According to the Empirical Rule, 99.7% of scores in a normal distribution fall within 2 standard deviations of the mean.
a. True
b. False
Answers
Answer:
False
Step-by-step explanation:
Here, we want to check the validity of the given statement. The statement is false.
Under the empirical rule, following a normal distribution, 99.7% of observed data lies within 3 standard deviations from the mean while 95% of observed data lies within 2 standard deviation from the mean and 68% of observed data lies within 1 standard deviation of the mean.
Please check attachment for diagrammatic representation of the empirical rule.
Related Questions
Evaluate −x^2−5 y^3 when x = 4 and y = 1
Answers
Answer:
Simplify:
[tex]-4^2-5(1^3)[/tex]
So you get:
[tex]-21\\[/tex]
Answer:
[tex]\huge\boxed{-21}[/tex]
Step-by-step explanation:
-x²-5y³
Given that x = 4, y = 1
[tex]-(4)^2-5(1)^3[/tex]
[tex]-16-5(1)\\-16-5\\-21[/tex]
Need Help
Please Show Work
Answers
Answer:
18 - 8 * n = -6 * n
The number is 9
Step-by-step explanation:
Let n equal the number
Look for key words such as is which means equals
minus is subtract
18 - 8 * n = -6 * n
18 -8n = -6n
Add 8n to each side
18-8n +8n = -6n+8n
18 =2n
Divide each side by 2
18/2 = 2n/2
9 =n
The number is 9
━━━━━━━☆☆━━━━━━━
▹ Answer
n = 9
▹ Step-by-Step Explanation
18 - 8 * n = -6 * n
Simple numerical terms are written last:
-8n + 18 = -6n
Group all variable terms on one side and all constant terms on the other side:
(-8n + 18) + 8n = -6n + 8n
n = 9
Hope this helps!
CloutAnswers ❁
━━━━━━━☆☆━━━━━━━
A waiter earns $11.00 an hour and approximately 10% of what he serves in a shift. If he works a 6 hour shift and takes $425 in orders, his total earnings for the six hours would be:
Answers
Answer:
108.50
Step-by-step explanation:
First find the wages
11* 6 = 66 dollars
Then figure the commission
10% of 425
.10 * 425
42.5
Add the two amounts together
42.5+66
108.50
[tex]4x - 2x = [/tex]
Answers
Answer:
2x
Step-by-step explanation:
These are like terms so we can combine them
4x-2x
2x
Answer:
2x
Explanation:
Since both terms in this equation are common, we can simply subtract them.
4x - 2x = ?
4x - 2x = 2x
Therefore, the correct answer should be 2x.
A manufacturer claims that the calling range (in feet) of its 900-MHz cordless telephone is greater than that of its leading competitor. A sample of 19 phones from the manufacturer had a mean range of 1160 feet with a standard deviation of 32 feet. A sample of 11 similar phones from its competitor had a mean range of 1130 feet with a standard deviation of 30 feet.
Required:
Do the results support the manufacturer's claim?
Answers
Complete question is;
A manufacturer claims that the calling range (in feet) of its 900-MHz cordless telephone is greater than that of its leading competitor. A sample of 19 phones from the manufacturer had a mean range of 1160 feet with a standard deviation of 32 feet. A sample of 11 similar phones from its competitor had a mean range of 1130 feet with a standard deviation of 30 feet. Required:
Do the results support the manufacturer's claim?
Let μ1 be the true mean range of the manufacturer's cordless telephone and μ2 be the true mean range of the competitor's cordless telephone. Use a significance level of α = 0.01 for the test. Assume that the population variances are equal and that the two populations are normally distributed
Answer:
We will fail to reject the null hypothesis as there is no sufficient evidence to support the manufacturers claim.
Step-by-step explanation:
For the first sample, we have;
Mean; x'1 = 1160 ft
standard deviation; σ1 = 32 feet
Sample size; n1 = 19
For the second sample, we have;
Mean; x'2 = 1130 ft
Standard deviation; σ2 = 30 ft
Sample size; n2 = 11
The hypotheses are;
Null Hypothesis; H0; μ1 = μ2
Alternative hypothesis; Ha; μ1 > μ2
The test statistic formula for this is;
z = (x'1 - x'2)/√[(σ1)²/n1) + (σ2)²/n2)]
Plugging in the relevant values, we have;
z = (1160 - 1130)/√[(32)²/19) + (30)²/11)]
z = 2.58
From the z-table attached, we have a p-value = 0.99506
This p-value is more than the significance value of 0.01,thus,we will fail to reject the null hypothesis as there is no sufficient evidence to support the manufacturers claim.
