The population of bacteria in 3 days will be approximately 44,503 bacteria.
Explanation:To calculate the future population of bacteria, we can use the formula P = P0(1+r)t, where P0 is the initial population, r is the growth rate, and t is the time in days. In this case, P0 is 29,000 bacteria, r is 15% or 0.15, and t is 3 days. Plugging in these values, we get:
P = 29000(1+0.15)3
Calculating this expression, we find that P is approximately 44,503 bacteria
Final answer:
The population of bacteria will be approximately 44,076 in 3 days, given an initial population of 29,000 and a growth rate of 15% per day.
Explanation:
To calculate the population of bacteria in 3 days, we need to use the formula:
P = P0 * (1 + r)^t
Where P is the final population, P0 is the initial population, r is the growth rate per day (expressed as a decimal), and t is the time in days.
In this case, the initial population is 29,000 and the growth rate is 15% per day (0.15). Plugging these values into the formula, we get:
P = 29,000 * (1 + 0.15)³
Simplifying the equation gives:
P = 29,000 * 1.15³
P = 29,000 * 1.520875
P ≈ 44,076
Therefore, there will be approximately 44,076 bacteria in 3 days.
The function h(x) is quadratic and h(3) = h(–10) = 0. Which could represent h(x)?
h(x) = x2 – 13x – 30
h(x) = x2 – 7x – 30
h(x) = 2x2 + 26x – 60
h(x) = 2x2 + 14x – 60
Answer:
[tex]h(x)=2x^2+14x-60[/tex]
Step-by-step explanation:
This question can be solved by two methods
Method 1: Substitute x=3 and x=-10 in all the equations and determine which equals to zero (ie., check h(3)=0 and h(-10)=0 for all the equations)
Equation 1
[tex]h(x)=x^2-13x-30[/tex]
[tex]h(3)=3^2-13(3)-30[/tex]
[tex]h(3)=-60[/tex]
As h(3)≠0, Equation 1 is discounted
Equation 2
[tex]h(x)=x^2-7x-30[/tex]
[tex]h(3)=3^2-7(3)-30[/tex]
[tex]h(3)=-42[/tex]
As h(3)≠0, Equation 2 is discounted
Equation 3
[tex]h(x)=2x^2+26x-60[/tex]
[tex]h(3)=2(3)^2+26(3)-60[/tex]
[tex]h(3)=36[/tex]
As h(3)≠0, Equation 3 is discounted
Equation 4
[tex]h(x)=2x^2+14x-60[/tex]
[tex]h(3)=2(3)^2+14(3)-60[/tex]
[tex]h(3)=0[/tex]
[tex]h(x)=2x^2+14x-60[/tex]
[tex]h(-10)=2(-10)^2+14(-10)-60[/tex]
[tex]h(-10)=0[/tex]
As h(3)=0 and h(-10)=0, Equation 4 represents h(x)
Method 2: Solve to find the roots of each equation where h(x)=0 using the quadratic formula. Roots should be x=3,x=-10
The quadratic formula is:
[tex]x=\frac{-b\±\sqrt{b^2-4ac}}{2a}[/tex]
where a, b and c are as below
[tex]h(x)=ax^2+bx+c=0[/tex]
Equation 1
[tex]h(x)=x^2-13x-30=0[/tex]
[tex]x=\frac{-b\±\sqrt{b^2-4ac}}{2a}[/tex]
[tex]x=\frac{13\±\sqrt{(-13)^2-4(1)(-30)}}{2(1)}[/tex]
[tex]x=15,x=-2[/tex]
As roots are not x=3 and x=-10, Equation 1 is discounted
Equation 2
[tex]h(x)=x^2-7x-30[/tex]
[tex]x=\frac{-b\±\sqrt{b^2-4ac}}{2a}[/tex]
[tex]x=\frac{-(-7)\±\sqrt{(-7)^2-4(1)(-30)}}{2(1)}[/tex]
[tex]x=10,x=-3[/tex]
As roots are not x=3 and x=-10, Equation 2 is discounted
Equation 3
[tex]h(x)=2x^2+26x-60[/tex]
[tex]x=\frac{-b\±\sqrt{b^2-4ac}}{2a}[/tex]
[tex]x=\frac{-(26)\±\sqrt{(26)^2-4(2)(-60)}}{2(2)}[/tex]
[tex]x=2,x=-15[/tex]
As roots are not x=3 and x=-10, Equation 3 is discounted
Equation 4
[tex]h(x)=2x^2+14x-60[/tex]
[tex]x=\frac{-b\±\sqrt{b^2-4ac}}{2a}[/tex]
[tex]x=\frac{-(14)\±\sqrt{(14)^2-4(2)(-60)}}{2(2)}[/tex]
[tex]x=3,x=-10[/tex]
As roots are x=3 and x=-10, Equation 4 represents h(x)
If you were to use the substitution method to solve the following system, choose the new equation after the expression equivalent to x from the second equation is substituted into the first equation.
