The number of minutes for 20 bacteria be left is 439minutes. The decay constant is 0.0081
What is exponential function?An exponential function is a mathematical function, which is used in many real-world situations. It is mainly used to find the exponential decay or exponential growth or to compute investments, model populations and so on.
The No of bacteria left at a particular time t is given as N(t)= Noe^-kt
where No= initial number of bacteria
k= decay constant and t = time
after 13 minutes
630= 700e^-13k
divide both sides by 700
630/700= e^-13k
0.9= e^-13k
ln0.9= -13k
k= ln0.9/-13 = -0.1054/-13 = 0.0081
time for 20 bacteria to be left =
20= 700e^-0.0081t
= 20/700=e^-0.0081t
0.0286= e^-0.0081t
ln0.0286= -0.0081t
-3.554= -0.0081t
divide both sides by -0.0081
t= -3.554/-0.0081= 439 minutes ( nearest minutes)
therefore the time for the bacteria to be left is 439minutes
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Factor 100x² 140xy + 49y²
Answer:
100 times square times Y 49 gives= 14000
Describe the function‘s end behavior. f(x)=−10+2x^5−9x^3
as x→∞,f(x)→
as x→−∞,f(x)→
The function‘s end behavior is falls to the left and rises to the right.
The given function is [tex]f(x)=-10+2x^5-9x^3[/tex].
What is the function?Functions are the fundamental part of the calculus in mathematics. The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x.
Use the degree and the leading coefficient to determine the behavior.
Falls to the left and rises to the right.
Find where the first derivative is equal to 0 to find the local maxima and minima.
x =−3√30/10 is a local maximum
x = 3√30/10 is a local minimum
Therefore, the function‘s end behavior is falls to the left and rises to the right.
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Cindy is attempting to calculate how much her car payment would be for a car that costs $27,000 to be repaid with monthly payments in 4 years at 4% APR.
Cindy's monthly payment of $609.63 will cost her $29,262.24 in 4 years at a 4% APR.
How is the total cost determined?The total cost that Cindy will spend on the car which costs $27,000 is computed by multiplying the monthly payment by 48 months (the payment period).
The monthly payment can be determined using an online finance calculator that compounds the interest rate monthly for four years.
Cost of car = $27,000
Annual Percentage Rate (APR) = 4%
Payment period = 4 years (monthly)
N (# of periods) = 48 months (4 years x 12)
I/Y (Interest per year) = 4%
PV (Present Value) = $27,000
FV (Future Value) = $0
Results:
PMT = $609.63
Sum of all periodic payments = $29,262.24
Total Interest = $2,262.45
Thus, Cindy will spend $29,262.24 for a car that costs $27,000, if she repays monthly for 4 years.
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A quality control activity analysis indicated the following four activity costs of a hotel. Verifying credit card information $189,800 Customer service training 379,600 Discounting room rates due to poor customer service 94,900 Correcting charges to customer invoices 284,700 Total $949,000
The percentage of the quality cost, that is taken up by the prevention and appraisal costs are:
Prevention cost - 40%Appraisal cost - 20%How to find the percentage of cost?The prevention cost would be the cost associated with customer service training as this ensures that less mistakes are made.
The appraisal cost would be the cost to verify credit card information.
The percentage of total quality control cost that prevention cost is, would be:
= 379, 600 / 949, 000 total
= 40 %
The percentage for appraisal cost is:
= 189, 800 / 949, 000
= 20 %
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The rest of the question is:
Present the percentage values of prevention and appraisal as a percentage of the quality cost.
In which quadrant is the number 5i located on the complex plane?
The number 5i located on the complex plane in I Quadrant.
What is Complex Plane?
The real axis and the imaginary axis are the graph's horizontal and vertical axes, which are orthogonal (or perpendicular). The labels Re and Im are typically present. The complex plane is the plane defined by these coordinates.
