Answer:
A) if and only if a = 0
Step-by-step explanation:
Since Z1 = 12 + 6݅ and Z2 = a + bi , then the product, Z1Z2 = (12 + 6)(a + bi)
Z1Z2 = (12 + 6)(a + bi)
Expanding the brackets, we have
Z1Z2 = 12a + 12bi + 6a + 6bi
Collecting like terms, we have
Z1Z2 = 12a + 6a + 12bi +6bi
Z1Z2 = 12a + 6a + (12b +6b)i
Simplifying, we have
Z1Z2 = 18a + 18bi
For Z1Z2 to be imaginary, then the real part must be zero.
That is 18a = 0 ⇒ a = 0
So, Z1Z2 is imaginary if and only if a = 0
Using this distribution, find the probability
that a teenager has 4 or more pairs of shoes
in their closet.
Answer:
P = 0.3
Step-by-step explanation:
Here, we are to use the probability distribution in the table to calculate the probability that a children has 4 or more shoes in his or her closet
When we say 4 or more, what we mean by this is that the teenager has 4 shoes or 5 shoes
In probability expressions, when we use the term ‘or’ we are simply talking about adding the terms involved
So what we can do here is to add the probability that the teenager has 4 shoes to the probability that the teenager has five shoes
From the table that would be; 0.1 + 0.2 = 0.3
Lapid.
(ii) Find the remainder when f(x) is
divided by (x - 1)(x + 2).
14) The remainder when the expression
ax' + bx + 2x + c is divided by x-1
is twice of that when it is divided by
x + 1. Show that c = 3a - b + 6.
ii) When a polynomial f(x) is divided by (x-1) and (x+2) it leaves remainder 5 and 17 respectively. find the remainder when f(x) is divided by (x-1) (x+2)
14) The remainder when the expression ax³ + bx² + 2x + c is divided by x-1
is twice of that when it is divided by x + 1. Show that c = 3a - b + 6.
Answer:
ii) R(x) = -4x + 9
14) c = 3a - b + 6 ( Proved)
Step-by-step explanation:
14) The correct expression is [tex]ax^3 + bx^2 + 2x + c[/tex]
To get the remainder when the expression [tex]ax^3 + bx^2 + 2x + c[/tex] is divided by
x - 1, let x - 1 = 0; x = 1
Remainder:
[tex]R_1(x) = a(1)^3 + b(1)^2 + 2(1) + c\\R_1(x) = a + b + 2 + c[/tex]
When [tex]ax^3 + bx^2 + 2x + c[/tex] is divided by x + 1
Let x + 1 = 0; x = -1
Remainder:
[tex]R_2(x) = a(-1)^3 + b(-1)^2 + 2(-1) + c\\R_1(x) = -a + b - 2 + c[/tex]
According to the question, R₁(x) = 2R₂(x)
a + b + 2 + c = 2(-a + b - 2 + c)
a + 2a +b - 2b + 2 + 4 = 2c - c
c = 3a - b + 6 ( Proved)
ii)
The dividend is f(x)
(x - 1)(x + 2) is the divisor, i.e. D(x) = (x - 1)(x + 2)
Let the quotient = A(x)
Let the Remainder, R(x) = ax + b..............(1)
Therefore, f(x) = A(x)D(x) + R(x)
f(x) = A(x)(x - 1)(x + 2) + R(x)...................(2)
When f(x) is divided by x - 1, x = 1
Put x = 1 into equation (2) knowing that R(1) = 5
f(1) = R(1) = 5
R(1) = a(1) + b = 5
a + b = 5....................(3)
When f(x) is divided by x + 2, x = -2
Put x = -2 into equation (2) knowing that R(-2) = 17
f(-2) = R(-2) = 17
R(-2) = a(-2) + b = 17
-2a + b = 17..................(4)
Subtracting equation (1) from (2)
-3a = 12
a = -12/3
a = -4
Substitute the value of "a" into equation (4)
-2(-4) + b = 17
8 + b = 17
b = 9
Since R(x) = ax + b
R(x) = -4x + 9
John used digits from 0 to 6 to create a three-digit PIN code. He forgot his PIN code. He remembers that his code contains different ascending digits. What is the maximum number of combinations John has to check to find his PIN code.
