Answer:
[tex]\huge\boxed{n = 108\ nickels}[/tex]
Step-by-step explanation:
Let the nickels with Katy be n
So, the condition is
n = 6 (Shaun nickels)
While Nickels of Shaun = 18 , So
n = 6 (18)
n = 108 nickels
On a particular production line, the likelihood that a light bulb is defective is 10%. seven light bulbs are randomly selected. What is the probability that at most 4 of the light bulbs will be defective
Answer:
0.9995
Step-by-step explanation:
10% = 0.10
1 - 0.10 = 0.9
n = number of light bulbs = 7
we calculate this using binomial distribution.
p(x) = nCx × p^x(1-p)^n-x
our question says at most 4 is defective
= (7C0 × 0.1⁰ × 0.9⁷) + (7C1 × 0.1¹ × 0.9⁶) + (7C2 × 0.1² × 0.9⁵) + (7C3 × 0.1³ × 0.9⁴) + (7C4 × 0.1⁴ × 0.9³)
= 0.478 + 0.372 + 0.1239 + 0.023 + 0.0026
= 0.9995
we have 0.9995 probability that at most 4 light bulbs are defective.
Use Green’s theorem to evaluate line integral along curve C ∮_c〖( 3ydx+2xdy )〗, C : The boundary of 0≤x≤π,0≤y≤sin x
Answer:
[tex]\displaystyle \oint_C {3y \, dx + 2x \, dy} = \boxed{\bold{2}}[/tex]
General Formulas and Concepts:
Calculus
Differentiation
DerivativesDerivative NotationDerivative Property [Multiplied Constant]:
[tex]\displaystyle (cu)' = cu'[/tex]
Derivative Rule [Basic Power Rule]:
Integration
IntegralsIntegration Rule [Fundamental Theorem of Calculus 1]:
[tex]\displaystyle \int\limits^b_a {f(x)} \, dx = F(b) - F(a)[/tex]
Integration Property [Multiplied Constant]:
[tex]\displaystyle \int {cf(x)} \, dx = c \int {f(x)} \, dx[/tex]
Multivariable Calculus
Partial Derivatives
Vector Calculus
Circulation Density:
[tex]\displaystyle F = M \hat{\i} + N \hat{\j} \rightarrow \text{curl} \ \bold{F} \cdot \bold{k} = \frac{\partial N}{\partial x} - \frac{\partial M}{\partial y}[/tex]
Green's Theorem [Circulation Curl/Tangential Form]:
[tex]\displaystyle \oint_C {F \cdot T} \, ds = \oint_C {M \, dx + N \, dy} = \iint_R {\bigg( \frac{\partial N}{\partial x} - \frac{\partial M}{\partial y} \bigg)} \, dx \, dy[/tex]
Step-by-step explanation:
Step 1: Define
Identify given.
[tex]\displaystyle \oint_C {3y \, dx + 2x \, dy}[/tex]
[tex]\displaystyle \text{Region:} \ \left \{ {{0 \leq x \leq \pi} \atop {0 \leq y \leq \sin x}} \right.[/tex]
Step 2: Integrate Pt. 1
Define vector functions M and N:Step 3: Integrate Pt. 2
We can evaluate the Green's Theorem double integral we found using basic integration techniques listed above:
[tex]\displaystyle \begin{aligned}\oint_C {3y \, dx + 2x \, dy} & = - \int\limits^{\pi}_0 \int\limits^{\sin x}_0 {} \, dy \, dx \\& = - \int\limits^{\pi}_0 {y \bigg| \limits^{y = \sin x}_{y = 0}} \, dx \\& = - \int\limits^{\pi}_0 {\sin x} \, dx \\& = \cos x \bigg| \limits^{x = \pi}_{x = 0} \\& = \boxed{\bold{2}}\end{aligned}[/tex]
∴ we have evaluated the line integral using Green's Theorem.
---
Learn more about multivariable calculus: https://brainly.com/question/14502499
---
Topic: Multivariable Calculus
Unit: Green's Theorem and Surfaces
How to simplify this expression??
