Front (a)
Side 1 (a)
Side 2 (a)
the value of (-1+√-3)³³+(-1-√-3)³³
The value of \(\displaystyle\sf (-1+\sqrt{-3})^{33}+(-1-\sqrt{-3})^{33}\) is approximately -2.
One-eighth of a number is -4,200.
What is the number?
-42,800
-37,800
-33,600
-42,000
Answer:
33,600
Step-by-step explanation:
take -4200 and multiply it by 8. You'd do this since the equation to get -4200 is
x(1/8) = -4200
multiply both sides by 8 to get rid of the fraction and you get x=33,600
What is the inverse function of f(x) = 4x + 3? A) f(x)-1 = x - 3 4 B) f(x)-1 = x - 4 3 C) f(x)-1 = 1 3 x + 3 D) f(x)-1 = 1 4 x - 4
Answer:
Step-by-step explanation:
The inverse of a trigonometric function f may be indicated using the inverse function ... For what value of k, if any, is f continuous at x = 2 ? (A) 1. (B) 2. (C) 3. (D) 7 ... X + 2 x ² + 1 dx. 3x + 2 X. + x. +C constant.
What is the first digit quotient for 18.6
Please respond ASAP
Answer: 18.6 is your answer because there is nothing behind the 6
Step-by-step explanation: hope this help :)
NO LINKS!!
1. Is it possible for the sequence t(n) = 5·2ⁿ to have a term with the value of 200? If so, which term is it? If not, justify why not.
2. Is it possible for the function f(x) = 5·2ˣ to have an output of 200? If so, what input gives this output? If not, justify why not.
Answer:
1) No,2) Yes, x ≈ 5.32-----------------------------
Part 1Given sequence:
t(n) = 5 · 2ⁿIf t(n) = 200, we can try to find the value of n:
5 · 2ⁿ = 2002ⁿ = 40There is no integer solution, since 32 < 40 < 64 or 2⁵ < 40 < 2⁶, the value of n should be between 5 and 6.
The sequence should include integer numbers, so there is no solution.
Part 2Given function:
f(x) = 5 · 2ˣSolve for x if f(x) is 200:
5 · 2ˣ = 2002ˣ = 40log 2ˣ = log 40x log 2 = log 40x = log 40 / log 2x = 5.32 (rounded)Answer:
1. No
\(\textsf{2.} \quad x=\dfrac{\ln 40}{\ln 2} \approx5.32\;(\sf 2\;d.p.)\)
Step-by-step explanation:
Question 1Given sequence:
\(t(n)=5 \cdot 2^n\)
To determine if the sequence has a term with a value of 200, substitute t(n)=200 into the equation and solve for n:
\(\implies 5 \cdot 2^n=200\)
\(\implies 2^n=40\)
\(\implies \ln 2^n=\ln 40\)
\(\implies n\ln 2=\ln 40\)
\(\implies n=\dfrac{\ln 40}{\ln 2}\)
\(\implies n=5.3219280...\)
In a sequence, n is a positive integer. Therefore, it is not possible for the sequence to have a term with the value of 200, as when t(n)=200, n is not a positive integer.
Question 2Given function:
\(f(x)=5 \cdot 2^x\)
To determine if the function has an output of 200, substitute f(x)=200 into the function and solve for x:
\(\implies 5 \cdot 2^x=200\)
\(\implies 2^x=40\)
\(\implies \ln 2^x=\ln 40\)
\(\implies x=\dfrac{\ln 40}{\ln 2}\)
\(\implies x=5.3219280...\)
Therefore, it is possible for the function to have an output of 200 when:
\(x=\dfrac{\ln 40}{\ln 2}\)
4. In a class of 35 students, 20 offer Physics,
18 offer Chemistry and 2 offer neither
Physics nor Chemistry
1) Illustrate the information on a Venn
diagram
il) How many students offer all the two
subjects?
1) How many students offer Physics!
1) How many students offer only one
subject
5 students offers all the two subjects.