2x – 3y = –29
x + 4y = 13
2(4y + 13) – 3y = –29
2(–4y + 13) – 3y = –29
2x – 3(4y + 13) = –29
2x – 3(–4y + 13) = –29 ...?
Answer:
can confirm that the answer above is correct
hope yall have a nice day
Step-by-step explanation:
How do you find the x-intercepts and y-intercepts of trinomials. E.g.(x^2-10x+25) How do you find the x-intercepts and y-intercepts of trinomials. E.g.(x^2-10x+25)
To find the x-intercepts, set the trinomial equal to zero and solve for x. Substitute x = 0 to find the y-intercept.
Explanation:To find the x-intercepts of a trinomial, you need to set the trinomial equal to zero and solve for x.
In the example given (x^2-10x+25), you would set the trinomial equal to zero as follows:
x^2-10x+25 = 0
Now, you can factor the trinomial or use the quadratic formula to solve for x. In this case, the trinomial can be factored as (x-5)(x-5) = 0.
So, the x-intercept is x = 5.
The y-intercept can be found by substituting x = 0 into the trinomial. In this case, when x = 0, the trinomial becomes y = 25.
So, the y-intercept is (0, 25).
Andrea drove 500 miles in 10 hours. find the average number of miles per hour that andrea drove
Average Cost. A company manufacturing snowboards has fixed costs of $200 per day and total costs of $3800 per day for a daily output of 20 boards.
Assuming that the total cost per day C(x) is linearly related to the total output per day x, write an equation for the cost function.
The cost function is a linear function that represents the relationship between the total cost and total output. The equation C(x) = $200 + $3600x/20 represents the cost function in this case.
Explanation:The cost function is a linear function that represents the relationship between the total cost and total output. In this case, the fixed costs are $200 per day, meaning they do not depend on the output. The total costs per day, C(x), can be expressed as the sum of fixed costs and variable costs:
C(x) = FC + VC(x)
Given that the total costs are $3800 per day for a daily output of 20 boards, we can write the equation as:
$3800 = $200 + VC(20)
Now, we can solve for VC(20) to find the variable cost:
VC(20) = $3800 - $200 = $3600
Therefore, the cost function equation is C(x) = $200 + $3600x/20, where x represents the total output per day.
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The area of a rectangle is 70 square inches and the length of the rectangle is 3 inches longer than the width.
The area of a rectangle is found by multiplying the length times the width.
Which equation models this situation?
w(w+3)=70w(w+3)=70
w + 3 = 70
3w = 70
w + 3w = 70
The correct equation to model the rectangle's area where the length is 3 inches more than the width and the area is 70 square inches is W(W + 3) = 70, which simplifies to W^2 + 3W = 70.
Explanation:The student is asking for the correct equation to model a rectangle's area where the length (L) is 3 inches more than the width (W), and the area is 70 square inches. To find an equation that models the situation, we need to express L in terms of W. Since L is 3 inches more than W, we can write L as W + 3. The area (A) of a rectangle is found by multiplying the length by the width, so A = L x W.
