Answer:
a
The null hypothesis is [tex]H_o : \sigma^2_1 = \sigma^2 _2[/tex]
The alternative hypothesis is [tex]H_a : \sigma_1 ^2 > \sigma^2_2[/tex]
b
[tex]F_{critical} = 1.8608[/tex]
c
[tex]F = 2.9085[/tex]
d
The decision rule is
Reject the null hypothesis
e
There is sufficient evidence to support the researchers claim
Step-by-step explanation:
From the question we are told that
The first sample size is [tex]n_1 = 30[/tex]
The sample variance for elementary school is [tex]s^2_1 = 8324[/tex]
The second sample size is [tex]n_2 = 30[/tex]
The sample variance for the secondary school is [tex]s^2_2 = 2862[/tex]
The significance level is [tex]\alpha = 0.05[/tex]
The null hypothesis is [tex]H_o : \sigma^2_1 = \sigma^2 _2[/tex]
The alternative hypothesis is [tex]H_a : \sigma_1 ^2 > \sigma^2_2[/tex]
Generally from the F statistics table the critical value of [tex]\alpha = 0.05[/tex] at first and second degree of freedom [tex]df_1 = n_1 - 1 = 30 - 1 = 29[/tex] and [tex]df_2 = n_2 - 1 = 30 - 1 = 29[/tex] is
[tex]F_{critical} = 1.8608[/tex]
Generally the test statistics is mathematically represented as
[tex]F = \frac{s_1^2 }{s_2^2}[/tex]
=> [tex]F = \frac{8324 }{2862}[/tex]
=> [tex]F = 2.9085[/tex]
Generally from the value obtained we see that [tex]F > F_{critical }[/tex] Hence
The decision rule is
Reject the null hypothesis
The conclusion is
There is sufficient evidence to support the researchers claim
The third and the sixth term of a geometric progression are 24 and 64/9 respectively. Find
a) the first term and common ratio
b) the sum of the first five terms
Answer:
Ai. Common ratio = 2/3
Aii. First term = 54
B. Sum of the first five terms = 422/3
Step-by-step explanation:
From the question given above, the following data were obtained:
3rd term (T3) = 24
6Th term (T6) = 64/9
First term (a) =?
Common ratio (r) =?
Sum of the first five terms (S5) =?
Ai. Determination of the common ratio (r).
T3 = ar²
T3 = 24
24 = ar²....... (1)
T6 = ar⁵
T6 = 64/9
64/9 = ar⁵......... (2)
The equation are:
24 = ar²....... (1)
64/9 = ar⁵......... (2)
Divide equation 2 by equation 1.
64/9 ÷ 24 = ar⁵ / ar²
64/9 × 1/24 = r³
8/27 = r³
Take the cube root of both side
r = 3√(8/27)
r = 2/3
Thus, the common ratio is 2/3
Aii. Determination of the first term (a).
T3 = ar²
3rd term (T3) = 24
Common ratio (r) = 2/3
First term (a) =?
24 = a(2/3)²
24 = 4a/9
Cross multiply
24 × 9 = 4a
216 = 4a
Divide both side by 4
a = 216/4
a = 54
Thus, the first term (a) is 54
B. Determination of the sum of the first five terms.
Common ratio (r) = 2/3
First term (a) = 54
Number of term (n) = 5
Sum of first five terms (S5) =?
Sn = a[1 –rⁿ] / 1 – r
S5 = 54[1 – (⅔)⁵] / 1 – ⅔
S5 = 54 [1 – 32/243] / ⅓
S5 = 54 (211/243) × 3
S5 = 54 × 211/81
S5 = 6 × 211/9
S5 = 2 × 211/3
S5 = 422/3
Thus, the sum of the first five terms is 422/3
If a cross section of the paperweight is cut parallel to the base, which shape describes the cross section?
Answer:
Yes, that's right: the cross section will be a rectangle (but also a parallelogram).
Step-by-step explanation:
Roman solved the equation 5 a + 2 b = 10 for a. His steps are shown below. 1. Subtract 2b: 5 a + 2 b minus 2 b = 10 minus 2 b. 5 a = 10 minus 2 b. 2. Multiply by 5: a = 50 minus 10 b. Which statement about Roman’s work is true? In step 1, he needed to add 2b to both sides of the equation. In step 1, he needed to divide both sides of the equation by 2b. In step 2, he needed to divide both sides of the equation by 5. In step 2, he needed to subtract 5 from both sides of the equation.
