Therefore , the solution of the given problem of variable comes out to be where weights are the probability of that outcome.
Variable : What is it ?A variable is a quality that may be measured and take on several values. A few examples of variables are height, age, salary, province of birth, school grades, and kind of dwelling.
Here,
Given :
A discrete random variable's anticipated value
So, in order to determine the expected value of a discrete random variable,
we may infer from the provided data that it is calculated as a weighting factor of the potential outcomes of that variable,
where weights are the probability of that outcome.
Therefore , the solution of the given problem of variable comes out to be where weights are the probability of that outcome.
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A function whose values repeat based on positions of a point that moves around a circle is called a sinusoid.: T/F
True. A function whose values repeat based on positions of a point that moves around a circle is called a sinusoid, using trigonometry approach.
The sine waves oscillate in a smooth, repetitive manner, defined in terms of distance from the [tex]x[/tex] axis to the point on the unit circle.
The main features of a sinusoidal function are its amplitude, its phase, and its frequency. Let us discuss the features one by one :
Amplitude specifies the maximum distance between the x axis i.e. the horizontal axis and the vertical position of the point or a the waveform. It is denoted by [tex]A[/tex].
Phase of a function refers to the horizontal position of the waveform with correspondence to one rotation. The extent or angle by which, a point or a waveform is shifted, is called the phase difference or phase shift.
Frequency is the measurement which tells us about how quickly the sinusoid completes cycles i.e. it simplifies the movement of the sinusoidal wave per unit time.
The sinusoid functions play key role in modern periodic phenomena such as sound and light waves, oscillators, average temperature variations throughout the year, sunlight intensity ,etc.
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four ambassadors and one advisor for each of them are to be seated at a round table with 12 chairs numbered in order 1 to 12. each ambassador must sit in an even-numbered chair. each advisor must sit in a chair adjacent to his or her ambassador. there are $n$ ways for the 8 people to be seated at the table under these conditions. find the remainder when $n$ is divided by $1000$.
Therefore , the solution of the given problem of combination comes out to be 479001.6.
Combination : What is it?Combinations are mathematical procedures that count the number of possible configurations from a set of items, where the selection direction is immaterial. You can select any arrangement of the parts in any combination. It's possible to mix together combinations and permutations.
Here,
Given : four ambassadors and one advisor for each of them are to be seated at a round table with 12 chairs numbered in order 1 to 12..
and n ways for seating 8 people.
Thus , to find this permutation- combination arrangement .
So,
nPr => 6 P 6 and * 12P6
nPr => 665280 * 720
nPr = > 47,90,01,600
and divide it by 1000 .
So ,
=> 479001600/1000
=> 479001.6
Therefore , the solution of the given problem of combination comes out to be 479001.6.
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Generate a plan and describe the steps needed to solve the equation.
Answer:
Step-by-step explanation:
1. Identify the equation and its variables.
The equation can be any type of equation, such as a linear equation, quadratic equation, or polynomial equation. Identify the variables in the equation and label them.
2. Find a strategy for solving the equation.
Depending on the type of equation, there are various strategies for solving the equation. For example, a linear equation can be solved using the addition-subtraction method, a quadratic equation can be solved using the quadratic formula, and a polynomial equation can be solved using the synthetic division method.
3. Use the strategy to solve the equation.
Follow the steps of the chosen strategy to solve the equation. This may involve expanding the equation, factoring, or rearranging the equation.
4. Check the solution.
Once the equation is solved, check the solution by plugging the answer back into the equation and verifying that it works.
5. Review and summarize the steps.
Review the steps taken to solve the equation and summarize them in a few sentences. This will help with understanding and remembering the steps.
Leslie has comprehensive insurance with a $500 deductible on her van. On Halloween her van is vandalized, and the damages total $1,766. Leslie submits a claim to her
insurance company.
a. How much must Leslie pay for the repair?
b. How much must the insurance company pay?
Answer:
a. Leslie must pay the first $500 of the repair costs, as that is her comprehensive insurance policy's deductible.
b. The insurance company must pay the remaining $1,266 of the repair costs, as that is the total cost of the repairs ($1,766) minus Leslie's portion of the cost (the $500 deductible).
How to write 12 and half kilometers in digits and decimal
Answer:
1000 mitre=1km
1.25 ×1000
Answer:
DIGIT FORM = 13km
DECIMAL FORM: 12.5km
Step-by-step explanation:
DIGIT Form: A digit can only be a whole number, so round 12 and a half (12/5 or 12.5) to the nearest whole number.
