the price after discount. Discount is the amount by which the origin price of an item is reduced. In this case, Marcia wants to buy a television with the origin prices is p dollars. The store is offering 25% discount.
p = the origin price
25% discount = 0.75p
The sale price = p - (0.25p)
So, the best description for Marcia's expression is multiplied p by 0.25 then subtracted that from p.
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The length of the bae of an iocele triangle i x. The length of a leg i 4x−3. The perimeter of the triangle i 66. Find x.
Answer:
x = 8
Step-by-step explanation:
since the triangle is isosceles then the 2 legs are congruent, that is both 4x - 3
the perimeter is the sum of the 3 sides , that is
x + 4x - 3 + 4x - 3 = 66
9x - 6 = 66 ( add 6 to both sides )
9x = 72 ( divide both sides by 9 )
x = 8
23.89$+41.25$ plis help plis
Answer:
$65.14
Step-by-step explanation:
You will line up the numbers according to the decimal points.
You add as you normally would, ignoring the decimal point.
When you get your answer you will bring the decimal point down.
(How your problem should look:)
$41.25
+ $23.89
$65.14
Determine whether each expression is equivalent to
(3+) t+3
9.27t
3².27t
Equivalent
O
Not Equivalent
K
3t² + 3t
Answer: The answer is 81m + 27t
Step-by-step explanation:
Answer: (3t)^t+3 and 3^t^2 x 27^t are both equivalent to the expression while 9^t x 27^t is not equivalent.
Step-by-step explanation:
how many solutions does have 9x+3=6x-12=3x
Answer: only one solution
Step-by-step explanation:
9x + 2/3 = 3x + 3 is a linear equation.
Linear equations only have one solution as the lowest power in numbers is 1.
9x + 2/3 = 3x + 3
9x - 3x = 3 - 2/3
3x = 7/3
x = (7/3)/3
x = 7/9
Write an equation of the line with the given slope and y-intercept
Slope: 4
y-intercept: -8
[tex]y = 4x -8\qquad \impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}[/tex]
is 23/25 greater than or less than9/10
23/25 is greater than 9/10
23/25=92/100
9/10=90/10
92>90
1.109, 1.1, 1.19, 1.1091 order these numbers from least to greatest
f(x) = -x² +9
Find f(-5)
Answer:
f(-5) = -16
Step-by-step explanation:
f(-5) = - [tex](-5)^{2}[/tex] + 9
-(25) + 9
-25+9
-16
Which is the order from least to greatest of the following: six fifths, eight ninths, 0.5, forty percent?
forty percent, 0.5, eight ninths, six fifths
six fifths, eight ninths, 0.5, forty percent
0.5, forty percent, six fifths, eight ninths
eight ninths, 0.5, six fifths, forty percent
The order from least to greatest is "forty percent, 0.5, eight-ninths, six-fifths".
What is a fraction?A fraction is a part of the whole represented by a/b, where a and b are any integers.
The given numbers are,
six fifths = 6/5 = 1.2
eight ninths = 8/9 = 0.9
0.5
40% = 0.4
Therefore, the order from least to greatest is "forty percent, 0.5, eight-ninths, six-fifths".
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(5x + 5)°
95°
Fill in the blanks based on the diagram.
Step 1: 5x +
Step 2: 5x
Step 3: x =
In the expression 5x + 5 = 95, the value of x is 18
What is an angle ?
An angle is the figure formed by two rays, called the sides of the angle, sharing a common endpoint, called the vertex of the angle.
The given angle 5x + 5 is equal to 95
We need to calculate the value of x
5x + 5 = 95
5x = 95 - 5
5x = 90
x = 90/5
x = 18
Therefore, the expression 5x + 5 = 95 is solve and the value of x is 18
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WILL GIVE 20 POINTS IF RIGHT PLEASE HELP
Given the points E(-4,k) and F(k,7) find the value of K so that the slope of EF is 2/3.
Answer:The answer is:
k
=
2
.
Given two point,
A
(
x
a
,
y
a
)
and
B
(
x
b
,
y
b
)
the slope of the line that passes from them is:
m
=
y
b
−
y
a
x
b
−
x
a
.
