Answer:
D. =
Step-by-step explanation:
Because 45 and 45 are the same number so they equal the same value
Answer:
Step-by-step explanation:
Answer B C D
Assume that Publication is the root class of an inheritance tree. You want to form a linked list of different publications in the inheritance tree, including Book, Report, Newspaper, etc. What is the best way to create a linked list using PublListNode and Publication classes? a. The Publication class is derived from the PublListNode class. b. The PublListNode class is derived from the Publication class. c. The Publication class contains the PublListNode class. d. The PublListNode class contains the Publication class.
Answer:
The best way to create a linked list using PublListNode and Publication classes is ensuring that:
d. The PublListNode class contains the Publication class.
Step-by-step explanation:
A linked list contains a set of address-connected nodes (elements). The first node is called a header address, while the last node is called a null address. A linked list can be a single list (linear list), double list, multiple linked list, or circular linked list. The PublListNode is a type of multiple linked list. It forms a linked list of different publications using an inheritance tree.
Use the t-distribution to find a confidence interval for a mean mu given the relevant sample results. Give the best point estimate for mu, the margin of error, and the confidence interval. Assume the results come from a random sample from a population that is approximately normally distributed. A 95% confidence interval for mu using the sample results x-bar equals 76.4, s = 8.6, and n = 42.
Point estimate = ?
Margin of error = ?
Answer:
Point estimate = 76.4
Margin of Error = 2.680
Step-by-step explanation:
Given that distribution is approximately normal;
The point estimate = sample mean, xbar = 76.4
The margin of error = Zcritical * s/√n
Tcritical at 95%, df = 42 - 1 = 41
Tcritical(0.05, 41) = 2.0195
Margin of Error = 2.0195 * (8.6/√42)
Margin of Error = 2.0195 * 1.327
Margin of Error = 2.67989
Margin of Error = 2.680
3. Solve the initial value problem. a. 2yy^ prime =e^ x-y^ 2 , given y(4) = - 2 .
It looks like the equation reads
2yy' = exp(x - y ²)
(where exp(blah) = e ^(blah))
This DE is separable:
2y dy/dx = exp(x) exp(-y ²)
==> 2y exp(y ²) dy = exp(x) dx
Integrating both sides gives
exp(y ²) = exp(x) + C
The initial condition tells you that y = -2 when x = 4, so that
exp((-2)²) = exp(4) + C
exp(4) = exp(4) + C
==> C = 0
Then the particular solution to this DE is
exp(y ²) = exp(x)
Solving for y as a function of x gives
y ² = x
y = ±√x
But bearing in mind that y = -2 < 0 when x = 4, only the negative square root solution satisfies the DE. So
y(x) = -√x
Y=2.5x+5.8
When x=0.6
Answer:
7.3
Step-by-step explanation:
y=2.5x+5.8
=2.5×0.6+5.8
= 1.5+.8
=7.3
Write out the sample space for the given experiment. Use the following letters to indicate each choice: O for olives, M for mushrooms, S for shrimp, T for turkey, I for Italian, and F for French. When deciding what you want to put into a salad for dinner at a restaurant, you will choose one of the following extra toppings: olives, mushrooms. Also, you will add one of following meats: shrimp, turkey. Lastly, you will decide on one of the following dressings: Italian, French
Answer: He can make 36 different salds
Step-by-step explanation:
( 7 x 10 ^-5) x (5 x 10 ^-8)
[tex]\huge{\colorbox{pink}{Solution}}[/tex]
Step 1 : Equation at the end of step 1
(((7•(x^10 ))-5)•x)•(5x^10-8)
Step 2 : Equation at the end of step 2 :
((7x^10 - 5) • x) • (5x^10 - 8)
Step 3 :
Trying to factor as a Difference of Squares:
3.1 Factoring: 7x^10-5
Theory : A difference of two perfect squares, A2 - B2 can be factored into (A+B) • (A-B)
Proof : (A+B) • (A-B) =
A² - AB + BA - B² =
A² - AB + AB - B² =
[tex] \: \: \: \: \: \blue {A² - B²}[/tex]
Note : AB = BA is the commutative property of multiplication.
Note : - AB + AB equals zero and is therefore eliminated from the expression.
