Answer:
The 95% confidence interval for the population mean is ($6510, $7138).
Step-by-step explanation:
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 = 7 - 1 = 6
95% confidence interval
Now, we have to find a value of T, which is found looking at the t table, with 6 degrees of freedom(y-axis) and a confidence level of [tex]1 - \frac{1 - 0.95}{2} = 0.975[/tex]. So we have T = 2.4469.
The margin of error is:
[tex]M = T\frac{s}{\sqrt{n}} = 2.4469\frac{340}{\sqrt{7}} = 314[/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 6824 - 314 = $6510.
The upper end of the interval is the sample mean added to M. So it is 6824 + 314 = $7138.
The 95% confidence interval for the population mean is ($6510, $7138).
Determine how many days t will the two isotopes have the same activity
Answer:
t = 1 ... one day
Step-by-step explanation:
3 x [tex]10^{18}[/tex] * [tex](.5)^{t}[/tex] = 6 x [tex]10^{18}[/tex] * [tex](.5)^{2t}[/tex]
3 x [tex]10^{18}[/tex] = [tex](.5)^{2t}[/tex] / [tex](.5)^{t}[/tex]
6 x [tex]10^{18}[/tex]
1/2 = [tex].5^{t}[/tex]
ln( 1/2) = t ln( [tex].5[/tex] )
t = ln( .5)/ln( [tex].5[/tex] )
t = 1
Devaughn is 10 years older than Sydney. The sum of their ages is 104. What is Sydney's age?
I
Answer:
Sydney's age = 42
Step-by-step explanation:
104 divided by 2 = 52
52 - 10 = 42
I am sorry if this is wrong. But this is what I learned at my school.
Please answer this question. Will give brainiest fast
Answer: The answer is C the one you chose
if the r-value, or correlation coefficient, of a data set is 0.941, what is the coefficient of determination
Answer:0.824
Step-by-step explanation:
The coefficient of determination is approximately 0.885 or 88.5%.
What is the correlation coefficient?A correlation coefficient (r) is a number between -1 and 1 that measures the strength and direction of a linear relationship between two variables.
The coefficient of determination (R-squared) is equal to the square of the correlation coefficient (r).
Therefore, to find the coefficient of determination with an r-value of 0.941, we can simply square it:
R-squared = r² = 0.941² = 0.885481
Thus, the coefficient of determination is approximately 0.885 or 88.5%.
This means that 88.5% of the variation in the dependent variable can be explained by the independent variable(s) in the data set.
Learn more about the correlation coefficient here:
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In the following scenario for a hypothesis test for a population? mean, decide whether the? z-test is an appropriate method for conducting the hypothesis test. Assume that the population standard deviation is known. Preliminary data analyses reveal that the sample data contain no outliers but that the distribution of the variable under consideration is probably mildly skewed. The sample size is 70.
Choose the correct answer below.
a. The z-test is not an appropriate method, because the sample size is too small to be useful.
b. The z-test is an appropriate method, because the sample contains no outliers.
c. The z-test is an appropriate method, because the sample size is sufficiently large that the skewness of the variable does not matter.
d. The Z-test is not an appropriate method, because the sample is not a large sample and the data are highly skewed.
ASAP!!!!!! SHOW WORK!!!! Thank you!!!!!!!!!
Its A trapezium
For Calculations Refer to the attachment
Answer:
SquareStep-by-step explanation:
Plot the points.
See the attached.
It is easy to calculate the length of sides and diagonals using the coordinates and the distance formula.
The sides are all equal to [tex]\sqrt{5}[/tex] units and the diagonals are both equal to [tex]\sqrt{10}[/tex] units.
This is a property of a square.
write your answer in simplest radical form
Answer:
y = 2
Step-by-step explanation:
y = √2 × √2 = 2
It's a 45-45-90 triangle
a game is played with a circular spinner that contains 7 different colors. the design of the spinner is the order in which the colors are arranged. how many ways can this spinner be designed
Answer:
This spinner can be designed in 5040 ways.
Step-by-step explanation:
Number of possible arrangements:
The number of possible arrangements of n elements is given by:
[tex]A_{n} = n![/tex]
In this question:
7 colors, so:
[tex]A_{7} = 7! = 5040[/tex]
This spinner can be designed in 5040 ways.
