Number of boys = a - b
Step-by-step explanation:Number of children in the class = a
Number of girls in the class = b
Number of boys = Total - Girls
a - b
Evaluate the following expressions a) (3 + 2i) - (8 - 5i) b) (4 - 2i)*(1 - 5i) c) (- 2 - 4i) / i d) (- 3 + 2i) / (3 - 6i)
a) 3 - 8 + 2i - (-5i) = -5 + 2i +5i = -5 + 7i
b) 4 - 20i - 2i + 10i² = 4 - 22i + 10([tex]\sqrt{-1}[/tex])² = 4 - 22i + 10(-1) = 4 - 10 -22i
= -6 -22i
c) Multiply both numerator and denominator by i
[tex]\frac{i(-2-4i)}{i^{2} }[/tex] = [tex]\frac{-2i - 4i^{2} }{i^{2} }[/tex] = [tex]\frac{-2i - 4(\sqrt{-1})^{2} }{(\sqrt{-1})^{2}}[/tex] = [tex]\frac{-2i - 4(-1)}{-1}[/tex] = [tex]\frac{-2i+4}{-1}[/tex] = 2i - 4 = -4 + 2i
d) Multiply both numerator and denominator by (3+6i)
[tex]\frac{(3+6i)(-3+2i)}{(3+6i)(3-6i)}[/tex] = [tex]\frac{-9+6i-18i+12i^{2} }{9-36i^{2} }[/tex] = [tex]\frac{-9-12i+12(\sqrt{-1} )^{2} }{9-36(\sqrt{-1} )^{2} }[/tex] = [tex]\frac{-9-12i+12(-1)}{9-36(-1)}[/tex] = [tex]\frac{-9-12-12i}{9+36}[/tex]
= [tex]\frac{-21-12i}{45}[/tex] = [tex]-\frac{21}{45} - \frac{12}{45}i[/tex]
Zachary has $40 to spend on his
vacation. He would like to save $10 for
souvenirs on the last day. He spent $12
at the waterpark and $8.50 on food.
With the remaining money, he would like to
play arcade games in the hotel. Each
game costs $1.50. Write an inequality for
the number of games he can play.
Refine your variable.
Answer: He can play 6 games
Step-by-step explanation:
40-10 = 30
30- 12 = 18
18- 8.50 = 9.50
9.50 divided by 1.50 = 6.3
A bird flies from the bottom of a canyon that is 52
3
5 feet below sea level to a nest that is 789
3
10 feet above sea level. What is the difference in elevation between the bottom of the canyon and the bird's nest?
The difference in the elevation between the canyon and the bird's nest is 737. 3 feet
How to determine the value
From the information given, we have that;
The distance below the sea level = 52 3/ 5 feet , this would take a negative valueThe distance above sea level = 789 3/ 10, this would take a positive valueLet's convert the mixed fractions to improper fraction;
= - 263/ 5 = - 52. 6 feet
789 3/ 10 = 7893/ 10 = 789. 3 feet
The difference in the elevation between the canyon and the bird's nest ;
= -52. 6 + 789. 9
= 737. 3 feet
Thus, the difference in the elevation between the canyon and the bird's nest is 737. 3 feet
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A group of 24 students and 3 adults visited the zoo. The admission fee for an adult was $4 more than the fee for a student. The total amount due
was $133.50.
What was the cost of each type of admission fee?
Select from the drop-down menus to correctly complete the statement.
Adult admission fees cost $___ and student admission fees cost $___
a 17-inch candle is lit and steadily burns until it is burned out. let b represent the burned length of the candle (in inches) and let r represent the remaining length of the candle (in inches). write a formula that expresses r in terms of b .
b r = 17 - b
when it is 8 inches tall after 9 inches have burned from the candle.
What do you mean by formula?A formula in mathematics is an assertion of a fact, rule, or principle using mathematical symbols. Equations, equalities, identities, inequalities, and asymptotic expressions are a few examples of formulae.
In the theory of logic, the word "formula" is also frequently used to refer to a sentential formula, also known as a propositional formula, or a formula in propositional calculus.
A 17 inch candle is lit and steadily burns until it is burned out.
Let b represent the burned length of the candle (in inches ) and let r represent the remaining length of the candle (in inches) .
