Answer:
Option b.
Step-by-step explanation:
Note: The given expression is not in correct form. Consider the given expression is [tex]i^0\times i^1\times i^2\times i^3\times i^4[/tex].
Let as consider the given expression is
[tex]i^0\times i^1\times i^2\times i^3\times i^4[/tex]
We know that,
[tex]i^0=1,i^2=-1,i^3=-i,i^4=1[/tex]
Using these values, we get
[tex]i^0\times i^1\times i^2\times i^3\times i^4=1\times i\times (-1)\times (-i)\times 1[/tex]
[tex]=i^2[/tex]
[tex]=-1[/tex]
The value of given expression is -1.
Therefore, the correct option is b.
HELP ASAP PLEASE (25 POINTS) Solve and reduce if possible. 5/12 − 7/8 = ?
Answer:
-11/24
Step-by-step explanation:
5/12 - 7/8
We need to get a common denominator of 24
5/12 *2/2 - 7/8 *3/3
10/24 - 21/24
-11/24
Answer:
-11/24
Step-by-step explanation:
Well to solve 5/12 - 7/8 we need to find the LCM.
12 - 12, 24, 36, 48
8 - 8, 16, 24, 32, 40
So the LCM is 24.
Meaning we need to make both denominators 24.
12*2 = 24 5*2 = 10
10/24
8*3 = 24 7*3 = 21
21/24
10/24 - 21/24
= -11/24
Thus,
the answer is -11/24.
Hope this helps :)
Dose anyone know the answer to this question?
Answer:
-3
Step-by-step explanation:
-3k / ( k-2) + 6 / ( k-2)
since the denominators are the same we can add the numerators
(-3k+6) / ( k-2)
Factor out -3
-3 ( k-2)/ ( k-2)
Cancel like terms
-3
Answer:
[tex]\boxed{\sf -3}[/tex]
Step-by-step explanation:
The denominators are same. Add fractions.
[tex]\displaystyle \sf \frac{-3k+6}{k-2}[/tex]
Factor out the expression in the numerator.
[tex]\displaystyle \sf \frac{-3(k-2)}{k-2}[/tex]
Cancel common terms.
[tex]\displaystyle \sf \frac{-3}{1}=-3[/tex]
Determine the convergence or divergence of the sequence with the given nth term. If the sequence converges, find its limit. (If the quantity diverges, enter DIVERGES.) an = (n − 2)! n!
Answer: Diverging
Step-by-step explanation:
Find explanations in the attached file
How many times will the digit '3' appear if we write a all whole numbers from 1 to 99?
Answer:
20
Step-by-step explanation:
The number 3 will appear in the numbers 3, 13, 23, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 43, 53, 63, 73, 83, 93. In these numbers it appears 20 times.
A bag contains ten tiles labeled B, C, D, E, F, G, H, I, J, and K. One tile will be randomly picked.
What is the probability of picking a vowel?
Write your answer as a fraction in simplest form.
Answer:
1/5
Step-by-step explanation:
B, C, D, E, F, G, H, I, J, K. = 10 tiles
E and I are vowels
P ( vowel) = vowels/ total
=2/10
= 1/5
In total, we are given 10 letters.
The vowers are; A, E, I, O, and U
In the bag, we can see we have 2 vowels (E and I)
This means that 2 out of the 10 letters are vowels (2/10).
We can simplify the fraction by dividing by 2.
2÷2/10÷2
1/5
Therefore, the answer is 1/5.
Best of Luck!
In a survey of 300 T.V. viewers, 40% said they watch network news programs. Find the margin of error for this survey if we want 95% confidence in our estimate of the percent of T.V. viewers who watch network news programs.
Answer:
0.05543Step-by-step explanation:
The formula for calculating the margin of error is expressed as;
[tex]M.E = z * \sqrt{\frac{p*(1-p)}{n} }[/tex] where;
z is the z-score at 95% confidence = 1.96 (This is gotten from z-table)
p is the percentage probability of those that watched network news
p = 40% = 0.4
n is the sample size = 300
Substituting this values into the formula will give;
[tex]M.E = 1.96*\sqrt{\frac{0.4(1-0.4)}{300} }\\ \\M.E = 1.96*\sqrt{\frac{0.4(0.6)}{300} }\\\\\\M.E = 1.96*\sqrt{\frac{0.24}{300} }\\\\\\M.E = 1.96*\sqrt{0.0008}\\\\\\M.E = 1.96*0.02828\\\\M.E \approx 0.05543[/tex]
Hence, the margin of error for this survey if we want 95% confidence in our estimate of the percent of T.V. viewers who watch network news programs is approximately 0.05543
PLLZZZZ help me find x you are AWSOME!! I need this ASAP
Answer:
27°
Step-by-step explanation:
D is 72° because it alternates with B, alternate angles are equal.