Try to get to every number from 1 to 10 using four 4's and any number of arithmetic operations (+, −, ×, ÷). You may also you parentheses.
Answers
Answer:
Step-by-step explanation:
1. 4/4+4-4=1
2. 4/4+4/4=2
3. 4+4/4-4=3
4. 4 × (4 − 4) + 4=4
5. (4 × 4 + 4) / 4=5
6. 44 / 4 − 4=6
7. 4+4-4/4=7
8. 4+4+4-4=8
9. 4+4+4/9=9
10. 44 / 4.4=10
Answer:
1 = (4 x 4)/(4 x 4) or (4 + 4)/(4 + 4) or (4 / 4) x (4 / 4) or (4 / 4)/(4 / 4)
2= (4 x 4)/(4 + 4) or 4 / ((4+4)/4)
3= (4 + 4 + 4)/4 or (4 x 4 - 4)/4
4 = 4 - (4 - 4)/4
5 = (4 x 4 + 4)/4
6 = 4 + (4 + 4)/4
7 = 4 - (4/4) + 4
8 = 4 + (4 x 4)/4
9 = 4 + 4 + (4/4)
10 - I tried the best. You might need ! or sqrt operator to get 4.
Updated:
I forgot we could use 4, 44, 444, or 4444, so that 10 could be expressed as:
10 = (44 - 4)/4
For the following graph, state the polar coordinate with a positive r and positive q (in radians). Explain your steps as to how you determined the coordinate (in your own words). I'm looking for answers that involve π, not degrees for your angles. State the polar coordinate with (r, -q). Explain how you found the new angle. State the polar coordinate with (-r, q). Explain how you found the new angle. State the polar coordinate with (-r, -q). Explain how you found the new angle.
Answers
Answer:
Points : ( 8, - 2π/3 ), ( - 8, π/3 ), ( - 8, - 5π/3 )
Step-by-step explanation:
For the first two cases, ( r, θ ) r would be > 0, where r is the directed distance from the pole, and theta is the directed angle from the positive x - axis.
So when r is positive, we can tell that this point is 8 units from the pole, so r is going to be 8 in either case,
( 8, 240° ) - because r is positive, theta would have to be an angle with which it's terminal side passes through this point. As you can see that would be 2 / 3rd of 90 degrees more than a 180 degree angle,or 60 + 180 = 240 degrees.
( 8, - 120° ) - now theta will be the negative side of 360 - 240, or in other words - 120
Now let's consider the second two cases, where r is < 0. Of course the point will still be 8 units from the pole. Again for r < 0 the point will lay on the ray pointing in the opposite direction of the terminal side of theta.
( - 8, 60° ) - theta will now be 2 / 3rd of 90 degrees, or 60 degrees, for - r. Respectively the remaining degrees will be negative, 360 - 60 = 300, - 300. Thus our second point for - r will be ( - 8, - 300° )
_________________________________
So we have the points ( 8, 240° ), ( 8, - 120° ), ( - 8, 60° ), and ( - 8, - 300° ). However we only want 3 cases, so we have points ( 8, - 120° ), ( - 8, 60° ), and ( - 8, - 300° ). Let's convert the degrees into radians,
Points : ( 8, - 2π/3 ), ( - 8, π/3 ), ( - 8, - 5π/3 )
Records indicate that x years after 2008, the average property tax on a three bedroom home in a certain community was T(x) =20x^2+40x+600 dollars.
Required:
a. At what rate was the property tax increasing with respect to time in 2008?
b. By how much did the tax change between the years 2008 and 2012?