Answer:
It's C
Step-by-step explanation:
In step 2, he should have divided. Have a great day!
Answer:
C: In step 2 he should divide the equation on both sides by 5.
Step-by-step explanation:
Took the test, got it right.
PLEAS HURRY I HAVE NO TIME LEFT
PLEASE HELP ME WITH THIS QUESTION
Question: Name each polygon by its number of sides and then classify it as CONVEX or CONCAVE and REGULAR or IRREGULAR
Answer:
no you scam me if I see what is promises I will help you
37/6 divided by 1/2.
Answer: 12 1/3
hope this helps.. stay safe and have a great day
Step-by-step explanation:
The length of a jogging trail is 3528 m. A jogger wants to complete the trail within 30 min.
How many meters must the jogger travel each minute?
Answer:
117.6 meter per min
Step-by-step explanation:
since the jogger wants to complete the trail in 30 minutes and the total length of the trail is 3528m you just need to divide the length of the trail (3528) by the total amount of time to get the answer
Answer:
117.6m per minute
Step-by-step explanation:
3528:30
588:5
30 divided by 6=5
3528 divided by 6=588
Then
5 divided by 5=1
588 divided by 5=117.6
117.6m:1
Write an equation in point-slope form of the line that passes through (-4,1) and (4.3).
Answer:
a
Step-by-step explanation:
:P
Leon visited Chicago, which is located on the shore of
Lake Michigan. The lake has a volume of about 4,920
_. Chicago was a major gateway to the west in
1825 when the Erie Canal was completed. When built,
the Erie Canal was 680 long and only 100_, or
10 deep. While in Chicago, Leon visited the Sear
Tower. One of the tallest buildings in the world, the
Sears Tower is 443 tall
during Leon's visit was about 7
Answer:
Step-by-step explanation:
Leon visited Chicago, which is located on the shore of
Lake Michigan. The lake has a volume of about 4,920
km cubed. Chicago was a major gateway to the west in
1825 when the Erie Canal was completed. When built,
the Erie Canal was 680 long and only 100 or
10 deep. While in Chicago, Leon visited the Sear
Tower. One of the tallest buildings in the world, the
Sears Tower is 443 tall
during Leon's visit was about 7
A rocket is launched from a tower. The height of the rocket, y in feet, is related to the time after launch, x in seconds, by the given equation. Using this equation, find out the time at which the rocket will reach its max, to the nearest 100th of a second.
y=−16x 2 +193x+128
Let x be -b/2a
x = -193/2•(-16)
x = -193/-32
x = 6.03125
Now, plug this value of x into every x in the function and simplify. The max is the y value.
Can you finish?
The time at which the rocket will hit the ground to the nearest hundredth of seconds is 13 seconds.
What is a quadratic equation?An algebraic equation of the second degree in x is a quadratic equation. The quadratic equation is written as ax2 + bx + c = 0, where x is the variable, and a must not be zero.
As per the given height of tower y in terms of time is seconds x
y = -16x² + 193x + 128
The height of the tower when the rocket hit the ground will be zero.
Thus, y = 0
0 = -16x² + 193x + 128
16x² - 193x - 128=0
By quadratic equation formula,
x = [-(-193) ± √((-193)²-4×16×(-128))]/ 2×16
x = [193 ± 213.168]/32
x = 12.69 and x = -0.63 since time can be never negative thus 12.69 seconds will be correct.
12.69 to the nearest hundred is 13.
Hence "The time at which the rocket will hit the ground to the nearest hundredth of seconds is 15 seconds".
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A ceramics teacher orders 5 blocks of gray clay for every 3 blocks of red clay.
How many blocks of gray clay will the teacher order if she orders 15 blocks of red
clay? *
17
20
25
28 ( plz help if you can)
Answer:
25
Step-by-step explanation:
trust me it's right it might be easier if you use paoer
00
3-2 Checking Accounts
12. Justin Nucci listed these items on his deposit slip: (bills) 8 one-hundreds,
27 fifties, 83 fives, 141 ones; (coins) 13 quarters, 117 nickels; (checks) $317.94,
$57.89, $527.24 and $77.49. He received cash back of 30 twenties and 11 tens.