Answer:
35 combinations
Step-by-step explanation:
The first digit cannot be 5 or 6 (Since the digits could not be in ascending order if that was the case).
If the first digit is 4, there is 1 possibility:
(4, 5, 6)
If the first digit is 3, there are 3 possibilities:
(3, 4, 5) (3, 4, 6) (3, 5, 6)
If the first digit is 2, there are 6 possibilities:
(2, 3, 4) (2, 3, 5) (2, 3, 6) (2, 4, 5) (2, 4, 6) (2, 5, 6)
If the first digit is 1, there are 10 possibilities :
(1, 2, 3) (1, 2, 4) (1, 2, 5) (1, 2, 6) (1, 3, 4) (1, 3, 5) (1, 3, 6) (1, 4, 5) (1, 4, 6) (1, 5, 6)
If the first digit is 0, there are 15 possibilities:
(0, 1, 2) (0, 1, 3) (0, 1, 4) (0, 1, 5) (0, 1, 6) (0, 2, 3) (0, 2, 4) (0, 2, 5) (0, 2, 6) (0, 3, 4) (0, 3, 5) (0, 3, 6) (0, 4, 5) (0, 4, 6) (0, 5, 6)
Therefore, he would need to try at most 35 combinations.
HELP PLEASEEE ASAAAAPPPPPPPPPPPP I WILL GIVE BRAINLY TO THE FIRST ONE!!!!!!!!
Answer:
the total amount is £ 756.
hope it helps..
Create a birthday Polynomial with 07.01.2006
Answer:
Step-by-step explanation:
the birthday date is : 07/01/2006 so the numbers are : 07012006 let's switch them : 60021070 we have 8 numbers so our highest degree is 7 6*(x∧7)+0*(x∧6)+0*(x∧5)+2*(x∧4)+1*(x³)+0*(x²)+7*x+0*(x∧0) 6*(x∧7)+2*(x∧4)+x³+7xHere is another example :
What is the equation for a straight line that would allow you to predict the value of Y from a given value of X. That is, calculate the value of "a" and the value of "b" and then substitute the 2 values into the generic equation (Y = a + bX) for a straight line. (Hint: calculate "b" first)
Answer:
[tex]m=-\frac{13}{20.8}=-0.625[/tex]
Nowe we can find the means for x and y like this:
[tex]\bar x= \frac{\sum x_i}{n}=\frac{16}{5}=3.2[/tex]
[tex]\bar y= \frac{\sum y_i}{n}=\frac{35}{5}=7[/tex]
And we can find the intercept using this:
[tex]b=\bar y -m \bar x=7-(-0.625*3.2)=9[/tex]
So the line would be given by:
[tex]y=-0.625 x +9[/tex]
Step-by-step explanation:
We have the following data:
X: 3,3,2,1,7
Y:6,7,8,9,5
We want to find an equationinf the following form:
[tex] y= bX +a[/tex]
[tex]a=m=\frac{S_{xy}}{S_{xx}}[/tex]
Where:
[tex]S_{xy}=\sum_{i=1}^n x_i y_i -\frac{(\sum_{i=1}^n x_i)(\sum_{i=1}^n y_i)}{n}[/tex]
[tex]S_{xx}=\sum_{i=1}^n x^2_i -\frac{(\sum_{i=1}^n x_i)^2}{n}[/tex]
So we can find the sums like this:
[tex]\sum_{i=1}^n x_i = 3+3+2+1+7=16[/tex]
[tex]\sum_{i=1}^n y_i =6+7+8+9+5=35[/tex]
[tex]\sum_{i=1}^n x^2_i =72[/tex]
[tex]\sum_{i=1}^n y^2_i =255[/tex]
[tex]\sum_{i=1}^n x_i y_i =99[/tex]
With these we can find the sums:
[tex]S_{xx}=\sum_{i=1}^n x^2_i -\frac{(\sum_{i=1}^n x_i)^2}{n}=72-\frac{16^2}{5}=20.8[/tex]
[tex]S_{xy}=\sum_{i=1}^n x_i y_i -\frac{(\sum_{i=1}^n x_i)(\sum_{i=1}^n y_i)}=99-\frac{16*35}{5}=-13[/tex]
And the slope would be:
[tex]m=-\frac{13}{20.8}=-0.625[/tex]
Nowe we can find the means for x and y like this:
[tex]\bar x= \frac{\sum x_i}{n}=\frac{16}{5}=3.2[/tex]
[tex]\bar y= \frac{\sum y_i}{n}=\frac{35}{5}=7[/tex]
And we can find the intercept using this:
[tex]b=\bar y -m \bar x=7-(-0.625*3.2)=9[/tex]
So the line would be given by:
[tex]y=-0.625 x +9[/tex]
Solve the equation x^2 – 16x + 25 = 0 to the nearest tenth.
