Answers
Answer:
More than 275 dollars of here budget goes to emergencies
Step-by-step explanation:
11% of 2750 is $302.50
Related Questions
Which rational expression is equivalent to this expression?
4/x-3. A) X-3/x+2•x+2/4. B) X-3/x+2/ 4/x+2. C) x+2/x-3• 4/x+2. D) x+2/x-3/ 4/x+2
Answers
The rational expression that is equivalent to the expression f(x) = 4/(x - 3) is {x + 2/x - 3} • {4/x + 2}.
What is rational function?A rational function is one that can be written as a polynomial divided by a polynomial. The domain of a rational function is the set of all numbers except the zeros of the denominator.Given is the expression as follows -
f(x) = 4/(x - 3)
[A] -
{x - 3/x + 2} • {x + 2/4} = {x - 3/4}
[B] -
{x - 3}/{x + 2} / {4/x + 2} = {x - 3}/{x + 2} × {x + 2/4} = {x - 3/4}
[C] -
{x + 2/x - 3} • {4/x + 2} = {4/x - 3}
[D] -
{x + 2/x - 3} / {4/x + 2} = {(x + 2)²/ 4x - 3}
Therefore, the rational expression that is equivalent to the expression f(x) = 4/(x - 3) is {x + 2/x - 3} • {4/x + 2}.
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give an example of a function that is discontinuous at one and only one point in its domain but is continuous at every other point is your point of discontinuity removable or essential
Answers
An example of a function that is discontinuous at one and only one point in its domain but is continuous at every other point is the function
f(x) = x^2.This function is continuous at every point in its domain, which is the set of all real numbers (-infinity < x < infinity). However, at the point x = 0, the function is discontinuous.
At x = 0, the function f(x) = x^2 is equal to 0, but if we approach the point x = 0 from the left (x = -0.1, -0.01, etc.), the function is equal to a negative value (-0.01, -0.0001, etc.), and if we approach the point x = 0 from the right (x = 0.1, 0.01, etc.), the function is equal to a positive value (0.01, 0.0001, etc.). This means that the function is not continuous at the point x = 0, and is therefore discontinuous at this point.
The point of discontinuity in this example is an essential discontinuity, which means that it cannot be removed by redefining the function at that point. This is because the function f(x) = x^2 is defined differently for x < 0 and x > 0, and there is no way to redefine the function at x = 0 to make it continuous.
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What is 37,056 rounded to the nearest thousand?
Answers
Answer:
Step-by-step explanation:
40k
A researcher compares two compounds (1 and 2) used in the manufacture of car tires that are designed to reduce braking distances for SUVs equipped with the tires. The mean braking distance for SUVs equipped with tires made with compound 1 is 41 feet, with a population standard deviation of 12.1. The mean braking distance for SUVs equipped with tires made with compound 2 is 46 feet, with a population standard deviation of 9.0. Suppose that a sample of 66 braking tests are performed for each compound. Using these results, test the claim that the braking distance for SUVs equipped with tires using compound 1 is shorter than the braking distance when compound 2 is used. Let μ1 be the true mean braking distance corresponding to compound 1 and μ2 be the true mean braking distance corresponding to compound 2. Use the 0.05 level of significance.
State the null and alternative hypotheses.
Determine critical value.
Calculate value of test statistic. Round your answer to two decimal places.
State conclusions
Answers
The critical value is -2.70
What is a null hypothesis?
Two alternatives being the same is the null hypothesis. The underlying assumption is that the observed difference is just the result of chance. It is feasible to estimate the probability that the null hypothesis is correct using statistical testing.
Here, we have
The objective of this experiment is to compare two compounds, designed to reduce braking distance, used in tire manufacturing to prove if the braking distance of SUVs equipped with tires made with compound 1 is shorter than the braking distance of SUVs equipped with tires made with compound 2.
So you have 2 independent populations, SUV's equipped with tires made using compound 1 and SUVs equipped with tires made using compound 2.
Two samples of 66 braking tests are made and the braking distance was measured each time, the study variables are determined as:
X₁: Braking distance of an SUV equipped with tires made with compound one.