What total deposit did he make?
603
120] Chapter 3 Banking
Answer: 4,405.66
Step-by-step explanation:
Add all the amounts together.
Help Please!! I WILL give brainliest and thanks!!
Which of these inequalities are equivalent to r > -11?
Check all that apply.
-r -33
-3r 33
Random answers get reported
Answer:
ez pts tysm
Step-by-step explanation:
If y= 6x + 8 what is y when x= -3
Answer:
y=2
Step-by-step explanation:
y = 26
If you substitute x for -3 in the equation y = 6x + 8, your equation becomes:
y = 6(-3) + 8 now you can simplify it and solve for y
6 x -3 = -18
18 + 8 = 26
y = 26
write an equation of a line that passes through (-6,4) and is PERPENDICULAR to y=3x-11
Answer:
y = -1/3x + 2
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDASEquality PropertiesAlgebra I
Perpendicular lines have the negative reciprocal slope of the original.
Slope-Intercept Form: y = mx + b
m - slope b - y-interceptStep-by-step explanation:
Step 1: Define
y = 3x - 11
Point (-6, 4)
Step 2: Find slope m
Negative Reciprocal of 3 = -1/3
Step 3: Define
y = -1/3x + b
Step 4: Find y-intercept b
Substitute in point: 4 = -1/3(-6) + bMultiply: 4 = 2 + bSubtract 2 on both sides: 2 = bRewrite: b = 2Step 5: Write perpendicular linear equation
y = -1/3x + 2
Renting the ice-skating rink for a birthday party costs $200 plus $4 per person. the rental costs $324 in total
If we can translate the statement "The ice rink costs $200 plus $4 per person to rent for a birthday celebration and the entire cost of the rental is $324" into an algebraic equation, we get 4x + 200 = 324, where x is the number of people at the birthday party. The solution of this equation i.e. the number of people at the birthday party is 31.
What is an algebraic equation?A statement of the equivalence of two expressions created by executing algebraic operations on a set of variables, such as addition, subtraction, multiplication, division, raising to a power, and root extraction, is known as an algebraic equation.
How to solve this problem?Let the number of people at the birthday party be x.
Given that the ice rink costs $200 plus $4 per person to rent for a birthday celebration. So, the rent is 4x + 200.
Also, given that the entire cost of the rental is $324.
We can write the corresponding algebraic equation as
4x + 200 = 324
Now we have to solve this equation.
So, 4x = 324 - 200 = 124
i.e. x = 124/4 = 31
Therefore the required algebraic equation is 4x + 200 = 324, where x is the number of people at the birthday party. Also, the solution of this equation i.e. the number of people at the birthday party is 31.
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how many 2/3 size pieces are in 4 wholes
Divide 4 wholes by 2/3 pieces to fnd number of pieces.
4 / 2/3
When you divide by a fraction, flip the fraction over then multiply:
4 x 3/2 = (4 x 3)/2 = 12/2 = 6
There are 6 pieces.
Answer:
6
Step-by-step explanation:
lets put this in terms of 3, because of 2/3. the number above the three will be divided by three to get to four. So if we multiply three by four to get twelve, we can put that over 3, and then find our answer. 12/3=4, so we know that is correct. and since we need to find how many 2/3 pieces we need, we divide 12/3 by 2/3 to get 6. so you need 6 2/3 pieces to get four wholes.
Each good worker can paint my new house alone in 12 hours. Each bad worker can paint my house alone in 36 hours. I need my house painted in 3 hours. If I can only find 3 good workers, how many bad workers must I also find in order to have my house painted on time?
Pls give explanation
In 3 hours, one good worker can paint one fourth of your house. Three good workers can thus paint three fourths of your house in three hours, leaving one fourth to be done by bad workers.
One bad worker can paint one twelfth of your house in 3 hours. There are three twelfths in one fourth, so you will need to hire three bad workers to have your house painted on time.
5+1000000000000000000
Answer:
1000000000000000005
Answer:
1000000000000005
Step-by-step explanation:
WILL GIVE BRAINLIEST
Answer: a.
