Performing an elementary row operation on a matrix does not change its determinant.
An elementary row operation is a transformation of a matrix that involves interchanging two rows, multiplying a row by a nonzero scalar, or adding a scalar multiple of one row to another row.
Let A be a matrix and let B be the matrix obtained from A by performing an elementary row operation. We want to show that det(A) = det(B).
If the row operation involves interchanging two rows, then the determinant of the resulting matrix is the negative of the determinant of the original matrix.
If the row operation involves multiplying a row by a nonzero scalar, then the determinant of the resulting matrix is the scalar multiplied by the determinant of the original matrix.
If the row operation involves adding a scalar multiple of one row to another row, then the determinant of the resulting matrix is the same as the determinant of the original matrix.
In any case, the determinant of the matrix is preserved under elementary row operations. Therefore, performing an elementary row operation on a matrix does not change its determinant.
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reflect shape A in the line x=-2
The mirror line will be on -2 on the x axis. Then from that, you reflect the shape
suppose that the probability that your mail is delivered before 2pm is .90 what is the probability that your mail will be delivered before 2pm for 2 consecutive days
The probability that your mail will be delivered before 2 pm for 2 consecutive days is 0.81.
Given,
The probability that your mail is delivered before 2 pm is 0.90.
To find:The probability that your mail will be delivered before 2 pm for 2 consecutive days
Probability that your mail will be delivered before 2 pm for 1 day = 0.90
Probability that your mail will be delivered before 2 pm for 2 consecutive days = P(1st day before 2pm) and
P(2nd day before 2pm)P(1st day before 2pm) and P(2nd day before 2pm) = 0.90 × 0.90= 0.81
Hence, The probability that your mail will be delivered before 2 pm for 2 consecutive days is 0.81.
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1.
Is the relation a function? Why or why not?
{(3, –1), (3, 0), (–3, 4), (3, 8)}
Yes; only one range value exists for each domain value.
No; the relation passes the vertical-line test.
No; three range values exist for domain value 3.
Yes; three range values exist for domain value 3.
The relation is not function . Because C)No; three range values exist for domain value 3.
What is function?
A mathematical phrase, rule, or law that establishes the link between an independent variable and a dependent variable (the dependent variable). In mathematics, functions exist everywhere, and they are crucial for constructing physical links in the sciences.
The given coordinates are {(3, –1), (3, 0), (–3, 4), (3, 8)}.
Here if 3 is output and -1 is input. We know that every function should have unique output.
In the given coordinates , we have 3 for three values.
Hence the correct option is C)No; three range values exist for domain value 3.
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what are the odds of answering at least 9 questions correctly out of 15 by choosing at random (and all questions are multiple choice and have 4 choices) ?
The odds of answering at least 9 questions correctly out of 15 by choosing at random is approximately 0.120
To solve this problem, we can use the binomial distribution, which models the probability of getting a certain number of successes in a fixed number of independent trials, each with the same probability of success.
In this case, we have 15 independent trials (the 15 questions) and the probability of success in each trial is 1/4 (the probability of guessing the correct answer among 4 choices). We want to find the probability of getting at least 9 successes.
Using a binomial distribution calculator, we can calculate this probability as
P(X ≥ 9) = 1 - P(X < 9) = 1 - binomcdf(15, 1/4, 8) ≈ 0.120
where binomcdf is the cumulative distribution function of the binomial distribution, which gives the probability of getting up to a certain number of successes (in this case, up to 8). The complement of this probability (1 minus the probability of getting up to 8 successes) gives the probability of getting at least 9 successes.
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Classify each number as rational or irrational.
Drag the choices into the boxes to correctly complete the table.
Answer:
only [tex]\sqrt{101}[/tex] is irrational
Step-by-step explanation:
an irrational number cannot be expressed as a fraction
0.329 = 329/1000
127.5 = 1275/10
-89 = -89
[tex]\sqrt[3]{64}[/tex] = 4
In a diagram, ∠A and ∠B are vertical angles, and ∠B is a complementary angle with ∠C. If ∠A=22°, write an equation that you can use to solve for ∠C.