Therefore, the equation that models this situation is W(W + 3) = 70. To see why, let's insert the expression for L into the area formula:
A = L x W = (W + 3) x W
This simplifies to:
A = W^2 + 3W
Since we know the area A is 70 square inches, we substitute and get the equation:
W^2 + 3W = 70
Which is the correct model for the given situation.
A board that is 19.5 meters long is cut into two pieces one piece is 7.2 meters whats and equation that solves how long the other half is
Answer:
7.2+x=19.5
x=19.5-7.2
x=12.2
your welcome
Step-by-step explanation:
Suppose a local vendor charges $2 per hot dog and that the number of hot dogs sold per hour is given by
x(t) = −4t^2 + 20t + 64,
where t is the number of hours since 10 AM,
0 ≤ t ≤ 4.
Find an expression for the revenue per hour R as a function of x?
Given the equation Square root of 2x plus 1 = 3, solve for x and identify if it is an extraneous solution.
^ I really don't understand this topic, whatsoever. Could someone help?
By squaring both sides and solving for [tex]\(x\),[/tex] we find [tex]\(x = 4\)[/tex] as the solution, which is not extraneous upon substitution into the original equation.
To solve the equation [tex]\(\sqrt{2x + 1} = 3\),[/tex] we need to isolate[tex]\(x\).[/tex] Here's how:
1. Square both sides of the equation to eliminate the square root:
[tex]\[ (\sqrt{2x + 1})^2 = 3^2 \][/tex]
[tex]\[ 2x + 1 = 9 \][/tex]
2. Subtract 1 from both sides to isolate [tex]\(2x\)[/tex]:
[tex]\[ 2x = 9 - 1 \][/tex]
[tex]\[ 2x = 8 \][/tex]
3. Divide both sides by 2 to solve for [tex]\(x\)[/tex]:
[tex]\[ x = \frac{8}{2} \][/tex]
[tex]\[ x = 4 \][/tex]
Now, we have [tex]\(x = 4\)[/tex]. To determine if it's an extraneous solution, we need to check if it satisfies the original equation.
Substitute [tex]\(x = 4\)[/tex] into the original equation:
[tex]\[ \sqrt{2(4) + 1} = 3 \][/tex]
[tex]\[ \sqrt{9} = 3 \][/tex]
[tex]\[ 3 = 3 \][/tex]
Since the equation holds true, [tex]\(x = 4\)[/tex]is a valid solution, not an extraneous one.
Therefore, the solution to the equation [tex]\(\sqrt{2x + 1} = 3\) is \(x = 4\),[/tex]and it is not an extraneous solution.
Suppose y varies directly with x, and y=25 when x=140. What is the value of x when y=36?
108/250 in simplest form in a whole number.
how is a tangent different from a chord
Answer:
A tangent is a line, ray, or line segment that intersects a circle at exactly one point (called the point of tangency) and contains no points inside the circle. A chord is a segment with both endpoints on a circle. Tangents intersect the circle at one point, while a chord intersects at two.
I've checked this answer, E counted it as correct. Hope this helped!!!
A tangent touches a circle at one point, while a chord connects any two points on the circle's circumference.
A tangent and a chord are both important concepts in geometry, but they have distinct characteristics.
A tangent is a line that intersects a circle at exactly one point, touching the circle's circumference at that point.
It never crosses the circle. Tangents are perpendicular to the radius that intersects the point of tangency.
On the other hand, a chord is a line segment connecting any two points on a circle's circumference. Unlike tangents, chords can intersect the circle at multiple points.
The diameter is a special case of a chord that passes through the center of the circle.
Hence,
Tangents touch a circle at one point, while chords connect two points on a circle's circumference.
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What is eight dozen in standard form?
Point B is between A and C on segment AC. Use the given information to write an equation in terms of x. Solve the equations. Then find AB and BC.