2x+72°+2x= 180° because it is a straight line.
4x+72°=180°
4x=108°
x=27°
Next number in this series is? 2 2 1/2 1 1/2 2
First, let's figure out the pattern that this series follows. We can see that the first number is increased by 1/2 to get to 2 1/2. Then, the second number is decreased by 1 to get to 1 1/2. Finally, the pattern repeats.
So, let's apply this pattern to find the next number in this series.
2, 2 1/2, 1 1/2, 2, 1
The next number in this series is 1.
Hope this helps!! :)
A group of students were asked to choose their favorite course. The results are shown in the two-way frequency table. Which of the following can be concluded from the joint and marginal frequencies of the table? Math is the most popular subject in the 10th grade. History is the least popular subject in the 9th grade. Science is more popular than math among 12th grade students. Students in the 11th grade like English more than students in the 12th grade. The overall favorite course is history.
A.) III and IV only
B.) II and V only
C.) I, III, and V
D.) II and IV only
The answer is C.) I, III, and V
The statement 1, 2, and 5 will be correct hence option (C) will be correct.
What is a frequency table?A frequency table is a list of objects with the frequency of each item shown in the table.
In other words, a frequency table is a table in which we have some data and their frequency.
The frequency of an occurrence or a value is the number of times it happens.
In option (C)
1st statement;
Math is the most popular subject in the 10th grade.
In 10th grade, maths is 104 rest are less so it is correct.
3rd statement;
Science is more popular than math among 12th-grade students.
The number of science lovers in the 12th is 78
The number of maths lovers in 12th is 52
So it is also correct.
5th statement;
Overall favorite course is history.
A number of overall favorite courses is history = 403 which is higher than others hence it is also correct.
So option (C) is correct rest are incorrect.
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if 5x - 17 = -x +7, then x =
Answer:
x=4
Step-by-step explanation:
5x - 17 = -x +7
Add x to each side
5x+x - 17 = -x+x +7
6x -17 = 7
Add 17 to each side
6x-17+17 = 7+17
6x =24
Divide each side by 6
6x/6 = 24/6
x = 4
Answer:
4
Step-by-step explanation:
5x - 17 = -x + 7
Add x on both sides.
5x - 17 + x = -x + 7 + x
6x - 17 = 7
Add 17 on both sides.
6x - 17 + 17 = 7 + 17
6x = 24
Divide both sides by 6.
(6x)/6 = 24/6
x = 4
Which inequality is shown in this graph?
(0, 2) (-1,-2)
a) y>=-4x+2
b) y>=4x+2
c) y<=-4x+2
d) y<=4x+2
Answer:
B y ≥ 4x + 2
Step-by-step explanation:
1. find slope of the line: (y² - y¹) / (x² - x¹)
(0, 2) and (-1, -2)
(-2 - 2) / (-1 - 0) = -4 / -1 = 4
y = 4x + 2*
*+2 because that is the y-intercept as shown by point (0, 2)
2. the line is solid, therefore the inequality is ≤ or ≥. dashed line would mean < or >
3. the shaded region is on the right side of the line, so the values are greater than. therefore, you use ≥
4. final equation: y ≥ 4x + 2
A savings account has a rate of 2.25% . Find the effective annual yield of interest is compounded quarterly
Answer:
The effective yield is 2.269% to the thousandth.
Step-by-step explanation:
Effective annual yield compounded quarterly, given API
(1+API/4)^4 - 1
= (1+0.0225/4)^4 - 1
= 0.022691
Solve for x. a) 10 b) 12 c) 13 d) 11
Answer:
A : 10
Step-by-step explanation:
Answer:
the correct answer is 12
Step-by-step explanation:
6/8=9/x
cross multiply
6x=72
divide by six
x=12
The perimeter of △ABC equals 26 in and the midpoints of the sides are M, N and K. Find the perimeter of △MNK.