Solve for:
∫_(-1)^1 x^3+1/2 dx
Answer:
[tex]\int _{\left(-1\right)}^1\frac{x^3+1}{2}dx[/tex]
[tex]=\frac{1}{2}\cdot \int _{\left(-1\right)}^1x^3+1dx \Leftarrow(take \: constant\: out)[/tex]
[tex]=\frac{1}{2}\left(\int _{\left(-1\right)}^1x^3dx+\int _{\left(-1\right)}^11dx\right) \Longleftarrow (Sum\:Rule)[/tex]
[tex]\int _{\left(-1\right)}^1x^3dx=0[/tex]
[tex]\int _{\left(-1\right)}^11dx=2[/tex]
[tex]=\frac{1}{2}\left(0+2\right)[/tex]
[tex]=1[/tex]
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Please help. I don't understand how to solve for number 17, 19, and 21. Please show how you solved each problem
(17) From the plot, you see that
Pr[$15,500 ≤ x ≤ $18,500] = 99.7%
We can split up the probability on the left at the mean, so that
Pr[$15,500 ≤ x ≤ $17,000] + Pr[$17,000 ≤ x ≤ $18,500] = 99.7%
Any normal distribution is symmetric about its mean, so the two probabilities here are the same. The one on the left is what you want to compute. So you have
2 × Pr[$15,500 ≤ x ≤ $17,000] = 99.7%
==> Pr[$15,500 ≤ x ≤ $17,000] = 49.85%
(19) The mean of a normal distribution is also the median, so half the distribution lies to either side of the mean. Mathematically, we write
Pr[x ≥ $17,000] = 50%
The plot shows that
Pr[$16,500 ≤ x ≤ $17,500] = 68%
and by using the same reasoning as in (17), we have
Pr[$16,500 ≤ x ≤ $17,000] + Pr[$17,000 ≤ x ≤ $17,500] = 68%
2 × Pr[$17,000 ≤ x ≤ $17,500] = 68%
Pr[$17,000 ≤ x ≤ $17,500] = 34%
Now
Pr[x ≥ $17,000] = 50%
Pr[$17,000 ≤ x ≤ $17,500] + Pr[x ≥ $17,500] = 50%
34% + Pr[x ≥ $17,500] = 50%
==> Pr[x ≥ $17,500] = 16%
(21) From the plot,
Pr[$16,000 ≤ x ≤ $18,000] = 95%
This means (by definition of complement) that
Pr[x ≤ $16,000 or x ≥ $18,000] = 100% - 95% = 5%
and by symmetry,
Pr[x ≤ $16,000 or x ≥ $18,000] = 5%
Pr[x ≤ $16,000] + Pr[x ≥ $18,000] = 5%
2 × Pr[x ≤ $16,000] = 5%
==> Pr[x ≤ $16,000] = 2.5%
2. Caveman Sampson chases a saber tooth tiger at an average speed of 3 miles per hour. The tiger runs at an average speed of 5 miles per hour, but rests for 2 hours after running for 2 hours. How long, in hours, will it take Sampson to catch the tiger if the tiger starts 2 miles in front of him and they start running at the same time?
A. 7 hours B. 6 hours C. 5 hours D. 4 hours
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Answer:
D. 4 hours
Step-by-step explanation:
The tiger will run (5 mi/h)(2 h) = 10 mi in 2 hours. That will put it 2+10 = 12 miles from Sampson's starting location.
Samson can run 12 miles in time ...
time = distance/speed = (12 mi)/(3 mi/h) = 4 h
Sampson will get to the tiger's location after 4 hours, just as the tiger is ending its rest period.
__
The graph shows the position of Sampson (red) and the tiger (blue) x hours after the chase starts. The distance (y miles) is measured from Sampson's starting point, assuming the tiger is running away.
The slope of a line is −6. What is the slope of any line parallel to this line?
Answer:
-6
Step-by-step explanation:
Parallel lines have the same slope
If a line has a slope of -6, all lines parallel to this will have a slope of -6
Determine the type of quadrilateral given the following coordinates. Show and explain all steps to prove your answer. A(2, 3) B(-1, 4) C(0, 2) D(-3, 3)
Answer:
The quadrilateral is a parallelogram
Step-by-step explanation:
If you plot the points on the graph it resembles the shape of a parallelogram. It prove this you need to check if the lengths are correct. The slope between point A and point B is 1/3 and the slope between point C and point D is also 1.3. The slope between point B and D is 1/2 and the slope between point A and point C is also 1/2
hope this helps
The quadrilateral is a parallelogram from the graph and the coordinates formed are parallel and the opposite sides have equal length.