AB= 3x; BC= x; AC= 20
AB= 2x-5; BC= 6x; AC= 27
AB= 4x+7; BC= 5x-8; AC= 53 ...?
In the given sets, the concept AB + BC = AC is used to create equations in terms of x. After each equation is solved, you can find the lengths of AB and BC by substituting the value of x into their respective original equations.
Explanation:For this mathematics problem, you have to make use of the concept that the sum of the parts equals the whole. Specifically, this concept translates to the equation AB + BC = AC, as AC is the entire segment that encompasses both parts AB and BC.
For each of the sets you provided:
Set 1: AB=3x, BC=x, AC=20. Your equation based on the concept we discussed will be 3x+x=20. By simplifying this, you'll get 4x=20 and, therefore, x=5. To find AB and BC, substitute x=5 into the individual equations. AB=3x=3*5=15 and BC=x=5. Set 2: AB=2x-5, BC=6x, AC=27. The equation in terms of x is now 2x-5+6x=27. Combining like terms results in 8x-5=27, and solving for x gives x=4. With x=4, AB=2x-5=2*4-5=3, and BC=6x=6*4=24. Set 3: AB=4x+7, BC=5x-8, AC=53. Use the formula to get the equation 4x+7+5x-8=53, which simplifies to 9x-1=53. Solving for x gives you x=6. Therefore, AB=4x+7=4*6+7=31 and BC=5x-8=5*6-8=22. Learn more about Setting up and Solving Equations here:
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40% of the students at Rockledge Middle School are musicians. 75% of those musicians have to read sheet music when they play their instruments If 38 of the students can play their instruments without reading sheet music, how many students are there at Rockledge Middle School?
he ages of four groups of workers are shown. Which group has the largest range?
Answer:
b
Step-by-step explanation:
Answer:
D) Group D
Step-by-step explanation:
A range: 38
B range: 48
C range: 40
D range: 51
Solve the equation.
6 = 2(x + 8) - 5x
A. 2/3
B. 3 1/3
C. - 2/3
D. -3 1/3
Over the past year, your friend Maura has been saving up for an epic road trip to travel across the country this summer. Her goal is to squeeze in as many sights as she can with her available budget of $2000.
Give an example of a sound financial decision Maura might make to support this goal. Why is it sound? Then give an example of a poor financial decision Maura might make considering her goal. Why is it a poor decision?
Are the graphs of −5y=2x+3 and y=25x+4 parallel, perpendicular, or neither?
The graphs of the system of equations −5y=2x+3 and y=25x+4 are neither parallel nor perpendicular.
What is a linear equation?It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.
It is given that:
The system of equations is:
−5y=2x+3 and y=25x+4
The slope of parallel graphs is the same. The reciprocal slopes of a perpendicular are opposite.
These equations are neither because they have slopes of 25 and -2/5.
Thus, the graphs of the system of equations −5y=2x+3 and y=25x+4 are neither parallel nor perpendicular.
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1. Miguel tosses a coin three times. which diagram represents the sample space of the three tosses?
Tree diagram can be used to represent the sample space. The correct option is option C.
What is a tree diagram?In probability, a tree diagram can be used to represent the sample space. Tree diagrams represent a series of independent events or conditional probabilities.
As it is given that the coin is tossed three times, therefore, the number of stages in the tree diagram will be three, where each time the coin is tossed will result in either heads or tails.
Now, the tree diagram of the coins can be drawn as shown below.
Further, comparing it with our diagram, the only possible option is option c where the number of levels in the tree is three and each toss result in either heads or tails.
Hence, the correct option is option C.
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If x = a + bi and y = –a – bi, x + y = 0
Answer:
inverse property
Laura was making a recipe that said the ingredients were for 6 people, but she needed to make it for 8 people. the recipe called for 2 2/3 cups of milk and 1/4 cup oil. how many of these liquid ingredients did she need for 8 people?
