There are 4 elements in the set A and 8 elements in set B that is n(A) = 4 and n(B) = 8
Cardinality of a setThis is the total number of elements in a set. Given the following sets;
A = {c, d, e, f}
B = {odd numbers greater than 5 and less than 23}
B = {7,9,11,13, 15, 17, 19, 21}
Since there are 4 elements in the set A and 8 elements in set B hence n(A) = 4 and n(B) = 8
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I need help please to get my HS diploma...did not graduate :(
Which of the following equations has roots x=−2, x=3 (multiplicity 2), and x=1, and passes through the point (0,-18)?
f(x) = x^4 - 5x^3 + x^2 + 21x - 18
=======================================================
Explanation:
The root x = -2 means x+2 is a factor. This is because we add 2 to both sides of x = -2 to get x+2 = 0.
Similarly, x = 3 leads to x-3 being another factor. It's a double root so we really have two copies of (x-3)
The last root is x = 1 which gives the factor x-1.
The four factors are: (x+2)(x-3)(x-3)(x-1)
Let's use the FOIL rule to expand out the first two factors
(x+2)(x-3) = x^2-3x+2x-6 = x^2-x-6
Do the same for the last two factors
(x-3)(x-1) = x^2-1x-3x+3 = x^2-4x+3
--------------------
So far we have:
(x+2)(x-3) = x^2-x-6
(x-3)(x-1) = x^2-4x+3
which leads to
(x+2)(x-3)(x-3)(x-1) = (x^2-x-6)(x^2-4x+3)
From here I'll use the box method to multiply these trinomials. Check out the diagram below. Each inner cell is the result of multiplying the headers. Example: x^2 times x^2 = x^4 in the upper left corner.
I've color-coded the inner cells to show the like terms. Add up those like terms:
-4x^3 + (-x^3) = -5x^33x^2 + (4x^2) + (-6x^2) = x^2-3x + 24x = 21xTherefore we end up with
(x^2-x-6)(x^2-4x+3) = x^4 - 5x^3 + x^2 + 21x - 18 which is choice B
--------------------
To verify this answer, plug in x = 0 and you should get y = -18 to show that we have the correct y intercept. If we tried this with choice A, then we'd get y = 18 which helps eliminate choice A.
Furthermore, plug in x = -2 into choice B and you should get y = 0 as an output. The same applies to x = 3 and x = 1. This confirms that they are roots or x intercepts of the polynomial.
Another way to verify the answer is to use something like WolframAlpha to type in (x+2)(x-3)(x-3)(x-1). Under the "expanded form" subsection, it says x^4 - 5x^3 + x^2 + 21x - 18
The Campbell Company is considering adding a robotic paint sprayer to its production line. The sprayer's base price is $1,020,000, and it would cost another $22,000 to install it. The machine falls into the MACRS 3-year class, and it would be sold after 3 years for $599,000. The MACRS rates for the first three years are 0.3333, 0.4445, and 0.1481. The machine would require an increase in net working capital (inventory) of $19,500. The sprayer would not change revenues, but it is expected to save the firm $386,000 per year in before-tax operating costs, mainly labor. Campbell's marginal tax rate is 25%. (Ignore the half-year convention for the straight-line method.) Cash outflows, if any, should be indicated by a minus sign. Do not round intermediate calculations. Round your answers to the nearest dollar. What is the Year-0 net cash flow? $ What are the net operating cash flows in Years 1, 2, and 3? Year 1: $ Year 2: $ Year 3: $ What is the additional Year-3 cash flow (i.e, the after-tax salvage and the return of working capital)? $ If the project's cost of capital is 11%, what is the NPV of the project? $ Should the machine be purchased? -Select-
1. The Year-0 net cash flow is -$1,061,500.
2. The net operating cash flows in Years 1, 2, and 3 are as follows:
Year 1: $288,750 ($386,000 x 1 - 0.25)
Year 2: $288,750 ($386,000 x 1 - 0.25)
Year 3: $288,750 ($386,000 x 1 - 0.25)
3. The additional Year-3 cash flow (i.e, the after-tax salvage and the return of working capital) is $468,750 {($599,000 x 1 - 0.25) + $19,500}.
