Answer:
2 + 7i
Step-by-step explanation:
(4 + 8i) + (-2 - i)
open the brackets
4 + 8i - 2 - i
add or subtract like terms
2 + 7i
Answer:
2+7i
Step-by-step explanation:
Open the brackets.
4+8i-2-i
You will get…
2+7i
find the coordinates of 6x² + 6x = 12
Answer:
1 , -2
Step-by-step explanation:
6x^2 + 6x = 12
6x^2 + 6x - 12 = 0
using middle term break method
6x^2 + (12 - 6)x - 12 = 0
6x^2 + 12x - 6x - 12 = 0
6x(x + 2) - 6(x + 2) = 0
(x + 2)(6x - 6) = 0
either (x + 2) = 0 OR (6x - 6) = 0
x + 2 = 0
x = 0 -2
x = -2
6x - 6 = 0
6x = 6
x = 6/6
x = 1
therefore , x = 1 , -2
Select the correct answer.
Which expression is equivalent to the given expression?
In(2e/x)
A. In 2 - In x
B. In 1 + In 2 - ln x
C. 1 + In 2 - In x
D. In 2 + ln x
Answer:c
Step-by-step explanation:
The equivalent expression is 1 + In 2 - In x.
How to estimate an equivalent to the given expression?Given:
[tex]$\ln \left(\frac{2 e}{x}\right)$[/tex]
Apply log rule:
[tex]$$\log _{C}\left(\frac{a}{b}\right)=\log _{c}(a)-\log _{c}(b)$[/tex]
[tex]$&\ln \left(\frac{2 e}{x}\right)=\ln (2 e)-\ln (x) \\[/tex]
= ln (2e) - ln (x)
Apply log rule:
[tex]$\log _{c}(a b)=\log _{c}(a)+\log _{c}(b)$[/tex]
ln (2e) = ln (2) + ln (e)
= ln (2) + ln (e) - ln (x)
Apply log rule:
[tex]$\log _{a}(a)=1$[/tex]
= ln (2)+1-ln (x)
Therefore, the correct answer is option C. 1 + In 2 - In x.
To learn more about log rule
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Which expression is equivalent to 3/x5y?
Answer:
option B
Step-by-step explanation:
[tex]\sqrt[3]{x^5 \ y} = (x^5 \ y )^\frac{1}{3} \ \ \ \ \ \ \ \ \ \ \ \ [ \ \sqrt[n]{x} = x^\frac{1}{n} \ \ , \ (xy)^a = x^a y^a]\\\\[/tex]
[tex]= x^{ (5 \times \frac{1}{3} )} \ y ^{\frac{1}{3} \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ [ \ ( x^a )^b = x^{ab} \ ]\\\\\\[/tex]
[tex]= x^{\frac{5}{3} }\ y^{\frac{1}{3}}[/tex]
Which expression can be used to convert 22 Australian dollars to US dollar
Answer:26.4
Step-by-step explanation:1.2 x22
Describe the transformation of f(x) = sin x to g(x) = sin x – 7.
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Answer:
C. 7 units down
Step-by-step explanation:
The y-coordinate of a point on a graph is the function value. It tells how far up from the x-axis the point is located. When 7 is subtracted from the function value, the y-coordinate is 7 less than it was. That is, the point has moved 7 units down.
The area of a circle is 64 pi ft squared. What is the circumference, in feet? Express your answer in terms of pi
Determine whether the given value is a statistic or a parameter. A homeowner measured the voltage supplied to his home on all 7 days of a given week,and the average​ (mean) value is 120.7 volts.
A. The given value is a parameter for the week because the data collected represent a population.
B. The given value is a statistic for the week because the data collected represent a population.
C. The given value is a statistic for the week because the data collected represent a sample.
D. The given value is a parameter for the week because the data collected represent a sample
Answer:
A. The given value is a parameter for the week because the data collected represent a population
Step-by-step explanation:
Parameters in a study refers to the numbers that are used to summarize the data for the entire population. Whereas, a statistic are used to summarize the data from a sample only.
In the context, it is given that a person measures the voltage supply to his home for all the seven days and finds the average value of the voltage. The homeowner here considers the population of his sample to make his study.