Answer:
[tex]3\frac{5}{9}[/tex] cups of milk and [tex]\frac{1}{3}[/tex] cups of oil for 8 people .
Step-by-step explanation:
Cups of milk for 6 people = [tex]2 \frac{2}{3} =\frac{8}{3}[/tex]
Cups of milk for 1 people = [tex]\frac{\frac{8}{3}}{6}=\frac{4}{9}[/tex]
Cups of milk for 8 people = [tex]\frac{4}{9} \times 8= \frac{32}{9}[/tex]
Cups of oil for 6 people = [tex]\frac{1}{4}[/tex]
Cups of oil for 1 people = [tex]\frac{\frac{1}{4}}{6}= \frac{1}{24}[/tex]
Cups of oil for 8 people = [tex]\frac{8}{24}=\frac{1}{3}[/tex]
Hence [tex]3\frac{5}{9}[/tex] cups of milk and [tex]\frac{1}{3}[/tex] cups of oil for 8 people .
Which is the correct description of the transformation of triangle JKL to triangle JꞌKꞌLꞌ?
A.a 90° clockwise rotation around point A of pre-image JKL
B.a 90° counterclockwise rotation around point A of pre-image JKL
C.a 180° clockwise rotation around point A of pre-image JKL
D.a reflection across point A of pre-image JKL
Answer:
A. 90° clockwise rotation around point A of pre-image JKL
Step-by-step explanation:
May I have brainliest please? :)
Statistics show that the sales force of Golden Wholesalers successfully closed 1,711 sales out of 1,950 sales calls. What was their percent success rate?
In 2005 at camp at 450 campers five years later the number of campers rose to 750 right now when you're equation that represents the number of campers that attend camp
Final answer:
To represent the number of campers attending the camp, use the equation y = mx + c, where y represents the number of campers, m represents the rate of increase, x represents the number of years, and c represents the initial number of campers. Using the given information, solve for the rate of increase (m) and initial number of campers (c). Substitute the values in the equation to find the number of campers attending the camp right now.
Explanation:
To represent the number of campers attending the camp right now, we can use the equation: y = mx + c, where y represents the number of campers attending the camp, m represents the rate at which the number of campers increase, x represents the number of years since 2005, and c represents the initial number of campers in 2005.
From the information provided, we know that in 2005 there were 450 campers and five years later, in 2010, the number of campers rose to 750. We can use these two points to find the values of m and c.
Using the formula: (y2 - y1) / (x2 - x1) = m, we can calculate the value of m as: (750 - 450) / (2010 - 2005) = 60. Therefore, the rate of increase is 60 campers per year. Now, we can substitute the values of m and c in the equation to find the number of campers attending the camp right now. y = 60x + 450.
The linear equation representing the number of campers attending camp each year, starting from 2005 with 450 campers and increasing by 60 campers per year, is C = 450 + 60t, where C is the number of campers and t is the number of years after 2005.
Explanation:In 2005, there were 450 campers at a camp. Five years later, the number of campers increased to 750. To represent the growth in the number of campers, we can write a linear equation. Assuming the number of campers increases at a constant rate each year, we first find the rate of increase.
Rate of increase per year = (Number of campers in 2010 - Number of campers in 2005) / (2010 - 2005)
Rate of increase per year = (750 - 450) / (5)
Rate of increase per year = 300 / 5 = 60 campers per year
Let's denote C as the number of campers and t as the number of years after 2005. The equation that represents the number of campers is:
C = 450 + 60t
This equation indicates that starting with 450 campers in 2005, every year there are 60 more campers attending the camp.
A bag contains 18 coins consisting of quarters and dimes. The total value of the coins is $2.85. Which system of equations can be used to determine the number of quarters, q, and the number of dimes, d, in the bag?
Answer:
Simultaneous Equation
Step-by-step explanation:
A bag contains 18 coins consisting of quarters and dimes. The total value of the coins is $2.85. Which system of equations can be used to determine the number of quarters, q, and the number of dimes, d, in the bag?