4. The NPV of the project is ($13,139).
5. The machine should not be purchased because it does not yield a positive NPV.
What is the net present value?The net present value (NPV) shows the difference between the present value of cash inflows and the present value of cash outflows over a period of time.
It is determined by calculating the present values of cash flows using their present value factors as below:
Data and Calculations:Initial cash outlay = $1,061,500 ($1,020,000 + $22,000 + $19,500)
Salvage value = $599,000
Increase in net working capital = $19,500
Annual savings before tax = $386,000
Tax rate = 25%
Annuial savings after tax = $288,750 ($386,000 x 1 - 0.25)
Determination of Net Present Value (NPV):Year Cashflows PV Factor Present Value
0 -$1,061,500 1 -$1,061,500
1 $288,750 0.901 $260,164
2 $288,750 0.812 $234,465
3 $288,750 0.731 $211,076
3 $468,750 0.731 $342,656
Net present value -$13,139
Thus, the project should not be undertaken by The Campbell Company due to the negative NPV that it yields.
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Which of the following are reasons used in the proof that the angle-bisector
construction can be used to bisect any angle?
Check all that apply.
0 A. All of the radii of a circle
are congruent.
. B. SSS triangle congruence postulate
. C. Any line segment can be extended
indefinitely.
. D. CPCTC
The angle-bisector construction can be used to bisect any angle and this is proven by:
A. All of the radii of a circle are congruent.B. SSS triangle congruence postulate. D. CPCTC.What is the proof that the angle-bisector construction can bisect any angle?The angle-bisector construction means that a line is made that can divide an angle into two congruent angles.
This is shown by the fact that all the radii of a circle are congruent and that the corresponding parts of congruent triangles are also congruent (CPCTC) when an angle bisector is made on a circle or triangle respectively.
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Mark decided to make Christmas presents for his classmates. he bought 10lb of two types of candies: caramel candies for $2.80 per pound and chocolate candies for $3.50 a pound.
Write a function f(x) that represents the total cost of candy, where x is the weight of the less expensive candy
Brainliest for correct answer
The function for the given situation is f(x)=35.0-0.7x.
Given that, Mark bought 10 pound of two types of candies, caramel candies for $2.80 per pound and chocolate candies for $3.50 a pound.
What is the function?Functions are the fundamental part of the calculus in mathematics. The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x.
Now, the function for the given situation is as follows:
If x is the weight of the less expensive candy, the 10-x is the weight of the high expensive candy.
So, f(x)=2.80x+3.50(10-x)
⇒ f(x)=2.80x+35.0-3.50x
⇒ f(x)=35.0-0.7x
Therefore, the function for the given situation is f(x)=35.0-0.7x.
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Find the monthly interest payment in the situation described below. Assume that the monthly interest rate is 1 divided by 12 of the annual interest rate.
You maintain an average balance of $675 on your credit card, which carries a 24%
annual interest rate.
The monthly interest payment is
The monthly interest payment is 162
What is Interest?Interest, in its most simple form, is calculated as a percent of the principal.
First,
monthly interest rate,
= 0.24/12
= 0.02.
Now,
Average monthly interest,
=0.02×$675
= $13.50.