Answer:
13 in.
Step-by-step explanation:
Theorem:
The segment that joins the midpoints of two sides of a triangle is parallel to the third side and half the length of the third side.
Each side of triangle MNK has as endpoints two midpoints of sides of triangle ABC, so each side of triangle MNK is half the length of a side of triangle ABC.
p = 26 in./2 = 13 in.
Where L is the length, in feet, of the pendulum, and π is approximately 22/7. How long must the pendulum be if one complete cycle takes 8 seconds?
Answer:
The simple pendulum should be 15.9 m long.
Step-by-step explanation:
Approximately (for small amplitudes), the period of a simple pendulum is
T = 2*pi * sqrt (L/g), L=length
using pi = 22/7, and g=9.8 m/s^2
8 = 2* 22/7 * sqrt(L/9.8)
solve for L
L = (8*7/(2*22))^2 * 9.8
= 15.874 m
That's quite a long pendulum!
Which statement is false?
OA. The inequality sign always opens up to the larger number.
OB. The greater number in an inequality is always above the other number on the vertical number line.
OC. The smaller number in an inequality is always located to the left of the other number on the horizontal number line.
OD.
The inequality sign always opens up to the smaller number.
Answer:
OD is false, because it condradicts OA, and we know that OA is true, I mean, we write 2<3
Answer
The inequality sign always open up to the smaller number
The answer is D
An appliance company determines that in order to sell x dishwashers, the price per dishwasher must be p = 420 - 0.3x. It also determines that the total cost of producing x dishwashers is given by C(x) = 5000 + 0.3x2. How many dishwashers must the company produce and sell in order to maximize profit? g
The company must produce and sell 350 dishwashers in order to maximize profit.
How to determine the number of dishwashersTo determine the number of dishwashers the company must produce and sell in order to maximize profit, we need to find the value of x that corresponds to the maximum point of the profit function.
The profit (P) is given by the equation:
P(x) = Revenue - Cost
The revenue is calculated by multiplying the price per dishwasher (p) by the number of dishwashers sold (x):
Revenue = p * x
The cost is given by the function C(x):
Cost = C(x)
Therefore, the profit function can be expressed as:
P(x) = p * x - C(x)
Substituting the given expressions for p and C(x):
P(x) = (420 - 0.3x) * x - (5000 + 0.3x²)
Expanding and simplifying the equation:
P(x) = 420x - 0.3x² - 5000 - 0.3x²
Combining like terms:
P(x) = -0.6x² + 420x - 5000
To find the value of x that maximizes profit, we need to find the vertex of the quadratic function. The x-coordinate of the vertex can be determined using the formula:
x = -b / (2a)
In our case, a = -0.6 and b = 420:
x = -420 / (2 * -0.6)
x = -420 / (-1.2)
x = 350
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350 dishwashers must the company produce and sell in order to maximize profit.
Maxima means a point at which the function attains the maximum value.
Given the following information:
Price per dishwasher, p = 420 - 0.3x
Total cost of producing x dishwashers, C(x) = 5000 + 0.3x2
Profit= Total Selling price- Total Cost Price
Total Selling price of x dishwasher, S.P= xp
S.P=x(420 - 0.3x)
S.P=420x - 0.3x²
Profit= 420x - 0.3x² - ( 5000 + 0.3x²)
Profit= 420x - 0.3x² - 5000 - 0.3x²
Profit= -0.6x²+420x-5000
So, profit, f(x)=-0.6x²+420x-5000
To determine the value of x so that maximum profit is possible:
1. Calculate the first derivative of profit function and calculate the value of x by equating it to zero.
2. Select that value of x for which the profit function attains the maximum value, to check the maxima calculate 2nd derivative, if it gives a negative value for the value of x. Then, x is the point of maxima for the given function.
[tex]f(x)=-0.6x^2+420x-5000\\f\prime(x)=-1.2x+420\\f\prime(x)=0\\-1.2x+420=0[/tex]
Calculating the value of x by transposing,
x=420/1.2
x=350
To check maxima, calculating second derivative.
[tex]f\prime(x)=-1.2x+420=0\\f\prime\prime(x)=-1.2[/tex]
2nd derivative is negative, it means that x=350 is the point of maxima.
Thus, a company must produce and sell 350 dishwashers in order to maximize profit.
