Answer:
The sample consisting of 64 data values would give a greater precision.
Step-by-step explanation:
The width of a (1 - α)% confidence interval for population mean μ is:
[tex]\text{Width}=2\cdot z_{\alpha/2}\cdot \frac{\sigma}{\sqrt{n}}[/tex]
So, from the formula of the width of the interval it is clear that the width is inversely proportion to the sample size (n).
That is, as the sample size increases the interval width would decrease and as the sample size decreases the interval width would increase.
Here it is provided that two different samples will be taken from the same population of test scores and a 95% confidence interval will be constructed for each sample to estimate the population mean.
The two sample sizes are:
n₁ = 25
n₂ = 64
The 95% confidence interval constructed using the sample of 64 values will have a smaller width than the the one constructed using the sample of 25 values.
Width for n = 25:[tex]\text{Width}=2\cdot z_{\alpha/2}\cdot \frac{\sigma}{\sqrt{25}}=\frac{1}{5}\ [2\cdot z_{\alpha/2}\cdot \sigma][/tex]
Width for n = 64:[tex]\text{Width}=2\cdot z_{\alpha/2}\cdot \frac{\sigma}{\sqrt{64}}=\frac{1}{8}\ [2\cdot z_{\alpha/2}\cdot \sigma][/tex]
Thus, the sample consisting of 64 data values would give a greater precision.
The number of data values would you expect to give a greater precision (a smaller width) for estimating the population mean is 64 and this can be determined by using the formula of width.
Given :
The first sample will have 25 data values.The second sample will have 64 data values. 95% confidence interval.The following steps can be used in order to determine the number of data values would you expect to give a greater precision for estimating the population mean:
Step 1 - The below formula of width is used in order to determine the number of data values.
Step 2 - The formula of width is given below:
[tex]w = 2\times z_{\alpha /2}\times \dfrac{\sigma}{\sqrt{n} }[/tex]
where [tex]z_{\alpha /2}[/tex] is the z-score, [tex]\sigma[/tex] is the standard deviation, and 'n' is the sample size.
Step 3 - Now, at n = 25 the formula of 'w' becomes:
[tex]w = 2\times z_{\alpha /2}\times \dfrac{\sigma}{\sqrt{25} }[/tex]
[tex]w = \dfrac{1}{5}\left(2\times z_{\alpha /2}\times\sigma }\right)[/tex]
Step 4 - Now, at n = 64 the formula of 'w' becomes:
[tex]w = 2\times z_{\alpha /2}\times \dfrac{\sigma}{\sqrt{64} }[/tex]
[tex]w = \dfrac{1}{8}\left(2\times z_{\alpha /2}\times\sigma }\right)[/tex]
The number of data values would you expect to give a greater precision (a smaller width) for estimating the population mean is 64.
For more information, refer to the link given below:
https://brainly.com/question/12402189
What is the slope of the equation y-3=-4(x-5) ?
Answer:
m(slope)=-4
Step-by-step explanation:
the slope is the thing you see before x so in this case y-3=-4x+20 so the slope or m is -4.
The slope of the equation y - 3 = -4 ( x - 5 ) is -4.
Given,
y - 3 = -4 ( x - 5 )
We need to find the slope of this equation.
What is the equation of a line with a slope?The equation is given by:
y - b = m ( x - a)
Where (a, b) is a point that the line passes through and m = slope.
We have,
y - 3 = -4 ( x - 5 )
Here we see that the equation is in the form of y - b = m ( x - a).
Where,
(a, b) = (5, 3)
m = -4
We have,
Slope = m
m = -4
Thus the slope of the equation y - 3 = -4 ( x - 5 ) is -4.
Learn more about how to find slope from a graph here:
https://brainly.com/question/23164168
#SPJ2
Which is the closet to the volume of the concrete needed to fill the pillar?
Answer:
c) 21.4
Step-by-step explanation:
9.5 times 1.5 times 1.5 is 21.375 or 21.4 rounded
What’s the correct answer for this?
which type of graph would you use to show the number of candy bars collected by each trick or treater in the neighborhood
Answer:
bar graph
Step-by-step explanation:
y axis = number of kids
X axis = types of candy bars
ANYONE PLZZZ THSI IS DUE IN AN HOUR!!!!! Will mark the brainliest
Answer:
A is correct.
Step-by-step explanation:
Left figure's area = base x height = L x h x 6 = 6Lh
Right figure's area = L x h + L x h + L x h + L x h + L x h + L x h = 6Lh
Hope this helps!
:)
At the Boxer carnival, you can exchange 40 tickets for various assortments of
prizes. Some of those assortments are below. How many tickets does it take
to get a single tacky mirror?
