Answers
Range of the function will be real line.
What do you mean by the range of the function?
Variable values change. This can be represented as a set of values called the function's domain and scope.
domain:
The domain of a function is the set of numbers representing all possible values of x.
range:
A range is a set of numbers representing each potential value that y might have based on a function.
Range of the given function will be real line as for all values of x , value of y is changing and belong to real number. Therefore, range of the function will be real line.
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Related Questions
if ride cast birr 50 to pick up and 10 birr per km how much you go with birr1350
Answers
The distance the ride will go for birr 1350 is 130 kilometres.
How to find the distance the ride can go base on the amount?The ride cost birr 50 to pick up and 10 birr per km. The distance you can go with birr 1350 can be calculated as follows;
Let's use equation to represent the total amount spent on the distance covered.
Therefore,
let
x = total distance travelled in kilometresy = total amount in birrHence,
y = 50 + 10x
Therefore,
where
y = 1350
y = 50 + 10x
1350 = 50 + 10x
1350 - 50 = 10x
1300 = 10x
divide both sides by 10
x = 1300 / 10
x = 130 km
Therefore, the ride will go 130 km.
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HELP PLEASE all I need is the answer of b and c. The whole of the table is correct
Answers
b. You have a table that says 1-6 x 1-6 multiply 6x6 to get 36, that is your total number of squares. This number will also be our denominator.
Now you need to count the number of 1s (just the blue ones). You have 10 number 1s. This will be our numerator.
Let’s combine our two numbers into a fraction. Our numerator of 10 and denominator of 36 = 10/36
We need to simplify this number since it is not in its smallest possible form. A number that will factor into both 10 and 36 is 2.
After dividing both the top and bottom by 2 we get a simplified fraction of 5/18. This is our answer.
Part C.
First thing to know is that we already have the denominator of these fractions, it’s 36 all of the fractions we find will use the denominator 36.
Let’s start with 2, we have 8/36 which simplifies to 2/9
Next, 3: we have 6/36 which simplifies to 1/6
Next 4: we have 4/36 which simplifies to 1/9
Next 5: we have 2/36 which simplifies to 1/18
So it looks like the number 5 is the one that will simplify to become our answer!
What is the equation of the circle shown on the graph
Answers
The equation of the circle shown on the graph is (x + 2)² + (y - 1)² = 4.
What is an equation of a circle?
A circle can be characterized by its centre's location and its radius's length.
Let the center of the considered circle be at the (h, k) coordinate.
Let the radius of the circle be 'r' units.
Then, the equation of that circle would be:
(x - h)² + (y - k)² = r²
The center of the circle is at (-2, 1) and the radius of the circle is 2 units. Then the equation of the circle will be
(x - (-2))² + (y - 1)² = 2²
(x + 2)² + (y - 1)² = 2²
(x + 2)² + (y - 1)² = 4
Hence, the equation of the circle shown on the graph is (x + 2)² + (y - 1)² = 4.
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The members of the senior class are planning a dance. They use the equation r=p n to determine the total receipts. What is n expressed in terms of r and p ?
1) n=r+p
2) n=r-p
3) n={p}/{r}
4) n={r}/{p}
1)
2)
3)
4)
Answers
The n expressed in terms of r and p is n=r/p.
How to solve the word problems?
Systems of linear equations must be used to solve some word problems. Here are some hints to help you determine when you need to create a system of linear equations in a word problem:
There are two separate numbers at play, such as the total number of adults and children, the total number of large boxes and little boxes, etc.Each quantity has a value attached to it, such as the cost of an adult or kid ticket, the number of products in a large box as compared to a small box, etc.You must frequently create two distinct linear equations in two variables in order to solve these issues.
So, it is expressed as:
r=pn
n=r/p
Hence, The n expressed in terms of r and p is n=r/p.
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Use spherical coordinates. Evaluate
âˆB(x2+y2+z2)2dVâˆB(x2+y2+z2)2dV,
where B is the ball with center the origin and radius 1.
Answers
Cole has c oatmeal cookies. He lets 5 of his friends share them fairly. Write an expression that shows how many cookies each friend gets.