DECIMAL Form: It cannot be a whole number and must consist of a number followed by a decimal point (a period) and then another number.
DON'T FORGET TO ADD KILOMETERS (km) AFTER YOUR ANSWER.
The signal of Micha's Wi-Fi router covers a circular area, whose border is modeled by the equation (x – 10)2 + y2 = r2. She discovers the boundary is located at (2, 6). What is the radius of the signal?
10
square root 40
40
100
The radius of the signal is 10 units. The 1st option is the answer
How to determine the radius of the signal?
The equation of a circle is a mathematical expression that describes the properties of a circle. It is typically represented in the form of (x - h)²+ (y - k)² = r², where (h, k) is the center of the circle, and r is the radius
Since the border is modeled by the equation (x – 10)² + y²= r² and the boundary is located at (2, 6).
To get the radius of the signal substitute x = 2 and y = 6 into the given equation and solve for r:
(x – 10)² + y²= r²
(2 – 10)² + 6²= r²
(-8)² + 6²= r²
64 + 36 = r²
100 = r²
r² = 100
r = √100
r = 10 units
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Sydney invests $100 every month into an account that pays 0.8% annual interest, compounded monthly. Benny invests $80 every month into an account that pays 2.2%
annual interest rate, compounded monthly.
a. Determine the amount in Sydney's account after 10 years.
b. Determine the amount in Benny's account after 10 years.
c. Who had more money in the account after 10 years? Sydney
d. Determine the amount in Sydney's account after 30 years. $40,672.12
e. Determine the amount in Benny's account after 30 years.
f. Who had more money in the account after 30 years? Benny
For Sydney with $100 at 5%, monthly, for 10 year we get 229050.
What is meant by annual interest rate?Annual percentage rate (APR) refers to the yearly interest generated by a sum that's charged to borrowers or paid to investors. APR is expressed as a percentage that represents the actual yearly cost of funds over the term of a loan or income earned on an investment.
The interest rate is the amount a lender charges a borrower and is a percentage of the principal—the amount loaned. The interest rate on a loan is typically noted on an annual basis known as the annual percentage rate (APR).
Let the equation be
A = [ p(1 + r/n)nt ] + [ PMT ((( 1 + r/n)nt - 1) / (r / n)) ]
For Sydney with $100 at 5%, monthly, for 10 year
A = [ 100(1 + 0.05/12)(12)(10) ] + 100 (((1 + 0.05/12)(12)(10) - 1) / (0.05 / 12)) ]
= 229050
Therefore, the correct answer is 229050.
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Which set of ordered pairs does not represent a function?
what is the total number of points of intersection of the graphs of the equations y 5 ex and xy 5 20 ?
A. The total number of points of intersection of the graphs of the equations y = 5e^x and xy = 20 is two.
To find the points of intersection, we must solve the two equations for x and y.
For the first equation, y = 5e^x, we can solve for x by taking the natural logarithm of both sides and getting x = ln(y/5).
For the second equation, xy = 20, we can solve for y by dividing both sides by x and getting y = 20/x.
We can then substitute the expression for x in terms of y into the expression for y in terms of x and solve for y to get y = 20/(ln(y/5)). This is a nonlinear equation that must be solved numerically.
By using numerical methods, we can solve the equation and find the two points of intersection, which are (x, y) = (3.68, 4.64) and (x, y) = (0.87, 22.95).
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what type of congruence transformation can you use to show that the figures are congruent to one another?
If a figure can be transformed into another figure by a sequence of translations, rotations, and reflections, and the size and shape remain the same, the figures are congruent.
A congruence transformation is a type of transformation that preserves the size and shape of a figure. The most common congruence transformations are translations, rotations, and reflections.
Translations involve moving a figure a certain distance in a certain direction without changing its size or orientation.
Rotations involve rotating a figure around a certain point without changing its size or shape.
Reflections involve flipping a figure over a certain line without changing its size or shape.
In order to show that two figures are congruent, you can use a combination of these congruence transformations to match one figure to the other. By using these transformation you can map each point of one figure to a corresponding point on the other figure and if the size and shape of figures remain the same, that means that the figures are congruent.
It's important to notice that Congruence is an equivalence relation and it's reflexive, symmetric, and transitive.
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Answer the screenshot
The domain of the given rational function R(x) = 6x/(x + 1) include the following: A. the domain of R(x) is {x|x ≠ 1}.
What is a domain?In Mathematics, a domain can be defined as the set of all real numbers for which a particular function is defined.
