The value of given expression is F(x) = (-3 +4√-1)
What is the expression?An expression is a set of numbers or variables combined using the operations + , – , × or ÷ . Arithmetic expression that contains only numbers and mathematical operators and algebraic expression that contains variables, numbers and mathematical operators.
Given i = √-1
F(x) = ( 1 + 2i)²
F(x) = ( 1 + 4i² + 4i)
F(x) = ( 1 - 4 + 4√-1)
F(x) = ( -3 + 4√-1)
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5. an elevator in a building starts with five passengers and stops at 7 floors. if each passenger is equally likely to get off at any floor and all the passengers leave independently of each other, what is the probability that no two passengers will get off at the same floor?
The probability that no two passengers gets off at the same floor will be 0.15.
As per the question statement, an elevator in a building starts with five passengers and stops at 7 floors where each passenger is equally likely to get off at any floor and all the passengers leave independently of each other.
We are required to calculate the probability that no two passengers gets off at the same floor.
Here, since repetition is not allowed,
That is, the total number of ways for 5 passengers are to be assigned to seven floors but no two passengers on the same floor
= 7P5 = [(7!)/(7 - 2)!] = [(7!)/(2!)] = (7 * 6 * 5 * 4 * 3) = 2520
And, the total number of ways to assign 5 passengers to 7 floors, with repetition being allowed will be
= (7)⁵ = 16807.
Therefore, the probability that no two passengers gets off at the same floor will be = (2520/16807) = 0.14993 ≈ 0.15
Probability: It is that branch of Mathematics which deals with the numerical descriptions concerning the extent to which an event is likely to occur, or how likely it is for a proposition to be true, and is measured by the ratio of the favorable cases to the whole number of cases possible.
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Is the function y=x^2-x linear or not?
Answer:
NOT linear
Step-by-step explanation:
Your equation is:
y = x^2 - x
Since the y has no exponent, (which is a power of 1) and the x has an exponent of 2, this function is a parabola. It is not linear. (Linear functions have a graph that is a line)
Functions that are NOT linear have exponents greater than 1, or variables in the denominator, or, variables inside a radical.
Name a principal and interest rate where the amount of simple interest earned in 10 years would be $200. Justify your answer.
The relation between a principal and interest rate is;
⇒ P = $20 / r
Where, P is the principal amount and r is the interest rate.
What is Simple interest?
The simple interest is defined as;
Simple interest = P r t
Where, P is principal amount.
r is rate and t is time period.
Given that;
Simple interest = $200
Time period = 10 years.
Let principal amount = P
And, The interest rate = r
So, We get;
Simple interest = P r t
Substitute all the values, we get;
Simple interest = P r t
$200 = P × r × 10
Pr = $20
P = $20 / r
Thus, We get the relation between a principal and interest rate is;
⇒ P = $20 / r
Where, P is the principal amount and r is the interest rate.
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for any two real numbers a and b where b ≠0 and for all integers is this true
Given:-
[tex]64^{\frac{1}{4}},256^{\frac{1}{8}},125^{\frac{1}{3}}[/tex]To find:-
The simplified value.
So now we have,
[tex]\begin{gathered} 64=2\times2\times2\times2\times2\times2 \\ 256=2\times2\times2\times2\times2\times2\times2\times2 \\ 125=5\times5\times5 \end{gathered}[/tex]So we have,
[tex]64=2^6,256=2^8,125=5^3[/tex]So now,
[tex]\begin{gathered} 64^{\frac{1}{4}}=(2^6)^{\frac{1}{4}},256=(2^8)^{\frac{1}{8}},125=(5^3)^{\frac{1}{3}} \\ 64=4,256=2,125=5 \end{gathered}[/tex]So the value is,
[tex]4,6,5[/tex]_1) Given: L = √2
M-3√3
N =√16
P = √9
Which expression results in a rational number?
(3) N + P
(4) P+L
(1) L + M
(2) M + N
The expression that results in rational number is P+N
What is rational numbers?Any integer that can be expressed as p/q, where q ≠ 0, is referred to as rational.
