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Answer:
(a) sum: (a+c) +(b+d)i
product: (ac -bd) +(bc +ad)i
(b) (b+d)=0 and (bc+ad)=0 ⇒ a=c, d=-b or b=d=0
Step-by-step explanation:
(a) Combining like terms the sum is ...
(a +bi) +(c +di) = (a+c) +(b+d)i . . . . sum
And the product is ...
(a+bi)(c+di) = ac +(ad+bc)i +bd·i²
Since i = √-1, i² = -1 and the product can be written as ...
(a+bi)(c+di) = (ac-bd) +(ad+bc)i . . . . product
__
(b) If both the sum and product are real numbers, then we have ...
b +d = 0
ad +bc = 0
The first equation tells us d = -b. Substituting that into the second equation, we get ...
a(-b) +b(c) = 0
b(c -a) = 0
The zero product rule tells us this will be true if and only if b = 0 or c = a.
if b = 0, then d = 0 and both numbers are real.
if c = a, then c+di = a-bi and the numbers are conjugates.
Hence, if both the sum and product are real, both are real numbers or they are conjugates.
Find the simple interest. The rate is an annual rate unless otherwise noted. Assume 365 days in a year and 30 days per month Round to the nearest cent $600 at 3% for 1 year
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Answer:
$18
Step-by-step explanation:
The interest is computed using the formula ...
I = Prt
where P is the principal, r is the annual rate, and t is the number of years. The interest is ...
I = $600×0.03×1 = $18
During a test period, an experimental group of 10 vehicles using an 85 percent ethanol-gasoline mixture showed mean CO2 emissions of 667 pounds per 1000 miles, with a standard deviation of 20 pounds. A control group of 14 vehicles using regular gasoline showed mean CO2 emissions of 679 pounds per 1000 miles with a standard deviation of 15 pounds. At α = 0.05, in a left-tailed test (assuming equal variances) the test statistic is:______.
A. 1.321.
B. -2.508.
C. -2.074.
D. -1.717.
Answer:
-1.683
Step-by-step explanation:
Given :
Group 1 :
x1 = 667 ; n1 = 10 ; s1 = 20
Group 2 :
x2 = 679 ; n2 = 14 ; s2 = 15
The test statistic assuming equal variance :
x1 - x2 / √[Sp² * (1/n1 + 1/n2)]
sp² = [(n1 - 1)*s1² + (n2 - 1)*s2²] ÷ (n1 + n2 - 2)
Sp² = [(10 - 1)*20² + (14 - 1)*15²] = 296.59
Test statistic =
(667 - 679)/ √[296.59 * (1/10 + 1/14)]
-12 / 7.1304978
Test statistic = - 1.682
How does sample size affect determinations of statistical significance? The smaller the sample size, the more confident one can be in one's decision to reject or retain the null hypothesis. The smaller the sample size, the greater the probability that the variable has an effect. The larger the sample size, the more accurate the estimation of the true population value. The larger the sample size, the greater the probability that the variable has an effect.
Answer:
The larger the sample size, the more accurate the estimation of the true population value.
Step-by-step explanation:
As large will be the sample size more data will be shown and more are the c c changes of it being an estimate of a true population. The sample size can be determined on the basis of use of experience, target variance, confidence level, and target for power..........................................................
Answer:
..............................what this
What are Julie’s taxable wages as a data-entry operator if her withholding allowances total $1,500 and her annual gross pay is $24,500?
Julie's Taxable Wages:
Julie's taxable wages as a data-entry operator is:
= $23,000.
Data and Calculations:
a) Annual gross pay = $24,500
Total withholding allowances = 1,500
Taxable wages (income) = $23,000 ($24,500 - $1,500)
b) Julie's total withholding allowance of $1,500 is the total exemption that reduces how much income tax her employer can deduct from Julie's paycheck. This means that $1,500 will be deducted from $24,500, the gross pay, before arriving at her taxable income.
Thus, Julie's taxable wages represent the difference between her annual gross pay and her total withholding allowances.
