Answers
The numeric value of the function f(x) = 14/[3 + ae^(kx)] at x = 2 is given as follows:
f(2) = 0.172.
How to obtain the numeric value of the function?The function for this problem is defined as follows:
f(x) = 14/[3 + ae^(kx)]
When x = 0, y = 2, hence we can obtain the coefficient a as follows:
2 = 14/(3 + a)
6 + a = 14
a = 8.
Hence:
f(x) = 14/[3 + 8e^(kx)]
When x = 1, y = 1/2, hence the coefficient k is given as follows:
0.5 = 14/(3 + 8e^k)
1.5 + 4e^k = 14
4e^k = 12.5
e^k = 12.5/4
k = ln(12.5/4)
k = 1.14.
Hence:
f(x) = 14/[3 + 8e^(1.14x)]
Then the numeric value of the function at x = 2 is given as follows:
f(2) = 14/[3 + 8e^(1.14(2))]
f(2) = 0.172.
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Related Questions
25. Write a linear equation for each of the following scenarios. Then, solve for the variable
you created.
a. Kayla has a certain amount of money. If she spends $12.00, then she has of the
original amount left. What was the original amount of money Kayla has?
Equation:
Answer:
Answers
The linear equation for the scenario is y = x - 12
Writing the linear equation for each of the scenarioFrom the question, we have the following parameters that can be used in our computation:
Kayla has a certain amount of money. She spends $12.00, then she has of the original amount leftRepresent the original amount with x
and the amount left with y
So, we have
Amout left = x - 12
Using the variable representtaion, we have
y = x - 12
Hence. the scenario is y = x - 12
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What fraction is equal to 15/18
Answers
if A C B, then A n B = A U B
1) sometimes
2) never
3) always
Answers
if A C B, then A n B = A U B is always true
How to determine if A C B, then A n B = A U BThe statement "if A C B, then A n B = A U B" can be rephrased as "if A is a subset of B, then the intersection of A and B is equal to the union of A and B".
Every element of A is also an element of B. Therefore, the intersection of A and B contains all the elements of A.
On the other hand, the union of A and B contains all the elements of A and all the elements of B. Since A is a subset of B, all the elements of A are already included in B, so the union of A and B is just equal to B.
Therefore, we have:
A n B = A (since all the elements of A are in both A and B)
A U B = B (since A is a subset of B)
So A n B = A U B = B, which means that the original statement "if A C B, then A n B = A U B" is true
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Decompose the following figure into separate pieces draw the pieces
Answers
The question's single element is divided into
three triangles and a rectangle.What is a composite shapeA composite shape is a geometrical figure formed from two or multiple elementary shapes layered and intermixed.
These simpler elements may comprise of
polygons such as triangles, rectangles, or pentagons)circles, or other geometric figures.As the base forms are overlapped or mixed to create an entirely new shape, they form a composite figure with a combined outline more intricate than any single component.
The single element in the question is separated to form
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PLEASE I REALLY NEED THIS HELP
solve the triangle. round to the nearest tenth
Answers
The correct solution of the triangle is seen in option D
How do you solve the triangle?In this case, we would need to use the sine rule so as to solve the triangle as we have in the problem that is before us here. The sine rule states that;
a/Sin A = b/SinB = c/SinC
We know that we can be able to obtain the angle C using the sine rule;
29/Sin 42 = 33/SinC
SinC = 33Sin42/29
C = Sin-1(33Sin42/29)
C = 49.6 degrees
The angle B is now;
180 - (42 + 50)
B = 88.4 degrees
Then;
b/Sin 88 = 29/Sin42
b = 29 Sin 88/Sin42
b = 28.98/0.669
b = 43.3
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Ice Mountain Ski Resort is Philip's favorite place to go in the winter. This year, his aunt bought him a season pass. Philip used his season pass discount to get $13.75 off of the price of a new helmet. After the discount, the helmet's price was $116.25.