THANK YOU SO MUCH <333
Answer:
[tex]22^\circ + m\angle C = 90^\circ[/tex]
Step-by-step explanation:
Pre-Solving:
We are given that [tex]\angle A[/tex] (which is equal to 22°) and [tex]\angle B[/tex] are vertical angles, and that [tex]\angle B[/tex] is complementary to [tex]\angle C[/tex].
We want to write an equation that will help us solve [tex]\angle C[/tex].
Solving:
Recall that vertical angles are congruent by vertical angles theorem.
This means that [tex]\angle A \cong \angle B[/tex]; it also means that the measure of [tex]\angle B[/tex] is also 22°.
Also recall that complementary angles add up to 90°.
This means that [tex]m\angle B + m\angle C = 90^\circ[/tex].
Since we deduced that [tex]m\angle B[/tex] is 22°, we can substitute that value into the equation.
Hence, an equation that can be used to solve for [tex]\angle C[/tex] is:
[tex]22^\circ + m\angle C = 90^\circ[/tex]
Answer:
m∠A = m∠B
m∠A = 22°
m∠B + m∠C = 90°
Step-by-step explanation:
∠A and ∠B are vertical angles. (Given)
By definition of vertical angles, a pair of angles with the same vertex and that are on opposite sides of two intersecting straight lines are congruent.
It is given that ∠A is 22°, and is a vertical angle with ∠B.
∴ ∠A ≅ ∠B (Definition of Vertical Angles).
IF m∠A = 22° and ∠A ≅ ∠B, THEN m∠B = 22° (Transitive Property of Equality).
∠B is complementary with ∠C (Given)
m∠B + m∠C = 90° (given).
m∠B = 22° (⇒Transitive Property of Equality)
Plug in 22 for m∠B in the given equation:
22 + m∠C = 90
Isolate the term, m∠C. Note the equal sign, what you do to one side, you do to the other. Subtract 22 from both sides of the equation:
m∠C + 22 (-22) = 90 (-22)
m∠C = 90 - 22
m∠C = 68°
~
Therefore, your system of equation will be:
m∠A = m∠B
m∠A = 22°
m∠B + m∠C = 90°
~
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Omar invests £2800 for 3 years at 1.75% simple interest per year.
How much is the investment worth at the end of the 3 years?
Answer:
£2947
Step-by-step explanation:
the formula for simple interest is interest = prt.
p is the principal value, or what omar had at the beginning.
r is the rate at that you gain interest.
t is the amount of time in years.
so, plugging in our values, we multiply 2800*3*0.0175 to get 147.
now, since that was the amount of interest omar gained, we still have to add the original amount that he had, and 2800+147 = 2947.
so, the answer is £2947.
Crook Island is 25 km due east of the Isle of Strutay.
Grass Rock is 21 km due south of Crook Island.
Emerald Cay is 19 km due east of Grass Rock.
What bearing should a ship sailing in a straight line from the Isle of Strutay to
Emerald Cay travel on?
Give your answer in degrees to 1 d.p.
The ship sailing in a straight line from the Isle of Strutay to Emerald Cay should travel on a bearing of approximately 72.6°.
How to calculate the bearingWe can use the Law of Cosines to find this angle. Let's call this angle θ.
cos θ = (a² + b² - c²) / (2ab)
where a is the distance between the Isle of Strutay and Crook Island (25 km), b is the distance between Crook Island and Emerald Cay (40 km), and c is the distance between the Isle of Strutay and Emerald Cay (65 km).
cos θ = (25² + 40² - 65²) / (2 x 25 x 40)
cos θ = 0.275
θ = cos⁻¹(0.275)
θ ≈ 72.6°
Therefore, the ship sailing in a straight line from the Isle of Strutay to Emerald Cay should travel on a bearing of approximately 72.6° (east of north).