The form of a rational number, which is a type of real number in mathematics, is p/q when q is not equal to 0. Examples of rational numbers include 1/2, 1/5, 3/4, and other such values. For example, any integer is a rational number. The number one can be written as 10,000/10000, -2 over -2, or 1/1.
Here, L = √2
M=3√3
N =√16
P = √9
we know [tex]\sqrt{16} =4 , \sqrt{9} =3[/tex]
only P and N are rational numbers.
P+N = 4+3 = 7/1
which is a rational number.
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Which expressions represent the volume of the cube? Select all that apply.
A cube with side length 3-fourths foot.
3343ft3
(34)3ft3
2716ft3
2764ft3
916ft2
(34)2ft2
The volume of cube with side length 3/4 of a foot is (27/64) square feet which is the fourth option.
We know that the formula for the volume of a cube is given by:-
Volume of cube = (side)*(side)*(side) = [tex]side^3[/tex]
Cube
In geometry, a cube is a three-dimensional solid object bounded by six square faces, facets or sides, with three meeting at each vertex.
The cube is the only regular hexahedron and is one of the five Platonic solids. It has 6 faces, 12 edges, and 8 vertices.
We have,
side = (3/4) foot
Hence, we can write,
Volume of cube = (3/4)*(3/4)*(3/4) = (27/64) square feet.
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help pleeeaseee i don’t understand what to do!
Answer:
The difference of a number and seven ⇒ n - 7
The product of seven and a number ⇒ 7n
The quotient of a number and seven ⇒ n/7
The sum of seven and a number ⇒ n + 7
Step-by-step explanation:
Difference ⇒ subtraction.
Product ⇒ multiplication.
Quotient ⇒ division.
Sum ⇒ addition.
how could you determine the number of feet per second a squirrel can run?
We are asked that how could we determine the number of feet per second a squirrel can run?
Recall that rate (also known as speed) is given by
[tex]r=\frac{d}{t}[/tex]Where d is the distance in feet.
t is
The northern hemisphere of planet earth has an inner core that is made up of iron and nickel. This iron nickel core is 30% of the volume of the northern hemisphere. If the diameter of the earth is 8,000 miles, what is the volume of iron-nickel core?
It turns out that the dynamo effect depends on the presence of up to 20% nickel in the Earth's core, a metal that behaves very differently from iron under extreme temperatures. Unlike the northern hemisphere mineral-rich crust and mantle, the core is made almost entirely of metal—specifically, iron and nickel. The shorthand used for the core's iron-nickel alloys is simply the elements' chemical symbols—NiFe. Elements that dissolve in iron, called siderophiles, are also found in the core.
Explain about the volume of iron nickel core?The core is almost entirely comprised of metal, notably iron and nickel, in contrast to the crust and mantle, which are rich in minerals. Iron-nickel alloys found in the core are denoted by their chemical symbols, NiFe. The core also contains siderophiles, or substances that dissolve in iron.volume calculation for the earth. Since the Earth is nearly spherical, its volume (V) may be determined using the formula V = 4/3 pi x r3, where r is its radius.The core of the earth is made up of iron, nickel, and other heavy metals like gold since they are the heaviest of all the metals and gravitated into the center of the planet.To learn more about iron nickel core refer to:
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factor (GCF) the binomial 25x^2 -15x and find one of its factors.
The most appropriate choice for factorization will be given by
[tex]\\5x(5x - 3)\\[/tex] is the required factorization.
(5x - 3) is one of the factor of [tex]25x^2 - 15x[/tex]
What is factorization?
Algebraic expression consist of number and variables connected with addition, subtraction, multiplication and division.
Factorization is the process of breaking of algebraic expression into algebraic expressions of smaller degree.
The algebraic expressions of smaller degree are called factors.
Here,
[tex]25x^2 - 15x\\5x(5x - 3)\\[/tex]
This is the required factorization.
