A call center required the number of agents is equal to 18.
One of the most frequent themes in quantitative aptitude that is tested in government exams is time and work. One of the subjects that candidates are knowledgeable about even before they begin preparing for competitive exams.
The idea of time and effort is still the same, but there may be some variation in the questions that are posed. The majority of the questions on this topic are 1-2 word problems, but candidates should also be ready for questions about data sufficiency and data interpretation that may come up over the course of their work.
A 24/7 calling center works as follows: every agent works 5 days in a row and has two days rest, e.g., every week works Tuesday Saturday and rests on Sunday and Monday.
total working day of call center = 7
agent's working day =5
so, required the minimal number of agents-
[tex]=\frac{7!}{2!.5!}\\\\=\frac{35}{2}\\\\= 17.5 = 18[/tex]
So, at least required number of agents = 18.
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show that the improper integral g(x0dx is divergent but the average value of g on the interval 4,infinoty is finite
To show that the improper integral g(x)dx is divergent, but the average value of g on the interval 4, infinity is finite, we can consider a function g(x) = 1/x, which is mostly used as an example for a divergent integral.
The improper integral of g(x) from 4 to infinity is given by:
[tex]\int\limits {g(x)} \, dx = \int\limits {(1/x)} \, dx[/tex] from 4 to infinity
= lim (upper limit -> infinity) [ln|x|] from 4 to x
= [ln|x|] from 4 to infinity
= ln(infinity) - ln(4) = infinity - ln(4) = infinity
As the limit of the integral is infinity, the integral is divergent.
However, the average value of g on the interval [4, ∞) is given by:
average value = (1/∞ - 4) * ∫(1/x)dx from 4 to infinity
= (1/∞ - 4) * (infinity - ln(4))
= -4 + ln(4)
= ln(4) - 4
which is a finite value when the integral is divergent
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Quadrilateral DEFG is similar to quadrilateral HIJK. Find the measure of side JK.
Round your answer to the nearest tenth if necessary.
Quadrilateral DEFG is similar to quadrilateral HIJK The measure of side JK is 8.
Since quadrilateral DEFG is similar to quadrilateral HIJK, we know that the ratio of corresponding side lengths is equal. This means that if we know the length of one side of one of the quadrilaterals, we can use that ratio to find the length of the corresponding side in the other quadrilateral.
For example, if we know that side DE is 8 units long, we can use the ratio of side JK to side DE (x/8) to find the length of side JK. We can also use the same ratio of side IJ to side DF which is x/4.
Let's assume that the length of side DE is 8 units. We can use the ratio of side JK to side DE (x/8) to find the length of side JK.
[tex]x/8 = x/4[/tex]
Cross-multiplying and simplifying the equation we get
[tex]4x = 8x[/tex]
[tex]x = 8[/tex]
Therefore, the measure of side JK is 8 units.
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for each of the following sets of functions either find a function f(x) in their span such that f(x) > 0 for all x
f(x) = 7x - 1, which is a linear equation with a positive leading coefficient, making f(x) > 0 for all x.
Set 1: {f(x) = x + 1, f(x) = x - 1}
Function f(x) = x^2 + 2 can be found in the span of the two given functions. This can be seen by expanding the equation:
f(x) = x^2 + 2 = (x + 1) + (x - 1) = 2x;
thus, f(x) = 2x + 2, which is a quadratic equation with a positive leading coefficient, making f(x) > 0 for all x.
Set 2: {f(x) = 4x - 2, f(x) = 3x + 1}
Function f(x) = 7x - 1 can be found in the span of the two given functions. This can be seen by expanding the equation:
f(x) = 7x - 1 = (4x - 2) + (3x + 1) = 7x;
thus, f(x) = 7x - 1, which is a linear equation with a positive leading coefficient, making f(x) > 0 for all x.
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Complete question:Find a function f(x) in the span of the functions f1(x) = x and f2(x) = -x such that f(x) > 0 for all x.
Sam has 3 1/4 pounds of blueberries. Ben also has some blueberries. Together, they have 9 2/3 pounds of blueberries. Create an equation to represent the number of pounds of blueberries, b, Ben has.
The required blueberries Ben has 6 5/12 pounds.
What are equation models?The equation model is defined as the model of the given situation in the form of an equation using variables and constants.