Answers
Answer:
$130
Step-by-step explanation:
price of helmet =discount+ price after discount
=$13.75+$116.25
=$130
5. Select all expressions that are equivalent to 3^8.
A. 3^2x3^4
B. 3²x3^6
C. 3^16/3^2
D. 3^12/3^4
E. (3^4)²
F. (3¹)^7
Answers
The expressions that are equivalent to 3^8 are:
B 3²x3^6D. 3^12/3^4E. (3^4)²How to solve the expressionsWe have to solve these out
3^8. = 6561
From the options
A. 3^2x3^4
= 9 x 81
= 729
B 3²x3^6
= 9 x 729
= 6561
C. 3^16/3^2
= 43046721/9
= 4782969
d. 3^12/3^4
= 531441 / 81
= 6561
E. (3^4)²
= 3⁴ x 3⁴
= 3⁴⁺⁴
= 3⁸
= 6561
F. (3¹)^7
= 3⁷
= 2187
The expressions that are equivalent to 3^8 are:
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if A C B, then
1) A U B = B
2) A n B = 0
3) A n B =B
Answers
If in the set A ⊂ B then the statement A U B = B
What is a set?A set is a collection of well defined items.
Since we have A ⊂ B, we want to determine which statement of the set is true. To determine that, we proceed as follows.
Given that A ⊂ B which means that A is a subset of B. which implies that all the elements of the set A are in set B, then this implies that A U B = B.Since all the elements in set A are in set B.The statement A n B = 0 is false since all elements in A are in BAlso, the statement A n B = B is false since all elements in set A are in BSo, if A ⊂ B then the statement A U B = B
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9. What is the measure of ZHLI?
H
K
30°
Answers
The missing angle of the given image is: ∠HLI = 150°
How to find the measure of the missing angle?There are different terms in this type of case when looking for missing angles and they include:
Corresponding angles
Supplementary angles
Opposite angles
Alternate angles
Now, we are given that:
∠JLI = 30°
We know that the sum of angles on a straight line is 180°. Thus:
∠HLI = 180° - 30°
∠HLI = 150°
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Least common multiple of 5 and 2x-5
Answers
2. Marshall wants to save at least $175
for a new video game system and
some games. So far, he has saved
$68.50.
Part A
Write an inequality to represent the
amount of money, a, that Marshall still
needs to save.
Part B
Solve the inequality. Which of the
following describes how much money
Marshall still needs to save?
A He needs to save at least $106.50
more.
B He needs to save at most $106.50
more.
He needs to save at least $243.50
more.
D He needs to save at most $243.50
more.
Answers
The solutions to the inequality word problem are:
2) a + $68.50 ≥ $175
3) A He needs to save at least $106.50 more.
How to solve Inequality word problems?2) We are told that Marshall wants to save at least $175 for a new video game system and some games.
So far, he has saved $68.50.
If the amount of money he needs to save extra is a, then the inequality we have:
a + $68.50 ≥ $175
3) a + $68.50 ≥ $175
subtracting $68.50 from both sides gives:
a ≥ 175 - 68.5
a ≥ $106.5
He needs to save at least $106.50 more.
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Let sin(2x) – sin(x) = 0, where 0 ≤ x < 2π. What are the possible solutions for x? Left-brace StartFraction pi Over 6 EndFraction, StartFraction 5 pi Over 6 EndFraction Right-brace Left-brace StartFraction pi Over 3 EndFraction, StartFraction 5 pi Over 3 EndFraction right-brace Left-brace StartFraction pi over 6 EndFraction, StartFraction pi Over 2 EndFraction, StartFraction 5 pi Over 6 EndFraction, StartFraction 3 pi Over 2 EndFraction right-brace
Answers
The possible solutions for x for the equation sin(2x) – sin(x) = 0 will be (π/3, 5π/3). Then the correct option is B.
Given that:
sin(2x) – sin(x) = 0
Simplify the equation, then the value of 'x' is calculated as,
sin(2x) – sin(x) = 0
sin(2x) = sin(x)
2 sin x cos x = sin x
cos x = 1/2
cos x = cos (π/3, 5π/3)
x = π/3, 5π/3
The possible solutions for x for the equation sin(2x) – sin(x) = 0 will be (π/3, 5π/3). Then the correct option is B.
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What transformation maps the pre-image (red) onto the image (blue)?
O reflection
O glide reflection
O rotation
O translation
Answers
Answer: Translation
Step-by-step explanation:
To get from the pre-transformation shape (red) to the transformed image (blue), a translation takes place. This is where the shape is not rotated, reflected, or stretched, but simplify "slided" or "shifted" somewhere else.