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2.2 When we simplify surds. we often leave a square-root or cube-root in the denominator. However, the calculator rationalizes the answer so that there is no surd in the denominator. With that said. rationalise and also solve for x in the following: √√√4 + x = 3 3 1-√2 b.
a. To rationalize the expression √√√4 + x = 3 3, we need to get rid of the cube roots in the denominator.
First, we simplify the cube root of 4:
√√√4 = √√2
So, our expression becomes:
√√2 + x = 3 3
To get rid of the cube root in the denominator, we need to multiply both sides by the conjugate of the denominator:
(3 - √2)(√√2 + x) = 3
Expanding the left side:
3√√2 + 3x - 2√2 - √2√√2x = 3
Simplifying:
3x - 2√2 - √2√√2x = 3 - 3√√2
Combining like terms:
(3 - √2)x = 3 - 3√√2 + 2√2
Simplifying:
(3 - √2)x = (3 + 2√2) - 3√√2
Dividing both sides by (3 - √2):
x = [(3 + 2√2) - 3√√2]/(3 - √2)
Simplifying:
x = (3 + 2√2)(3 + √2)/7
b. To rationalize and solve for x in the expression 1-√2:
We need to get rid of the radical in the denominator by multiplying both the numerator and denominator by its conjugate:
1 - √2 / 1 - √2 * 1 + √2 / 1 + √2
Simplifying, we get:
(1 - √2)(1 + √2) / (1 - √2)(1 + √2)
= 1 - 2
= -1
So, x = -1.
Therefore, the rationalized expressions are:
a. √√2 + x = (3 + 2√2)(3 + √2)/7
b. 1-√2 = -1
I need help!
What is the perimeter of the rectangle pictured below? Show all work for full credit.
Answer:
≈38.57 units.
Step-by-step explanation:
To find the perimeter of a rectangle, we need to add up the lengths of all its sides.
First, gather the coordinates:
R - (4, 5)
U - (8, -3)
F - (-6, 0)
O - (-2, -8)
Using the coordinates given, we can calculate the lengths of the sides of the rectangle using the distance formula:
d = √((x2 - x1)^2 + (y2 - y1)^2)
So, for the rectangle with vertices R, U, F, and O, we have:
Side RU: d = √((8 - 4)^2 + (-3 - 5)^2) = √(16 + 64) = √80
Side UF: d = √((-6 - 8)^2 + (0 - (-3))^2) = √(196 + 9) = √205
Side FO: d = √((-6 - (-2))^2 + (0 - (-8))^2) = √(16 + 64) = √80
Side OR: d = √((-2 - 4)^2 + (-8 - 5)^2) = √(36 + 169) = √205
Since opposite sides of a rectangle are congruent, we have RU = FO and UF = OR. Therefore, the perimeter of the rectangle is:
Perimeter = RU + UF + FO + OR
Perimeter = √80 + √205 + √80 + √205
Perimeter ≈ 38.57
Therefore, the perimeter of the rectangle is approximately 38.57 units.
You are making saltwater taffy. In total, you’ve received 66 pounds of saltwater taffy from this batch. You split the batch into 3-pound bags of taffy. How many bags of saltwater taffy did you receive from this batch?
help asap will give brainliest!
The exact value of the volume of the sphere is V = 20.833π cm³ and the exact value is V = 64.45 cm³
What is the volume of the Sphere?A sphere is defined as symmetrical and round in shape. It is also referred to as a three dimensional solid, that has all its surface points at equal distances from the center.
The formula for the volume of a sphere is:
V = ⁴/₃πr³
where:
V = volume
r = radius
The radius of a sphere is half its diameter.
We are given diameter = 5cm
Thus: r = 5/2 = 2.5 cm
V = ⁴/₃π * 2.5³
V = 20.833π cm³
V = 64.45 cm³
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I NEED HELP PLEASE
Number 6,7,8
Is it open or closed?
The part 7 is closed and the part 8 is not closed where as the part 6 is neither open nor closed.
