Answer:
a) The sample mean is 1260 and the standard deviation is 48.
b) The 90% confidence interval for the mean of all tree-ring dates from this archaeological site is (1230, 1290).
Step-by-step explanation:
Question a:
Mean is the sum of all values divided by the number of values. So
[tex]\overline{x} = \frac{1285 + 1187 + 1222 + 1194 + 1268 + 1316 + 1275 + 1317 + 1275}{9} = 1260[/tex]
Standard deviation is the square root of the sum of the differences squared between each value and the mean, divided by the one less than the sample size. So
[tex]s = \sqrt{\frac{(1285-1260)^2 + (1187-1260)^2 + (1222-1260)^2 + (1194-1260)^2 + (1268-1260)^2 + ...}{8}} = 48[/tex]
The sample mean is 1260 and the standard deviation is 48.
Question b:
We have the standard deviation for the sample, which means that the t-distribution is used to solve this question.
The first step to solve this problem is finding how many degrees of freedom,which is the sample size subtracted by 1. So
df = 9 - 1 = 8
90% confidence interval
Now, we have to find a value of T, which is found looking at the t table, with 8 degrees of freedom(y-axis) and a confidence level of [tex]1 - \frac{1 - 0.9}{2} = 0.95[/tex]. So we have T = 1.8595
The margin of error is:
[tex]M = T\frac{s}{\sqrt{n}} = 1.8595\frac{48}{\sqrt{9}} = 30[/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 1260 - 30 = 1230
The upper end of the interval is the sample mean added to M. So it is 1260 + 30 = 1290
The 90% confidence interval for the mean of all tree-ring dates from this archaeological site is (1230, 1290).
a tube has a radius of 4 inches and a height of 4 inches. what's its approximate volume?
Step-by-step explanation:
that is the same as the volume of a cylinder :
pi×r²×height = pi×4²×4 = pi×64 = 201.0619298... in³
≈ 201 in³
Volume is a three-dimensional scalar quantity. The volume of the tube is 201.0619 inches³.
What is volume?A volume is a scalar number that expresses the amount of three-dimensional space enclosed by a closed surface.
The volume of a cylinder is given by the formula as shown below,
Volume of a cylinder = πr²h
where r is the radius of the cylinder while h is the height of the cylinder.
Given that a tube has a radius of 4 inches and a height of 4 inches. Therefore, the volume of the tube will be,
The volume of the tube = π × R² × h
= π × (4 inches)² × (4 inches)
= 64π inches³
= 201.0619 inches³
Hence, the volume of the tube is 201.0619 inches³.
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PLZ HELP ME WITH MY MATH HOMEWORK!!!!!! SHOW WORK
Answer:
Step-by-step explanation:
-(4q+8) + 6q = 12q - 5/6(18q + 6)
Open brackets:
<=> - 4q - 8 + 6q = 12q - 5/6*18q - 5/6*6
<=> - 4q - 8 + 6q = 12q - 15q - 5
Put q in one side and non q in one side:
<=> - 4q + 6q - 12q + 15q = 8 - 5
<=> 5q = 3
<=> q = 3/5
A $300 bike is marked down to $175. Find the percent markdown to the nearest whole percent.
Answer:
58
Step-by-step explanation:
58 because you divide 200 by 100 then getting that answer (3) then divide 175 by 3 which equals one percent and you get 58.333 you round it to the nearest whole and u get 58
[tex]\sf 3x+6y=12[/tex]
Answer:
[tex]3x + 6y = 12[/tex]
[tex]3x + 6y - 6y = 12 - 6y[/tex]
[tex]3x = 12 - 6y[/tex]
[tex] \frac{3x}{3} = \frac{12}{3} - \frac{6y}{3} [/tex]
[tex] \frac{3x}{3} = 1 = x[/tex]
[tex] \frac{12}{3} - \frac{6y}{3} [/tex]
[tex] = \frac{12 - 6y}{3} [/tex]
[tex] = \frac{6(2 - y)}{3} [/tex]
[tex] \frac{6}{3} = 2[/tex]
[tex] = 2( - y + 2)[/tex]
[tex]x = 2( - y + 2)[/tex]
Answer:
x=2(3-y)
Step-by-step explanation:
3x+6y=12
x+2y=4
x=4-2y
=2(2-y)
Can you please help me
Answer: 1/6
Step-by-step explanation:
Given:
4/9 and 11/18
Solve:
STEP ONE: Make the denominators equal by determining the LCM
LCM = Least Common Multiple
First Five multiples of 9 = 9, 18, 27, 36, 45
First FIve multiples of 18 = 18, 36, 54, 72, 90
As we can see from the list above, both 18 and 36 overlap, however, 18 is less than 36. Therefore, 18 is the LCM.