I WILL GIVE 35 POINTS TO THOSE WHO ANSWER THIS QUESTION RIGHT NOOOO SCAMS PLEASE
Answers
Answer:
F1 8,-2 F2 -5,-3
Step-by-step explanation:
Somebody please help me with this
Answers
The measure of angle in degrees is 63 degree
We are given that;
The triangle ABC inscribed in the circle.
Now,
m<BAC-63
From isosceles triangle CBD,
m/CBD=m/BCD = 32
This implies that,
m/BDC+32+32=180
m/BDC+64 = 180
m/BDC=180-64
m/BDC = 126
m/BAC =1/2(m/BDC)
= 1/2(126)
= 63
Therefore, by the triangles the answer will be 63 degrees.
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In the spring of 2017, the Consumer Reports National Research Center conducted a survey of 1,007 adults to learn about their major healthcare concerns. The survey results showed that 575 of the respondents lack confidence they will be able to afford health insurance in the future.
(a)
What is the point estimate of the population proportion of adults who lack confidence they will be able to afford health insurance in the future. (Round your answer to two decimal places.)
(b)
At 90% confidence, what is the margin of error? (Round your answer to four decimal places.)
(c)
Develop a 90% confidence interval for the population proportion of adults who lack confidence they will be able to afford health insurance in the future. (Round your answer to four decimal places.)
to
(d)
Develop a 95% confidence interval for this population proportion. (Round your answer to four decimal places.)
to
Answers
a) The point estimate of the population proportion of adults who lack confidence they will be able to afford health insurance in the future is 0.57
b) At 90% confidence, the margin of error is 0.0324.
c) The 90% confidence interval is (0.5376, 0.6024).
d) The 95% confidence interval is (0.5314, 0.6086).
(a) The point estimate of the population proportion of adults who lack confidence they will be able to afford health insurance in the future can be found by dividing the number of respondents who lack confidence (575) by the total number of respondents (1,007):
Point estimate = 575/1007 = 0.57 (rounded to two decimal places)
(b) The margin of error can be calculated using the formula:
Margin of error = z√(p'(1-p')/n)
where z is the z-score associated with the desired level of confidence, p' is the point estimate, and n is the sample size. For a 90% confidence level, the z-score is 1.645.
Margin of error = 1.645√(0.57*(1-0.57)/1007) ≈ 0.0324 (rounded to four decimal places)
(c) The 90% confidence interval can be calculated using the formula:
Point estimate ± Margin of error
Substituting the values:
0.57 ± 0.0324
The 90% confidence interval is (0.5376, 0.6024) (rounded to four decimal places).
(d) The 95% confidence interval can be calculated in the same way, but with a different z-score. For a 95% confidence level, the z-score is 1.96.
Margin of error = 1.96√(0.57(1-0.57)/1007) ≈ 0.0386 (rounded to four decimal places)
0.57 ± 0.0386
The 95% confidence interval is (0.5314, 0.6086) (rounded to four decimal places).
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The data shown are the number of grams per serving of 30 selected brands of
cakes. Construct a frequency distribution using 5 classes.
32 47 51 41 46 30
46 38 34 34 52 48
48 38 43 41 21 24
25 29 33 45 51 32
32 27 23 23 34 35
Answers
The given data results in the following Frequency Distribution
Class Frequency
21-27 3
28-34 8
35-41 7
42-48 8
49-55 4
In statistics, frequency distribution is a way of organizing data into categories, or intervals, and counting how many observations fall into each category. It helps us understand the distribution of data and identify patterns within it.
To construct a frequency distribution using 5 classes, we need to first determine the range of the data:
Range = Maximum value - Minimum value
= 52 - 21
= 31
We can then calculate the width of each class:
Width = Range / Number of classes
= 31 / 5
= 6.2
Since we cannot have a fractional width, we round up to the nearest whole number. The class width is therefore 7.
Next, we need to determine the class intervals, or boundaries, which are the values that define each class. We start with the minimum value and add the class width successively:
Class 1: 21-27
Class 2: 28-34
Class 3: 35-41
Class 4: 42-48
Class 5: 49-55
We can now count how many observations fall into each class. The resulting frequency distribution is shown below:
Class Frequency
21-27 3
28-34 8
35-41 7
42-48 8
49-55 4
In this frequency distribution, we can see that the majority of the observations fall into the middle three classes, with fewer observations in the first and last classes. This suggests that the data is roughly symmetric and evenly distributed around the center.
