Option (B) (3 + 2i) (3 - 2i) is the expression that has the whole number product.
Whole number:
Whole number refers the numbers without fractions and it is a collection of positive integers and zero and represented by the symbol “W” and the set of numbers are {0, 1, 2, 3, 4, 5, 6, 7, 8, 9,……………}.
Given,
Here we have the following expression:
(A) (4- 2i) (4 - 2i)
(B) (3 + 2i) (3 - 2i)
(C) (-6+ i)(3- i)
(D) (-4+3i)(4-3i)
Now, we need to find the whole number product.
In order to find the solution we have to perform the multiplication on the given expression,
First expression will gives the following,
(A) (4 - 2i) (4 - 2i)
When we apply the (a-b)² formula in it then we get,
=> 4²+ (2i)² - (2 x 4 x 2i)
=> 16 - 4 - 16i
=> 12 - 16i
Which is not a whole number product.
Second expression,
(B) (3 + 2i) (3 - 2i)
Apply the (a + b)(a - b) formula in it,
Then we get,
=> 3² - (2i)²
=> 9 + 4
=> 13
Therefore, this one is the whole number product.
Third expression,
(C) (-6 + i) (3 - i)
When we perform the multiplication on it, then we get,
=> -18 + 6i +3i -i²
=> -18 + 9i + 1
=> -17 + 9i
his one is not a whole number product.
Final expression,
(D) (-4 + 3i) (4 - 3i)
When we perform the multiplication on it, then we get,
=> -16 + 12i + 12i - (3i)²
=> -16 + 24i + 9
=> -7 + 24i
This one is also no the whole number product.
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i need help answering this question
Answer:
Step-by-step explanation:
there is no question?
Different liquids freeze at different temperatures, called their freezing points. Liquid acetone, used in nail polish remover, has a freezing point of – 137°F. Water has a freezing point of 32°F. How much warmer is the freezing point of water than the freezing point of acetone? °F
The freezing point of water in relation to the freezing point of acetone, is 169 °F
How to find the difference in freezing points?The difference between the freezing point of water (how much warmer the freezing point of water is) and the freezing point of acetone can be found by the formula:
= Freezing point of water - Freezing point of acetone
Freezing point of water = 32°F
Freezing point of Acetone = – 137°F
In relation to the freezing point of acetone, the degrees warmer that the freezing point of water is:
= 32 - (- 137)
= 32 + 137
= 169 °F
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The average cost per night of a hotel room in New York City is $273 (Smart Money, March 2009). Assume this estimate is based on a sample of 45 hotels and that the sample standard deviation is $65.
Show all work for each solution
a. With 95% confidence, what is the margin of error?
b. What is the 95% confidence interval estimate of the population mean?
c. Two years ago the average cost of a hotel room in New York City was $229. Discuss the change in cost over the two-year period.
With 95% confidence, the margin of error is 19.523, population mean is (253.477, 292.523) and the change in cost over the two-year period is 19.21%.
In the given question,
The average cost per night of a hotel room in New York City(y) = $273
Number of rooms in hotel(n) = 45.
The sample standard deviation(s) = $65
(a.) Now finding the margin of error, with 95%(0.95) confidence.
The formula of margin of error is
ME= [tex]z_{\alpha /2}\times \frac{s}{\sqrt n}[/tex]
Now find the value of [tex]z_{\alpha /2}[/tex].
[tex]\alpha[/tex] = 1-0.95
[tex]\alpha[/tex] = 0.05
[tex]\alpha[/tex]/2 = 0.05/2
[tex]\alpha[/tex]/2 = 0.025
Now the value of [tex]z_{\alpha /2}[/tex]
[tex]z_{\alpha /2}=z_{0.025}[/tex]
From the standard table of z is 2.015.
Now putting the value in formula
ME= 2.015 × 65/√45
ME= 2.015 × 65/6.708
ME= 2.015 × 9.689
ME= 19.523
Hence, with 95% confidence, the margin of error is 19.523.
(b) Now finding .the 95% confidence interval estimate of the population mean.