Answers
Answer:
a) 40 dollars
b) 480 dollars
Step-by-step explanation:
Given the average property tax on a three bedroom home in a certain community modelled by the equation T(x) =20x²+40x+600, the rate at which the property tax is increasing with respect to time in 2008 can be derived by solving for the function T'(x) at x=0
T'(x) = 2(20)x¹ + 40x° + 0
T'(x) = 40x+40
At x = 0,
T'(0) = 40(0)+40
T'(0) = 40
Hence the property tax was increasing at a rate of 40dollars with respect to the initial year (2008).
b) There are 4 years between 2008 and 2012. To know how much that the tax change between the years 2008 and 2012, we will find T(4) - T(0)
Given T(x) =20x²+40x+600
T(4) =20(4)²+40(4)+600
T(4) = 320+160+600
T(4) = 1080 dollars
Also T(0) =20(0)²+40(0)+600
T(0) = 0+0+600
T(0)= 600 dollars
T(4) - T(0) = 1080 - 600
T(4) - T(0) = 480 dollars
Hence, the tax has changed by $480 between 2008 and 2012
Tessa’s employee benefits include family health care coverage. She contributes 18% of the cost. Tessa gets paid biweekly and $108.00 is taken out of each paycheck for family health care coverage. How much does her employer contribute annually for the family coverage? Clearly show your work.
Answers
The answer is $12792
Explanation:
It is known Tessa pays $108.00 to contribute to family coverage every two weeks and this represents 18% of the total payment. This implies the employer pays the 82% missing (100% - 18% = 82%). Additionally, with this information, it is possible to know the amount the employer has to pay every two weeks that represents 82%. The process is shown below:
1. Write the values you know and use x to represent the value you need to find
108 = 18
x = 82
3. Cross multiply
x 18 = 8856
4. Find the value of x by solving this simple equation
x = 8856 ÷ 18
x = 492 - Amount the employer pays every two weeks for Tessa's family coverage
Now that we know the money the employer pays every two weeks, it is possible to calculate the annual amount of money. Follow the process below.
1. Consider one year has a total of 52 weeks and divide this number of weeks by 2 because the payment for the family coverage occurs every 2 weeks
52 ÷ 2 = 26
2. Finally, multiply the money paid by the employer every two weeks by 26
26 weeks x $492 = $12792- This is the total the employer pays annually
Please help with this
Answers
Answer:
A
Step-by-step explanation:
● first one:
The diagonals of a rhombus are perpendicular to each others wich means that they form four right angles.
STP is one of them so this statement is true.
● second one:
If ST and PT were equal this would be a square not a rhombus.
● third one:
If SPQ was a right angle, this woukd be a square.
● fourth one:
Again if the diagonals SQ and PR were equal, this would be a square.
What is the value of x to the nearest tenth?
Answers
Answer:
x=9.6
Step-by-step explanation:
The dot in the middle represents the center of the circle, so therefore, the line that is represented by 16 is the radius. Since that is the radius, the side that is the hypotenuse of the small triangle is also 16, since they have the same distance.
The line represented by 25.6 with x as its bisector shows that when we divide it by 2, the other side of the triangle besides the hypotenuse is 12.8.
Now that we have the two sides of the triangle, we can find the last side (represented by x). Use pythagorean theorem:
[tex]a^2 +b^2=c^2\\x^2+(12.8)^2=16^2\\x^2+163.84=256\\x^2=92.16\\x=9.6[/tex]
Find the area of the shape shown below.
3.5
2
2
Answers
Answer:
26.75 units²
Step-by-step explanation:
Cube Area: A = l²
Triangle Area: A = 1/2bh
Step 1: Find area of biggest triangle
A = 1/2(3.5)(2 + 2 + 5)
A = 1.75(9)
A = 15.75
Step 2: Find area of 2nd biggest triangle
A = 1/2(5)(2)
A = 1/2(10)
A = 5
Step 3: Find area of smallest triangle
A = 1/2(2)(2)
A = 1/2(4)
A = 2
Step 4: Find area of cube
A = 2²
A = 4
Step 5: Add all the values together
A = 15.75 + 5 + 2 + 4
A = 20.75 + 2 + 4
A = 22.75 + 4
A = 26.75
Last Sunday, the average temperature was 8\%8%8, percent higher than the average temperature two Sundays ago. The average temperature two Sundays ago was TTT degrees Celsius. Which of the following expressions could represent the average temperature last Sunday?
Answers
Work Shown:
T = average Celsius temperature two Sundays ago
8% = 8/100 = 0.08
8% of T = 0.08T
L = average Celsius temperature last sunday
L = 8% higher than T
L = T + (8% of T)
L = T + 0.08T
L = 1.00T + 0.08T
L = (1.00 + 0.08)T
L = 1.08T
The 1.08 refers to the idea that L is 108% of T
Answer:
b and d
Step-by-step explanation:
khan
How to graph the line y=4/3x
Answers
Answer:
make a table of values
Step-by-step explanation:
then plot using those values
The required graph has been attached which represents the line y = 4/3x
What is a graph?A graph can be defined as a pictorial representation or a diagram that represents data or values.
