The range of x values between which a zero can be found is -9/4 < x < -4.
Since x + 4 and 4x + 9 are linear factors of the quadratic expression, the quadratic expression can be written as:
Q(x) = k(x + 4)(4x + 9)
where k is some constant.
To find the values of x for which Q(x) = 0, we can set each factor equal to zero and solve for x:
x + 4 = 0 --> x = -4
4x + 9 = 0 --> x = -9/4
Therefore, the zeros of Q(x) are x = -4 and x = -9/4.
To find the range of x values between which a zero can be found, we need to determine the sign of Q(x) in each of the three intervals:
1. x < -9/4
2. -9/4 < x < -4
3. x > -4
For x < -9/4, both x + 4 and 4x + 9 are negative, so Q(x) = k(negative)(negative) = k(positive), which is positive.
For x > -4, both x + 4 and 4x + 9 are positive, so Q(x) = k(positive)(positive) = k(positive), which is also positive.
For -9/4 < x < -4, x + 4 is positive and 4x + 9 is negative, so Q(x) = k(positive)(negative) = k(negative), which is negative.
Therefore, the range of x values between which a zero can be found is -9/4 < x < -4.
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Use similar triangles to calculate the height, h cm, of triangle ABE. 10 cm 36 cm D B 20 cm E Optional working I h = Answ cm Search
Answer:
h=24
Step-by-step explanation:
Since the traingles are similar we can calculate the scale factor
20/10 = 2
So the Linear Scale Factor is 2
We can use that to figure out the ratio between the 2 triangles
Since DC = 10 and AE = 20
We cans say that the ratio between DBC and ABE is 2:1
Using this we can see that the ratio of the height is split into 2:1 and the total is 3
Knowing this we can calculate the the heights of both triangles
36 / 3 = 12
Height of small traingle = 1*12 = 12
Height of large triangle = 2*12 = 24
1
(Lesson 8.2) Which statement about the graph of the rational function given is true? (1/2 point)
4. f(x) = 3*-7
x+2
A. The graph has no asymptotes.
B.
The graph has a vertical asymptote at x = -2.
C. The graph has a horizontal asymptote at y =
+
Answer:
B. The graph has a vertical asymptote at
x = -2.
The statement about the graph of the given rational function that is true is: B. The graph has a vertical asymptote at x = -2.
To understand the graph of the rational function f(x) = (3x - 7) / (x + 2), we need to consider its behavior at various points. First, let's investigate the possibility of asymptotes. Asymptotes are lines that the graph approaches but never touches. There are two types of asymptotes: vertical and horizontal.
A vertical asymptote occurs when the denominator of the rational function becomes zero. In this case, the denominator is (x + 2), so we need to find the value of x that makes it zero. Setting x + 2 = 0 and solving for x, we get x = -2. Therefore, the rational function has a vertical asymptote at x = -2 (option B).
To determine if there is a horizontal asymptote, we need to compare the degrees of the numerator and the denominator. The degree of a term is the highest power of x in that term. In the given rational function, the degree of the numerator is 1 (3x) and the degree of the denominator is also 1 (x). When the degrees are the same, we look at the ratio of the leading coefficients, which are 3 (numerator) and 1 (denominator). The ratio of the leading coefficients is 3/1 = 3.
If the ratio of the leading coefficients is a finite value (not zero or infinity), then the rational function will have a horizontal asymptote. In this case, the horizontal asymptote is y = 3 (option C).
Hence the correct option is (b).
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out of 500 people , 200 likes summer season only , 150 like winter only , if the number of people who donot like both , the seasons is twice the people who like both the season , find summer season winter season , at most one season with venn diagram
Answer:
250 people like the summer season, 200 people like the winter season, and 50 people like both seasons.
Step-by-step explanation:
Let's assume that the number of people who like both summer and winter is "x". We know that:
- 200 people like summer only
- 150 people like winter only
- The number of people who don't like either season is twice the number of people who like both seasons
To find the value of "x", we can use the fact that the total number of people who don't like either season is twice the number of people who like both seasons:
150 - 2x = 2x
Solving for "x", we get:
x = 50
150 people like the winter season, 200 people like the summer season.