So:
−
2
=
6
−
2
k
−
4
⇒
−
2
(
k
−
4
)
=
4
⇒
−
2
k
+
8
=
4
⇒
−
2
k
=
−
4
⇒
k
=
2
.
Step-by-step explanation:The answer is:
k
=
2
.
Given two point,
A
(
x
a
,
y
a
)
and
B
(
x
b
,
y
b
)
the slope of the line that passes from them is:
m
=
y
b
−
y
a
x
b
−
x
a
.
So:
−
2
=
6
−
2
k
−
4
⇒
−
2
(
k
−
4
)
=
4
⇒
−
2
k
+
8
=
4
⇒
−
2
k
=
−
4
⇒
k
=
2
.
The volume of the solid bounded above by the parabolic cylinder
z
=
1
−
y
2
, below by the plane
3
x
+
3
y
+
z
+
10
=
0
, and on the sides by the circular cylinder
x
2
+
y
2
−
x
=
0
. (A triple integral)
The volume of the solid bounded above by the parabolic cylinder is 191π/64.
Given:
the Parabolic cylinder z=1−y^2 and below the plane 3x+3y+z+10=0 and on the sides of circular cylinder x^2+y^2−x=0.
[tex]x^2+y^2-x=(x-\frac12)^2 +y^2-\frac14=0[/tex]
Recenter the circle with x−1/2=u and integrate the volume over the disk
u^2+y^2 = 1/4.
[tex]\int_{u^2+y^2 < \frac14} [(1-y^2)-( -2x-3y-10)][/tex]
[tex]=\int_{u^2+y^2 < \frac14} (2u+3y-y^2 +12)[/tex]
[tex]=\int_{u^2+y^2 < \frac14} (12-y^2)[/tex]
[tex]=\int_0^{2\pi}\int_0^{1/2} (12-r^2 \sin^2\theta)rdr d\theta =\frac{191\pi}{64}\\[/tex]
Therefore The volume of the solid bounded above by the parabolic cylinder is 191π/64.
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What is What is 2/5+(1/2)2
The 2 is an exponent
And the others are fractions
2/5+(1/2)
The value is 13/20
We do simplification here
2/5+1/4
=(8+5)/20
=13/20
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Ken reads 1 1/2 pages in a book in 3/4 minute. How many minutes does it take him to read one page
9. Emily measured the depth of water in a bathtub at two-minute intervals after the tap was turned off and the
stopper released. The table shows her data.
a) Make a scatter plot for the data.
b) Describe the correlation of the scatter plot.
c) What will the approximate depth be at 15 seconds?
Considering the data in the table, it is found that:
a) The scatter plot is given by the image at the end of the answer.
b) The correlation of the scatter plot is negative, as when the input increases the output decreases.
c) The estimate for the depth at 15 seconds is of 50.37 cm.
How to built the scatter plot?The scatter plot is built inserting all the points in the table, which are in the following format:
(Time, Depth).
Hence the points are given as follows:
(2, 47), (4, 41), (6, 38), (8, 37), (10, 32), (12, 24), (14, 20), (16, 19).
From both the table and the scatter plot given by the image at the end of the answer, as the input increases, the output decreases, hence the scatter plot has a negative correlation.
To make a prediction for a given input, the line of best fit has to be constructed using these points.
Inserting these points into a linear regression calculator, the line of best fit is:
y = -2.07x + 50.89.
At a time of 15 seconds = 0.25 minutes, the depth will be of:
y = -2.07 x 0.25 + 50.89 = 50.37 cm.
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Elena said the equation 8x + 16 = 2x + 16 has no solutions because 8x is greater than 2x. Do you agree with Elena? Explain your reasoning.
Answer:6x
Step-by-step explanation: Put the x's on one side and other on the other side
Answer:
The equation has a solution,
x = 0Step-by-step explanation:
Given equation,
→ 8x + 16 = 2x + 16
Now the value of x will be,
→ 8x + 16 = 2x + 16
→ 8x - 2x = 16 - 16
→ 6x = 0
→ x = 0/6
→ [ x = 0 ]
Hence, the value of x is 0.