We have been given the equation of a line below as:
y = 4/3x
Rewrite in slope-intercept form.
y = (4/3)x
Use the slope-intercept form to discover the slope and y-intercept.
Here the slope is 4/3 and y-intercept = (0, 0)
Any line can be graphed using two points. Select two x values, and plug them into the equation to find the corresponding y values.
When substitute the value of x = 0, then the value of y = 0, and When substitute the value of x = 3, then the value of y = -4,
Hence, the graph represents the line y = 4/3x
Therefore, the required graph of the line y=4/3x will be shown in the as attached file.
Learn more about the graphs here:
brainly.com/question/16608196
#SPJ2
Find the first three nonzero terms in the power series expansion for the product f(x)g(x).
f(x) = e^2x = [infinity]∑n=0 1/n! (2x)^n
g(x) = sin 5x = [infinity]∑k=0 (-1)^k/(2k+1)! (5x)^2k+1
The power series approximation of fx)g(x) to three nonzero terms is __________
(Type an expression that includes all terms up to order 3.)
Answers
Answer:
∑(-1)^k/(2k+1)! (5x)^2k+1
From k = 1 to 3.
= -196.5
Step-by-step explanation:
Given
∑(-1)^k/(2k+1)! (5x)^2k+1
From k = 0 to infinity
The expression that includes all terms up to order 3 is:
∑(-1)^k/(2k+1)! (5x)^2k+1
From k = 0 to 3.
= 0 + (-1/2 × 5³) + (1/6 × 10^5) + (-1/5040 × 15^5)
= -125/2 + 100000/6 - 759375/5040
= -62.5 + 16.67 - 150.67
= - 196.5
If a dog has 2,000,000 toys and he gives 900,000 away. Then gets 2,000 more, also looses 2,000,000. He's sad but then also got 5,000,000,000 more and gives 1,672,293 out. How much does he have now? And how much he gave away. And how much he got.
Answers
Answer:
See below.
Step-by-step explanation:
He does not have enough to loose 2,000,000 at that point, so this whole problem is nonsense.
Select the correct answer from each drop-down menu.
The function f is given by the table of values as shown below.
x 1 2 3 4 5
f(x) 13 19 37 91 253
Use the given table to complete the statements.
The parent function of the function represented in the table is
.
If function f was translated down 4 units, the
-values would be
.
A point in the table for the transformed function would be
.
Answers
Answer:
3^x9, 15, 33, 87, 249(4, 87) for exampleStep-by-step explanation:
a) First differences of the f(x) values in the table are ...
19 -13 = 6, 37 -19 = 18, 91 -37 = 54, 253 -91 = 162
The second differences are not constant:
18 -6 = 12, 54 -18 = 36, 162 -54 = 108
But, we notice that both the first and second differences have a common ratio. This is characteristic of an exponential function. The common ratio is 18/6 = 3, so the parent function is 3^x.
__
b) Translating a function down 4 units subtracts 4 from each y-value. The values of f(x) in the table would be ...
9, 15, 33, 87, 249
__
c) The x-values of the function stay the same for a vertical translation, so the points in the table of the transformed function are ...
(x, f(x)) = (1, 9), (2, 15), (3, 33), (4, 87), (5, 249)
Answer: I think this is it:
The parent function of the function represented in the table is exponential. If function f was translated down 4 units, the f(x)-values would be decreased by 4. A point in the table for the transformed function would be (4,87)
Step-by-step explanation: I got it right on Edmentum!
Two charged particles, Q1, and Q2, are a distance r apart with Q2 = 5Q1 Compare the forces they exert on one another when F1 is the force Q2 exerts on Q1and F2 is the force Q1 exerts on Q2.
a) F2 = 5F1.
b) F2 =-5F1.
c) F2 = F1.
d) F2 = -F1.
e) 5F2 = F1.
Answers
Answer:
d) F2 = -F1.
Step-by-step explanation:
According to Coulomb's law of forces on electrostatic charges, the force of attraction is proportional to the product of their charges, and inversely proportional to the square of their distance apart.