Thus it is a parameter for the entire week as the data represents a population.
simpify 20/[(5-{24/2-(7-5of3)}]
Answer:
Why do we need an order of operations?
Example: In a room there are 2 teacher's chairs and 3 tables each with 4 chairs for the students. How many chairs are in the room?
We know there are 14, but how do we write this calculation? If we just write
2 + 3 x 4
how does a reader know whether the answer is
2 + 3 = 5, then multiply by 4 to get 20 or
3 x 4 = 12, then 2 + 12 to get 14?
There are two steps needed to find the answer; addition and multiplication. Without an agreed upon order of when we perform each of these operations to calculate a written expression, we could get two different answers. If we want to all get the same "correct" answer when we only have the written expression to guide us, it is important that we all interpret the expression the same way.
One way of explaining the order is to use brackets. This always works. To say that the 3 x 4 is done before the adding, we would use brackets like this:
2 + (3 x 4)
The brackets show us that 3 x 4 needs to be worked out first and then added to 2. However, we can also agree on an order of operations, which is explained below.
Another example: Calculate 15- 10 ÷ 5
If you do the subtraction first, you will get 1. If you do the division first, which is actually correct according to the rules explained below, you will get 13. We need an agreed order.
Find the investment value when compounded anually.
P = $120,000, r= 5.3%, t = 8 yr
Given:
[tex]P=\$120,000[/tex]
[tex]r=5.3\%[/tex]
[tex]t=8\text{ years}[/tex]
To find:
The value of the investment when the interest is compounded annually.
Solution:
The formula for amount is:
[tex]A=P\left(1+\dfrac{r}{n}\right)^{nt}[/tex]
Where, P is the principal, r is the rate of interest in decimal, n is the number of time interest compounded in an years, and t is the number of years.
The interest is compounded annually. So, [tex]n=1[/tex].
Substituting [tex]P=120000, r=0.053, n=1, t=8[/tex] in the above formula, we get
[tex]A=120000\left(1+\dfrac{0.053}{1}\right)^{1(8)}[/tex]
[tex]A=120000\left(1.053\right)^{8}[/tex]
[tex]A=181387.85936[/tex]
[tex]A\approx 181387.86[/tex]
Therefore, the value of the investment after 8 years is $181,387.86.
1. Estimate the area of the irregular shape. Explain your method and show your work.
2. The coordinates of the vertices of △LMN are L (-2, 4), M (3, -1), and N (0, -4). Determine whether △LMN is a right triangle and support your decision. Show all work.
3. The coordinates of the vertices of quadrilateral PQRS are P (-6, 2), Q (-1, 4), R (2, 2), and S (-3, 0). Alexandra states that quadrilateral PQRS is a parallelogram. Prove or disprove Alexandra’s statement. Show all work.
Answer:
Step-by-step explanation:
1. Do not see a figure, and unsafe to download and execute .docx.
2. Vectors LM<5,-5>, NM<3,3>, NL<2,-8>
Since LM.NM = 15-15 = 0, LM and NM are orthogonal, hence the given points form a right triangle.
3. A parallelogram has opposite sides parallel.
Slope PQ = (4-2) / (-1 - -6) = 2/5
Slope RS = (2-0) / (2- -3) = 2/5
Therefore PQ || RS
Slope PS = (2-0)/(-6- -3) = -2/3
Slope QR = (4-2)/(-1 -2) = -2/3
Therefore PS | QR
Since opposite sides are parallel, PQRS is a parallelogram
Answer:
Step-by-step explanation:
1. There are 31 complete are almost complete squares.
Top line is about 3.5 squares
Right side is about 1.8
Bottom about 3.5 and left side about 1.2.
Total approximately 41 square units.
2. If it is a right triangle then 2 sides will be perpendicular.
Slope of LM = (-1-4)/(3 +2 = -1
Slope of MN = (-4+1)/ -3 = -3/-3 = 1.
So as the product of the slope = -1 * 1 = -1 the angles between LM and MN is a right angle and LMN is a right triangle.
How many side of the triangle are congruent? Explain.
A) 0
B) 2
C)3
D) not enough information given
Answer:
Option B
Step-by-step explanation:
In the given triangle,
Two sides of the triangle measure 2 cm and one side measures 3 cm.