This ultimately implies that, a domain is the set of all possible input numerical values or numbers (x-values) to a function and the domain of a graph comprises all the input numerical values (real numbers) which are located on the x-coordinate.
In order to determine the domain of this rational function, we would use an online graphing calculator to plot it and then write its domain in interval notation based on the graph as follows:
Domain = (-∞, 1) U (1, ∞)
By using set builder notation, the domain of this rational function R(x) = 6x/(x + 1) can be re-written as follows;
Domain = {x|x ≠ 1}.
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Does 12/16 20 form a right triangle?
The sides given as 16cm , 12cm and 20cm forms a right triangle because the sides satisfies the condition of Pythagoras Theorem .
What is Pythagoras Theorem ?
The Pythagoras Theorem states that the square of the longest side (hypotnuse) is equal to the sum of the square of the other two sides .
The sides of the triangle are given as ⇒ 16cm , 12cm and 20cm ;
here the hypotnuse (longest side) is = 20 cm ;
According to Pythagoras theorem ,
⇒ [tex]20^{2} =12^{2} +16^{2}[/tex] ;
⇒ [tex]400 =144+256[/tex] ;
⇒ [tex]400=400[/tex] ;
So , The condition of Pythagoras theorem is satisfied .
Therefore , the given sides can form a Right Triangle .
The given question is incomplete , the complete question is
Does the sides 16cm , 12cm and 20cm form a right triangle ?
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Solve for X, Leave in simplest radical form.
Answer:
12
Step-by-step explanation:
1) FInd the sides of small triangle. Since it has 2 congruent angles it also has to congruent sides opposite those angles. So the sides adjacent (connected to) the right angle are both 6.
2) Find the hypotenuse (side opposite the right angle) in the small triangle
a^2 +b^2 = c^2
6^2 +6^2 = c^2
36+36 = c^2
72 = c^2
c = [tex]\sqrt{72}[/tex]
In simplified radical form [tex]\sqrt{72\\[/tex] = 6[tex]\sqrt{2}[/tex]
3) Now find the sides of big triangle. It has 2 congruent angles therefore it has two congruent side opposite those angles. We know that one of the sides is 6[tex]\sqrt{2}[/tex] because it is also the hypotenuse of the small triangle. The other side adjacent to the right angle is also 6[tex]\sqrt{2}[/tex].
4) Now find x which is the hypotenuse of the big triangle.
[tex](6\sqrt{2} )^{2}[/tex]+ [tex](6\sqrt{2} )^{2}[/tex]= [tex]c^{2}[/tex]
(36*2)+(36*2) = [tex]c^{2}[/tex]
144 = [tex]c^{2}[/tex]
c = 12
so x = 12
I need help pls help me
The quadratic equation y = x² - 2x - 3 have ordered points at (0, -3), (2, -3), (-2, 5) and (4, 5)
What is an equation?An equation is an expression composed of variables and numbers linked together by mathematical operations.
Quadratic equation is a polynomial that have a degree of 2. The degree of a polynomial is the highest exponent of the variables.
Given that:
y = x² - 2x - 3
When x = 0; y = (0)² - 2(0) - 3 = -3
When x = 2; y = (2)² - 2(2) - 3 = -3
When x = -2; y = (-2)² - 2(-2) - 3 = 5
When x = 4; y = (4)² - 2(4) - 3 = 5
The equation y = x² - 2x - 3 is a quadratic equation.
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The scatter plot above shows the average rent (in dollars) for a 111-bedroom apartment in New York City each year between 200020002000 and 201320132013. Which of the following is the best estimate of the average change in rent each year
The best estimate of the average change in rent each year include the following: C. $40.
How to determine the average change in rent each year?Mathematically, the rate of change is also referred to as slope or gradient and it can be calculated by using this formula;
Rate of change, m = (Change in y-axis, Δy)/(Change in x-axis, Δx)
Rate of change, m = (y₂ - y₁)/(x₂ - x₁)
Next, we would determine the rate of change of the value of y with respect to the value of x on the scatter plot, which represents a line that is passing through the points (0, 800) and (10, 1200):
Rate of change, m = (1200 - 800)/(10 - 0)
Rate of change, m = 400/10
Rate of change, m = 40.
Based on the scatter plot, we can reasonably infer and logically deduce that the average rate of change in rent each year is equal to 40 dollars.
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Complete Question:
The scatter plot below shows the average rent (in dollars per month) for a 1-bedroom apartment in New York City each year between 2000 and 2013.