Its sample mean is X[bar]₁= 41 feet
And the Standard deviation S₁= 12.1 feet
X₂: Braking distance of an SUV equipped with tires made with compound two.
Its sample mean is X[bar]₂= 46 feet
And the Standard deviation S₂= 9.0 feet
We don't have any information on the distribution of the study variables, nor the sample data to test it, but since both sample sizes are large enough n₁ and n₂ ≥ 30 we can apply the central limit theorem and approximate the distribution of both variables sample means to normal.
The researcher's hypothesis, as mentioned before, is that the braking distance using compound one is less than the distance obtained using compound 2, symbolically: μ₁ < μ₂
The statistical hypotheses are:
H₀: μ₁ ≥ μ₂
H₁: μ₁ < μ₂
α: 0.05
The statistic to use to compare these two populations is a pooled Z test
Z= {(X[bar]₁-X[bar]₂) - (μ₁ - μ₂)}/√S₁²/n₁+S₂²/n₂ ≈ N(0;1)
Z = {(41-46)-0}/√146.41/66+81/66
Z = -5/1.85
Z = -2.70
The rejection region of this hypothesis test is one-tailed to the right, so you'll reject the null hypothesis to small values of the statistic. The critical value for this test is:
Z(α) = Z(0.05) = -1.645
Decision rule:
If Z(H₀) ≥ -1.645, then you do not reject the null hypothesis.
If Z(H₀) < -1.645, then you reject the null hypothesis.
Since the statistic value is greater than the critical value, the decision is to not reject the null hypothesis.
At a 5% significance level, you can conclude that the average braking distance of SUVs equipped with tires manufactured used compound 1 is greater than the average braking distance of SUVs equipped with tires manufactured used compound 2.
Hence, the critical value is -2.70.
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Cans of paint weigh 6 pounds each. Let x represent the number of cans of paint and y represent the total weight of the cans. Write the equation to this situation as slope intercept form (y=mx+b). Then create a table of possible values
Answers
The equation for the relationship between the number of cans of paint, x, and the total weight of the cans, y, in slope-intercept form is y = 6x + 0. This equation can be derived from the formula for the slope-intercept form of a line, y = mx + b, where m is the slope of the line and b is the y-intercept. In this case, since the weight of each can of paint is 6 pounds and there is no y-intercept (the line passes through the origin), the slope of the line is 6 and the y-intercept is 0.
A table of possible values for the number of cans of paint, x, and the total weight of the cans, y, based on this equation is shown below:
x (number of cans of paint) y (total weight of cans)
1 6
2 12
3 18
4 24
5 30
As the table shows, for each additional can of paint, the total weight of the cans increases by 6 pounds. This is because each can of paint weighs 6 pounds, and the weight of the cans is equal to the number of cans multiplied by the weight of each can.
Answer: y = 6x
Step-by-step explanation:
For each can of paint (x) 6 pounds is added. This is represented as;
y = 6x
For the table of possible values, we will plug a value in for x, and then evaluate the function for y. See attached.
y = 6(1) = 6
y = 6(2) = 12
y = 6(3) = 18
An experiment was conducted in which planks of wood painted red and green were shown to pigeons to investigate a pigeon's ability to select a certain color. Pigeons could accurately select the color of the plank of wood 20 percent of the time. A simulation was conducted in which a trial consisted of a pigeon being shown eight planks of wood and its number of successes being recorded. This process was repeated many times, and the results are shown in the histogram.
Based on the results of the simulation, which of the following is closest to the probability that there were at most three successes in a trial?
Answers
The probability that there were at most three successes in a trial is approximately 0.9.
It looks like the histogram shows the probability mass function (PMF) for the number of successes in a trial. The PMF for a random variable gives the probability of each possible value of the random variable.
To find the probability that there were at most three successes in a trial, we need to add up the probabilities of 0, 1, 2, and 3 successes. From the histogram, it looks like the probabilities of these values are approximately 0.2, 0.4, 0.2, and 0.1, respectively. Adding these up, we get an approximate probability of 0.2 + 0.4 + 0.2 + 0.1 = 0.9.
Therefore, the probability that there were at most three successes in a trial is approximate $\boxed{0.9}$.
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How do I solve a whole number and a fraction?