We are aware that in a two-dimensional plane, an ordered pair's x- and y-coordinates are treated as the real and imaginary parts of the complex number, respectively.
i.e., a+bi=(a,b) -- Quadrant I,
-a+bi=(-a,b) -- Quadrant II,
a-bi=(a,-b) -- Quadrant III
and
-a-bi=(-a,-b) -- Quadrant IV
The complex number that is being presented is 5i, aland it is located in quadrant I.
As a result, the complex number in question belongs in Quadrant I.
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An exponential function will have:
Answer:
Exponential functions have the form f(x) = bx, where b > 0 and b ≠ 1.
Step-by-step explanation:
At this rate, if Candidate A received 45 votes, how many votes did Candidate B receive?
The number of votes that Candidate B received, given the rate and the votes received by Candidate A, is 63 votes
How to find the number of votes?The question shows that for every 5 votes received by Candidate A, Candidate B will receive 7 votes.
This means that if Candidate A has 45 votes, the number of votes that Candidate B would receive can be found to be :
= Number of votes received by Candidate A / Number of votes Candidate A receives per Candidate B x Number of votes Candidate B receives per Candidate A
= 45 / 5 x 7
= 9 x 7
= 63 votes
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The first part of the question is:
Candidate A receives about 5 votes for every 7 votes received by Candidate B.
Find x:
X=________________
Assuming [tex]\overline{BC}[/tex] is a diameter, minor arc [tex]AB[/tex] has a measure of [tex]180^{\circ}-108^{\circ}=72^{\circ}[/tex].
Using the inscribed angle theorem, [tex]36=x+3 \implies x=\boxed{33}[/tex].
Use the graph or table to find the equation that represents the relationship.
The linear equations that represent the relationships in the question order are;
y = 4·x - 1y = -x + 4[tex]y = \frac{1}{4} \cdot x -1[/tex][tex]y = -x + \frac{1}{4}[/tex]What is a linear equation?A linear equation is an equation of the form; y = m·x + c
The slope of the line is found as follows;
(-5 - (-21))/(-1 - (-5)) = 4
The equation is y - (-5) = 4·(x - (-1)) = 4·x + 4
y = 4·x + 4 - 5 = 4·x - 1
y = 4·x - 1The y-intercept is (0, 4), the x-intercept is (4, 0)
The slope is therefore; (0 - 4)/(4 - 0) = -1
The equation is therefore; y - 0 = -1 × (x - 4) = -x + 4
y = -x + 4The y-intercept is (0, -1), the x-intercept is (4, 0)
The slope is therefore; (0 - (-1))/(4 - 0) = 1/4
The equation is therefore; y - 0 = (1/4) × (x - 4) = x/4 - 4/4 =
y = x/4 - 1The slope of the line is; [tex]\dfrac{-3\frac{3}{4} - \left(-\frac{3}{4}\right) }{4-1} = -1[/tex]
y - (-3/4) = -1 × (x - 1) = -x + 1
y = -x + 1 - (3/4) = -x + 1/4
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Fill in the t-table below for the equation. Then graph the line on the grid by selecting two of the points
from your table.
y=-3x - 4
X
-1
0
1
y
The complete table of values of the linear equation y = -3x - 4 is
x y
-1 -1
0 -4
1 -7
How to complete the table of values?From the question, we have the following parameters that can be used in our computation:
y = -3x - 4
Also, we have the following table of values
x y
-1
0
1
The above table of values mean that the x values are
x = -1, 0 and 1
Substitute x = -1, 0 and 1 in the equation y = -3x - 4
So, we have the following representation
When x = -1
y = -3(-1) - 4 = -1
When x = 0
y = -3(0) - 4 = -4
When x = 1
y = -3(1) - 4 = -7
So, we have the following ordered pairs
(-1, -1), (0, -4) and (1, -7)
When represented on the table of values, we have
x y
-1 -1
0 -4
1 -7
The above represents the complete table of values
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The admission fee at a local zoo is $1.50 for children and $5.00 for adults. On a certain day, 3700
people enter the zoo and
$11, 500.00 is collected. How many children and how many adults
attended?