Answer:
1.8 and 14.3
Step-by-step explanation:
Our equation is a quadratic equation so we will use the dicriminant method
Let Δ be our dicriminant a=1b= -16c= 25Δ= (-16)²-4*25*1=156≥0 so we have two solutions : x and y x= (16-[tex]\sqrt{156}[/tex])/2= 1.7555≈ 1.8y=(16+[tex]\sqrt{156}[/tex])/2=14.244≈ 14.3Translate into an algebraic expression:40 increased by x%
Answer:
2/5x
Step-by-step explanation:
x% of 40= x/100×40
= 40/100x = 2/5x
factorising can someone plz helpw itht the last one than you
Answer:
3x^2(3+x)
Step-by-step explanation:
Answer: 3x^2(3+1)
Because it is divisible by 3 and x^2
1/5 of a chocolate chip cookie has 30 cal how many calories are in a whole cookie
Answer:
150 cal
Step-by-step explanation:
5x30=150
Answer:
150 calories.
Step-by-step explanation:
Assuming there is the same amount of chocolate as well as cookie dough throughout the whole cookie.
You know that 1/5 of a chocolate chip cookie has 30 calories.
Find one cookie, by multiply 5 to both numbers. Set the equation:
1/5x = 30
Isolate the variable. Multiply 5 to both sides:
(1/5x) * 5 = (30) * 5
x = 30 * 5
x = 150
150 calories is your answer.
Bacteria in a petri dish doubles every 10 minutes.
a) If there are 10 bacteria initially, how many are there after 120 minutes?
b) If there are 10 bacteria initially, when would there be a million bacteria?
(Show step by step)
Answer:
Step-by-step explanation:
Givens
Petri Dish A sees a double ever 10 minutes
Petri Dish B sees a double ever 6 minutes
Consequences
A doubles 60 / 10 = 6 times.
B doubles 60 / 6 = 10 times.SolutionIf you work best with numbers then suppose there are 100 bacteria in both dishes at the beginningA = 100 * 2^6B = 100 * 2^10A will have 100 * 64 = 6400 bacteria growing inside AB will have 100 * 1024 = 102400 bacteria growing inside BB/A = 102400 / 6400 = 16There are 16 times as many in B than in A
1,305 divided by 31,828 x100
Answer:
[tex]4 \frac{1}{10}[/tex]
Step-by-step explanation:
=> [tex]\frac{1305}{31828} * 100[/tex]
=> 0.041 * 100
=> 4.1
=> [tex]4 \frac{1}{10}[/tex]
Jerry wants to buy his grandpa’s old car for $500.00. He works 10 hours a week at $7.50 an hour. How many weeks will he need to work before he earns enough money to buy the car?
Answer:
she needs to save up for 3 months
Step-by-step explanation:
convert 4 1/3 feet to inches
Answer:
52 inches
Step-by-step explanation:
Answer:
we have, 1 feet =12 inches
13/3 foot =12×13/3 inches
=52 inches.
thereforethe , the answer is 52 inches.
A package of 8-count AA batteries cost $6.16. A package of 20-count AA batteries cost $15.60. Which statement about the unit prices is true?