(5x - 3) is one of the factor of [tex]25x^2 - 15x[/tex]
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Jason is testing two fertilizers, grow well and green grow, so he went to a nursery and bought 50 tomato plants of the same variety. He planted all 50 plants In an identical environment. He then administered grow well to 25 of the tomato plants and green grow to the remaining 25 tomato plants
The true statements is:
(A) The number of tomato plants treated with Green Grow that are over 18 inches tall is more than the number of tomato plants treated with Grow Well that are over 18 inches tall.
Jason is testing with two fertilizers namely, grow well and green grow.
Jason brought 50 tomato plants of the same variety and planted them in an identical environment.
Jason administered grow well to 25 and green grow to the remaining 25.
The values and recorded data from the above histograms are:
Grow Well
height numbers of plants
12 - 14 14
15 - 17 6
18 - 20 3
21 - 23 2
Green Grow
height numbers of plants
12 - 14 4
15 - 17 3
18 - 20 6
21 - 23 12
From the table,
(A) The number of tomato plants over the height of 18 inches, when treated with green grow is, GG = 6 + 12 = 18
The number of tomato plants over the height of 18 inches, when treated with grow well is, GW = 3 + 2 = 5
Therefore, GG > GW
Hence, the statement is true.
(B) As statement A is true, this statement is false.
(C) The tomato plants over 18 inches when administered with green grow, GG = 6 + 12 = 18
The tomato plants over 18 inches when administered with grow well, GW = 3 + 2 = 5.
As GG ≠ GW, the statement is false.
(D) As the number of tomato plants over 18 inches when treated with green grow is greater than when treated with grow well. Hence, the statement is false.
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The complete question is mentioned below:
Jason is testing two fertilizers, Grow Well and Green Grow, so he went to a nursery and bought 50 tomato plants of the same variety. He planted all 50 plants in an identical environment. He then administered Grow Well to 25 of the tomato plants and Green Grow to the remaining 25 tomato plants. After four weeks, Jason measured the heights of the tomato plants to the nearest inch and recorded their heights in the following histograms.
Grow Well
height numbers of plants
12 - 14 14
15 - 17 6
18 - 20 3
21 - 23 2
Green Grow
height numbers of plants
12 - 14 4
15 - 17 3
18 - 20 6
21 - 23 12
Which of the following statements is true for the data sets above?
A. The number of tomato plants treated with Green Grow over the height of 18 inches is more than the number of tomato plants treated with Grow Well over the height of 18 inches.
B. All of the statements are false for the given data sets.
C. The number of tomato plants treated with Green Grow over 18 inches equals the number of plants treated with Grow Well over 18 inches.
D. The number of tomato plants treated with Green Grow over the height of 18 inches is to the number of tomato plants treated with Grow Well over the height of 18 inches.
16. The greatest distance between the Sun and
greatest distance between the Sun and Saturn
Jupiter is about 8.166 x 10^8 kilometers. The
is about 1.515 x 10⁹ kilometers. What is the
difference of these two distances?
The difference of the distance given for Sun, Saturn and Jupiter is 6.984 x 10⁸ kilometers.
What is termed as the scientific notations?Every day, we use numbers in our lives. Scientific notation is a method of writing extremely large and extremely small numbers. Scientific notation consists of two parts: a coefficient between 1 and 10 and a power of ten. The mantissa is the difference between the whole part (left of a decimal point) and also the decimal part (right of a decimal point) of the coefficient. The exponent would be positive or negative depending on which way the decimal point is moved.For the given question;
The greatest distance between the Sun and Jupiter is about 8.166 x 10⁸ kilometers.
The greatest distance between the Sun and Saturn is about 1.515 x 10⁹ kilometers.
Write this distance in the form of 10⁸ , the point will shift towards right one decimal.
Sun and Saturn distance = 15.15 x 10⁸ kilometers.
Difference = Sun and Saturn distance - Sun and Jupiter distance
Put the values,
Difference = 15.15 x 10⁸ - 8.166 x 10⁸
Difference = 6.984 x 10⁸ kilometers.