Here,
Let the amount of blueberries Ben has to be x,
According to the question,
Together, they have 9 2/3 pounds of blueberries.
x + 3 1/4 = 9 2/3
x = 9 2/3 - 3 1/4
x = 9 + 2/3 - 3 -1/4
x = 6 + 5/12
x = 6 5/12 pounds
Thus, the required blueberries Ben has 6 5/12 pounds.
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what is the hypothesis of the following conditional statement?
If we walk home from school, it takes 30 minutes.
a. we walk home from school
b. it takes 30 minutes
c. we do not walk home from school
d. we walk
The hypothesis of the conditional statement is;
Option A: we walk home from school
How to identify the hypothesis?A hypothesis is defined as an educated guess while using reasonable thought patterns, about the answer to a scientific question. Now, the hypothesis can either be supported or not supported at all, but then it depends on the data gathered.
A conditional statement is defined as a set of rules performed provided a certain condition is met. Thus, it is sometimes referred to as If-Then statement because if a condition is said to be met, then an action is said to have been performed " .
Thus, the conditional statement here is: " we walk home from school ".
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Check image for questions!
(Answers are already there, just gotta figure out where they go)
50 points!
The equation y is 2x - 3 describes the line with a slope of 2 and a Y-intercept of -3.
Linear equation?Use m is used to show the slope of a line.
m = 2
c is used to signify the line's y-intercept. c = -3
For the line's equation, the slope-intercept is: y = mx + c
In the equation above, replace c = -3 with m = 2 ,y = 2x - 3
Consequently, the equation of the line with a Y-intercept of -3 and a slope of 2 is as follows: y = 2x - 3.
For the line's equation, the slope-intercept is: y = mx + c
In the equation above, replace c = -3 with m = 2 ,y = 2x - 3
Consequently, the equation of the line with a Y-intercept of -3 and a slope of 2 is as follows: y = 2x - 3.
The complete question is,
The line with a -3 Y-intercept and a 2 slope has what equation?
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if the relation represents a function, find the domain and range. (enter your answers using interval notation. if the relation is not a function, enter none in the domain and range answer blanks.)
If the relation is represented by the equation y = 2x + 1, the domain would be all real numbers (-infinity, +infinity) and the range would be all real numbers greater than or equal to 1 (1, +infinity).
A relation is a function if for every input (x) there is exactly one output (y). To determine if a relation is a function, we can use the vertical line test, which states that if a vertical line can be drawn through the graph and intersects the relation more than once, then the relation is not a function.
If the relation is a function, we can find the domain and range by analyzing the relation. The domain is the set of all x-values and the range is the set of all y-values. In interval notation, the domain is written as (a, b) and the range is written as (c, d).
So, the domain and range answers depend on the relation which is given and it should be specified.
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What is 2.4 divided by -0.06?
(With work pls)
Answer:
To find the result of 2.4 divided by -0.06, we need to use the following steps:
Step 1: Change the division problem into a multiplication problem by flipping the divisor and multiplying by its reciprocal.
-0.06 ÷ 2.4 = -0.06 x 1/(2.4)
Step 2: To find the reciprocal of 2.4, we need to divide 1 by 2.4
1/(2.4) = 0.416666666666667
Step 3: Multiply the original dividend (2.4) by the reciprocal of the divisor (0.416666666666667)
2.4 x 0.416666666666667 = -0.1
So, 2.4 divided by -0.06 is equal to -0.1
It's worth noting that -0.1 is a negative number which makes sense since the divisor is negative, hence the result is the opposite of the result when dividing by a positive number.
I need assistance for this problem below:
The image of quadratic function f(x) = x² is equal to g(x) = 6 · x².
How to derive and graph the image of a quadratic equation
In this question we see the representation of quadratic equation f(x) = x², from which we need to generate the image of this function, this can be done by a rigid transformation known as vertical dilation:
g(x) = k · f(x), k > 1
Where:
f(x) - Original functiong(x) - Resulting functionIf we know that f(x) = x² and k = 6, then the image of function is:
g(x) = 6 · x²
Whose representation on Cartesian plane is shown in the image attached below.
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A new apartment building has 33 floors, with 24 apartments on each floor. How many apartments are in the building?