Student that offers Physic only = 15 students
Student that offers chemistry only = 13 students
Students that offers only one subject = 28 students
How to solve a Venn diagram?Total student in the class = 35
20 offer physics.
18 offer chemistry
2 offer neither physics nor chemistry.
Therefore,
x = student that offer both subject
35 = 20 + 18 - x + 2
35 - 2 - 20 - 18 = -x
-5 = -x
x = 5
Therefore, 5 students offers all the two subjects.
Student that offers Physic only = 20 - 5 = 15
Student that offers chemistry only = 18 - 5 = 13
Students that offers only one subject = 13 + 15 = 28
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Find y' for the following.
Answer:
\(\displaystyle y' = \frac{5x - 2xy^2}{2y(x^2 - 3y)}\)
General Formulas and Concepts:
Calculus
Differentiation
DerivativesDerivative NotationDerivative Property [Multiplied Constant]: \(\displaystyle \frac{d}{dx} [cf(x)] = c \cdot f'(x)\)
Derivative Property [Addition/Subtraction]: \(\displaystyle \frac{d}{dx}[f(x) + g(x)] = \frac{d}{dx}[f(x)] + \frac{d}{dx}[g(x)]\)
Basic Power Rule:
f(x) = cxⁿf’(x) = c·nxⁿ⁻¹Derivative Rule [Product Rule]: \(\displaystyle \frac{d}{dx} [f(x)g(x)]=f'(x)g(x) + g'(x)f(x)\)
Derivative Rule [Chain Rule]: \(\displaystyle \frac{d}{dx}[f(g(x))] =f'(g(x)) \cdot g'(x)\)
Implicit Differentiation
Step-by-step explanation:
Step 1: Define
Identify
\(\displaystyle 5x^2 - 2x^2y^2 + 4y^3 - 7 = 0\)
Step 2: Differentiate
Implicit Differentiation: \(\displaystyle \frac{dy}{dx}[5x^2 - 2x^2y^2 + 4y^3 - 7] = \frac{dy}{dx}[0]\)Rewrite [Derivative Property - Addition/Subtraction]: \(\displaystyle \frac{dy}{dx}[5x^2] - \frac{dy}{dx}[2x^2y^2] + \frac{dy}{dx}[4y^3] - \frac{dy}{dx}[7] = \frac{dy}{dx}[0]\)Rewrite [Derivative Property - Multiplied Constant]: \(\displaystyle 5\frac{dy}{dx}[x^2] - 2\frac{dy}{dx}[x^2y^2] + 4\frac{dy}{dx}[y^3] - \frac{dy}{dx}[7] = \frac{dy}{dx}[0]\)Basic Power Rule [Product Rule, Chain Rule]: \(\displaystyle 10x - 2 \Big( \frac{d}{dx}[x^2]y^2 + x^2\frac{d}{dx}[y^2] \Big) + 12y^2y' - 0 = 0\)Basic Power Rule [Chain Rule]: \(\displaystyle 10x - 2 \Big( 2xy^2 + x^22yy' \Big) + 12y^2y' - 0 = 0\)Simplify: \(\displaystyle 10x - 4xy^2 - 4x^2yy' + 12y^2y' = 0\)Isolate y' terms: \(\displaystyle -4x^2yy' + 12y^2y' = 4xy^2 - 10x\)Factor: \(\displaystyle y'(-4x^2y + 12y^2) = 4xy^2 - 10x\)Isolate y': \(\displaystyle y' = \frac{4xy^2 - 10x}{-4x^2y + 12y^2}\)Simplify: \(\displaystyle y' = \frac{5x - 2xy^2}{2y(x^2 - 3y)}\)Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Differentiation
Book: College Calculus 10e
The hole for a support needs to be6 feet deep. It is currently 2 feet 9 inches deep. How much deeper must the hole be. Use the conversion factor 12 inches/ 1 foot
The hοle needs tο be 39 inches deeper.
What is the cοnversiοn factοr?A cοnversiοn factοr is a number used tο change οne set οf units tο anοther, by multiplying οr dividing. When a cοnversiοn is necessary, the apprοpriate cοnversiοn factοr tο an equal value must be used. Fοr example, tο cοnvert inches tο feet, the apprοpriate cοnversiοn value is 12 inches equals 1 fοοt.