Thus, the difference of the distances is found as 6.984 x 10⁸ kilometers.
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Standard Form & Scientific Notation• 3 examples of converting from standard form to scientific notation• 3 examples of converting from scientific notation to standard form
Required:
We need to convert from standard form to scientific notation and also scientific notation to standard form.
Explanation:
a) Convert from standard form to scientific notation:
1) Consider the number 4,520,000.
The given number can be written as follows.
[tex]4,520,000=452\times10000[/tex][tex]=452\times10^4[/tex][tex]=452\times10^4\times\frac{10^2}{10^2}[/tex][tex]=452\times\frac{10^4\times10^2}{10^2}[/tex][tex]=\frac{452}{100}\times10^6[/tex][tex]=4.52\times10^6[/tex]The scientific notation of s
[tex]4.52\times10^6[/tex]2) Consider the number
[tex]35.98\times10^3[/tex]Multiply and divide by 10.
[tex]35.98\times10^3=35.98\times10^3\times\frac{10}{10}[/tex][tex]=\frac{35.98}{10}\times10^3\times10[/tex][tex]=3.598\times10^4[/tex]The scientific notation is
[tex]3.598\times10^4[/tex]3) Consider the number.
[tex]600.89\times10^{-8}[/tex]Multiply and divide by 100.
[tex]600.89\times10^{-8}=600.89\times10^{-8}\times\frac{100}{100}[/tex][tex]=\frac{600.89}{100}\times10^{-8}\times10^2[/tex][tex]=6.0089\times10^{-6}[/tex]The scientific notation is
[tex]6.0089\times10^{-6}[/tex]b) convert from scientific notation to standard form:
1)
Consider the notation:
[tex]6.285\times10^{-5}[/tex][tex]Use\text{ }10^{-5}=\frac{1}{100000}.[/tex][tex]6.285\times10^{-5}=\frac{6.285}{100000}[/tex][tex]=0.00006285[/tex]The standard form is 0.00006285.
2) Consider the notation.
[tex]7.9\times10^4[/tex][tex]Use\text{ }10^4=10000.[/tex][tex]7.9\times10^4=7.9\times10000[/tex][tex]=79000[/tex]The standard form is 79,000.
3) Consider the notation.
[tex]9.008\times10^5[/tex][tex]Use\text{ }10^5=100000.[/tex][tex]9.008\times10^5=9.008\times100000[/tex][tex]9.008\times10^5=900800[/tex]The standard form is 900,800.
what is the justification for step 3 in the solution process?
0.8a-0.1a=a-2.5
Step 1: 0.7a=a-2.5
Step 2: -0.3a=-2.5
Step 3: a=8.3
In step 3 each side of the equation is divided by - 0.3 to obtain the value of a = 8.3.
Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation.
Consider the expression,
0.8a - 0.1a = a - 2.5
Step 1,
Subtracting similar terms,
a( 0.8 - 0.1 ) = a - 2.5
0.7a = a - 2.5
Step 2: Subtracting the term a from each side of the equation.
0.7a - a = a - 2.5 - a
- 0.3a = - 2.5
Step 3: Multiplying each side of the equation by - 1.
- 0.3a × - 1 = - 2.5 × - 1
0.3a = 2.5
Dividing each side of the equation by 0.3.
a = 2.5/0.3
a = 8.3
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simplify:
4(6+7)
O 13
O 17
O 24
O 52
Answer:
52
Step-by-step explanation:
[tex](4 \times 6) + (4 \times 7) \\ 24 + 28 = 52[/tex]
Answer:
4th answer is correct
Step-by-step explanation:
We have to solve this sum according to the BODMAS theorem.
That is:
B - Brackets
O - Of
D - Division
M - Multiplication
A - Addition
S - Subtraction
Let us solve it now.
4 ( 6 + 7 )
4 × 13
52
100 points need asap
Determine the solutions to the equation below. 5|x−2|+3=8
x=1 and x=3
x=−9 and x=13
x=−3 and x=−1
Answer: X = 1 and X = 3
Step-by-step explanation:
By filling in both the possible X values (1 and 3) you get two equations.