(Partial product)
Red :
Blue :
Green :
Yellow :
Total Product:
Simple equation when u break it down: 33 x 24=792 apartments
How many apartments are in the building?A building, or edifice, is an enclosed structure with a roof and walls that is standing in one location more or less permanently, such as a house or factory (although there are also portable buildings). Buildings come in a variety of sizes, shapes, and uses, and they have been modified throughout history for a wide range of reasons, including the availability of building materials, weather, land prices, ground conditions, particular uses, prestige, and aesthetic considerations.
given:
new apartments' building =33 floor
apartments on each =24 floor
33*24=792
792 apartments are in the building
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PLEASE HELP
A recipe for soup calls for 4 tablespoons of lemon juice and 1/2 cup of olive oil. The given recipe serves 4 people, but a cook wants to make a larger batch that serves 120 .
a) How many cups of lemon juice will the chef need for the larger batch?
b) How many pints of olive oil will the chef need for the larger batch?
120 table spoons of lemon juice.
15 cups of olive oil.
NO LINKS!!!
55, Write an equation satisfying the given conditions.
Part (a)
The two limit statements tell us that this an exponential decay function.
The curve goes up forever when heading to the left (negative infinity) as indicated by the notation [tex]\displaystyle \lim_{\text{x}\to-\infty}f(x) = \infty[/tex]
At the same time, the curve slowly approaches the horizontal asymptote y = -2, when moving to the right, because of this notation [tex]\displaystyle \lim_{\text{x}\to\infty}f(x) = -2[/tex]
An exponential decay function like [tex]\text{y} = (0.5)^{\text{x}}[/tex] has a horizontal asymptote of y = 0, aka the x axis. The y value approaches 0 but never gets there. Each output is positive.
Shift everything down 2 units to arrive at [tex]\text{y} = (0.5)^{\text{x}}-2[/tex] and this will move the horizontal asymptote down the same amount.
There's nothing really special about the 0.5; you can replace it with any value in the interval 0 < b < 1.
---------
Answer: [tex]\text{f(x)} = (0.5)^{\text{x}}-2[/tex]====================================================
Part (b)
I'll use this template
[tex]\text{y} = ab^{\text{x}}+c[/tex]
Plugging in x = 0 leads to y = a+c which is the y intercept. Set this equal to the stated y intercept 7 and we get a+c = 7.
We want the [tex]ab^{\text{x}}[/tex] portion to approach zero, which leads to c = 4 so we approach the stated horizontal asymptote.
So,
a+c = 7
a+4 = 7
a = 7-4
a = 3
We go from this
[tex]\text{y} = ab^{\text{x}}+c[/tex]
to this
[tex]\text{y} = 3b^{\text{x}}+4[/tex]
The value of b doesn't matter.
I'll go for b = 0.7 so we get to [tex]\text{f(x)} = 3(0.7)^{\text{x}}+4[/tex]
---------
Answer: [tex]\text{g(x)} = 3(0.7)^{\text{x}}+4[/tex]====================================================
Part (c)
The parent function [tex]\text{y} = \log(\text{x}})[/tex] has a domain of [tex](0, \infty)[/tex]. In other words it is the interval [tex]0 < \text{x} < \infty[/tex]
If we replaced each input x with x-5, then we shift the xy axis 5 units to the left. It gives the illusion the log curve moves 5 units to the right.
The vertical asymptote also moves 5 units to the right. We go from a domain of [tex](0, \infty)[/tex] to a domain of [tex](5, \infty)[/tex]
The base of the log doesn't matter.
---------
Answer: [tex]\text{h(x)} = \log(\text{x}-5)[/tex]Check out the graphs below. I used GeoGebra, but Desmos is another good option.
How many full 2 3/4-in. sheets can be cut from 26 1/8-in. stock?
The required number of sheets cut from the stock are 9.
What is mixed fraction?A mixed fraction is one that is represented by both its quotient and remainder. For example, 2 1/3 is a mixed fraction, where 2 is the quotient, 1 is the remainder. An amalgam of a whole number and a legal fraction is a mixed fraction.
According to question:
We have,
We need sheets of length = 2 (3/4) in from 26 (1/8) in stock.
So, 2 (3/4) = 11/4 in
26 (1/8) = 209/8
Then,
Number of sheets = 209/8 / 11/4
Number of sheets = 836/88
Number of sheets = 9.5
So, 9 sheets can be cut.
Thus, required number of sheets are 9.