How many children attended?
How many adults attended?
Determine which set of ordered pairs represent a
Function and justify your selection.
{(-1,4), (2, 4), (8,4), (10,4)}
{(0, -2), (3, 7), (0, 2), (18,2))
{(-1,3), (-1,-1), (-1,-12), (-1,0)}
{(1, 2), (2, 3), (3, 4), (3,5)}
Justification: (What is your reasoning?)
Answer:
{(-1,4), (2, 4), (8,4), (10,4)}
all of the x-values are different
Step-by-step explanation:
The other three options have duplicate x-values with different y-values.
Ms. Rios mowed
1
4
of her lawn. Her son mowed
3
7
of it. Who mowed most of the lawn? How much of the lawn still needs to be mowed?
Her son mowed the most lawn
35%of the lawn meeds to be mowed
What is square root of -36 classified as
Answer:
undefined
Step-by-step explanation:
The square root of any negative number is undefined because there is no possible solution. - × - = + and + × + = +
Consider the expression 4x^2+x+34x 2 +x+34, x, squared, plus, x, plus, 3. Complete 222 descriptions of the parts of the expression.
[tex]72x^{2}+3x+3[/tex]Answer:
Step-by-step explanation:
[tex]1. (4x^{2}+34x^{2} +34x^{2} )+(x+x+x)+3\\ 2. 72x^{2} +3x+3[/tex]
A small toy rocket is launched from a 18-foot pad. The height (h, in feet) of the rocket t seconds after
taking off is given by the formula h = - 3t^2 + 3t+18. How long will it take the rocket to hit the
ground?
The time it would take the rocket to hit the ground upon launch is; 3 seconds.
At what time does the rocket hit the ground?It follows from the task content that the time taken for the rocket in discuss to hit the ground upon launch is to be determined.
Since the given formula for the height in terms of time, t is;
h = - 3t² + 3t + 18
It follows that ; when the rocket hits the ground; the height; h = 0.
Therefore;
0 = - 3t² + 3t + 18
0 = -3t² + 9t - 6t + 18
0 = -3t ( t - 3 ) - 6 ( t - 3)
-3t - 6 = 0 OR. t - 3 = 0.
t = -2. OR. t = 3.
Therefore, since the time after launch can only be positive; the time taken for the rocket to hit the ground is; 3 seconds.
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How do you find equivalent in math?
To find equivalent expression in math is the fractions with distinct numerators and denominators but the same value are said to be equivalent fractions.
In mathematics, equivalent fractions are those with the same denominator and differing numerators.
The multiplicity of a member of a multiset in mathematics is the number of times the member appears in the multiset. The multiplicity of a root, for instance, is how many times a given polynomial has a root at a particular point.
It's crucial to understand the concept of multiplicity in order to correctly count without mentioning exceptions (for example, double roots counted twice). Thus, "counted with multiplicity" is used.
This can be highlighted by counting the number of different elements, as in "the number of separate roots," if multiplicity is disregarded. However, multiplicity is always taken into account when a set (as opposed to a multiset) is established, therefore the word "different" is not necessary.
For instance, if we simplify 5/15, we get a fraction that is equal to 1/3, which is equal to 5/15.
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Emy has 13 1/4 kilograms of sweet potatoes.She gave away 5 12 kilogramsof corn to her neighbors.how many kilograms of corn than potatoes did she gave away?
Answer:
2 1/4 kg
Step-by-step explanation:
Use the discriminant to determine how many and what kind of solutions the quadratic equation 2x^2 - 4x = -2 has.
Please explain how you got the solution.
20 Points! Thanks!
Answer: One Real Solution
We can Identify the coefficients a, b, and c from your equation because as it says, it is in the format of the quadratic equation ( ax^2 + bx + c = 0 )
a=2,b=-4,c=2
Now we can use the discriminant to determine how many solutions this has using the equation b^2 - 4ac
Once we plug in our coefficients:
(-4)^2 - 4 x 2 x 2
Once we simplify, we get 0.
