Given:
2(-36- 3i )+ (5+2i)(12-2i)
Open the parenthesis
2(-36- 3i) + 5( 12 - 2i) + 2i ( 12 - 2i)
- 72 - 6i + 60 - 10i + 24i + 4 ( Note: i² = -1)
Re-arrange
-72+60 + 4 - 6i - 10i + 24i
= -8 + 8i
what is the value of 6 3/4 (-11.5)
We are given the following expression
[tex]6\frac{3}{4}(-11.5)[/tex]As you can see, a mixed number is being multiplied with a negative decimal number.
First, convert the mixed number to a simple fraction then multiply with the decimal number
[tex]6\frac{3}{4}=\frac{6\cdot4+3}{4}=\frac{24+3}{4}=\frac{27}{4}[/tex]Now multiply it with the negative decimal number
[tex]\frac{27}{4}(-11.5)=-\frac{310.5}{4}=-77.625[/tex]So the resultant decimal number may be written back into the mixed form as
[tex]-77.625=-77\frac{5}{8}[/tex]Therefore, the result of the given expression is -77 5/8
Use Pythagorean theorem to find right triangle side lengthsFind the value of c in the triangle shown below.682Choose 1 answer:A = 28B= 64=9= 10
EXPLANATION
Given the Right Triangle, we can apply the Pythagorean Theorem in order to get the value of x as shown as follows:
[tex]\text{Hypotenuse}^2=Short_-leg^2+Long_-leg^2[/tex]Replacing terms:
[tex]x^2=6^2+8^2[/tex][tex]x^2=36+64=100[/tex]Applying the square root to both sides:
[tex]x=\sqrt[]{100}=10[/tex]Hence, the solution is x=10
The Neckware association of America reported that 3% of ties sold in the United States are bow ties. If 4 customers who purchased a tie randomly selected,find the probability that at least 1 purchased a bow tie
Pr (people with bow ties) = 3% = 0.03
p = 0.03
Pr (people without bow tie) = 1 - 0.03 = 0.97
q = 0.97
n = 4 customers
[tex]Pr(at\text{ least 1 purchased a bow tie) = 1 - Pr(none purchased a bow tie)}[/tex]To find the probability that at least 1 purchased a bow tie, we will use a binomial probability formula:
[tex]p(x=^{}X)=^nC_xp^xq^{n\text{ - x}}[/tex][tex]\begin{gathered} \text{Pr(none purchased a bow tie) = p(x = 0)} \\ \text{p(x = 0) = }^4C_0\times p^0\times q^{4\text{ - }0} \\ \text{p(x = 0) = 1 }\times\text{ 1}\times q^4=(0.97)^4 \\ \text{p(x = 0) = }0.8853 \\ \\ \text{Pr(none purchased a bow tie) = }0.8853 \end{gathered}[/tex][tex]\begin{gathered} Pr(at\text{ least 1 purchased a bow tie) = 1 - 0.8853} \\ Pr(at\text{ least 1 purchased a bow tie) = 0.1147} \end{gathered}[/tex]Find the links of the sides of these special triangles
From the triangle, we express the tangent of 60° as:
[tex]\tan 60\degree=\frac{Z}{7}[/tex]But tan(60°) = √(3), then:
[tex]\begin{gathered} \frac{Z}{7}=\sqrt[]{3} \\ \Rightarrow Z=7\sqrt[]{3}\text{ ft} \end{gathered}[/tex]The population of Somewhere, USA was estimated to be 658,100 in 2003, with an expected increase of 5% per year. At the percent ofincrease given, what was the expected population in 2004? Round your answer to the nearest whole number.
To solve for the expected population in 2004:
[tex]\begin{gathered} \text{Estimated population for 2003=658100} \\ \text{rate = 5 \%} \\ nu\text{mber of year = 1} \end{gathered}[/tex]Using compound interest formular to solve for the expected popupation:
Expected population = Amount
[tex]\begin{gathered} A=p(1+\frac{r}{100})^n \\ A\text{ = 658100 (1+}\frac{5}{100})^1 \\ A=658100\text{ (1+0.05)} \\ A=658100(1.05) \\ A=691005 \end{gathered}[/tex]Hence the expected population in 2004 = 691,005
John has two apples, he gives Jane 251. How many apples does John have? Please help 2nd grade is so hard.