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In the equation 10+4y=-4y+2,the variable y represents the same value. Is y = 1, 0, -1, or -2 the solution of this equation explain
The solution to the equation 10+4y=-4y+2 is -1 because the variable y represents the same value.
What is equation?An equation is a formula in mathematics that expresses the equality of two expressions by connecting them with the equals sign =. In its most basic form, an equation is a mathematical statement that shows that two mathematical expressions are equal. 3x + 5 = 14, for example, is an equation in which 3x + 5 and 14 are two expressions separated by a 'equal' sign. A mathematical equation that depicts the relationship between two expressions on opposite sides of the sign. It mostly consists of one variable and one equal to symbol. 2x - 4 = 2 is an example.
Here,
10+4y=-4y+2
8y=-8
y=-1
The solution of equation 10+4y=-4y+2 is -1 as the variable y represents the same value.
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shola collects N2x salary every month. when he takes away his expenditure of N5000, the salary is less than or equal to N2500. How much does Shila collects every months?
Answer:
less than or equal to N7500
Step-by-step explanation:
N2x - N5000 = N2500
N2x = N7500
Which inequality is true when x= 4?
For the value of x = 4, the inequality equation that is true is option C: x/2 < 3.
What is an inequality?
In Algebra, an inequality is a mathematical statement that uses the inequality symbol to illustrate the relationship between two expressions. An inequality symbol has non-equal expressions on both sides. It indicates that the phrase on the left should be bigger or smaller than the expression on the right, or vice versa.
The first inequality equation is - x + 5 < 3
Substitute the value of x = 4 in the equation.
4 + 5 < 3
Now, simplify the equation -
9 < 3
It is known that 9 is not less than 3, but greater than 3.
Therefore, this inequality is false.
The second inequality equation is - 9x > 36
Substitute the value of x = 4 in the equation.
9(4) > 36
Now, simplify the equation -
36 < 36
It is known that 36 is not less than 36, but equal 36.
Therefore, this inequality is false.
The third inequality equation is - x/2 < 3
Substitute the value of x = 4 in the equation.
4/2 < 3
Now, simplify the equation -
2 < 3
It is known that 2 is less than 3.
Therefore, this inequality is true.
The fourth inequality equation is - 18 < x + 8
Substitute the value of x = 4 in the equation.
18 < 4 + 8
Now, simplify the equation -
18 < 12
It is known that 18 is not less than 12, but greater than 12.
Therefore, this inequality is false.
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Which inequality is true when x = 4?
A. x + 5 < 3
B. 9x > 36
C. ×/2 < 3
D. 18 < x + 8
60⁰
m
Find the area of each triangle round to the nearest tenth
For math thanks !!!!!
Answer:
5.2 square units
Step-by-step explanation:
You want the area of a triangle with sides 4 and 3, and the angle between them measuring 60°.
AreaThe formula for the area of a triangle is ...
A = 1/2ab·sin(C)
ApplicationHere, we have a=4, b=3, C=60°, so the area is ...
A = 1/2·4·3·sin(60°) = 3√3 ≈ 5.2 . . . . square units
The area of the triangle is about 5.2 square units.
#7 in need help with this problem please
You cannot use the Hypotenuse-Leg congruence theorem to prove the similarity of triangles JKM and LKM, as they are not right triangles.
What is the HL congruence theorem?The Hypotenuse-Leg congruence theorem states that if the hypotenuse and one leg of two right triangles have the same measure then these two triangles are said to be congruent to each other.
The triangles JKM and LKM are not right triangles, as they do not have an angle of 90º, hence the HL congruence theorem cannot be used to prove their similarity.
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Standardized tests for certain subjects, given to high school students, are scored on a scale of 1 to 5. Let A represent the score on a randomly selected exam for subject A and let B represent the score on a randomly selected exam for subject B. The distributions of scores for each subject’s standardized tests are displayed in the table and the histograms.
The probability of a score lower than three is given as follows:
0.38.
How to obtain the probabilities?A probability is obtained as the division of the number of desired outcomes by the number of total outcomes.
As the table gives the probability distribution, we must just take the probabilities of the desired events from the table.
The probability of a score lower than three is given as follows:
P(X < 3) = P(X = 1) + P(X = 2).
Taking the values from the table, the probability is of:
P(X < 3) = 0.18 + 0.20
P(X < 3) = 0.38.