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Write an inequality to represent the domain of the situation :
Write an inequality to represent the range of the situation :
If the equation of the function is c (x) = n (1.35)^x, the value of n is :
Answers
An inequality to represent the domain of the situation: 0 ≤ x ≤ 6
An inequality to represent the range of the situation: 4 ≤ y ≤ 24
If the equation of the function is [tex]c(x) = n(1.35)^x[/tex], the value of n is: 4.
What is a domain?In Mathematics and Geometry, a domain refers to the set of all real numbers for which a particular function is defined.
Furthermore, the vertical extent of any graph of a function represents all range values and they are always read and written from smaller to larger numerical values, and from the bottom of the graph to the top.
By critically observing the graph of this logarithmic function shown in the image attached above, we can reasonably and logically deduce the following domain and range:
Domain = [0, 6] or 0 ≤ x ≤ 6.
Range = [4, 24] or 4 ≤ y ≤ 24.
Next, we would determine the value of n by using the y-intercept (0, 4);
[tex]c(x) = n(1.35)^x\\\\4=n(1.35)^0[/tex]
n = 4.
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I need help on these
Answers
The length of the segment in circle (9) is the radius x = 6. And the length of the segment in (10) is x = 8.9
What are the radius and diameter properties of a circleA circle is a two-dimensional shape that is defined as a set of points that are equidistant from a single fixed point, called the center. The radius of a circle is the distance from the center to any point on the circumference. All radii of a circle are equal in length. While the diameter of a circle is a straight line passing through the center of the circle and touching two points on the circumference. The diameter is always twice the length of the radius.
For question (9):
the segments indicated as x and 6 are radii of the circle so;
x = 6
For question (10):
the radius = 31.6/2 = 15.8
also;
the radius = 6.9 + x
so;
x = 15.8 - 6.9
x = 8.9.
Therefore, the The length of the segment in circle (9) is the radius x = 6. And the length of the segment in (10) is x = 8.9
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What is a coterminal angle of 23 times pi over 3
60°
120°
240°
300°
Answers
240° is the coterminal angle of 23×π÷3.
First, we can simplify 23 times π over 3 by noticing that 2π is equivalent to 6 pi over 3, so we can add 2π to 23 times pi over 3 until we get an angle between 0 and 2π (or 0 and 360 degrees).
23 times π over 3 is equivalent to an angle of 360 degrees times (23 times π over 3)/(2π), which simplifies to 360 degrees times 23/2, or 4140 degrees.
To find a coterminal angle between 0 and 360 degrees, we can subtract 360 degrees until we get an angle in that range.
4140 - 360(11) = 240
Therefore, a coterminal angle of 23 times pi over 3 between 0 and 360 degrees is 240 degrees.
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Which linear equation is represented in the graph?
A. y = 2x – 1
B. y = –2x – 1
C. y = –2x + 1
D. y = 2x + 1
Answers
The equation of the line passing through the given points is y = -2x+1.
Given that is a line passing through two points (0, 1) and (2, -3) we need to find the equation of the line using them,
We know that the equation of a line passing through points (x₁, y₁) and (x₂, y₂) is =
y-y₁ = y₂-y₁ / x₂-x₁ (x-x₁)
Here (x₁, y₁) and (x₂, y₂) are (0, 1) and (2, -3),
Therefore, the required equation is =
y-1 = -3-1/2 (x-0)
y-1 = -2x
y = -2x+1
Hence, the equation of the line passing through the given points is y = -2x+1.
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PLS HELP MARKING AS BRAINLIST!!
Answers
Answer:
C = 117.92° or 118°
Step-by-step explanation:
Law of Cosine: [tex]c^2=a^2+b^2-2ab*cos(C)[/tex]
Plug in your values to solve for C°
A = 50 , B = 55 , C = 90
[tex]90^2=50^2+55^2-(2*50*55)*cos(C)[/tex]
[tex]8100=2500+3025-5500*cos(C)[/tex]
Subtract 2500 and 3025 to move to other side.
