The exponential equation is N ( t ) = a ( b )^t , where a = 50 and b = 3
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 number of bacteria in the culture at a given time be N ( t )
The culture increases by a factor of 2
So , the value of r = 200 % , r = 2
Now , when t = 0 , the number of bacteria in the culture N ( 0 ) = 50
So , the exponential equation is
N ( t ) = N ( 0 ) ( 1 + r )^t
Substituting the values in the equation , we get
N ( t ) = 50 ( 1 + 2 )^t
N ( t ) = 50 ( 3 )^t
On simplifying the equation , we get
N ( t ) = a ( b )^t , where a = 50 and b = 3
Hence , the exponential equation is N ( t ) = 50 ( 3 )^t
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Please someone help me
Question: A line passes through the point (9, 5) and has a slope of -4/3. Write an equation in slope-intercept form for this line.
Answer:
[tex]y=-\frac{4}{3}x+17[/tex]
Given:
x = 9
y = 5
m = -4/3
Step-by-step explanation:
Slope intercept form is y = mx+b
Plug in x, y, and m to solve for b.
[tex]5=-\frac{4}{3}(9)+b[/tex]
[tex]b=5+\frac{4}{3}(9)=17[/tex]
Now that you have b, plug in m and b back into the equation
[tex]y=-\frac{4}{3}x+17[/tex]
I need help, been struggling for a while.
Answer:
-2
Step-by-step explanation:
5x/2 = -5
5 x/2=2 (-5)
5x= 2 (-5)
5x= -10
5x/5=-10/5
x=-10/5
x=-2
Write the function in vertex form for this parabola focus=(3, 2.5)
The equation of parabola in vertex form is [tex]$$\boxed{x^2 - 6x + 9 = 0}$$[/tex]
How to find the equation of parabola?To write the equation of a parabola in vertex form, we use the following formula:
[tex]$$(x-h)^2=4p(y-k)$$[/tex]
where (h,k) is the vertex and p is the distance between the focus and the vertex.
Given that the focus of the parabola is at (3, 2.5), we can determine that the vertex of the parabola is also at (3, 2.5). Let's substitute these values into the formula:
[tex]$$(x-3)^2=4p(y-2.5)$$[/tex]
To find the value of p, we need to use the fact that the distance between the focus and vertex is p. The distance formula is:
[tex]$$d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$$[/tex]
Substituting the values we know:
[tex]$$\begin{aligned} d &= \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \ &= \sqrt{(3 - 3)^2 + (2.5 - 2.5)^2} \ &= 0 \end{aligned}$$[/tex]
Since d = 0, we know that p = 0 and the equation simplifies to:
[tex]$$(x-3)^2=0$$[/tex]
Expanding the left side:
[tex]$$x^2 - 6x + 9 = 0$$[/tex]
So the equation of the parabola in vertex form is:
[tex]$$\boxed{(x-3)^2=4 \cdot 0 (y-2.5)}$$[/tex]
Or
[tex]$$\boxed{x^2 - 6x + 9 = 0}$$[/tex]
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The thickness of a flange on an aircraft component is uniformly distributed between 0.95 and 1.05 millimeters.
a) Determine the proportion of flanges that exceeds 1.01 millimeters.
b) What thickness is exceeded by 90% of the flanges?c) Determine the mean and variance of flange thickness.
Mean = (millimeters)
variance = (millimeters2)
With the thickness of a flange on an aircraft component is uniformly distributed between 0.95 and 1.05 millimeters.
a) 40% of the flanges exceeds 1.01 millimeters.
b) 1.04 millimeters is the thickness that is exceeded by 90% of the flanges.
c) The mean of flange thickness is 1 millimeters and the variance of flange thickness is 0.01 millimeters^2.
a) To determine the proportion of flanges that exceeds 1.01 millimeters, we need to find the area under the probability density function (pdf) of the thickness that is greater than 1.01 millimeters.