Check : 7 is not a square !!
Ruling : Binomial can not be factored as the
difference of two perfect squares.
Equation at the end of step 3 :
x • (7x10 - 5) • (5x10 - 8)
Step 4 :
4.1 Factoring: 5x^10-8
Check : 5 is not a square !!
Ruling : Binomial can not be factored as the
difference of two perfect squares.
Final result : ☞ x • (7x10 - 5) • (5x10 - 8)
→ 3.5 × 10^-12
____________________________
Hope It Helps You ✌️
Find the slope of the line which passes through the points A (-4, 2) and B (1,5).
Answer:
3/5 so A.
Step-by-step explanation:
Answer:
slope = [tex]\frac{3}{5}[/tex]
Step-by-step explanation:
Calculate the slope m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (- 4, 2) and (x₂, y₂ ) = (1, 5)
m = [tex]\frac{5-2}{1-(-4)}[/tex] = [tex]\frac{3}{1+4}[/tex] = [tex]\frac{3}{5}[/tex]
The state of California has a mean annual rainfall of 22 inches, whereas the state of New York has a mean annual rainfall of 42 inches. Assume that the standard deviation for both states is 7 inches. A sample of 30 years of rainfall for California and a sample of 45 years of rainfall for New York has been taken.
(a) Show the sampling distribution of the sample mean annual rainfall for California.
(b) Show the sampling distribution of the sample mean annual rainfall for New York.
(c) In which of the preceding two cases, part (a) or part (b), is the standard error of x smaller? Why?
The standard error is [larger, smaller] for New York because the sample size is [larger, smaller] than for California.
Answer:
a) [tex]E(\bar x) = \mu_{1} = 22[/tex] inches
The sampling distribution of the sample means annual rainfall for California is 1.278.
b)
[tex]E(\bar x) = \mu_{2} = 42[/tex] inches
The sampling distribution of the sample means annual rainfall for New York is 1.0435.
c)
Here, The standard error of New York is smaller because the sample size is larger than for California.
Step-by-step explanation:
California:
[tex]\mu_{1} = 22[/tex] inches.
[tex]\sigma_{1}[/tex] = 7 inches.
[tex]n_{1}[/tex] = 30 years.
New York:
[tex]\mu_{2} = 42[/tex] inches.
[tex]\sigma_{2}[/tex] = 7 inches.
[tex]n_{2}[/tex] = 45 years.
a)
[tex]E(\bar x) = \mu_{1} = 22[/tex] inches
[tex]\sigma^{p} _{\bar x} = \frac{\sigma_{1} }{\sqrt n_{1} } \\\\\\\sigma^{p} _{\bar x} = \frac{7}{\sqrt 30} \\\\\sigma^{p} _{\bar x} = 1.278[/tex]
b)
[tex]E(\bar x) = \mu_{2} = 42[/tex] inches
[tex]\sigma _{\bar x} = \frac{\sigma_{2} }{\sqrt n_{2} } \\\\\\\sigma_{\bar x} = \frac{7}{\sqrt45} \\\\\sigma _{\bar x} = 1.0435[/tex]
c)
Here, The standard error of New York is smaller because the sample size is larger than for California.
Simplify.
Multiply and remove all perfect squares from inside the square roots. Assume z is positive.
√z ∗ √30z^2 ∗ √35z^3
Answer:
Step-by-step explanation:
You need to put parentheses around the radicands.
√z · √(30z²) · √(35z³) = √(z·30z²·35z³)
= √(1050z⁶)
= √(5²·42z⁶)
= √5²√z⁶√42
= 25z³√42
The obtained expression would be 25z³√42 which is determined by the multiplication of the terms of expression.
What is Perfect Square?A perfect Square is defined as an integer multiplied by itself to generate a perfect square, which is a positive integer. Perfect squares are just numbers that are the products of integers multiplied by themselves.
What are Arithmetic operations?Arithmetic operations can also be specified by adding, subtracting, dividing, and multiplying built-in functions. The operator that performs the arithmetic operations is called the arithmetic operator.