Answer :
1
Step-by-step-explanation :
[tex] {x}^{2} + 4x + 5 - {(x + 2)}^{2} \\ {x}^{2} + 4x + 5 - ( {x}^{2} + 4x + 4) \\ [/tex]
[tex]{x}^{2} + 4x + 5 - {x}^{2} - 4x - 4 = {x}^{2} - {x}^{2} + 4x - 4x + 5 - 4 = 5 - 4 = 1[/tex]
Answer:
(x+1) • (x-5)
Step-by-step explanation:
The first term is, x2 its coefficient is 1 .
The middle term is, -4x its coefficient is -4 .
The last term, "the constant", is -5
Step-1 : Multiply the coefficient of the first term by the constant 1 • -5 = -5
Step-2 : Find two factors of -5 whose sum equals the coefficient of the middle term, which is -4 .
-5 + 1 = -4 That's it
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -5 and 1
x2 - 5x + 1x - 5
Step-4 : Add up the first 2 terms, pulling out like factors :
x • (x-5)
Add up the last 2 terms, pulling out common factors :
1 • (x-5)
Step-5 : Add up the four terms of step 4 :
(x+1) • (x-5)
A household survey of 10 families was conducted by students of 4th year MBBS. In the collected data, the ages of heads of families were: 32, 34, 35, 36, 36, 42, 44, 46, 48, and 52. The mean age of heads of families is
a. 36
b. 38.5
c. 40
d. 40.5
e. 42
Answer:
Which polynomial is prime?
7x2 – 35x + 2x – 10
9x3 + 11x2 + 3x – 33
10x3 – 15x2 + 8x – 12
12x4 + 42x2 + 4x2 + 14
Step-by-step explanation:
Which polynomial is prime?
7x2 – 35x + 2x – 10
9x3 + 11x2 + 3x – 33
10x3 – 15x2 + 8x – 12
12x4 + 42x2 + 4x2 + 14 SO IT IS RIGHT
please help! algebra 2 work
22)
Subtract (4 - 21) - (3 - 51)
A)
1+3i
B)
1-71
7+3i
D)
7-7i
Answer:
1 +3i
Step-by-step explanation:
(4 - 2i) - (3 - 5i)
Subtract the reals
4 - 3 =1
Subtract the imaginary
-2i - -5i
-2i + 5i = 3i
1 +3i
Answer:
A
Step-by-step explanation:
Subtract all real numbers
4 - 3 = 1
Subtract all imaginary numbers
-2i - (-5i) = 3i
Put back together
1 + 3i
Best of Luck!
PLS HELP:Find all the missing elements:
Answer:
b = 9.5 , c = 15Step-by-step explanation:
For b
To find side b we use the sine rule
[tex] \frac{ |a| }{ \sin(A) } = \frac{ |b| }{ \sin(B) } [/tex]a = 7
A = 23°
B = 32°
b = ?
Substitute the values into the above formula
That's
[tex] \frac{7}{ \sin(23) } = \frac{ |b| }{ \sin(32) } [/tex][tex] |b| \sin(23) = 7 \sin(32) [/tex]Divide both sides by sin 23°
[tex] |b| = \frac{7 \sin(32) }{ \sin(23) } [/tex]b = 9.493573
b = 9.5 to the nearest tenthFor cTo find side c we use sine rule
[tex] \frac{ |a| }{ \sin(A) } = \frac{ |c| }{ \sin(C) } [/tex]C = 125°
So we have
[tex] \frac{7}{ \sin(23) } = \frac{ |c| }{ \sin(125) } [/tex][tex] |c| \sin(23) = 7 \sin(125) [/tex]Divide both sides by sin 23°
[tex] |c| = \frac{7 \sin(125) }{ \sin(23) } [/tex]c = 14.67521
c = 15.0 to the nearest tenthHope this helps you
0.25÷3=x÷1 1/2 That fraction is one and a half.