Population Mean = y ± ME
Population Mean = 273 ± 19.523
Population Mean = {(273-19.523), (273+19.523)}
Population Mean = (253.477, 292.523)
(c) Now two years ago the average cost of a hotel room in New York City was $229 then the change in cost over the two-year period is
The change in cost = difference between the cost/old cost
The change in cost = (273-229)/229 *100
The change in cost = 44/229 *100
The change in cost = 0.1921 *100
The change in cost = 19.21%
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Pls help urgent someone hurry please
Proved that the triangle ABW ≅ triangle DCW
In the given question,
The length of WA = The length of WD
The measure of angle 5 = The measure of angle 7
Here we have to prove that one angle and two sides of the triangle ABW is equal to the one angle and two sides of the triangle DCW
Consider the triangle ADW,
In the triangle ADW the length of the WA is equal to the length of WD.
Therefore the measure of angle A is equal to the measure of angle D.
So in triangle ABW and the triangle DCW, one side and two angles are equal.
Therefore the triangle ABW and triangle DCW are congruent
Hence, proved that the triangle ABW ≅ triangle DCW
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394.6/ 9 but use compatible numbers to estimate the quotient
The quotient estimated value of 394.6/9 is 43.84
What is quotient?A quotient is the number which is generated when we perform division operations on two numbers. Basically, it is the result of the division method. There are four main terminologies used in the arithmetic division such as divisor, dividend, quotient and remainder. For example, 15/3= 5 .The number that is being divided ( 15) is called the dividend, and the number that it is being divided by (3) is called the divisor. The result of the division(5) is the quotient.
Therefore the quotient of 394.6/9= 43.84
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A pool can be filled by one pipe in 3 hours and by a second pipe in 5 hours. How long will it take using both pipes to fill
the pool?
Answer:
i think it 8h
Step-by-step explanation:
Find the average rate of change of the given function on the interval [1,6]. g(x)=2x2−x
Answer:13
Step-by-step explanation:
g(1)=2(1)^2-1= 1
g(6)=2(6)^2-6=66
66-1/6-1=13
Question 6
A road drops 795 feet for every 265 feet forward, determine the slope of the road. The
slope can be positive or negative.
The slope of the road is 159/53
What is a slope?
How steeply a line slopes from left to right is known as its slope. By dividing a line's rise, or vertical change, by run, or horizontal change, one can calculate a line's slope, the slope of a line is always constant (it never varies).
To calculate the slope of a line using the formula
m = rise / run = (y₂ - y₁)/(x₂ - x₁)
where, m = slope
(x₁, y₁) = coordinates of the first point in the line
(x₂, y₂) = coordinates of the second point in the line
Here, we have
rise = 795
run = 265
by using the slope formula,
m = rise/run
m = 795/265
m = 159/53
Hence, the slope of the road is 159/53.
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??? brianlest?? help please
math
Answer:
try to show it step by step
write each system of equations as a matrix
Answer:
Step-by-step explanation:
Which expression uses the commutative property of addition and the associative property of
multiplication to rewrite the expression 3 (28) +7?
O 7+(3-2).8
O 3 (8-2)+7
O 7+3 (16)
O (3-2) 8+7
The expression that uses the commutative property of addition and the associative property of multiplication to rewrite the expression 3 (28) +7 is 7+(3-2).8
The commutative property of addition states that a change in the order of the numbers being added does not affect the sum. We can define commutative property of addition as adding the numbers in any order will give the same answer.
a + b = b + a
3(2x8) + 7 = 7 + 3(2x8)
The associative property of multiplication says that while multiplying three numbers, regardless of the way the numbers are grouped, the end result will always be the same.
a(b x c) = (a x b) c
7 + 3(2x8) = 7 + (3.2)8
Therefore, the expression that uses the commutative property of addition and the associative property of multiplication to rewrite the expression 3 (28) +7 is 7+(3-2).8
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Please solve :) and hurry!
The price for 7 bags of trail mix and 4 bananas is 15.45 dollars.
The expression for x trail bag and y bananas is 1.35x + 1.50y.
How to represent expression?In maths, an expression is a combination of numbers, variables, functions (such as addition, subtraction, multiplication or division etc.)
Therefore, the cost of a bag of trail mix at the corner store is 1.35 dollars and the cost of a banana is 1.5 dollars.
The cost for 7 bags of trail mix and 4 bananas can be computed as follows;
let
x = bags of trail mix
y = number of banana
Therefore,
1.35x + 1.50y
1.35(7) + 1.50(4) = 9.45 + 6 = 15.45
Therefore, let's find the expression for x trail bag and y bananas.