Write a formula that expresses r in terms of b r = 17 - b
Preview b. When 6.8 inches have burned from the candle, the remaining length of the candle is 10.2 inches.
Therefore the point should be on the graph of r in terms of b. c. On the graph below:
i, represent the linear relationship between l and b ii. plot the point that represents the candle when it is 8 inches tall after 9 inches have burned from the candle.
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If it takes my car 2.2 seconds to accelerate from 8.9 m/s to 35.76 m/s, what is my cars average acceleration in that time?
Your cars average acceleration in that time is 12.21m/s^2
What is my cars average acceleration in that time?The given parameters are
Initial velocity, u = 8.9 m/s
Final velocity, v = 35.76 m/s
Time, t - 2.2 seconds
The average acceleration is calculated using
v = u + at
So, we have
35.76 = 8.9 + 2.2a
Evaluate the like terms
26.86 = 2.2a
Divide by 2.2
a = 12.21
Hence, your cars average acceleration in that time is 12.21m/s^2
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What is the inequality shown
Answer:
it shows that the answer is (-2,8(
the brackets are the symbols of inequality
a random sample of 36 swimmers have a mean time of 3.91 minutes and a population standard deviation of 0.16 minutes. construct a 95% confidence interval of the population mean
Answer:
ksjsbs jsioeie jsisjbdbd
Step-by-step explanation:
Answer:
Step-by-step explanation:
For f (x):
f (x) = (x + 3) ^ 2 - 2
For x = -1
f (-1) = (-1 + 3) ^ 2 - 2
f (-1) = (2) ^ 2 - 2
f (-1) = 4 - 2
f (-1) = 2
For x = 3
f (3) = (3 + 3) ^ 2 - 2
f (3) = (6) ^ 2 - 2
f (3) = 36 - 2
f (3) = 34
AVR = ((34) - (2)) / ((3) - (- 1))
AVR = 8
For g (x):
linear graph with and intercept of negative 3 over 2 and x intercept of 3
y = mx + b
b = -3/2
For me we have:
0 = m (3) - 3/2
3m = 3/2
m = 1/2
The function g (x) is:
g (x) = (1/2) x - 3/2
For x = -1
g (-1) = (1/2) (- 1) - 3/2
g (-1) = -1/2 - 3/2
g (-1) = -4/2
g (-1) = -2
For x = 3
g (3) = (1/2) (3) - 3/2
g (3) = 3/2 - 3/2
g (3) = 0
AVR = ((0) - (- 2)) / ((3) - (- 1))
AVR = 1/2
For h (x):
Using the table we have:
AVR = ((62) - (14)) / ((3) - (- 1))
AVR = 12
(2y to the power of -3)(3y)to the negative 2 power) (6y to the negative 2 power)to the power of 2)
Evaluation of the equation is [tex]\frac{y^{-14} }{6718464}[/tex]
Here from the question, we get the evaluation
[tex][(2y)^{-3} (3y)^{-2} (6y)^{-2}]^{2}[/tex]
Now evaluate it in the simple form we have
[tex][(\frac{1}{2y} )^{3} (\frac{1}{3y} )^{2} (\frac{1}{6y} )^{2} ]^{2}[/tex]
[tex][\frac{1}{8y^{3} } \frac{1}{9y^{2} } \frac{1}{36y^{2} } ]^{2}[/tex]
[tex][\frac{1}{2592y^{7} } ]^{2}[/tex]
[tex]\frac{1}{6718464y^{14} }[/tex]
[tex]\frac{y^{-14} }{6718464}[/tex]
Therefore we get the simplest form of the evaluation.
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in what rate of interest rupees 4000 amount to Rupees 6000 in 2 years find it
with full process
A 25% rate of interest is required for Rupees 4000 amount to Rupees 6000 in 2 years.
Here we are given the following-
Principal amount = Rs 4000
Amount received after 2 years = Rs 6000
Time period = 2 years
Let the rate of interest = r%
Then, according to the simple interest formula-
Simple interest = Principal × time period × rate/100
and Simple interest = Final amount - principal amount
Here, simple interest = 6000 - 4000 = Rs 2000
Thus,
2000 = 4000 × 2 × r/100
2000/4000 = 2 × r/100
1/2 = 2 × r/100
1/4 = r/100
r = 100/4
r = 25
Thus, the rate of interest is 25%.