21. Juanita is packing a box that is 18 inches long and 9 inches high. The total volume of the box.1,944 cubic inches. Use the formula V = lwh to find the width of the box. Show your work
The width of the box is 12 inches
Explanations:
The formula for calculating the volume of a rectangular box is expressed as:
[tex]V=\text{lwh}[/tex]where:
• l is the ,length ,of the box
,• w is the ,width, of the box
,• h is the ,height ,of the box
Given the following parameters
• length = 18 inches
,• heigh = 9 inches
,• volume = 1,944 cubic inches
Substitute the given parameters into the formula to calculate the width of the box as shown:
[tex]\begin{gathered} 1944=18\times w\times9 \\ 1944=162w \end{gathered}[/tex]Divide both sides by 162 to have:
[tex]\begin{gathered} 162w=1944 \\ \frac{\cancel{162}w}{\cancel{162}}=\frac{1944}{162} \\ w=12\text{inches} \end{gathered}[/tex]Hence the width of the box is 12 inches
- 2/3 (x+12)+2/3 x=-5/4 x+2
We will have the following:
[tex]-\frac{2}{3}(x+12)+\frac{2}{3}x=-\frac{5}{4}x+2\Rightarrow-\frac{2}{3}x-8+\frac{2}{3}x=-\frac{5}{4}x+2[/tex][tex]\Rightarrow-\frac{2}{3}x+\frac{2}{3}x+\frac{5}{4}x=2+8\Rightarrow\frac{5}{4}x=10[/tex][tex]\Rightarrow5x=40\Rightarrow x=8[/tex]So, the value of x is 8.
Can you help me with this true and false problem?
FALSE.
Explanations:Given the linear relations 2x - 3y = 4 and y = -2/3 x + 5
Both equations are equations of a line. For the lines to be perpendicular, the product of their slope is -1
The standard equation of a line in slope-intercept form is expressed as
[tex]y=mx+b[/tex]m is the slope of the line
For the line 2x - 3y = 4, rewrite in standard form
[tex]\begin{gathered} 2x-3y=4 \\ -3y=-2x+4 \\ y=\frac{-2}{-3}x-\frac{4}{3} \\ y=\frac{2}{3}x-\frac{4}{3} \end{gathered}[/tex]Compare with the general equation
[tex]\begin{gathered} mx=\frac{2}{3}x \\ m=\frac{2}{3} \end{gathered}[/tex]The slope of the line 2x - 3y = 4 is 2/3
For the line y = -2/3 x + 5
[tex]\begin{gathered} mx=-\frac{2}{3}x \\ m=-\frac{2}{3} \end{gathered}[/tex]The slope of the line y = -2/3 x + 5 is -2/3
Take the product of their slope to determine whether they are perpendicular
[tex]\begin{gathered} \text{Product = }\frac{2}{3}\times-\frac{2}{3} \\ \text{Product = -}\frac{4}{9} \end{gathered}[/tex]Since the product of their slope is not -1, hence the linear relations do not represent lines that are perpendicular. Hence the correct answer is FALSE
A population of 2000 is decreasing by 4% each year. In how many years the population will be reduced in half?
the initial amount is 2000
the rate of change is 4%
t=time in years
Therefore we have the next exponential decay function
[tex]\begin{gathered} y=2000(1-0.04)^t \\ y=2000(0.96)t \end{gathered}[/tex]Half of the population is y=1000 so we need to find find the value of t
[tex]1000=2000(0.96)^t[/tex]we need to isolate the t
[tex]\frac{1000}{2000}=0.96^t[/tex][tex]\frac{1}{2}=0.96^t[/tex]Using logarithms
[tex]\begin{gathered} \ln (\frac{1}{2})=\ln (0.96^t) \\ \ln (\frac{1}{2})=t\ln (0.96^t) \end{gathered}[/tex][tex]t=\frac{\ln (\frac{1}{2})}{\ln (0.96^{})}=16.98\approx17[/tex]ANSWER
in 17 years the population will be reduced in half
16. Given the graph below, write the equation of the line graphed. Equation:
We have the following:
The equation has the following form
[tex]y=mx+b[/tex]where m is the slope and b is y-intercept
The slope formula is as follows
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]The point are (-4, 8) and (6, -4)
replacing:
[tex]m=\frac{-4-8}{6-(-4)}=\frac{-12}{10}=-\frac{6}{5}[/tex]In the graph we can see that the y-intercept is equal to 4, therefore, the equation would be
[tex]y=-\frac{6}{5}x+4[/tex]2(3 + v) =
Please help solve this problem and thank you
Answer:
6 +2v
Step-by-step explanation:
This is distributive property. That means you will multiply each term inside the parentheses by the term on the outside of the parentheses.