Answers
An expression that shows number of cookies each friend got is c/5.
What is an expression?An expression is a combination of terms that are combined by using mathematical operations such as subtraction, addition, multiplication, and division.
Given that, Cole has c oatmeal cookies. He lets 5 of his friends share them fairly.
Total number of cookies =c
Sharing among 5 friends
Number of cookies each friend got =Total number of cookies/5
= c/5
Therefore, an expression that shows number of cookies each friend got is c/5.
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A student has started a lawn care business. He charges $15 per hour to mow lawns and $20 per
hour for gardening. Because he is still in school, he is only allowed to work for at most 20 hours per
week. His goal is to make at least $300 per week.
1. Create a system of equations or inequalities that models the situation. Define the variable you use
PLEASE I CANT FAIL MY FINAL
Answers
Answer:
idrk i would at least need how many hours he gardens and how many hours he mows the lawn, for just mowing the lawn he would need to do that for 20 hours completely, for gardening he would need to work 15 hours.
Step-by-step explanation: yaaa
Which of the following statements are always true? A) If f(t) is increasing, then the left-hand sum gives an overestimate of the integral from a to b of f(t)dt. B) If f(t) is concave up, then the left-hand sum gives an overestimate of the integral from a to b of f(t)dt.
Answers
The statement that is true about integrals is; A) If f(t) is increasing, then the left-hand sum gives an overestimate of the integral from a to b of f(t)dt.
How to interpret Riemann sums?Left-Hand Sums and Right-Hand Riemann sums usually give us different approximations of the specific area under a curve.
Now, If one sum gives us an overestimated value and then the other gives us an underestimated value, then we can try to find out what exactly the actual area under the curve might possibly be. It should be noted that left-hand sum will be an under-estimate of the specific area of R. Thus, as f is increasing, a left-hand sum will definitely use the smallest value of f on each sub-interval. This therefore tells us that any left-hand sum will not cover all of R and also any right-hand sum will be an over-estimated value of the area of R.
Thus, Since f is increasing, a right-hand sum will utilize the largest value of f on each specific sub-interval. Thus, right-hand sum will definitely cover R and others.
From the above, option A is true because if the graph is increasing then the left-hand sum gives an overestimated value of the actual value.
Meanwhile, option B is false because if the graph is concave upwards, then the trapezoid approximation is an overestimated value, and as such the midpoint will be underestimated.
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assume that we have a single-cycle implementation of a processor, which has a clock cycle of 14 ns. suppose that we split this single-cycle processor to a 5-stage pipelined processor where the times for each of t
Answers
The approximate speed-up ratio between pipelined and non-pipelined system to execute 100 instructions is 4.03
The term ratio in math defines as an ordered pair of numbers a and b, written a / b where b does not equal 0.
Here we have given that
And we need to determine the approximate speed-up ratio between pipelined and non-pipelined system to execute 100 instructions.
While we looking into the given question we have identified the following values,
=> Number of pipeline segments = stages in pipeline,
=> n = 5
Here we know that,
=> Clock cycle time per operation = clock cycle per stage = 14 ns
And the number of instructions = 100
Here the formula to calculate the startup is written as,
=> T[without pipeline] = no. of instructions × stages in pipeline × clock cycle per stage
=> 100 × 5 × 14
=> T[with pipeline] = (time for pipelined execution without stalls) + (overhead due to stalls)
=> (5 + 99) × 20 + 20 × 20 = 124 × 20
Therefore, the startup is
=> [500 x 14] / [124 x 14]
=> 4.03
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If a 5 1/4 inch line on a map represents a 9 mile road, how many miles would be represented by a 3 1/2 line
Answers
A (3 + 1/2) inches line represents a real distance of 5.985 miles.
How many miles would be repesented by a (3 + 1/2) inch line?First, we know that a (5 + 1/4) inch line on a map represents a 9 mile road, then the conversion from miles to inches is given by the quotient between these two, we will get:
9mi/(5 + 1/4) in = 9mi/(5.25) in = 1.71 mi/in
So, any distance in inches can be multiplied by the above number to get the corresponding measure in miles.
