Answer:
[tex]MSE = 10[/tex]
Step-by-step explanation:
Given
[tex]SSTR = 200[/tex]
[tex]SST = 800[/tex]
Required
Determine MSE
This is calculated as:
[tex]MSE = \frac{1}{ddf} * SSE[/tex]
Where:
[tex]SSE = SST - SSTR[/tex]
[tex]ddf \to[/tex] denominator df
So, we have:
[tex]SSE = 800 - 200[/tex]
[tex]SSE = 600[/tex]
To calculate the df, we have:
[tex]r = 13[/tex] --- observations
[tex]n = 5[/tex] treatments
So:
[tex]ddf = Total\ df - Numerator\ df[/tex]
[tex]Total = n*r-1 = 5*13 -1 = 64[/tex]
[tex]Numerator =n - 1 = 5 - 1 =4[/tex]
[tex]ddf =64-4=60[/tex]
So, we have:
[tex]MSE = \frac{1}{ddf} * SSE[/tex]
[tex]MSE = \frac{1}{60} * 600[/tex]
[tex]MSE = 10[/tex]
A well-known brokerage firm executive claimed that 60% of investors are currently confident of meeting their investment goals. An XYZ Investor Optimism Survey, conducted over a two week period, found that in a sample of 100 people, 69% of them said they are confident of meeting their goals. Test the claim that the proportion of people who are confident is larger than 60% at the 0.01 significance level.
The null and alternative hypothesis would be:________
a. H0:μ=0.6H0:μ=0.6
H1:μ≠0.6H1:μ≠0.6
b. H0:μ=0.6H0:μ=0.6
H1:μ<0.6H1:μ<0.6
c. H0:μ=0.6H0:μ=0.6
H1:μ>0.6H1:μ>0.6
d. H0:p=0.6H0:p=0.6
H1:p≠0.6H1:p≠0.6
e. H0:p=0.6H0:p=0.6
H1:p>0.6H1:p>0.6
f. H0:p=0.6H0:p=0.6
H1:p<0.6H1:p<0.6
The test is:________
a. two-tailed
b. left-tailed
c. right-tailed
The test statistic is:_______ (to 3 decimals)
The p-value is:_______ (to 4 decimals)
Based on this we:________
a. Fail to reject the null hypothesis
b. Reject the null hypothesis
We are testing a hypothesis. So, first we identify the null and the alternative hypothesis, then we find the test statistic, and with the test statistic, the p-value is found.
Null and alternative hypothesis:
Claim the the proportion is of 60%, thus, the null hypothesis is:
[tex]H_0: p = 0.6[/tex]
Test if the proportion is greater than 60%, thus, the alternative hypothesis is:
[tex]H_1: p > 0.6[/tex]
And the answer to the first question is given by option c.
Classification:
We are testing if the proportion is greater than a value, so it is a right-tailed test.
Test statistic:
[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, [tex]\sigma[/tex] is the standard deviation and n is the size of the sample.
0.6 is tested at the null hypothesis:
This means that [tex]\mu = 0.6, \sigma = \sqrt{0.4*0.6}[/tex]
Survey, conducted over a two week period, found that in a sample of 100 people, 69% of them said they are confident of meeting their goals.
This means that [tex]n = 100, X = 0.69[/tex]
Value of the test statistic:
[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
[tex]z = \frac{0.69 - 0.6}{\frac{\sqrt{0.4*0.6}}{\sqrt{100}}}[/tex]
[tex]z = 1.837[/tex]
The test statistic is z = 1.837.
p-value:
The p-value of the test is the probability of finding a sample proportion above 0.69, which is 1 subtracted by the p-value of z = 1.837.
Looking at the z-table, z = 1.837 has a p-value of 0.9669.
1 - 0.9669 = 0.0331
The p-value is 0.0331.