1 goldfish, 2 tacky mirrors, 1 stuffed tiger
5 goldfish, 1 stuffed tiger
2 goldfish, 3 tacky mirrors
Answer:
g = number of tickets for goldfish
t = number of tickets for tacky mirrors
s = number of tickets for stuffed tiger
1g + 2t + 1s = 40
5g + + 1s = 40
2g + 3t = 40
using the second equatin we can find a value for s
1s = 40 -5g
now substitute in the first equation to get rid of s
1g + 2t + (40-5g) = 40
-4g + 2t = 0
now use this new equation with equation 3 and solve for one of the values
-4g + 2t = 0
2g + 3t = 40
multipy the second equation by 2 and then combine
-4g + 2t = 0
4g + 6t = 80
8t = 80
t = 10 (so it takes 10 tickets to get a takcy mirror)
2g + 3(10) = 40
2g = 10
g = 5 (five tickets to get a goldfish)
s = 40 -5(5)
s = 15 (fifteen tickets for a stuffed tiger)
1(5) + 2(10) + 1(15) (substitute back in the first equation)
5 + 20 + 15
40 it works!
Write the equation of the line, given the y- and x-intercepts:
y-intercept (0, 19), x-intercept (–9.5, 0)
Answer:
y=2x+19
Step-by-step explanation:
Slope: 0-19/-9.5-0=-19/-9.5=2
y-intercept: 19
Answer:
y=2x+19
Step-by-step explanation:
If you were to roll one die, one time what is the probability it will land on a number other than 3?
Answer:
3
Step-by-step explanation:
Answer:
1/6 (16.667%)
Step-by-step explanation:
there is six sides on on the dice. So there is only one side of the dice that has the number 3. 1/6 is the probability.
How many decimal places are in the product of the expression below?
256
x142
one
two
three
four
Answer:
36352.0
Step-by-step explanation:
For 256x142 = 36352.0
There is none actually
PLS PLS HELP FAST. Given an isosceles triangle with a leg length of 12. Determine the length of the hypotenuse.
Answer:
12*sqrt(3)
Step-by-step explanation:
since it is isosceles its angles are 45, 45, 90, therefore the hypotenuse is 12*sqrt(3).
Triangle PQR is similar to triangle FGH.
Solve for n.
QP:10.5
QR:9
RP:6
GF:7
HF:4
GH:n
Answer:
n = 6
Step-by-step explanation:
See attachment for diagram
Triangle PQR is similar to triangle FGH.
Similar triangles are similar in shape but different in size.
The ratio of their corresponding sides are equal.
QP=10.5
QR=9
RP=6
GF=7
HF=4
GH=n
(Hypotenuse in ∆PQR)/ (hypothenuse in ∆FGH)
=(Adjacent in ∆PQR)/(adjacent in ∆FGH)
= 6/4 = 9/n
Cross multiply
6×n = 9×4
6n = 36
n = 36/6
n = 6
Therefore ratio of their corresponding sides = 3/2
Please answer this correctly
Answer:
13
Step-by-step explanation:
Find the scale factor by 39 / 30
Take that times 10
1.3 x 10 = 13
Since the questions states these two shapes are "similar" the side will have identical scale factors.
Divide the longest side of the bigger shape to the smaller shape.
39 / 30 = 1.3
The scale factor is 1.3.
Now, multiply the shortest side if the smaller shape by the scale factor.
10 * 1.3 = 13
Therefore, the length of w is 13mm
Best of Luck!
what is the solution for x^2 +14x +15
Step-by-step explanation:
the solution are
x = 1 or x = -15
x^2 + 14x - 15 =0
x^2 + 14x = 15
to write the left hand side as a perfect square we add 49 to both sides :
x^2 + 14x + 49 = 15 + 49
x^2 + 2.x.7 + 7^2 = 64
using the identity (a^2 + b^2) = a^2 + 2ab + b^2
(x + 7)^2 = 64
x + 7 = √64 or x + 7 = -√64
x = 8 - 7 or x = - 8 - 7
= 1 = - 15
Many random number generators allow users to specify the range of the random numbers to be produced. Suppose that you specify that the random number Y can take any value between 0 and 2. Then the density curve of the outcomes has constant height between 0 and 2, and height 0 elsewhere.
(a) Is the random variable Y discrete or continuous? Why?
This is a discrete random variable because the set of possible values is an interval.
This is a continuous random variable because the set of possible values is an interval.
This is a discrete random variable because it has a finite sample space.
This is a continuous random variable because it has a finite sample space.
(b) What is the height of the density curve between 0 and 2? Draw a graph of the density curve.
