Answer:
Calculated t= 0.011659
t ≥ t ( 0.025,11) = 2.201
So the null hypothesis is accepted.
Step-by-step explanation:
Student Math Writing Difference d²
math score − writing score
1 540 474 66 4356
2 432 380 52 2704
3 528 463 65 4225
4 574 612 -38 1444
5 448 414 34 1156
6 502 526 -24 576
7 480 430 50 2500
8 499 453 46 2116
9 610 615 -5 25
10 572 541 31 961
11 390 335 55 3025
12 593 613 -20 400
∑ 6168 5856 312 23488
1) We state our null and alternative hypothesis as
H0: ud= 0 Ha: ud≠0
2) The significance level alpha is set at α= 0.05
3) The test statistic under H0 is
t= d`/ sd/√n
which has t distribution with n-1 degrees of freedom.
4) The critical region is t ≥ t ( 0.025,11) = 2.201
5) Computations
d`= ∑di/n= 312/12= 31.2
Variance = ∑(di- d`)²/n-1= 1/n-1 [ ∑di²-( ∑di)²/n]
= 1/11[ 23488- (312)²/12]
= 1/11[ 23488- 8112] = 1/11[15376]= 5976.7272
Standard Deviation= √ 5976.7272= 77.2510= 77.25
Now t= 3.12/77.25/√12= 0.011659
The calculated t value= 0.011659 falls in the acceptance region . So we accept our null hypothesis and reject the alternative hypothesis.
on a function map, the values for the domain of the function appear on the ______ and the values for the range appear on the _______
Answer:
domain is x
range is y
Step-by-step explanation:
The values for the domain of the function appear on the x-axis and the values for the range appear on the y-axis.
What is the range and domain of a function?A function's range is the set of all values that the function accepts, and its domain is the set of all values for which the function is defined.
The domain is for the independent variable while the range is for the dependent variable.
For example f(x) = x²
Now if we put x = 1 then it is called as domain variable while the value of function at x = 1 its that f(1) = 1 called range variable.
The range is the interval where the function f(x) is defined whereas the domain is the input interval of the independent variable (x).
For example f(x) = x²
Now if we put x = 1 then it is called as domain variable while the value of function at x = 1 its that f(1) = 1 called range variable.
Hence "The values for the domain of the function appear on the x-axis and the values for the range appear on the y-axis".
For more details about the range and domain of the function,
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if Xandy are integers and(x-y)=4, what is the main minimum possibile value of xy?
Answer:
-4
Step-by-step explanation:
Hello,
x-y=4 <=> x=y+4
so, xy=y(y+4)
[tex]y(y+4)=y^2+4y=(y+2)^2-4[/tex]
so this is minimum for y = -2 and the minimum value is -4
thanks
what is 2k-3(2k-3)=45
Answer:
k = -9
Step-by-step explanation:
Please show me how to solve this! Y^7Z^3/y^4z
Answer:
(y^3)(z^2)
Step-by-step explanation:
subtract the common based exponents
▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓
[tex]\sf{\dfrac{y^7z^3}{y^4z}}\\\\=\tt{\dfrac{y^7}{y^4}×\dfrac{z^3}{z^1}}\\\\=\tt{y^{(7-4)}×z^{(3-1)}}\\\\=\tt{(y^3)×(z^2)}\\\\\pmb{\green{\boxed{\bold{y^3z^2}}}}[/tex]
▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓
GUYS I MESSED UP ON THE LAST ONE PLEASE HELP ME AGAIN what algebraic expression represents GK
Answer:
GK = 9x-5
Step-by-step explanation:
GK = GH +HJ + JK
= (GJ - HJ) + (HJ) + (HK - HJ)
= (4x-3-x) + (x) + (6x-2-x)
= 3x-3 + x + 5x-2
= (3x+5x+x)+(-3-2)
GK = 9x-5
A package of fish weighs 2.5 pounds. The price is $3.50 per pound. What is the price of this package?