The people at a party tried to form teams with the same number of people on each team, but when they tried to split up into teams of 2, 3, 5, or 7, exactly one person was left without a team. What is the smallest number of people (greater than $\color[rgb]{0.35,0.35,0.35}1$) who could have been at the party?
The smallest number of people when one could have been at the party is 211 people.
How to illustrate the information?This is a least common multiple question, also known as an LCM. We know this because all groups would have formed evenly if the one extra person had not arrived at the party. This means that there are 1 more people at the party than a number 2, 3, 5, or 7.
In this case, the number will be:
= (2 × 3 × 5 × 7) + 1
= 210 + 1
= 211
Applicable multiples of 7
(7 × 10) = 70 → 70 + 1 = 71 → 71/3 = 23 R2 → not possible
(7 × 20) = 140 → 140 + 1 = 141 → 141/3 = 47 → not possible
(7 × 30) = 210 → 210 +1 = 211 → 211/3 = 70 R1 → possible.
Therefore, the number of people is 211.
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i dont understand it
The given expression 7x - y = -9 in the slope intercept form can be represented as y = 7x + 9.
The expression given to us is -
7x - y = -9
We have to represent this in the slope intercept form.
The slope intercept form can be represented as -
y = mx + c
where, y = y coordinate of the line
m = slope of the line
x = x coordinate of the line
c = y intercept of the line
Thus, representing the given expression in the slope intercept form, we have
7x - y = -9
=> -y = -7x - 9
=> y = 7x + 9
Thus, the given expression in the slope intercept form can be represented as y = 7x + 9.
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g if the standard deviation of the lifetimes of television tubes is estimated to be 100 h, how large a sample must we take in order to be (a) 95%, (b) 99%, and (c) 99.73% confident that the error in the estimated mean lifetime will not exceed 20 h?.
Question content area top Part 1 The length of the base of an isosceles triangle is 2x-6. The length of a leg is x. The perimeter of the triangle is 43 . Find x.
The value of x in the isosceles triangle is 9.25.
What is the value of x?An isosceles triangle is a polygon that has three sides. The opposite length have the same length and equal angles. has two opposite sides. If the two angles are equal , it means the triangle is an isosceles.
Th perimeter of an isosceles triangle is the sum of the length of the three sides of the triangle.
Perimeter = (2 x length of leg) + base
43 = (2x x) + 2x - 6
43 = 2x + 2x - 6
43 = 4x - 6
43 - 6 = 4x
37 = 4x
x = 37 / 4
x = 9.25
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vthe waitress at the restaurant provided really good service so you and your friends decided to add on an 20% tip to your $32 bill. how much money will be added onto the bill for the tip?
The answer of the given question is $6.4, this is the money that need to be added onto the bill for the tip.
How to calculate a 20% tip?
To calculate tip, we need to multiply the total bill by 1 plus the decimal percentage tip we'd like to leave. If we wanted to leave a 20% tip, we would add 1 to 0.20 to get 1.20. Then, multiply the bill by 1.20 to get the total amount we'd leave including tip.
In this case, we have a $32 bill and we would like to add on an 20% tip. So, it will be as follows:
20% = 0.20
1 + 0.20 = 1.20
Total bill will be 1.20 x $32 = $38.4
Hence, the tip amount is $38.4 - $32 = $6.4
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THE RIGHT ANSWER GETS 10 POINTS AND BRAINLIEST
An oil company fills 1 over 12 of a tank in 1 over 3 hour. At this rate, which expression can be used to determine how long it will take for the tank to fill completely? (1 point)
a
1 over 12 • 3 hours
b
1 over 3 • 12 hours
c
1 over 3 • 1 over 12 hour
d
3 • 12 hours
Answer:
B. 1 over 3 x 12 hours
Step-by-step explanation:
The oil company fills 1/12 of a tank in 1/3 an hour. So, you multiply 1/3 times 12, since 12 is a full tank. It'll take 4 hours to fill the tank at this rate.