Thus, the annual interest payments,
= 12×$13.50
= $162
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Find any stationary points of the graph of [tex]y = 2x^2 + e^-x^4[/tex]
[tex]y = 2x {}^{2} + e {}^{ - x {}^{4} } [/tex]
[tex] \frac{dy}{dx} = 4x +( e {}^{ - x {}^{4} } )( - 4x {}^{3} )[/tex]
[tex] \frac{dy}{dx} = 4x - 4x {}^{3} e { }^{ - x {}^{4} } [/tex]
[tex] \frac{dy}{dx} = 4x(1 - x {}^{2} e {}^{ - x {}^{4} } )[/tex]
[tex] \frac{dy}{dx} = 0 \\ 4x = 0 \: \: \: \: \: 1 - x {}^{2} e {}^{ - x {}^{4} } = 0[/tex]
[tex]4x = 0 \\ x = 0 \: \: \: \: \: \: y(0) = 0 + e {}^{0} = 1[/tex]
[tex] \frac{x {}^{2} }{e {}^{x {}^{4} } } = 1 \\ x {}^{2} = e {}^{x {}^{4} } \\ 2ln(x) = x {}^{4} \\ these \: 2 \: functions \: do \: not \: intersect[/tex]Stationary point ( 0 , 1 )-7 + p = 3 for p
help before my dad comes home
Answer:
p=10
Step-by-step explanation:
-7+p=3
+7-7+p=3+7
p=10
Answer:
Hello! The answer to this question is 10.
Step-by-step explanation:
You have to get p by itself so we will add 7 to both sides:
-7 + p = 3
+7 +7
-------------
p = 10
When doing so, we get p = 10.
You can check your work:
-7 + 10 ⇒ 10 - 7 = 3
Therefore, p = 10 is the correct answer.
For the polynomial function ƒ(x)= −2x2 − 4x + 16, find all local and global extrema.
For the given quadratic equation we only have a maximum at y = 18.
How to find the extrema of the given function?
Here we have:
[tex]f(x) = -2x^2 - 4x + 16[/tex]
Notice that this is a quadratic equation of negative leading coefficient.
Then we have a maximum at the vertex, and both arms tend to negative infinity as x tends to infinity or negative infinity.
The vertex is at:
x = -(-4)/(2*(-2)) = -1
The maximum is:
[tex]f(-1) = -2*(-1)^2 - 4*(-1) + 16 = -2 + 4 + 16 = 18[/tex]
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factor equation. answer is second picture. I do not know to get there though. step by step. f=3-2(3a)^(2) is the equation.
Answer:
[tex]f=-18a^2+3[/tex]
Step-by-step explanation:
Given equation:
[tex]f=3-2(3a)^2[/tex]
[tex]\textsf{Apply exponent rule} \quad (ab)^n=a^n b^n:[/tex]
[tex]\implies f=3-2(3^2a^2)[/tex]
Rewrite 3² as 9:
[tex]\implies f=3-2(9a^2)[/tex]
Remove the parentheses:
[tex]\implies f=3-2 \cdot 9a^2[/tex]
Multiply the numbers 2 · 9 = 18 :
[tex]\implies f=3-18a^2[/tex]
Rearrange to make the variable the first term:
[tex]\implies f=-18a^2+3[/tex]
one of the two of A two digit is three times the other digit. if you interchange the digits of this two digit number and add the resulting number to the original number you get 88.what is the original number. give solution
ASAP PLEASE
Given that, one digit of a two digit number is three times the other digit.
Let assume that digit at ones place be x.
digit at ones place be x.So, digit at tens place be 3x.
digit at ones place be x.So, digit at tens place be 3x.So, two digit original number = 10 × 3x + 1 × x = 30x + x = 31x
Now, number formed on interchanging its digits, i.e.
Reverse number = 10 × x + 1 × 3x = 10x + 3x = 13x
According to statement, if we interchange the digits of this two digit number and add the resulting number to the original number, we get 88.
[tex]\begin{gathered}\sf \: 31x + 13x = 88 \\ \\ \end{gathered}[/tex]
[tex]\begin{gathered}\sf \: 44x = 88 \\ \\ \end{gathered}[/tex]
[tex]\begin{gathered}\sf \: x = \dfrac{88}{44} \\ \\ \end{gathered}[/tex]
[tex]\begin{gathered}\sf\implies \: x = 2 \\ \\ \end{gathered}[/tex]
So, two digit number is 31 × 2 = 62
Hence,
[tex]\begin{gathered}\sf\implies \: \boxed{ \bf{ \:Original \: number \: = \: 62 \: \: }} \\ \\ \end{gathered}[/tex]
[tex]\rule{190pt}{2pt}[/tex]
Answer:
26 or 62
Step-by-step explanation:
If one of the two digits of a two-digit number is three times the other digit, then the options for the two-digit number are:
13 or 3126 or 6239 or 93If you interchange the digits of this two-digit number and add the resulting number to the original number, you get 88.