Answer:
$8.75
Step-by-step explanation:
If you do
$3.50 x 2.5 you get
$8.75
What is 7x+7=2(x+1)
Answer:
7X+7=2(X+1)
7X+7=2X+2
7x-2X =2-7
5X/5 =-5/5
. X =-1
What is a number multiplied by 12 is 84
Hey there! I'm happy to help!
Let's call our number n. Here is the information we have.
n×12=84
We want to figure out what n equals. To do this, we have to get it by itself in the equation. What we will do is cancel out the 12 by dividing both sides by 12.
n×12/12=84/12
n=7
Therefore, our number is 7.
Have a wonderful day! :D
6x^2 + 9x = 0 :) please help !!
Solution for 6x^2+9x=0 equation:
Simplifying
6x2 + 9x = 0
Reorder the terms:
9x + 6x2 = 0
Solving
9x + 6x2 = 0
Solving for variable 'x'.
Factor out the Greatest Common Factor (GCF), '3x'.
3x(3 + 2x) = 0
Ignore the factor 3.
Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:
Simplifying
x = 0
Solving
x = 0
Move all terms containing x to the left, all other terms to the right.
Simplifying
x = 0
Subproblem 2
Set the factor '(3 + 2x)' equal to zero and attempt to solve:
Simplifying
3 + 2x = 0
Solving
3 + 2x = 0
Move all terms containing x to the left, all other terms to the right.
Add '-3' to each side of the equation.
3 + -3 + 2x = 0 + -3
Combine like terms: 3 + -3 = 0
0 + 2x = 0 + -3
2x = 0 + -3
Combine like terms: 0 + -3 = -3
2x = -3
Divide each side by '2'.
x = -1.5
Simplifying
x = -1.5
Solution
x = {0, -1.5}
what is the answer for 5(u-5)
Answer:
5u-25
Step-by-step explanation:
We have to simplify by distributing 5 to the variable and the number.
5(u-5)
5(u)5(-5)
5u-25
Please answer the second conversion. Convert 25 ML to L
Answer:
0.025 l
Hope it helped u if yes mark me BRAINLIEST
Cups of dog food is recommended for a 25 pound dog
Answer:
100 cups of food is for a 25 pound dog
SOLVING QUADRATIC EQUATIONS
2) Solve 2x2 - 5 = 27
Answer:
x = ±4
Step-by-step explanation:
Step 1: Write out quadratic
2x² - 5 = 27
Step 2: Add 5 to both sides
2x² = 32
Step 3: Divide both sides by 2
x² = 16
Step 4: Take the square root of both sides
x = ±4
∴ x can equal -4 or 4
Answer:
[tex] \boxed{ \bf \huge \: x =4}[/tex]
[tex] \rm \: Or,[/tex]
[tex] \boxed{\bf \huge \: x = - 4}[/tex]
Step by step explanation:
Given Equation is :-
[tex]\sf \implies \: 2 {x}^{2} - 5 = 27[/tex]
We need to find the value of [tex]x[/tex] using Quadric formula.
Firstly, Subtract 27 from both of the side(s):-
[tex]\sf \implies2 {x}^{2} - 5 - 27 = 27 - 27[/tex]
On Simplification:-
Add -5-27 as (-) and (-) equals to (+). -5-27 would be represented as 5+27, which results to 32.
[tex]\sf\sf \implies2 {x}^{2} - 32 = 0[/tex]
Then, for this equation , a=2, b=0, c=-32.
Put the values :-
That is,
[tex]\sf \implies2 {x}^{2} + 0x + ( - 32) = 0[/tex]
As we know, that the quadratic formula is:-
[tex]\sf \implies \: x = \dfrac{ -b \pm \sqrt{b {}^{2} - 4ac } }{2a} [/tex]
Put the values :-
[tex]\sf \implies \: x = \dfrac{ - 0 \pm \sqrt{0 {}^{2} \: - 4(2) ( - 32)} }{2(2)} [/tex]
On Simplification:-
[tex]\sf \implies \: x = \dfrac{ - 0 {}^{} \pm \sqrt{ {0 } - \: 8 \times - 32}}{2 \times 2} [/tex]
[tex]\sf \implies \: x = \dfrac{ - 0 \pm \: \sqrt{ - 8 \times - 32} }{4}[/tex]
[tex]\sf \implies x = \dfrac{ - {0}^{}\pm \: \sqrt{ + 256} }{4} [/tex]
As 0 has no value here,
[tex]\sf \implies \: x = \dfrac{ \pm \sqrt{256} }{4} [/tex]
On cancelling,
Remove the square of 256 ( √256)
[tex]\sf \implies \: x = \dfrac{ \pm \cancel{ \: 256}}{ \cancel4} [/tex]
[tex]\sf \implies \: x = ± + 4[/tex]
It may be represented as,
[tex]\sf \implies \: x = - 4[/tex]
Or,
[tex]\sf \implies \: x = 4[/tex]
_______________________________
I hope this helps!