The current depth οf the hοle is 2 feet 9 inches, which is the same as 2 + 9/12 = 2.75 feet (since there are 12 inches in 1 fοοt).
Tο find οut hοw much deeper the hοle needs tο be, we need tο subtract the current depth frοm the required depth:
6 feet - 2.75 feet = 3.25 feet
Hοwever, we are asked tο express the answer in inches, sο we need tο cοnvert the 3.25 feet tο inches using the given cοnversiοn factοr:
3.25 feet x 12 inches/1 fοοt = 39 inches
Therefοre, the hοle needs tο be 39 inches deeper.
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Bob took his family out to lunch. He bought 3 hot dogs and 2 hamburgers for $11. If the guy in front of him bought 2 hot dogs and 4 hamburgers for $16, what is the cost of one hamburger?
Answer:
Hotdog: $1.50
Hamburger: $3.25
Step-by-step explanation:
You write down the 2 equations based off of the information as I did:
Let x = cost of a hotdog
Let y = cost of a hamburger
and so:
3x + 2y = 11
2x + 4y = 16
Now, we need to find x and y:
We will make both equations equal to y to compare them to each other.
2y = 11 - 3x
y = 5.5 - 1.5x
4y = 16 - 2x
y = 4 - 0.5x
4 - 0.5x = 5.5 - 1.5x
x = $1.5
Now plugging in x into the equation:
2(1.5) + 4y = 16
3 + 4y = 16
4y = 13
y = $3.25
And so hotdog = $1.5 and hamburger = $3.25
Help me plss i don’t understand this
Answer:
See attached image, I vote for option A, but I agree it is a confusing question.
Step-by-step explanation:
See attached image.
will mark brainliest please this is urgent
Solve for w . p=w/t
Answer:
w = pt
Step-by-step explanation:
\(p=\frac{w}{t}\\\\p*t=\frac{w}{t}*t\\\\pt=w\\\\\boxed{w=pt;t\neq 0}\)
Hope this helps.
Which expression is equivalent to 27 + 45?
Answer:
8 x 9
Have a nice day!
in how many ways can be arranged 2 different words in necklace?
Answer:
3
Step-by-step explanation:
chain by chain
parllel
series
- Calculate CV for the following numbers: 5, 8, 9, 2, 6. OA. 40.82 B. 120 OC. 0.4083 OD. 1.2
The coefficient of variation or CV of the given numbers is 45.64%.
Given numbers are,
5, 8, 9, 2, 6
We have to find Coefficient of variation.
CV = (Standard deviation / sample mean ) × 100
Sample mean = Sum of the values / total number of values
= (5 + 8 + 9 + 2 + 6) / 5
= 6
Standard deviation = √[(Σ(x - mean)² / (n - 1)]
Σ(x - mean)² = (5 - 6)² + (8 - 6)² + (9 - 6)² + (2 - 6)² + (6 - 6)²
= 30
Standard deviation = √(30 / (5 - 1) = 2.7386
CV = (2.7386 / 6) × 100
= 45.64%
Hence CV is 45.64%.
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someoneplease help me
GIVING BRAINLIST TO FIRST RIGHT ANSWER
A. (4,-2)
B. (0,1)
C. (1,0)
D. (-1,0)
Answer:
C (1,0)
Step-by-step explanation:
Answer:
C. (1,0)
Step-by-step explanation:
When you go 3 to the left, you end up at (0, -2). When you go up 2, you get (1,0).
6 feet 8 inches divided by 2
Answer:
3 ft 4 in.
Step-by-step explanation:
6/2 = 3
8/2 = 4
6 ft 8 in. divided by 2 = 3 ft 4 in.
How many triangles can be constructed with sides measuring 15 cm, 7 cm, and 5 cm?
more than one
none
one
Answer:
More than one
Step-by-step explanation:
Trust me, I know.