2(3 + v)
2(3) + 2(v)
6 +2v
A rectangle has a diagonal of length 10 cm and a base of length 8 cm . Find its height
Given:
The length of diagonal of rectangle is d = 10 cm.
The length of base is b = 8 cm.
Explanation:
The relation between length, height and diagonal of rectangle is given by pythagoras theorem. So
[tex]d^2=l^2+h^2[/tex]Substitute the values in the equation to obtain the value of h.
[tex]\begin{gathered} (10)^2=(8)^2+h^2 \\ 100=64+h^2 \\ h=\sqrt[]{100-64} \\ =\sqrt[]{36} \\ =6 \end{gathered}[/tex]So the height of rectangle is 6 cm.
Answer: 6 cm
How many megagrams(Mg) are there in 3.6 tons?[ ? ] MgMass in MgEnter
Step 1
Given;
[tex]3.6\text{tons}[/tex]Required; To find how many megagrams(Mg) are in 3.6 tonnes
Step 2
Find how many megagrams(Mg) are in 3.6 tonnes
[tex]\begin{gathered} 1\text{ tonne=1000000}g \\ 1\text{ megagram=1}000000g \end{gathered}[/tex]Therefore,
[tex]1\text{ tonne = 1 megagram}[/tex][tex]\frac{1\text{ tonne}}{3.6\text{ tonnes}}=\frac{1\text{ megagram}}{x\text{ megagram}}[/tex][tex]\begin{gathered} x\text{ megagram(1 tonne)=1 megagram(3.6 tonnes)} \\ \frac{x\text{ megagram}(1\text{ tonne)}}{1\text{ tonne}}\text{=}\frac{\text{1 megagram(3.6 tonnes)}}{1\text{ tonne}} \\ x=\text{ 3.6 megagrams} \\ x=3.6Mg \end{gathered}[/tex]
A car has 34,000,miles on its odometer and accumulates an average of 100 more each week. What is the function rule that represents the total m miles the car will have on the odometer after w weeks?
Answer:
Step-by-step explanation:
M= 100m +34,000w
Answer: it would be A. for you, but for me it was C.:
m = 34,000 + 100w
what I mean is the answers were jumbled around.
What are examples of vertical stretch and compression and horizontal stretch and compression?
Examples of vertical stretch and compression and also horizontal stretch/vertical compression are explained below considering x² and
sin(x) function.
What is vertical stretch/vertical compression ?
A vertical stretch is derived if the constant is greater than one while the vertical compression is derived if the constant is between 0 and 1.Vertical stretch means that the function is taller as a result of it being stretched while vertical compress is shorter due to it being compressed and is therefore the most appropriate answer.example : If the graph of x² is is transformed to 2x² Then the function is compressed Vertically.
If the graph of x² is is transformed to x²/2 Then the function is stretch Vertically.
What is horizontal stretch/vertical compression ?
We know that if f(x) is transformed by the rule f(x+a) then the transformation is either a shift ''a'' units to the left or to the right depending on a is positive or negative respectively this phenomenon is horizontal stretch and compression.example : If the function y = sin(x) is transformed to y = sin(2x) Then the function is compressed horizontally.
example : If the function y = sin(x) is transformed to y = sin(x/2) Then the function is stretch horizontally.
Read more about vertical stretch/compressed here:
brainly.com/question/24465194
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use the following graph to find the mean, median, and mode
Given:
A graph
To determine the Mean, Median, and Mode based on the given graph, we first get the data set as shown below:
2,5,5,5,5,6,9,11,12,13,14,15,18,20
Next, we find the Mean by getting the average:
[tex]\begin{gathered} Mean=\frac{2+5+5+5+5+6+9+11+12+13+14+15+18+20}{14} \\ Simplify \\ Mean=\frac{140}{14} \\ Mean=10 \end{gathered}[/tex]Then, we get the Median by getting the average of the two middle values since there is an even number of data values:
[tex]\begin{gathered} Median=\frac{9+11}{2} \\ Simplify \\ Median=10 \end{gathered}[/tex]Now, we get the Mode by finding the number that appears most frequently. Hence, the Mode is 5.