Answers
Answer:
To solve a problem involving a whole number and a fraction, you can first convert the whole number to a fraction by writing it as a fraction with a denominator of 1. For example, if the whole number is 4, you can write it as the fraction 4/1.
Then, you can add or subtract the fractions as you would normally, making sure to find a common denominator if necessary. For example, suppose you want to add the whole number 4 and the fraction 3/5. You can first write 4 as the fraction 4/1, giving you:
4/1 + 3/5
To add these fractions, you need to find a common denominator. A common denominator for 1 and 5 is 5, so you can rewrite the fractions with denominators of 5:
4/1 = 20/5
3/5 = 3/5
Now you can add the fractions:
20/5 + 3/5 = 23/5
So the solution to the problem is 23/5.
If you need to multiply or divide the whole number and fraction, you can treat the whole number as a fraction with a denominator of 1 and then perform the multiplication or division as you would normally with fractions.
Step-by-step explanation:
In multiplication, we simply solve by multiplying the whole number by the numerator of the given fraction. We can take the expression 6 • 2/3 for example:
The numerator is 2, so solving would result in (6 • 2)/3 as a fraction. This equals out to 12/3, which can be reduced to 4; this means 6 • 2/3 = 4.
Division, however, is a bit different. When dividing a whole number by a fraction, we use the Skip, Flip, Multiply method. Again, we can use 6 / 2/3 as an example.
1. Skip
Since our first divisor is 6, it remains the same.
2. Flip
Our second divisor is 2/3. Since it is a fraction, we can flip it so it becomes 3/2.
3. Multiply
With our new expression, we can now multiply what we have to find our answer!
6 • 3/2 = 18/2, which reduces to 9.
Now we know that 6 / 2/3 = 9. One thing to consider when dividing a whole number by a fraction is that the whole number is the fraction of the product. In this case, we would say 6 is 2/3 of 9, and this helps us to remember that the quotient always will be larger than what we began with, whereas in multiplication, the product is smaller than what we began with.
Select all of the following equation(s) that are quadratic in form. x4 – 6x2 – 27 = 0 3x4 = 2x 2(x + 5)4 + 2x2 + 5 = 0 6(2x + 4)2 = (2x + 4) + 2 6x4 = -x2 + 5 8x4 + 2x2 – 4x = 0
um consider it serious or don't :)
Answers
The quadratic equations, or the equations that are quadratic in form, for this problem is given as follows:
6(2x + 4)² = 2x + 4 + 2.x^4 - 6x² - 27 = 0.6x^4 = -x² + 5.What is a quadratic equation?The degree of a function is given by the highest exponent that appears in the definition of the function.
A quadratic function is a function that has a degree of 2.
The standard format of a quadratic function is given as follows:
y = ax² + bx + c.
(in which the coefficient a must assume a value different of zero).
The quadratic function in this problem is given as follows:
6(2x + 4)² = 2x + 4 + 2.
As (2x + 4)² = 4x² + 16x + 16, meaning that the highest exponent would be of 2.
However, equations of the fourth degree can also be quadratic in form, as long as the exponents go as follows: 4, 2 and 0.
Hence these following equations are also quadratic in form:
x^4 - 6x² - 27 = 0.6x^4 = -x² + 5.They are classified as quadratic in form because a transformation such as y = x² can make them quadratic.
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Two logarithmic functions are graphed f(x) = log (x) and g(x) = log3(x). Describe the effect on the shape of their graphs.
Responses
ABy decreasing the base number the graph was affected vertically. A lower base number caused the graph to rise at a slower rate.
By decreasing the base number the graph was affected vertically. A lower base number caused the graph to rise at a slower rate.
BBy decreasing the base number the graph was affected horizontally. A lower base number caused the graph to spread out faster along the x-axis.
By decreasing the base number the graph was affected horizontally. A lower base number caused the graph to spread out faster along the x-axis.
CBy decreasing the base number the graph was affected horizontally. A lower base number caused the graph to become more compressed.
By decreasing the base number the graph was affected horizontally. A lower base number caused the graph to become more compressed.
DBy decreasing the base number the graph was affected vertically. A lower base number caused the graph to rise at a faster rate.