Answer:
The unit prices will be within the range of $0.77 ≤x≤$0.78
Step-by-step explanation:
If a package 8-count AA batteries cost $6.16 and a package of same 20-count AA batteries cost $15.60, to calculate the unit price, the following steps must be carried out:
8 counts AA batteries = $6.16
A unit price (i.e 1 count) = x
Cross multiplying
8 × x = 6.16 × 1
x = 6.16/8
x = $0.77 for a unit price
Similarly, if 20-count AA batteries cost $15.60, then:
20 counta = $15.60
1 count = x
Cross multiplying
20 × x = $15.60 × 1
x = $15.60/20
x = $0.78 for a unit price
From above calculation, of can be seen that the unit price is almost similar but with a difference of $0.01 ($0.78-$0.77) which is insignificant. Based on this, we can conclude that a unit price of the battery is between the range
$0.77 ≤x≤$0.78
Answer:
The 8-count pack of AA batteries has a lower unit price of 0.77
per battery.
Step-by-step explanation:
a right square pyramid has a slant height of 20 feet, and the length of a side of the base is 32 feet. what is the height, h, of the pyramid?
Answer:
The pyramid's height h = 12 ft
Step-by-step explanation:
Notice that the slant height of the pyramid forms a right angle triangle with the segment that joins the bottom end of the slant height with the center of the pyramid's base, and with the pyramid height (h).
The segment joining the slant height with the center of the pyramid's base is one half of the side of the base in length, so that it; 16 feet.
then we have a right angle triangle with hypotenuse given by the pyramid's slant height (20 ft), a leg given by 16 ft, and we need to find the length of the second leg (pyramid's height (h).so we use the Pythagorean theorem:
[tex]hyp^2=leg_1^2+leg_2^2\\(20\,ft)^2= (16\,ft)^2+h^2\\h^2=400\,ft^2-256\,ft^2\\h^2=144\,ft^2\\h=12 \,ft[/tex]
Answer:
C.12ft
Step-by-step explanation:
for people on edmentum
What's the difference?
Answer:
first one is the right one
Step-by-step explanation:
Find the distance between a point (–7, –19) and a horizontal line at y = 3. Choices are in the attachment...
Explanation:
The distance we're after is the vertical distance from the point to the line. So we only care about the difference in y values from y = -19 to y = 3
You can count out the spaces or use subtraction along with absolute value
distance from P to Q = |P-Q|
distance from -19 to 3 = |-19-3|
distance from -19 to 3 = |-22|
distance from -19 to 3 = 22
The absolute value is to ensure the result is never negative.
What is the line of best fit? Why do we want the sum of the residuals to be as close to zero as possible?
Answer:
Step-by-step explanation:
What sis line of best fit?
The line of best fit may be explained as a straight line which is drawn to pass through a set of plotted data point which gives the best and most approximate relationship between the data points. A line of best fit is required to give the best approximate value between the set of plotted data points such that it allows making inference on new data points while also ensuring the least possible deviation from the original data points.
Why do we want the sum of the residuals to be as close to zero as possible?
The line of best fit will be the line which gives the least value of residual error. The residual error is reffered to as the difference between the line drawn and the individual data point plotted. These errors are squared and summed together, the line which produces the least residual error is Considered as the leading ne of best fit for the data.
We want the sum of our residual error to be as close to zero as possible, this is to reduce the deviation between our original or plotted data and the modeled data produced by our line of best fit.
Answer:
Step-by-step explanation:
We wan the residuals to be closest to zero because they will help use later in the equation.
52:PLEASE HELP Find the slope of the line that passes through the points (8,2) and (9,7)
Answer:
5/1
Step-by-step explanation:it goes up 5 and over 1
Answer:
5Solution,
Let the points be A and B
A ( 8 , 2 ) -----> (X1 , y1 )
B ( 9 , 7 ) -------> (x2 , y2)
Now,
Slope =[tex] \frac{y2 - y1}{x2 - x1} [/tex]
[tex] = \frac{7 - 2}{9 - 8} [/tex]
[tex] = \frac{ 5}{1} [/tex]
[tex] = 5[/tex]
Hope this helps..
Good luck on your assignment...
3. Write an exponential equation for each coin that will give the coin's value, V, at any time, t. Use
the formula:
Vt) = P(1 + r) where V(t) is the value of the coin in t years, Please HELP! help on number three
Answer:
Coin A : [tex]V(t)=25(1.07)^t[/tex]
Coin B : [tex]V(t)=40(1.05)^t[/tex]
Step-by-step explanation:
Consider the given formula is
[tex]V(t)=P(1+r)^t[/tex]
where, P is current value, V(t) is the value of the coin in t years, and r is annual appreciation rate.