Therefore, the answer is:
Mean:10, Median:10, Mode:5
find the missing lenghts, the triangle in each pair are similar.
Since the triangles are similar, we have that
[tex]\frac{50}{40}=\frac{x}{52}[/tex]then
[tex]x=\frac{52\times50}{40}=65[/tex]then the answer will be D) 65Mark is roofing an old gymnasium that measures 270’x390’, and needs to calculate how many “squares “ he will need.(1 “square=100 ft square). The gym’s roof is a standard gable roof with 3’ of overhang on all sides. The roof angle measures 22.55 degrees from horizontal. How many squares of roofing does mark need ?
First, because of the roof having an inclination, we need to calculate the lenght of the surface we want to roof. The width will be the same.
Let's take a look at the situation:
Since we're on a right triangle, we can say that:
[tex]\cos (22.25)=\frac{G}{R}[/tex]Solving for R,
[tex]\begin{gathered} \cos (22.25)=\frac{G}{R}\rightarrow R\cos (22.25)=G \\ \\ \Rightarrow R=\frac{G}{\cos (22.25)} \end{gathered}[/tex]Since we already know that the lenght of the gym's floor is 390',
[tex]\begin{gathered} R=\frac{390^{\prime}}{\cos (22.25)} \\ \\ \Rightarrow R=421.38^{\prime} \end{gathered}[/tex]We get that the lenght of the surface we want to roof is 421.38'
Now, let's take a look at the surface we want to roof:
Since the roof is a standard gable roof with 3’ of overhang on all sides, we add 6' to each dimension:427
Our total roofing area would be:
[tex]427.38^{\prime}\cdot276^{\prime}=117956.88ft^2[/tex]We then divide this total area by the area of one of our "squares":
[tex]\frac{117956.88}{100}=1179.56[/tex]We round to the nearest integer from above, since we can't buy a fraction of a square.
(this is called ceiling a number)
[tex]1179.56\rightarrow1180[/tex]Therefore, we can conclude that Mark needs 1180 squares of roofing.
Which of the following expressions is equivalent to 2-3?A -2-31B-23C231D- 2-3
2 - 3
the correct answer is letter C
If we follow the rules of the exponents, the power is negative so we change the negative sign writing the numerator in the denominator,
A side of the triangle below has been extended to form an exterior angle of 133º. Find the value of x. 133° 21° xo
In order to find the value of x, we need to remember that the sum of the interior angles of a triangle is 180°
so we have the next equation
21+x+(180-133)=180
21+x+47=180
x=180-21-47
x=112°
Determine whether 17y = 3x − 19 is quadratic or not. Explain.No; there is no x2 term, so a = 0.No; there is no x-term, so b = 0.No; there is no constant term, so c = 0.Yes; it can rewritten in the form y = ax2 + bx + c.
The standard form of quadratic equation is given as,
[tex]ax^2+bx\text{ + c = 0 where a }\ne\text{ 0}[/tex]The equation is given as,
[tex]17y\text{ = 3x - 19}[/tex]Therefore,
[tex]\text{From the given equation x}^2\text{ is not present and also a = 0.}[/tex]Thus the given equation is not a quadratic equation.
Suppose that a regression line for some data transformed with logarithmspredicts that when x equals 4, log(y) will equal 2.671. What does theregression line predict y will equal when x equals 4?
Explanation:
The information that we have is that when the value of x is 4
[tex]x=4[/tex]The logarithm of y is 2.671
[tex]log(y)=2.671[/tex]The question is:
What does the regression line predict y will equal when x =4?
That means we need to solve for y in
[tex]log(y)=2.671[/tex]To find the predicted y-value.