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The highest recorded temperature on earth is 134 degrees fahrenheit. the lowest is -128.6 degrees fahrenheit. what is the difference between these temperatures?
The difference between the highest recorded temperature on Earth of 134 degrees Fahrenheit and the lowest recorded temperature of -128.6 is equal to 262.6 degrees Fahrenheit.
In mathematics, the difference can be described as the result of the subtraction of one numeral or value to another.
Hence the difference between the highest recorded temperature and the lowest recorded temperature on Earth can be found by the subtraction of the highest and lowest recorded temperatures.
The difference in the two temperatures = highest recorded temperature - lowest recorded temperature
Difference in Farenheit = 134 - ( -128.6)
Difference in Farenheit = 134 + 128.6
Difference in Farenheit = 262.6
Hence, the difference between the highest recorded temperature and the lowest recorded temperature is calculated to be 262.6 degrees fahrenheit.
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Waylon made $14, $62, $40, and $36
mowing lawns. How much did he make
mowing lawns?
select translation, reflection, or rotation to identify the single transformation that transforms ∆rst to ∆r′s′t′.
The single transformation that transforms ∆RST to ∆R'S'T' is a reflection.
Part A:
For the first figure it is visible that the orientation of the pre-image (∆RST) is similar to that of the image (∆R'S'T').The image is received from the pre-image through moving the pre-image a few units down. Therefore, the single transformation that transforms ∆RST to ∆R'S'T' is a translation.
Part B:
For the second figure ,it is visible that the orientation of the pre-image (∆RST) is similar to that of the image (∆R'S'T').The image is received from the pre-image through moving the pre-image a few units down and a few units to the right. Therefore, the single transformation that transforms ∆RST to ∆R'S'T' is a translation.
Part C:
For the third figure it is visible that the orientation of the pre-image (∆RST) isn't similar to that of the image (∆R'S'T').The image is received from the pre-image through rotating the pre-image a few 180 degrees. Therefore, the single transformation that transforms ∆RST to ∆R'S'T' is a rotation.
Part D:
For the fourth figure it is visible that the orientation of the pre-image (∆RST) isn't similar to that of the photograph (∆R'S'T').The image is received from the pre-image through reflecting the pre-image.
Therefore, the single transformation that transforms ∆RST to ∆R'S'T' is a reflection.
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Write 2.1 terminating as a mixed number
Answer:
2 [tex]\frac{1}{10}[/tex]
Step-by-step explanation:
.10
change it to 10/100
reduce by 10
1/10
Answer: 2 1/10
Step-by-step explanation:
Convert the decimal number to a fraction by placing the decimal number over a power of ten. Since there is 1 number to the right of the decimal point, place the decimal number over 10^1(10). Next, add the whole number to the left of the decimal.
2 1/10
the owner of the good deals store opens a new store across town. for the new store, the owner estimates that, during business hours, an average of 909090 shoppers per hour enter the store and each of them stays an average of 121212 minutes. the average number of shoppers in the new store at any time is what percent less than the average number of shoppers in the original store at any time? (note: ignore the percent symbol when entering your answer. for example, if the answer is 42.1\b.1b, point, 1, percent, enter 42.142.142, point, 1.)
The answer is 60%
According to the original information given, the estimated average number of shoppers in the original store at any time(x) is 45.
In the question, it states that, in the new store, the manager estimates that an average of 90 shoppers per hour(60 minutes) enter the store, which is equivalent to 1.5 shoppers per minute(s).
The manager also estimates that each shoppers stays in the store for an average of 12 minute (t). Thus, by Little's law there are, on average,
x = s x t
=> x = 1.5 x 12
=> x = 18
Hence, there are 18 shoppers at any time in the new store.
Now, Percentage of shoppers
[tex]\frac{45-18}{45}[/tex] x 100 = 27/45 x 100 = 2700/45 = 60%
Therefore, the answer is 60%
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-6(a+8) show your work
i need this ASAP
Answer:
-6a - 48
What is the distributive property?The distributive property states that for an expression a(b + c), it can be evaluated to ab + ac.