The number of people who don't like summer and winter is twice the number of people who like both seasons.
The number of people who like both the seasons= x
The number of people like summer 200
The number of people who like winter 150
The number of people who don't like summer and winter is twice the number of people who like both seasons.
To find the value of x, we can use the equation:
150-x= 2x
150= 3x
x= 50
The number of people who like both seasons is 50
The number of people who don't like both seasons is 100
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given g(x)=-4x-4, find g(-2)
Answer:
g(-2) = 4.
Step-by-step explanation:
To find g(-2), we simply need to substitute -2 for x in the function g(x) and simplify:
g(-2) = -4(-2) - 4
g(-2) = 8 - 4
g(-2) = 4
Therefore, g(-2) = 4.
Solve the initial value problem. Dy/dx = 4x^-3/4, y(1) = 3 a. y = 16x^1/4 - 13 b. y = 16x1/4 + 48 c. y = -3/4^x7/4-13/4 d. y= 4x^1/4 - 1
The solution to the given initial value problem is (d) y = 4x^(1/4) - 1.
Given the initial value problem,
dy/dx = 4x^(-3/4), y(1) = 3
Integrating both sides with respect to x, we get
∫dy = ∫4x^(-3/4)dx
y = -8x^(-1/4) + C
where C is the constant of integration.
To find the value of C, we use the initial condition y(1) = 3
3 = -8(1)^(-1/4) + C
C = 3 + 8 = 11
Therefore, the solution to the initial value problem is
y = -8x^(-1/4) + 11
Simplifying further,
y = 11 - 8/x^(1/4)
Hence, the correct option is d) y = 4x^(1/4) - 1 is not the solution to the given initial value problem.
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An object moving vertically is at the given heights at the specified times. Find the position equation s = 1/2 at^2 + v0t + s0 for the object.
At t = 1 second, s = 136 feet
At t = 2 seconds, s = 104 feet
At t = 3 seconds, s = 40 feet
The position equation for the object is: s = -80t^2 + 208t + 88, where s is the position of the object (in feet) at time t (in seconds).
We can use the position equation s = 1/2 at^2 + v0t + s0 to solve for the unknowns a, v0, and s0.
At t = 1 second, s = 136 feet gives us the equation:
136 = 1/2 a(1)^2 + v0(1) + s0
136 = 1/2 a + v0 + s0 ----(1)
At t = 2 seconds, s = 104 feet gives us the equation:
104 = 1/2 a(2)^2 + v0(2) + s0
104 = 2a + 2v0 + s0 ----(2)
At t = 3 seconds, s = 40 feet gives us the equation:
40 = 1/2 a(3)^2 + v0(3) + s0
40 = 9/2 a + 3v0 + s0 ----(3)
We now have a system of three equations with three unknowns (a, v0, s0). We can solve this system by eliminating one of the variables. We will eliminate s0 by subtracting equation (1) from equation (2) and equation (3):
104 - 136 = 2a + 2v0 + s0 - (1/2 a + v0 + s0)
-32 = 3/2 a + v0 ----(4)
40 - 136 = 9/2 a + 3v0 + s0 - (1/2 a + v0 + s0)
-96 = 4a + 2v0 ----(5)
Now we can solve for one of the variables in terms of the others. Solving equation (4) for v0, we get:
v0 = -3/2 a - 32
Substituting this into equation (5), we get:
-96 = 4a + 2(-3/2 a - 32)
-96 = 4a - 3a - 64
a = -160
Substituting this value of a into equation (4), we get:
-32 = 3/2(-160) + v0
v0 = 208
Finally, substituting these values of a and v0 into equation (1), we get:
136 = 1/2(-160)(1)^2 + 208(1) + s0
s0 = 88
Therefore, the position equation for the object is:
s = -80t^2 + 208t + 88
where s is the position of the object (in feet) at time t (in seconds).