For coin A, current value is 25 dollars and annual appreciation rate is 7%.
[tex]V(t)=25(1+0.07)^t[/tex]
[tex]V(t)=25(1.07)^t[/tex]
For coin B, current value is 40 dollars and annual appreciation rate is 5%.
[tex]V(t)=40(1+0.05)^t[/tex]
[tex]V(t)=40(1.05)^t[/tex]
Therefore, the required equations for coin A and B are [tex]V(t)=25(1.07)^t[/tex] and [tex]V(t)=40(1.05)^t[/tex] respectively.
Solve for x. Please help
Answer:
x = 37/45
Step-by-step explanation:
Here's how similar triangles work. We set up an equation as SIDE 1A/ SIDE 1B = SIDE 2A/ SIDE 2B
Ok, so these 2 triangles are similar, so we can set up a butterfly equation:
Side 1a would be 8x
Side 1b would be 5x +3
Side 2a would be 10x - 2
Side 2b would be 7x
----------------------------------------------------
Our equation would be
8x/(5x+3) = (10x-2)/7x
We cross multiply to get 8x(10x-2) = 7x(5x+3)
Instead of solving and getting squares, we can x on both sides and we get:
8(10x - 2) = 7(5x+3) ----> we simplify to get
80x - 16 = 35x + 21 ----> it's easy sailing from here.
45x = 37
x = 37/45
gosh i hope it's right...
Question 26: write the equation that describes the line with slope=5 and y-intercept =8 in slope intercept form.example: y=mx+b
Answer:
y = 5x + 8
Step-by-step explanation:
Start with y = mx + b: general slope-intercept form, equation of a line:
Replace m with 5, y with 8 and x with 0 (since the y-intercept is (0, 8):
8 = 5(0) + b. Then b must be 8, and the desired equation is
y = 5x + 8
By first calculating the angle of LMN, calculate the area of triangle MNL. You must show all your working.
Answer:
16.66cm²
Step-by-step Explanation:
Given:
∆LMN with m<N = 38°
Length of side NL = 7.2cm
Length of side ML = 4.8cm
Required:
Area of ∆MNL
Solution:
Step 1: Find Angle LMN using the sine rule sin(A)/a = sin(B)/b
Where sin(A) = Sin(M) = ?
a = NL = 7.2cm
sin(B) = sin(N) = 38°
b = ML = 4.8cm
Thus,
Sin(M)/7.2 = sin(38)/4.8
Cross multiply
4.8*sin(M) = 7.2*sin(38)
4.8*sin(M) = 7.2*0.6157
4.8*sin(M) = 4.43304
Divide both sides by 4.8
sin(M) = 4.43304/4.8
sin(M) = 0.92355
M = sin-¹(0.92355) ≈ 67.45°
Step 2: Find m<L
angle M + angle N + angle L = 180 (sum of angles in a triangle)
67.45 + 38 + angle L = 180
105.45 + angle L = 180
Subtract 105.45 from both sides
Angle L = 180 - 105.45
Angle L = 74.55°
Step 3: Find the area of ∆MNL using the formula ½*a*b*sin(C)
Where,
a = NL = 7.2 cm
b = ML = 4.8 cm
sin(C) = sin(L) = sin(74.55)
Thus,
Area of ∆MNL = ½*7.2*4.8*0.9639
= ½*33.31
= 16.655
Area of ∆MNL ≈ 16.66cm²
The mean per capita income is 19,292 dollars per annum with a variance of 540,225. What is the probability that the sample mean would be less than 19269 dollars if a sample of 499 persons is randomly selected? Round your answer to four decimal places.
Answer:
The probability is 0.2423.
Step-by-step explanation:
Given mean per capita = 19292 dollars
Given the variance = 540225
Now find the probability that the sample mean will be less than 19269 dollar when the sample is 499.
