After simplifying the expression to a singles complex number, it becomes 1+√3i.
A complex number is a unique kind of number in the number system, it has two parts. One it called the real part which is a real number and an imaginary part which is also a real part but accompanied by the specific notation called iota.
Here a complex number Z is provided to us,
Z = [2+√(12)]/2
As we can see,
Here we have √12
We can write it as,
√(2×2×3)
= 2√(3)
Here, √1 is given that special notation "IOTA (i)" which we mentioned earlier.
=2√3i
So, Z becomes,
Z = (2+2√3i)/2
Z= 1+√3i
So, the simpler form of Z = [2+√(12)]/2 is Z= 1+√3i.
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The radius, R, of a sphere is 4.8 cm. Calculate the sphere's volume, V. Use the value 3.14 for it, and round your answer to the nearest tenth. (Do not round any intermediate computations.) 0 V = 3 em Х 5 ?
The formula to calculate the volume of a sphere is given to be:
[tex]V=\frac{4}{3}\pi r^3[/tex]where r is the radius.
From the question, we have the following parameters:
[tex]\begin{gathered} \pi=3.14 \\ r=4.8 \end{gathered}[/tex]Therefore, the volume is calculated to be:
[tex]\begin{gathered} V=\frac{4}{3}\times3.14\times4.8^3 \\ V=463.0 \end{gathered}[/tex]The volume is 463.0 cm³.
Write the equation in vertex form for the parabola with vertex (0, 6) and focus (0, 3).
Answer:
Stepbystep explanation:
the axis of the parabola is x=0So the parabola is of the form (x−0)2=4a(y−6)Now the length of latus rectum =4a=4× the distance between focus and vertex =4×3=12Hence the parabola is x2=−12(y−
At 95% confidence, how large a sample should be taken to obtain a margin of error of 0.042 for the estimation of a population
proportion? Assume that past data are not available for developing a planning value for p*. Round up to the next whole number.
The sample size should be taken as 545.6 to obtain a margin of error of 0.042 for the estimation of a population proportion.
What is sample size?
The process of deciding how many observations or replicates to include in a statistical sample is known as sample size determination. Any empirical study with the aim of drawing conclusions about a population from a sample must take into account the sample size as a crucial component. The sample size chosen for a study is typically influenced by the cost, convenience, or ease of data collection as well as the requirement that the sample size have adequate statistical power.
As given in the question,
Confidence level is 95% and the margin of error is 0.042
So,
1  α = 0.95,
α = 0.05,
E = 0.042
planning value (p) = 0.5
To calculate Sample size the formula is:
[tex]n = \frac{p(1p)(Z_{a/2})^2}{E^2}[/tex]
From the table we can find that:
[tex]Z_{a/2} = 1.96[/tex]
Putting the values given in the question in formula:
[tex]n = \frac{0.5(0.5)(1.96)^2}{(0.042)^2}[/tex]
[tex]n = \frac{(0.25)(1.96)^2}{(0.042)^2}[/tex]
[tex]n = \frac{(0.25)(3.841)}{0.00176}[/tex]
n = 545.6
Hence the sample size is 545.6
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Find the value of x that will make AB5x + 20AВ.3x + 60x= [?]Enter
ANSWER:
The value of x is 20
STEPBYSTEP EXPLANATION:
By properties of the angles we know that these angles are equal, since they are alternative external angles. Thanks to that we can do the following equality to calculate the value of x:
[tex]5x+20=3x+60[/tex]Solving for x:
[tex]\begin{gathered} 5x3x=6020 \\ 2x=40 \\ x=\frac{40}{2} \\ x=20 \end{gathered}[/tex]Find the length of CD.express the awnser as a fraction times pie.