Hence,
1.35x + 1.50y
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Two integers are separated by 24 units on a number line. The sum of the integers is -12 and the quotient is -3. What are the two integers?
Answer:
6 and - 18
Step-by-step explanation:
let the 2 integers be a and b , then
a + b = - 12 → (1)
[tex]\frac{a}{b}[/tex] = - 3 → (2)
multiply both sides by b ( b ≠ 0 )
a = - 3b
substitute a = - 3b into (1)
- 3b + b = - 12
- 2b = - 12 ( divide both sides by - 2 )
b = 6
substitute b = 6 into (1) and solve for a
a + 6 = - 12 ( subtract 6 from both sides )
a = - 18
the two integers are - 18 and 6
Please help please and thank you..
The value of x for the triangle by the mid point theorem is obtained as 5.
What is defined as the mid-point theorem?The line segment of a triangle connecting the midpoint in two the triangle's sides is thought to be parallel to that third side and also half the length of the third side, according to the midpoint theorem. A location that is at, close, or equally far both from ends of a line segment is referred to as the midpoint. To put it another way, the midpoint is indeed the place in a fact where the beginning and the conclusion meet.For the given diagram in the question.
As, the sides of the triangle is divided in equal parts.
By the mid -point theorem-
(1/2)24 = x + 7
12 = x + 7
x = 12 - 7
x = 5
Thus, the value of x for the triangle by the mid point theorem is obtained as 5.
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Can someone help me with this
Answer:
x=20
Step-by-step explanation:
It looks like the opposite end of the 70 is angle between I and D. So assuming that angle is also 70 I would subtract 90 and 70 which equals 20. X=20
A study was commissioned to find the mean weight of the residents in certain town. The study found the mean weight to be 193 pounds with a margin of error of 9 pounds. Which of the following is not a reasonable value for the true mean weight of the residents of the town?
Considering the confidence interval, the non-reasonable value for the true mean weight of the residents of the town is:
A value that is less than 184 or more than 202.
How to obtain the confidence interval?The confidence interval for a population mean is given by the point estimate of this mean, which is the sample mean, plus/minus the margin of error.
For the context of this problem, these parameters are given as follows:
Point estimate: 193 pounds.Margin of error: 9 pounds.Hence the lower bound of the interval is:
193 pounds - 9 pounds = 174 pounds.
The upper bound of the interval is:
193 pounds + 9 pounds = 202 pounds.
All the values that are in the interval are reasonable values for the population mean, hence, in the context of this problem, the not reasonable values are given as follows:
A value that is less than 184 or more than 202.
(as they would be outside the confidence interval).
Missing InformationThe options are not given, hence the answer was given in general terms.
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The time is takes an object to move a certain distance is inversely propotional to the speed that it's travelling at.
it takes a car 12 minutes to travel the length of a road if it goes at an average speed of 60mph
a) How long would it take the car to travel down the same road if it travelled at an average speed of 30mph
B) if it takes the car 36 minutes to drive down the road, what will it's average speed
Answer:
a) 24 minutes
b) 20 mph
Step-by-step explanation:
Speed - distance -time:time= 12 min
[tex]\sf = \dfrac{12}{60} \ hour[/tex]
speed = 60 mph
[tex]\sf \boxed{distance =speed * time}[/tex]
[tex]\sf = 60 * \dfrac{12}{60}\\\\ = 12 \ m[/tex]
a) Speed = 30 mph
[tex]\sf \boxed{time = \dfrac{distance}{speed}}[/tex]
[tex]\sf = \dfrac{12}{30}\\\\ = \dfrac{2}{5} \ hour\\\\ = \dfrac{2}{5}*60\\\\= 2 * 12\\\\= 24 \ minutes[/tex]
It will take 24 minutes.
c) time = 36 minutes
[tex]\sf = \dfrac{36}{60} \hour[/tex]
[tex]\sf \boxed{speed= \dfrac{distance}{time}}[/tex]
[tex]\sf = \dfrac{12}{ \dfrac{36}{60}}\\\\\\ = 12* \dfrac{60}{36}\\\\= 20 \ mph[/tex]
Average speed = 20 mph
Please help! What is the standard form of the following equation?
y= 5x+0.5
-5x+y=-0.5
-5x+y=0.5
-5x-y=0.5
-5x+y= 0.5
The standard form of the equation, 3y = 9x -12, is -5x + y = 0.5. The correct option is the third option -5x+y=0.5
Writing an equation is standard formFrom the question, we are to write the given equation is standard form.