Below is the calculation:
[tex]\bar{X} \sim N(\mu =19292, \ \sigma = \frac{\sqrt{540225}}{\sqrt{499}}) \\\bar{X} \sim N(\mu =19292, \ \sigma = 32.90) \\\text{therefore the probability is:} \\P (\bar{X}< 19269) \\\text{Convert it to standard normal variable.} \\P(Z< \frac{19269-19292}{32.90}) \\P(Z< - 0.6990) \\\text{Now getting the probability from standard normal table}\\P(Z< -0.6990) = 0.2423[/tex]
Written Response! Please help!
Evelyn believes that if she flips a coin 480 times, it will land tails up exactly 240 times. What would you tell Evelyn about her prediction?
Based on Evelyn's response, it can be said that she predicts that there is a 50% chance of the coin landing on tails and a 50% chance of the coin landing on heads.
What is the probability?Probability determines the chances that an event would happen. The probability the event occurs is 1 and the probability that the event does not occur is 0.
The probability that the coin lands on tails is half of the number of times the coin is tossed. This means she belives that there is an equal chance that the coin would land on either heads or tails.
To learn more about probability, please check: https://brainly.com/question/13234031
identify an equation in slope intercept form for the line parellel to y=-3x+7 that passes through (2,-4)
Answer:
y= -3x+2
Step-by-step explanation:
Parallel lines have the same slope. We can form an incomplete equation:
y= -3x+b
(make sure to see why the slope is -3)
We can plug in the coordinates of (2, -4):
-4= -3(2)+b
-4= -6+b
2=b
b is 2! We can form an equation: y= -3x+2
****PLEASE HELP BRAINLIEST IF ANSWERED****
What is the sum of the measures of the interior angles of a 9-gon? *
1800 degrees
360 degrees
1260 degrees
720 degrees
Answer:
its 1260°.
as by the formulae,
(n-2)×180°
we get,
sum of interior angle =(9-2)×180°
=1260°.....is anwer.
Fred can mow a lawn in 60 minutes. rocky can mow the same lawn in 40 minutes. how long does it take for both fred and rocky to mow the lawn if they are working together? express your answer as a reduced fraction.
Answer:
24 minutes
Step-by-step explanation:
Fred can mow a lawn in 60 minutes.
Fred's Rate [tex]=\frac{1}{60}[/tex]
Rocky can mow the same lawn in 40 minutes.
Rocky's rate [tex]=\frac{1}{40}[/tex]
Let the time it will take both of them = x minutes
Therefore:
[tex]\frac{1}{60}+\frac{1}{40}=\frac{1}{x}\\$Multiply all through by 1200$\\1200\times \frac{1}{60}+1200\times\frac{1}{40}=1200\times\frac{1}{x}\\20+30=\frac{1200}{x}\\50=\frac{1200}{x}\\$Cross multiply\\50x=1200\\Divide both sides by 50\\x=24\\[/tex]
It would take the two of them 24 minutes to mow the lawn.
What single transformation maps ∆ABC onto ∆A'B'C'? A. rotation 90° clockwise about the origin B. rotation 90° counterclockwise about the origin C. reflection across the x-axis D. reflection across the line y = x
Answer:
B. rotation 90° counterclockwise about the origin.
Step-by-step explanation:
Transformation is the process by which the size or orientation of a given figure is altered without any effect on its shape. Examples are; rotation, reflection, translation and dilation.
Rotation is the process of turning a figure about a reference point called the origin. While reflection is turning a figure about a line to produce its image.
In the given question, ∆ABC is mapped onto ∆A'B'C' by rotating it at 90° counterclockwise about the origin.
The correct option is (B). rotation 90°counterclockwise about the origin.
Given, ∆ABC and ∆A'B'C' are shown in attached figure.
We have to map ∆ABC onto ∆A'B'C',.
A transformation is a general term for four specific ways to manipulate the shape and or position of a point, a line, or geometric figure.
Transformation is also the process by which the size or orientation of a given figure is altered without any effect on its shape.
A rotation is a transformation in which the object is rotated about a fixed point.The direction of rotation can be clockwise or anticlockwise.
It is clear from the fig that the ∆ABC can be mapped over ∆A'B'C' by the rotation of 90°counterclockwise about the origin.
Hence the correct option is (B). rotation 90°counterclockwise about the origin.
For more details follow the link:
https://brainly.com/question/1571997