Decision:
The p-value of the test is 0.0331 > 0.01, and thus:
a. Fail to reject the null hypothesis
For another example of a problem of a test of hypothesis, you can take a look at:
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factorize : ( p- q ) cube
Answer:
[tex]( {p - q}^{3} ) \\ = {p}^{2} - 3 {p}^{2} q + 3p {q}^{2} - {q}^{3} [/tex]
write your answer as an integer or as a decimal rounded to the nearest tenth
Answer:
FH ≈ 6.0
Step-by-step explanation:
Using the sine ratio in the right triangle
sin49° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{FH}{FG}[/tex] = [tex]\frac{FH}{8}[/tex] ( multiply both sides by 8 )
8 × sin49° = FH , then
FH ≈ 6.0 ( to the nearest tenth )
Answer:
6
Step-by-step explanation:
sin = opposite/hypotenuse
opposite = sin * hypotenuse
sin (49) = 0,75471
opposite = 0,75471 * 8 = 6,037677 = 6
Find the greatest rational number r such that the ratios 8/15 ÷ r and 18/35 ÷ r are whole numbers?
The answer is "[tex]\bold{\frac{2}{105}}[/tex]", and the further calculation can be defined as follows:
When the "r" is the greatest common divisor for the two fractions.
So, we will use Euclid's algorithm:
[tex]\to \bold{(\frac{8}{15}) -(\frac{188}{35})}\\\\\to \bold{(\frac{8}{15} -\frac{188}{35})}\\\\\to \bold{(\frac{56-54}{105})}\\\\\to \bold{(\frac{2}{105})}\\\\[/tex]
this is [tex]\bold{(\frac{8}{15}) \ \ mod \ \ (\frac{18}{35})}[/tex]
we can conclude that the GCD for [tex]\bold{\frac{54}{105}}[/tex], when divided by [tex]\bold{\frac{2}{105}}[/tex], will be the remainder is 0. Rational numbers go from [tex]\bold{\frac{2}{105}}[/tex] with the latter being the highest.
So, the final answer is "[tex]\bold{\frac{2}{105}}[/tex]".
Learn more:
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Starting with a fresh bar of soap, you weigh the bar each day after you take a shower. Then you find the regression line for predicting weight from number of days elapsed. The slope of this line will be:__________.
Answer:
The slope will be negative
Step-by-step explanation:
The slope of the regression line tells us about the relationship or behavior of the dependent and independent variables. In the scenario above, where the weight is being compared with the number of days elapsed. What is expected of the weight and quantity of a bar soap each time it is used for a shower is that it will decrease in weight. Therefore, as the number of days increases, and hence, number of showers rise, the weight of soap will decrease. Hence, we'll obtain a negative slope, one in which the increase in a variable leads to decrease in the other.
Where r is the radius of the cylinder and h is the height of the cylinder.
Find the surface area when r is 7 inches and h is 9 inches.
Sa of cylinder= 2(pi)rh + 2(pi)r squared
Answer:
703.7 in²
Step-by-step explanation:
SA = 2πrh+2πr²
= 2×π×7×9+2×π×7²
= 224π
= 703.7 in² (rounded to the nearest tenth)
Answer:
224π
in²
Step-by-step explanation:
Please help me with this on the picture
9514 1404 393
Answer:
(-5, 4)
Step-by-step explanation:
The inside corner moves from (2, -2) to (-3, 2). That is 5 is subtracted from the x-coordinate, and 4 is added to the y-coordinate. (x, y) ⇒ (x -5, y +4)
The translation vector can be written horizontally as (-5, 4), or vertically as ...
[tex]\displaystyle\binom{-5}{4}[/tex]
What is an explicit formula for the geometric sequence -64,16,-4,1,... where the first term should be f(1).
Answer:
[tex]a_{n} = -64(-\frac{1}{4})^{n-1}[/tex]
it seems like the first term is -64, so lets write the formula accordingly:
a_n = a1(r)^(n-1)
where 'n' is the number of terms
a1 is the first term of the sequence
'r' is the ratio
the ratio is [tex]-\frac{1}{4}[/tex] because -64 * [tex]-\frac{1}{4}[/tex] = 16 and so on...
the explicit formula is :
[tex]a_{n}[/tex] = [tex]-64(-\frac{1}{4} )^{n-1}[/tex]
prove that 2^n+1>(n+2).sin(n)
Step-by-step explanation:
F(n)=|sin(n)|+|sin(n+1)|
then
F(n+π)=|sin(n+π)|+|sin(n+π+1)|=|sin(n)|+|sin(n+1)|=F(n)
and
F(π−n)=|sin(π−n)|+|sin(π−n+1)|=|sinn|+|sin(n−1)|≠F(n)
so we must prove when n∈(0,π), have
F(n)>2sin12
when n∈(0,π−1),then
F(n)=sinn+sin(n+1)=sinn(1+cos1)+sin1cosn
and n∈(π−1,π),then
F(n)=sinn−sin(n+1)
How prove it this two case have F(n)>2sin12? Thank you
and I know this well know inequality
|sinx|+|sin(x+1)|+|sin(x−1)|≥2sin1,x∈R
please helpppp i need it by tonight its very important
Answer:
m<1=145
m<2=35
m<3=35
Step-by-step explanation:
measure one is supplementary(the angles add to 180) to measure four.
so we do 180-35=145
measure 2 is congruent to measure four because they are corresponding angles
so measure 2=35
and measure 3 is also congruent to measure 4 because the are corresponding angles
so m<3=35
The segments shown below could form a triangle.
A
C
7
9
12
B
А
a
A. True
B. False
Answer:
TRUE
Step-by-step explanation:
I SEEN SOME ONE ELSE WIT 5 STARS SAY SO(:
The given segment can form triangle. Therefore, the given statement is true.
What is triangle?A polygon has three edges as well as three vertices is called a triangle. It's one of the fundamental geometric shapes. In Euclidean geometry, each and every three points that are not collinear produce a distinct triangle and a distinct plane. In other words, every triangle was contained in a plane, and there is only single plane that encompasses that triangle.
All triangles are enclosed in a single plane if all of geometry is the Euclidean plane, however this is no longer true in higher-dimensional Euclidean spaces. Unless when otherwise specified, this article discusses triangles within Euclidean geometry, namely the Euclidean plane. The given segment can form triangle.
Therefore, the given statement is true.
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terms are there. Divide 51 into three parts in AP so that the largest exceeds the smallest by 10.
The first three terms of the Arithmetic Progression are 12, 17 and 22.
For an ARITHMETIC PROGRESSION, AP ;
First term = a
Second term = a + d
Third term = a + 2d
Where, d = common difference ;
If third term exceeds smallest by 10 ;
Third term - first term
a + 2d - a = 10
2d = 10
d = 10/2
d = 5
Sum of the three terms :
a + (a + d) + a + 2d = 51
3a + 3d = 51
d = 5
3a + 3(5) = 51
3a + 15 = 51
3a = 51 - 15
3a = 36
a = 12
The AP would be:
First term, a = 12
Second term, a + d = 12 + 5 = 17
Third term = a + 2(d) = 12 + 10 = 22
Therefore , the first three terms of the AP are :
12, 17 and 22
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look at the image below
Answer:
201.1 km²
Step-by-step explanation:
Surface area of a sphere= 4πr², where r = radius
so,
4πr²
= 4×π×4²
= 64π
= 201.1 km² (rounded to the nearest tenth)
Shawn has 4 times as many candies as Jason, who has a third as many candies as
lan. If Shawn has 64 candies, how many candies does Ian have?
12/1,000 into decimal
0.012 is the answer!
I hope this helps you out! :D
[tex]\\ \sf\longmapsto \dfrac{12}{1000}[/tex]
1000 has 3zeros hence decimal will go 3 points left[tex]\\ \sf\longmapsto 0.012[/tex]
More:-
[tex]\\ \sf\longmapsto \dfrac{1}{10}=0.1[/tex]
[tex]\\ \sf\longmapsto \dfrac{1}{100}=0.01[/tex]
Triangle ABL is an isosceles triangle in circle A with a radius of 11, PL = 16, and ∠PAL = 93°. Find the area of the circle enclosed by line PL and arc PL. Show all work and round your answer to two decimal places.