The given equation is
y = 5x + 0.5.
The standard form of a linear equation is
Ax + By = C
Where A, B, and C are constants
x and y are variables
Now, we will write the given equation is the standard form of a linear equation.
y = 5x + 0.5
Subtract 5x from both sides of the equation
y - 5x = 5x - 5x + 0.5
y - 5x = 0.5
Rewrite the equation, so that it would correspond to the standard form of a linear equation
-5x + y = 0.5
Hence, the standard form is -5x + y = 0.5
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How would I solve this? i know how to solve easier variations but not like this the question is:
Write a linear function f with the values f (-1) = 8 and ƒ (5) = 6.
The linear function with values of f(-1)=8 and f(5)=6 is f(x) = [tex]\frac{-x+23}{3}[/tex].
What is linear function?
A straight line on the graph has the equation or formula y = f(x) = px + q is linear function .One independent and one dependent variables are present. X and Y are the independent and dependent variables, respectively. P is the y-intercept or constant term, and it also represents the value of the dependent variable. A straight line on the coordinate plane is represented by a linear function.
Here the given values are f(-1)=8 and f(5)=6.
We know that f(x)=y , Then the points are (-1,8) and (5,6).
Using slope formula ,
=> slope m= [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
=> slope m = -2/6=-1/3
Now using slope formula,
=> [tex]y-y_1=m(x-x_1)[/tex]
=>y-8=-1/3(x+1)
=>3y-24=-x-1
=> 3y=-x+23
=> y = [tex]\frac{-x+23}{3}[/tex]
Hence the linear function is f(x) = [tex]\frac{-x+23}{3}[/tex].
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(42x³ + 16x² + 46x +42) ÷ (7x + 5)
응
write an equation in slope-intercept form the table. help fast please
x: -4, 0, 4, 8, 12
y: 5, 6, 7, 8, 9
The linear equation in the table is written as:
y = (1/4)*x + 6
How to write the linear equation?The linear equation in slope-intercept form is written as:
y = m*x+ b
Where m is the slope and b is the y-intercept.
We know that if a line passes through two points (x₁, y₁) and (x₂, y₂), then the slope is:
m = (y₂ - y₁)/(x₂ - x₁)
Here we can use the first two points on the table:
(-4, 5) and (0, 6), so the slope is:
m = (6 - 5)/(0 + 4) = 1/4
And because of the point (0, 6) we know that the y-intercept is 6, then the line is:
y = (1/4)*x + 6
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Use the z-distribution table on pages A-1 and A-2 or technology to solve. Suppose a set of data is normally distributed. Below which z-score do approximately 34 of the data lie?
The z-score under which 3/4 of the data lies is of:
Z = 0.675.
Normal Probability DistributionThe z-score of a measure X of a variable that has mean symbolized by [tex]\mu[/tex] and standard deviation symbolized by [tex]\sigma[/tex] is obtained by the rule presented as follows:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score represents how many standard deviations the measure X is above or below the mean of the distribution, depending if the obtained z-score is positive or negative.Using the z-score table, the p-value associated with the calculated z-score is found, and it represents the percentile of the measure X in the distribution.The z-score under which 75% of the distribution lies is the 75th percentile, hence it is the value of Z with a p-value of 0.75.
Looking at the z-table, this value is of 0.675, as 0.675 is the mean of the p-values of Z = 0.67 and Z = 0.68.
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Describe the transformers of the parent function, f(x)=x, performed to create g(x).
g(x)= -3 • f(x) + 1
The function g(x) is a reflection over the x-axis and stretch by 3 units and shifted upward by 1 unit of the parent function f(x).
What is a function?A capability is a declaration, idea, or rule that lays out a relationship between two factors. Capabilities might be found all through science and are fundamental for the advancement of huge connections.
The functions are given below.
f(x) = x
g(x) = -3f(x) + 1
g(x) = -3x + 1
The parent function is a reflection over the x-axis and stretch by 3 units and shifted upward by 1 unit.
The functions g(x) and f(x) are shown below.
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A scientist claims that 9% of viruses are airborne.