Therefore, in this triangle two sides measuring 2 cm are congruent.
Option B is the correct option.
Eden has a part-time job
She is paid £7.20 per hour
This week she worked for 18½ hours
Work out Eden's total pay for this week
Answer:
$133.20
Step-by-step explanation:
You make 7.20 an hour for 18 1/2 hours. You must multiply to know how much she made that week
7.20/hr = ?/18 1/2 hr
7.20 x 18 1/2
7.20 x 18.5=
133.20
In triangle ABC, the measure of angle B is 22° more than three times the measure of angle A. The measure of angle C is 53° more than the measure of angle A. Find the measure of each angle.
Answer:
105
Step-by-step explanation:
53+22=75, 180-75=105
How many one-to-one functions are there from the set {A, B, C} to the set {x, y, z, t, w, k}?
Answer:
120 different one-to-one functions
Step-by-step explanation:
A one-to-one function means that each element from the domain can be mapped into only one element from the range (like for a typical function), and each element from the range can be mapped only once.
This means that, for two different inputs x₁ and x₂, we can't have:
f(x₁) = f(x₂)
Because that would mean that two different values of the domain are being mapped into the same element from the range.
Ok, now that we know this, let's count the number of possible "mappings" for each element in the domain.
For the first element, A, we have the options {x, y, z, t, w, k} (a total of 6 options).
For the second element, B, we will have an option less (because one was already taken) so here we have 5 options.
For the last element on the domain, C, there will be again an option less than in the previous case, so here we have 4 options.
The total number of combinations (each combination defines a different one-to-one function) is equal to the product between all the options for each case, then the total number of one-to-one functions is:
C = 6*5*4 = 120
There are 120 different one-to-one functions.
1. Find the equation and solve for k: y varies inversely as x and y = 6 when x = 18.
An inverse function is y = k/x
replace x and y with the given values:
6 = k/18
Solve for k by multiplying both sides by 18:
k = 108
1. Find the equation and solve for k: y varies inversely as x and y = 6 when x = 18.
Solution:-[tex]\sf{The \: relation \: y \: varies \: inversely \: as \: x \: translates \: to \: y = \frac{k}{x}.}[/tex]
Substitute the values to find k:
[tex]\sf\rightarrow{y= \frac{k}{x} }[/tex]
[tex]\sf\rightarrow{6= \frac{k}{18} }[/tex]
[tex]\sf\rightarrow{k=(6)(18)}[/tex]
[tex]\sf\rightarrow{K={\color{magenta}{108}}}[/tex]
Answer:-[tex]\sf{The \: equation \: of \: variations \: is \: y={ \color{red}{ \frac{108}{x} }}}[/tex]
[tex]{\huge{\color{blue}{━━━━━━━━━━━━}}}[/tex]
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Listed below are the top 10 salaries (in millions of dollars) of television personalities in a recent year.
38 36 35 27 15 13 12 10 9.6 8.4
Use the sample data to construct a 95% confidence interval for the population mean and correctly interpret your answer.
Answer:
The correct answer is "(11.69, 29.11)".
Step-by-step explanation:
Given:
[tex]38 \ 36\ 35\ 27\ 15\ 13\ 12\ 10\ 9.6\ 8.4[/tex]
[tex]n=10[/tex]
As per the question,
Mean,
[tex]\bar x=20.40[/tex]
Standard deviation,
[tex]s=12.17[/tex]
or,
[tex]df=10-1[/tex]
[tex]=9[/tex]
For 95% confidence interval,
[tex]t^*=2.262[/tex]
hence,
The 95% confidence interval will be:
= [tex]\bar x \pm \ t^*\times \frac{s}{\sqrt{10} }[/tex]
By substituting the values, we get
= [tex]20.40 \pm 2.262\times \frac{12.17}{\sqrt{10} }[/tex]
= [tex](11.69, 29.11)[/tex]
Consider the following. (Assume that the coins are distinguishable and that what is observed are the faces or numbers that face up.) Three coins are tossed; the result is at most one tail. What sets of elements are included in the sample space?