Let's call the random variable X representing the thickness of the flange. The pdf of X is uniform, so it has constant value over the interval [0.95, 1.05]. Therefore, the proportion of flanges that exceeds 1.01 millimeters can be found as follows:
P(X > 1.01) = (1.05 - 1.01) / (1.05 - 0.95) = (1.05 - 1.01) / 0.1 = 0.04 / 0.1 = 0.4
So, 40% of the flanges exceed 1.01 millimeters.
b) To find the thickness that is exceeded by 90% of the flanges, we need to solve for X in the following equation:
P(X > X) = 0.9
Substituting the values for the pdf, we get:
(X - 0.95) / (1.05 - 0.95) = 0.9
Solving for X, we get:
X = 0.95 + 0.9 * (1.05 - 0.95) = 0.95 + 0.9 * 0.1 = 0.95 + 0.09 = 1.04
So, 1.04 millimeters is the thickness that is exceeded by 90% of the flanges.
c) The mean of X can be calculated as follows:
Mean = (0.95 + 1.05) / 2 = 1
The variance of X can be calculated as follows:
Variance = (1.05 - 0.95)^2 / 12 = 0.01
So, the mean and variance of flange thickness are:
Mean = 1 millimeters
Variance = 0.01 millimeters^2
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In a class of class of 50 students, the number of students who offer accounting is twice as the number who offer Economics 10 students offer neither of the two subjects and 5 students offer both subjects (1) How many offer Accounting and Economics. :.) How many offer only
one subject
The Venn diagram shows that the number of students who offer accounting is 30 and offer Accounting and Economics are only 5.
How to explain the Venn diagram?It should be noted that a Venn diagram is an illustration which uses circles to show the relationship between the objects.
We are given that class of 50 students, the number of students who offer accounting is twice as the number who offer Economics 10 students offer neither of the two subjects and 5 students offer both subjects
The number of students who offer Economics are;
= 10 + 5
= 15
Since accounting is twice as the number who offer Economics.
The number of students who offer accounting are;
= 25 + 5
= 30
The number of students who offer only one subject will be as follows;
= 25 + 10
= 35
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y = x -2
Slope
Intercept where is m= and b=
Answer:
Slope: 1
Y-Intercept: -2
y=x-2
Graph it by plotting a point at (0,-2) and then by going up one to the right. One up and then one to the right and repeat twice. Now you can graph this easily. Hope this helped!!
Step-by-step explanation:
Suppose each of the apples weighs about 5 ounces. Can you buy 24 apples for $9? Explain
Yes You can buy 24 apples for $0.125 per pound. This price will not available except in festival or discounts sale.
what are ounces ?
An ounce is a unit of weight or mass commonly used in the United States and other countries. It is usually abbreviated as oz. One ounce is equal to 1/16th of a pound or approximately 28.35 grams. Ounces are often used to measure small quantities of food or ingredients in recipes, as well as for measuring the weight of small objects.
According to the question:
To determine whether you can buy 24 apples for $9, we need to find the cost per apple.
If 24 apples cost $9, then the cost per apple is:
$9 / 24 apples = $0.375 per apple
Since each apple weighs about 5 ounces, there are about 3 apples per pound:
16 ounces / 5 ounces per apple ≈ 3.2 apples per pound
Therefore, the cost per pound of apples is:
$0.375 per apple / 3 apples per pound = $0.125 per pound
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9th grade math i need help in
The value of f(1) will be 45.
What is the function?A relationship between a group of inputs and one output is referred to as a function. In plain English, a function is an association between inputs in which each input is connected to precisely one output. A domain, codomain, or range exists for every function. Typically, f(x), where x is the input, is used to represent a function.
Given a function f(n) = 45.(4/5)ⁿ⁻¹
To calculate the value of f(1) we will substitute the value of the n by 1.
f(1) = 45.(4/5)¹⁻¹
f(1) = 45.(4/5)⁰
f(1) = 45
To calculate the value of f(n -1) we will substitute the value of the n by
n - 1.
f(n -1) = 45.(4/5)ⁿ⁻¹⁻¹
that can also be written as, from the rule of power
f(n -1) = (45.(4/5)ⁿ⁻¹)/4/5
f(n -1) = (45.(4/5)ⁿ⁻¹) * 5/4
f(n -1) = f(n) * 5/4
so,
f(n) = f(n-1) * 4/5
Therefore, the value of f(1) will be 45, and the value of f(n) = f(n-11)*4/5.
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32 +2³-4 please I need this rn :)
The answer is 36. you basically add and subtract to the left and right.
32+8= 40
40-4=36
(you get the 8 because 2 x 2 x 2 = 8)
what fraction is .1667
To convert 0.1667 to a fraction, we write it as 1667/10000, and simplify it to 1/6. Hence, the fraction of .1667 is 1/6.