What is close polynomial and open polynomial?
The terms "closed polynomial" and "open polynomial" are not commonly used in mathematics. However, we can talk about sets of polynomials being open or closed.
In general, a set of polynomials is said to be open if, for any polynomial in the set, there is a small "neighborhood" of polynomials around it that is also contained in the set. Intuitively, this means that the set "opens up" in all directions around any point in the set.
A set of polynomials is said to be closed if it contains all of its limit points. In other words, if a sequence of polynomials in the set converges to a polynomial outside of the set, then that polynomial must be added to the set to make it closed.
For example, the set of all quadratic polynomials with a nonzero discriminant is closed under addition, scalar multiplication, and multiplication of polynomials, so it is a closed set. The set of all cubic polynomials with real coefficients is an open set, since for any cubic polynomial, we can find a small "neighborhood" of cubic polynomials around it by adjusting the coefficients slightly.
6.The polynomial set {(x² + x − 4) - (x²+x+8)} is equivalent to the set {-12}. A single point set like this is neither open nor closed in the usual topologies on the real numbers.
7.The polynomial set (2-x)(1 + 3x) is the set of all polynomials of degree at most 2 with a leading coefficient of -3. This set is closed under addition, scalar multiplication, and multiplication of polynomials, so it is a closed set.
8.The polynomial set (5b-3c)(7b - 3c) is equivalent to the set {25b² - 36bc + 9c²}, which is the set of all quadratic polynomials in b and c with a nonzero discriminant. This set is not closed under addition, since the sum of two polynomials in this set can have a zero discriminant. Therefore, it is not a closed set.
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6^-5 in expanded form?
Answer: To write 6^-5 in expanded form, we need to first recall the definition of negative exponents. If a number a is raised to a negative exponent, it means that we take the reciprocal of a raised to the absolute value of the exponent. In other words:
a^(-n) = 1 / a^n
Using this definition, we can write:
6^-5 = 1 / 6^5
Now, we can expand 6^5 using repeated multiplication or by using a calculator. 6^5 means 6 multiplied by itself five times:
6^5 = 6 × 6 × 6 × 6 × 6 = 7776
Therefore, we can write:
6^-5 = 1 / 6^5 = 1 / 7776
So, the expanded form of 6^-5 is 1/7776.
Step-by-step explanation:
27, Two of the smallest mammals on Earth
are the bumblebee bat and the Etruscan
pygmy shrew. How much shorter is the
bat than the shrew?
Therefore, the bumblebee bat is 0.5 centimeters shorter than the Etruscan pygmy shrew.
What is inequality?Inequalities are used in many areas of mathematics, including algebra, calculus, and geometry. They are also used in other fields such as economics, physics, and engineering to model real-world situations where values can vary within certain bounds. Solving inequalities involves finding the set of values that satisfy the inequality. This can be done using algebraic techniques such as adding or subtracting the same quantity from both sides of the inequality, multiplying or dividing both sides of the inequality by a positive number, or using the properties of absolute value. The solution to an inequality is often expressed as an interval or a set of numbers that satisfy the inequality.
Here,
According to the Guinness World Records, the bumblebee bat is the smallest mammal in the world, measuring only about 3 centimeters in length, while the Etruscan pygmy shrew measures about 3.5 centimeters in length.
To find out how much shorter the bat is than the shrew, we can subtract the length of the bat from the length of the shrew:
3.5 cm - 3 cm = 0.5 cm
The bumblebee bat and the Etruscan pygmy shrew are both very small mammals, but the bumblebee bat is actually shorter than the Etruscan pygmy shrew.
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SOMEONE HELP ASAP!!!!
what is an expression for the sum of m and 10
Answer:
x=m+10
Step-by-step explanation:
Ur just making it into an equation
:)
in a game of chance, the probability of winning $50 is 40 percent and the probability of having to pay $50 is 60 percent. what is the expected value of this game? select answer from the options below -$10 $0 $10 $25
In a game of chance, the probability of winning 50 is 40 percent and the probability of having to pay 50 is 60 percent. Therefore, the expected value of this game is -10. The correct answer is option A.