* Multiplication operation: Multiplies values on either side of the operator
For example 4*2 = 8
We have been the expression as:
⇒ √z · √(30z²) · √(35z³)
Multiply and remove all perfect squares from inside the square roots
⇒ √(z·30z²·35z³)
⇒ √(1050z⁶)
⇒ √(5²·42z⁶)
Assume z is positive.
⇒ √5²√z⁶√42
⇒ 25z³√42
Therefore, the obtained expression would be 25z³√42.
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Consider a set of data in which the sample mean is 26.826.8 and the sample standard deviation is 7.97.9. Calculate the z-score given that x.
Answer:
The answer is "0.59".
Step-by-step explanation:
Please find the whole question in the attached file.
Given:
[tex]\mu=26.8\\\\\sigma=6.4\\\\X=30.6[/tex]
Using formula:
[tex]z=\frac{X-\mu}{\sigma}[/tex]
[tex]=\frac{30.6-26.8}{6.4}\\\\=\frac{3.8}{6.4}\\\\=\frac{380}{640}\\\\=\frac{38}{64}\\\\=\frac{19}{32}\\\\=0.59375\approx 0.59[/tex]
In order for the parallelogram to be a
rectangle, x = [?]
Diagonal AC = 7x - 35
Diagonal BD = 3x + 45
A
B.
D
C С
Explanation:
For any rectangle, the diagonals are the same length.
AC = BD
7x-35 = 3x+45
7x-3x = 45+35
4x = 80
x = 80/4
x = 20
Nick buys a bag of cookies that contains 9 chocolate chip cookies, 8 peanut butter cookies, 4 sugar cookies and 5 oatmeal cookies. What is the probability that Nick reaches in the bag and randomly selects a chocolate chip cookie from the bag, eats it, then reaches back in the bag and randomly selects an oatmeal cookie
Answer:
7/26
Step-by-step explanation:
Add all of it up.
9 + 8 + 4 +5 = 26
26 cookies, but done twice so,
26 × 2 = 52
14/52 = 7/26
SAQ 5.1
1. Find the first four terms of the sequence whose general term is given by
i.
ii.
7 x 3"
n-2 5 x
2. Say what the pattern of is for each of the following sequences and give the next three
terms
i.
ii.
2, 6, 12, 20
8, 0.8, 0.08, 0.008
1 1 1 '2'3'4
Answer:
1. (i) 7, 21, 63, 189
(ii) 20, 10, 5, 2.5
2. (i) n²+n (where n = 1, 2, 3, ..)
(ii) 8/(10^n) (where n = 1, 2, 3, ..)
(iii) 1/(n+1) (where n = 1, 2, 3, ..)
PLEASE HELPPPP
The cost function in a computer manufacturing plant is C(x) = 0.28x^2-0.7x+1, where C(x) is the cost per hour in millions of dollars and x is the number of items produced per hour in thousands. Determine the minimum production cost.
Given:
The cost function is:
[tex]C(x)=0.28x^2-0.7x+1[/tex]
where C(x) is the cost per hour in millions of dollars and x is the number of items produced per hour in thousands.
To find:
The minimum production cost.
Solution:
We have,
[tex]C(x)=0.28x^2-0.7x+1[/tex]
It is a quadratic function with positive leading efficient. It means it is an upward parabola and its vertex is the point of minima.
If a quadratic function is [tex]f(x)=ax^2+bx+c[/tex], then the vertex of the parabola is:
[tex]\text{Vertex}=\left(-\dfrac{b}{2a},f(-\dfrac{b}{2a})\right)[/tex]
In the given function, [tex]a=0.28, b=-0.7, c=1[/tex]. So,
[tex]-\dfrac{b}{2a}=-\dfrac{-0.7}{2(0.28)}[/tex]
[tex]-\dfrac{b}{2a}=1.25[/tex]
Putting [tex]x=1.25[/tex] in the given function to find the minimum production cost.
[tex]C(x)=0.28(1.25)^2-0.7(1.25)+1[/tex]
[tex]C(x)=0.28(1.5625)-0.875+1[/tex]
[tex]C(x)=0.4375+0.125[/tex]
[tex]C(x)=0.5625[/tex]
Therefore, the minimum production cost is 0.5625 million dollars.
Answer:
The minimum cost is 0.5625.
