Solution :
a). [tex]$\text{Set up hypothesis}$[/tex]
[tex]$\text{Null hypothesis}$[/tex] : There is no significance between them.
[tex]$H_0:\mu_1=\mu_2$[/tex]
[tex]$\text{Alternate hypothesis}$[/tex] : There is significance between them.
[tex]$H_1:\mu_1!=\mu_2$[/tex]
b). Test statics
[tex]$X(\text{mean}) = 2.214$[/tex]
Standard deviation [tex]$(s.d1)=1.718; \text{Number}(n_1)=20$[/tex]
[tex]$Y(\text{mean})=2.0115$[/tex]
Standard deviation [tex]$(s.d2)=1.8917; \text{Number}(n_2)=20$[/tex]
We use the test statics :
[tex]$t=\frac{X-Y}{\sqrt{\frac{s.d1^2}{n_1}+\frac{s.d2^2}{n_2}}}$[/tex]
[tex]$t_0=\frac{2.214-2.0115}{\sqrt{\frac{2.95152}{20}+\frac{3.57853}{20}}}$[/tex]
[tex]$t_0=0.35$[/tex]
[tex]$|t_0|=0.35$[/tex]
c. The critical value of |t| with minimum [tex]$(n_1-1)$[/tex] , i.e. 19 d.f is [tex]$2.093$[/tex]
We got [tex]$|t_0|$[/tex] = 0.35439 and |t| = 2.093
Please Help!! I WILL MARK BRAINLIEST
Answer:
f-¹(x) = 2x – 8
f-¹(4) = 2(4) – 8 —> f-¹(4)= 8 - 8 =0
The length of one rectangle in a quilt is 6 inches. Its width is 3 inches. About how many of these rectangles do you need to cover an area of 7,500 square inches?
Step-by-step explanation:
Area=2(L+W)
A=2(6+3)
A=2(9)
A=18in²
therefore, 7500/18
=416.66in²
Solve for x.
4x - 14
x + 85
x = [?]
Answer:
x = 33
Step-by-step explanation:
4x - 14 = x + 85
3x = 99
x = 99/3
x = 33
A researcher collected data on years spent in college and yearly income. He found that the longer someone is in college, the lower his/her income is. Which of the following is true based on this research? Select all that apply.
The line of best fit for this data would be increasing from left to right on the scatter plot.
The slope of the line of best fit for this data would be negative.
The -intercept for the line of best fit for this data would be zero.
The line of best fit for this data is horizontal because the variables are not related.
If you divided the data into two groups and found the average years of college and average yearly income from each of the two groups, you could find the estimated slope of the line of best fit by using the slope formula on those representative points.
Answer:
A
Cdfvvbghnjmk,l.;/‘Step-by-step explanation:
[tex]\tt\red{See \; attachment!}[/tex]
Using the paths shown below, how long is the shortest route from Hillsdale to Belmont?
I need help
Answer:
26.6 miles
there are two ways you could go, you could go from Hillsdale to Danville to Arcadia to belmont, wich is 27.8 miles or you could go from Hillsdale to Arcadia to belmont wich is only 26.6
A theater company charges $7.50 per ticket for people of all age groups. If c represents the total number of children who bought tickets and a represents the total number of adults who bought tickets, which expression best represents the total money earned by the company from the sale of tickets. WITCH ONE
c + 7.5a
7.5(c + a)
15(c + a)
7.5c + a
Answer:
I believe it is 7.5c + a
Step-by-step explanation:
when a variable is placed beside a number, you will multiply the number by the variable. here, we know the the variable means kids. 7.5 per kid that buys tickets, plus the adults. Hope that helps!
Find the measure of angle AGE in the figure below. Enter only
the number.
Answer:
AGE = 129 degrees
Step-by-step explanation:
When 12 radios were left, how many hours had gone by?
Hellpp
Which Which value of x makes this equation true? -3x+10=5x-8
value of x makes this equation true? -3x+10=5x-8
Answer:
9/4
Step-by-step explanation:
-3x+10=5x-8
or, -3x-5x = -8-10
or, -8x=-18
or, 8x=18 (i.e. - is cancelled)
or, x=18/8
i.e. x=9/4
Hence, the value of x is 9/4
Answer:
The value of x is 9/4
Step-by-step explanation:
-3x+ 10 = 5x - 8
Add 3x both side
-3x + 3x + 10 = 5x + 3x - 8
10 = 8x - 8
Now, Add 8 both side
10 + 8 = 8x - 8 + 8
18 = 8x
8x = 18
Now, Divide by 8 from both side
8x/8 = 18/8
x = 9/4
Thus, The value of x is 9/4
FOR VERIFICATION ONLY:-3x + 10 = 5x - 8
-3(9/4) + 10 = 5(9/4) - 8
-27/4 + 10 = 45/4 - 8
-27 + 4 × 10/4 = 45 - 8 × 4/4
-27 + 40/4 = 45 - 32/4
13/4 = 13/4
Hence, L.HS = R.H.S
-TheUnknownScientist
Which is the most reasonable measure for the capacity of a bathtub?