5|1-2| + 3 = 8
5|3-2| + 3 = 8
Both of these equations when simplified equal eight on both sides because the first one has the absolute value of -1 times 5 plus 3 which is eight. The second equation is the same besides the fact that it's the absolute value of 1, not -1 but it makes no difference.
a quarter of which is 15
how much more is 6.302 than 6.002 ?
Answer:
Step-by-step explanation:
0.3
Answer:
It is 0.3 more or 0.300 more
Step-by-step explanation:
6.002 + 0.3 or 0.300 = 6.302
6.302- 0.300 or 0.3 = 6.002
Hope I helped
What is the function g(x) that results when translating the function
f(x)=|x|
to the left 12 units and reflecting it over the x-axis?
g(x) =
The image of the function after the translation is g(x) = -|x - 12|
How to determine the equation of g(x) after the transformation?From the question, the given parameters are:
f(x) = |x|
The transformation is given as
Translate the function to the left 12 units and reflect it over the x-axis
Mathematically, this transformation can be represented as
(x, y) = (x - 12, -y)
When represented as a function, we have
g(x) = -f(x - 12)
So, we have
g(x) = -|x - 12|
So, we have the following equation
f'(x) = -|x - 12|
Hence, the equation of g(x) is g(x) = -|x - 12|
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Find the distance between the parallel lines. If necessary, round to the nearest whole number y=2x+7 y=2x-2
The distance between the two parallel lines are found as 9 units.
What is defined as the parallel lines?Parallel lines are two or more lines which lie within the same plane but never intersect. They are equal in distance and share the same slope. Many pairs of angles are formed when two parallel lines are intersected by some other line known as a transversal.For the given question;
The two equation of the lines are given as;
y = 2x + 7 ; y = 2x - 2
Complaining both equation with standard form of line in point slope form.
y - y1 = m(x - x1)
The equations are in slope intercept form, yielding two points (0,7) and (0,7). (0, -2).
Now, find the distance using the distance formula.
d = √(x₂ - x₁)² + (y₂ - y₁)²
Put the values in the equation.
d = √(0 - 0)² + (-2 - 7)²
d = √(-9)²
d = 9
Thus, the distance between the two parallel lines are found as 9 units.
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NEED ANSWER ASAP. please help
what is the value of x?
- 20
- 40
- 8
- 12
Answer:
8
Step-by-step explanation:
8x-4=60
8x=64
x=64/8
x=8
Answer:
x = 8
Step-by-step explanation:
Alternate Interior Angles Theorem
If a line intersects a set of parallel lines in the same plane at two distinct points, the alternate interior angles that are formed are congruent.
Therefore, equate the two angles and solve for x:
⇒ (8x - 4)° = 60°
⇒ 8x - 4 = 60
⇒ 8x - 4 + 4 = 60 + 4
⇒ 8x = 64
⇒ 8x ÷ 8 = 64 ÷ 8
⇒ x = 8
Estimate a 10% tip on a bill of $159.63 by first rounding the bill amount to the nearest ten dollars.
Answer: Tip Total: $ 16.00Total (Bill + Tip): $ 176.00
Which rounding to the dearest ten dollars will be 186.00
URGENT!! ILL GIVE
BRAINLIEST! AND 100 POINTS
Find the measures of the numbered angles in the figure, shown to the right. Name the theorem that justifies each answer.
Question content area bottom
Part 1
Complete the table below.
Measure
Justification
The measurement of all four angles is 105°
What is an angle?
When two solid lines or rays intersect at a single endpoint, an angle is created. The vertex about an angle is the location where two points come together.Vertex: The intersection of two lines or sides at an angle is called a vertex. In the diagram, O is the vertex.Arms: The angle's two sides are linked at a single end. The arms of just an angle are OA and OB.180° [Linear pair with angles] = m1 + 75°
The opposite angles of either a rectangle are equal: m1 = 180° - 75° = 105° m2 = m1.