From inspection of the listed pairs of numbers, the only pair that sums to 88 is 26 and 62:
⇒ 26 + 62 = 88
Therefore, the original number is either 26 or 62.
https://what is answer for let x,y,z be three natural number .such that x
The combinations of ordered triplets that are possible is equal to: A. 18.
How to find the possible number of ordered triplet?Since the common difference (d) between the consecutive terms in an arithmetic progression (AP) is constant, we have:
d = y - x = z - y
Rearranging the terms, we have:
x = y - d
z = y + d
From the given equation:
x + y + z = 30
y - d + y + y + d = 30
3y = 30
y = 30/3
y = 10.
So the arithmetic progression (AP) is given by:
(10 - d), 10, (10 + d)....
Since the common difference (d) is a natural number which would be from 1 to 9, the combinations of ordered triplets that are possible is as follows:
Number of possibilities = 9 × 2
Number of possibilities = 18.
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Complete Question:
If x, y, z are three natural numbers in A.P. such that x + y + z = 30 then the possible number of ordered triplet (x, y, z) is?
A. 18
B. 19
C. 20
D. 21
3 squares are positioned to form a triangle. the small square is labeled 6 units, medium square is 8 units, and large square is not labeled. answer these questions about the right triangle. what is the area of the square of the leg 6? what is the area of the square of the leg 8? what is the area of the hypotenuse square? what is the length of the hypotenuse?
The area of the square of the leg 6 is 36 square units.
The area of the square of the leg 8 is 64 square units.
The area of the square of the hypotenuse square is 100 square units.
The length of the hypotenuse is 10 units.
Formula Used
Area of square, A = [tex](a)^{2}[/tex]
Here, [tex]a[/tex] is the length of the side of the square.
Pythagoras Theorem is given as,
[tex]h^{2} =p^{2} +b^{2}[/tex]
Here, [tex]h, p, b[/tex] are the hypotenuse, perpendicular, and the base of a right angle triangle respectively.
Area of the Square of the Leg 6
Length of the edge of the square = 6 units
Area of square = 6*6
= 36 square units
Area of the Square of the Leg 8
Length of the edge of the square = 8 units
Area of square = 8*8
= 64 square units
Area of the Hypotenuse Square and the Length of the Hypotenuse
Applying Pythagoras theorem,
[tex]h^{2} = (8)^{2} +(6)^{2}[/tex]
[tex]h^{2} = 64+36[/tex]
[tex]h = \sqrt{100}[/tex]
[tex]h = 10 units[/tex]
Therefore, the area of the hypotenuse square is 100 square units and the length of the hypotenuse comes out to be10 units.
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Answer: in the picture
Step-by-step explanation:
A curve goes from 8 to 20 on the x-axis.
What would the height need to be for this curve to be a density curve?
StartFraction 1 Over 8 EndFraction
StartFraction 1 Over 12 EndFraction
StartFraction 1 Over 20 EndFraction
1
Picture posted below…
Answer: 1/12
Step-by-step explanation:
The total area of the rectangle needs to be 1.
Since 20-8=12, the height needs to be 1/12.
Find 62% of 300
18.6
1.9
186
18.7
Which systems of equations have no solution?
Answer:
same slope, different intercepts (parallel lines essentially)
Step-by-step explanation:
Patricia's garden is surrounded by a fence. What is the perimeter of the
fence?
Answer:
The perimeter of the garden is [tex]12a[/tex].
Step-by-step explanation:
[tex]3a+14+4(a-6)+10+5a=12a[/tex]
Order the following numbers from least to greatest.