To convert the decimal number 0.1667 to a fraction, we can write it as 1667/10000. This fraction can be simplified by dividing both the numerator and the denominator by their greatest common factor, which is 167.
1667 ÷ 167 = 10
10000 ÷ 167 = 60 + 40/167
So, the fraction equivalent to 0.1667 is 1667/10000, which can be simplified to 10/60 + 40/167.
10/60 can be simplified to 1/6, so the final simplified fraction is:
0.1667 = 1/6 + 40/167
Therefore, the fraction equivalent to 0.1667 is 1/6.
Converting a decimal to a fraction involves expressing a decimal number as a ratio of two integers. To convert a decimal to a fraction, the decimal is written in the form of a fraction, with the decimal value as the numerator and a power of 10 as the denominator. The resulting fraction can be simplified by finding the greatest common factor between the numerator and denominator, and then dividing both by that factor. For example, to convert 0.1667 to a fraction, we write it as 1667/10000, and simplify it to 1/6.
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Gino records how much milk his family drinks each week in February. He graphs the volumes, to the nearest one fourth of a gallon, on the line plot below. What is the total volume of milk Gino's family drank on the 2 weeks where they drank the most milk?
The total volume of milk would be 1/2 gallons.
What is volume?Volume is defined as the space occupied within the boundaries of an object in three-dimensional space. It is also known as the capacity of the object.
Given that,
Volume = 1/4 gallons
The number of weeks = 2
So, the total volume =
1/4 × 2 = 1/2 gallons
Hence, the total volume of milk would be 1/2 gallons
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The sum of a number times 2 and 29 is at least −25
Answer:
Step-by-step explanation:
Let's start by translating the given sentence into an equation:
2x + 29 ≥ -25
To solve for x, we can isolate x on one side of the inequality:
2x ≥ -25 - 29
2x ≥ -54
x ≥ -27
Therefore, the solution to the inequality is x ≥ -27.
what is how do you find DAC
The value of DAC in the figure would be 47 degrees.
How to find the measure of DAC?From the question, we have the following parameters that can be used in our computation:
The angles EAD, DAC and CAB are all on a straight line which means they add up to 180 degrees.
Angle CAB is in a triangle which means all the angles add up to 180 degrees and the value of this angle is:
= 180 - 80 - 57 = 43 degrees
The value of DAC would then be;
= 180 - EAD - CAB
Substitute the known values in the above equation, so, we have the following representation
= 180 - 90 - 43
= 90 - 43 = 47 degrees
Hence, the angle is 47 degrees
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steve is standing on a porch of a shore house in malibu. the elevatioin of the porch is about 138 feet steve's eye level is 5 feet above the porch floor. if steve can see a band of surfers on the water at an angle of depression approximately 29 degrees how far are the surfers from his eyes?
geometry trig unit.
The distance is 295 feet from the surfers from his eyes.
What is geometry?Geometry is the description of figures in a space with a specific number of dimensions and types. Plane geometry is the most prevalent sort of geometry (dealing with objects like the point, lines, circles, triangles, and polygons),
According to the given question, we have attached a figure which represents the given situation.
Let the distance would be x from the surfers from his eyes
As per the figure, using the sine ratio to find x:
sin 29° = perpendicular/hypotenuse
Substitute the known values and solve for x:
sin 29° = 143/x
0.4848 = 143/x
x = 294.96
x ≈ 295 feet
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How to solve for r
100 000= 8000(1+ r/12000)^72
without using GDC
I don't understand how GDC works :(
I know the answer is 3.72% but I need to show how I got it
The solution for r in the equation is 428.43
How to determine the solution for rFrom the question, we have the following parameters that can be used in our computation:
100000 = 8000(1+ r/12000)^72
Divide through by 8000
So, we have
12.5 = (1+ r/12000)^72
Take the 72th root of both sides
So, we have
1 + r/12000 = 1.03570211065
Subtract 1
r/12000 = 0.03570211065
So, we have
r = 428.4253278
Hence, the value of r is 428.43
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Convert 2 pints into milliliters. Round your answer to the nearest whole number.
Answer:
To convert 2 pints into milliliters, we need to use the conversion rate that 1 pint equals 473.176 milliliters.
Therefore, we can calculate that 2 pints is equal to 946.352 milliliters. Rounded to the nearest whole number, this would be 946 milliliters.
e by 1
3. Mr. Bauer placed the letters in the word
BASKETBALL into a bag. What is the
probability of choosing the letter B, not
replacing it, and then choosing a vowel?