Answers
A. By decreasing the base number the graph was affected vertically. A lower base number caused the graph to rise at a slower rate.
What is a logarithm function?
The logarithm is exponentiation's opposite function in mathematics. This indicates that the exponent to which b must be raised in order to obtain a number x is the logarithm of x to the base b. For instance, because 1000 = 10³, its logarithm in base 10 is 3, or log₁₀ 10³= 3.
Given function are
f(x) = log x and g(x) = log₃ x.
The rate of raise of the graph g(x) is more than that of the graph f(x).
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(Factoring Algebraic Expressions MC)
Factor −7x2 + 35x.
−7x(x + 5)
7x(−x + 5)
7(−x2 + 35x)
x(7x + 35)
Answers
Answer:
7x ( - x + 5 )
Step-by-step explanation:
- 7x² = 7x × - x
35x = 7x × 5
- 7x² + 35x = 7x ( - x + 5 )
could any one please help me with this question
Answers
Answer:
10°
Step-by-step explanation:
The sum of the measures of the exterior angles of any polygon, one per vertex, is 360°.
x + 3x + 4x + 5x + 6x + 8x + 9x = 360
36x = 360
x = 10
In a polygon, an exterior angle is supplementary to its adjacent interior angle.
The smallest exterior angle is x, and x = 10.
Answer: 10°
Calculate the area
Of this square
Answers
The area of the shape as shown in the diagram is 11.25 cm².
What is area?Area is the region occuppied by a plane shape.
To calculate the area of the shape, we use the formula below.
Formula:
A = LW+l²................ Equation 1Where:
A = Area of the shapeFrom the diagram,
Given:
L = 4.5 cmW = 2 cml = 1.5 cmSubstitute these question into equation 1
A = (4.5×2)+(1.5²)A = 9+2.25A = 11.25 cm²Hence, the area of the shape is 11.25 cm².
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what is the number x such that G.C.F(x,54)=6 and L.C.M(x,54)=432.
Answers
By the Application of Prime factorization method the value of x is 48
what is Prime factorization method?
Writing all numbers as the product of primes is a procedure known as prime factorization. Consider the case of the number 20, for instance. We can divide that into two elements. Well, that's four times five, we can say. Furthermore, 5 is a prime number.
Solution:
HCF = ( X, 54 ) = 6
LCM = ( X, 54 ) = 432
a = x b = 54
using property
a * b = LCM * HCF
54a = 6 * 432
a = (6 * 432) / 54
a = 48
Hence the value of x is 48.
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Which of the following shows a correct method to calculate the surface area of the cylinder?
cylinder with diameter labeled 2.8 feet and height labeled 4.2 feet
SA = 2π(2.8)2 + 2.8π(4.2) square feet
SA = 2π(1.4)2 + 2.8π(4.2) square feet
SA = 2π(2.8)2 + 1.4π(4.2) square feet
SA = 2π(1.4)2 + 1.4π(4.2) square feet
Answers
You can quickly calculate the radius of a cylinder using an online calculator.
How to Find Radius of a Cylinder?The term "cylinder" refers to a three-dimensional solid shape made up of two circular bases joined by two parallel lines. We may calculate the radius of the cylinder using the formula for cylinder volume.A cylinder's capacity or the quantity of space it takes up are both determined by the cylinder's volume. V = πr²h, a formula, is used to compute it.Cylinder radii (r) √(V / π × h), where V denotes a cylinder's volume, h denotes its height, and (Pi) denotes a mathematical constant having a roughly 3.14 value.Solved Examples on the Radius of a Cylinder Calculator ExampleWhat is the radius of a cylinder with a capacity of 100 cubic units and a height of 5 units?
Solution:
The radius of a cylinder (r) is equal to (V / h).
= √(100 / π × 5)
= 2.523 units
As a result, a cylinder's radius is 2.523 units.
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Answer:
Step-by-step explanation:
its a
2. Calculate On landing, the plane touches the runway with a speed of 65 m/s. The figure shows the speed of the plane after 1 second. Calculate the acceleration of the plane during its landing.
Answers
The plane touches the runway with a speed of 65 m/s then the acceleration of the plane during its landing will be equal to 65 m/s².