4.12310562562 4.5 4.23
Answer:
4.12310562562, 4.23, 4.5
Compute the probability of drawing two spades from a deck of cards
In a playing card there are 52 cards. (i) '2' of spades: Number of favourable outcomes i.e. '2' of spades is 1 out of 52 cards.
MATH: GRAPHS AND FUNCTIONS...HELP!
Solution: Check the picture I uploaded.
Anne has n pairs of shoes, and Fiona has 3 times as
many pairs of shoes. If Fiona gives Anne 6 pairs of
shoes, the girls will have an equal number of shoes.
How many pairs of shoes did Anne have originally?
Answer:
Anne has n
Fiona has 3n
3n=6
so n=2
so Anne have 2
Write the equation of the line that passes through the points (1,1) and (2,4). Write your answer in slope intercept form. Step by step please
Answer: y = 3x - 2
Step-by-step explanation:
gradient = (4 - 1)/(2 - 1) = 3/1 = 3
y = 3x + c needs to work for both points
Substitute (1,1) into equation
1 = 3 x 1 + c
c = 1 - 3 = -2
y = 3x - 2
Refrigerators-’N-More sells appliances with a 20% markup from their purchase cost. Alice makes a 5% commission rate on her daily sales. If the store buys a washer and dryer set for $600, what would Alice’s commission be if she sold those appliances?
The price of the washer and dryer set after the markup is
.
The amount of Alice’s commission would be
The price of the washer and the dryer set is $720.
The commission earned by Alice is $36.
What is the price of the washer and dryer set ?Percentage can be described as a fraction an amount expressed as a number out of hundred. Percentage is a measure of frequency.
Price after the mark up = ( + percentage mark up) x cost price
(1 + 0.20) x $600 = $720
Commission earned by Alice = 5% x 720 = $36
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Choose the number sentence that applies the commutative property to the example.
3 × 4 = 12
6 + 6 = 12
12 × 1 = 12
6 × 2 = 12
4 × 3 = 12
The number sentence that applies the commutative property to the example is 4 × 3 = 12
Commutative propertyCommutative property can be additive or multiplicative. It is a way of changing the position of a function or value in an expression without affecting the result
Examples are
A +B = B +A
AB = BA
Although the value were interchanged, the result were not affected. Hence the number sentence that applies the commutative property to the example is 4 × 3 = 12 since changing 3 and 4 does not affect the result
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Find the H.C.F. of the following expressions:36(x³+x²y-12xy²), 54(x³y+4x³y²-21xy)
Answer:
18x
Step-by-step explanation:
The HCF is the highest factor common to both expressions. We can find it by factoring both expressions and identifying common factors.
Factorization
36(x³+x²y-12xy²) = 18x·2·(x +4y)(x -3y)
54(x³y+4x³y²-21xy) = 18x·3y·(x +7)(x -3)
The highest common factor is 18x.
c = √a² + b². This is the formula for the length of the hypotenuse c of a right triangle. Solve this formula for a.
Answer:
a = sqrt(c^2 - b^2)
see image.
Step-by-step explanation:
If you square both sides of the equation, you get the Pythagorean Theorem back again.
c = sqrt(a^2 + b^2)
c^2 = a^2 + b^2
Solve for a means to get a all by itself on one side of the equation. Subtract b^2 and then take the square root. See image.
simplify the expression
Answer:
-4sin(2x)
Step-by-step explanation:
Angle sum identities can be used to simplify this expression.
cos(a+b) = cos(a)cos(b) -sin(a)sin(b)sin(a+b) = sin(a)cos(b) +sin(b)cos(a)sin(2x) = 2sin(x)cos(x)NumeratorThe cosine function is even, so cos(-x) = cos(x). The cosine of the sum is ...
cos(90°+x) = cos(90°)cos(x) -sin(90°)sin(x) = -sin(x)
Then the numerator simplifies to ...