Given the figure of the circle B
the radius of the circle = r = BC = 9
the measure of the angle CBD = 40°
We will find the length of the arc CD
The length of the arc is given by the formula:
[tex]l=\theta\cdot r[/tex]where: θ is the central angle opposite to the arc measured in radians
so, we will convert the given angle from degree to radian
[tex]\theta=40\cdot\frac{\pi}{180}=\frac{2}{9}\pi[/tex]Substitute with the given values
so, the length of the arc =
[tex]l=\frac{2}{9}\pi\cdot9=2\pi[/tex]So, the answer will be:
The length of the arc CD = 2π
1. The data set represents the number of cars in a town given a speeding ticketeach day for 10 days.2 4 5 5 7 7 8 8 8 121. What is the median? Interpret this value in the situation.*
ANSWER:
7
STEPBYSTEP EXPLANATION:
We have the following data:
[tex]2,4,5,5,7,7,8,8,8,12[/tex]The median is the data value that separates the upper half of a data set from the lower half. Therefore:
In this case, being even, the two data are half, but since the value is the same, that is, 7, the median is equal to 7.
The interpretation of this value is in the middle of the 10 days (days 5 and 6), 7 would be the number of cars in a town given a a speeding ticket.
The factors of 6 are also the factors of which number? A 5 C 20 B 10 D 30
Solution:
Factors of a number are defined as numbers that divide another number evenly or exactly without giving any remainder.
Hence,
The factors of 6 are the numbers that can divide 6 without any remainder.
[tex]\text{Factors of 6 =1,2,3,6}[/tex][tex]\begin{gathered} \text{Factors of 5=1,5} \\ \text{Factors of 20=1,2,4,5,10,20} \\ \text{Factors of 10=1,2,5,10} \\ \text{Factors of 30=1,2,3,5,6,10,15,30} \end{gathered}[/tex]From the above, we can deduce that the factors of 6 are also the factors of 30.
The corr
Given the definitions of f(x) and g(x) below, find the value of (gof)(9). f(x) = x + 11 g(x) = 3x2  x + 14
In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data
f(x) = x + 11
g(x) = 3x²  x + 14
(gof)(9) = ?
Step 02:
(gof)(x) = 3(x+11)²  (x+11) + 14
= 3(x² + 2(x)(11) + 121) + x  11 + 14
= 3(x²  22x + 121) + x  11 + 14
= 3x²  66x + 363 + x  11 + 14
= 3x²  65x + 366
(gof)(9) = 3(9)²  65(9) + 366
= 3(81)  585 + 366
= 243  585 + 366
= 24
The answer is:
(gof)(9) = 24
What is the answer to 2(7x3)+9
Answer:
14x+3 is the answer I think
The solution to the given equation would be [tex]14x+3[/tex].
Hope this helps!
Evaluate and simplify the expression
when a = 2 and b = 4.
4a  2(a + b) + 1 = [?]
Answer:
3
Stepbystep explanation:
4(a)  2(a + b) + 1 = [?]
4(2)  2(2+4) + 1
8  4  8 + 1
appilcation of bodmas
4  8 + 1
 4 + 1

3
I'll give brainliest!
Answer:
x equals to 11!!!
Answer:
11.
Stepbystep explanation:
1.02 x 10^11 = 102,000,000,000
Hope this helps!
Brainliest please, thanks!
A rectangular prism has dimensions of 2 cm by 2 cm by 5 cm. What is its surface area? Explain or show your reasoning
If a rectangular prism has dimensions of 2cm by 2 cm by 5 cm, then the surface area of the rectangular prism is 48 centimeter square
The length of the rectangular prism = 2 cm
The width of the rectangular prism = 2 cm
The height of the rectangular prism = 5 cm
The surface area of the rectangular prism = 2(lw+lh+hw)
Where l is the length
w is the width
h is the height
Substitute the values in the equation
The surface area of the rectangular prism = 2(2×2+2×5+2×5)
= 2(4+10+10)
= 2×24
= 48 centimeter square
Hence, if a rectangular prism has dimensions of 2cm by 2 cm by 5 cm, then the surface area of the rectangular prism is 48 centimeter square
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Can someone please explain to me where I did my math wrong and correct me. The answer is supposed to be $1065.00
The problem says: Lonnie Flanagan's weekly gross pay is $1250. Each week she has $64.37 in deductions, plus state tax of 2% of her gross pay, social security taxes of 6.2%, and Medicare taxes of 1.45%. What is her net pay?
I did 1250  64.37 = 1185.63
1185.63 (2%) = $23.71 State income Tax
1185.63 (6.2%) = $73.51 Social Security Tax
1185.63 (1.45%) = $17.19 Medicare tax
Then I added the 3 together.
$23.71 + $73.51 + $17.19 = $114.41
Then I subtracted $113.41 from $1250.
1250  113.41 = $135.59 net pay.
What did I do wrong?
The net pay for Lonnie Flanagan is $1065.
How to calculate the net pay?From the information, Lonnie weekly gross pay is $1250 and each week she has $64.37 in deductions, plus state tax of 2% of her gross pay, social security taxes of 6.2%, and Medicare taxes of 1.45%.
Her net pay will be:
= Gross pay  Deduction  Tax  Social security  Medicare
= $1250  $64.37  (2% × $1250)  (6.2% × $1250)  (1.45% × $1250)
= $1250  $64.37  $25  $$77.50  $18.125
= $1065
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Sam reads 30 pages of a book in 40 minutes. Which statement identifies a person with the same reading rate as Sam.
Answer:
The correct option is B
Leroy reads 22.5 pages in 30 minutes
At the rate of 3 pages in 4 minutes
Explanation:
Given that Sam reads 30 pages of books in 40 minutes, he reads at the rate of 3 pages in 4 minutes (3/4 = 0.75).
To know which of the options has the same rate as Sam's, we need to find which rate is equal to his'
A. Francine reads 40 pages in 55 minutes
Rate = 40/55 = 8/11
B. Leroy reads 22.5 pages in 30 minutes
Rate = 22.5/30 = 0.75
C. Paul reads 150 pages in 3.25 hours. Since 3.25 hours = 195 minutes
Rate = 150/195 = 0.77
D. Bill reads 60 pages in 2 hours
Rate = 60/120 = 0.5
Garcia Co. owns equipment that cost $81,600, with accumulated depreciation of $43,200.
Record the sale of the equipment under the following three separate cases assuming Garcia sells the equipment for (1) $50,600 cash, (2) $38,400 cash, and (3) $33,300 cash.
(1) $50,600 cash implies that $50,600  $38,400 = $12,200
Hence gets gain of $12,200.
(2) $38,400 cash implies that $38,400  $38,400 = $0
Hence No profit no loss.
(3) $33,300 cash implies that $33,300  $38,400 =  $5,100
Hence loss of $5,100.
Depreciation :Depreciation is the gross reduction in the book value of an asset due to regular use or wear and tear.
A capital gain occurs when Garcia Co. receives an amount in excess of the book value of the equipment.
If Garcia Co. receives an amount equal to the book value of the equipment, no profit or loss will result from the disposal.
If Garcia Co. receives an amount below the book value of the equipment, it will experience a capital loss.
In the given question cost of equipment is $81,600 with accumulated depreciation of $43,200 so that the book value will be
$81,600  $43,200 = $38,400.
Now (1) $50,600 cash implies that $50,600  $38,400 = $12,200
Hence gets gain of $12,200.
For (2) $38,400 cash implies that $38,400  $38,400 = $0
Hence No profit no loss.
For(3) $33,300 cash implies that $33,300  $38,400 =  $5,100
Hence loss of $5,100.
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please help! I do not understand and it is due tonight!!!!!!!
Consider that there are, generally, the following types of angles pairs,
1. Adjacent Angles: Angles that share a common side and are formed on the same vertex.
2. Complementary Angles: Angles that are adjacent and together form a right angle.
3. Supplementary Angles: Angles that are adjacent and whose sum of degree measures is 180 degrees.
a.
The adjacent angles to angle 4 are angles 1 and 3.
There are no complementary angles associated with angle 4.
The supplementary angles to angle 4, are angles 1 and 3.
Thus, the angle pairs that include angle 4 are,
[tex](\angle4\text{ and }\angle1),\text{ }(\angle4\text{ and }\angle3)[/tex]b.
The adjacent angles to angle 5 are angles 6 and 7.
There are no complementary angles associated with angle 5.
The supplementary angles to angle 5, are angles 6 and 7.
Thus, the angle pairs involving angle 5 are,
[tex](\angle5\text{ and }\angle6),\text{ }(\angle5\text{ and }\angle7)[/tex]
Cuál es la probabilidad de obtener exactamente 5 caras en 10 lanzamientos de una moneda?
The probability of getting exactly 5 heads in 10 tosses of a coin 24.6%
What is Probability ?
The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.
Ten times are spent flipping coins.
Total number of results = 2¹⁰ = 1024
C(10, 5) = 252 is the total number of favorable outcomes.
Probability is
252/1024,
which equals :
=0.24, or
=24.6%.
Therefore, the chance of getting exactly 5 "heads" out of a possible 10 is 0.246, or 24.6%.
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Given the equation 5X10=50 which properties will be used to solve for XA. Adition and subtractionB. Subtraction and divisionC. Adition and division D. Subtraction and Multiplication
Let's solve for x and see what properties are used
First, add 10 to both sides of the equation
[tex]\begin{gathered} 5x10=50 \\ 5x10+10=50+10 \\ 5x=60 \end{gathered}[/tex]Now, divide by 5 on both sides of the equation
[tex]\begin{gathered} \frac{5x}{5}=\frac{60}{5} \\ x=12 \end{gathered}[/tex]Therefore, the correct answer is C. Adition and division
If the events have the same theoretical probability of happening, then they are called
Answer:7937
Stepbystep explanation:7596
Artrigerator contains 5 cans of diet soda and 8 cans of regular soda. If three cans of soda are randomly selected without replacement, determine the probability that all can selected are diet soda. Use combinations to determine theprobabilityThe probability that all can selected are diet soda is(Type an integer or a simplified fraction)
The total number of cans in the refrigerator is 5 + 8 = 13
The number of diet soda cans is 5 while the number of regular soda cans is 8
If three cans are selected, the probability that the can is a diet soda can is
5/13
Since it was not replaced, the number of diet soda cans left would be 4 and the total number of cans left would be 12. The probability that the next selected can is a diet can is
4/12 = 1/3
Since it was not replaced, the number of diet soda cans left would be 3 and the total number of cans left would be 11. The probability that the next selected can is a diet can is
3/11
Thus, the probability that the three selected cans are diet soda cans is
5/13 * 1/3 * 3/11 = 5/143
= 0.035
the probability that the three selected cans are diet soda cans is 0.035
da can
r
Hello! Please take a look at the picture to see the questions, thank you!
In the question, we are asked to find the degree and the leading coefficient of the polynomial below
[tex]f(x)=3x^4+2x^3+5x^2+7[/tex]Explanation
The degree of the polynomial is the highest of all the degrees that make up the polynomial. Since each term in the polynomial has a degree we will pick the largest one.
Also, the leading coefficient is the coefficient of the term with the largest degree. Using these concepts, we can derive our answer as.
Answer:
[tex]4,3[/tex]Option A
A football team was able to run the ball for 8 yards on their first play. On the second play they lost 12 yards. The third play they lost another 11 yards. What was their total yards they gained?
The total yards gained or lost is the algebraic sum so the resultant yards is 15 yards thus they lose 15 yards.
What is the arithmetic operator?Arithmetic operators are four basic mathematical operations in which summation, subtraction, division, and multiplication involve.,
Subtraction = Minus of any two or more numbers.
Summation = addition of two or more numbers or variable
Let's consider all gained yards by positive (+) and all lost yards by negative ().
Given that,
In the first play = +8 yards (gain)
In second play = 12 yards (lost)
In the third play = 11 yards (Lost)
So total yards = +8  12  11 = 15 (Lost)
Therefore, the football team lost 15 yards.
Hence "The total yards gained or lost is the algebraic sum so the resultant yards is 15 yards thus they lose 15 yards".
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There is a 5% chance that the mean reading speed of a random sample of 21
second grade students will exceed what value?
There is a 5% chance that second graders will be faster than 94.597 wpm.
Sample size = 21
standard deviation = 10 wpm
SE = 10/sqrt(21) = 2.18 as a consequence.
Let X be the average reading speed of 21 secondgrade students. z = (X  91)/2.18 Normal(91,2.18) (91,2.18).
If the 95th percentile of a standard normal variable z is 1.65 [5% probability], the outcome is 91 + 1.65 x 2.18 = 94.597.
So there's a 5% chance that the average reading speed of a random sample of 21 secondgraders will be faster than 94.597 wpm.
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The graph of f(x) = x^3 is stretched vertically by a factor of 6. The graph
is then translated 9 units to the right and 3 units down. Write the equation of the transformed function.
Answer:
Transformed equation: 6(x9)³  3
Stepbystep explanation:
Answer:
6(x  9)^3  3
Stepbystep explanation:
1. Vertical Stretching : f(x) > g(x): [tex]g(x) = 6x^{3}[/tex]
2. Horizontal Move: g(x) > h(x): [tex]h(x) = 6{(x  9)}^{3}[/tex]
3. Vertical Move: h(x) > F(x): [tex]F(x) = 6{(x  9)} ^{3}  3[/tex]
O GRAPHS AND FUNCTIONSFinding values and intervals where the graph of a functioning is..
a.
From the graph we notice that when x=1 the value of the function is zero; therefore:
[tex]f(1)=0[/tex]and it is not negative.
b.
The function is positive when its graph is above the xaxis. We notice that this happens in two regions of the graph:
From 4 to 3
From 1 to 4
Therefore, the function is positive in:
[tex]\lbrack4,3)\cup(1,4)[/tex]c.
The function is zero when the graph intersect the xaxis; from the graph we have that the function is zero for:
[tex]\begin{gathered} x=3 \\ x=1 \\ x=4 \end{gathered}[/tex]Calculate the perimeter and area of the triangle formed by the coordinates K (4,1), L (2,2), and M (3,1). Round your answer to two decimal places.
PERIMETER:
You can calculate the perimeter of a triangle knowing the coordinates, by calculating the distance between every point, as follows:
[tex]\bar{KL}=\sqrt[]{(x_2x_1)^2+(y_2y_1)^2}[/tex]Where x1=4, y1=1, x2=2 and y2=2, replace these values:
[tex]\begin{gathered} \bar{KL}=\sqrt[]{((2)(4))^2+(2(1))^2} \\ \bar{KL}=\sqrt[]{(2)^2+(3)^2} \\ \bar{KL}=\sqrt[]{4+9}=\sqrt[]{13}=3.61 \end{gathered}[/tex]Now, you have to do the same for the other segments, let's continue with LM:
[tex]\begin{gathered} \bar{LM}=\sqrt[]{(x_3x_2)^2+(y_3y_2)^2} \\ x_3=3\text{ and }y_3=1\text{ by replacing:} \\ \bar{LM}=\sqrt[]{(3_{}(2))^2+((1)2)^2} \\ \bar{LM}=\sqrt[]{(5)^2+(3)^2} \\ \bar{LM}=\sqrt[]{25+9}=\sqrt[]{34}=5.83 \end{gathered}[/tex]Same for segment KM:
[tex]\begin{gathered} \bar{KM}=\sqrt[]{(x_3x_1)^2+(y_3y_1)^2} \\ \bar{KM}=\sqrt[]{(3(4))^2+((1)(1))^2} \\ \bar{KM}=\sqrt[]{(7)^2+(0)^2} \\ \bar{KM}=\sqrt[]{49+0^{}}=\sqrt[]{49}=7 \end{gathered}[/tex]The perimeter can be calculated as KL+LM+KM:
[tex]\begin{gathered} P=\bar{KL}+\bar{LM}+\bar{KM}=3.61+5.83+7 \\ P=16.44 \end{gathered}[/tex]AREA:
The area can be calculated by using the next formula:
[tex]A=\frac{1}{2}\mleft\lbrace\lbrack(x_1\cdot y_2)+(x_2\cdot y_3)+(x_3\cdot y_1)\mright]\lbrack(x_1\cdot y_3)+(x_3\cdot y_2)+(x_2\cdot y_1)\rbrack\}[/tex]Then, you have to replace the values to find the area:
[tex]\begin{gathered} A=\frac{1}{2}\lbrace\lbrack((4)_{}\cdot2)+((2)\cdot(1))+(3\cdot(1))\rbrack\lbrack((4)\cdot(1))+(3\cdot2)+((2)\cdot(1))\rbrack\} \\ A=\frac{1}{2}\lbrace\lbrack(8)+(2)+(3)\rbrack\lbrack(4)+(6)+(2)\rbrack\} \\ A=\frac{1}{2}\lbrace\lbrack9\rbrack\lbrack12\rbrack\} \\ A=\frac{1}{2}\mleft\lbrace\lvert21\rvert\mright\rbrace \\ A=\frac{21}{2}=10.50 \end{gathered}[/tex]Edgar drew a scale drawing of the town library. The scale of the drawing was 5
centimeters: 2 meters. The parking lot is 34 meters wide in real life. How wide
is the parking lot in the drawing?
Answer:
85 cmStepbystep explanation:
The scale factor is:
5 cm ÷ 2 mFind the width of the parking lot in the drawing:
5 cm ÷ 2 mx cm ÷ 34 mCross multiply and find the value of x:
x = 5*34/2x = 85 cmneed help due tommorow
Finding the ratio of
a)1:9
b)2 : 7
c) 2 : 5
What is Ratio?
A ratio indicates how often one number contains another number. For example, if a fruit bowl contains 8 oranges and 6 lemons, the ratio of oranges to lemons is 8 to 6. Similarly, the ratio of lemons to oranges is 6:8 and the ratio of oranges to whole fruit is 8:14.
Given,
Total no. of students = 42
a) Students who prefer punk to students who prefer hiphop
No. of students in punk = 2
No. of students in hiphop = 18
The Ratio will be,
punk : hiphop = 2:18
= 1:9
b) Students who prefer rock to total no. of students that are surveyed
No. of students in rock = 12
Total no. of students = 42
The Ratio will be,
rock : total students = 12 : 42
= 2 : 7
c) Students who prefer rock or classic rock to students who prefer all music
No. of students in rock = 12
Total no. of students who likes other music = 42  12
= 30
The Ratio will be,
rock : total students with different music = 12 : 30
= 2 : 5
Hence, The ratio comparison in three different way
a)1:9
b)2 : 7
c) 2 : 5
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13 (6x – 5) – x = 13 – 2(x + 1) find x
Answer:
x = 76/79 or 0.962
Stepbystep explanation:
Figure out how many offspring there would be for the fifth and sixth generations using the equation
Explanation
We are given the following:
The table above models the function:
[tex]\begin{gathered} f(x)=a(4)^x \\ where \\ a=initial\text{ }value\text{ }(when\text{ }the\text{ }generation)=0 \\ x=generation \end{gathered}[/tex]We are required to determine how many offspring there would be for the fifth and sixth generations using the equation.
This is achieved thus:
[tex]\begin{gathered} \text{ Offspring:} \\ Fifth\text{ }generation\to a(4)^x \\ where \\ a=6 \\ x=5 \\ F\imaginaryI fth\text{ }generat\imaginaryI on\to6(4)^5=6144 \end{gathered}[/tex][tex]\begin{gathered} Sixth\text{ }generation\to a(4)^x \\ where \\ a=6 \\ x=6 \\ S\imaginaryI xth\text{ }generat\imaginaryI on\to6(4)^6=24576 \end{gathered}[/tex]Hence, the answers are:
[tex]\begin{gathered} 5th\text{ }generation=6144 \\ 6th\text{ }generation=24576 \end{gathered}[/tex]