What is a parallelogram?A parallelogram is a quadrilateral whose opposite sides are parallel and equal in length. The opposite angles of a parallelogram are equal. The diagonals of a parallelogram bisect each other.
For the given situation,
The coordinates are A(2, 3) B(-1, 4) C(0, 2) D(-3, 3).
The graph below shows these points on the coordinates and the points ABDC forms the parallelogram.
This can be proved by finding the distance between these points.
The formula of distance between two points is
[tex]AB=\sqrt{(x2-x1)^{2}+ (y2-y1)^{2}}[/tex]
Distance AB is
⇒ [tex]AB=\sqrt{(-1-2)^{2}+ (4-3)^{2}}[/tex]
⇒ [tex]AB=\sqrt{(-3)^{2}+ (1)^{2}}[/tex]
⇒ [tex]AB=\sqrt{9+ 1}[/tex]
⇒ [tex]AB=\sqrt{10}[/tex]
Distance BD is
⇒ [tex]BD=\sqrt{(-3+1)^{2}+ (3-4)^{2}}[/tex]
⇒ [tex]BD=\sqrt{(-2)^{2}+ (-1)^{2}}[/tex]
⇒ [tex]BD=\sqrt{4+ 1}[/tex]
⇒ [tex]BD=\sqrt{5}[/tex]
Distance DC is
⇒ [tex]DC=\sqrt{(0+3)^{2}+ (3-2)^{2}}[/tex]
⇒ [tex]DC=\sqrt{(3)^{2}+ (1)^{2}}[/tex]
⇒ [tex]DC=\sqrt{9+ 1}[/tex]
⇒ [tex]DC=\sqrt{10}[/tex]
Distance CA is
⇒ [tex]CA=\sqrt{(2-0)^{2}+ (3-2)^{2}}[/tex]
⇒ [tex]CA=\sqrt{(2)^{2}+ (1)^{2}}[/tex]
⇒ [tex]CA=\sqrt{4+ 1}[/tex]
⇒ [tex]CA=\sqrt{5}[/tex]
Thus the lengths of the opposite sides are equal, the given points forms the parallelogram.
Hence we can conclude that the quadrilateral is a parallelogram from the graph and the coordinates formed are parallel and the opposite sides have equal length.
Learn more about parallelogram here
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A set of triplets weighted 4lb 3oz , 3 lb 9oz and 4 lb 5 oz . What is the total weight of all three babies ?
Answer:
12 lb 1 oz
Step-by-step explanation:
Add the amounts together
4lb 3oz ,
3 lb 9oz
4 lb 5 oz
-------------------
11 lb 17 oz
But 16 oz is 1 lb so subtract 16 oz and add 1 lb
11 lb 17 oz
+1lb - 16 oz
--------------------
12 lb 1 oz
ng and
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copy segments and compare segments for cong
find the length indicated.
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20
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Step-by-step explanation:
Put an 'X' in 35% of the rectangles. A 'Y' in 25% of the rectangles and a 'Z' in 15%. Show in detail how you determine how rectangles to mark.
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Answer:
X X X X X X XY Y Y Y YZ Z ZStep-by-step explanation:
There are 20 rectangles, so 35% of them is ...
0.35 × 20 = 7 . . . . will be marked with X
25% of them is ...
0.25 × 20 = 5 . . . . will be marked with Y
15% of them is ...
0.15 × 20 = 3 . . . . will be marked with Z
_____
Additional comment
The total number of markings is 7+5+3 = 15, which is fewer than the number of rectangles. Consequently, it is not necessary to put more than one mark in any given rectangle, unless you just want to .
please help!!!
find x
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Answer:
x = (17/2)√2
Step-by-step explanation:
The ratios of sides of an isosceles right triangle are ...
1 : 1 : √2
In this problem, that is identical to ...
x : x : 17
That is, ...