Answer:
x = 1/8Step-by-step explanation:
Given the expression 0.25÷3=x÷1 1/2, we are to look for the value of x from the given equation. Rewriting the equation we will have;
[tex]\dfrac{0.25}{3} = \dfrac{x}{1\frac{1}{2} }[/tex]
On simplification;
[tex]0.25 * \frac{1}{3} = x * \frac{2}{3} \\ \\ \frac{25}{100}*\frac{1}{3} =\frac{2x}{3}\\\\ \frac{1}{4} * \frac{1}{3} = \frac{2x}{3}\\\\ \frac{1}{12} = \frac{2x}{3}\\\\cross \ multiply\\\\2x * 12 = 3\\\\24x = 3\\\\Divide \ both \ sides \ by \ 24\\\\24x/24 = 3/24\\\\x = 1/8[/tex]
Hence the value of x in the expression is 1/8
Six people attend the theater together and sit in a row with exactly six seats.
a. How many ways can they be seated together in the row?
b. Suppose one of the six is a doctor who must sit on the aisle in case she is paged. How many ways can the people be seated together in the row with the doctor in an aisle seat?
c. Suppose the six people consist of three married couples and each couple wants to sit together with the husband on the left. How many ways can the six be seated together in the row?
Answer
A. 720 ways
B. 240 ways
C. 6 ways
There are 720 ways they can be seated in a row together, 120 ways can the people be seated together in a row with the doctor in an aisle seat, and 6 ways can the six be seated together in a row.
What is a permutation?A permutation is defined as a mathematical process that determines the number of different arrangements in a set of objects when the order of the sequential arrangements.
It is assumed that six people will attend the theater together and sit in a row of six.
The following are the various ways they can be seated in a row together:
⇒ 6!
⇒ 6 × 5 × 4 × 3 × 2 × 1
⇒ 720
If the doctor sits in the aisle seat, the remaining 5 persons can sit in the remaining 5 seats 5! ways
The total possibilities are as follows:
⇒ 5 × 4 × 3 × 2 × 1
= 120
Consider that the six persons are made up of three married couples.
In addition to the aforementioned, divide the six chairs into three groups of two seats each.
There is one choice in each block for the husband to be placed on the left and the wife to be positioned on the right and the 3 couples can be seated in the 3 blocks in 3! ways.
⇒ 3 × 2 × 1
The required answer is 6.
Thus, there are 720 ways they can be seated in a row together, 120 ways can the people be seated together in a row with the doctor in an aisle seat, and 6 ways can the six be seated together in a row.
Learn more about permutation here:
brainly.com/question/1216161
#SPJ2
According to a report in USA Today, more and more parents are helping their young adult children purchase their first home. Suppose eight persons in a random sample of 40 young adults who recently purchased a home in Kentucky received help from their parents. You have been asked to construct a 95% confidence interval for the population proportion of all young adults in Kentucky who received help from their parents. What is the margin of error for a 95% confidence interval for the population proportion
Answer:
the margin of error
= 1.96 x 0.0632
= 0.124
Step-by-step explanation:
this question has the sample size, n = 40
8 people have received help from their parents from this sample.
8/40 = 0.2
which is the sample proportion
z = 1 - 0.2
= 0.8
to calculate standard error
√pz/n
= √0.2 x 0.8/40
= √0.16/40
= 0.0632
at 95% confidence level
z(alpha/2) = 1.96
therefore the margin of error
= 1.96 x 0.0632
= 0.124
You are to manufacture a rectangular box with 3 dimensions x, y and z, and volume v=8000. Find the dimensions which minimize the surface area of this box.
Answer:
20 by 20 by 20
Step-by-step explanation:
Let the total surface of the rectangular box be expressed as S = 2xy + 2yz + 2xz
x is the length of the box
y is the width and
z is the height of the box.
S = 2xy + 2yz + 2xz ... 1
Given the volume V = xyz = 8000 ... 2
From equation 2;
z = 8000/xy
Substituting into equation 1;
S = 2xy + 2y(8000/xy)+ 2x(8000/xy)
S = 2xy+16000/x+16000/y
Differentiating the resulting equation with respect to x and y will give;
dS/dx = 2y + (-16000x⁻²)
dS/dx = 2y - 16000/x²
Similarly,
dS/dy = 2x + (-160000y⁻²)
dS/dy = 2x - 16000/y²
Note that at the turning point, ds/dx = 0 and ds/dy = 0, hence;
2y - 16000/x² = 0 and 2x - 16000/y² = 0
2y = 16000/x² and 2x = 16000/y²
2y = 16000/(8000/y²)²
2y = 16000×y⁴/64,000,000
2y = y⁴/4000
y³ = 8000
y =³√8000
y = 20
Given 2x = 16000/y²
2x = 16000/20²
2x = 16000/400
2x = 40
x = 20
Since Volume of the box is V = xyz
8000 = 20(20)z
8000 = 400z
z = 8000/400
z = 20
Hence, the dimensions which minimize the surface area of this box is 20 by 20 by 20.