Then for (3 + 1/2) inches we will get:
(3 + 1/2) in*1.71 mi/in = 5.985 mi
So a line of (3 + 1/2) inches has represents a distance of 5.985 miles.
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10. use the division algorithm to divide 116 by 3, and then, based on your work, determine which of the following statements is true. (a) q
Answers
By using the division algorithm to divide 116 by 3 will be 38.
The given integers a and b are 116 and 3 respectively.
Let q be the counter variable and r be the variable to store the new dividend after each loop.
Division algorithm,
If a<b
return 0;
else
q = 0;
r = a;
repeat
q = q+1;
r = r-b;
until r<b;
return q, r;
Working:
116 is not less than 3, implies
r = 116 -3 = 113
q = 0+1=1
Repeating until we get q = 38, r = 2 = a
2<3, hence returns q = 38, r =2
The question is incomplete, the complete question is:
use the division algorithm to divide 116 by 3, and then, based on your work, determine which of the following statements is true.
(a) q = 39 (b) q =32 (c) q = 38
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Write the sentence as an equation.
126 is equal to 26 fewer than the product of 41 and w
NEED ANSWER ASAP
Answers
I believe that would be the answer!!
To cater a holiday banquet, Food Service LLC agrees to buy one hundred pumpkin pies from Great Desserts Inc. To be enforceable, the agreement must be in writing if the pies cost at least
$500
Answers
In order to cater a holiday banquet, food service LLC agrees to buy one hundred pumpkin pies from great desserts inc. to be enforceable, the agreement must be in writing if the pies cost at least $500.
What is an Agreement?
This refers to the legally binding contract that exists between two or more entities where the terms of the contract have been drawn up and the terms have been agreed upon by all parties involved, subject to certain conditions before it can be enforceable.
Hence, we can see that in order to cater a holiday banquet, food service LLC agrees to buy one hundred pumpkin pies and because they are a limited liability company, there needs to be a minimum threshold and this can be done, if the cost of the pies is at least $500.
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TRUE OR FALSE cedric needs to find the surface area of the triangular prism. there is a piece of information missing you need to find it before you can solve the problem.
Answers
It is true, we have to find the surface area of the triangular prism we have to find a piece of information that is missing.
In the given question we have to find the surface area of the triangular prism.
We have to follow the some step to find the surface area of the triangular prism.
Step 1: Calculate the values of b(1), b(2), and b(3), the triangle base's three sides. Additionally, calculate the values of h, the triangle base's height, and l, the prism's length (the length between the bases).
Step 2: Use the formula for calculating the area of a triangle (A=1/2bh), where b is one of b(1), b(2), or b(3), to determine the area of a triangular base (whichever one is perpendicular to h). Given that this region contains two triangle bases, multiply the result by two.
Step 3: Multiply the perimeter of a base triangle by the prism's length to find the area of its rectangular sides: A=(b(1)+b(2)+b(3))l.
Step 4: Combine the outcomes from steps 3 and 4. This is the surface area of the triangular prism.
Since the question is not clear so I have write the step to find the area of triangular prism. Using this method we can find the area of triangular prism.
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Isosceles trapezoid ABCD is shown.
A
B
D
C
Which three statements are correct?
ZBAC ZCAD
ZACD ZACB
ZADC ZBCD
AD
AB
AC
BC
CD.
BD
ہے
Answers
From the given Isosceles trapezoid ABCD, the three correct statements are:
∠ADC ≅ ∠BCD
AD ≅ BC
AC ≅ BD
What is Isosceles trapezoid?An isosceles trapezoid is a trapezoid with equal base angles and hence equal left and right side lengths.
Particularly in isosceles trapezoids, there are unique correlations. "Equal legs" is what the term "isosceles" denotes. Non-parallel sides on isosceles trapezoids have the same lengths. The "legs" are another name for these equal sides.
A triangle with two equal sides is said to be isosceles. Also equal are the two angles that face the two equal sides. A triangle with two congruent sides is referred to as being isosceles, in other words.