STEP TWO: Compare the size and determine the greater one.
4/9 = (4 × 2) / (9 × 2) = 8/18
11/18 = 11/18
Since 11 > 8, therefore, 11/18 is greater than 8/18
STEP THREE: Find the difference between the two fractions.
11/18 - 4/9
=11/18 - 8/18
=(11 - 8) / 18
= 3 / 18
= 1/6
Hope this helps!! :)
Please let me know if you have any questions
What is the value of 40 1/2÷3 1/2
Answer:
81/7 (11.57, 11 4/7)
Step-by-step explanation:
Lets rewrite these mixed fractions
[tex]40\frac{1}{2}=\frac{81}{2}[/tex]
[tex]3\frac{1}{2} =\frac{7}{2}[/tex]
Here we can do divide these two numbers:
[tex]\frac{\frac{81}{2} }{\frac{7}{2} }=\frac{81}{7}[/tex]
The answer therefore is 81/7, or 11.571 (11 4/7)
CAN SOMEONE HELP ME WITH THIS?
Answer:
d
Step-by-step explanation:
Solve for x. 2^4x-7=16
Answer:
23/16
Step-by-step explanation:
2*4 x x-7 = 16
16x - 7 = 16
16x = 16 + 7
16x = 23
x = 23/16
Give me a rating XD <3
Q: Solve for x: 8x-2-5x=8
A. OX=13
B. OX=2 1/2
C. OX=3 1/3
D. OX=7
Answer:
c. 3 1/3
Step-by-step explanation:
8x-2-5x=8
3x=10
x=10/3=3 1/3
Answer:
x=[tex]3\frac{1}{3}[/tex]
Step-by-step explanation:
Hi there!
We want to find the value of x in this expression:
8x-2-5x=8
Our goal is to isolate x on one side
Combine like terms on the left side (add the terms with x together)
3x-2=8
Add 2 to both sides (-2+2=0)
3x-2=8
+2 +2
__________
3x=10
Divide both sides by 3
x=[tex]\frac{10}{3}[/tex]
Simplify the improper fraction
x=[tex]3\frac{1}{3}[/tex]
Hope this helps!
During a visit to the tide pools, Brent observed 16 sea stars, 4 sea urchins, and 52 sea anemones. What is the ratio of sea anemones to sea stars?
Answer:
16 to 52
Step-by-step explanation:
3-8(1+8x)=-133
Solve for x
Answer:
x=2
Step-by-step explanation:
Expanding, we have 3 - 8-64x=-133.
Combining like terms, we have -5 - 64x=-133
Adding 5 to both sides, we have -64x= -128
Dividing by -64, we have x = 2
Fill in the blanks to solve 900 x 6
Answer:
The answer is 900 ×6= 5,400 u can use a calculator
Need help please and thank you.
Answer:
[tex]log_4(\frac{1}{64})=-3[/tex]
Step-by-step explanation:
[tex]log_b(b^x)=x[/tex]
Let b = base and x = the exponentLooking at the equation given, we know the base (the number with the exponent) is 4, the exponent itself is -3, and the value is 1/64. Based on this information, fill in the formula and simplify any values.
[tex]log_4(4^{-3})=-3\\log_4(\frac{1}{64})=-3[/tex]
Therefore, the logarithmic form is [tex]log_4(\frac{1}{64})=-3[/tex].
11)
Given the function, f(x) = x2 + 5x - 3 evaluate f(-2).
Answer:
f(- 2) = - 9
Step-by-step explanation:
Substitute x = - 2 into f(x) , that is
f(- 2) = (- 2)² + 5(- 2) - 3 = 4 - 10 - 3 = 4 - 13 = - 9
Given the function f(x) = -5x + 2, find the range ofly for x = -1, 0, 1.
O 7, 2, -3
O 7, 2, 3
O-7, -2, 3
0-7, -2, -3
Answer:
A
Step-by-step explanation:
f(-1)=7, f(0)=2, f(1)=-3
Find an equation in slope-intercept form of the line satisfying the specified conditions.
Through (8,-3), perpendicular to -6x + 7y=-62.
Answer:
[tex]y = - \frac{7}{6} x + 6 \frac{1}{3} [/tex]
Step-by-step explanation:
Slope-intercept form
y= mx +c, where m is the slope and c is the y-intercept.