What is acceleration?The rate of change in an object's velocity concerning time is known as acceleration in mechanics. The vector quantity of accelerations. The direction of the net force that is acting on an object determines its acceleration.
Since acceleration has both a magnitude and a direction, it is a vector quantity. Velocity is a vector quantity as well. The definition of acceleration is the change in velocity vector over a time interval divided by the time interval.
As per the given information in the question,
Velocity, v = 65 m/s
Time, t = 1 sec.
Use the equation of acceleration,
a = v/t
a = 65/1
a = 65 m/s²
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A particular truck in a transportation fleet was
driven 109,970 miles last year. In comparison,
it was driven 40% less this year. How much
was the truck driven this year?
Answers
bro this is middle school work not college
Please show your work
Jamie is a salesperson in a jewelry store and earns $150 per week, plus 15% of her weekly sales. If Jamie makes $229.50 in one week, what are her sales for that week
Answers
Answer:
$530--------------------------------
If the amount of sales for current week is x, Jamie's earning is:
150 + 0.15x = 229.50Solve it for x:
150 + 0.15x = 229.500.15x = 229.50 - 1500.15x = 79.50x = 79.50/0.15x = 530given the function h(x)=8x-3/4x+5 as the values of x increase towards infinity, use a table to find out what happens to the values of h(x)
Answers
according to question,
given data.
h(x)=8x-3/4+5
then,
which of the following conditions must be met to conduct a two-proportion significance test? the populations are independent. the probabilities of success multiplied by the sample sizes are greater than or equal to 10 and the probabilities of failure multiplied by the sample sizes are greater than or equal to 10 for each population. each sample is a simple random sample.
Answers
All the given three conditions are true for conducting a two proportion significance test.
To check the significance of two proportions, following conditions should be met
Data of each group must be collected from the population using a random sampling. That means data values must be independent.Population should be independent of each other.The two populations must be approximately or normally distributed. To check the assumption of the normality, we have the following condition: “The probabilities of success multiplied by the sample sizes are greater than or equal to 10 and the probabilities of failure multiplied by the sample sizes are greater than or equal to 10 for each population.” If this condition is met, we say that populations are normally distributed.Hence, all the three conditions must be met to conduct a two-proportion significance test.
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One item on a questionnaire asks students how many times in a typical week they eat at a fast-food restaurant. The responses for a sample of n = 10 students are summarized in the frequency distribution. What is the best measure of central tendency for these data?
X f
5+ 2
4 3
3 2
2 1
1 1
0 1
Answers
Answer:
the mean (i.e. the average)
Step-by-step explanation:
There's no clear outlier or inconsistency therefore the mean should be used.
Solve. p/1 6/7=−4.4(refer to the picture)
enter your answer as a mixed number in simplest form in the box.
Answers
Answer:
p = -8 6/35
Step-by-step explanation:
p/(1 6/7)=−4.4
To solve for p, multiply each side by 1 6/7
p/(1 6/7) * ( 1 6/7)=−4.4 * (1 6/7)
p = - 4.4 * ( 1 6/7)
Change each number to fractions
p = -44/10 * 13/7
p = -286/35
Change to a mixed number
p = -8 6/35
The double number line shows that Bira has ridden 28m on a carousel, which is 80% of a full rotation on the carousel
Answers
The distances that represent the percentages are given as follows:
Distance of 28 m -> 80% of a rotation.Distance of 7 m -> 20% of a rotation.Distance of 35 m -> 100% of a rotation.What is a proportion?A proportion is a fraction of a total amount, used along with the unit measures and basic arithmetic operations to obtain the desired measures in the context of a problem.
28m is 80% of the distance, hence 100% of the distance is obtained applying the proportion as follows:
0.8x = 28
x = 28/0.8
x = 35.
Then the distance that represents 20% of a rotation is calculated as follows:
0.2 x 35 = 7 meters.
Missing InformationThe complete problem is given by the image shown at the end of the answer.
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Draw a line segment with a length of 3 1/2 and a midpoint of -1.
Answers
The line segment of length 3 1/2 is sketched with mid pint at -1 and attached
What is a line segment?A line segment in geometry has two different points on it that define its boundaries.