[tex]8100-2500-3025=-5500*cos(C)[/tex]
[tex]2575=-5500*cos(C)[/tex]
Divide -5500 to leave cos(C) byitself
[tex]-\frac{2575}{5500} =cos(C)[/tex]
Inverse Cos(C) to get C byitself solving it in degree.
[tex]C=cos^{-1}(-\frac{2575}{5500} )[/tex]
C = 117.916339°
Round to Hundredths place or Whole Degree.
C = 117.92° or 118°
Change to vertex form, with step by step. Thanks
Answers
The quadratic function x² - 10x + 20 in vertex form is f(x) = (x - 5)² -5. The vertex of this parabola is (5, 15).
To convert the quadratic function in standard form, f(x) = ax² + bx + c, to vertex form, f(x) = a(x - h)² + k, where (h, k) is the vertex of the parabola, follow these steps:
Complete the square by adding and subtracting (b/2a)²inside the parentheses:
f(x) = x² - 10x + 20
f(x) = (x²- 10x + 25) - 5
Factor the expression inside the parentheses as a perfect square:
f(x) = (x - 5)² -5
Write the function in vertex form by pulling out the value of a from the perfect square:
f(x) = 1(x - 5)² -5
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Which of the following are more precise than a weight of 1,000 pounds? Check all that apply.
Answers
Find the surface area of the figure below. Round to the nearest 10th.
Answers
The surface area of the given composite figure is: 484.38 cm²
How to find the surface Area?The formula for the area of a rectangle is:
Area = Length * Width
The formula for the area of a square is:
Area = side * side
The surface area is simply the area of each of the surfaces of the figure.
Thus, surface area of the given composite figure is:
4(13 * 10) + (10 * 10) + (10 * 10) - 3π(5²))
= 484.38 cm²
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Helpp please guyssssss
Answers
Answer:
The answer and step by step explanation is above
Please help me with these 6th grade math questions.
Answers
Answer:
1. s < 40
2. w ≤ 12
3. D ≥ 110
4. D ≤ 3 1/2
5. w ≥ 30
6. m ≥ 45
7. t ≠ 21
8. c < 45
9. D > 1/5
10. s ≠ 45 5/6
11. h ≥ 48
12. P ≠ 5
We often use the phrase "to the power of" when talking about exponents. For example, x¹³ is
referred to as x to the power of 13. Why do you think that they would name it like this? How does
increasing the exponent of a number increase its "power"?
Hint: Use a number as an example. (for instance 2) if you keep increasing the power, what happens
to the answer? (i.e. compare 2¹, 22, 23, 24, ..., 213, 214, ... until you see the answer you are looking
for!)
Answers
The phrase, raise to the power of is used when referring to exponents because the power or strength increases with the addition of more numbers. For instance, 2 raised to the power of 1 is not as strong as 2 raised to the power of 100.
Why the phrase is used?The usage of this phrase stems from the fact that numbers tend to increase in strength as they are raised to an increasing number of figures.
The strength that numbers carry differs as they increase or decrease. Just as 10 is greater than 1 or 2, so will different powers of exponents differ in strengths.
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A hot air balloon is currently 100 feet above ground. After 5 minutes, the hot air balloon is 40 feet above ground. Write an equation
Answers
Answer:
100 + 5f = 40
5f = -60
f = -12 feet per minute (decrease of 12 feet per minute)
The US Fish and Wildlife Service reported that the mean length of a 6 year old trout in the Arolik River in Alaska is 480 and standard deviation of 40 mm. Assume length of trout is normally distributed,
a) Find the 58th percentile of the lengths
Answers
The 58th percentile of the lengths is 489.4 mm.
What is the 58th percentile of the lengths?The 58th percentile of the lengths is calculated from normal distribution curve as shown below.
The mean of the distribution is at the 50th percentile.
The 58th percentile is between the mean and 1 standard deviation above the mean.
Mean (50%) = 480 mm
58% = ?
1 standard deviation above the mean (84%)= M + S.D = 480 mm + 40 mm = 520 mm
We are going to interpolate, to find the approximate value of the length.
50 ----- 480 mm
58 ----- ?
84 ------- 520 mm
(58 - 50)/(84 - 50) = (x - 480)/(520 - 480)
0.235(40) = x - 480
9.4 = x - 480
x = 489.4 mm
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