The dimensions which minimize the surface area of this box is 20 *20* 20. This can be calculated by using surface area and volumes.
The calculation for total surface area:Let the total surface of the rectangular box be expressed as:
S = 2xy + 2yz + 2xz
where,
x is the length of the box
y is the width and
z is the height of the box.
S = 2xy + 2yz + 2xz .................(1)
Given:
Volume V = xyz = 8000 .............(2)
From equation 2;
z = 8000/xy
Substituting into equation 1;
S = 2xy + 2y(8000/xy)+ 2x(8000/xy)
S = 2xy+16000/x+16000/y
Differentiating the resulting equation with respect to x and y will give;
dS/dx = 2y + (-16000x⁻²)
dS/dx = 2y - 16000/x²
Similarly,
dS/dy = 2x + (-160000y⁻²)
dS/dy = 2x - 16000/y²
Note that at the turning point, ds/dx = 0 and ds/dy = 0, hence;
2y - 16000/x² = 0 and 2x - 16000/y² = 0
2y = 16000/x² and 2x = 16000/y²
2y = 16000/(8000/y²)²
2y = 16000×y⁴/64,000,000
2y = y⁴/4000
y³ = 8000
y =³√8000
y = 20
Given 2x = 16000/y²
2x = 16000/20²
2x = 16000/400
2x = 40
x = 20
Since, Volume of the box is V = xyz
8000 = 20(20)z
8000 = 400z
z = 8000/400
z = 20
Hence, the dimensions which minimize the surface area of this box is 20*20*20.
Find more information about Surface area here:
brainly.com/question/1090412
The solution system to 3y-2x=-9 and y=-2x+5
Answer:
[tex]\boxed{(3,-1)}[/tex]
Step-by-step explanation:
Hey there!
Well to find the solution the the given system,
3y - 2x = -9
y = -2x + 5
So to find x lets plug in -2x + 5 for y in 3y - 2x = -9.
3(-2x + 5) - 2x = -9
Distribute
-6x + 15 - 2x = -9
-8x + 15 = -9
-15 to both sides
-8x = -24
Divide -8 to both sides
x = 3
Now that we have x which is 3, we can plug in 3 for x in y = -2x + 5.
y = -2(3) + 5
y = -6 + 5
y = -1
So the solution is (3,-1).
Hope this helps :)
Identify which equations have one solution, infinitely many solutions, or no solution. No solution: One solution: Infinitely solution:
Answer:
Top left: no
Top middle: one
Top right: no
Bottom left: infinite
Bottom middle: one
Bottom right: one
Step-by-step explanation:
Top left: no
Top middle: one
Top right: no
Bottom left: infinite
Bottom middle: one
Bottom right: one
How many petals are on the graph? Find the trigonometric form of a given function.
Answer:
Attachment 1 : Option A,
Attachment 2 : Option C
Step-by-step explanation:
( 1 ) Here we know that " n " is 6. Now remember if n is odd, the number of petals on the graph will be n. However if n is even, the number of petals on the graph will be 2n.
6 is even, and hence the number of petals will be 2(6) = 12 petals. Solution : 12 petals
( 2 ) To solve such problems we tend to use the equation [tex]z = x + y * i = r(cos\theta +isin\theta)[/tex] where [tex]r = \sqrt{x^2+y^2}[/tex] etc. Here I find it simpler to see each option, and convert each into it's standard complex form. It might seem hard, but it is easy if you know the value of (cos(5π / 3)) etc...