Answer:
a) [tex]P(<1)=(HHH,HHT,HTH,THH)[/tex]
b) [tex]n=(HHH, HHT, HTH, HTT, THH, THT, TTH, TTT).[/tex]
Step-by-step explanation:
From the question we are told that:
3 coin are tossed
Therefore
Sample space [tex]n=(HHH, HHT, HTH, HTT, THH, THT, TTH, TTT).[/tex]
Generally the sets that correspond with the result of at most one tail is therefore given as follows
[tex]P(<1)=(HHH,HHT,HTH,THH)[/tex]
Therefore
The result is at most one tail when
[tex]P(<1)=(HHH,HHT,HTH,THH)[/tex]
The shortest route from London to Oxford is 55 miles.
A lorry is expected to take 1.1 hours to travel this route.
The lorry actually travels by a different route which increases the distance by 15%, but it still arrives in 1.1 hours.
By how many more mph than the expected speed does the lorry travel?
Answer:
so to find the mph of the lorry for the original route we divide 66 by 55 since it 66 is 1.1 of 60
66 divided by 55=1.2
so it takes 1 minutes 12 seconds for the lorry to go a mile
now we multiply 55 by 1.15=63.25
so we divide 66 by 63.25=1.04347826087
so it takes 1 minute and 1 second for the the lorry to go a miles
1 minute 1 second is 59 miles per hour
1 minute 12 seconds is 50 miles per hour
so the lorry travels 9 mph over its expected speed
Hope This Helps!!!
=================================================
Explanation:
distance = rate*time
d = r*t
r = d/t
r = 55/1.1
r = 50
The lorry's original speed is 50 mph when going the original route.
-----------------
Now consider the longer route, which is 15% longer compared to the original 55 mile route. So the longer route is 1.15*55 = 63.25 miles exactly. Or you could say 15% of 55 = 0.15*55 = 8.25 which adds onto the original 55 to get 55+8.25 = 53.25; either way the longer distance is 63.25 miles.
Computing the new rate or speed gets us
r = d/t
r = 63.25/1.1
r = 57.5
-----------------
When traveling the original route, the lorry goes 50 mph. When traveling the longer route, the lorry goes 57.5 mph. This is a difference of 57.5 - 50 = 7.5 mph
Meaning that the lorry must drive 7.5 mph faster on the longer route compared to the shortest route. This is if the driver wants to make the trip in the same 1.1 hour timeframe.
Note: 1.1 hours = 1.1*60 = 66 minutes = 1 hour, 6 minutes.
HELP ASAP PLEASE Alaina has $28 in her account. She wants to purchase a pair of shoes that costs $45. If Alaina makes the purchase, which integer will represents the amount of money in Alaina's account?
Answer:
-17
Step-by-step explanation:
28-45= -17 dollars in her account
Weekly demand for a certain brand of a golf ball at The Golf Outlet is normally distributed with a mean of 35 and a standard deviation of 5. The profit per box is $5.00. Write an Excel formula that simulates the weekly profit:
= 5 * 35 * NORMSINV(RAND())
= 5* NORMINV(RAND(), 35, 5)
= 5 * RANDBETWEEN(5, 35)
= NORMINV(RAND(), 5 * 35, 5)
Answer:
= 5 * NORMINV(RAND(), 35, 5)
Step-by-step explanation:
From the given information:
The total weekly profit is achieved by the multiplication of the unit profit (5) and the weekly demand.
Here, the weekly demands obey a normal distribution where the mean = 35 and the standard deviation = 5.
Using the Excel Formula:
The weekly profit can be computed as:
= 5 * NORMINV(RAND(), 35, 5)
One evening Papa John’s sold a total of 33 pizzas topped with pepperoni, sausage, or pepperoni and sausage. There were 29 pizzas that had pepperoni. Of these, 15 also had sausage. How many more pizzas had pepperoni only than had sausage only?
Answer:
10
Step-by-step explanation:
Total pizza topped with pepperoni, sausage or pepperoni and sausage = 33
Number of pizzas with pepperoni = 29
Number of pizzas with pepperoni and sausage = 15
Pizza with pepperoni only = 29 - 15 = 14
Pizza with sausage only = 33 - 29 = 4
Pepperoni only than sausage only :
14 - 4 = 10
A shopkeeper bought bycicle for rs 3520 and a mobile for rs 4690 . he sold both the items for rs 8650 calculate how much money did he gain
Answer:
Rs 440
Step-by-step explanation:
Price of bicycle = 3520
Price of mobile = 4690
Cost Price of both mobile and bicycle = 3520 + 4690
=> 8210
Selling price of both mobile and bicycle = 8650
Profit = selling price - cost price
= 8650 - 8210
= 440
Therefore he gained Rs 440
A scale model of a building has a scale of 3 : 79.