Please let me know if you have any questions.
~MisterBrian
which expression is equivalent to -14-6
Your cell phone dies. Cost of repair is $20 plus $16 per hour. You have $68 for the repair. How many hours can you afford?
Answer:
3 hours
Step-by-step explanation:
$20 + $16 = $36 base
$36 + $16 = $52
$52 + $16 = $68
3 HOURS
Determine the volume of fluid in the graduated cylinder shown.
My area is calculated by 1/2( base * height), who am I? *
O
square
O triangle
O circle
O sphere
Answer:
Triangle
Step-by-step explanation:
Basically, you have to multiply the base and the height of the triangle, and then divide it by two.
Answer:
O triangle
Step-by-step explanation:
Triangle area = (base*heigth)/2
19. If a school board determines that there should be 3 teachers for every 50 students, how many teachers are needed for an enrollment of 5400 students?
Answer:
324 teachers
Step-by-step explanation:
3 teachers of every 50 students
__ teachers of 5400 students
so,
[tex]5400 \div 50 = 108[/tex]
therefore,
[tex]3 \times 108 = 324[/tex]
Sarina throws a ball up into the air, and it falls on the ground nearby. The ball's height, in feet, is modeled by the function ƒ(x) = –x2 – x + 3, where x represents time in seconds. What's the height of the ball when Sarina throws it? Question 4 options: A) 4 feet B) 1 foot C) 3 feet D) 2 feet
Answer:
(C) 3 feet
Step-by-step explanation:
We have a function of f(x) here. When Sarina throws the ball, it has been 0 seconds since she threw it.
Since x represents the amount of seconds, we can find the height of the ball (f(x)) by substituting x in as 0.
[tex]-0^2 - 0 + 3[/tex]
0 squared is 0, 0 minus zero is 0, and 0+3 = 3, so
[tex]f(x) = 3[/tex]
Meaning that when Sarina threw the ball, it's height was 3 feet.
Hope this helped!
WILL GIVE BRAINLIEST: If the graph of 2x+3y − 6=0 is perpendicular to the graph of ax − 3y=5. What is the value of a?
Answer:
a = [tex]\frac{9}{2}[/tex]
Step-by-step explanation:
To find the value of a, find the Slope of both the equations.
For lines to be perpendicular to each other [tex]m_{1}m_{2} = - 1[/tex]
For line 1:
2x + 3y − 6 = 0 represent the line in y=mx +c form
3y = -2x + 6
y = [tex]\frac{-2}{3} x[/tex] + [tex]\frac{6}{3}[/tex]
y = [tex]\frac{-2}{3} x[/tex] + 2
[tex]m_{1}[/tex] = [tex]\frac{-2}{3}[/tex]
For line 2:
ax - 3y = 5
ax = 5 + 3y
ax - 5 = 3y
y = [tex]\frac{ax}{3} - \frac{5}{3}[/tex]
[tex]m_{2}[/tex] = [tex]\frac{a}{3}[/tex]
Apply the condition of perpendicularity:
[tex]\frac{-2}{3}[/tex] * [tex]\frac{a}{3}[/tex] = - 1
[tex]\frac{2a}{9} = 1[/tex]
a = [tex]\frac{9}{2}[/tex]
Select the correct answer.
What is the solution for x in the equation?
-4 + 5x - 7 = 10 + 3x - 2x
A.x=4/21
B.x=21/4
C.x=13/4
D.x=4/13
Answer:
B
Step-by-step explanation:
I've taken a picture of the way I solved it.