A line segment is sometimes referred to as a section of a line that links two places. The difference between a line and a line segment is that a line has no endpoints and can go on forever in either direction.
How to make the line segmentThe endpoints is important before a line can be defined as a line segment, however the midpoint will be essential in calculating for the endpoints
The mid point of the line is given to be -1
the other ends will be 3 1/2 /2
1.75
from -1 add and subtract 1.75 to get the endpoint's
-1 + 1.75 = 0.75
-1 - 1.75 = 2.75
each unit on the number line is 0.3333
to get 0.75 from 0 count two units to give 0.6667 then a bit more to get to 0.75
to get 2.75 from 2 count two strokes to get to 2.6667, then add a little more to get 2.75
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Assume that a random variable is normally distributed with a mean of 1,300 and a variance of 271. Complete parts a
through c below.
a. What is the probability that a randomly selected value will be greater than 1,350?
The probability is
(Round to four decimal places as needed.)
Answers
Answer:
I believe if I just believe that you can work this out then you can do it thank you You are intelligent you can do this
Please show work thank you
Rational functions
Answers
Division followed by simplification of mentioned rational function gives:
(x + 1)/(x + 4)
What is factorization?Factoring an algebraic expression specifically means writing a given expression as the product of its factors. These factors may be numbers, variables, or algebraic expressions.
1, 2, 6, and 12 are all divisors of 12 because they divide 12 equally. This is an important algebraic operation, which is used to simplify expressions, simplify fractions, and solve equations. This is also called algebraic factorization.
Factorization of x² + 2x - 3
x² + 3x - x - 3
(x² + 3x) - (x + 3)
x(x + 3) - 1(x + 3)
(x + 3)(x - 1)
Factorization of x² + 3x - 4
x² + 4x - x - 4
(x² + 4x) - (x + 4)
x(x + 4) - 1(x + 4)
(x + 4)(x - 1)
Factorization of x² - 2x - 3
x² - 3x + x - 3
(x² - 3x) + (x - 3)
x(x - 3) + 1(x - 3)
(x - 3)(x + 1)
Using identity, a² - b² = (a + b)(a - b)
x² - 9 = x² - 3²
x² - 3² = (x + 3)(x - 3)
Now, for the division:
(x² + 2x - 3)/(x² - 9) ÷ (x² + 3x - 4)/(x² - 2x - 3)
[(x + 3)(x - 1)/(x + 3)(x - 3)] ÷ [(x + 4)(x - 1)/(x - 3)(x + 1)]
By reciprocal of (x + 4)(x - 1)/(x - 3)(x + 1)
[(x + 3)(x - 1)/(x + 3)(x - 3)] × [(x - 3)(x + 1)/(x + 4)(x - 1)]
= (x + 1)/(x + 4)
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Pleas Help ASAP Giving brainliest if correct <3
Answers
Answer: the first one is 7/9 and the second one is option 2
Step-by-step explanation:
4+7 = 11
< or> = open dot
A store charges a rate per minute plus a flat fee to rent cleaning supplies. A 30 minute rental $110.50. A 40 minute rental costs $145. How much for a 25 minute rental
Answers
The cost of a 25-minute rental will be $92.00.
To find the amount a 25-minute rental would cost, we need to first determine the rate per minute and the flat fee. We can do this by setting up the following system of equations:
30 minutes x rate + flat fee = $110.50
40 minutes x rate + flat fee = $145
To solve this system of equations, we can multiply the first equation by 2 and subtract the second equation from it to eliminate the rate:
(30 minutes x 2) x rate + flat fee x 2 = 2 x $110.50
80 minutes x rate + flat fee x 2 = 2 x $110.50
Subtracting the second equation from the first equation, we get:
flat fee x 2 - flat fee x 2 = 2 x $110.50 - 2 x $145
flat fee x 2 - flat fee x 2 = -$34.50
Since the left side of the equation is equal to zero, we can divide both sides by 2 to solve for the flat fee:
flat fee - flat fee = -$34.50 / 2
flat fee - flat fee = -$17.25
Since the left side of the equation is also equal to zero, the flat fee must be zero.