Missing InformationThe problem is given by the image presented at the end of the answer.
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4 groups of 3 give me answer
The question 4 groups of 3 can be calculated to be a total of 12 objects across all groups.
How to solve for the total number in the groupThe total number of groups are 4 in number
Each of the 4 groups have 3 objects in it.
That is 3 in 4 places
This can be solved by 4 * 3 = 12
Hence we can say that the solution for the questions that says 4 groups of 3 is 12
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Your kite is stuck in a tree that is 45 feet tall. The angle your string makes with the ground is 68°. Rather than worrying about the kite, you decide to calculate how much string you have let out. Assuming the string is held tight and makes a straight line to the ground, how much string have you let out?
Answer:
48.53 = 49 feet
Step-by-step explanation:
sin 0 = opposite/hypotenuse
sin 68 = AB/AC = 45/x
x = 45/sin 68 = 45/0.9272 = 48.53
48.53 rounded = 49 feet
Answer:
You have let out 48.5 feet of string
Step-by-step explanation:
Attached is a sketch of the problem.
We can use SOH CAH TOA to find our answer.
In this acronym, O is the opposite side, A is the adjacent side, and H is the hypotenuse. S is for the SIN function. C is for the COS function. T is for the TAN function.
We can calculate the length of the string by using the SIN function.
So we can say the sine of angle x is the opposite side divided by the hypotenuse.
[tex]sin(x)=\frac{O}{H}[/tex]
Lets solve for [tex]H[/tex].
Multiply each term by [tex]H[/tex].
[tex]H*sin(x)=\frac{O}{H} *H[/tex]
Simplify the right side by cancelling the common factor of [tex]H[/tex].
[tex]H*sin(x)=O[/tex]
Divide both sides of the equation by [tex]sin(x)[/tex].
[tex]\frac{H*sin(x)}{sin(x)} =\frac{O}{sin(x)}[/tex]
Simplify the right side by cancelling the common factor of [tex]sin(x)[/tex].
[tex]H=\frac{O}{sin(x)}[/tex]
Now lets evaluate the length of the string.
In this example we are given
[tex]x=68\\O=45[/tex]
[tex]H=\frac{45}{sin(68)}[/tex]
[tex]H=48.5341[/tex]
determine the relative order of the metric prefixes of kilo-, micro-, centi-, and milli-. for the same base unit, choose... is less than choose... , which is less than choose... , which is less than choose... .
The relative order of the metric prefixes Milli- < Centi- < Micro- < Kilo-
The relative order of the metric prefixes of kilo-, micro-, centi-, and milli- is milli-, centi-, micro-, and kilo-. This order is determined by the exponential values of each prefix.
Milli- is equal to 10-3, centi- is equal to 10-2, micro- is equal to 10-6 and kilo- is equal to 103. The exponential values are used to determine the relative order of the prefixes. The lowest exponential value is milli-, making it the smallest metric prefix and the highest exponential value is kilo-, making it the largest metric prefix.
When the exponential values are compared, it is clear that the order of the prefixes is milli- < centi- < micro- < kilo-. This order is used to determine the relative size of the metric prefixes when measuring the same base unit.
For example, if the base unit is meter, then millimeter is the smallest measure and kilometer is the largest measure. The exponential values of the metric prefixes determine the relative order of the base unit.
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What is the effect on the graph of f(x) = x² when it is transformed to
• h(x) = 5x2 + 10?
The transformation applied is the one in option D, a vertical dilation of scale factor of 5, and a shift of 10 units up.
What is the effect of the transformation?Here we start with the parent quadratic function:
f(x) = x²
And we have the transformed function:
h(x) = 5x² + 10
We can write this as:
A vertical dilation of a scale factor 5, which will give:
h(x) = 5*f(x)
And then a translation of 10 units upwards, which gives:
h(x) = 5*f(x) + 10
Replacing the function f(x) we will get:
h(x) = 5*x² + 10
Then the correct option is D.
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A cylinder has a height of 7 yards and a diameter of 26 yards. What is its volume? Use ≈ 3.14 and round your answer to the nearest hundredth.
The volume of the cylinder is 3,714.62 cubic yards.