[tex]x=\dfrac{17}{\sqrt{2}}=\boxed{\dfrac{17}{2}\sqrt{2}}\qquad\text{after rationalizing the denominator}[/tex]
Identify the errors made in finding the inverse of
y = x2 + 12x
x= y2 + 12x
y2 = x -12
y2 = -11x
y= V-11x, for x 20
Describe the three errors
Answer:
x = y² + 12x
y² = x - 12
y² = -11x.
Step-by-step explanation:
We need to find the inverse of the given function , which is ,
[tex]\rm\implies y = x^2 + 12x [/tex]
Step 1 : Interchange x and y :-
[tex]\rm\implies x = y^2 + 12y [/tex]
But according to the steps given in the Question , in very first step in 12x , x is not replaced by y . After which , the steps go wrong in the question .
The 3 errors :-
x = y² + 12x y² = x - 12 y² = -11x.gegygwugduwbudbwbdubwudbuwh7fh7whf8hw8hf8hw8hf8e
Answer:
yes
Step-by-step explanation:
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The duration of shoppers' time in Browse Wrld's new retail outlets is normally distributed with a mean of 27.8 minutes and a standard deviation of 11.4 minutes. How long must a visit be to put a shopper in the longest 10 percent
Answer:
A visit must be of at least 42.39 minutes to put a shopper in the longest 10 percent.
Step-by-step explanation:
Normal Probability Distribution
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Mean of 27.8 minutes and a standard deviation of 11.4 minutes.
This means that [tex]\mu = 27.8, \sigma = 11.4[/tex]
How long must a visit be to put a shopper in the longest 10 percent?
The 100 - 10 = 90th percentile, which is X when Z has a p-value of 0.9, so X when Z = 1.28.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]1.28 = \frac{X - 27.8}{11.4}[/tex]
[tex]X - 27.8 = 1.28*11.4[/tex]
[tex]X = 42.39[/tex]
A visit must be of at least 42.39 minutes to put a shopper in the longest 10 percent.
What is the slope of the line that goes through (-1, – 7) and (3, 9)?
Answer:
4
Step-by-step explanation:
We can find the slope using the slope formula
m = ( y2-y1)/(x2-x1)
= ( 9 - -7)/( 3 - -1)
= (9+7)/(3+1)
=16/4
= 4
What would you do to isolate the variable in the equation below, using only one
step?
X + 9 = - 12
O Subtract 9 from both sides of the equation.
O Add 9 to both sides of the equation.
का
O Subtract 12 from both sides of the equation.
O Add 12 to both sides of the equation.
Answer:
O Subtract 9 from both sides of the equation.
Step-by-step explanation:
Notice that on the left hand side of the equation, you have two parts: X and 9. The variable is X, so we must do something to the 9 to remove it. Remember that we can cancel things by adding the negative of it. For example, 47+(-47)=0. Therefore, the opposite of 9 is -9. That essentially means subtracting 9.
1. What kind of special angle pair do the 2
angles make? (corresponding,
supplementary, or vertical)
Answer:
supplementary angle is whose is mesure is 180
Camille is attending a fundraiser. She pays for her admission and buys raffle tickets for $5dollar each. If she buys 10 raffle tickets, then she would spend a total of $135 at the fundraiser.
The number S of dollars Camille spends at the fundraiser is a function of r, the number of raffle tickets she buys.
Write the function's formula.
Answer:
50r + a = 135
Admission cost was $85
Step-by-step explanation:
We are missing a crucial amount of information here. It is how much she spent on her admission. We can create an equation symbolizing this problem.
5r + a = 135
We know that she purchases 10 tickets so we can substitute that in r and solve for a.
50 + a = 135
a = 85
Best of Luck!
Find the inverse relationship of the function y=2x+5
Answer:
y=x-5/2
Step-by-step explanation:
Swap y and x
x=2y+5
since a function has to be in the form y=mx+c
take 5 to the other side in order to remain with 2y then divide both sides by 2
x-5/2=y
y=x-5/2
Answer:
Duke is a very good team and
Q is equidistant from the sides of TSR. Find the value of x.
T
(2x + 240°
30°
S
R
Lets do
[tex]\\ \sf\longmapsto 2x + 24 = 30 \\ \\ \sf\longmapsto 2x = 30 - 24 \\ \\ \sf\longmapsto 2x = 6 \\ \\ \sf\longmapsto x = \frac{6}{2} \\ \\ \sf\longmapsto x = 3[/tex]
Refer to the picture above
Answer:
3.14
Step-by-step explanation:
First find the circumference of the circle:
[tex]2\pi r[/tex] = Circumference.