Answer:
none
Step-by-step explanation:
i have proof i just took the test
The double number line shows that Toni can type 180 words in 2 minutes.
Based on the ratio shown in the double number line, how many words can Toni type in 3
minutes
Answer:
Toni can type 270 words in 3 minutes.
Step-by-step explanation:
Given that the double number line shows that Toni can type 180 words in 2 minutes, based on the ratio shown in the double number line, to determine how many words can Toni type in 3 minutes, the following calculation must be performed:
(180/2) x 3 = X
90 x 3 = X
270 = X
Thus, Toni can type 270 words in 3 minutes.
Write the fact family for 3, 4, and 12
Answer:
3×4=12
4×3=12
12÷3=4
12÷4=3
Step-by-step explanation:
This is a multiplication/division fact family
Multiplication and Division are inverse opperations
Hope this helps
Write the equation of the line in fully simplified slope-intercept form.
-12-11-10-9-
12
11
10
9
R
5
4
2
654-3-2-1
-2
3
4
-5
-6
-8
6
-10
-11
-12
34567 8 9 10 11 12
The equation of the line in fully simplified slope-intercept form is y = x + 7.
We have,
From the graph,
The coordinates of the line are:
(0, 7), (-7, 0), and (-2, 5).
We can use any coordinates the line touches on the graph.
We will use,
(0, 7) and (-7, 0)
The equation can be written in the form y = mx + c
m = (0 - 7) / (-7 - 0)
m = -7/-7
m = 1 ______(1)
And,
(0, 7) = (x, y)
So,
y = mx + c ______(2)
7 = 1 x 0 + c
7 = c
c = 7 ______(3)
Now,
From (1), (2), and (3).
y = x + 7
Thus,
The equation of the line in fully simplified slope-intercept form is y = x + 7.
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If the resistance in an electrical circuit is held constant, the amount of current flowing through the circuit varies directly as the amount of voltage applied to the circuit. When 8 volts are applied to a circuit, 160 milliamperes (mA) of current flow through the circuit. Find the new current if the voltage is increased to 9 volts.
The new current if the voltage is increased to 9 volts is given as follows:
0.18A = 180 mA.
What is Ohm's First Law?Ohm's First Law states that a circuit's voltage is obtained as the multiplication of the resistance and of the current, as follows:
V = RI.
In which:
V is the voltage.R is the resistance.I is the current.When 8 volts are applied to a circuit, 160 milliamperes (mA) = 0.16 A of current flow through the circuit, hence the resistance is obtained as follows:
8 = 0.16R
R = 8/0.16
R = 50 ohms.
Then the new current if the voltage is increased to 9 volts is given as follows:
9 = 50I
I = 9/50
I = 0.18A = 180 mA.
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1.1 Outline any FOUR non-price competition strategies that food outlets like Nandos, KFC, Chicken Licken and other businesses specialising in chicken, ensure their operational success in the monopolistic competitive firm.
The food outlets can use these four non-price competition strategies to ensure their operational success in the monopolistic competitive market are:
Physical and quality improvementsOutlet locationTaste differentiationConsumer advertising.What are non-price competition strategies?Non-price competition strategies are competitive approaches that can help food outlets to de-emphasize pricing as a competitive strategy.
Instead of pricing, the food outlets can improve the physical and quality aspects of their chicken brands, increase consumer advertising, trade promotions, product differentiation, and locate their outlets in niche markets.
Thus, physical and quality improvements, outlet location and trade promotions, differentiation, and advertising can become non-price competition strategies for these food outlets.
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If x=-2 is a solution to the equation f(x)=g(x) which of these statements must be true?
A) The graphs of f and g intersect each other at x=-2.
B) The graphs of f and g intersect each other at x=2.
C) The graphs of f and g intersect the x-axis at -2.
D) The graphs of f and g intersect the y-axis at -2.
Answer:B
Step-by-step explanation:I didn’t the test
Trust me
Answer: B
I found out once i finished the test
The measures of the angles of a triangle are in the extended ratio of 3:7:10. What is the measure of the LARGEST angle?
pls help me quick
9514 1404 393
Answer:
90°
Step-by-step explanation:
The ratio of the largest angle to the total is ...