To find out what the expected value of this game is, we will need to use the formula:
Expected value (E) = (probability of winning x amount won) - (probability of losing x amount lost)
Let's substitute the values given in the question:
Probability of winning = 0.4
Amount won = 50
Probability of losing = 0.6
Amount lost = 50
Expected value (E) = (0.4 x 50) - (0.6 x 50)
= 20 - 30
= -10
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Find the number of sides of a polygon if the sum of the measures of its interior angles is twice the sum of the measures of its exterior angles.
Answer:
n=6 sides
Step-by-step explanation:
We know that the sum of Interior angles of Polygon = 180(n-2)
Sum of Exterior angles of Polygon = 360
so 180(n-2)=2x360
Therefore, by solving we get n=6 sides.
The number of sides of a regular polygon is 6 sides.
What is the formula for interior angle of a regular polygon?The formula for calculating the sum of interior angles is (n-2)×180° where is the number of sides. All the interior angles in a regular polygon are equal. The formula for calculating the size of an interior angle is: interior angle of a polygon = sum of interior angles ÷ number of sides.
Given that, the sum of the measures of its interior angles is twice the sum of the measures of its exterior angles.
We know that, the sum of the measures of its exterior angles is 360°.
Now, the sum of the measures of its interior angles
= 2×360°
= 720°
Now, (n-2)×180°=720°
n-2=4
n=6
Therefore, the number of sides of a regular polygon is 6 sides.
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Giving 26 brainly points
Review
Directions: Simplify the following by subtracting the exponents.
1.
8r6
__
8r
2.
s5t4
____
s2t3
3.
3q2r2s
____
3qrs
4.
x3y6z
_____
x2y2z
5.
m7n3o
_____
m2n2o
6.
x4
___
x
7.
z3
___
z5
8.
a3b2
_____
ab2
9.
d4f3
_____
df
10.
mn2
_____
mn2
11.
10c5d6
______
10c4d3
12.
b8c4d2
________
b5c4d2
13.
xy
___
xy
14.
s2t4
_____
st
15.
m2n2
______
m4n4
Answer:
can you like write it out normally please, i can answer it then
Step-by-step explanation:
Suppose a ring that is 20 millimeters
in diameter has to be resized to fit a finger 16 millimeters in
diameter. What is the length of the bar that should be inserted
in order to make the ring fit the finger?
The length οf the bar that shοuld be inserted tο make the ring fit the finger is apprοximately 12.57 millimeters.
What is length οf the bar?Length οf bar = π × (new diameter - οriginal diameter), where π is the cοnstant pi, and new diameter and οriginal diameter are in millimeters.
The οriginal diameter οf the ring is 20 millimeters, and the new diameter that the ring needs tο fit is 16 millimeters.
Therefοre, the length οf the bar that shοuld be inserted is:
length οf bar = π × (16 - 20)
= π × (-4)
≈ -12.57 millimeters
Since the length οf the bar cannοt be negative, we can assume that it shοuld be 12.57 millimetres lοng.
Therefοre, the length οf the bar that shοuld be inserted tο make the ring fit the finger is apprοximately 12.57 millimeters.
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10
What is the decimal multiplier to decrease by 3.4%?
Answer:
0.96%
Step-by-step explanation:
do not answer with 0.966% it WILL be wrong and is a VERY common calculation error due to a very small mistake
A forester stands on level ground an unknown distance from a large tree. The angle of elevation to the top of the tree is 37 degrees. When the forester moves 20 ft closer to the tree, the angle of elevation to the top of the tree is 52 degrees.
What is the height of the tree?
Using Trigonometric functions, the height of the tree is approximately 50.6 feet.
Let's call the height of the tree "h" and the distance between the forester's original position and the base of the tree "x". Then, when the forester moves 20 feet closer to the tree, the distance between the new position and the base of the tree is "x - 20".