The answer here will be option c, but let's prove it,
cos(5π / 3) = 1 / 2,
sin(5π / 3) = [tex]-\frac{\sqrt{3}}{2}[/tex]
Plugging those values in for " [tex]8\left(\cos \left(\frac{5\pi }{3}\right)+i\sin \left(\frac{5\pi }{3}\right)\right)[/tex] "
[tex]8\left(-\frac{\sqrt{3}i}{2}+\frac{1}{2}\right)[/tex]
= [tex]8\cdot \frac{1}{2}-8\cdot \frac{\sqrt{3}i}{2}[/tex] = [tex]4-4\sqrt{3}i[/tex]
Hence proved that your solution is option c.
Please answer this correctly without making mistakes
Answer:
10 9/20
Step-by-step explanation:
Hey there!
If Hillsboro to Campbell is 16 2/20 and Hillsboro to Oxford is 5 13/20,
we’ll do
16 2/20 - 5 13/20
Imrpoper form
322/20 - 113/20
322 - 113
209/20
10 9/20 miles from Oxford to Campbell.
Hope this helps :)
Which rule describes this transformation? (Zoom in to see it clearly)
Answer:
(x,y) -> (x+6, y-3)
Step-by-step explanation:
I followed c and it translated like the last ans choice.
A bike wheel. A bike wheel is 26 inches in diameter. What is the bike wheel's diameter in millimeters (1 inch = 25.4 millimeters)?
Answer:
its multiple choice
A. 26inches (1inch/25.4mm)
B. 26inches (25.4mm/1inch)
C. 25.4inches (1mm/26inch)
D. 26inches (1mm/25.4inch)
and its b
Which of the following statements are true? Select all that apply.
If the equation were graphed, it would be a horizontal line.
Both functions have the same slope.
The origin is the y-intercept for the function expressed in the table.
The linear equation does not have a y-intercept.
The table and the graph express an equivalent function.
Answer:
Both functions have the same slope.The origin is the y-intercept for the function expressed in the table.The table and the graph express an equivalent function.Step-by-step explanation:
Both functions have the same slope
The slope is m in the equation; y =mx+c which is the formula for a straight line.
m = change in Y/change in x
Using 2 points: (1,3/4) and ( 4,3) from the table;
= (3 - 3/4) / ( 4 - 1)
= 2.25/3
= 0.75 which is 3/4 which is the same as the slope of the function in the equation.
The origin is the y-intercept for the function expressed in the table.
Slope of function in table is known to be 0.75. Find c to complete equation.
3 = 0.75 ( 4) + c
3 = 3 + c
c = 0
c is the y-intercept. The origin of a line is 0 so if c is 0 then the origin is the y intercept.
The table and the graph express an equivalent function.
The function for the table as calculated is;
y = 0.75x + 0
y = 0.75x
This is the same as the function for the equation for the graph which is y = 3/4x.
Answer:Both functions have the same slope.
The origin is the y-intercept for the function expressed in the table.
The table and the graph express an equivalent function.
Step-by-step explanation:
Compare the linear functions expressed below by data in a table and by an equation.
A 2-column table with 4 rows. Column 1 is labeled x with entries negative 6, negative four-thirds, 1, 4. Column 2 is labeled y with entries negative StartFraction 9 Over 2 EndFraction, negative 1, three-fourths, 3. y = three-fourths x.
Which of the following statements are true? Select all that apply.
If the equation were graphed, it would be a horizontal line.
Both functions have the same slope.
The origin is the y-intercept for the function expressed in the table.
The linear equation does not have a y-intercept.
The table and the graph express an equivalent function.
In recent years, the interest rates on home mortgages have declined to less than 6%. However, a
recent study shows that the rate charged on credit card debt is more than 14%. A sample of 10 credit
cards showed that the mean rate charged is 15.64% with a standard deviation of 1.561%. At 1% level
of significance, is it reasonable to conclude the mean rate charged is greater than 14%?