What this law means is that both particles will experience an equal amount of force on them, due to the presence of the other particle. This force is not just as a result of their individual charges, but as a result of the product of their charges. Also, the force is a vector quantity that must have a direction alongside its magnitude, and the force on the two particles will always act in opposite direction, be it repulsive or attractive.
Simply this question and get marked branlist
Answers
Answer:
72/n^5r
Step-by-step explanation:
Answer:
Below
Step-by-step explanation:
13)
● 2d^3 × c^6 × 8d^5 × c^2
Isolate the similar terms
● (2×8)× (d^3 × d^5)×(c^6×c^2)
● 16 × d^(3+5) × c^(6+2)
● 16 × d^8 × c^8
● 16 × (dc)^8
● 16(dc)^8
■■■■■■■■■■■■■■■■■■■■■■■■■■
● 8n×r^(-4) ×9×n^(-6)×r^3
Isolate the similar terms
● (8×9)× (r^(-4)×r^3) × (n×n^(-6))
● 72 × r^(-4+3) × n^(1-6)
● 72 × r^-1 × n^(-5)
● 72 ×(1/r) × (1/n^5)
● 72/(r×n^5)
Evan’s dog weighs 15 3/8 pounds. What is this weight written as a decimal? A. 15.125 Ib B. 15.375 Ib C. 15.385 Ib D. 15.625 Ib Please include ALL work!
Answers
Answer:
ok as we know 15 is a whole number by itself and 3/8 is the decimal part
so we know it is 15. something
that something is 3/8 to find decimal you do 3/8
3/8 is = .375
so 15.375 is the answer
hope it helps
brainliest give me pls
If vectors i+j+2k, i+pj+5k and 5i+3j+4k are linearly dependent, the value of p is what?
Answers
Answer:
[tex]p = 2[/tex] if given vectors must be linearly independent.
Step-by-step explanation:
A linear combination is linearly dependent if and only if there is at least one coefficient equal to zero. If [tex]\vec u = (1,1,2)[/tex], [tex]\vec v = (1,p,5)[/tex] and [tex]\vec w = (5,3,4)[/tex], the linear combination is:
[tex]\alpha_{1}\cdot (1,1,2)+\alpha_{2}\cdot (1,p,5)+\alpha_{3}\cdot (5,3,4) =(0,0,0)[/tex]
In other words, the following system of equations must be satisfied:
[tex]\alpha_{1}+\alpha_{2}+5\cdot \alpha_{3}=0[/tex] (Eq. 1)
[tex]\alpha_{1}+p\cdot \alpha_{2}+3\cdot \alpha_{3}=0[/tex] (Eq. 2)
[tex]2\cdot \alpha_{1}+5\cdot \alpha_{2}+4\cdot \alpha_{3}=0[/tex] (Eq. 3)
By Eq. 1:
[tex]\alpha_{1} = -\alpha_{2}-5\cdot \alpha_{3}[/tex]
Eq. 1 in Eqs. 2-3:
[tex]-\alpha_{2}-5\cdot \alpha_{3}+p\cdot \alpha_{2}+3\cdot \alpha_{3}=0[/tex]
[tex]-2\cdot \alpha_{2}-10\cdot \alpha_{3}+5\cdot \alpha_{2}+4\cdot \alpha_{3}=0[/tex]
[tex](p-1)\cdot \alpha_{2}-2\cdot \alpha_{3}=0[/tex] (Eq. 2b)
[tex]3\cdot \alpha_{2}-6\cdot \alpha_{3} = 0[/tex] (Eq. 3b)
By Eq. 3b:
[tex]\alpha_{3} = \frac{1}{2}\cdot \alpha_{2}[/tex]
Eq. 3b in Eq. 2b:
[tex](p-2)\cdot \alpha_{2} = 0[/tex]
If [tex]p = 2[/tex] if given vectors must be linearly independent.
In 2018, the population of a district was 25,000. With a continuous annual growth rate of approximately 4%, what will the
population be in 2033 according to the exponential growth function?
Round the answer to the nearest whole number.
Answers
Answer:
40,000 populationsStep-by-step explanation:
Initial population in 2018 = 25,000
Annual growth rate (in %) = 4%
Yearly Increment in population = 4% of 25000
= 4/100 * 25000
= 250*4
= 1000
This means that the population increases by 1000 on yearly basis.
To determine what the population will be in 2033, we need to first know the amount of years we have between 2018 and 2033.