Learn more about taxable income here: https://brainly.com/question/8653999
A (5,3) and B (2,-1) are two verticles of a square ABCD and D is on the x axis. Find the coordinate of C and D
Answer:
1) D(1,0), C(-2,-4) or 2) D(9,0), C(6,-4)
Step-by-step explanation:
The vector AB is (2-5, -1-3)= (-3,-4)
The modul of the vector is equal to sqrt (3squared+4squared)=5 (the length of the side AB of square)
Explore the point D (the coordinates of the point is (x,0), y=o, because it is an axis x). AD (x-5, -3)
The modul of AD is sqrt ((x-5)^2+(-3)^2)= sqrt (x^2-10x+25+9), it is equal to the side AD which is equal to AB
sqrt(x^2-10x+34)= 5
x^2-10x+34=25
x^2-10x+9=0
x=1, x=9
D is (1,0) or D is (9,0),
find C, (for D1(1,0))
Find the midpoint of BD (O)
xo= (2+1)/2= 1.5
y0=(-1+0)/2= -0.5
It is the midpoint of Ac too
x0= (xa+xc)/2 1.5 = (5+xc)/2 xc= -2
y0=(ya+yc)/2 -0.5= (3+yc)/2 yc=-4
c(-2,-4)
Find C2 (for D(9,0))
Find the midpoint of BD (O)
x0= (2+9)/2=5.5
y0= (-1+0)/2=-0.5
o(5.5, -0.5)
It is the midpoint of Ac too
x0= (xa+xc)/2 5.5= (5+x)/2 x=6
y0=(ya+yc)/2 -0.5= (3+x)/2 y=-4
Suppose the distributor charges the artist a $40.00 cost for distribution, and the streaming services pays $4.00 per unit. (Note: One unit = one thousand streams)
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Formula: y = 40x + 4 (Graph Attached)
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
After how many streams will you pay for the distributor charges? (Hint: this is where the line crosses the x-axis, round to the nearest thousand)
Answer:
356 streams
Step-by-step explanation:
From the graph, you will see that the line cross the x-axis at x = 8.8
Substitute into the expression y = 40x + 4
y = 40(8.8)+4
y = 352 + 4
y = 356
Hence the distributor charges will be paid for after 356 streams
A car dealership is advertising a car for $16,299.99. If the sales tax rate is 6.5 percent, what
is the total tax paid for the car?
A. S993 34
B. $1.000.00
CS1.059 50
DS1.359.19
Answer:
C. 1059.50
Step-by-step explanation:
Sales price x sales tax rate = sales tax
16299.99 x .065 (6.5%) = 1059.50
What are the zeros of this function?
Answer:
The zeros of this function would be: x = 4 and x = 6, assuming that option got caught off while you were taking a picture.
Step-by-step explanation:
When they're asking for the zeros of this type of function, where is forms this kind of U-shape or also known as a quadratic equation, they're asking what the x-value is when y = 0, or when the line of the function touches the x-axis. Notice that it happens when x = 4 and when x = 6.
In short, it's asking what the x-value is of the points of the function when it intersects the x-axis. Hopefully my explanation wasn't too confusing. Good luck on the rest of the quiz!
in a fruit punch drink,the 3 ingredients are apple juice,orange juice and cramberry juice.if 3/4 of the drink is apple juice and 1/10 is orange juice then write the ratio of cranberry juice to apple juice to orange juice in its simplest form
Answer:
3 : 15 : 2
Step-by-step explanation:
Let cranberry juice = x,
3/4 + 1/10 + x = 1
x = 3/20
Ratio = cranberry : apple : orange
= 3/20 : 3/4 : 1/10
= 3 : 15 : 2 (Times everything with 20)
what percent is equal to 7/25
Solve this inequality: 14 <-7x
Answer:
-2 > x
Step-by-step explanation:
14 <-7x
Divide each side by -7, remembering to flip the inequality
14/ -7 > -7x/-7
-2 > x
Find the midpoint of the line segment defined by the points: (5, 4) and (−2, 1) (2.5, 1.5) (3.5, 2.5) (1.5, 2.5) (3.5, 1.5)
Answer:
[tex]\boxed {\boxed {\sf (1.5 , 2.5)}}[/tex]
Step-by-step explanation:
The midpoint is the point that bisects a line segment or divides it into 2 equal halves. The formula is essentially finding the average of the 2 points.
[tex](\frac {x_1+x_2}{2}, \frac {y_1+ y_2}{2})[/tex]
In this formula, (x₁, y₁) and (x₂, y₂) are the 2 endpoints of the line segment. For this problem, these are (5,4 ) and (-2, 1).
x₁= 5 y₁= 4 x₂= -2 y₂= 1Substitute these values into the formula.
[tex]( \frac {5+ -2}{2}, \frac {4+1}{2})[/tex]
Solve the numerators.
5+ -2 = 5-2 = 3 4+1 = 5[tex]( \frac {3}{2}, \frac{5}{2})[/tex]
Convert the fractions to decimals.