[tex]2 * \pi * 6[/tex] = [tex]12\pi[/tex]
Find the ratio of the angle in relation to the entire circle:
[tex]30^o[/tex] is what we have. So:
[tex]\frac{30^o}{360^o} = \frac{1}{12}[/tex]
Use the ratio and multiply the circumference to find the length:
[tex]12\pi * \frac{1}{12}[/tex] = [tex]\pi[/tex]
Round answer to the hundredth:
[tex]\pi = 3.14[/tex]
You want to buy a house that has a purchase price of $180,000 you plan to make a down payment of 10% of the purchase price and then while the rest what is the dollar value of the down payment?
Step-by-step explanation:
=10% of $180000
= 10*$180000/100
=$180
mited
Find any relative extrema of the function. List each extremum along with the x-value at which it occurs. Identify intervals over which the function is
increasing and over which it is decreasing. Then sketch a graph of the function.
f(x) = -x^3+ 9x?
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Answer:
relative minimum -6√3 at x = -√3relative maximum 6√3 at x = √3decreasing on x < -√3 and x > √3increasing on -√3 < x < √3see below for a graphStep-by-step explanation:
I find it convenient to draw the graph first when looking for relative extrema.
The function can be differentiated to get ...
f'(x) = -3x^2 +9
This is zero when ...
-3x^2 +9 = 0
x^2 = 3
x = ±√3 . . . . . x-values of relative extrema
Then the extreme values are ...
f(±√3) = x(9 -x^2) = (±√3)(9 -3) = ±6√3
The lower extreme (minimum) corresponds to the lower value of x (-√3), so the extrema are ...
(x, y) = (-√3, -6√3) and (√3, 6√3)
__
Since the leading coefficient is negative and the degree is odd, the function is decreasing for values of x below the minimum and above the maximum. It is increasing for values of x between the minimum and the maximum.
decreasing: x < -√3, and √3 < x
increasing: -√3 < x < √3
A cone has a volume of 4000cm3
. Determine the height of the cone if the diameter of the cone
is 30 cm.
Answer:
17cm
Step-by-step explanation:
Given that the Volume of a cone is 4,000 cm³. And we need to determine the height of the cone , if the diameter is 30cm .
Diagram :-
[tex]\setlength{\unitlength}{1.2mm}\begin{picture}(5,5)\thicklines\put(0,0){\qbezier(1,0)(12,3)(24,0)\qbezier(1,0)(-2,-1)(1,-2)\qbezier(24,0)(27,-1)(24,-2)\qbezier(1,-2)(12,-5)(24,-2)}\put(-0.5,-1){\line(1,2){13}}\put(25.5,-1){\line(-1,2){13}}\multiput(12.5,-1)(2,0){7}{\line(1,0){1}}\multiput(12.5,-1)(0,4){7}{\line(0,1){2}}\put(17.5,1.6){\sf{15cm }}\put(9.5,10){\sf{17\ cm }}\end{picture} [/tex]
Step 1: Using the formula of cone :-
The volume of cone is ,
[tex]\rm\implies Volume_{(cone)}=\dfrac{1}{3}\pi r^2h [/tex]
Step 2: Substitute the respective value :-
[tex]\rm\implies 4000cm^3 =\dfrac{1}{3}(3.14) ( h ) \bigg(\dfrac{30cm}{2}\bigg)^2 [/tex]
As Radius is half of diameter , therefore here r = 30cm/2 = 15cm .
Step 3: Simplify the RHS :-
[tex]\rm\implies 4000 cm^3 = \dfrac{1}{3}(3.14) ( h ) (15cm)^2\\ [/tex]
[tex]\rm\implies 4000 cm^3 = \dfrac{1}{3}(3.14) ( h ) 225cm^2\\ [/tex]
Step 4: Move all the constant nos. to one side
[tex]\rm\implies h =\dfrac{ 4000 \times 3}{ (3.14 )(225 )} cm \\[/tex]
[tex]\implies \boxed{\blue{\rm Height_{(cone)}= 16.98 \approx 17 cm }}[/tex]
Hence the height of the cone is 17cm .