SolveTo distribute, expand the algebraic expression using the aforementioned policy.
[tex]-6(a+8)[/tex]
Multiply a and b together.
[tex]-6\times a=-6a[/tex]
Then, multiply a and c together.
[tex]-6\times8=-48[/tex]
Finally, add the two values together.
[tex]-6a+(-48)=-6a-48[/tex]
Final Answer[tex]\boxed{\bold{-6a-48}}[/tex]
Hey there!
Distributive Property formula:
a(b + c)
= a(b) + a(c)
= a * b + a * c
= ab + ac
Your equation: -6(a + 8)
Solving:
-6(a + 8)
= -6(a) - 6(8)
= -6 * a - 6 * 8
= -6a - 48
Therefore, your answer should be:
-6a - 48
Good luck on your assignment & enjoy your day!
~Amphitrite1040:)
part a a wall is covered with 6 wood panels. each panel is a square with a side length of x feet. write an expression to represent the total area, in square feet, covered by the wood panels. the expression for total area: part b a rectangle has a length of 6 centimeters and a width of x 10 centimeters. write expressions to represent the perimeter of the rectangle. the expression for perimeter: part c write expressions to represent the area of the rectangle.
6x² is the total area, in square feet, covered by the wood panels.
What is area?
The region that an object's shape defines as its area.The area of a figure or any other two-dimensional geometric shape in a plane is how much space it occupies.A wall is covered with 6 wood panels. Each panel is a square with a side length of "X" feet.So based on this, we can say that The expression to represent the total area, in square feet,
So, the wood panels is to be considered as the 6 × x² = 6x²
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You add a mixture of salt, sugar, and cooking oil to a glass of water. You stir everything together and wait a few minutes. What will you see in the glass? (2 points)
a
All of the parts of the mixture will disappear because they are all soluble in water.
b
The salt and sugar will seem to disappear, and the oil will float on the surface of the water.
c
The salt and sugar will settle to the bottom of the glass, and the oil will float on top of the water.
d
The salt will settle to the bottom of the glass, and the sugar and oil will disappear in the glass.
Answer:b. the salt and sugar will disappear and the oil will float on the surface of water
Step-by-step explanation: If you stir salt and sugar it will dissapear but oil in thick and if you know it will float to the surface
3/5 ÷ 2
help please! (10 points)
Answer:
i think the answer is 0.3 but im not sure i just used a calculator
What is the value of f(15) if the function is f(x)=(x)(2x+5)
Answer:
525
Step-by-step explanation:
f(x)=(x)(2x+5)
f(x)=2x^2+5x
f(15)=2*(15)^2 + 5*15
= 2*225 + 75
=450 + 75
=525
lee jogged 3 1/11 laps in teh morning and 2 3/22 laps in the evening how many laps did lee jog in all? simlify and write the answer as a improper fraction
Lee jogged a total of 5 3/22 laps
How to calculate the total laps ?
Lee jogged 3 1/11 laps in the morning
He then jumped 2 3/22 laps in the evening
Therefore the total laps jogged can be calculated by adding both values together
3 1/11 + 2 3/22
34/11 + 47/22
= 113/22
= 5 3/22
Hence the total laps jogged is 5 3/22 laps
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I need help with this asap
Answer is 32.5 because the other ones isnt it
What is the range of the function represented by the graph?
A.
y ≥ 1
B.
y ≤ 1
C.
1 ≤ y ≤ 6
D.
all real numbers
Answer:
A. y is more than are equal to 1
Step-by-step explanation:
range is y, lowest point is 1, highest is all real numbers, so range is anything more than 1
Answer:
B. y <= 1
Step-by-step explanation:
Because the function touches the point 1 on the y-line of the graph and goes upward into infinity, all values of y will be greater than or equal to one.
HELP what is 1.025 × 10 5 . In standard form
Answer:
102500
Step-by-step explanation:
The result can be shown in multiple forms.
Scientific Notation:
1.025
10
5
Expanded Form:
102500
Brian invests £6600 into his bank account.
He receives 0.6% per year compound interest.
How much will Brian haverafter 6 years?
Give your answer to the
nearest penny where appropriate.