[tex](1.5, 2.5)[/tex]
The midpoint of the line segment is (1.5 , 2.5)
lim(x-0) (sinx-1/x-1)
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Answer:
as written: the limit does not existsin(x-1)/(x-1) has a limit of sin(1) ≈ 0.841 at x=0Step-by-step explanation:
The expression written is interpreted according to the order of operations as ...
sin(x) -(1/x) -1
As x approaches 0 from the left, this approaches +∞. As x approaches 0 from the right, this approaches -∞. These values are different, so the limit does not exist.
__
Maybe you intend ...
sin(x -1)/(x -1)
This can be evaluated directly at x=0 to give sin(-1)/-1 = sin(1). The argument is interpreted to be radians, so sin(1) ≈ 0.84147098...
The limit is about 0.841 at x=0.
evaluate (-1)^6-4^0+(3/7)^0
Answer:
The answer is 1
.............
please mark this answer as brainlist
Write an inequality for the shaded region shown in the figure.
Answer:
the equation of the circle is x^2 + y^2 < 36
NOT LESS OR EQUAL cause of the dotted lines
and the theory behind this is because the square root of 36 is +-6 so when the equation is less than +-6 the shade cannot go outside these point, if you know what i mean
hope that answers your question :)
what is the value of x
Answer:
c 112⁰
Step-by-step explanation:
cuz the triangle is the same and x is on a straight line so get 180 - 68 = 112
Answer:
the angle opposite to x is 61 degree (being alternate angle)
so
x+ 61 = 180(being linear pair)
or, x = 180 - 61
so, x = 119
the answer is 119(d).
Which of the following rational functions is graphed below?
10
- 10
10
tho
A. F(x) =
3
X-7
B. F(x) = x + 3
X-7
C. F(x) =
(x+3)(x-7)
(x+3)(x-7)
D. F(X)
1
(x + 7(x-3)
7\x-
Check the picture out and please help me lol
Vertical asymptote:
A vertical asymptote is a value of x for which the function is not defined, that is, it is a point which is outside the domain of a function;
In a graphic, these vertical asymptotes are given by dashed vertical lines.
An example is a value of x for which the denominator of the function is 0.
In this graphic:
Dashed vertical lines at: [tex]x = -3, x = 7[/tex], thus, for [tex]x - (-3) = x+3[/tex] and [tex]x - 7[/tex] the denominator is zero.
Thus, the function graphed is:
[tex]F(x) = \frac{1}{(x+3)(x-7)}[/tex]
And the correct answer is given by option C.
To take a look at a problem with asymptote, you can check this item https://brainly.com/question/4084552.
The graph is for the rational function f(x) = 1/(x + 3)(x - 7).
Option C is the correct answer.
We have,
To understand the graph of the function f(x) = 1/((x + 3)(x - 7)).
Vertical Asymptotes:
The function has vertical asymptotes at the values of x for which the denominator becomes zero.
The denominator is (x + 3)(x - 7), so the vertical asymptotes occur at
x = -3 and x = 7.
Horizontal Asymptote:
The highest power of x in the denominator is x², and there is no x² term in the numerator, the function approaches 0 as x goes to positive or negative infinity.
The horizontal asymptote is y = 0.
x-Intercept:
To find the x-intercept, we set y = 0 and solve for x:
0 = 1/((x + 3)(x - 7))
Since the numerator can never be zero, the only way the fraction can be zero is if the denominator is zero:
(x + 3)(x - 7) = 0
Solving for x:
x + 3 = 0
x = -3
x - 7 = 0
x = 7
So, the x-intercepts are (-3, 0) and (7, 0).
y-Intercept:
To find the y-intercept, we set x = 0:
f(0) = 1/((0 + 3)(0 - 7)) = 1/(-3 * -7) = 1/21
The y-intercept is (0, 1/21).
Thus,
The graph is for the rational function f(x) = 1/(x + 3)(x - 7).
Learn more about functions here:
https://brainly.com/question/28533782
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HELP URGENT !!!!!!
what happens if the lines that are being cut by the transversal are not parallel
if 405 is to be divided among three persons A, B, C in the ratio of 3:5:7, how much money does each one get? Express them in percentages.
Step-by-step explanation:
Pls Mark me
Brainliest!!!!An automobile went 84 miles on 6.5 gallons of gasoline. At this rate, how many gallons would be needed to travel 126 miles
Answer:
10 gallons
Step-by-step explanation:
84 ÷ 6.5 =12.9(The unit rate.)