One real solution.
I hope this helps.
In this case, we first need to simplify the given quadratic equation 2x² - 4x = -2, and to do so, we perform the following simplification steps:
For a quadratic equation of the form ax² + bx + c = 0, the discriminant is calculated using the following formula:
Δ = b² - 4ac
In this case, we have that the equation that we must solve is 2x²-4=-2, which implies that the corresponding coefficients are:
a = 2b = -4c = 2By introducing these values into the formula we get:
Δ = b² - 4ac = (-4)² - 4·(2)·(2) = 0
Therefore, the discriminant for the given quadratic equation is Δ=0=0, which is zero, and indicates that the equation 2x²-4=-2 has only one real root.
We can say: It has a Real solution.Gloria is preparing to visit her grandmother in Florida and needs to buy some new clothes for the trip. She buys 3 t shirts and pays $48
How much would she pay for 1 t shirt?
How much would she pay for 5 t shirts?
Answer:
Step-by-step explanation: How much is 1 t shirt
Choose the symbol that correctly compares these numbers.
18.6? 18.7
O A. <
OB. =
O C. >
Answer: A
Step-by-step explanation:
18.6 is less than 18.7
so 18.6<18.7
A rectangular yard measuring 35 ft by 55 ft is bordered (and surrounded) by a fence. Inside, a walk that is 3 ft wide goes all the way along the fence. Find the area of this walk. Be sure to include the correct unit in your answer.
The area of walk is 504 square feet
Area of rectangleThe area of rectangle is define as a product of length L and width w
calculate the area of rectangle yard
Area = L x W,
where A equal the Area, L equals the length and W equal width.
A = 35 x 55
A= 1925 square feet
Area of the rectangular yard is 1925 square feet
From the question, we have 3ft wide goes all the way along the fence inside.
Therefore, we subtract six feet from each of the value of length ( 35) and width (55) because each side has 3feet .
Area = L x W
A = 29 x 49
A = 1421 square feet
Area of new rectangle formed by allowing for three foot walk is 1421 square feet
Area of Walk
To get the area walk; we subtract area of new rectangular formed from area of rectangular yard
Area of Walk = Area of Rectangular yard - Area of new rectangle
Area of Walk = 1925 - 1421
Area of Walk = 504 square feet.
Therefore, the area of walk is 504 square feet.
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The table shows the lengths of hiking trails. It took Lannie 1.9 hours
to hike Ranger Cove Trail. It took Ava 4 hours to hike Mohawk Trail.
Write and solve an equation to find the average hiking rate for
Lannie. Write and solve an equation to find the average hiking rate
for Ava. What is the difference between their average hiking rates?
Round to the nearest tenth.
The difference between their average hiking rates is 0.51 miles/hour.
Given that, it took Lannie 1.9 hours to hike Ranger Cove Trail. It took Ava 4 hours to hike Mohawk Trail.
What is the speed?The speed formula can be defined as the rate at which an object covers some distance. Speed can be measured as the distance travelled by a body in a given period of time. The SI unit of speed is m/s.
Using speed =Distance/Time
Here, Ranger Cove distance =4.8 miles and time =1.9 hours
Now, rate =4.2/1.9
= 2.21 miles/hour
Mohawk Trail distance =6.8 miles and time =4 hours
Now, rate =6.8/4
= 1.7 miles/hour
The difference between their average hiking rates
= 2.21-1.7
= 0.51 miles/hour
Hence, the difference between their average hiking rates is 0.51 miles/hour.
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Slope = ½; (h, k) = (1, -2) find the slope-point
The linear equation with a slope of 1/2 and that passes through the point (1, -2) is written in point-slope form as:
y = (1/2)*(x - 1) - 2
How to find the equation of the line?For a linear equation with a slope m and a known point (h, k), the slope-point form is written as:
y = m*(x - h) + k
Where y and x are the two variables.