4cos(-x)cos(90°+x) = -4cos(x)sin(x) = -2sin(2x)
DenominatorMatching the denominator expression to the sine of a sum relation, we see
sin(30° -x)cos(x) +sin(x)cos(30° -x) = sin((30°-x) +x) = sin(30°) = 1/2
Simplified ExpressionThe simplified expression is the ratio of the simplified numerator to the simplified denominator:
= -sin(2x)/(1/2)
= -4sin(2x)
Express - 6 + √25 as a complex number in the form a + bi.
- 6 + √-25 =
Answer:
[tex]-6+5i[/tex]
Step-by-step explanation:
[tex]-6+\sqrt{-25}\\\\=-6+5i[/tex]
When finding the area of a rectangular prism, do you prefer to find the area of the base first and then multiply it by the height or to multiply all three dimensions at once?
Answer: I prefer to find the area of the base first and then multiply by the height
PLS HELP WITH THIS ILL GIVE BRAINLIEST
Answer:
bbStep-by-step explanation:
The vertex and direction of opening can be read from the vertex-form equation of a quadratic.
Direction of openingConsider the "parent" quadratic function ...
y = x²
For this function, the value of y cannot be negative. Larger positive values of x will give larger positive values of y. And, negative values of x that have greater magnitude (are farther from the y-axis) will also give larger positive values of y.
This means that the farther away from the y-axis an x-value is, the farther away from the x-axis is the corresponding y-value. The graph of this is said to "open upward." This will be the case for any positive coefficient of x². (Red graph in the first attachment.)
If the coefficient of x² is negative, then larger-magnitude x-values result in more negative y-values. This makes the graph "open downward." (Blue graph in the first attachment.)
VertexThe vertex form of a quadratic equation is ...
y = a(x -h)² +k . . . . . . vertex (h, k); vertical scale factor 'a'
The value of 'a' is the coefficient of the x² term when this is simplified to standard form: y = ax² +bx +c. That is, the sign of 'a' tells you whether the graph opens upward (a > 0) or downward (a < 0).
The other constants in the vertex form equation tell you how the function has been translated. The value of k is a vertical translation quantity. Since it is added to each function value, it tells the number of units the function is translated upward.
The value h is a horizontal translation quantity. It seems slightly counter-intuitive that the function graph is translated to the right h units when h is subtracted from the x-value. That is the case.
As you may have noticed from the graphs in the first attachment, the vertex (turning point) of the parent function graph is at (x, y) = (0, 0). The vertex of the function ...
y = a(x -h)² +k
is located at (x, y) = (h, k).
1.You want the opening direction of y = -2(x +3)² -1. You need look no further than the leading minus sign. It tells you the graph opens downward. (Red graph in the second attachment.)
Of course, the -1 at the end of the equation is the vertical translation of the vertex. That vertex is (-3, -1), as shown by the graph.
2.You want the vertex of y = -1/2(x +5)² +7. Writing this so the binomial term has a minus sign, we have ...
y = -1/2(x -(-5))² +7
Comparing this to the vertex form ...
y = a(x -h)² +k
we identify the parameters to be ...
a = -1/2 . . . . opens downward
h = -5
k = 7 . . . . the vertex is (h, k) = (-5, 7)
The graph is the blue graph in the second attachment. It opens downward and has its vertex at (-5, 7).
__
Additional comment
A lot of math is about matching patterns. Here, you're asked to match the given equations to the "vertex form" pattern, and identify corresponding parts of the pattern: the leading coefficient (a), the horizontal translation (h), and the vertical translation (k). Once you know what the parts of the pattern mean, you can answer the questions easily.
If Art has a 7/1 ARM, how long will the fixed interest rate be applied to his loan?
Answer:
step-by-step explanation:
A 7/1 ARM is a mortgage that has a fixed interest rate in the beginning, then switches to an adjustable or variable one. The 7 in 7/1 indicates the initial fixed period of seven years. After that, the interest rate adjusts once yearly based on the index stated in the loan agreement, plus a margin set by the lender.