[Vertically opposing angles] m2 = m1 = 105° m2 = m3 = 105°
m∠3 = m∠4 = 105° Coordinating angles
As a result, the measurement of all four angles is 105°.
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please help and show steps am failing class
answer:
D. y = 3x + 9
perpendicular means negative reciprocal of the number next to x
so if its 5x perpendicular would be -1/5x
make the equation look like y = ...
2x + 6y = 6
6y = -2x + 6
y = (-2x + 6)/6
y = -2x/6 + 6/6
y = -1/3x + 1
perpendicular line would be a negative reciprocal so
-1/3x would have a perpendicular that would be 3x
D. is the only one that has 3x
Can you please help me find the limit and identify any vertical asymptotes? Thanks
Given: The limit below
[tex]\lim_{x\to7^-}(\frac{1}{x-7})[/tex]To Determine: The limit and the vertical asymptotes
Solution
[tex]\begin{gathered} \lim_{x\to7^-}(\frac{1}{x-7}) \\ \mathrm{For}\:x\:\mathrm{approaching}\:7\:\mathrm{from\:the\:left},\:x<7\quad \Rightarrow \quad \:x-7<0 \\ The\:denominator\:is\:a\:negative\:quantity\:approaching\:0\:from\:the\:left \\ Hence \\ \operatorname{\lim}_{x\to7^-}(\frac{1}{x-7})=-\infty \end{gathered}[/tex]For the vertical asymptote
[tex]\begin{gathered} Vertical-asymptote \\ For\:rational\:functions,\:the\:vertical\:asymptotes\:are\:the\:undefined\:points \\ also\:known\:as\:the\:zeros\:of\:the\:denominator,\:of\:the\:simplified\:function. \end{gathered}[/tex]The denominator of the rational function given is
[tex]\begin{gathered} denominator:x-7 \\ x-7=0 \\ x=7 \end{gathered}[/tex]Hence:
limit = - ∞
Vertical asymptote: x = 7
What is the horizontal distance in inches covered by 12 stair steps if each is 11 in. wide?
The total horizontal distance covered by 12 stair steps is 132 inches.
What is an equation?An equation is an expression that can be used to show the relationship between numbers and variables.
Given that:
Each stair step is 11 inches wideThere are 12 stair stepsTotal horizontal distance = 12 stairs * 11 in/stair = 132 inches
Total horizontal distance is 132 inches
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Question 3(Multiple Choice Worth 5 points)(05.01)A picture is 5 inches wide and 8 inches tall: A photographer wants to use a scale factor of 2.5 to enlarge a picture. What will the area of the picture be after it is enlarged?40 in2250 in2100 in281.9 in2
Find the new dimentions of the enlarged picture multiplying the length of each side by the scale factor of 2.5:
[tex]\begin{gathered} 5in\times2.5=12.5in \\ 8in\times2.5=20in \end{gathered}[/tex]Now, multiply width times height to find the area of the picture (assuming that it has a rectangular shape):
[tex]12.5in\times20in=250in^2[/tex]Therefore, the area of the enlarged picture will be 250 squared inches.
Next questionA man uses a loan program for small businesses to obtain a loan to help expand his vending machine business. The man borrows $27,000 for 3 years with a sirinterest rate of 1.5%. Determine the amount of money the man must repay after 3 years.The man must repay
Simple interest formula (not compound interest formula) is used here, as much as i know.
the formula is:
f = p * (1 + r * n).
f is the future value
p is the present value
r is the interest rate per time period
n is the number of time periods
Given
[tex]\begin{gathered} P=27000 \\ r=1.5\%=\frac{1.5}{100}=0.015 \\ n=3years \end{gathered}[/tex]Therefore, we have
[tex]f=27000(1+0.015\times3)=\text{ \$}28215[/tex]Hence, the answer is
[tex]\begin{equation*} \text{\$}28215 \end{equation*}[/tex]which expression is equivalent to 4/5-1/2
4/10-1/10
6/5-5/7
4/7-1/7
8/10-5/10