Thus, three correct statements are -
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Given the following exponential function, identify whether the change represents growth or decay, and determine the percentage rate of increase or decrease.
y=420(1.04)^x
Answers
4% is the percentage rate of increase or decrease in exponential function.
What exactly makes a function exponential?
A mathematical function using the following formula is an exponential function: f (x) = an x. where an is a constant known as the function's base and x is a variable.
The transcendental number e, or roughly 2.71828, is the most often encountered exponential-function base.
We have,
y = 420( 1.04)ˣ
The equation represents exponential growth because the growth factor is greater than 1.
The general form equation is
y(x)= a(1-r)^x such that r is the growth percent.
1 + r = 1.04
r = 0.04 ⇒ 4%
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I need help with my math homework
Answers
Answer:
Read explanation :)
Step-by-step explanation:
Activity 1: When it says direction it refers to the tiles going horizontal and vertical for example the 4 and 9 going vetical to make vertical you must first add 4 + 9 which equals 13 then add a 2 under the 9 so it equals 15. And for 8 and 4 horizontal you must add 8 + 4 which equals 12 so add a three in between the 8 and 4 and for the 7 there is a two on the right of it so add 7 + 2 to equal 9 then add 6 to equal 15 then add a 1 in between the 8 and the 6 to equal 15 and add the 5 in the middle.
Activity 2: On the addition table on the left side of the table the number is the number you add to the number on top for example: the 2 at the top of the table plus the 6 on the same vertical line going down so it would be 2 + 6 which equals 8 as it tells you the answer and for 7 on the left side of the table and 3 at the top of the table with the vertical line would be 7 + 3 which equals 10.
Your Welcome Hope This Helps You.
PLEASE ANSWERE ASAP
If BC = 16.7 ft, what is AY?
Answers
Answer:
Since YA=AX, XB=BZ, ZC=CY, it follows that A, B and C are the midpoints of the sides TX, XZ, ZY. AB, BC, AC are parallel to the sides and equal to their half. In fact, AB = YC=ZC. Therefore BC=AY.)
Good luck;)
Step-by-step explanation:
Annette's Floral Shop has a charge account with Southern Flowers, a wholesaler where she
buys her floral supplies. This month, Annette has purchased 16 dozen roses at $30.96 per
dozen, 40 dozen chrysanthemums at $17.80 per dozen, and 20 dozen tulips at $21.10 per
dozen. In her state, Annette must pay a 6% sales tax on all orders. At the end of the month,
what is the balance on Annette's charge account?
Answers
Total balance in Annette's charge account is $1727.12 with 6% of tax on all order.
What is Percentage ?The Latin phrase "per centum," which meaning "by the hundred," was the source of the English word "percentage." Fractions having a denominator of 100 are called percentages. In other words, it is a relationship where the value of the entire is always assumed to be 100.
Finding the percentage of a whole in terms of 100 is what percentage calculation refers to. A percentage can be found in one of two ways:
use the unitary approach.by adjusting the fraction's denominator to 100.It should be noted that when the denominator is not a factor of 100, the second technique of percentage calculation is not applied. In these situations, we employ the unitary technique.
1 dozen of Rose costs = $30.96
1 dozen of chrysanthemums costs = $17.80
1 dozen of of tulips costs = $ 21.10
Total Spending = 16 dozens of roses + 40 dozen of chrysanthemums + 20 dozens of tulips
= 16 * 30.96 + 40 * 17.80 + 20 *21.10
= $1629.36
There is a 6% sales tax on all order = 6% of 1629.36 = $ 97.76
Total balance in Annette's charge account is $ 97.76 + 1629.36 = $1727.12.
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Total balance in Annette's charge account is $1727.12 with 6% of tax on all order.
What is Percentage ?
The Latin phrase "per centum," which meaning "by the hundred," was the source of the English word "percentage." Fractions having a denominator of 100 are called percentages. In other words, it is a relationship where the value of the entire is always assumed to be 100.
Finding the percentage of a whole in terms of 100 is what percentage calculation refers to. A percentage can be found in one of two ways:
Use the unitary approach.
by adjusting the fraction's denominator to 100.
It should be noted that when the denominator is not a factor of 100, the second technique of percentage calculation is not applied. In these situations, we employ the unitary technique.