Step-by-step explanation:
If there is a negative mark next to the whole fraction, that means both of the numbers are negative.
I am not sure if this answer is accurate. Please inform me if I am incorrect. TY.
oscar earns 12 per hourfor the first 8 hours he works each day. for every hour worked 8, he earns 1 1/4 of his normal hourly wage. on Thursday he wroked from 8:00 A.M. to 11:45 A.M., took a 30 minute lunch break, and he left work for the day at 6:45. how much money (in dollars) did oscar earn Thursday?
Answer:
freeeeeeeeeeeeeee pointtttttttttttt
Step-by-step explanation:
Fixed expenses should
A. be less than discretionary spending
B. be more than discretionary spending
CC. not total more than your gross pay
D. not total more than your net income
Calculating Percent Change
Determine the Percent Change for each of the following.
Express each answer as a percent, rounded to the nearest tenth.
A quantity decreases from 20 to 15-% decreased
A quantity increases from 15 to 20-% increase
The price of a Latte dropped from $3.12 to $2.9-% decrease
The cost of Gasoline rose from $2.9 to $3.12-% increase
Answer:
the last one is an increase of $.22
Step-by-step explanation:
the last one is an increase of $.22
A rectangular room is 4 times as long as it is wide, and its perimeter is 80 meters. Find the dimension of the room
The minimum diameter for a hyperbolic cooling tower is 57 feet...
Answer:
Can give you the example then you have to figure out.
Step-by-step explanation:
We are assuming the center of the tower is at the origin, so we can use the standard form of a horizontal hyperbola centered at the origin: \displaystyle \frac{{x}^{2}}{{a}^{2}}-\frac{{y}^{2}}{{b}^{2}}=1
a
2
x
2
−
b
2
y
2
=1, where the branches of the hyperbola form the sides of the cooling tower. We must find the values of \displaystyle {a}^{2}a
2
and \displaystyle {b}^{2}b
2
to complete the model.
First, we find \displaystyle {a}^{2}a
2
. Recall that the length of the transverse axis of a hyperbola is \displaystyle 2a2a. This length is represented by the distance where the sides are closest, which is given as \displaystyle \text{ }65.3\text{ } 65.3 meters. So, \displaystyle 2a=602a=60. Therefore, \displaystyle a=30a=30 and \displaystyle {a}^{2}=900a
2
=900.
To solve for \displaystyle {b}^{2}b
2
, we need to substitute for \displaystyle xx and \displaystyle yy in our equation using a known point. To do this, we can use the dimensions of the tower to find some point \displaystyle \left(x,y\right)(x,y) that lies on the hyperbola. We will use the top right corner of the tower to represent that point. Since the y-axis bisects the tower, our x-value can be represented by the radius of the top, or 36 meters. The y-value is represented by the distance from the origin to the top, which is given as 79.6 meters. Therefore,
x
2
a
2
−
y
2
b
2
=
1
Standard form of horizontal hyperbola
.
b
2
=
y
2
x
2
a
2
−
1
Isolate
b
2
=
(
79.6
)
2
(
36
)
2
900
−
1
Substitute for
a
2
,
x
,
and
y
≈
14400.3636
Round to four decimal places
The sides of the tower can be modeled by the hyperbolic equation
\displaystyle \frac{{x}^{2}}{900}-\frac{{y}^{2}}{14400.3636 }=1,\text{or}\frac{{x}^{2}}{{30}^{2}}-\frac{{y}^{2}}{{120.0015}^{2} }=1
900
x
2
−
14400.3636
y
2
=1,or
30
2
x
2
−
120.0015
2
y
2
=1
The shape of hyperbolic cooling tower is a conic section that can be described with a formula equation.
a = 28.5, b ≈ 52.65
[tex]Equation \ of \ hyperbola;\ \dfrac{x^2}{28.5^2} - \dfrac{(y-155)^2}{56.62^2} = 1[/tex]
Reasons:
The parameters of the hyperbolic cooling tower are;
Minimum diameter = 57 feet
The height at which the diameter occurs = 155 ft.