Answer:
Yes it is reasonable to conclude the mean rate charged is greater than 14%
Step-by-step explanation:
From the question we are told that
The population mean is [tex]\mu = 0.14[/tex]
The sample size is [tex]n = 10[/tex]
The sample mean is [tex]\= x = 0.1564[/tex]
The standard deviation is [tex]\sigma = 0.01561[/tex]
The level of significance is [tex]\alpha = 0.01[/tex]
The null hypothesis is [tex]H_o: \mu = 0.14[/tex]
The alternative hypothesis is [tex]H_a : \mu > 0.14[/tex]
Generally the test statistic is mathematically represented as
[tex]t = \frac{ \= x - \mu }{ \frac{\sigma }{\sqrt{n} } }[/tex]
substituting values
[tex]t = \frac{ 0.1564 - 0.14 }{ \frac{0.01561 }{\sqrt{10} } }[/tex]
[tex]t = 3.322[/tex]
Now the p-value obtained from the z-table is
[tex]p-value = P(t > 3.322) = 0.00044687[/tex]
Since the [tex]p-value < \alpha[/tex] then we reject the null hypothesis, hence we can conclude that the mean rate charged is greater than 14%
Simplify to create an equivalent expression.
-k-(-8k+7)
a=7k−7
b=-7k-7
c=7k+7
d=-7k+7
choose one
Answer:
a. 7k - 7
Step-by-step explanation:
Step 1: Write out expression
-k - (-8k + 7)
Step 2: Distribute negative
-k + 8k - 7
Step 3: Combine like terms
7k - 7
And we have our answer!
Please help, thanks!!!!!
Answer:
[ 2+0+8. 0+0+12][-4+10+2. 0+25+3]
[10. 12]
[8. 28]
Option 3 is the solution
A population has a mean and a standard deviation . Find the mean and standard deviation of a sampling distribution of sample means with sample size n. nothing (Simplify your answer.) nothing (Type an integer or decimal rounded to three decimal places as needed.)
Complete Question
A population has a mean mu μ equals = 77 and a standard deviation σ = 14. Find the mean and standard deviation of a sampling distribution of sample means with sample size n equals = 26
Answer:
The mean of sampling distribution of the sample mean ( [tex]\= x[/tex]) is [tex]\mu_{\= x } = 77[/tex]
The standard deviation of sampling distribution of the sample mean ( [tex]\= x[/tex]) is
[tex]\sigma _{\= x} = 2.746[/tex]
Step-by-step explanation:
From the question we are told that
The population mean is [tex]\mu = 77[/tex]
The standard deviation is [tex]\sigma = 14[/tex]
The sample size is [tex]n = 26[/tex]
Generally the standard deviation of sampling distribution of the sample mean ( [tex]\= x[/tex]) is mathematically represented as
[tex]\sigma _{\= x} = \frac{ \sigma }{ \sqrt{n} }[/tex]
substituting values
[tex]\sigma _{\= x} = \frac{ 14}{ \sqrt{26} }[/tex]
[tex]\sigma _{\= x} = 2.746[/tex]
Generally the mean of sampling distribution of the sample mean ( [tex]\= x[/tex]) is equivalent to the population mean i.e
[tex]\mu_{\= x } = \mu[/tex]
[tex]\mu_{\= x } = 77[/tex]
A bag contains 6 red marbles, 3 blue marbles and 1 green marble. What is the probability that a randomly selected marble is not blue?
Answer:
3/10
Step-by-step explanation:
6+3+1=10
since there are 3 blue marbles, we put the 3 into the place of the numerator
and since there is 10 marbles in total it goes into the denominator
The probability that a randomly selected marble is not blue will be 0.70.
What is probability?Its basic premise is that something will almost certainly happen. The percentage of favorable events to the total number of occurrences.
A bag contains 6 red marbles, 3 blue marbles and 1 green marble.
The total number of the event will be
Total event = 6 + 3 + 1
Total event = 10
Then the probability that a randomly selected marble is not blue will be
Favorable event = 7 {red, green}
Then the probability will be
P = 7 / 10
P = 0.70
More about the probability link is given below.
https://brainly.com/question/795909
#SPJ2
Are you able to find tri-sector (equally divided by 3) rays for an arbitrary angle with straightedge-and-compass construction?
Answer:
Step-by-step explanation:
No, it is an ancient problem which has been proved to be impossible (in 1837), at least not for an arbitray angle.
However, we can trisect certain angles, such as 90 degrees, but rather than trisection, we are just constructing 30 degree angles.