Step-by-step explanation:
The cost function is
C(x) = 0.28x^2 - 0.7 x + 1
Differentiate with respect to x.
[tex]C = 0.28x^2 - 0.7 x + 1\\\\\frac{dC}{dt} = 0.56 x - 0.7\\\\\frac{dC}{dt} = 0\\\\0.56 x - 0.7 = 0\\\\x = 1.25[/tex]
The minimum value is
c = 0.28 x 1.25 x 1.25 - 0.7 x 1.25 + 1
C = 0.4375 - 0.875 + 1
C = 0.5625
Which expression is equivalent to the area of square A, in square inches?
1. 1/2(10)(24)
2. 10(24)
3. (10+24)^2
4. 10^2 + 24^2
Answer:
4.) 10^2 + 24^2
Step-by-step explanation:
From the attached diagram, the area of a square A is given by the measure of the square of its hypotenus :
The hypotenus is given by :
Hypotenus² = opposite² + Adjacent²
Hypotenus² = 10² + 24²
The square of hypotenus = 10^2 + 24^2
Find z such that 6% of the standard normal curve lies to the right of z.
P(Z ≥ z) = 1 - P(Z ≤ z) = 0.06
==> P(Z ≤ z) = 0.94
==> z ≈ 1.7507
What is the range of the function f(x) = 3x2 + 6x – 8?
O {yly > -1}
O {yly < -1}
O {yly > -11}
O {yly < -11}
Answer:
Range → {y| y ≥ -11}
Step-by-step explanation:
Range of a function is the set of of y-values.
Given function is,
f(x) = 2x² + 6x - 8
By converting this equation into vertex form,
f(x) = [tex]3(x^2+2x-\frac{8}{3})[/tex]
= [tex]3(x^2+2x+1-1-\frac{8}{3})[/tex]
= [tex]3[(x+1)^2-\frac{11}{3}][/tex]
= [tex]3(x+1)^2-11[/tex]
Vertex of the parabola → (-1, -11)
Therefore, range of the function will be → y ≥ -11
The range of the function f(x) = 3x² + 6x - 8 is {y|y ≥ -11}
What is the range of a function?The range of a function is the set of output values of the function
Since f(x) = 3x² + 6x - 8, we differentiate f(x) = y with respect to x to find the value of x that makes y minimum.
So, df(x)/dx = d(3x² + 6x - 8)/dx
= d(3x²)/dx + d6x/dx - d8/dx
= 6x + 6 + 0
= 6x + 6
Equating the experssion to zero, we have
df(x)/dx = 0
6x + 6 = 0
6x = -6
x = -6/6
x = -1
From the graph, we see that this is a minimum point.
So, the value of y = f(x) at the minimum point is that is a t x = - 1 is
y = f(x) = 3x² + 6x - 8
y = f(-1) = 3(-1)² + 6(-1) - 8
y = 3 - 6 - 8
y = -3 - 8
y = -11
Since this is a minimum point for the graph, we have that y ≥ -11.
So, the range of the function is {y|y ≥ -11}
So, the range of the function f(x) = 3x² + 6x - 8 is {y|y ≥ -11}
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Sam is making a table of values and a graph for the equation 16x + y = −48. He says that when x = 3, y = 0. Is Sam correct?
Answer:
No
Step-by-step explanation:
16x + y = −48
Substitute the point into the equation and see if it is true
16(3) +0 = -48
48 = -48
This is not true so the point is not a solution
Help plz help needed i need the answer
Answer:
x = ±sqrt(26)
Step-by-step explanation:
ln ( x^2 -25) = 0
Raise each side to base e
e^ln ( x^2 -25) = e^0
x^2 -25 = 1
Add 25 to each side
x^2 -25 +25 = 1+25
x^2 = 26
Take the square root of each side
sqrt(x^2) = ±sqrt(26)
x = ±sqrt(26)
Answer:
The third option
Step-by-step explanation:
If we rewrite this in log form, we get
[tex]e {}^{0} = {x}^{2} - 25[/tex]
Remeber anything to the 0 power is 1, so simplifying the equation first
[tex]1 = {x}^{2} - 25[/tex]
Add 25 to both sides
[tex]26 = {x}^{2} [/tex]
Take the square root of both sides
[tex]x = \sqrt{26} [/tex]
Square root are both so
[tex]x = - \sqrt{26} [/tex]
Is also a answer.