O 5 liters
© 159 liters
O 159 milliliters
1000 milliliters
The graph above shows the cost, in dollars, of apples as
a function of the number of pounds of apples purchased
at a particular grocery store. The equation above defines
the cost C, in dollars, for p pounds of pears at the same
store. Which of the following statements accurately
compares the cost per pound of apples and the cost per
pound of pears at this store?
A. Apples cost approximately $0.07 less per pound
than pears do.
B. Apples cost approximately $0.04 less per pound
than pears do.
C. Apples cost approximately $0.73 less per pound
than pears do.
D. Apples cost approximately $0.62 more per pound
than pears do.
The accurate statement is A. Apples cost approximately $0.07 less per pound.
Cost of Apples per pound using the given graph:The constant of proportionality would give us the cost of per pound. From the graph, when number of pounds (p) = 3, cost in dollars (C) = 4.
Constant of proportionality = C/p = 4/3
Therefore, Cost of apples per pound = 4/3 = $1.33 (approximated)
Cost of Pears per pound using the given equation:[tex]C = \frac{7}{5} p[/tex]
The constant of proportionality of the equation function will give us the cost per pound for pears.
From the equation, the we can deduce that [tex]\frac{7}{5}[/tex] represents the cost of pears per pound (constant of proportionality).
Thus:
Cost of pears per pound = 7/5 = $1.40
The difference between the cost per pound of pears and the cost per pound of apples would be:
$1.40 - $1.33 = $0.07
Therefore, we can conclude that apples cost approximately $0.07 less per pound.
Learn more about constant of proportionality here:
https://brainly.com/question/11703625
Rob can complete his bus route in 4 hours. Joan can complete her bus route in 3 hours. If they both left the terminal at 3:00 am and after each completed route returned to the terminal, determine the next time they would leave the terminal at the same time.
Answer:
3:00 pm
Step-by-step explanation:
Given
[tex]Rob = 4\ hrs[/tex]
[tex]Joan = 3\ hrs[/tex]
[tex]Start\ Time = 3:00\ am[/tex]
Required
The next time they leave at the same time
To do this, we first list out the multiples of 4 and 3 (i.e. their time of completing each route)
So, we have:
[tex]Rob: 4, 8, 12, 16, 20...[/tex]
[tex]Joan: 3,6,9,12,15,18....[/tex]
The least common multiple in the above is:
[tex]Least = 12hrs[/tex]
This means that they will meet at the terminal after 12 hours
So, their meeting time is:
[tex]Time = 3:00am + 12\ hrs[/tex]
[tex]Time = 3:00\ pm[/tex]
What is the distance between (-8,2) and (4,4)
Answer:
d = 2√3
Step-by-step explanation:
What is the correct ratio?
D)32/40
Hope it helps you
Answer:
[tex]\frac{24}{40}[/tex]
Step-by-step explanation:
Sin = [tex]\frac{opposite}{hypotenuse}[/tex] (relative to the angle asked for)
The opposite of Angle Z is 24
The hypotenuse no matter what would always be 40; therefore,
Sin(Z) = [tex]\frac{24}{40}[/tex]
Hope this helps!
Enter the value for x that makes the equation √x-7=-4
Answer:
Your answer is 9
Step-by-step explanation:
√9=3
3-7=-4
12. Which statement best describes the effects on the graph of f(x) = log2 xwhen f(x) is replaced by
f(x-2) + 1?
a. The graph is vertically stretched by a factor of 3, horizontally translated 2 units right, and
vertically translated 1 unit up.
b. The graph is vertically compressed by a factor of 3, horizontally translated 2 units right, and
vertically translated 1 unit up.
c. The graph is horizontally stretched by a factor of 3, horizontally translated 2 units left, and
vertically translated 1 unit up
d. The graph is vertically compressed by a factor of , vertically translated 2 units down, and
horizontally translated 1 unit left.
Answer:
B.
Step-by-step explanation:
Hope it helps thx#CARRYONLEARNING!Determine the rate of change of the function given by the table.
A) 2
B) 1
C) -1
D) -2
A pollster believes that 20% of the voters in a certain area favor a bond issue. If 49 voters are randomly sampled from the large number of voters in this area, approximate the probability that the sampled fraction of voters favoring the bond issue will not differ from the true fraction by more than 0.08. (Round your answer to four decimal places.)