We can use the tangent function to set up two equations relating the height of the tree to the angles of elevation:
tan(37°) = h/x ...(1)
tan(52°) = h/(x - 20) ...(2)
We can solve this system of equations to find the value of "h". First, we can rearrange equation (1) to get:
x = h/tan(37°)
Then, we can substitute this expression for "x" into equation (2) and solve for "h":
tan(52°) = h/(h/tan(37°) - 20)
Simplifying and solving for "h", we get:
h = (20 tan(52°) tan(37°)) / (tan(52°) - tan(37°))
Using a calculator, we can evaluate this expression and find that:
h ≈ 50.6 ft
Therefore, the height of the tree is approximately 50.6 feet.
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In AABC,
48
48
50
Given: AQRS where m2 Q = 20° and m/S= 90°
1,000 meters
Q
What is the length, to the nearest meter, of RS?
R
S
The length of RS is approximately 73 meters (to the nearest meter).
What is Law of sines ?
The Law of Sines is a trigonometric formula that relates the side lengths of a triangle to the sine of its angles. It states that in any triangle ABC:
a / sin(A) = b / sin(B) = c / sin(C)
where a, b, and c are the side lengths of the triangle, and A, B, and C are the opposite angles.
This formula can be used to solve for the unknown sides or angles of a triangle when given enough information about the other sides and angles. The Law of Sines is especially useful when dealing with triangles that are not right triangles, or when only a few side lengths and angles are known.
According to the question:
We can solve this problem by using the Law of Sines and the fact that the sum of the angles in a triangle is 180 degrees.
First, we can find the measure of angle A in triangle ABC:
A = 180 - 48 - 48 = 84 degrees
Next, we can use the Law of Sines to find the length of side AC:
sin(84) / 50 = sin(48) / AC
AC = sin(84) * 50 / sin(48) ≈ 64.4
Now, we can use the fact that the sum of the angles in triangle AQS is 180 degrees to find the measure of angle QAS:
QAS = 180 - 20 - 90 = 70 degrees
Finally, we can use the Law of Sines again to find the length of RS:
sin(70) / RS = sin(48) / AC
RS = sin(70) * AC / sin(48) ≈ 72.6
Therefore, the length of RS is approximately 73 meters (to the nearest meter).
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PLEASE HELP EASY MATH QUESTION! WILL GIVE BRAINYLEST AND 5 STARS!!!
A coin is flipped at the start of every game to determine if Team A (heads) or Team B (tails) will get the ball first.
Part A: Find the theoretical probability of a fair coin landing on heads. (1 point)
Part B: Flip a coin 12 times and record the frequency of each outcome. Determine the experimental probability of landing on heads. Please include the frequency of each outcome in your answer. (2 points)
Part C: Compare the experimental probability to the theoretical probability. (1 point)
(SHOW YOUR WORK)
The theoretical probability is 0.5 and the experimental probability is 0.583
What is the theoretical probability?Part A:
Since the coin is fair, the probability of it landing on heads is 0.5 or 50%.
The theoretical probability of a fair coin landing on heads is 0.5.
Part B:
Let's denote the outcome of flipping the coin as H (heads) or T (tails). We flip the coin 12 times and record the frequency of each outcome:
NB: This is an assumption and not a given data;
Outcome Frequency
H 7
T 5
The experimental probability of landing on heads is calculated by dividing the number of times the coin landed on heads by the total number of coin flips:
Experimental probability of landing on heads = number of heads / total number of flips
Experimental probability of landing on heads = 7 / 12 = 0.583
Part C:
Comparing the experimental probability to the theoretical probability, we can see that they are different. The theoretical probability is 0.5, while the experimental probability is 0.583. This difference can be attributed to the randomness of the coin flips and the fact that we only flipped the coin 12 times, which is a relatively small sample size. As we increase the number of coin flips, the experimental probability should converge to the theoretical probability.