-6x +7y= -62
Rewriting this equation into the slope-intercept form:
7y= 6x -62
[tex]y = \frac{6}{7} x - \frac{62}{7} [/tex]
The product of the slope of 2 perpendicular lines is -1.
Let the slope of the unknown line be m.
[tex]m( \frac{6}{7} ) = - 1[/tex]
[tex]m = - 1 \div \frac{6}{7} [/tex]
[tex]m = - \frac{7}{6} [/tex]
Substitute the value of m into the equation:
[tex]y = - \frac{7}{6} x + c[/tex]
To find the value of c, substitute a pair of coordinates into the equation.
When x= 8, y= -3,
[tex] - 3 = - \frac{ 7}{6} (8) + c[/tex]
[tex] - 3 = - \frac{28}{3} + c[/tex]
[tex]c = \frac{28}{3} - 3[/tex]
[tex]c = \frac{19}{3} [/tex]
[tex]c = 6 \frac{1}{3} [/tex]
Thus, the equation of the line is [tex]y = - \frac{7}{6} x + 6 \frac{1}{3} [/tex].
6x + 34x - 6 =8(5x + 10)
[tex]6x+34x -6 = 8(5x+10)\\\\\implies 40x -6 = 40x +10\\\\\implies 40x -40x = 10+6 \\\\\implies 0 =16\\\\\text{Which is not true. So no solution.}[/tex]
What type of association does the graph show between x and y
Answer:
Nonlinear positive association
Step-by-step explanation:
It is nonlinear because it does not form a straight line.
It is positive because it is going up to the right.
I hope this helps!
if 24 bags of sugar with equal weight weigh 21 kg, how many bags of sugar would weigh 122kg?
Answer:
24 bags = 21 kg
1.142 bag = 1 kg
About 139 bags = 122 kg
You start off with 24 bags that equal the same amount as 21 kg. You need to find out how many bags of sugar equal the same amount as 122 kg. The first line is a ratio and to find your answer you need to figure out what is 1 kilogram equal to in the amount of bags. You divide both sides by 21 leaving 1.142 bag equal to 1 kilogram. In order to find 122 kilograms, you have to multiply both sides by 122 kilograms which would give you about 139 bags = 122 kilograms.
Your final answer: 139 bags
I hope this helped!
If Janet earned e extra credit points. Mona earned 32 fewer extra credit points than Janet.
What is the expression that shows how many extra credit points Mona earned?
How many terms are in the expression?
A pair of pants costs $24.60 when it is on sale for 25% off. What was the
original cost of the pants? (still....no labels!)
well, we know the pants are 25% off, that means the current sale price is only 75% of the original price, say the original price is "x" or 100%. So we know that $24.60 is 75%, what is the 100%?
[tex]\begin{array}{ccll} amount&\%\\ \cline{1-2} 24.6&75\\ x&100 \end{array}\implies \cfrac{24.6}{x}=\cfrac{75}{100}\implies \cfrac{24.6}{x}=\cfrac{3}{4} \\\\\\ 98.4=3x \implies \cfrac{98.4}{3}=x\implies 32.8=x[/tex]
Simplify the expression 16+(−5)−6/7j−2/7j+6
If Jenny can read 7 books in 8 days, exactly how many days would it take her to read 20 books?
Answer:
17 and a half days OR 18 days
Step-by-step explanation:
7 books : 8 days
20 books: x days
cross multiply
x = (8×20)÷ 7
x = 17.5
therefore
17 and a half days or 18 days
Find the equation of the line
Answer:
Y = 4x - 9
Step-by-step explanation:
Hope this helps! If it’s wrong I’m really sorry.
Pls give brainliest!
Answer:
...
Step-by-step explanation:
please help ill mark brainliest
Answer:
x=3
Step-by-step explanation:
6(x+5)=4(x+9)
6x+30=4x+36
2x+30=36
2x=6
x=3
I’m failing pls help I’ll brainlest ASAP
Kendall tracked the amount of water his windowsill plant needed each week over ten weeks. Her data is shown below.
Which of the following is true?
A.
There is a negative association between the number of weeks and the ounces of water the plant needed.
B.
There is a positive association between the number of weeks and the ounces of water the plant needed.
C.
There is no association between the number of weeks and the ounces of water the plant needed.
D.
There is both a positive and negative association between the number of weeks and the ounces of water the plant needed.