Amount of years we have between 2018 and 2033 = 2033-2018
= 15 years
After 15 years, the population will have increased by 15*1000 i.e 15,000 more than the initial population.
Hence the population in 2033 will be Initial population + Increment after 15years = 25,000+15000 = 40,000 population.
The function fix) = (x - 4)(x - 2) is shown.
What is the range of the function?
8
all real numbers less than or equal to 3
all real numbers less than or equal to -1
all real numbers greater than or equal to 3
all real numbers greater than or equal to - 1
6
2
16
2
14
COL
40
8
G D
Answers
Answer:
The range of the function f(x)= (x-4)(x-2) is all real numbers greater than or equal to -1
Step-by-step explanation:
Find the area of the surface generated by revolving x=t + sqrt 2, y= (t^2)/2 + sqrt 2t+1, -sqrt 2 <= t <= sqrt about the y axis
Answers
The area is given by the integral
[tex]\displaystyle A=2\pi\int_Cx(t)\,\mathrm ds[/tex]
where C is the curve and [tex]dS[/tex] is the line element,
[tex]\mathrm ds=\sqrt{\left(\dfrac{\mathrm dx}{\mathrm dt}\right)^2+\left(\dfrac{\mathrm dy}{\mathrm dt}\right)^2}\,\mathrm dt[/tex]
We have
[tex]x(t)=t+\sqrt 2\implies\dfrac{\mathrm dx}{\mathrm dt}=1[/tex]
[tex]y(t)=\dfrac{t^2}2+\sqrt 2\,t+1\implies\dfrac{\mathrm dy}{\mathrm dt}=t+\sqrt 2[/tex]
[tex]\implies\mathrm ds=\sqrt{1^2+(t+\sqrt2)^2}\,\mathrm dt=\sqrt{t^2+2\sqrt2\,t+3}\,\mathrm dt[/tex]
So the area is
[tex]\displaystyle A=2\pi\int_{-\sqrt2}^{\sqrt2}(t+\sqrt 2)\sqrt{t^2+2\sqrt 2\,t+3}\,\mathrm dt[/tex]
Substitute [tex]u=t^2+2\sqrt2\,t+3[/tex] and [tex]\mathrm du=(2t+2\sqrt 2)\,\mathrm dt[/tex]:
[tex]\displaystyle A=\pi\int_1^9\sqrt u\,\mathrm du=\frac{2\pi}3u^{3/2}\bigg|_1^9=\frac{52\pi}3[/tex]
What is the solution to this system of linear equations?
y-x = 6
y + x = -10
(-2,-8)
(-8.-2)
(6.-10)
(-10.6)
Answers
Answer:
The correct answer is A
Step-by-step explanation:
Answer:
(-8, -2)
Step-by-step explanation:
y-x = 6
y + x = -10
Add the two equations together to eliminate x
y-x = 6
y + x = -10
--------------------
2y = -4
Divide by 2
2y/2 = -4/2
y = -2
Now find x
y+x = -10
-2+x = -10
x = -8
Sarah has $30,000 in her bank account today. Her grand-father has opened this account for her 15 years ago when she was born. Calculate the money that was deposited in the account 15 years ago if money has earned 3.5% p.a. compounded monthly through all these years.
Answers
Answer:
Deposit value(P) = $17,760 (Approx)
Step-by-step explanation:
Given:
Future value (F) = $30,000
Number of Year (n) = 15 year = 15 × 12 = 180 month
rate of interest (r) = 3.5% = 0.035 / 12 = 0.0029167
Find:
Deposit value(P)
Computation:
[tex]A = P(1+r)^n\\\\ 30000 = P(1+0.0029167)^{180} \\\\ 30000 = P(1.68917) \\\\ P = 17760.2018[/tex]
Deposit value(P) = $17,760 (Approx)
#2. Given the following conditional statement; which answer is
represents the biconditional statement: "If Mr. Anderson is a ninja, then
he can run like Naruto."
Mr. Anderson is a ninja iff he can run like Naruto.
Mr. Anderson can run like Naruto iff he is a ninja.
Mr. Anderson is Naruto iff he can run like a ninja.
Answers
Answer:
Mr. Anderson can run like Naruto iff he is a ninja.