If the scientist is accurate, what is the probability that the proportion of airborne viruses in a sample of 533 viruses would differ from the population proportion by less than 3%? Round your answer to four decimal places.
The probability that the proportion of airborne viruses in a sample of 533 viruses would differ is 0.0062.
How to calculate the probability?From the information, the scientist claims that 9% of viruses are airborne and the proportion of airborne viruses in a sample is 533 viruses.
The requirement to solve the probability between z-values is to know that the probability between the z-values is the difference between the probability of the greatest z-value and the lowest z-value.
The mean is 0.09 and the standard deviation is 0.012.
The probability will be:
= 1 - P[Z < (0.12 - 0.09/0.013)]
= 1 - P(Z < 2.5)
= 1 - 0.99379
= 0.0062
This shows the concept of solving probability regarding z values.
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Pixel A is located 80 km from the Jacksonville radar. How many seconds did it take for the radar pulse to travel to the target at Pixel A and return to the radar? (It will be a very small answer!)
C= 3 × 10^8 m s−1
R= 80,000
R= CT/2
[tex]C=3\times 10^8~\frac{m}{s}\hspace{5em}R=80000\implies R=8\times 10^4 \\\\[-0.35em] ~\dotfill\\\\ R=\cfrac{CT}{2}\implies 2R=CT\implies \cfrac{2R}{C}=T\implies \cfrac{2(8\times 10^4)}{3\times 10^8}=T \\\\\\ \cfrac{16\times 10^4}{3\times 10^8}=T \implies \cfrac{16}{3}\times\cfrac{10^4}{10^8}=T\implies \cfrac{16}{3}\times\cfrac{1}{10^8\cdot 10^{-4}}=T \\\\\\ \cfrac{16}{3}\times\cfrac{1}{10^{8-4}}=T \implies \cfrac{16}{3\times 10^4}=T\implies \cfrac{16}{30000}=T\implies \cfrac{1}{1875}=T[/tex]
if h(x)= 1-7x find the value of 23-h(9)=
85
Step-by-step explanation:
Given,
[tex]{ \pink{ \sf{h(x) = 1 - 7x}}} \: { \to} \: { \tt{eq}^{n} (1)}[/tex]
Put x = 9 in Eqⁿ (1)
[tex]{ \pink{ \sf{h(9) = 1 - 7(9)}}}[/tex]
[tex]{ \pink{ \sf{h(9) = 1 - 63}}}[/tex]
[tex]{ \red{ \boxed{ \pink{ \sf{h(9) = - 62}}}}}[/tex]
Let
[tex]{ \green{ \sf{23 - h(9)}}} \: { \to} \: { \tt{ {eq}^{n} (2)}}[/tex]
Substitute the value of h(9) in Eqⁿ (2)
[tex]{ \green{ \sf{23 - ( - 62)}}}[/tex]
[tex]{ \green{ \sf{23 + 62}}}[/tex]
[tex] = { \pink{ \boxed{ \red{ \sf{85}}}}}[/tex]
A notebook computer has a mass of 2.25 kilograms . about how many pounds does the notebook weigh
Answer:
5 pounds
Step-by-step explanation:
1 kg = 2.205 lbs.
2.25×2.205
⇒4.96125
A rectangle has a width (3x-2) and a length of (5x). The rectangle has the same perimeter as a square with a perimeter of 44 units.
Find the value of x.
Check the picture below.
Write an inequality that represents the graph
The line represents that x is anywhere from negative infinity to 1:
x < 1
Answer: x<1
Step-by-step explanation:
X is less than one on the graph because everything on the darker line is the solution.
Ex:
-1<1
help pleas now...............math
The value of q after solving the expression, q/3+2/3 = 8q/3-5/3, is 1.
According to the question,
We have the following expression:
q/3+2/3 = 8q/3-5/3
Now, taking 3 as the denominator on both the sides:
(q+2)/3 = (8q-5)/3
Now, 3 in the denominator on the left hand side can be divided by 3 in the denominator on the right hand side:
q+2 = 8q-5
Now, changing the sides of this expression:
8q-5 = q+2
Moving q from the right hand side to the left hand side:
8q-q-5 = 2
7q -5 = 2
Moving 5 from the left hand side to the right hand side:
7q = 2+5
7q = 7
q = 7/7
q = 1
Hence, the value of q after solving the given expression is 1.
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