10/(3+7+10) = 10/20 = 1/2
The largest angle is half the total of all angles:
1/2×180° = 90° . . . . measure of the largest angle
A class contains 5 girls and 7 boys. Two are selected for a class committee. What is the probability that a girl and boy are selected?
The probability of selecting a girl and a boy for the class committee can be calculated by considering the total number of outcomes and the number of favorable outcomes.
Identify the number of girls and boys in the class. In this case, there are 5 girls and 7 boys.
Determine the total number of students in the class. That is 5 + 7 = 12.
Determine the number of ways to select two students from the class.
Here we can use the combination formula, which is written as C(n, r), where n is the total number of items and r is the number of items to be chosen.
In our case, n = 12 (total number of students) and r = 2 (number of students to be selected).
C(12, 2) = 12! / (2!(12-2)!) = 66.
Determine the number of favorable outcomes.
In this case, we want to select one girl and one boy. We multiply the number of girls by the number of boys: 5 x 7 = 35.
To find the probability, we divide the number of favorable outcomes (35) by the total number of outcomes (66):
Probability = Number of favorable outcomes / Total number of outcomes = 35 / 66 = 5/6.
So, the probability of selecting a girl and a boy for the class committee is 5/6.
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Annalise buys a pair of sunglasses for 30% off and saves $15. What is the original price of the pair of sunglasses?
*
Answer:
$50
Step-by-step explanation:
We will call x the original price of the sunglasses.
We can create the equation below using the information given.
\(x*\frac{30}{100} =15\)
Now solve for x.
\(x = 15*\frac{100}{30}\)
\(x = \frac{100}{2}\)
\(x=50\)
Inso ice cream machines make a total of 320 gallons in a certain amount of time.
Working together for the same length of time, how many gallons of ice cream can 4
machines make?
The gallons of ice cream 4 machines can make is 650 gallons.
How to find the number of gallons of ice cream 4 machine can make?Two ice cream machines make a total of 320 gallons in a certain amount of time.
Working together for the same length of time, the number of gallons of ice creams 4 machine can make can be calculated as follows:
Therefore,
If 2 ice cream machine = 320 gallons
4 ice cream machine = ?
cross multiply
Hence,
gallons of ice cream made by 4 machines = 320 × 4 / 2
gallons of ice cream made by 4 machines = 1280 / 2\
Therefore,
gallons of ice cream made by 4 machines = 640 gallons
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What is the effective annual rate of an account that pays interest at the nominal rate of
7% per year, compounded daily? Compounded hourly?
Answer:
To find the effective annual rate (EAR) of an account that pays interest at the nominal rate of 7% per year, compounded daily, we can use the following formula:
EAR = (1 + r/n)^n - 1
where r is the nominal annual interest rate (expressed as a decimal), and n is the number of times the interest is compounded in a year.
For daily compounding, n = 365 (since there are 365 days in a year), so we have:
EAR = (1 + 0.07/365)^365 - 1 = 0.0725 or 7.25%
To find the effective annual rate for hourly compounding, we need to adjust the value of n to account for the fact that interest is compounded more frequently. There are 365 days * 24 hours = 8,760 hours in a year, so we can use n = 8,760:
EAR = (1 + 0.07/8760)^8760 - 1 ≈ 0.0727 or 7.27%
Therefore, the effective annual rate for hourly compounding is approximately 7.27%.
\(\sqrt{a^{2}+ab+b^{2}} +\sqrt{ a^{2}+ac+c^{2} } \geq \sqrt{ b^{2}+bc+c^{2}\)
Answer:
Solution given:
\(\sqrt{a^{2}+ab+b^{2}} +\sqrt{a^{2}+ac+c^{2}}+ \sqrt{ b^{2}+bc+c^{2}}\)
\(\sqrt{(a+b)²} +\sqrt{ (a+c)² }+\sqrt{(b+c)²}\)
a+b+a+c+b+c
2a+2b+2c
2(a+b+c)