At 0.6% per year compound interest. Brian will get 6841.19 after 6 years.
What is compound interest?The interest earned on savings that is computed using both the original principle and the interest accrued over time is known as compound interest.
It is said that Italy in the 17th century is where the concept of "interest on interest" or compound interest first appeared. It will accelerate the growth of a total more quickly than simple interest, which is solely computed on the principal sum.
Money multiplies more quickly thanks to compounding, and the more compounding periods there are, the higher the compound interest will be.
Based on the given conditions, formulate: 6600×(0.6%+1) 6
Evaluate the equation/expression: 6841.19264
Round the number: 6841.19
Answer: 6841.19
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How do you work this problem and what is the answer
an airplane is taking off headed due north with an air speed of 173 miles per hour at an angles of 18
The vector that represents the resultant velocity of the plane will be V = 30.72 i + 135.89 j + 53.46 k.
What is a vector?The quantity which has magnitude, and direction, and follows the law of vector addition is called a vector.
An airplane is taking off headed due north with an air speed of 173 miles per hour at an angle of 18° relative to the horizontal. The wind is blowing with a velocity of 42 miles per hour at an angle of S 47° E.
Let north be the y-axis and east be the x-axis. Then the vector equation will be given as,
V = (42 sin 47°) i + (173 cos 18° - 42 cos 47°) j + (173 sin 18°) k
V = 30.72 i + 135.89 j + 53.46 k
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Please help
Simplify the expression by combining like terms:
Answer:
2b² + 2b
Step-by-step explanation:
b + 3b² + b - b²
= 3b² - b² + b + b
= 2b² + 2b
Answer:
[tex] \sf \: {2b}^{2} + 2b [/tex]
Step-by-step explanation:
Given expression,
→ b + 3b² + b - b²
Let's simplify the expression,
→ b + 3b² + b - b²
→ (3b² - b²) + (b + b)
→ (2b²) + (2b)
→ 2b² + 2b
→ 2b(b + 1)
Hence, answer is 2b² + 2b.
If h(x)=-4/5x+6/7 find the following values. Simplify your answer.
h(1)=
h(2)=
h(-1/2)
Hence , on solving the given expression , we get values of h(1) = 58/35 , h(2) = 86 /35 and h(-1/2) =26 /35.
A operate in maths may be a special relationship among the inputs (i.e. the domain) and their outputs (known because the codomain) wherever every input has specifically one output, and therefore the output are often derived back to its input.We have given an expression h(x)=-4/5x+6/7 .
Putting x = 1 in h(x) , we get
h(1) = 4/5(1) +6/7
= 4/5 +6/7
= 28 + 30 /35
= 58 /35
Putting x = 2 in h(x) , we get
h(2) = 4/5(2) +6/7
= 8/5 + 6/7
= 56 + 30 /35
= 86 /35
Putting x = -1/2 in h(x) , we get
h(-1/2) = 4/5(-1/2) +6/7
= -2/5 + 6/7
= -14 + 30 /35
= 26 /35
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Marques has a points card for a movie theater. • He receives 70 rewards points just for signing up. • He earns 9.5 points for each visit to the movie theater. • He needs 184 points for a free movie ticket. Write and solve an equation which can be used to determine v, the number of visits Marques must make to earn a free movie ticket. Equation:
JUST LOOKING FOR THE EQUATION!!!!
thank you!!!
Answer:
184-70
=114
114/9.5
=12
Step-by-step explanation:
1. Needed points is 184 and rewards points was 70
2. So he need extra 114 points for free movie ticket
3. 114 divide by 9.5 which is earn piont for every time he buy ticket
The equation 70 + 9.5x = 184 represents the situation and the number of visits is 12 if Marques has a points card for a movie theater.
What is a linear equation?It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.
It is given that:
Marques has a points card for a movie theater. • He receives 70 rewards points just for signing up
Let x be the number of visits.
The linear equation can be framed as follows:
70 + 9.5x = 184
9.5x = 184 - 70
After solving the above linear equation in one variable:
9.5x = 114
x = 12
Thus, the equation 70 + 9.5x = 184 represents the situation and the number of visits is 12 if Marques has a points card for a movie theater.
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