The third option is the answer
The length of a rectangle is 4 in longer than its width.
If the perimeter of the rectangle is 32 in, find its area.
Answer:
60 sq in
Step-by-step explanation:
Perimeter = 2l + 2w
If l = w+4
Perimeter = 2(w+4) + 2w
Perimeter = 4w+8
32 = 4w + 8
24 = 4w
6 = w
If w = 6, l = 6+4 = 10
Area = l * w
Area = 10 * 6
Area = 60
The quantity demanded each month of the Walter Serkin recording of Beethoven's Moonlight Sonata, produced by Phonola Media, is related to the price per compact disc. The equation
p = −0.00051x + 5 (0 ≤ x ≤ 12,000)
where p denotes the unit price in dollars and x is the number of discs demanded, relates the demand to the price. The total monthly cost (in dollars) for pressing and packaging x copies of this classical recording is given by
C(x) = 600 + 2x − 0.00002x2 (0 ≤ x ≤ 20,000).
Hint: The revenue is
R(x) = px,
and the profit is
P(x) = R(x) − C(x).
Find the revenue function,
R(x) = px.
R(x) =
Answer:
[tex]R(x) = -0.00051x^2 + 5x[/tex]
[tex]P(x) = -0.00049x^2 + 3x-600[/tex]
Step-by-step explanation:
Given
[tex]p = -0.00051x + 5[/tex] [tex]\to[/tex] [tex](0 \le x \le 12,000)[/tex]
[tex]C(x) = 600 + 2x - 0.00002x^2[/tex] [tex]\to[/tex] [tex](0 \le x \le 20,000)[/tex]
Solving (a): The revenue function
We have:
[tex]R(x) = x * p[/tex]
Substitute [tex]p = -0.00051x + 5[/tex]
[tex]R(x) = x * (-0.00051x + 5)[/tex]
Open bracket
[tex]R(x) = -0.00051x^2 + 5x[/tex]
Solving (b): The profit function
This is calculated as:
We have:
[tex]P(x) = R(x) - C(x)[/tex]
So, we have:
[tex]P(x) =-0.00051x^2 + 5x - (600 + 2x - 0.00002x^2)[/tex]
Open bracket
[tex]P(x) =-0.00051x^2 + 5x -600 - 2x +0.00002x^2[/tex]
Collect like terms
[tex]P(x) = 0.00002x^2-0.00051x^2 + 5x - 2x-600[/tex]
[tex]P(x) = -0.00049x^2 + 3x-600[/tex]
establish this identity
Answer:
see explanation
Step-by-step explanation:
Using the identities
tan x = [tex]\frac{sinx}{cosx}[/tex] , sin²x = 1 - cos²x
sin2x = 2sinxcosx
Consider left side
cosθ × sin2θ
= [tex]\frac{sin0}{cos0}[/tex] × 2sinθcosθ ( cancel cosθ )
= 2sin²θ
= 2(1 - cos²θ)
= 2 - 2cos²θ
= right side , then established
Which is an x-intercept of the graph of the function?
Answer:
D
Step-by-step explanation:
X intercept=y=0. 0=tan(x-5pi/6). x-5pi/6=0, x=5pi/6
Evaluating functions (pic attached)
f(x) = 2x³ - 3x² + 7
f(-1) = 2(-1)³ - 3(-1)² + 7
=> f(-1) = 2(-1) - 3(1) + 7
=> f(-1) = -2 -3 + 7
=> f(-1) = 2
f(1) = 2(1)³ - 3(1)² + 7
=> f(1) = 2(1) - 3(1) + 7
=> f(1) = 2 -3 + 7
=> f(1) = 6
f(2) = 2(2)³ - 3(2)² + 7
=> f(2) = 2(8) - 3(4) + 7
=> f(2) = 16 - 12 + 7
=> f(2) = 11
Two containers designed to hold water are side by side, both in the shape of a
cylinder. Container A has a diameter of 10 feet and a height of 8 feet. Container B has
a diameter of 12 feet and a height of 6 feet. Container A is full of water and the water
is pumped into Container B until Container A is empty.