Seeing as one gallon can get you 12.9 miles;
126÷12.9=9.7
So the answers 9.7 gallons, but if you need to round, then 10 to get a whole number.
Answer:
9.75
Step-by-step explanation:
We can write a ratio to solve
84 miles 126 miles
-------------- = -------------------
6.5 gallons x gallons
Using cross products
84 x = 6.5 * 126
84x=819
84x/84 = 819/84
x = 9.75
(-1)×(-1)×(-1)×(2m+1) times where m is a natural number,is equal to?
1. 1
2.-1
3.1 or-1
4.None
Answer:
(2). -1
Step-by-step explanation:
The given parameter can be represented as:
[tex](-1)^{2m + 1}[/tex]
See comment for correct question
Required
The end result
From the question, we understand that m is a natural number
This means that:
[tex]2m + 1 \to[/tex] odd number
So:
[tex](-1)^{2m + 1} = -1[/tex] --- i.e. -1 to the power of an odd number will give -1
Hence; (2) is correct
a road rises 16 feet for every 50 feet of horizontal distance covered. in percent what is the grade of the road?
Answer:
32%
Step-by-step explanation:
The slope of the road is measured as
slope = [tex]\frac{rise}{run}[/tex] = [tex]\frac{16}{50}[/tex]
To express as a percentage multiply the fraction y 100% , that is
slope = [tex]\frac{16}{50}[/tex] × 100% = 16 × 2 = 32%
Percent decrease from 20 to 11
Answer:
45 percent
Step-by-step explanation:
20-11=9
9 divided by 20= 0.45
0.45 x 100= 45%
Solve for x.
A. 1
B. 5
C. 3
D. 12
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Answer:
A. 1
Step-by-step explanation:
Arc AB is twice the measure of the angle ABC. The sum of the arc measures around the circle is 360°.
2(43x)° +(272x +2)° = 360°
358x +2 = 360 . . . . . . . . . . . . divide by °, collect terms
358x = 358 . . . . . . . . subtract 2
x = 1 . . . . . . . . . . divide by 358
Solve the following system of equations for x to the nearest hundredth : y + 2x + 1 = 0; 4y - 4x ^ 2 - 12x = - 7
Answer:
+3.464; -3.464
Step-by-step explanation:
call A = y + 2x + 1 = 0 => y = (1 - 2x)
call B: 4y - 4(x^2) - 12x = -7
=> replace y from A to B =>
4(1 - 2x) - 4(x^2) - 12x = -74 - 8x - 4(x ^ 2) - 12x = -7-8x - 4(x ^ 2) - 12x = -7 - 4 = -11-4(x^2) - (8x - 12x) = -11-4(x^2) + 4x = -11-4(x^2) + 4x + 11 = 0=> get delta Δ = (-4^2) - 4*(-4 * 11) = 192
=> Δ > 0 => got 2 No
=> x1 = [tex]\frac{-4 + \sqrt{192} }{2 * -4}[/tex] = [tex]\frac{1 - 2\sqrt{3} }{2}[/tex] = -1.232
=> x2 = [tex]\frac{-4 - \sqrt{192} }{2 * -4}[/tex]=[tex]\frac{1 + 2\sqrt{3} }{2}[/tex]= 2.232
=> replace x from B into A
=> y1 = (1 - 2x) = (1 - 2 * -1.232) = 3.464
=> y2 = (1 - 2x) = (1 - 2 * 2.232) = - 3.464
find area of a square garden having a length 45m
Answer:
A = 2025 ft^2
Step-by-step explanation:
The area of a square is given by
A = s^2 where s is the side length
A = 45^2
A = 2025 ft^2
Answer:
Step-by-step explanation:
The area of any square is s^2
s in this case is 45
Area = s^2
Area = 45 * 45
Area = 2025 m^2
The hypotenuse of a right triangle measures 14 cm and one of its legs measures 1 cm. Find the measure of the other leg. If necessary, round to the nearest tenth.
Answer:
b=14 cm
Step-by-step explanation:
Use pythagorean equation
A^2+b^2=c^2
1^2+b^2=14^2
1+b^2=196
b^2=195
b=13.964
what should be the rate of simpe interest such that the interest is double of the sun at 10 years
Answer:
you never showed the chocies
Step-by-step explanation:
WORTH 30 POINTS PLEASE HELP!!!!! WILL GIVE POINTS
Answer:
2/3 and 4/6
Step-by-step explanation:
