Answers
So, let's simplify
(8 - 10i) - (22 - 6i) =
8 -10i -22 +6i = (adding like terms)
-4i -14i
Related Questions
Lars created a painting with an area of 42 square inches and a length of 6 inches. They create a second painting with an area of 28 square inches. It has the same width as the first painting. What is the length of the second painting?
Answers
The length of the second painting is 4 in.
What is Area of Rectangle?
Area of rectangle is length times of breadth.
Given that :
Lars created a painting with an area of 42 square inches and a length of 6 inches. now, calculating B of painting using formula :
Area of Rectangle=Length × Width
42 = 6 x b
b = 42/6
b = 8 in.
it is given that :
area of second painting = 28 square inches
and having same width as the first painting that is b = 8 in.
Now, calculating length second of painting using formula :
Area of Rectangle=Length × Width
28 = l x 8
l = 28/8
l = 4 in.
Therefore, the length of the second painting is 4 in.
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URGENT TWO WAY TABLES
Answers
Answer: A) 6 B) 19.5
Step-by-step explanation:
A) 2,4,6,8,10
B) 8+16+30+24=78
78/4=19.5
Let me known if question b was right
Mick O'Meara budgeted $315 per month for electricity and $238 per month for gas. His expenses for a twelve-month period were $3,950 for electricity and $3,055 for gas.How much less did he budget annually for the two expenses than he needed?$339$344$357$369None of these choices are correct.
Answers
In order to know how much he budgeted annually for each expense, we need to multiply each month budget by 12:
annual budget for electricity: 12 * 315 = 3780
annual budget for gas: 12 * 238 = 2856
So, the total annual budget was:
3780 + 2856 = 6636
On the other hand, his real expenses for that year were:
3950 + 3055 = 7005
Then, to find how much less he budget than he needed, we can find the difference between those two values:
7005 - 6636 = 369
Therefore, the last option is correct.
At Bright Futures Middle School, 576 students ride their bike to school . If this number is 75% of the school enrollment, then how many students are enrolled
Answers
In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data
students on bike = 576
% students on bike = 75%
total students = ?
Step 02:
total students
[tex]\text{ \% students on bike = }\frac{students\text{ on bike }}{\text{total students }}\cdot100[/tex][tex]\begin{gathered} 75\text{ = }\frac{576}{\text{total students }}\cdot100 \\ \text{total students = }\frac{576}{75}\cdot100 \end{gathered}[/tex]total students = 768
The answer is:
The number of total students is 768.
Completely the instructions to move from one point to another along the line y = 2/3x+1. Down 4 units then. Units.
Answers
The parent function given is,
[tex]y=\frac{2}{3}x+1[/tex]We were told the parent function was translated 4 units down, which means
[tex]\begin{gathered} y=\frac{2}{3}x+(1-4) \\ y=\frac{2}{3}x-3 \end{gathered}[/tex]Hence, the transformed function would be,
[tex]y=\frac{2}{3}x-3[/tex]Let us now plot the graph of the parent function and the transformed function in order to compare the two graphs.
From the graph above, the parent function is represented in the green line while the transformed function is represented in the black line.
Therefore, the answer is
Down 4 units, then left 6 units.
help me please im not understanding on the right side it says: to the total number of people present. Express as a simplified ratio
Answers
ANSWER
4 : 9
EXPLANATION
The total number of people present is the number of females plus the number of males:
[tex]125+100=225[/tex]The ratio of number of males to total number of people is:
[tex]\frac{100}{225}[/tex]We have to simplify this fraction. Both 100 and 225 are divisible by 5:
[tex]\begin{gathered} 100\colon5=20 \\ 225\colon5=45 \end{gathered}[/tex]Therefore:
[tex]\frac{100}{225}=\frac{20}{45}[/tex]And then again, 20 and 45 are divisible by 5:
[tex]\begin{gathered} 20\colon5=4 \\ 45\colon5=9 \end{gathered}[/tex]Therefore:
[tex]\frac{100}{225}=\frac{20}{45}=\frac{4}{9}[/tex]We can't simplify more than that, so the ratio is 4 : 9
find the slope of a line that is PARALLEL to y=3/5x-2
Answers
Parallel lines have the same slope.
In this case, the slope of the line is 3/5.
Then, any line that satisfies y=3/5*x+C, being C any constant, is parallel to our line.
Then, when C=0 for example, we have the line y=3/5*x that is parallel and goes through the center of coordinates (0,0).
Graphically, we can see that they a re parallel:
Answer: y = 3/5*x + C, with C=constant. There are infinte solutions if no other restriction is made, so for example y=3/5*x is parallel to y=3/5*x-2.
factor out 2x^4 = 9x^2
Answers
Solution
Step 1
Rearrange the equation
[tex]2x^{4\text{ }}-9x^2=0[/tex]Step 2
factorise the equation
[tex]x^2(2x^2-9)=0[/tex]Hence by factorization, the answer is
x^2(2x^2 - 9) = 0
y - 32 = -2(x-48)what is y
Answers
y - 32 = -2( x - 48)
y - 32 = -2x + 96
y = -2x + 96 + 32
y = -2x + 128
This is due tomorrow! Smart people help me, please!!
Answers
A parent is buying two types of chocolate truffles for the children. The oldest child likes white chocolate (W), the younger two like dark chocolate (D) and the spouse likes white chocolate (W). Four white chocolate truffles (W) cost the same as three dark chocolate truffles (D). If the parent bought 8 white chocolate truffles(W) and 10 dark chocolate truffles (D), and spent $50.00, how much was each dark chocolate truffle?2.422.343.13
Answers
SOLUTION
Given the information on the question tab;
[tex]Let\text{ the price for a white chocolate truffle be W, and the price for a dark chocolate truffle be D;}[/tex][tex]\begin{gathered} From\text{ the statements made in the question;} \\ 4W=3D-----(1) \\ 8W+10D=50----(2) \end{gathered}[/tex][tex]\begin{gathered} From\text{ equation \lparen1\rparen;} \\ W=\frac{3D}{4}-----(3) \\ substituting\text{ W=}\frac{3D}{4}\text{ into equation \lparen2\rparen} \end{gathered}[/tex][tex]\begin{gathered} 8\times\frac{3D}{4}+10D=50 \\ 6D+10D=50 \\ 16D=50 \\ D=\frac{50}{16} \\ D=3.125\approx3.13 \end{gathered}[/tex]Final answer:
Each dark chocolate truffle costs $3.13
Identify the coefficient and the exponent for each term
Answers
Answer:
Coefficients are 6 and 4. The exponents are 3 and 1.
Step-by-step explanation:
The coefficient of a term is the number next to variable, the number that the variable is multiplied by.
Remember that if you are subtracting by a term, you are adding the "negative" term.
Meaning:
6x³ - 4x = 6x³ + (-4x)
The exponent of a term is the power (the little number on top). When the exponent (power) is not shown, it is just 1.
Meaning:
-4x = -4x¹
3. Carlos Quintero, Treasurer of X Corp is analyzing an investment on two projects, C and D. The data to
consider are shown below
Initial Investment
Annual Rate of
Return
Pessimistic
Most Likely
Optimistic
Amount
$135,000
39%
27%
25%
Project C
Probability
.30
.45
.25
Amount
$145,000
25%
15%
30%
Project D
Probability
.35
.40
.25
A. Determine the rates of return for each of the two projects. (6 points)
Answers
The rates of return for each of the two projects for X Corp are as follows:
Project C = 30.1%Project D = 19.75%.What is the rate of return?The rate of return refers to the percentage gain or loss over the initial cost of the investment.
For this purpose, the rate of return is expressed as the percentage of the expected returns (which is a product based on the probability of different scenarios) over the initial investment cost.
Project C Project D
Amount Probability Amount Probability
Initial Investment $135,000 $145,000
Annual Rate of Return
Pessimistic 39% .30 25% .35
Most Likely 27% .45 15% .40
Optimistic 25% .25 30% .25
Returns from Project C:Pessimistic $15,795 ($135,000 x 39% x 30%)
Most likely $16,402.50 ($135,000 x 27% x 45%)
Optimistic $8,437.50 ($135,000 x 25% x 25%)
Total expected returns = $40,635
Rate of return = 30.1% ($40,635/$135,000 x 100)
Returns from Project D:Pessimistic $9,062.50 ($145,000 x 25% x 35%)
Most Likely $8,700 ($145,000 x 15% x 40%)
Optimistic $10,875 ($145,000 x 30% x 25%)
Total expected returns = $28,637.50
Rate of return = 19.75% ($28,637.50/$145,000 x 100)
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What is the volume of the cone rounded to the nearest tenth? The diagram is not drawn to scale. The height of the cone is 19 yd.A) 2646.3 yd^3B) 1462.4 yd^3C) 1039.0 yd^3D) 975.0 yd^3
Answers
Answer:
To find the volume of the cone rounded to the nearest tenth
we have that,
Volume of the cone (V) is,
[tex]\frac{1}{3}\pi r^2h[/tex]where r is the radius and h is the height of the cone.
Given that,
r=7 yd
h=19 yd
Substitute the values we get,
[tex]V=\frac{1}{3}\pi(7)^2\times19[/tex]we get,
[tex]V=\frac{931}{3}\pi[/tex]we know that pi is approximately equal to 3.14, Substitute the value we get,
[tex]V=\frac{931}{3}(3.14)[/tex]we get,
[tex]V=974.446\approx975\text{ yd}^3[/tex]Answer is: Option D:
[tex]\begin{equation*} 975\text{ yd}^3 \end{equation*}[/tex]Use a truth table to determine whether the two statements are equivalent.
Answers
The answer is option(b) i.e,the given statements are not equivalent.
What is Truth table?
A truth table is a breakdown of a logic function by listing all possible values the function can attain. Such a table typically contains several rows and columns, with the top row representing the logical variables and combinations, in increasing complexity leading up to the final function.
Let's proof it by using truth table :
p q (~q → ~p) (~p → ~q)
F F T T
F T T F
T F F T
T T T T
As you've seen in truth table (~q → ~p) ≠ (~p → ~q)
Therefore, the answer is option(b) i.e,the given statements are not equivalent.
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andrews family spent 410 on 2 adult tickets to go to the concert. maxs family spent 375 on 3 tickets and 2 child tickets 3 how much is the adult ticket how much is a child ticket
Answers
Let 'x' represents the cost of the ticket for an adult, and 'y' be the cost of a child's ticket.
Andrew's family spend 410 on two adult tickets.
[tex]2x=410[/tex]From the above expression,
[tex]\begin{gathered} x=\frac{410}{2} \\ =205 \end{gathered}[/tex]Thus, the cost of an adult ticket is 205.
Given that the Max's family spend 375 for 3 tickes, and two of them is for childrens.
[tex]\begin{gathered} x+2y=375 \\ 205+2y=375 \\ 2y=375-205 \\ 2y=170 \\ y=\frac{170}{2} \\ y=85 \end{gathered}[/tex]Thus, the cost for tickets for the childrens is 85.
A container of orange juice cost $3.29 for 59 ounces. What is the unit rate to the nearest penny?
Answers
Answer:
6 cents
A sporting goods store charges $22.00 for a football before tax. The store holds a sale that marks all prices down by 20% before tax. If the sales tax is 5%, what is the cost of the discounted football after tax?
Answers
The cost of the discounted football after applying the tax is $18.48
Discount:
Discount refers the difference between the price paid for and it's par value. Discount is a sort of reduction or deduction in the cost price of a product.
Given,
A sporting goods store charges $22.00 for a football before tax. The store holds a sale that marks all prices down by 20% before tax.
Here we need to calculate the cost of the discounted football after the tax of 5%.
We know that the cost of the football is $22.00 before tax.
So, if we apply the discount of 20% on it , then the cost of the foot ball is,
Discount = 22 x 20/100
Discount = 4.4
So, the cost of the foot ball after discount is,
=> 22 - 4.4
=> 17.6
Now, we have to apply the tax 5% on it, then we get,
=> 17.6 x 5/100
=> 17.6 x 0.05
=> 0.88
Therefore, the cost of the discounted football after the tax of 5% is.
=> 17.6 +0.88
=> 18.48
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bridget is growing seven plants for her science project. here are the heights of the plants after four weeks. what is the mode?
Answers
Given the data:
Plant Height(Cm)
1 9
2 10
3 10
4 6
5 9
6 7
7 10
The mode of a data set is the value that occurs most frequently.
From the data above, the height that occurs most frequently is 10 cm.
Therefore, the mode is 10.
ANSWER:
Solve for the triangle where there is a question mark!
Answers
SOLUTION
Given the question in the image, the following are the solution steps to answer the question.
STEP 1: Label the right-angled triangle
STEP 2: Write the trigonometry ratios
[tex]\begin{gathered} \sin \theta=\frac{\text{opposite}}{\text{hypotenuse}} \\ \cos \theta=\frac{\text{adjacent}}{\text{hypotenuse}} \\ \tan \theta=\frac{\text{opposite}}{\text{adjacent}} \end{gathered}[/tex]STEP 3: Write the given values to decide which ratio to use
Let the part with the question be represented by m
[tex]\begin{gathered} \text{adjacent}=7,\text{hypotenuse}=12,m=\text{?} \\ U\sin g\text{ the cos ratio from step 2;} \\ \cos m=\frac{7}{12} \\ m=\cos ^{-1}(\frac{7}{12})=\cos ^{-1}0.5833333333 \\ m=54.31466529 \\ m\approx54.31 \end{gathered}[/tex]Therefore, the value of mising angle labelled m is approximately 54.31 degrees
43% adults favor the use of unmanned drones by police agencies. Twelve U.S. adults are randomly selected. Find the probability that the number of U.S. adults who favor theuse of unmanned drones by police agencies is (a) exactly three, (b) at least four, (c) less than eight(a) P(3) =(Round to three decimal places as needed.)
Answers
EXPLANATION:
According to the established pattern that only 43 out of 100 adults favor the use of drones, now we must find out from the only twelve adults surveyed how much corresponds to 43 percent.
The first thing we must do is make the relation 12 equals 100, then 43 percent how much?
[tex]\begin{gathered} 12\rightarrow100 \\ x\leftarrow43 \\ x=\frac{12\times43}{100} \\ \textcolor{#FF7968}{x=5.16}\text{\textcolor{#FF7968}{ ; }} \\ \text{the answer is }\text{\textcolor{#FF7968}{5.16 }}\textcolor{#FF7968}{that}\text{\textcolor{#FF7968}{ is less than eight }}\text{; } \end{gathered}[/tex]What is the vertical shift for the absolute value function below?f(x) = 9|x + 11 + 2
Answers
Since the function is shifted 2 units up, the vertical shift is 2
A colony of 4,050 bacteria doubles in size every 297 hours. What will the population be 594 hours from now?
Answers
Answer:
About 280,000
Step-by-step explanation:
Answer:
16,200
Step-by-step explanation:
594 ÷ 297 = 2
4,050 × 2 × 2 = 16,200
another way: 4,050 × 2^2 = 16,200
Use the parabola tool to graph the quadratic function f(1) = 2x^2+16x+30Graph the parabola by first plotting its vertex and then plotting a second point on the parabola.
Answers
vertex(-4,-2)
focus(-4,-15/8)
Axis of symmetry,x=-4
directrix, y=-17/8
x y
-6 6
-5 0
-4 -2
-3 0
-2 6
Nadine tried to solve the equation 12x - 19 equals -4 (3 x - 9) - 15 but made a mistake which line shows evidence of Nadines mistake
Answers
Answer:
Line 4
Explanation:
The initial expression is:
12x - 19 = -4(3x - 9) - 15
The mistake was made on line 4, the correct steps to solve the expression are:
[tex]\begin{gathered} 12x-19=-4(3x-9)-15 \\ 12x-19=-12x+36-15 \\ 12x-19=-12x+21 \\ 24x-19=21 \\ 24x-19\textcolor{#FF7968}{+19}=21\textcolor{#FF7968}{+19} \\ \textcolor{#FF7968}{24x=40} \\ x=\frac{40}{24}=\frac{5}{3} \end{gathered}[/tex]Because on line 4 they subtract 19 from the right side and the correct step is to add 19 to the right side.
what are the reasons ? and is there anymore statements
Answers
The first reason is GIVEN
If angles ∠XWY and ∠RTU are supplemetary, it means they add up 180°. It demands that lines It demands that lines It demands that
b. 9m2 + 6m + 6 = 5 has real roots and imaginary roots
Answers
the given equation is
[tex]\begin{gathered} 9m^2+6m+6=5 \\ 9m^2+6m+1=0 \end{gathered}[/tex]we will calculate
[tex]D=b^2-4ac[/tex]so
[tex]\begin{gathered} =6^2-4\times9\times1 \\ =36-36 \\ =0 \end{gathered}[/tex]as D is 0 so it has one real root
The manager of a small company that produces roof tile has determined that the total cost in dollars, C(x), of
producing x units of tile is given by C(x) = 200x + 900, while the revenue in dollars, R(x), from the sale of x units of tile
is given by R(x)=230x. Find the break-even point and the cost and revenue at the break-even point.
The break-even point is
The cost at the break-even point is $
The revenue at the break-even point is
units.
www
Answers
The break-even point=30, The cost of producing x units of tile =6900$, revenue from the sale of x units of tile at the break-even point=6900$.
What is equation?A mathematical statement known as an equation is made up of two expressions joined together by the equal sign. A formula would be 3x - 5 = 16, for instance. When this equation is solved, we discover that the value of the variable x is 7.
What is revenue?Revenue is the total amount of money made from the sale of products and services that are essential to the business's core operations. Sales or turnover are other terms used to describe commercial revenue. Some businesses make money from royalties, interest, or other fees.
The manager of a small company that produces roof tile has determined that the total cost in dollars, C(x), of producing x units of tile is given by C(x) = 200x + 900, while the revenue in dollars, R(x), from the sale of x units of tile is given by R(x)=230x.
C(x) = 200x + 900
R(x)=230x
200x+900=230x
30x=900
x=30
C(x)=200*30+900
=6900
R(x)=230*30=6900
30 is the break-even point; At the break-even point, the cost of producing 30 units of tile is $6900, and the revenue from those sales is $6900.
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This data is from a sample. Calculate the mean, standard deviation, and variance. Suggestion: usetechnology. Round answers to two decimal places.х23.542.131.116.321.132.144.813.529.9Mean?Standard deviation?Variance?Ooops - now you discover that the data was actually from a population! So now you must give thepopulation standard deviationPopulation Standard Deviation?
Answers
The formula to find the mean of a data set is:
[tex]\begin{gathered} \bar{x}=\frac{\text{Sum of all the items}}{\text{ Number of items}} \\ \text{ Where }\bar{\text{x}}\text{ is the mean of a sample} \end{gathered}[/tex]So, in this case, we have:
[tex]\begin{gathered} \bar{x}=\frac{23.5+42.1+31.1+16.3+21.1+32.1+44.8+13.5+29.9}{9} \\ \bar{x}=\frac{254.4}{9} \\ \bar{x}=28.27 \end{gathered}[/tex]Therefore, the mean of the given data set rounded to two decimal places is 28.27.
Standard deviationThe sample standard deviation formula is:
[tex]\begin{gathered} s=\sqrt[]{\frac{\sum ^n_{i\mathop=1}(x_i-\bar{x})^2}{n-1}} \\ \text{ Where} \\ \text{ n is the number of data points} \\ x_i\text{ is each of the values of the data} \\ \bar{x}\text{ is the mean of the data set} \end{gathered}[/tex]So, in this case, we have:
[tex]\begin{gathered} s=\sqrt[]{\frac{(23.5-28.27)^2+(42.1-28.27)^2+(31.1-28.27)^2+(16.13-28.27)^2+(21.1-28.27)^2+(32.1-28.27)^2+(44.8-28.27)^2+(13.5-28.27)^2+(29.9-28.27)^2}{8}} \\ s=\sqrt[]{\frac{(-4.77)^2+(13.83)^2+(2.83)^2+(-11.97)^2+(-7.17)^2+(3.83)^2+(16.53)^2+(-14.77)^2+(1.63)^2}{8}} \\ s=\sqrt[]{\frac{22.72+191.36+8.03+143.2+51.36+14.69+273.35+218.05+2.67}{8}} \\ s=\sqrt[]{\frac{925.44}{8}} \\ s=\sqrt[]{115.68} \\ s=10.76 \end{gathered}[/tex]Therefore, the sample standard deviation of the given dataset rounded to two decimal places is 10.76.
VarianceThe standard deviation is the square root of the variance. Thus, the formula to find the variance of a sample is,
[tex]s^2=\frac{\sum^n_{i\mathop{=}1}(x_i-\bar{x})^2}{n-1}[/tex]So, in this case, we have:
[tex]s^2=115.68[/tex]Therefore, the sample variance of the given dataset rounded to two decimal places is 115.68.
PopulationStandard deviationThe population standard deviation formula is:
[tex]\begin{gathered} \sigma=\sqrt[]{\frac{\sum ^n_{i\mathop{=}1}(x_i-\bar{x})^2}{N}} \\ \text{Where} \\ \sigma\text{ is the population standard deviation} \\ x_i\text{ is each of the values of the data} \\ N\text{ is the number of data points} \end{gathered}[/tex]So, in this case, we have:
[tex]\begin{gathered} s=\sqrt[]{\frac{(23.5-28.27)^2+(42.1-28.27)^2+(31.1-28.27)^2+(16.13-28.27)^2+(21.1-28.27)^2+(32.1-28.27)^2+(44.8-28.27)^2+(13.5-28.27)^2+(29.9-28.27)^2}{9}} \\ s=\sqrt[]{\frac{(-4.77)^2+(13.83)^2+(2.83)^2+(-11.97)^2+(-7.17)^2+(3.83)^2+(16.53)^2+(-14.77)^2+(1.63)^2}{9}} \\ s=\sqrt[]{\frac{22.72+191.36+8.03+143.2+51.36+14.69+273.35+218.05+2.67}{9}} \\ s=\sqrt[]{\frac{925.44}{9}} \\ s=\sqrt[]{102.83} \\ s=10.14 \end{gathered}[/tex]Therefore, the population standard deviation of the given dataset rounded to two decimal places is 10.14.
if Dixon is 6 ft tall,, how tall is ariadne?
Answers
Notice that the triangles formed by the shadows are similar, therefore:
[tex]\frac{x}{6}=\frac{15}{18},[/tex]where x is Adriadne's height. ( We will omit the units to simplify the calculations).
Solving the above equation for x, we get:
[tex]x=\frac{15}{18}*6.[/tex]Simplifying the above result, we get:
[tex]x=5ft.[/tex]Answer:[tex]5ft.[/tex]