Which of the following is the best estimate of the average change in rent each year?
answer choices
$0.5
$1
$40
$400
Fun Park charges an entry fee of $2 for any family with less than 5 members. Fun Park charges $3 less than the number of family members for entry of any family with 5 or more members. How much would a family with 10 members be charged?
Answer:
$7
Step-by-step explanation:
Got it right on a test
The long jump pit was recently rebuilt to make it level with the runway. volunteers provided pieces of wood to frame in the pit. each piece of wood provided measures 6 ft, which is approximately 1.8 to 8 7. determine the amount of wood, in meters, needed to rebuild the frame.
The amount of wood, in meters, needed to rebuild the frame is 1.8288 m.
What is amount and example?
amount to (something) : to produce (a total) when added together. The bill amounted to 10 dollars. They have debts amounting to thousands of dollars.
To calculate the amount of wood, in meters, needed to rebuild the frame, we can use the following formula:
wood (m) = (wood (ft) x 0.3048) / 6
Since each piece of wood provided measures 6 ft (approximately 1.8 to 8.7), we can calculate the amount of wood, in meters, needed to rebuild the frame as follows:
wood (m) = (6 ft x 0.3048) / 6
wood (m) = 1.8288 m
Therefore, the amount of wood, in meters, needed to rebuild the frame is 1.8288 m.
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What are real numbers?
Is the quotient of two real numbers an integer?
Answer:
real number, in mathematics, a quantity that can be expressed as an infinite decimal expansion. Real numbers are used in measurements of continuously varying quantities such as size and time, in contrast to the natural numbers 1, 2, 3, …, arising from counting
Step-by-step explanation:
The quotient of any two integers is an integer.
A real number is a number that can be measured and represented on a number line; this includes fractions, decimals, irrational numbers, rational numbers, and basically every number you encounter. With that in mind, the quotient of 2 real numbers is not necessary an interger as 2.01/ 1 is not an integer
1. what is the equation in slope-intercept form of a line whose slope is 9 and whose y-intercept is -3?
The equation in slope-intercept form of a line whose slope is 9 and whose y-intercept is -3 is equals to the y = 9x-3.
Slope intercept form of an equation : The slope intercept form is one of method to determine the equation of a straight line in the coordinate plane. The equation of a straight line is a relation which:
the coordinates of any point must be satisfied if point on the line.the coordinates of any point can't satisfied if point not on the line.Let us assume a straight line of slope 'm' and y-intercept 'b'. The equation of slope intercept form for a straight line with slope, say, 'm', and the y-intercept, 'b', is
y = mx + b
Now, the slope of line , m = 9
y-intercept of line, b = - 3
As we know slope intercept form of a line is, y = mx + b , so plugging the known values of slope and y-intercept in it,
=> y = 9x - 3
So, required equation in slope intercept form of line is y = 9x - 3.
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what is the order these go
Answer:
see attached
Step-by-step explanation:
You want the steps in order for constructing a perpendicular to a line through an external point.
PerpendicularEssentially, the procedure identifies two points on the line (P and Q) that are equidistant from the external point (R), then proceeds to draw a perpendicular bisector of the segment between those two points. The external point is already equidistant from P and Q, so we only need to find another equidistant point (S) to complete the construction.
See the attachment for the ordering of the instruction steps. (Note the step numbers are not in order on the left.)
jason is a skilled rapper. he has already rapped a 40-word intro to a song and continues to rap 5 words per second
write an inequality to determine how many more seconds t he will rap to complete the song if the total song, including the intro, is at least 500 words.
drag each numbers or symbol into each box to correctly complete the inequality
hint
500
40
3
>
500
40
+
check
de toch
o
Answer:
500 > 40 + 5t
Step-by-step explanation:
At least 500
40 intro = initial, constant
t = time in seconds
5 words per second
Please mark as brainliest
Colin deposited $1,230 in an account that pays 3.19% simple interest for three years.a. What will the interest be for the three years?
b. What will be the new balance after three years?
[tex]~~~~~~ \textit{Simple Interest Earned Amount} \\\\ A=P(1+rt)\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill & \$1230\\ r=rate\to 3.19\%\to \frac{3.19}{100}\dotfill &0.0319\\ t=years\dotfill &3 \end{cases} \\\\\\ A = 1230[1+(0.0319)(3)] \implies \stackrel{balance}{\boxed{A \approx 1347.71}}~\hfill \underset{interest}{\stackrel{1347.71~~ - ~~1230}{\boxed{117.71}}}[/tex]
A company models its net income, in thousands of dollars, with the function f(x) = 9x2 – 54x – 144, where x is the number of units of its product sold. How many units of its product does the company need to sell in order for the net income to equal $0?