Answer:
Perfort the indicated operation Show your solution in
the gevin below
Simply:
3 (2x - 2) -2 (x - 2)
A: 3x -3
B: 3x -4
C: 4x -2
D: 4x -4
Answer:
4x-2
Step-by-step explanation:
6x-6-2x+4
=4x-2
Rebecca can swim 90 meters in 2 minutes. If you graph this with minutes on the x-axis and meters on the y-axis, what will be the slope of the line?
May I please have some help with this problem?
The slope of a line is the average rate of change of the line.
The slope of the line would be 45
From the question, we understand that she can swim 90 meters in 2 minutes.
So, the slope (m) of the line of the graph would be
[tex]m=\frac{90 - 0}{2 - 0}[/tex]
Simplify the numerator, and the denominator
[tex]m=\frac{90}{2}[/tex]
Divide 90 by 2
[tex]m=45[/tex]
Hence, the slope of the line would be 45
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A large bag contains 29 balls of different colors. The balls are of the same size, weight, surface, such that besides the color they cannot be differentiated. Among the 29 balls, 8 are green, 4 are yellow, 6 are red, 5 are blue, and 6 are black.
(a) What is the probability of getting exactly 1 green, 1 yellow and 2 red when pulling 8 balls? number (rtol=0.01, atol=0,0001)
(b) What is the probability of getting first a green, then another green, and then in any order 2 yellow and 2 red when pulling 6 balls? number (rtol=0.01. atol=0.0001)
(c) What is the probability of getting first and last a green, and then in any order 2 yellow and 2 red when pulling 8 balls? (Note: If there are remaining balls, they need to be either blue or black) number (rtol=0.01, atol=0.0001)
(d) What is the probability of getting 2 blue and 2 non-blue when pulling 4 balls? number (rtol=0.01, atol=0.0001)
(e) Recalculate part (d) using a binomial distribution. number (rtol=0.01, atol=0.0001)
Answer:
White
6
Red
9
Green
Total number of balls =5+6+9
=20
(i) Probability =
Total cases
favourable cases
P(Green) =
20
9
(ii) P(White or red) =
20
5+6
=
20
11
(iii) P(neither green nor white) = P(Red)
=
20
6
=
10
3
The probability of getting exactly 1 green, 1 yellow, and 2 red when pulling 8 balls is 0.000303.
The probability of getting first a green, then another green, and then in any order 2 yellow and 2 red when pulling 6 balls is 0.00283.
(a) Probability of getting exactly 1 green, 1 yellow, and 2 red when pulling 8 balls:
Total number of balls = 29
Total number of balls to be pulled = 8
Number of ways to choose 1 green out of 8 = C(8, 1) = 8
Number of ways to choose 1 yellow out of the remaining 7 = C(7, 1) = 7
Number of ways to choose 2 red out of the remaining 6 = C(6, 2) = 15
Total favorable outcomes = 8 x 7 x 15 = 840
Total possible outcomes = C(29, 8) = 2,765,905
Probability
= favorable outcomes / possible outcomes
= 840 / 2,765,905
= 0.000303
Therefore, the probability of getting exactly 1 green, 1 yellow, and 2 red when pulling 8 balls is 0.000303.
(b) Total number of balls = 29
Total number of balls to be pulled = 6
Number of ways to choose 1 green out of 8 = C(8, 1) = 8
Number of ways to choose another green out of the remaining 7 = C(7, 1) = 7
Number of ways to choose 2 yellow out of the remaining 5 = C(5, 2) = 10
Number of ways to choose 2 red out of the remaining 3 = C(3, 2) = 3
Total favorable outcomes = 8 x 7 x 10 x 3 = 1,680
Total possible outcomes = C(29, 6) = 593,775
Probability
= favorable outcomes / possible outcomes
= 1,680 / 593,775
= 0.00283
Therefore, the probability of getting first a green, then another green, and then in any order 2 yellow and 2 red when pulling 6 balls is 0.00283.
(c) Probability of getting first and last a green, and then in any order 2 yellow and 2 red when pulling 8 balls:
Total number of balls = 29
Total number of balls to be pulled = 8
Number of ways to choose the first green = C(8, 1) = 8
Number of ways to choose the last green = C(7, 1) = 7
Number of ways to choose 2 yellow out of the remaining 6 = C(6, 2) = 15
Number of ways to choose 2 red out of the remaining 4 = C(4, 2) = 6
Number of ways to choose the remaining 2 balls (either blue or black) = C(5, 2) = 10
Total favorable outcomes = 8 x 7 x 15 x 6x 10 = 50,400
Total possible outcomes = C(29, 8) = 2,765,905
Probability
= 50,400 / 2,765,905 ≈ 0.0182
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