The height of the real building is 24 m.
Find the height of the scale model.
Give your answer in cm to 2 dp.
Answer:
The height of the scale model is of 91.14 cm.
Step-by-step explanation:
Scale problems are solved by proportions, using rule of three.
A scale model of a building has a scale of 3 : 79.
This means that 3m on the drawing represent 79m of real height.
The height of the real building is 24 m.
3m - 79m
xm - 24m
Applying cross multiplication
[tex]79x = 72[/tex]
[tex]x = \frac{72}{79}[/tex]
[tex]x = 0.9114[/tex]
In centimeters:
Multiplying by 100:
0.9114*100 = 91.14 cm.
Show that the number 6 is a rational number by finding a ratio of two integers equal to the number
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Answer:
6 = 6/1 = 12/2 = 18/3
Step-by-step explanation:
The simplest ratio of integers with a value of 6 is ...
6 = 6/1
We can multiply numerator and denominator by any non-zero integer value to obtain an equivalent:
6 = 12/2 = 18/3 = -54/-9
A comet travels at an average speed of 273,000 km/h.
It takes 8 days for the comet to reach Earth.
Find the distance, in km, the comet travelled
Answer: 52,416,000 km
Step-by-step explanation:
If a comet travels 273,000 km/hr
1) Multiply 273,000 km by 24 hours to find how far the comet travels in one day
2) multiply the answer from 1 by 8 to determine how far it travels in 8 days
1) [tex]\frac{273,000 km}{hr}[/tex]*[tex]\frac{24 hr}{1 day}[/tex] = [tex]\frac{6,552,000km}{day}[/tex] (hours cancel out)
2)[tex]\frac{6,552,000km}{day}[/tex]*8 day= 52,416,000 km in 8 days
The comet approximately travelled 52,416,000km from when it began to travel to when it reached Earth. Hope this helped :)
When comparing two box-plots that show the same type of information, what determines agreement within the data?
A.the range of the quartiles in each data set
B.the median of each data set
C.the mean of each data set
D.the number of values in each data set
Answer:
c.the mean of each data set
Answer:
A
Step-by-step explanation:
What should the m<3 be for —- ?
9514 1404 393
Answer:
m∠3 = 63°
Step-by-step explanation:
Where a transversal crosses parallel lines, all of the obtuse angles are congruent, and all of the acute angles are congruent. The obtuse and acute angles are supplementary.
Angle 1 is an obtuse angle; angle 3 is an acute angle.
angle 3 = 180° - angle 1 = 180° -117° = 63°
The measure of angle 3 is 63°.
_____
Additional comment
There are a number of applicable theorems describing the different angle relationships. Taken together, they are summarized by the first statement above. For example, we could declare angles 1 and 4 to be "corresponding" (hence, congruent), and angles 4 and 3 to be a "linear pair", hence supplementary. The net result is that angle 1 is supplementary to angle 3, as we said above.
We could also get there via relations between alternate exterior angles, alternate interior angles, consecutive exterior or interior angles, and other ways. While that terminology is useful to understand in some problems, it is largely irrelevant here.
A boat can carry 22 people 940 people went on the boat how many trips did the boat do
Which of the following statistics would provide a good comparison between data sets?
Group of answer choices
all of these
correlation
interquartile range
mean
The following statistics which would provide a good comparison between data sets is all of the above and is denoted as option A.
What is Statistics?This refers to the branch of science which involves the collection and interpretation of data sets or variables. There are different ways or techniques which are used and they vary according to the features of the data set.
There are statistics which provide a good comparison between data sets include the following below:
correlationinterquartile rangemeanThis comparison is done so as to to prove that there are no differences between them and other reasons.
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A custodian has 5 1/2 gallons of paint. Each of the bookcases she is painting requires 1/2 gallon of paint. How many bookcases will the custodian be able to paint with that amount of paint
A. 3
B. 4
C. 11
D. 15