The area bounded by a chord and arc it intercepts is known as a segment of a circle segment of a circle
The area of the circle enclosed by line PL and arc PL is approximately 37.62 square units
The reason the above value is correct is as follows:
The given parameters in the question are;
The radius of the circle, r = 11
The length of the chord PL = 16
The measure of angle ∠PAL = 93°
Required:
The area of part of the circle enclosed by chord PL and arc PL
Solution:
The shaded area of the given circle is the minor segment of the circle enclosed by line PL and arc PL
The area of a segment of a circle is given by the following formula;
Area of segment = Area of the sector - Area of the triangle
Area of segment = Area of minor sector APL - Area of triangle APL
Area of minor sector APL:
Area of a sector = (θ/360)×π·r²
Where;
r = The radius of the circle
θ = The angle of the sector of the circle
Plugging in the the values of r and θ, we get;
Area of the minor sector APL = (93°/360°) × π × 11² ≈ 98.2 square units
Area of Triangle APL:
Area of a triangle = (1/2) × Base length × Height
Therefore;
The area of ΔAPL = (1/2) × 16 × 11 × cos(93°/2) ≈ 60.58 square units
Required shaded area enclosed by line PL and arc PL:
Therefore, the area of shaded segment enclosed by line PL and arc PL is found as follows;
Area of the required segment PL ≈ (98.2 - 60.58) square units = 37.62 square units
The area of the circle enclosed by line PL and arc PL ≈ 37.62 square units
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The area of the circle enclosed by line segment PL and circle arc PL is 37.80 square units.
The calculation of the area between line segment PL and circle arc PL is described below:
1) Calculation of the area of the circle arc.
2) Calculation of the area of the triangle.
3) Subtracting the area found in 2) from the area found in 1).
Step 1:
The area of a circle arc is determined by the following formula:
[tex]A_{ca} = \frac{\alpha\cdot \pi\cdot r^{2}}{360}[/tex] (1)
Where:
[tex]A_{ca}[/tex] - Area of the circle arc.
[tex]\alpha[/tex] - Arc angle, in sexagesimal degrees.
[tex]r[/tex] - Radius.
If we know that [tex]\alpha = 93^{\circ}[/tex] and [tex]r = 11[/tex], then the area of the circle arc is:
[tex]A_{ca} = \frac{93\cdot \pi\cdot 11^{2}}{360}[/tex]
[tex]A_{ca} \approx 98.201[/tex]
Step 2:
The area of the triangle is determined by Heron's formula:
[tex]A_{t} = \sqrt{s\cdot (s-l)\cdot (s-r)^{2}}[/tex] (2)
[tex]s = \frac{l + 2\cdot r}{2}[/tex]
Where:
[tex]A_{t}[/tex] - Area of the triangle.
[tex]r[/tex] - Radius.
[tex]l[/tex] - Length of the line segment PL.
If we know that [tex]l = 16[/tex] and [tex]r = 11[/tex], then the area of the triangle is:
[tex]s = \frac{16+2\cdot (11)}{2}[/tex]
[tex]s = 19[/tex]
[tex]A_{t} = \sqrt{19\cdot (19-16)\cdot (19-11)^{2}}[/tex]
[tex]A_{t} \approx 60.399[/tex]
Step 3:
And the area between the line segment PL and the circle arc PL is:
[tex]A_{s} = A_{ca}-A_{t}[/tex]
[tex]A_{s} = 98.201 - 60.399[/tex]
[tex]A_{s} = 37.802[/tex]
The area of the circle enclosed by line segment PL and circle arc PL is 37.80 square units.
Convert 0.450 to a proper fraction
Answer:
9/20
Step-by-step explanation:
450/1000
this is not the answer, because it is not simplified
so here we have to find common factor and simplifying
________________________________________________
450/1000 is simplified to 9/20, and it can no longer be simplified.