Answer:
The probability that the sampled fraction of voters favoring the bond issue will not differ from the true fraction by more than 0.08 is 0.7698
Step-by-step explanation:
Given
n = 64
p = 0.20
X/n -p < 0.06
x-np <0.06n
x-np <0.06 * 64
x-np <3.84
Z score
= (x-np)/sqrt (np(1-p))
= -3.84/ sqrt (64*0.20*0.80)
= -1.20
P (x/n-p<0.06) = P(-1.2<z<1.20) = 1-2*0.1151 = 0.7698
write and solve proportion answer the question.
25%of what number w is 9
□= 25
100
w= □
Answer:
Answer is 36.
You can simply get this by writing and expression for it
25/100 x w=9
25w/100=9
w= 9x100/25
w=36.
Answer:
36
Step-by-step explanation:
9/w=25/100
cross multiplication:
9*100=25w
900=25w
900=25w / 25
36=w
Find the radius of convergence and the interval of convergence.
[tex]\displaystyle \sum \limit_{n=1}^\infty \frac{x^\text{n}}{2^\text{n}(n+1)^2}[/tex]
Answer:
Radius of Convergence: 2
Interval of Convergence: [-2, 2]
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
BracketsParenthesisExponentsMultiplicationDivisionAdditionSubtractionLeft to RightEquality Properties
Multiplication Property of EqualityDivision Property of EqualityAddition Property of EqualitySubtraction Property of EqualityAlgebra I
Exponential Rule [Multiplying]: [tex]\displaystyle b^m \cdot b^n = b^{m + n}[/tex]Exponential Rule [Dividing]: [tex]\displaystyle \frac{b^m}{b^n} = b^{m - n}[/tex]Calculus
Series Convergence Tests
P-Series: [tex]\displaystyle \sum \limit_{n = 1}^\infty \frac{1}{n^p}[/tex]Direct Comparison Test (DCT)Alternating Series Test (AST)Ratio Test: [tex]\displaystyle \lim_{n \to \infty} \bigg| \frac{a_{n + 1}}{a_n} \bigg|[/tex]Radius of Convergence (ROC)
Ratio TestInterval boundInterval of Convergence (IOC)
Testing endpointsStep-by-step explanation:
Step 1: Define
[tex]\displaystyle \sum \limit_{n = 1}^\infty \frac{x^n}{2^n(n + 1)^2}[/tex]
Step 2: Find ROC
Apply Ratio Test
[Series] Set up [Ratio Test]: [tex]\displaystyle \lim_{n \to \infty} \bigg|\frac{x^{n + 1}}{2^{n + 1}(n + 2)^2} \cdot \frac{2^n(n + 1)^2}{x^n} \bigg|[/tex][Ratio Test] Rewrite exponentials [Exponential Rule - Multiplying]: [tex]\displaystyle \lim_{n \to \infty} \bigg|\frac{x^n \cdot x}{2^n \cdot 2(n + 2)^2} \cdot \frac{2^n(n + 1)^2}{x^n} \bigg|[/tex][Ratio Test] Simplify: [tex]\displaystyle \lim_{n \to \infty} \bigg| \frac{x}{2(n + 2)^2} \cdot (n + 1)^2 \bigg|[/tex][Ratio Test] Multiply: [tex]\displaystyle \lim_{n \to \infty} \bigg| \frac{x(n + 1)^2}{2(n + 2)^2} \bigg|[/tex][Ratio Test] Evaluate limit: [tex]\displaystyle \bigg| \frac{x}{2} \bigg| < 1[/tex][Ratio Test] Isolate x: [tex]\displaystyle |x| < 2[/tex]Our ROC is 2.
Step 3: Find IOC
Test endpoints
[ROC] Find interval bound: [tex]\displaystyle -2 < x < 2[/tex]x = -2
Substitute in x [Series]: [tex]\displaystyle \sum \limit_{n = 1}^\infty \frac{(-2)^n}{2^n(n + 1)^2}[/tex][Series] Rewrite [Exponential Rules - Multiplying]: [tex]\displaystyle \sum \limit_{n = 1}^\infty \frac{(-1)^n2^n}{2^n(n + 1)^2}[/tex][Series] Simplify: [tex]\displaystyle \sum \limit_{n = 1}^\infty \frac{(-1)^n}{(n + 1)^2}[/tex]Test convergence of modified series: Alternating Series Test
[AST] Condition 1 [Limit Test]: [tex]\displaystyle \lim_{n \to \infty} \frac{1}{(n + 1)^2} = 0 \ \checkmark[/tex][AST] Condition 2 [aₙ vs bₙ comparison]: [tex]\displaystyle \frac{1}{(n + 2)^2} \le \frac{1}{(n + 1)^2} \ \checkmark[/tex]At x = -2, the series is convergent.