How to get the volume of the cylinder?We know that the volume of a cylinder of radius R and height H is given by:
V = pi*R²*H
where pi = 3.14
In this case, we also know that:
H = 7yd
And the diameter is 26 yards, the radius is half of that, then:
R = 26yd/2 = 13yd
Then the volume is:
V = 3.14*(13 yd)²*7yd = 3,714.62 yd³
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A grocery chain determines the cost and revenue models using the following functions: C(x)=1.2x−0.012x2, 0≤x≤150 R(x)=3.6x−0.06x20≤x≤150, where x is the number of unit items sold. Determine the interval on which the profit function P(x) = R(x) − C(x) is increasing.
Answer:
Yesterday I have received amount of be with you i need to pay
The interval on which the profit function is increasing is [0, 25).
Given that:
The cost function is, C(x) = 1.2x - 0.012x²
The revenue function is, R(x) = 3.6x - 0.06x²
Here, x i is the number of units sold, and 0 ≤ x ≤ 150.
The profit function is:
P(x) = R(x) - C(x)
= (3.6x - 0.06x²) - (1.2x - 0.012x²)
= 2.4x - 0.048x²
Find P'(x).
P'(x) = 2.4 - 0.096x
The profit function is increasing when P'(x) > 0.
2.4 - 0.096x > 0
2.4 > 0.096x
25 > x
That is x < 25.
Hence the function is increasing in the interval [0, 25).
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a population of bacteria growing exponentially can be modeled as P(t)= P0e kt , where is the time in hours and P0 is the initial population. if the population has a doubling time of 3 hours, calculate the growth constant .
A population of bacteria growing exponentially can be modeled as P(t)= P0e kt, where is the time in hours and P0 is the initial population. if the population has a doubling time of 3 hours, the growth constant is k = ln(2) / 3 = 0.231049.
The growth constant (k) can be calculated by taking the natural log of 2 (ln(2)) and dividing it by the doubling time (3 hours). Therefore, the growth constant is 0.231049. This equation models exponential growth, which is a type of growth where the rate of increase is proportional to the population size. In this case, the population doubles every 3 hours.
This exponential growth is modeled using the equation P(t)= P0e^kt, where P(t) is the population size at a given time, P0 is the initial population size, and k is the growth constant. By finding the growth constant, we can predict the population size at any given time. The growth constant is found by taking the natural log of 2 (ln(2)) and dividing it by the doubling time (3 hours).
This equation is used to find the amount of growth per unit time and is the same regardless of the population size. This equation can be used to predict the population size at any given time, allowing us to estimate the population size in the future.
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Determine the intercepts of the line.
�
yy-intercept:
(
(left parenthesis
,
,comma
)
)right parenthesis
�
xx-intercept:
(
(left parenthesis
,
,comma
)
)right parenthesis
A coordinate plane. The x- and y-axes each scale by one-tenth. A graph of a line intersects the points zero, four-tenths and three-tenths, zero.
Jose is building a rectangular shaped garden and needs to know how many square feet it will cover. The dimensions of the garden will be 8 feet in length and (3n+2) in width. What is the area of the garden space?
A) 24n+16
B) 11n+10
C) 40n
Thank you!!!
Answer:
The equation for the area of a rectangle is length*width. For this problem, it says the length is 8 and the width is (3n+2). All you have to do is multiply 8 by (3n+2).
8(3n+2)=A
24n+16=A
Option A is correct
part a: the number of transistors per ic in 1972 seems to be about 4,000 (a rough estimate by eye). using this estimate and moore's law, what would you predict the number of transistors per ic to be 20 years later, in 1992? prediction
Using Moore's Law, which states that the number of transistors on a chip doubles approximately every two years, the estimated number of transistors per IC in 1992 would be 64,000.
The law claims that we can expect the speed and capability of our computers to increase every two years because of this, yet we will pay less for them. In more simple terms, the observation by Gordon Moore in 1965 that the number of transistors in a dense integrated circuit (IC) doubles roughly every two years is known as Moore's law.
This is calculated by doubling the estimate of 4,000 transistors every two years for a total of 8 doublings (16 years).
To know more about Law here
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What is the distance between the points (-7.5, -11) and (2, -11)?
Answer:
9.5
Step-by-step explanation:
Distance (d) = [tex]\sqrt{(2-(-7.5)^2)+(-11-(-11)^2)}\\ \sqrt{(9.5)^2+(0)^2}\\ \sqrt{90.25} \\9.5[/tex]