The diameter of the tower = 175 feet
Total height of the tower = 200 feet
Height at which the center of the hyperbola occurs = 155 feet
Solution:
The equation of a hyperbola is; [tex]\dfrac{(x - h)^2}{a^2} - \dfrac{(y- k)^2}{b^2} = 1[/tex]
The center of the hyperbola = (0, 155)
[tex]a = \dfrac{57}{2} = 28.5[/tex]
At y = 155,
Therefore;
[tex]\dfrac{x^2}{28.5^2} - \dfrac{(y -155)^2}{b^2} = 1[/tex]
At y = 200 feet [tex]x = \dfrac{75 \ feet}{2} = 37.5 \ feet[/tex]
Therefore;
[tex]\dfrac{37.5^2}{28.5^2} - \dfrac{(200 -155)^2}{b^2} = 1[/tex]
b² = 2769.0340909
b ≈ 52.62
The equation of the hyperbola is therefore;
[tex]\dfrac{x^2}{28.5^2} - \dfrac{(y-155)^2}{56.62^2} = 1[/tex]
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Thanks in advance!
Answer:
y = 8x + 13
Step-by-step explanation:
slope-intercept form: y = mx + b
Given equation: [tex]y = -\frac{1}{8}x -2[/tex]
Second equation: unknown
Slope: unknown
Given point: (-2, -3)
When two lines are perpendicular, their slopes are negative reciprocals. So, since the slope(m) of the given line is [tex]-\frac{1}{8}[/tex], the slope of the line perpendicular to it is 8.
Now we know the slope of the line. To find the y-intercept, input the values of the slope and the given point into the equation format and solve for b:
y = mx + b
-3 = 8(-2) + b
-3 = -16 + b
13 = b
The y-intercept is 13.
Now that we know the slope and the y-intercept, we can write the equation:
y = 8x + 13
Hope this helps :)
Which of the following shows the correct sums that would be found when clustering is used to find the answer to the problem 34 x 12?
340 + 68 = 408
340 + 34 = 374
340 + 68 = 398
300 + 8 = 308
The first option is correct.
The calculation is as follows:if we multiply the 34 and 12 so it comes 408
And according to first option, it we add 340 and 68 so it comes 408.
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1/4 divided 3 please help me
Answer: 1/12
Step-by-step explanation:
how many hectares of land are there in a field that is 450 m long and 1200 dm wide.
Answer:
Step-by-step explanation:
Given
[tex]Length = 450\ m[/tex]
[tex]Width = 1200\ m[/tex]
Required
Determine the number of hectares in this dimension
First, we need to calculate the area of the land
[tex]Area = Length * Width[/tex]
[tex]Area = 450m * 1200dm[/tex]
Convert dm to m
[tex]Area = 450m * 120m[/tex]
[tex]Area = 54 000 m^2[/tex]
[tex]1 hectare = 0.0001m^2[/tex]
So, we have:
[tex]1\ hectare = 0.0001m^2[/tex]
Multiply by 54000
[tex]Hectare = 0.0001 * 54000[/tex]
[tex]Hectare = 5.4[/tex]
Hence, there are 5.4 hectares
11. Estimate the number of quart containers Ethan
can fill from a container with 8 quarts of water.
Answer:
A little over 4 and a half
Step-by-step explanation:
8 divided by 2 (making it one half) is 4 and 7/8 is greater than 1/2
Which are the partial products of 3706 x 4?
Answer:
There are no partial products to this equation. There is only one product! Okay first we will multiply 4 x 6 to get 4 in our ones place, carry the 2 over the zero put the 2 down 4 x 7 is 28 put the 8 down carry the 2, 4 x 3 is 12 + 2 is 14! So you're final product is 14,824!!!
The partial products of the given expression will be ( 3000 x 4 ) + ( 706 x 4 ).
What is multiplication?Multiplication is the process of determining the product of two or more numbers in mathematics. A product, or an expression that specifies factors to be multiplied, is what happens when you multiply two numbers in mathematics.
The accepted method for representing both integer and non-integer numbers is the decimal numeral system. Decimal notation is the term used to describe the method of representing numbers in the decimal system.
The given product is 3706 x 4 and can be written as:-
3706 x 4 = [ 3000 x 4 + 706 x 4 ]
Therefore, the partial products of the given expression will be ( 3000 x 4 ) + ( 706 x 4 ).
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