Solving the quadratic equation, it is found that the company needs to sell 8 products for the net income to be equal $0.
What is the quadratic equation for the net income of the company?An equation is a mathematical statement that is made up of two expressions connected by an equal sign. In its simplest form in algebra, the definition of an equation is a mathematical statement that shows that two mathematical expressions are equal. For instance, 3x + 5 = 14 is an equation, in which 3x + 5 and 14 are two expressions separated by an 'equal' sign.
here, we have,
It is given by:
f(x) = 9x² - 54x - 144.
It can be simplified as follows:
f(x) = 9(x² - 6x - 16)
Then:
f(x) = 9[(x + 2)(x - 8)]
It has a net income equals to 0 when:
f(x) = 0,
hence:
x + 2 = 0 -> x = -2.
x - 8 = 0 -> x = 8.
The amount of products sold is positive, hence, the company needs to sell 8 products for the net income to be equal $0.
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If 4 pineapples cost $9.60, what is the cost of 10 pineapples? Use unit costs and show your work.
a realtor wishes to enclose 600m of land in a rectangular plot and then divide it into two plots with a fence parallel to one of the sides. what are the dimensions of the rectangular plot that require the least amount of fencing
The dimensions of the rectangular plot that require the least amount of fencing is :
A(17.32, 17.32) = 600
P(17.32, 17.32) = 121.24
Now, According to the question:
600 [tex]u^2[/tex] of land to be enclosed by fence
Area inside plot should be maximized, amount of fence should be minimized
If we draw a quick sketch, we get something like this:
_____ _____
| | |
| | |
| | |
| | |
The two rectangles could be different sizes but if one rectangle size maximizes area then it would make sense to use that some rectangle for both sides.
Let's put some variables into our picture so we can define our constraints.
y y
| | |
x | x | x |
| | |
| | |
Now we just need an equation to connect our unknowns (how much fence to use) to our constraint (it has to have an exact area of 600 u^2.
A = x × 2y = area = 600
P = 3x + 4y = perimeter = a minimum
First we solve the area equation for y:
y = [tex]\frac{600}{2x}[/tex] = [tex]\frac{300}{x}[/tex]
and then we substitute that result into our perimeter equation:
P = 3x + 4 (300/x)
P = 3x + 1200/x
Our perimeter equation is: P(x) = 3x + 1200/x OR P(x) = 3x +1200[tex]x^-^1[/tex]
We can find what value of x makes our perimeter as small as possible (a minimum) by graphing or by using Calculus.
In Calculus we know that maximums and minimums always occur when the derivative is zero. This is because the slope (rate of change) at these points in a graph are always flat or zero. Our derivative is
P'(x) = 3 - 1200[tex]x^-^2[/tex]
When set equal to zero, we can solve for x:
3 - 1200[tex]x^-^2[/tex]= 0
1 - 400[tex]x^-^2[/tex] = 0
1 = 400/[tex]x^{2}[/tex]
[tex]x^{2}[/tex] = 400
x = ± 20
Our fence length can't be a negative number so our answer must be 20u.
If our x length is 20, then our y length must be 300/x to ensure our area is 600 u^2.
The y length is 300/(20) = 15
Let's put all of our numbers into our picture to see if it make sense.
15 15
| | |
20 | 20 | 20 |
| | |
| | |
15 15
Sure enough our area is 600.
Here's what we have right now:
A(20, 15) = 600
P(20, 15) = 120
How about we try something a little bigger like 20.5 for x and 14.63 for y?
A(20.5, 14.63) = 600
P(20.5, 14.63) = 120.02
How about we try something a little smaller like 19.5 for x and 15.38 for y?
A(19.5, 15.38) = 600
P(19.5, 15.38) = 120.02
It looks like if we try to change x, even a little, to make it bigger or smaller the perimeter only gets bigger.
You might have guessed at the beginning that a square is the best shape to use to maximize area, so let's try that as well.
Each rectangle is 300 u^2. We want a square so each side would be √(300) = 17.32
17.32 17.32
| | |
17.32 | 17.32 | 17.32 |
| | |
17.32 17.32
A(17.32, 17.32) = 600
P(17.32, 17.32) = 121.24
Hence, The dimensions of the rectangular plot that require the least amount of fencing is :
A(17.32, 17.32) = 600
P(17.32, 17.32) = 121.24
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Find the dimensions of a rectangular lot whose length is 2km more than its width if the area is 24km²?