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Let A = 2, B = 3, C = 9, and D = 15.
Find the value of each expression listed below. -2 -14 10 2 -6 -10 14 6
-A + C - (D ÷ B)----------------------> (answer)
B × (-C) - (-D) + A----------------------> (answer)
(C + D) ÷ B + A----------------------> (answer)
D ÷ B + A - C----------------------> (answer)
Step-by-step explanation:
Put A = 2, B = 3, C = 9 and D = 15 to the given expressions.
Use PEMDAS.
-A + C - (D : B)
-2 + 9 - (15 : 3) = -2 + 9 - 5 = 7 - 5 = 2
B × (-C) - (-D) + A
3 × (-9) - (-15) + 2 = -27 + 15 + 2 = -12 + 2 = -10
(C + D) : B + A
(9 + 15) : 3 + 2 = 24 : 3 + 2 = 8 + 2 = 10
D : B + A - C
15 : 3 + 2 - 9 = 5 + 2 - 9 = 7 - 9 = -2
What is the converse of r->(~q v p)
Answer:
[tex]r => (\neg q \ \lor p) \ \equiv \ q \ \land \ \neg p => \neg r[/tex]
Step-by-step explanation:
In general, remember that the converse of [tex]a => b[/tex] is [tex]\neg b => \neg a[/tex] , therefore in this case [tex]a = r \ \ , b = \neg q \ \lor p[/tex]
so [tex]r => (\neg q \ \lor p) \ \equiv \ q \ \land \ \neg p => \neg r[/tex]
WILL MARK BRAINLIST------ What is the least number of degrees that you could rotate Figure (b) around its center so that it appears to be unchanged?
Answer:
20*
Step-by-step explanation:
Your welcome plz mark me the brainlist
The world's largest university (by enrollment) is University A, followed by University B. If the enrollment in University A is 3.5 million more students than University B and their combined enrollment is 9.5 million students, find the enrollment for each university?
"Smokers are much more likely to speed, run red lights, and get involved in car accidents than nonsmokers."(a) Can you think of reasons why this statement might be misleading?(b) Can you suggest a causal link between smoking and car accidents?
Answer: Smokers pay less attention to driving while trying to light a cigarette.
Step-by-step explanation:
( A ) reasons for, why the given statement was misleading.
Following are the reasons for accidents
(i) Drunk Driving.
(ii) Driving during the night.
(iii) Smoking.
(iv) Unsafe lane changes.
(v) Driving the wrong way.
(vi) Bad weather e.g fog.
From the list above, it is shown that, smoking is also one of the major cause of car accidents on the roads.
( B.) Smokers tends to pay less attention to driving why trying to light a cigarette.
Simply this expression (3 + 2i)^2
Answer:
5 + 12i
Step-by-step explanation:
(3 + 2i)^2 = (3 + 2i)(3 + 2i) = 9 + 6i + 6i + 4i^2 = 9 + 12i - 4 = 5 + 12i
Answer:
5 + 2i
Step-by-step explanation:
since [tex]\sqrt{-1} = i[/tex]
Use the perfect square formula ( a + b )^2
= 3^2 + 2 · 3 · 2i + (2i)^2
= 5 + 2i
or,
[tex]5+2\sqrt{-1}[/tex]
For the functions f(x)=−7x^2−x and g(x)=9x^2−4x, find (f−g)(x) and (f−g)(1)
Answer:
See below.
Step-by-step explanation:
[tex]f(x)=-7x^2-x\\g(x)=9x^2-4x\\(f-g)(x)=f(x)-g(x)\\(f-g)(x)=(-7x^2-x)-(9x^2-4x)\\(f-g)(x)=-7x^2-x-9x^2+4x\\(f-g)(x)=-16x^2+3x\\\\(f-g)(1)=-16(1)^2+3(1)\\(f-g)(1)=-16+3=-13[/tex]
Find all the zeros of the polynomial function p(x) = x3 – 5x2 + 33x – 29
Answer:
[tex]\large \boxed{\sf \ \ x=1, \ \ x=2+5i, \ \ x=2-5i \ \ }[/tex]
Step-by-step explanation:
Hello,
I assume that we are working in [tex]\mathbb{C}[/tex], otherwise there is only one zero which is 1. Please consider the following.