To the nearest tenth, what is the percent of Container B that is empty after the
pumping is complete?
Container A
play
Container B
10
d12
8
h6
O
Answer: Volume of Cylinder A is pi times the area of the base times the height
π r2 h = (3.1416)(4)(4)(15) = 753.98 ft3
Volume of Cylinder B is likewise pi times the area of the base times the height
π r2 h = (3.1416)(6)(6)(7) = 791.68 ft3
After pumping all of Cyl A into Cyl B
there will remain empty space in B 791.68 – 753.98 = 37.7 ft3
The percentage this empty space is
of the entire volume is 37.7 / 791.68 = 0.0476 which is 4.8% when rounded to the nearest tenth
.
Step-by-step explanation: I hope that help you.
Note: you may not need to type in the percent sign.
===========================================================
Explanation:
Let's find the volume of water in container A.
Use the cylinder volume formula to get
V = pi*r^2*h
V = pi*5^2*8
V = 200pi
The full capacity of tank A is 200pi cubic feet, and this is the amount of water in the tank since it's completely full.
We have 200pi cubic feet of water transfer to tank B. We'll keep this value in mind for later.
-----------------------
Now find the volume of cylinder B
V = pi*r^2*h
V = pi*6^2*6
V = 216pi
Despite being shorter, tank B can hold more water (since it's more wider).
-----------------------
Now divide the results of each section
(200pi)/(216pi) = 200/216 = 25/27 = 0.9259 = 92.59%
This shows us that 92.59% of tank B is 200pi cubic feet of water.
In other words, when all of tank A goes into tank B, we'll have tank B roughly 92.59% full.
This means the percentage of empty space (aka air) in tank B at this point is approximately 100% - 92.59% = 7.41%
Then finally, this value rounds to 7.4% when rounding to the nearest tenth of a percent.
10v-6v=28
Simplify your answer as much as possible
Step-by-step explanation:
10v-6v=28
4v=28
v=28/4
v=7
Answer:
10v-6v=28
or, 4v = 28
or, v = 28/4
or, v = 7
hence 7 is the required value of v
if √3CosA = sin A , find the acute angle A
Answer:
Here is your answer.....
Hope it helps you....
Which statement is true about the slope of the graphed line?
Answer: positive
Step-by-step explanation: because it is going up from the left to the right
2 squared plus b squared equal 256
Answer:
[tex]2^2+b=256[/tex]
b=252
Step-by-step explanation:
[tex]2^2+b=256[/tex]
4+b=256
b=252
I wasn't very sure about what you are asking, but I hope this helps!
A subcommittee of six is to be selected from a committee containing 10 democrats and 12 republicans. In how many ways can at least 1 democracy be selected for the subcommittee?
Answer:
the number of ways to select at least 1 democrat in the subcommittee is 69,486 ways
Step-by-step explanation:
Given;
number of the subcommittee, = 6
number of democrats = 10
number of republicans, = 12
The number of ways to select at least 1 democrat in the subcommittee is calculated as follows;
Let D represent Democrats
let R represent Republicans
= (1D & 5R) or (2D & 4R) or (3D & 3R) or (4D & 2R) or (5D & 1R) or (6D)
= 10C₁ x 12C₅ + 10C₂ x 12C₄ + 10C₃ x 12C₃ + 10C₄ x 12C₂ + 10C₅ x 12C₁ + 10C₆
[tex]=( \frac{10!}{9!1!} \times \frac{12!}{7!5!} )+ (\frac{10!}{8!2!} \times \frac{12!}{8!4!})+ (\frac{10!}{7!3!} \times \frac{12!}{9!3!})+ (\frac{10!}{6!4!} \times \frac{12!}{10!2!})+ (\frac{10!}{5!5!} \times \frac{12!}{11!1!}) \\\\ +(\frac{10!}{4!6!})\\\\= (7,920) + (17,820) + (26,400) + (13,860)+ (3,276) + (210)\\\\= 69,486 \ ways[/tex]
Therefore, the number of ways to select at least 1 democrat in the subcommittee is 69,486 ways