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can someone please help asap
Step-by-step explanation:
Equation of a circle
(x-h)^2 + (y-k)^2 = r^2
so the given circle has center at (h,k) = (5,-10)
new circle center will be at x = 1 left of 5 = 4 y = 2 down from -10 = -12
(4,-12)
Equation then becomes (x-4)^2 + ( y+ 12)^2 = 64
1/3 of the dozen fruits in a fruit seller cart are apple. If 1/4 of all the fruits are oranges and the rest of the fruits are bananas, find how many dozen bananas are there in the fruits sellers cart
Apples make up one-third of the dozen fruits in a fruit vendor cart. If bananas make up the remaining fruit and oranges make up 1/4 of the total fruit, there are 2.5 dozen bananas in the fruit vendor's cart.
First, let's calculate how many apples are in the cart:
1/3 of 6 dozen fruits = 2 dozen fruits are apples
Next, let's calculate what proportion of the fruits are oranges:
1/4 of all fruits = (1/4) x 6 dozen = 1.5 dozen fruits are oranges
To find the number of dozen bananas, we can subtract the number of dozen apples and oranges from the total number of dozen fruits in the cart:
Total number of dozen fruits = 6 dozen
Number of dozen apples = 2 dozen
Number of dozen oranges = 1.5 dozen
Number of dozen bananas = Total number of dozen fruits - Number of dozen apples - Number of dozen orangesNumber of dozen bananas = 6 dozen - 2 dozen - 1.5 dozen
Number of dozen bananas = 2.5 dozen
Therefore, there are 2.5 dozen bananas in the fruit seller's cart.
The complete question is:-
1/3 of the 6 dozen fruits in a fruit seller cart are apple. If 1/4 of all the fruits are oranges and the rest of the fruits are bananas, find how many dozen bananas are there in the fruits sellers cart
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Write 3/5
as a percentage.
Answer:
Step-by-step explanation:
3/5 x 100= 60%
Can someone PLEASE HELP ME!!!
In a laboratory experiment, the population of bacteria in a petri dish started off at 7400 and is growing exponentially at 13% per hour. Write a function to represent the population of bacteria after t hours, where the rate of change per minute can be found from a constant in the function. Round all coefficients in the function to four decimal places. Also, determine the percentage rate of change per minute, to the nearest hundredth of a percent.
The function to represent the bacteria population after t hours is f(t) = 7400 * [tex]e^(0.13/60 * t)[/tex].
What is derivative?A derivative is a measure of how much a function changes as its input value changes. It is defined as the limit of the rate of change of the function with respect to its input as the change in the input approaches zero.
According to question:The function to represent the bacteria population after t hours, where the function's constant can be used to calculate the rate of change per minute is:
f(t) = 7400 * [tex]e^(0.13/60 * t)[/tex]
where:
f(t) = population of bacteria after t hours
e = Euler's number (approximately 2.71828)
t = time in hours
0.13/60 = rate of change per minute (converted from 13% per hour)
To determine the percentage rate of change per minute, we can calculate the derivative of the function with respect to time (t):
df/dt = 7400 * 0.13/60 * [tex]e^(0.13/60 * t)[/tex]
At t = 0 (the start of the experiment), the rate of change per minute is:
df/dt = 7400 * 0.13/60 * [tex]e^(0.13/60 * 0)[/tex] = 12.1166
To express this rate of change as a percentage, we can divide it by the initial population and multiply by 100:
rate of change per minute = (df/dt) / P(0) * 100% = 12.1166 / 7400 * 100% = 0.1638% (rounded to the nearest hundredth of a percent)
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AB= 10, AC= 4x-5, and BC =2x - 5. Find BC
Answer: 55
Step-by-step explanation:
I believe you are talking about a triangle.
This is soo easy, you got this you professional.
Find x:
10 + 4x-5+ + 2x - 5 = 180
Add like terms
6x = 180
x=30
Find BC:
2(30) - 5
55
BC = 55