To solve for y, we make 10 the base of the two sides of the equation as shown in the following expression:
[tex]10^{log(y)}=10^{2.671}[/tex]Due to the properties of logarithms, on the left side, we will be left only with 'y'
[tex]y=10^{2.671}[/tex]And finally, solving the operations on the right-hand side, the result is:
[tex]y=468.813[/tex]Answer:
[tex]y=468.813[/tex]What is the answer for 5p+10 = 8p+1
The equation is given to be:
[tex]5p+10\: =\: 8p+1[/tex]We can solve for p using the following steps:
Step 1: Subtract 10 from both sides of the equation
[tex]\begin{gathered} 5p+10-10=8p+1-10 \\ 5p=8p-9 \end{gathered}[/tex]Step 2: Subtract 8p from both sides of the equation
[tex]\begin{gathered} 5p-8p=8p-9-8p \\ -3p=-9 \end{gathered}[/tex]Step 3: Multiply both sides by -1
[tex]\begin{gathered} -1\times(-3p)=-1\times(-9) \\ 3p=9 \end{gathered}[/tex]Step 4: Divide both sides by 3
[tex]\begin{gathered} \frac{3p}{3}=\frac{9}{3} \\ p=3 \end{gathered}[/tex]ANSWER:
[tex]p=3[/tex]A rectangular parking lot has length that is 3 yards less than twice its width. If the area of the land is 299 square yards, what are the dimensions of the land?The parking lot has a width of square yards.
Answer:
• Width = 13 yards
,• Length = 23 yards
Explanation:
Let the width of the parking lot = w yards.
The length is 3 yards less than twice its width.
[tex]\implies\text{Length}=(2w-3)\text{ yards}[/tex]The area of the land = 299 square yards.
[tex]w(2w-3)=299[/tex]We then solve the equation above for w.
[tex]\begin{gathered} 2w^2-3w=299 \\ \implies2w^2-3w-299=0 \end{gathered}[/tex]Factor the resulting quadratic expression.
[tex]\begin{gathered} 2w^2-26w+23w-299=0 \\ 2w(w-13)+23(w-13)=0 \\ (2w+23)(w-13)=0 \end{gathered}[/tex]Solve for w.
[tex]\begin{gathered} 2w+23=0\text{ or }w-13=0 \\ 2w=-23\text{ or }w=13 \\ w\neq-\frac{23}{2},w=13 \end{gathered}[/tex]Since w cannot be negative, the parking lot has a width of 13 yards.
Finally, find the length of the parking lot.
[tex]\begin{gathered} 13l=299 \\ l=\frac{299}{13}=23\text{ yards} \end{gathered}[/tex]The length of the parking lot is 23 yards.
2. Jim is 8 years old, and his Uncle Bill is 512 times older than he his. What is his Uncle Bill's age?
Answer:
Uncle Bill has ignored the laws of nature and the known universe and reached a stunning 4096 years old
Step-by-step explanation:
Just multiply 8 * 512
500 * 8 = 4000, 12 * 8 = 96, 4000 + 96 = 4096
Answer:44
Step-by-step explanation:
Which describes the product when two fractions greater than 0 and less than 1 are multiplied?
When you multiply two numbers, one of them greater than 0 and the other one lower than 1. The result is a number that is lower than the first one, that is, a number lower than the number greate than 0.
Amy's cookie shop had expenses of the following: flour $45.00sugar $92.00butter $53 she earns $12 per dozen. what is her profit,if she sells 9 dozen?what is the total dollar amount for expenses?what is the total dollar amount for earnings or revenue?
If she earns $12 per dozen, the following will be the profit if she sells 9 dozen:
[tex]9\cdot12=108[/tex]Profit would be $108.
*The dollar amount of expenses would be:
[tex]e=\frac{190\cdot108}{12}\Rightarrow e=1710[/tex]The expenses would be $1710 if she were to sell 9 dozen.
*The total amount of revenue would be $108 for the 9 dozen sold.
URGENT!! ILL GIVE
BRAINLIEST!!!!! AND 100 POINTS!!!!!
Order the numbers from least to greatest
Answer:
-1, √4/5, -6/5, √3, 2, -3√9, 2√125
Step-by-step explanation:
1. Tyra bought a lolli-pop with a diameter of 2 inches. What is the circumference of the lolli-pop to the nearest tenth of an inch? A. 3.9 inches B. 15.7 inches C. 6.3 inches D. 7.9 inches
A lollypop have a circular shape
Diameter D is the line in a circumference that divides it in half
then calculate directly π• D
to the nearest tenth
π•D = 3.14 x 2 = 6.28
then nearest number is 6.3 , or 6.30. Option C)