1 dozen of Rose costs = $30.96
1 dozen of chrysanthemums costs = $17.80
1 dozen of of tulips costs = $ 21.10
Total Spending = 16 dozens of roses + 40 dozen of chrysanthemums + 20 dozens of tulips
= 16 * 30.96 + 40 * 17.80 + 20 *21.10
= $1629.36
There is a 6% sales tax on all order = 6% of 1629.36 = $ 97.76
Total balance in Annette's charge account is $ 97.76 + 1629.36 = $1727.12.
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A recent survey, 35 percent indicated chocolate was their favorite flavor of ice cream. Suppose we select a sample of ten people and ask them to name their favorite flavor of ice cream. a. How many of those in the sample would you expect to name chocolate? b. What is the probability exactly four of those in the sample name chocolate? c. What is the probability four or more name chocolate?
Answers
a. You would expect 3.5 of those in the sample to name chocolate.
b. The probability exactly four of those in the sample name chocolate is 0.2438.
c. The probability four or more name chocolate is 0.5829..
a. If 35% of people in the general population indicate that chocolate is their favorite flavor of ice cream, then we would expect 35% × 10 = 3.5 people in a sample of 10 to name chocolate as their favorite flavor. Since we cannot have a fractional number of people, we can round this down to 3 people.
b. The probability that exactly 4 people in a sample of 10 name chocolate as their favorite flavor can be calculated using the binomial distribution. The probability of each individual event (i.e., a person naming chocolate as their favorite flavor) is 0.35, and there are 10 total events. The probability of exactly 4 successes (people naming chocolate as their favorite flavor) is given by the formula:
(10 choose 4) × ([tex]0.35^4[/tex]) × ([tex]0.65^6[/tex])
Where "choose" denotes the binomial coefficient, and the exponent indicates the number of times each event occurs. Plugging in the values, we get:
(210) × (0.0036125) × (0.274625) = 0.2438
So the probability that exactly 4 people in the sample name chocolate as their favorite flavor is approximately 0.2438.
c. To calculate the probability that 4 or more people in the sample name chocolate as their favorite flavor, we can use the same formula as above, but sum the probabilities for each possible number of successes greater than or equal to 4. For example, the probability of 4 successes is given by:
(10 choose 4) × ([tex]0.35^4[/tex]) × ([tex]0.65^6[/tex])
The probability of 5 successes is given by:
(10 choose 5) × ([tex]0.35^5[/tex]) × ([tex]0.65^5[/tex])
And so on. Summing the probabilities for each possible number of successes greater than or equal to 4, we get:
0.2438 + 0.1933 + 0.1047 + 0.0380 + 0.0081 = 0.5829
So the probability that 4 or more people in the sample name chocolate as their favorite flavor is approximately 0.5829.
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PLEASE HELP MEE!!
What is the inverse of the function shown?
Answers
The inverse of the function shown is (x + 5).
What is the inverse of the function?
A function that can reverse into another function is known as an inverse function or anti-function. In other words, the inverse of a function "f" will take y to x if any function "f" takes x to y. When a function is written as "f" or "F," its inverse is written as "[tex]f^{-1}[/tex]" or "[tex]F^{-1}[/tex]." Here, (-1) should not be confused with an exponent or a reciprocal.
Coordinates of the given line are (8,3) and (-2,-7)
The function of the given graph for two points form is
[tex]y-y_{1} = \frac{y_{2}-y_{1} }{x_{2} -x_{1}} (x-x_{1} )[/tex]
or, [tex]y-3 = \frac{-7-3 }{-2-8} (x-8 )[/tex]
or, y - 3 = x - 8
or, y = x -8 + 3 = x - 5
y = x - 5
To find the inverse, replace x with y and y with x then, we get
x = y - 5
y = x + 5
[tex]f^{-1}[/tex] = x + 5
Hence, the inverse of the function shown is (x + 5).
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Suppose the heights of 18-year-old men are approximately normally distributed, with mean 69 inches and standard deviation 6 inches. If a random sample of fifteen 18-year-old men is selected, what is the probability that the mean height x is between 68 and 70 inches? (Round your answer to four decimal places.)