To get the number of dimes and the number of quarters q will definitely have to be by simultaneous equation
let the number of dimes be d
let the number of quarters be q
let the cost of quarters/ one be Q
let the cost of dime/one be D
q+d=18--------------1
Qq+Dd=2.85.........2
from equation 1
q=18-d
substituting the value of q into equation 2
Q(18-d)+Dd=2.85
if cost of quarters/ one is given and the cost of dime/one is also given we can go ahead to find
q and d
In this mathematical problem involving a system of equations, we use the information provided about the total number of coins and their total value to form two equations: q + d = 18 and 0.25q + 0.10d = 2.85.
Explanation:The subject of this question is Mathematics, specifically dealing with a system of equations. Given the problem, the system of equations can be formulated from the conditions that the student has 18 coins in total and their combined value is $2.85. These conditions give us two equations:
q + d = 18, this equation represents the total number of quarters (q) and dimes (d).0.25q + 0.10d = 2.85, this equation represents the total value of the quarters and dimes in the bag.Learn more about System of Equations here:
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Use substitution to solve the system
5x+4y=12
Y=2x-10
Locate the absolute extrema of the function on the closed interval:
y = 3x^(2/3) - 2x, [-1, 1]
The absolute maximum occurs at x = -1, where y = 5. The absolute minimum occurs at x = 1, where y = 1.
Explanation:To find the absolute extrema of a function on a closed interval, we first need to find the critical points of the function within that interval. The critical points occur where the derivative of the function is equal to zero or does not exist.
In this case, the function is y = 3x^(2/3) - 2x, and the closed interval is [-1, 1].
We can find the derivative of the function:
y' = 2x^(-1/3) - 2
Setting the derivative equal to zero and solving for x:
2x^(-1/3) - 2 = 0
x^(-1/3) = 1
Raising both sides to the power of -3 gives:
x = 1
We found one critical point at x = 1. Now we need to check the endpoints of the closed interval, which are -1 and 1. Evaluating the function at these points:
y(-1) = 3(-1)^(2/3) - 2(-1) = 5
y(1) = 3(1)^(2/3) - 2(1) = 1
Therefore, the absolute maximum of the function occurs at x = -1, where y = 5, and the absolute minimum occurs at x = 1, where y = 1.
five less than a number is at least -28 written as an inequality.
To write the inequality 'five less than a number is at least -28' in mathematical symbols, we need to assume the number is 'x' and express 'five less than a number' as 'x - 5'. We then represent 'at least -28' as '≥ -28'. By combining these expressions, we get the inequality x - 5 ≥ -28. To solve it, we add 5 to both sides to isolate the variable 'x' and obtain x ≥ -23.
Explanation:To write the inequality, we need to translate the phrase 'five less than a number is at least -28' into mathematical symbols. Let's assume the number is represented by 'x'. 'Five less than a number' can be written as 'x - 5'. The phrase 'at least -28' means the number has to be greater than or equal to -28, which can be written as '≥ -28'.
Putting it together, the inequality is: x - 5 ≥ -28.
To solve this inequality, we can add 5 to both sides to isolate the variable 'x'. This gives us: x ≥ -28 + 5, which simplifies to x ≥ -23.
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Please Help.
1. Population density is the number of people per unit of area. What is the population density of a state that has 1,627,260 people in 1,490 square miles? Round to the nearest whole number.
A. 10,521 per square mile
B. 1,050 per square mile
C. 1,092 people per square mile
D. 109 people per square mile
The correct answer is:C. 1,092 people per square mile
To calculate the population density of a state, we divide the total population by the total area. In this case, the state has 1,627,260 people living within 1,490 square miles. We perform the following calculation:
Population Density = Total Population / Total Area
Population Density = 1,627,260 people / 1,490 square miles
When we perform the division, we get approximately 1092.12 people per square mile. Rounding to the nearest whole number, we get a population density of 1,092 people per square mile.
Therefore, the correct answer is:C. 1,092 people per square mile