Answer: The word "BASKETBALL" has 2 B's and 3 vowels (A, E, A). The probability of choosing the letter B, not replacing it, and then choosing a vowel is:
(2/10) * (2/9) * (3/8) = 6/90 = 1/15
So, the probability of choosing the letter B, not replacing it, and then choosing a vowel is 1/15.
Step-by-step explanation:
You have a sample of 35.2g of MgSO4. How many moles of MgSO4 are in the sample? Show all your work
Answer:
Step-by-step explanation:
The answer is 120.3676. i assume you are converting between grams MgSO4 and mole. You can view more details on each measurement unit: molecular weight of MgSO4
Answer the question below
Answer:
1. Kevin has 12 pieces of paper.
2. Including Sybill and her friends, each person will get 1/8 of the 1/2 slice.
Step-by-step explanation:
1. This is because if 1 piece of paper turned divided into fourths would 4/1 or 4 “fourths” of paper. So multiply that by 3 since there is 3 pieces of paper and we are following the same steps. 3 x 4 = 12. Hence if you divide 3 pieces of paper into fourths, you will have 12 fourths.
2. Since we are splitting the 1/2 piece four (which includes sybill and her 3 friends) ways, the equation would be: 1/2 divided by 4
Divide:
1/2 divided by 4-
1/2 : 4 = 1/2 · 1/4 = 1 · 1/2 · 4 = 1/8
Hence, each friend and Sybill her self will receive a 1/8 piece.
Use the Associative Property of Addition to write an expression equivalent to (W+4)+2
Answer:W+6
Step-by-step explanation:
Determine the intercepts of the line.
Do not round your answers.
3x + 2y = 5
Y=0
X=0
Answer:
Step-by-step explanation:
X axis intercept (y=0)
3x+2(0)=5
3x=5
x=5/3
Y axis intercept (x=0)
3(0)+2y=5
2y=5
y=5/2
so, the interception points are: (5/3,0) and (5/2,0)
Barbara buys a chandelier online for $612. If shipping and handling are an additional 28% of the price, how much shipping and handling will Barbara pay?
Barbara will therefore shell out $171.36 for the cost of shipping and handling.
Price is what word?The amount of money, or its equivalent, for which anything being offered for sale, purchased, or otherwise transacted. A price on someone's head is a sum provided for their capture, whether they are alive or dead.
We must calculate 28% of the chandelier's original purchase price in order to calculate the value Sarah will charge for shipping and handling.
Step 1
Calculate 28% of $612
We can multiply a value by 0.28 to get 28% of it, or reduce it by 100 & then multiply the result by 28. So:
28% of $612 = 0.28 x $612 = $171.36
Step 2
Add the cost of shipping and handling to the purchase price.
Simply include the shipping & handling fee to the original price to get the chandelier's total cost with shipping and handling included:
Total cost = $612 + $171.36 = $783.36
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Andrea needs to line the interior sides of a gift box in the shape of a regular octagonal prism with decorative paper. If the box is 2.5
Inches deep, what is the amount of decorative paper she needs to use?
20 in²
100 in ²
12.5 in2
40 in²
5 in
Answer:
12.5 in²
Step-by-step explanation:
based on the t-test assuming unequal variances on the t-testunequal worksheet, is the difference in mean mpg between 4 and 8 cylinder cars statistically significant?O Yes, the means appear to be similar. O No, the ratio of the variances is not greater than 4:1. O No, the calculated t Stat value is less than the critical t value. O Yes, the calculated t
When performing a t-test assuming unequal variances, the test statistic is a t-value, which is calculated by dividing the difference between the means of the two groups by the standard error of the difference.
To see if the difference in mean mpg between 4 and 8 cylinder cars is statistically significant, compare the estimated t-value to a critical t-value based on degrees of freedom and desired level of significance. The difference is regarded statistically significant if the estimated t-value is bigger than the crucial t-value.
As a result, the right response depends on the estimated t-value, the crucial t-value, and the level of significance utilized in the test.
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True or False: A simple random sample is a sample of n observations that has the same probability of being selected from the population as any other sample of n observations.
True. A simple random sample is a type of sampling method that is used to select a subset of observations from a larger population.
The key characteristic of a simple random sample is that each observation in the population has an equal probability of being selected to be part of the sample.