(c) Use your graph from (b) and the fact that probability is area under the curve to find P(Y ≤ 1).
Answer:
a) This is a continuous random variable because the set of possible values is an interval.
b) Height = 0.5
Graph attached.
c) P(Y≤1) = 0.5
Step-by-step explanation:
a) If the density curve of the outcomes has a constant height, we have a uniform distribution for values between 0 and 2 (outside this range, the density function has a value of 0).
This function is continous and has a value for each real number. The set of possible values has a is an interval between 0 and 2, all with equal probability (the ones that are otuside this interval have 0 probability, so they are not possible values).
b) The height is calculated so that the total area under the density curve has to be equal to 1.
Then, we have to calculate the integral between 0 and 2 of the density function:
[tex]\int\limits^2_0 {U(x)} \, dx =\int\limits^2_0 {H} \, dx =H\int\limits^2_0 dx=H(x_2-x_1)=H(2-0)=1\\\\2H=1\\\\H=0.5[/tex]
The height is H=0.5
(Graph attached)
c) The probability can be calculated by integrating the density function (which is equal to the area under the curve) between 0 and 1, or using the graph.
With the graph, we see that the area is equal to the height (0.5) by the width of the interval (1), so the total area is 0.5 x 1 = 0.5.
The probability P(Y≤1) is equal to 0.5.
Using the uniform distribution, it is found that:
a)
This is a continuous random variable because the set of possible values is an interval.
b)
The height is [tex]\frac{1}{2}[/tex], and the sketch is given at the end of this answer.
c)
P(Y ≤ 1) = 0.5
An uniform distribution has two bounds, a and b.
The probability of finding a value of at lower than x is:
[tex]P(X < x) = \frac{x - a}{b - a}[/tex]
In this problem, uniformly distributed between 0 and 2, thus [tex]a = 0, b = 2[/tex].
Item a:
Values in an interval, thus continuous. Discrete are for sample spaces, which is not the case here.
Item b:
The height is:
[tex]h = \frac{1}{b - a} = \frac{1}{2}[/tex]
The graph is sketched at the end of this answer.
Item c:
[tex]P(Y \leq 1) = \frac{1 - 0}{2 - 0} = \frac{1}{2} = 0.5[/tex]
Thus, P(Y ≤ 1) = 0.5.
A similar problem is given at https://brainly.com/question/13547683
Help Please???? Question is above, it has to do with repeating decimal converting to a fraction
Milly measured a cereal box it was 2inches wide six inches long and three inches what is the volume
Answer:
2*6*3
Step-by-step explanation:
I need help with this??
please answer quick ! 6 9/10 - 2 2/9 = ?
Answer:
4 61/90
Step-by-step explanation:
6 - 2 = 4
9 / 10 - 2 / 9 = 61 / 90
If you could help me, please answer the attachment below.
What is the number of permutations for a 4 digit number using the digits 0 – 9, if numbers cannot be repeated.
Answer:
Number of permutations for a 4 digit number using the digits 0 – 9 (10 available digits in total), supposing numbers cannot be repeated, is calculated by:
10P4 = 10!/(10-4)! = 5040
Hope this helps!
:)
The bar graph below shows the number of aluminum cans collected by students in the month of October. How many cans did seigi and Ariel collect together
Answer:
1 2 3 4 5 6 7 8 9 10 bars are there
A bag of fertilizer covers 3000 square feet of lawn. Find how many bags of fertilizer should be purchased to cover a rectangular lawn 230 feet by 180 feet
Answer:
14 bags
Step-by-step explanation:
Dimension of lawn : 230 feet by 180 feet
area of rectangle is given by length * width
Since lawn is rectangular area of lawn = 230 feet * 180 feet = 41,400 sq. feet
Given that one bag of fertilizer covers 3000 square feet of lawn.
Thus , to find no. of bags required to cover whole lawn will be
total area of lawn/area which one bag of fertilizer covers
no. of bags required to cover whole lawn = 41,400 sq. feet/3000 sq. feet
= 13.8 bags.
As no. of bags cannot be fractional , hence rounding bag to nearest unit place is 14 bags.