We can now use either of the original equations to solve for the rate per minute. Using the first equation, we get:
30 minutes x rate + flat fee = $110.50
30 minutes x rate = $110.50
rate = $3.68
We can now use this rate to find the cost of a 25-minute rental:
25 minutes x $3.68 + flat fee = $92.00 (Since the flat fee is zero)
Thus, a rental of 25 minutes costs $92.00.
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What is the surface area of the box shown? Will give Brainliest!!
Answers
Answer:
304
Step-by-step explanation:
To find the surface area of a rectangular prism with length 4, width 10, and height 8, you can use the formula 2 * (length * width + width * height + height * length).
Plugging in the given values, the surface area is equal to 2 * (4 * 10 + 10 * 8 + 8 * 4) = 2 * (40 + 80 + 32) = 2 * 152 = 304.
Answer: 304
Step-by-step explanation:
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The number of bacteria in a sample is increasing according to an exponential model. After four hours, the sample contained 400 bacteria. After twelve hours, the sample contained 1,600 bacteria. Write an exponential growth model for the number of bacteria in the sample after x hours.
Answers
The solution is Option A.
The exponential growth model for the number of bacteria in the sample after x hours is [tex]P ( x ) = 200 e ^{(\frac{ln 4}{8})x }[/tex]
What is exponential growth factor?
The exponential growth or decay formula is given by
x ( t ) = x₀ × ( 1 + r )ⁿ
x ( t ) is the value at time t
x₀ is the initial value at time t = 0.
r is the growth rate when r>0 or decay rate when r<0, in percent
t is the time in discrete intervals and selected time units
Given data ,
Let the equation for the number of bacteria in the sample after x hours = P
The value of the equation P ( x ) is given by
After 4 hours , the sample contained 400 bacteria
So ,
when x = 4
[tex]P ( 4 ) = ae ^{4b }=400[/tex] be equation (1)
After 12 hours , the sample contained 1600 bacteria
And , when x = 12
[tex]P ( 12 ) = ae ^{12b }=1600[/tex] be equation (2)
Divide equation (2) by equation (1) , we get
[tex]\frac{P ( 12 )}{P ( 4 )} = \frac{ae ^{12b }}{ae ^{4b }} = \frac{1600}{400}[/tex]
On simplifying the equation , we get
e¹²ᵇ⁻⁴ᵇ = 4
e⁸ᵇ = 4
Taking logarithm on both sides of the equation , we get
8b = ln (4)
Divide by 8 on both sides , we get
b = ln (4) / 8
Substituting the value for b in equation (1) , we get
[tex]ae ^{4*ln (4) / 8 }=400[/tex]
[tex]ae ^{ln (4) / 2}=400[/tex]
On simplifying the equation , we get
a x 2 = 400
Divide by 2 on both sides of the equation , we get
a = 200
Therefore , the exponential growth equation is given by
Substitute the values of a and b in the equation , we get
[tex]P ( x ) = 200 e ^{(\frac{ln 4}{8})x }[/tex]
Hence , The exponential growth model for the number of bacteria in the sample after x hours is [tex]P ( x ) = 200 e ^{(\frac{ln 4}{8})x }[/tex]
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Please give me detailed information
Answers
The values of x, y and z are 24, 10 and 17 using the similar triangles properties and triangles sum properties.
What are the characteristics of a triangle?A triangle in geometry is a three-sided polygon with three edges and three vertices. The fact that a triangle's internal angles add up to 180 degrees is its most crucial characteristic. This characteristic is known as the triangle's angle sum property.
Calculation:Given that ΔHPS≅ΔCNF.
We can see that angle H in triangle HPS is obtuse whereas angle N in triangle CNF is obtuse so comparing this we get,
6x - 29 = 115
6x = 144
x = 24
Comparing angle C and angle P we get
4z - 32 = 36
4z = 68
z = 17
Now the remaining angle in trinagle CNF is angle F which is 3y - 1 as we know that sum of angles in a triangle is 180 and the angle C and N are 36 and 115 we can say that F is 29
Now to find y we equalise it to 29
3y - 1 = 29
3y = 30
y = 10.
The values of x, y and z are 24, 10 and 17 using the similar triangles properties and triangles sum properties.
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