Step-by-step explanation:
This is because, in the statement "If Mr. Anderson is a ninja, then he can run like Naruto.", the sub-statement, "he can run like Naruto.", depends on the sub-statement 'If Mr Anderson is a Ninja'. This means that although Mr. Anderson is a Ninja, he can only run like Naruto if and only if he is a Ninja implying that if Mr Anderson is not a Ninja, he cannot run like Naruto.
So, Mr Anderson can run like Naruto iff he is a Ninja is the correct answer
Answer:
1
Step-by-step explanation:
Step 1: Subtract 3 from both sides of the inequality
Step 2
Step 3: Divide both sides of the inequality by the
coefficient of x.
What is the missing step in solving the inequality 5 -
8x < 2x + 3?
O Add 2x to both sides of the inequality
O Subtract 8x from both sides of the inequality
O Subtract 2x from both sides of the inequality
Add 8x to both sides of the inequality.
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Answer:
add 8x to both sides
Step-by-step explanation:
5-8x<2x+3
first step, subtract 3 from both sides:
2-8x<2x
second step,?
2<?x
so you need to add 8x first
Identify whether the sampling method is simple random, systematic, stratified, cluster, or convenience. Explain.
In a nationwide study of registered voters conducted by The New York Times, 390 people are randomly selected out of those registered as Republicans, 430 people are randomly selected out of those registered as Democrats, and 180 people are randomly selected out of those registered as Independents.
Answers
Answer: stratified
Step-by-step explanation:
In stratified sampling, you divide the population into subgroups, or strata, with similar characteristics, like here we have divided the population into subgroups that depend on their political alignment. This is used when you can expect that the results have a noticeable variation between the different subgroups. Usually, you want to have the same number of population for eac subgroup, but sometimes it is hard for different reasons (not enough people in one subgroup, for example)
In cluster sampling we also use subgroups, but the subgroup itself is the unit of the sampling, while in this case, we are randomly selecting individuals of the given subgroups.
So this would be a "stratified sampling".
The radius of a right circular cylinder is increasing at the rate of 7 in./sec, while the height is decreasing at the rate of 6 in./sec. At what rate is the volume of the cylinder changing when the radius is 20 in. and the height is 16 in.
Answers
Answer:
[tex]\approx \bold{6544\ in^3/sec}[/tex]
Step-by-step explanation:
Given:
Rate of change of radius of cylinder:
[tex]\dfrac{dr}{dt} = +7\ in/sec[/tex]
(This is increasing rate so positive)
Rate of change of height of cylinder:
[tex]\dfrac{dh}{dt} = -6\ in/sec[/tex]
(This is decreasing rate so negative)
To find:
Rate of change of volume when r = 20 inches and h = 16 inches.
Solution:
First of all, let us have a look at the formula for Volume:
[tex]V = \pi r^2h[/tex]
Differentiating it w.r.to 't':
[tex]\dfrac{dV}{dt} = \dfrac{d}{dt}(\pi r^2h)[/tex]
Let us have a look at the formula:
[tex]1.\ \dfrac{d}{dx} (C.f(x)) = C\dfrac{d(f(x))}{dx} \ \ \ (\text{C is a constant})\\2.\ \dfrac{d}{dx} (f(x).g(x)) = f(x)\dfrac{d}{dx} (g(x))+g(x)\dfrac{d}{dx} (f(x))[/tex]
[tex]3.\ \dfrac{dx^n}{dx} = nx^{n-1}[/tex]
Applying the two formula for the above differentiation:
[tex]\Rightarrow \dfrac{dV}{dt} = \pi\dfrac{d}{dt}( r^2h)\\\Rightarrow \dfrac{dV}{dt} = \pi h\dfrac{d }{dt}( r^2)+\pi r^2\dfrac{dh }{dt}\\\Rightarrow \dfrac{dV}{dt} = \pi h\times 2r \dfrac{dr }{dt}+\pi r^2\dfrac{dh }{dt}[/tex]
Now, putting the values:
[tex]\Rightarrow \dfrac{dV}{dt} = \pi \times 16\times 2\times 20 \times 7+\pi\times 20^2\times (-6)\\\Rightarrow \dfrac{dV}{dt} = 22 \times 16\times 2\times 20 +3.14\times 400\times (-6)\\\Rightarrow \dfrac{dV}{dt} = 14080 -7536\\\Rightarrow \dfrac{dV}{dt} \approx \bold{6544\ in^3/sec}[/tex]
So, the answer is: [tex]\approx \bold{6544\ in^3/sec}[/tex]