For further reading, google "angle trisection"
Answer 9 and 11 with explanation on how you solved it.
Answer:
(9). Range; {8, 5, 2, -1, -4}
(10). Range; {-15, -7, 1, 9, 17}
Step-by-step explanation:
Domain of a function is (x-values) determined by the input values and Range of a function is determined by the (y-values) output values of the function.
(9). For the given function,
f(x) = -3x + 2
If the Domain of this function is a set of values,
{-2, -1, 0, 1, 2}
For Range,
x -2 -1 0 1 2
f(x) 8 5 2 -1 -4
Therefore, Range of the function 'f' will be; {8, 5, 2, -1, -4}
(11). f(x) = 4x + 1
Domain is {-4, -2, 0, 2, 4}
Table for input-output values will be,
x -4 -2 0 2 4
f(x) -15 -7 1 9 17
Therefore, Range of the function will be {-15, -7, 1, 9, 17}
Multiple-Choice Questions
1. In 1995, Diana read 10 English books and 7 French books. In 1996, she read twice as many French books as English books. If 60% of the books that she read during the 2 years were French, how many English and French books did she read in 1996?
(A) 16
(B) 26
(0) 32
(D) 48
Answer:
(D) 48
Step-by-step explanation:
Let English book = x
Let french book = y
In 1995 x= 10
Y= 7
In 1996
Y = 2x
Total book read in the two years
0.6(Total) = y
0.4(total) = x
We don't know the exact amount of books read in 1996.
Total = 10 + 7 +x +2x
Total = 17+3x
0.6(total) = 7+2x
0.6(17+3x) = 7+2x
10.2 +1.8x= 7+2x
10.2-7= 2x-1.8x
3.2= 0.2x
3.2/0.2= x
16= x
So she read 16 English book
And 16*2 = 32 french book Making it a total of 16+32= 48 books in 1996
What happens to the probability of making a Type II error, beta,as the level of significance, alpha,decreases? Why?
Answer:
Lowering the level of significance, α increases the probability of making a Type II error, β.
Step-by-step explanation:
Lowering the level of significance, α increases the probability of making a Type II error, β.
This is because the region of acceptance becomes bigger, and it makes it less likely for one to reject a null hypothesis, when it is false, the type II error.
For a free lunch giveaway, a restaurant draws 1 card from a bowl of business cards. Val puts in 5 cards. The bowl has 50 cards. What is the probability that Val will win?
Answer:The probability Val will win is 1/5 or 10/50 or 2/10
Step-by-step explanation:
. One sample has M = 18 and a second sample has M = 14. If the pooled variance for the two samples is 16, what is the value of Cohen’s d?
Answer:
Cohen's d : 1.00
Step-by-step explanation:
We know that M₁ = 18, and M₂ = 14. Given that the pooled variance for the these two samples are 16, S²Pooled = 16, and therefore S - pooled = 4.
The formula to solve for the value of Cohen's d is as follows,
d = M₁ - M₂ / S - pooled,
d = 18 - 14 / 4 = 4 / 4 = 1
Therefore the value of Cohen's d = 1
Question 1 (5 points)
The line segment AB with endpoints A(-3, 6) and B(9, 12) is dilated with a scale
factor 2/3 about the origin. Find the endpoints of the dilated line segment.
OA) (-2, 4), (6,8)
B) (2, 4). (6,8)
OC) (4, -2), (6,8)
OD) (-2,4), (8,6)
Answer: A) (-2, 4), (6,8)
Step-by-step explanation:
When a point (x,y) is dilated by a scale factor of k , then the new points is given by (kx,ky).
Given: The line segment AB with endpoints A(-3, 6) and B(9, 12) is dilated with a scale factor [tex]\dfrac23[/tex] about the origin.
Let A' and B' b the endpoints of the dilated line segment.
Then, [tex]A'(\dfrac{2}{3}(-3), \dfrac23(6))=A'(-2,4)[/tex]
[tex]B'(\dfrac{2}{3}(9), \dfrac23(12))=B'(6,8)[/tex]
Hence, the correct option is A) (-2, 4), (6,8)