Answers
The probability that the mean height x is between 68 and 70 inches is found as 37.28%.
What is meant by the term z score?The z-score effectively represents the standardized distance in units of "number standard deviations" between the raw score (procured from a population assuming a normal distribution) as well as the population mean.The z-score is written as follows:
z = (x - μ)/σ
In which,
x = between 68 and 70 inches.
μ = mean 69 inches
σ = standard deviation 6 inches
Put the values in the formula,
Probability that the mean height x is between 68 and 70 inches
P(68 < x < 70) = (68 - 69 / 6) < z < (70 - 69 / 6)
P(68 < x < 70) = (-0.16) < z < (0.16)
P(68 < x < 70) = 0.4364 - 0.0636
P(68 < x < 70) = 0.3728
P(68 < x < 70) = 37.28%
Thus, the probability that the mean height x is between 68 and 70 inches is found as 37.28%.
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How do you form the complex conjugate of a complex number a+bi?
Answers
For example, the complex conjugate of 3+2i is 3-2i, and the complex conjugate of -1+4i is -1-4i.
To find the complex conjugate of a complex number, we can simply change the sign of the imaginary part of the number. This operation is useful in many mathematical operations involving complex numbers, such as taking the absolute value, finding the square root, and performing operations such as multiplication and division. It is also commonly used in solving equations involving complex numbers.
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Step-by-step explanation:
How do you form the complex conjugate of a complex nuciu
please helppp.
Find the function that is finally graphed after the following transformations are applied to the graph of y=√x in the order listed.
(1) Vertical stretch by a factor of
(2) Shift up 1 unit
(3) Shift left 5 units
Y= ????
Answers
The final function after the transformations are applied to the graph of y =√x is y = 2√(x - 5) +1.
What is transformation?
A point, line, or geometric figure can be transformed in one of four ways, each of which affects the shape and/or location of the object. Pre-Image refers to the object's initial shape, and Image, after transformation, refers to the object's ultimate shape and location.
Rule of transformation:
g(x) = c f(x+a) + b
If c > 1, then f(x) vertically starched by c factor. If 0< c < 1, then f(x) vertically compressed by c factor.
If a>0, then f(x) is shifted horizontally a unit right side. If a<0, then f(x) is shifted horizontally a unit left side.
If b>0, then f(x) is shifted vertically b unit upward. If a<0, then f(x) is shifted vertically b unit downward.
Putting c = 2, a = -5, b = 1, and f(x) = √x
y = 2√(x - 5) +1
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Express in a single log term
Answers
The simplified form of the given logarithmic expression as required in the task content bis Choice B; 2log8.
What is the simplified form of the expression as a single log term?It follows from the task content that the simplified form of the logarithmic expression is to be determined as a single log term.
On this note, since the given expression is;
2log2 + 2log4
It follows from factorisation that we have;
2 ( log 2 + log 4 )
Therefore, the expression in the parentheses can be simplified as a single log term using the sum of logarithms law as follows;
= 2 ( log ( 2 × 4 ) )
= 2 log 8.
Ultimately, the answer choice which represents the simplified form of the expression as a single log term is; Choice B; 2 log 8.
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Samuel went to the grocery store and purchased cans of soup and frozen dinners.
Each can of soup has 300 mg of sodium and each frozen dinner has
450 mg
of
sodium. Samuel purchased 5 more frozen dinners than cans of soup and they all
collectively contain 6000 mg of sodium. Write a system of equations that could be
used to determine the number of cans of soup purchased and the number of frozen
dinners purchased. Define the variables that you use to write the system.
Answers
A system of equations that could be used to determine the number of cans of soup purchased and the number of frozen dinners purchased is; 300a + 450b = 6000 and a + 5 = b.
The variables x and y respectively represents cans of soup and frozen dinners and a and b represents number of cans of soup and frozen dinners.
Let cans of soup be denoted by x
Let each frozen dinner be denoted by y
Now, we are told that each can of soup has 300 mg of sodium and each frozen dinner has 450 mg. Thus;
x = 300
y = 450
It is said that Samuel purchased 5 more frozen dinners than cans of soup and they all collectively contain 6000 mg of sodium.