Mathematically, this can be expressed as follows: Let N be the population size, and let n be the sample size. Then, the probability of any specific sample of n observations being selected from the population is given by the formula:
P(Sample) = (n!/N!)/(N-n)!
where n! represents the factorial of n (n factorial), and (N-n)! represents the factorial of N-n.
This means that if we were to draw multiple simple random samples of the same size from the same population, each sample would have an equal probability of being selected.
In conclusion, a simple random sample is a method of selecting a subset of observations from a population that ensures that each observation has an equal probability of being selected, and that each sample has an equal probability of being selected.
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Jimmy has a piggy bank and which she saves all of her R5,R2 and R1 coins. the coins are in a ratio of 2:5:7 respectively. if she has twelve R5 coins saved in her piggy bank. How much she saved
The total amount that Jimmy has saved is $420.
How much has she saved?
Ratio shows the relationship between two or more numbers. It is the number of times that one value is contained within other value.
Total amount saved = (sum of ratios x total value of R5 saved) / ratio that represents R5 saved
Sum of ratios = 2 + 5 + 7 = 14
Total value of R5 saved = 12 x 5 = R60
= (14 x 60) / 2 = $420
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What does p and p hat mean?
In statistics, p represents the true proportion p hat represents the sample proportion
p represents population that has a certain characteristic or falls into a certain category. It is a fixed, unknown value that we are trying to estimate.
p hat represents the sample proportion, which is an estimate of the true proportion based on a sample of the population. It is calculated by dividing the number of individuals in the sample with the characteristic or in the category by the total sample size.
For example, if we want to estimate the proportion of students who prefer chocolate ice cream, we could take a sample of 100 students and find that 60 of them prefer chocolate.
In this case, p hat would be 60/100 or 0.6. This is our estimate of the true proportion, p, of all students who prefer chocolate ice cream.
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Someone please help me with these.
The equations in the slope-intercept form are
p = 3b + 2 and p = (5/2)b + 15/2.
What is a slope?In mathematics, a line's slope, also known as its gradient, is a numerical representation of the line's steepness and direction
From the table and scatter plot;
(a). The line for 'Build it' passes through (1, 10) and (3, 15),
then the equation of the line is,
p = (5/2)b + 15/2
Similarly, the equation of the line-'All things home' is,
p = 3b + 2.
(b) the graphs of the lines are given in the attached image.
(c) The equation in the slope-intercept form;
p = 3b + 2 and p = (5/2)b + 15/2.
(d) When b = 65,
then p = 3(65) + 2 and p = (5/2)(65) + 15/2.
So, p = 197 and p = 170
Therefore, all the required values are given above.
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In the Reflecting Ball Game, a ball can be launched from points 1, 2, 3, 4, 5 or 6 in the direction shown. When a ball hits a side of rectangle $ABCD$, it bounces at a $90^{\circ}$ angle back into the playing field. The path of the ball ends when it hits corner point $A$, $B$, $C$, or $D$. The path for starting point 5 is shown in the diagram. Each of the $15$ non-overlapping squares of the playing field has an area of $2$ square centimeters. What is the length of the longest possible path for a ball launched from a starting point?
The maximum is 12 diagonals or a length of 12 × 2√2 =24√2 centimeters.
How to solveNote that the ball moves only on the diagonals of the 15 non-overlapping squares. Thus we must find the path that traverses the most diagonals.
From point 1, the path traverses 6 diagonals before ending up at D.
From point 2, the path traverses 12 diagonals before ending up at A (incidentally, it passes through point 5 in the specified direction so we do not need to check point 5).
From point 3, the path traverses 3 diagonals before ending up at B.
From point 4, the path traverses 9 diagonals before ending up at C.
From point 6, the path traverses 10 diagonals before ending up at D.
Thus the maximum is 12 diagonals, or a length of 12 × 2√2 =24√2 centimeters.
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what is the distance between the points -3,-8 and 6,-8
The distance between the points -3,-8, and 6,-8 is 3 units.
What is the distance between two points?The length of the line segment bridging two points on a plane is known as the distance between the points.
Look at the provided points.
Calculate the distance between the points using the given formula.
Given points are -3,-8 and 6,-8
Given two points lies the parallel to X-axis
The distance between the two points is
A (-3,-8) and B(6,-8) = X₂ - X₁
6 - 3 = 3 units.
Therefore, the distance between two points -3,-8 and 6,-8 is 3 units.
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