A car insurance company has determined that6% of all drivers were involved in a car accident last year. If14drivers are randomly selected, what is the probability of getting at most 3 who were involved in a car accidentlast year
Answer:
[tex]P(x \le 3) = 0.9920[/tex]
Step-by-step explanation:
Given
[tex]p = 6\%[/tex] --- proportion of drivers that had accident
[tex]n = 14[/tex] -- selected drivers
Required
[tex]P(x \le 3)[/tex]
The question is an illustration of binomial probability, and it is calculated using:
[tex]P(x ) = ^nC_x * p^x * (1 - p)^{n-x}[/tex]
So, we have:
[tex]P(x \le 3) = P(x = 0) +P(x = 1) +P(x = 2) +P(x = 3)[/tex]
[tex]P(x=0 ) = ^{14}C_0 * (6\%)^0 * (1 - 6\%)^{14-0} = 0.42052319017[/tex]
[tex]P(x=1 ) = ^{14}C_1 * (6\%)^1 * (1 - 6\%)^{14-1} = 0.37578668057[/tex]
[tex]P(x=2 ) = ^{14}C_2 * (6\%)^2 * (1 - 6\%)^{14-2} = 0.15591149513[/tex]
[tex]P(x=3 ) = ^{14}C_3 * (6\%)^3 * (1 - 6\%)^{14-3} = 0.03980719024[/tex]
So, we have:
[tex]P(x \le 3) = 0.42052319017+0.37578668057+0.15591149513+0.03980719024[/tex]
[tex]P(x \le 3) = 0.99202855611[/tex]
[tex]P(x \le 3) = 0.9920[/tex] -- approximated
Jack’s backpack weighs 15 pounds. Fernando’s backpack weighs less than Jack’s. Which graph shows how much Fernando’s backpack can weigh?
Answer:
A
Step-by-step explanation:
c and d out of the question
b has its circle filled in meaning it could be 15lbs, which it's not
A correct answer by default
Answer:b
Step-by-step explanation: it has a filled in diamond which mean it's that...
Simplify the following expression
Answer:
[tex]\frac{98p^{6}}{q}[/tex]
Step-by-step explanation:
Distribute the exponents
[tex](\frac{(7^{-2}p^{-6}q^{-8})}{2q^{-9}} )^{-1}[/tex]
[tex](\frac{q}{98p^{6}} )^{-1}[/tex]
Distribute the -1
[tex]\frac{98p^{6}}{q}[/tex]
Can someone do #4 and #5
Answer:
First, find two points on the graph:
(x₁, y₁) = (0, 2)(x₂, y₂) = (2, 8)Slope = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1}} = \frac{8-2}{2-0} =\frac{6}{2}=3[/tex]
16 + (-3) = 16 - 3 = 13
According to this diagram, what is tan 62°?
62°
17
18
280
90°
15
O A.
8
17
OB.끝
O c. 1
8
15
D.
15
8
O
E.
17
15
F.
15
17
Answer:
15/8
Step-by-step explanation:
tan(62)=P/B
tan(62)=15/8
5 A machine puts tar on a road at the rate of 4 metres in 5 minutes.
a) How long does it take to cover 1 km of road
b) How many metres of road does it cover in 8 hours?
Answer:
5 a) Total = 20.83 hrs = 20 hrs and 50 mins (1250mins total)
5 b) Total = 96 meters. = 0.096km in 8 hrs.
Step-by-step explanation:
1km = 1000 meters
5 mins = 4 meters
1000/4 = 250 multiplier
250 x 5mins = 1250 minutes
1250/60 = 20hrs + 50 minutes
50 / 60 = 0.83 = 20.83hrs
b) 8 hrs = 8 x 60 = 480 minutes
480/5 = 24 multiplier of 4 meters
24 x 4 = 96 meters
Which two shapes make up the digital camera below?
Rectangular prism and cylinder make up a camera.
What is rectangular prism and cylinder?A cube is a rectangular prism with all of its sides being the same length, a triangular prism has a triangle as its base, and a rectangular prism has a rectangle as its foundation. Another form of right prism that has a circle as its basis is a cylinder.