Answer:
4 km wide and 6 km long.
Step-by-step explanation:
Let the width be x, then the length is x+2 km.
Area = width * length
Substituting the given values:
24 = x(x + 2)
24 = x^2 + 2x
x^2 + 2x - 24 = 0
(x + 6)(x - 4) = 0
x = -6, 4
As x must be positive, then x = 4.
So, the dimensions are 4 and 4+2
= 4, 6,
Answer:
width = 3.46 km and length = 6.93 km
Step-by-step explanation:
let the width be : X km
then the length would be: 2X km
as area is length x width
therefore:
2X x X = 24
2X² = 24
X² = 24/2
X² = 12
X = [tex]\sqrt{12}[/tex]
X= 3.46
the width would be 3.46 km while the length would be 2X = (93.46) = 6.93 km
in early 2019, the us rate of recycling plastic water bottles was only 23%. a government agency designs an expensive program to increase the recycling rate. the program will be tested in texas and, if successful, it will be used nationally. a hypothesis test is conducted with h0: the proportion of water bottles that are recycled is still 23% after the program, and ha: the proportion of water bottles that are recycled is more than 23% after the program. what is a type i error and its consequence in this context?
A type I error, also known as a false positive, is when a test incorrectly rejects the null hypothesis. In this context, a type I error would mean that the test incorrectly concludes that the proportion of water bottles that are recycled is more than 23% after the program, when in reality it is still 23%.
1. Calculate the means of the two samples.
2. Calculate the standard deviation of the two samples.
3. Calculate the degrees of freedom (df) by subtracting 1 from the total
number of samples.
4. Calculate the t-statistic by subtracting the means of the two samples, dividing the result by the standard deviation, and then dividing that result by the square root of the degrees of freedom.
5. Calculate the critical value of t from the t-distribution table for the degrees of freedom and the chosen level of significance.
6. Compare the calculated t-statistic with the critical value of t.
7. Make a decision – accept or reject the null hypothesis.
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Paige has a cell phone plan that charges $0. 06 per minute plus a monthly fee of $15. 0. She budgets $25. 50 per month for
her total cell phone expenses without taxes.
What is the maximum number of minutes Paige could use her phone each month and still stay within her budget?
Therefore , the solution of the given problem of linear equation comes out to be 550 minutes she can use her cell phone.
The definition of a linear equation.A linear regression model is one that conforms to the algebraic equation y=mx+b. The slope is B, and the y-intercept is m. The previous clause is usually referred to as an "mathematical equation having two variables because both y and x are unique parameters. Two variables make up bivariate linear equations. Linear equations have a variety of applications, all of which have a zero outcome. Y=mx+b, where m stands for the gradient and b for the y-intercept, is the formula for a linear equation.
Here,
Given : 55=0.1(m-500)+50
where m is the number of minute
=> 55=0.1(m-500)+50
=> 55=0.1m-50+50
=>55=0.1m-0
=>55-0=0.1
=>55=0.1
=>0.1=0.1
=>550=m
Therefore , the solution of the given problem of linear equation comes out to be 550 minutes she can use her cell phone.
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PLS HELP!!!!!!!!!!!!!!
The population of bacteria in an experiment is increasing by 90% each dayIf there were 100 bacteria at the beginning of the experiment predict the number of bacteria in 5 days?
Answer: In five days, there will be around 2,476 bacteria.
Step-by-step explanation: Using the hint given, simply plug in the numbers to calculate the predicted amount of bacteria. Hope this helps!
[tex]100(1+0.9)^{5}=2,476.099[/tex]
Answer:
2476
Step-by-step explanation:
Given formula:
[tex]\textsf{Future Amount}=\sf I(1+r)^t[/tex]
Given values:
Initial amount (I) = 100 bacteriaGrowth rate (r) = 90% = 0.9Time periods (t) = 5 daysSubstitute the given values into the given formula and solve:
[tex]\begin{aligned}\implies \textsf{Future Amount}& =\sf 100(1+0.9)^5\\& =\sf 100(1.9)^5\\& =\sf 100(24.76099)\\& =\sf 2476.099\\& =\sf 2476\;(nearest\;whole\;number)\end{aligned}[/tex]
3) Five kilograms of flour can make 45 loaves of bread. How many loaves of bread can 6 kilograms make?
Answer:
54 loaves of bread
Step-by-step explanation:
45:5=9 (45 divided by 5 equals 9)
9x6=54 (9 times 6 equals 54)