The required simplified solution of the given expression is x=21/4. Option B is correct.
The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
here,
Given expression,
-4 + 5x - 7 = 10 + 3x - 2x,
Adding alike terms and And isolate the terms containing variable x,
-11 + 5x = 10 +x
5x - x = 10 + 11
4x = 21
x = 21 / 4
Thus, the required simplified solution of the given expression is x=21/4. Option B is correct.
Learn more about simplification here:
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i cant understand any of these if you guys can help that’d be great!
Answer:
1. -9/20
2. 1 7/12
3. -4 1/3
Step-by-step explanation:
When adding and subtracting fractions with unlike denominators, you must first make them like denominators. To do this we must:
1. Find the Least Common Multiple of the denominators (which is called the Least Common Denominator).
2. Change each fraction (using equivalent fractions) to make their denominators the same as the least common denominator.
3. Then add (or subtract) the fractions, as we wish!
The easiest way to this is by multiplying the denominators. Remember that whatever you do to the bottom, you also do to the top
1. -5/4 +4/5
if we multiply 4 and 5, we get 20. Our denominator will be 20 before we simplify.
our new equation is going to be -25/20 + 16/20. Now we can add these together to get an answer of -9/20. Which is in the simplist form.
One more thing: to make a mixed number an improper fraction, you multiply the whole number by the denominator, and add the numerator.
1X4=4
4+1=5
The improper fraction is 5/4.
To make a Whole number a fraction, multiply the number by the denominator
-5x3=15
The improper is -15/3.
To go from an improper to a mixed, divide the numerator by the denominator. The remainders are going to be the fraction attached.
The XYZ Car Rental Agency charges a flat rate $29 per day plus $0.32 per mile driven Write and algebraic expression for the rental cost of a car for x days that is driven y miles
simplify the following
3³×6-³×2^5
Answer:
4
Step-by-step explanation:
3³=27
6-³=1/216
2^5=32
27X1/216x32
=4
(−8r5t8)(−5rt) Please help
Answer:
40r^6t^9
Step-by-step explanation:
write the sentence as an equation
the product of y and 6, add to 310 is y
y(6)+310=y
equals is =
product of is ×
add to is +
Billy has some nickels and dimes worth $3.25. He has 3 times as many nickels as dimes. How many nickels does he have?
[tex]3d=n[/tex]
[tex]10d+5n=325[/tex]
[tex]10d+15d=325[/tex]
[tex]25d=325[/tex]
[tex]d=13[/tex]
[tex]n=39[/tex]
Hope this helps.
頑張って!
Please help find the perimeter and area of the polygon
Carmen has 1/6 of a loaf pumpkin bread. She cuts the loaf into six equal pieces and gives one piece to each of her six friends. How much of the whole loaf of bread does each of the six friends get?
Answer:
each friend gets 1/36 of the loaf of pumpkin bread
Step-by-step explanation:
1/6 of a loaf
1/6 divided by 6
turn 6 into a fraction → 6/1
1/6 ÷6/1
to divide multiply the reciprocal 6/1 → 1/6
1/6 x 1/6 = 1/36
each friend get 1/36
OR
6/x = 1/6
x= 36
6/36
if f(x)=4x^2-6
find all x such that f(x)= 106
Answer:
50
Step-by-step explanation:
Answer:
[tex]2\sqrt7,-2\sqrt7[/tex]
Step-by-step explanation:
So we have the function:
[tex]f(x)=4x^2-6[/tex]
And we want to find all x such that f(x) is 106. So, substitute 106 for f(x):
[tex]106=4x^2-6[/tex]
Add 6 to both sides:
[tex]112=4x^2[/tex]
Divide both sides by 4:
[tex]x^2=28[/tex]
Take the square root of both sides:
[tex]x=\pm\sqrt{28}[/tex]
Simplify the square root:
[tex]x=\pm\sqrt{28}=\pm\sqrt{4\cdot 7}=\pm2\sqrt7[/tex]
So, those are the two values that will satisfy our requirement.
And we're done!