A rectangular prism includes a total of 6 faces, 12 sides, and eight vertices. Like a cuboid, it contains three dimensions- the base width, the height, and the length. The top and base of the rectangular prism exist rectangular. The pairs of opposite faces of a rectangular prism exist as identical or congruent.
A cylinder contains traditionally been a three-dimensional solid, one of the most essential curvilinear geometric shapes. Geometrically, it includes been regarded as a prism with a circle as its base.
Hence, Rectangular prism and cylinder make up a camera.
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This graph represents which of these expressions?
Answer:
x > 43
Step-by-step explanation:
Open circle at 43, which means it is not equal to 43
Line goes to the right, which means x is greater than
x > 43
Answer:
B
Step-by-step explanation:
A number is equal to twice a smaller number plus 3. The same number is equal to twice the sum of the smaller number and 1. How many solutions are possible for this situation?
* Infinitely many solutions exist because the two situations describe the same line.
* Exactly one solution exists because the situation describes two lines that have different slopes and different y-intercepts.
* No solutions exist because the situation describes two lines that have the same slope and different y-intercepts.
* Exactly one solution exists because the situation describes two lines with different slopes and the same y-intercept.
Answer:
There is no solution to this.
Explanation :
We have a double system of equation to solve. Let x be the big number and let y be the smaller number, such that y < x.
x is equal to twice a smaller number plus 3, which translates into : x = 2y + 3
and x is equal to twice the sum of the smaller number and 1 : x = 2 * (y + 1)
We get this system to solve : [tex]\left \{{{x=2y+3} \atop {x=2(y+1)}} \right. \left \{{{x-2y=3} \atop {x-2y=2}} \right.[/tex]
It's either x minus 2y equals 3, or x minus 2y = 2 but it can't be both. No solutions exist because the situation describes two lines that have the same slope and different y-intercepts
2(4×+2)=10
[tex]6 \times + 4 = 10 \\ \\ 6 \times = 10 - 4 \\ \\ 6 \times = 6 \\ \\ [/tex]
that is the answer
Answer:
x = 3/4
Step-by-step explanation:
2(4x + 2) = 10 Remove the brackets
8x + 4 = 10 Subtract 4 from both sides
8x = 6 Divide by 8
x = 6/8
x = 3/4
Check
2(4*3/4 + 2) =?10
2( 3 + 2) = 10
2*5 = 10
10 = 10
Your parents deposit 2 50-dollar bills at the bank.
How much money did they deposit?
Answer: $100
Step-by-step explanation:
Considering 50 + 50 = 100
This means that the amount of money is $100
> There are 14 books on a shelf. 6 of these books are new. The rest of them are used (a) What is the ratio of new books to used books? (b) What is the ratio of used books to all books on the shelf
Answer:
a) 6:8
Because you have 14 books total if you substract 14 - 6= 8, so now you have
14 Books total
6 New Books
8 Used Books.
So, the ratio of new books to used books is 6:8 or if you simplified is 3:4.
b) 8:14
Because you have 8 used books compare to 14 books total. If you simplified your fraction you'll have 4:7
Step-by-step explanation:
Complete the table for the given rule.
Rule: y is 0.75 greater than x
x y
0
3
9
The complete table is
x y
0 0.75
3 3.75
9 9.75
What is equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
What is substitution?Substitution means putting numbers in place of letters to calculate the value of an expression or equation.
According to the given question.
We have values of x.
Also, one rule that y is 0.75 greater than x.
So, we have a equation for finding the value of y i.e.
[tex]y = x + 0.75..(i)[/tex]
For finding the value of y
At x = 0, substitute x = 0 in equation (i)
[tex]y = 0 + 0.75\\\implies y = 0.75[/tex]
At x = 3, substitute x = 3 in equation (i)
[tex]y = 3+0.75\\\implies y = 3.75[/tex]
At x = 9, substitute x = 9 in equation (i)
[tex]y = 9+0.75\\\implies y = 9.75[/tex]
Hence, the complete table is
x y
0 0.75
3 3.75
9 9.75
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