Here we know that the slope is 1/2, and the known point is (1, -2), then the values on the equation above are:
m = 1/2
h = 1
k = -2
Replacing that in the general formula for the linear equation in the slope-point form that is written above, we will get:
y = (1/2)*(x - 1) - 2
That is what we wanted to find.
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y.y^3.y^2 pleas help me and spread the gospel of God
Answer:
[tex]y^6[/tex]
Step-by-step explanation:
1) Use Product Rule: [tex]x^ax^b=x^{a+b}[/tex].
[tex]y^{1+3+2[/tex]
2) Simplify 1 + 3 to 4.
[tex]y^{4+2}[/tex]
3) Simplify 4 + 2 to 6.
[tex]y^6[/tex]
Thank you,
Eddie
someone pls help me m = -0.5d + 5
Answer:
Step-by-step explanation:
1) Subtract 5 from both sides.
[tex]m-5=-0.5d[/tex]
2) Divide both sides by -0.5.
[tex]-\frac{m-5}{0.5} =d[/tex]
3) Switch sides.
[tex]d=-\frac{m-5}{0.5}[/tex]
Thank you,
Eddie
¿cuál es el área en cm² de la base de un prisma que tiene una altura de 51 cm y un
volumen de 245,8 cm³?
Respuesta:
On solving the given question, we got Area of the base prism = bh/2 = (4.819 X 51)/2 = 122.89 cm2
What is a prism?A prism is a polyhedron in geometry that has an n-sided polygonal basis, a second base that is a shifted version of the first base, and n additional faces—necessarily all parallelograms. Connect the matching sides of the two bases.
h = 51 cm
a = 2cm
therefore,
volume of a Triangular Prism = (½) abh cubic cm
245.8 = [tex]\frac{1}{2}[/tex] X 2 X b X 51
[tex]= > b = \frac{245.8 X 2}{2 X 51}[/tex]
[tex]= > b = \frac{491.6}{102}[/tex]
[tex]= > b = 4.819[/tex]
Now Area of base of prism
Area of the base prism = bh/2 = (4.819 X 51)/2 = 122.89 cm2
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Need help pls on maths question
Answer please anyone help same doubht
Step-by-step explanation:
Answer:
Refer to the photos taken.
Step-by-step explanation:
You recently joined a gym. You had to pay a joining fee of $40, and you will pay $20 per month to maintain the membership. Part A (6 points) Write an equation in slope-intercept form that represents the cost of the membership in relation to time.
The cost of the membership is the initial joining fee plus the cost per month multiplied by the number of months.
If the cost after [tex]m[/tex] months is [tex]c[/tex] dollars, then [tex]c=20m+40[/tex].
Select the correct answer.
Which exponential equation is equivalent to this logarithmic equation?
log^5 x - log^5 25 = 7
Answer:
[tex]\textsf{D.} \quad 5^9=x[/tex]
Step-by-step explanation:
Given logarithmic equation:
[tex]\log_5x-\log_525=7[/tex]
[tex]\textsf{Apply the quotient log law}: \quad log_ax - \log_ay=\log_a \left(\dfrac{x}{y}\right)[/tex]
[tex]\implies \log_5\left(\dfrac{x}{25}\right)=7[/tex]
[tex]\textsf{Apply log law}: \quad \log_ab=c \iff a^c=b[/tex]
[tex]\implies 5^7=\dfrac{x}{25}[/tex]
Multiply both sides by 25:
[tex]\implies 25 \cdot 5^7=x[/tex]
Rewrite 5 as 5²:
[tex]\implies 5^2 \cdot 5^7=x[/tex]
[tex]\textsf{Apply exponent rule}: \quad a^b \cdot a^c=a^{b+c}[/tex]
[tex]\implies 5^{2+7}=x[/tex]
[tex]\implies 5^9=x[/tex]