1/12 tank: 1/3 hour
2/12 tank: 2/3 hour
3/12 tank: Full hour
3/12 is equivalent to 1/4, meaning 1/4 of the tank is filled after 1 hour. Thus, it'll take 4 hours.
How many quart of pure antifreeze mut be added to 5 quart of a 10% antifreeze olution to obtain a 30% antifreeze olution?
The amount of pure antifreeze that needs to be added = 1.429 quarts
What is antifreeze ?
A colored liquid called antifreeze, often known as engine coolant, is combined with water to assist regulate your engine in extremely hot weather.
Let x be the amount of pure antifreeze that needs to be added
The amount of pure antifreeze added (x) plus the amount of pure antifreeze in the 5 quart of 10% antifreeze solution [ 0.1*5] should be equal to the amount of pure antifreeze in the final mixture [ 0.3*(5+x) ]
The equation obtained is:
x+[0.10*5]=0.30(5+x)
x+0.5=1.5+0.30x
x-0.30x =1.5-0.5 = 1
0.70x=1
divide each side by 0.70
x=1.429 quarts
So, the amount of pure antifreeze that needs to be added = 1.429 quarts
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what is the rotational symmetry of this please somone tell me
The rotational symmetry of the above attached figure is 4 ...
What is the rotational symmetry ?
= Rotational symmetry is the number of times a shape can “fit into itself” , when it is rotated 360° about its centre....
Example: Rotational Symmetry of Equilateral Triangle..
Equal sides and angles define an equilateral triangle.
• How can u find rotational symmetry ?
= An object has rotational symmetry if that figure is itself after you rotate it less than 180 degrees. If it is itself after exactly 180 degrees no more no less then that figure has point symmetry.
The rotational symmetry of the above attached figure is 4 ...
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To raise money for after-school programs at an elementary school, a group of parents is holding a weekend of games in a community center. They charge $8 per person for entry into the event. The group would like to earn at least $600, after paying for the cost of renting the space, which is $40 an hour.
The inequality represents the situation group of parents who would like to earn at least $600, after paying for the cost of renting the space $40 an hour, and charging $8 per person for entry into the event is 8x - 4y ≥ 600, and x > 0, Y > 0.
We are given the following;
They charge $8 per person for entry into the event.
The group would like to earn at least $600, after paying for the cost of renting the space, which is $40 an hour.
Let the number of people be x and the number of hours they are present in the space be y.
Per person entry cost is $8.
Donations by all the people entering the space are 8x.
The per hour cost of rent is $40.
The total cost of renting the space is 40y which will be subtracted from the total amount of donations.
They plan to earn a minimum of $600.
So, the inequality will be given by;
8x - 4y ≥ 600 and x > 0, Y > 0.
Thus, the inequality represents the situation group of parents who would like to earn at least $600, after paying for the cost of renting the space $40 an hour, and charging $8 per person for entry into the event is 8x - 4y ≥ 600, and x > 0, Y > 0.
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What is the percent of increase from 5 to 8
Answer: 60%
Step-by-step explanation:
(5 × p) / 100 = 3
((5 × p) / 100) × 100 = 3 × 100
5p = 300
5p / 5 = 300 / 5
p = 60
Percent Increase = 60
describe the end behavior of each function
Answer:
f(x) = - x² + 2x - 2 :
x → - ∞
f(x) → - ∞
f(x) = x⁴ + 3x² + x - 3 :
x → ∞
f(x) → ∞
For the following right triangle, find the side length x.
24
10
x
The side length, x, of the right triangle will be 26 units.
According to the question,
We have the following information:
In a right triangle, two of the sides are 24 units and 10 units.
The complete question is that 24 units is the perpendicular and 10 units is the base of the given right triangle.
Let's denote hypotenuse with h, perpendicular with p and base with b.
We will find the hypotenuse of the triangle using the Pythagoras theorem:
[tex]h^{2} = b^{2} +p^{2}[/tex]
[tex]h^{2}= (24)^{2}+ (10)^{2}[/tex]
[tex]h^{2} = 476+100\\h^{2} = 576[/tex]
h = √576
h = 26 units
Hence, the side length, x, of the right triangle will be 26 units.
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