Use the change of variables s=y, t=y−x^2 to evaluate ∫∫Rxdxdy over the region R in the first quadrant bounded by y=0, y=16, y=x^2, and y=x^2−5. ∫∫R x dxdy=
Answer:
Step-by-step explanation:
[tex]s=y, t = y- x^2[/tex]
[tex]x^2=y-t[/tex]
[tex]x=\sqrt{s-t}[/tex]
[tex]y=0, y=16, y=x^2, and\\ y=x^2-5.[/tex]
[tex]y-x^2=0,y-x^2=-5[/tex]
therefore,
[tex]s=[(s,t)10\leq s\leq 16,-3\leq t \leq 0][/tex]
Taking partial derivatives
[tex]\frac{dx}{ds} =\frac{1}{2\sqrt{s-t} } \\\\\frac{dx}{dt} =\frac{1}{2\sqrt{s-t} } \\\\\frac{dy}{ds} =1\\\\\frac{dy}{dt} =0[/tex]
[tex]\frac{\delta (x,y)}{\delta (s,t)} =\left|\begin{array}{ccc}\frac{1}{2\sqrt{s-t} } &-\frac{1}{2\sqrt{s-t} } \\1&0\end{array}\right|[/tex]
[tex]=\frac{1}{2\sqrt{s-t} }[/tex]
[tex]\int\limits \int\limits_R {x} \, dx \, dy=\int\limits\int\limits_s {x} \sqrt{s-t} |\frac{\delta(x,y)}{\delta (s,t)} |dsdt[/tex]
[tex]=\int\limits^{16}_0\int\limits^0_{-5} \sqrt{s-t} \frac{1}{2\sqrt{s-t} } dt ds[/tex]
[tex]=\frac{1}{2} \int\limits^{16}_0 ds\int\limits^0_{-5} \, dt \\\\=\frac{1}{2} [s]^{16}_0[t]^0_{-5}\\\\=\frac{1}{2} (16)(5)\\\\=40[/tex]
Is the relationship shown by the data linear? If so, model the data with an equation x: -7,-5,-3,-1 y: 5,9,13,17
Answer:
Y = 2X + 19
Step-by-step explanation:
the relationship is linear
gradient equals 2
Please choose the correct answer.
Answer:
976
Step-by-step explanation:
would you stop it already
Answer: 976m^2
Step-by-step explanation:
An easy way to find the surface area of a prism is to find the area of each side and add them all together.
Area of rectangle:
14mx10m=140m^2
Area of rectangle:
25mx10=250m^2
Since there are 2 of the long rectangles, you multiply by 2:
250m^2x2=500m^2
Area of triangle:
(24mx14m)/2=168m^2
Since there are 2 triangles, you multiply by 2:
168m^2x2=336m^2
Surface Area:
140+500+336=976m^2
solve the equation 12x+6y=24 for x ? i need help
Answer:
x= -1/2y+2
Step-by-step explanation:
Let's solve for x.
12x+6y=24
Step 1: Add -6y to both sides.
12x+6y+−6y=24+−6y
12x=−6y+24
Step 2: Divide both sides by 12.
12x
12
=
−6y+24
12
x=
−1
2
y+2
Answer: x= -1/2y+2
Hope this helps.
Answer:
x=2−y/2
Step-by-step explanation:
Write the number pairs that relate the number of half dollar to the number of dimes
Answer:
0.10 + 0.10 + 0.10 + 0.10 + 0.10 equal to 5 dimes or a half of dollar.
Step-by-step explanation:
0.10 + 0.10 + 0.10 + 0.10 + 0.10 = 0.50 (half of a dollar)
Find the surface area of the cylinder. Round your answer to the nearest hundredth.
A. 569.26 in2
B. 724.34 in2
C. 795.45 in2
D. 1,707.77 in2
Answer:
C. 795.45 in^2
Step-by-step explanation:
The formula for the surface area of a cylinder is ...
SA = 2πr^2 +2πrh = 2πr(r +h)
For r=6 and h=15.1, the surface area is ...
SA = 2π(6)(6 +15.1) = π(12)(21.1) = 253.2π
SA ≈ 795.45 . . . . square inches
Mr. Vectadore is buying two new cowboy hats. All
together the hats cost $75.12. The second hat costs
twice as much as the first hat. What is the price of the
more expensive hat?
Round to the nearest hundredth.
Answer:
$50.08
Step-by-step explanation:
Let's use x to represent the lesser expensive hat and 2x to represent the more expensive hat since the more expensive hat is twice the price.
So, our equation would be 2x + x = 75.12
We can combine them together to make 3x.
Then, we make the 3x equal to 75.12
3x = 75.12
Now, we solve it.
Divide both sides by 3 to solve for x.
75.12/3 = 25.04
x = 25.04
Lastly, plug it in for 2x to get the price of the more expensive hat.
2(25.04) = ?
2(25.04) = 50.08
Therefore, the price of the more expensive hat is $50.08
Evaluate the expression shown for x = 12.
Negative StartFraction 5 over 6 EndFraction x + 7
Answer:
-3 !!!!!
Step-by-step explanation:
Answer:
-3
Step-by-step explanation:
just did the test on edg