First of all, we can notice that 1 is a trivial solution as
[tex]p(1) = 1^3-5\cdot 1^2 + 33\cdot 1-29=1-5+33-29=0[/tex]
It means that (x-1) is a factor of p(x) so we can find two real numbers, a and b, so that we can write the following.
[tex]p(x)=(x-1)(x^2+ax+b)=x^3+ax^2+bx-x^2-ax-b=x^3+(a-1)x^2+(b-a)x-b[/tex]
Let's identify like terms as below.
a-1 = -5 <=> a = -5 + 1 = -4
b-a = 33
-b = -29 <=> b = 29
So
[tex]\boxed{ \ p(x)=(x-1)(x^2-4x+29) \ }[/tex]
Now, we need to find the zeroes of the second factor, meaning finding x so that:
[tex]x^2-4x+29=0 \ \text{ complete the square, 29 = 25 + 4} \\ \\ <=> x^2-2\cdot 2 \cdot x+2^2+25=0 \\ \\ <=>(x-2)^2=-25=(5i)^2 \ \text{ take the root } \\ \\<=>x-2=\pm 5i \ \text{ add 2 } \\ \\ <=> x = 2+5i \ \text{ or } \ x = 2-5i[/tex]
Hope this helps.
Do not hesitate if you need further explanation.
Thank you
3 solutions for x<-2
Answer:
-3,-4,-5
Step-by-step explanation:
those are all numbers less than -2! your welcome! please give me brainliest!
Answer: -3, -16, and -642,000
Step-by-step explanation: In this problem, we're asked to state three solutions for the following inequality, x < -2.
The inequality x < -2 means that any number
less than -2 is a solution to the inequality.
For example, -3 is a solution because -3 is less than -2.
Another solution would be -16 because -16 is less than -2.
One other solution would be -642,000 because it's less than -2.
It's important to understand that these are only 3 possible
answers and there are many answers to choose from.
pls answer for my little friend A paperweight in the shape of a rectangular prism is shown (in the picture) If a cross section of the paperweight is cut parallel to the base, which shape describes the cross section? Rectangle Triangle Parallelogram Hexagon (DO NOT look answers up on another brainly answer pls)
Answer:
Hey there!
The cross section would be a rectangle. No matter where you cut the figure parallel to the base, the cross section would be a rectangle.
Let me know if this helps :)
Answer: Rectangle
Step-by-step explanation:
In a rectangular prism, every cross-section parallel to a side is a rectangle.
Hope it helps <3
a) John is 3 years older than his brother Brian, the product of their ages is 54 i) Express this information in equation form ii) Show this information as a quadratic equation iii) Hence, solve the equation to find their individual ages
Answer:
Brian is 6 years old, John is 9 years old
Step-by-step explanation:
i.
J = 3 + B
J x B = 54
ii.
(3 + B) x B = 54
B² + 3B = 54
iii.
(B + 9)(B - 6) = 0
B = -9 or 6 -- -9 is irrational as one cannot be negative years old
Brian = 6 years old; therefore, John = 9 years old
Which of the following statements is true?
A.
the segment bisects segment
B.
the segment DE bisects segment
C.
the segment is perpendicular to segment
D.
segment is congruent to segment
The correct statement about the line segment is,
⇒ the segment DE bisects segment AC.
What is Line segment?Line segment is a part of the line which have two endpoints and bounded by two distinct end points and contain every point on the line which is between its endpoint.
Given that;
Triangle ABC is shown in figure.
Now, We can see that;
⇒ AE = EC
Hence, the segment DE bisects segment AC.
Thus, The correct statement about the line segment is,
⇒ the segment DE bisects segment AC.
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if one tenth of a number is added to 2. the result is half of that number. what is the number?
Answer:
5
Step-by-step explanation:
According to the given question, the calculation of number is shown below:-
Let the number be x.
[tex]\frac{1}{10}[/tex] of x will be added to the number of 2, so that the result is half of x.
[tex]2 + \frac{1}{10} x = \frac{1}{2} x[/tex]
Now we will solve the above equation
[tex]2=\frac{1}{2} x-\frac{1}{10} x\\\\2=\frac{2x}{5}\\\\10=2x\\\\\frac{10}{2} =x\\\\[/tex]
x = 5
Therefore the correct answer is 5
Hence, the number based on the given information provided in the question is 5