∴ Current IOC is -2 ≤ x < 2 or [-2, 2); 2 undetermined
x = 2
Substitute in x [Series]: [tex]\displaystyle \sum \limit_{n = 1}^\infty \frac{2^n}{2^n(n + 1)^2}[/tex][Series] Simplify: [tex]\displaystyle \sum \limit_{n = 1}^\infty \frac{1}{(n + 1)^2}[/tex]Test convergence of modified series: Direct Comparison Test
[DCT] Condition 1 [Define comparing series]: [tex]\displaystyle \sum \limit_{n = 1}^\infty \frac{1}{n^2}[/tex][DCT] Condition 1 [Test convergence of comparing series]: [tex]\displaystyle p = 2 > 1, \ \sum \limit_{n = 1}^\infty \frac{1}{n^2} \ \text{convergent by p-series}[/tex][DCT] Condition 2 [aₙ vs bₙ comparison]: [tex]\displaystyle \frac{1}{(n + 1)^2} \le \frac{1}{n^2} \ \checkmark[/tex]At x = 2, the series is convergent.
∴ IOC for [tex]\displaystyle \sum \limit_{n = 1}^\infty \frac{x^n}{2^n(n + 1)^2}[/tex] is -2 ≤ x ≤ 2 or [-2, 2]
Topic: AP Calculus AB/BC (Calculus I/II)
Unit: Taylor Polynomials and Approximations - Power Series (BC Only)
Book: College Calculus 10e
What linear equation is represented by the table?
Please hurry!
Best answer gets Brainliest!!!!
A) Y= 2x
B) y= 4x
C) y= 4x -2
D) y= 2x - 2
Answer:
y = 4x - 2
Step-by-step explanation:
linear equation - y = mx + b
where m = slope and b = y intercept
The y intercept is the y value of the coordinate where x = 0
Looking at the table, we notice that when x = 0, y = -2
Which means that the y intercept ( b ) = -2
Slope = change in y over change in x
As y goes up 4 x goes up 1
Thus, slope ( m ) = 4
Now we plug in the identified slope and y intercept into " y = mx + b "
we get that the equation is y = 4x - 2
Please solve!
l = 48.1 m, w = 51.62 m, h = 3.42 m
Answer:
Volume? Surface area?
Step-by-step explanation:
Volume=8491.59
Surface area=5647.93
¿Existen o no existen los números?.
si existen pero que tipo de números? porque si existen
0.5 mg/mL = ___________ mcg/mL
Answer: 500 mcg/mL
Step-by-step explanation: 0.5 mg/mL = ___________ mcg/mL
0.5 mg/mL(1000)
500 mcg/mL
Answer:
500 mcg / mL
Step-by-step explanation:
this is the ansa when u do 0.5 mg/mL = ___________ mcg/mL
the radius of a cylindrical water tank is 4ft, and it’s height is 10ft. What is the volume of the tank?
Answer:
[tex]volume = 502.4ft^3[/tex]
Step-by-step explanation:
[tex]volume = \pi r^2 h = 3.14 \times 4^2 \times 10 = 502.4ft^3[/tex]
What is the scale factor from ADEF to AABC?
10
6
20
12
А
7
14
Answer:
The scale factor is 1/2
Step-by-step explanation:
Given
[tex]\triangle DE F[/tex] and [tex]\triangle ABC[/tex]
Required
The scale factor from [tex]\triangle DE F[/tex] to [tex]\triangle ABC[/tex]
Take a corresponding side in both triangles.
We have:
[tex]DE= 20[/tex] [tex]AB = 10[/tex]
The scale factor from [tex]\triangle DE F[/tex] to [tex]\triangle ABC[/tex] is:
[tex]k =\frac{AB}{DE}[/tex]
[tex]k =\frac{10}{20}[/tex]
[tex]k =\frac{1}{2}[/tex]
solve this: - 6 n = 30
Answer:
-6n=30
so find value of n
n=30÷(-6)
n=-5
so, value of n = -5
Answer:
-6 n = 30
or,n=30÷(-6)
or,n=-5
I need the answer fast pls
Answer:
B
Step-by-step explanation:
It's B because that's the only answer that talks about the highest temperature, which is mentioned in the question
In the number 3,941,608,572, which digit is in the hundred millions place?
Answer:
9
Step-by-step explanation:
A hundred millions is: 100,000,000
looking at the number the number in the place hundred millions place is 9, so the answer is 9.
Answer:900,000,000
The digit is 9
Step-by-step explanation:
PLEASE HELP!
Find the x value.
Answer:
72
Step-by-step explanation:
every angle in a triangle adds up to 180
57 + 51 + x = 180
x = 72
Answer:
The answer to the question is:
x=72°
Step-by-step explanation:
The total angles of a triangle is 180°
x+51°+57°=180°
x+108°=180°
x=180°-108°
x=72°