Let the no. of cans of soup be 'a' and no. of frozen dinner be 'b'. Thus, we will have the equation as;
ax + by = 6000
a(300) + b(450) = 6000
300a + 450b = 6000 ------(1)
We are told that Samuel purchased 5 more frozen dinners than cans of soup. This can be represented by the equation;
a + 5 = b ------(2)
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what is the square root of -75 in simplified form
Answers
Answer:
5[tex]\sqrt{3}[/tex]i
Step-by-step explanation:
[tex]\sqrt{-5(5)(3)}[/tex] You can pull out a 5 and you are left with [tex]\sqrt{-1}[/tex] and [tex]\sqrt{3}[/tex].
The [tex]\sqrt{-1}[/tex] = 1
5[tex]\sqrt{3}[/tex] i
Answer: [tex]5\sqrt{3} i[/tex]
Step-by-step explanation:
The square root of -75 is not a real number, because it is not possible to find a real number that when squared results in a negative number.
In mathematics, the square root of a number is defined as the number that, when multiplied by itself, equals the original number. For example, the square root of 4 is 2, because 2 x 2 = 4. Similarly, the square root of 9 is 3, because 3 x 3 = 9.
However, it is not possible to find a real number that, when squared, results in a negative number. This is because any real number multiplied by itself is always positive, regardless of whether the original number was positive or negative. For example, the square of -2 is 4, because (-2) × (-2) = 4, which is a positive number.
Double however, complex numbers are used to represent numbers that have a non-zero imaginary component, such as the square root of -1. Complex numbers are written in the form a + bi, where a and b are real numbers and i represents the imaginary unit.
Therefore, the square root of -75 can be written in simplified form as [tex]5\sqrt{3} i[/tex], where [tex]i[/tex] is the imaginary unit. This represents a complex number with a real component of 0 and an imaginary component of [tex]5\sqrt{3}[/tex].
The population of Kingsfield grew from 7,500 to 9,000
in one year. During the same time the population of
Queensville dropped from 32,000 to 25,600. Let the
original populations represent year 1. If these percentage
rates of decline and growth continue, during what year will
Kingsfield have a larger population than Queensville?
Answers
The time that it will take for Kingsfield to have a larger population than Queensville is given as follows:
3.58 years.
How to model the populations?The rates of decline and growth are constant, meaning that the populations for each town are modeled by exponential functions.
The rates for each town are given as follows:
Kingsfield: 9000/7500 = 1.2.Queensville: 25600/32000 = 0.8.Considering the initial population, the exponential functions for the population of each town after t years are given as follows:
Kingsfield: y = 7500(1.2)^t.Queensville: y = 32000(0.8)^t.Kingsfield will have a larger population than Queensville when:
[tex]7500(1.2)^t > 32000(0.8)^t[/tex]
Hence:
[tex]\left(\frac{1.2}{0.8}\right)^t > \frac{32000}{7500}[/tex]
(1.5)^t > 4.27
tlog(1.5) > log(4.27)
t > log(4.27)/log(1.5)
t > 3.58 years.
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t=10-x identify to dependent and independent variable
Answers
Answer: t is the dependent variable and x the independent variable
Step-by-step explanation: t is the dependent variable it depends upon the values of x that we put in.
x is the independent variable as we can use whatever values we want for x it is not affected by t
Billy is saving for a new DVD that costs $64. He already has $16. What % of the total cost has he
already saved?
Answers
Billy has already saved 25% of the total cost.
What is percentage?
A percentage in mathematics is a number or ratio that may be stated as a fraction of 100.In determining a percentage of a number, we should first divide it by 100 before multiply the outcome by 100. As a result, the proportion refers to a part per 100. The word "percent" refers to a fraction of one hundred. The letter "%" stands for it.
Given that, the cost of the DVD is $64.
He saved $16 for the DVD.
The percent of saving
= Saving amount/ cost of DVD × 100%
= (16/64) × 100%
= 0.25 × 100%
= 25%.
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