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Antonio, a professional wrestler, went on a very strict liquid diet for 26 weeks to lose weight. When he
began the diet, he weighed in at a healthy 235 pounds and during the diet, he consistently lost 1. 5% of his
body weight each week. His weight loss can be modeled by the function W (t) = 235(0. 985)' where Wis
his weight in pounds and t is the time in weeks that he has been on the diet.
What was his weight in pounds after 5 weeks?
How long did it take(in weeks) him to weigh in at 161. 05 pounds?
Antonio's weight after 5 weeks was 202.34 pounds, and it took him 19 weeks to weigh in at 161.05 pounds.
To find Antonio's weight after 5 weeks, we can simply substitute t = 5 into the given exponential function:
W(5) = 235(0.985)⁵
W(5) ≈ 209.88 pounds
So his weight after 5 weeks was approximately 209.88 pounds. To find how long it took him to weigh in at 161.05 pounds, we can set the function equal to 161.05 and solve for t:
161.05 = 235(0.985)ᵗ
0.685106383 ≈ 0.985ᵗ
t ≈ 25.5 weeks
So it took him approximately 25.5 weeks to weigh in at 161.05 pounds
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Complete question - Antonio, a professional wrestler, went on a very strict liquid diet for 26 weeks to lose weight. When he began the diet, he weighed in at a healthy 235 pounds and during the diet, he consistently lost 1. 5% of his body weight each week. His weight loss can be modeled by the function W (t) = 235(0. 985)ᵗ where W is his weight in pounds and t is the time in weeks that he has been on the diet. What was his weight in pounds after 5 weeks? How long did it take(in weeks) him to weigh in at 161. 05 pounds?
Use the given terms to generate a recursive rule. Sequence:13,15,23,55,183
To generate a recursive rule for the sequence 13, 15, 23, 55, 183, we need to identify the pattern in the sequence.
Looking at the differences between each term, we can see that:
15 - 13 = 2
23 - 15 = 8
55 - 23 = 32
183 - 55 = 128
So the differences are increasing by a factor of 4 each time.
Using this pattern, we can create a recursive rule:
a(1) = 13
a(n) = a(n-1) + 4^(n-2)
So for example,
a(2) = a(1) + 4^(2-2) = 13 + 1 = 14
a(3) = a(2) + 4^(3-2) = 14 + 4 = 18
a(4) = a(3) + 4^(4-2) = 18 + 16 = 34
a(5) = a(4) + 4^(5-2) = 34 + 64 = 98
a(6) = a(5) + 4^(6-2) = 98 + 256 = 354
And so on.
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I need help on the quesrion attached
A simplification of the expression [tex]\frac{x^3y^3 \cdot x^3 }{4x^2}[/tex] is [tex]\frac{x^4y^3 }{4}[/tex].
What is an exponent?In Mathematics, an exponent is a mathematical operation that is commonly used in conjunction with an algebraic equation or expression, in order to raise a given quantity to the power of another.
Mathematically, an exponent can be represented or modeled by this mathematical expression;
bⁿ
Where:
the variables b and n are numbers (numerical values), letters, or an algebraic expression.n is known as a superscript or power.By applying the division and multiplication law of exponents for powers of the same base to the given algebraic expression, we have the following:
[tex]\frac{x^3y^3 \cdot x^3 }{4x^2}=\frac{x^{3+3-2}y^3 }{4}\\\\\frac{x^{3+3-2}y^3 }{4}=\frac{x^4y^3 }{4}[/tex]
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Complete Question;
Simplify each of the expressions given.
(1 point) Write an equivalent integral with the order of integration reversed g(y) I hope F(x,y) dydt = F(x,y) dedy f(y) a = b= f(y) = g(y) =
The missing values are:
a = 0b = 1c = 1f(y) = yg(y) = 2 - yh(y) = 0k(y) = yGiven Integral:
[tex]\int\limits^1_0 \int\limits^{2-x}_x {F(x,y)} \, dydx = \int\limits^b_a \int\limits^{g(y)}_{f(y)} {F(x,y)} \ dxdy + \int\limits^c_b \int\limits^{h(y)}_{k(y)} {F(x,y)} \ dxdy \\[/tex]
To write the equivalent integral with the order of integration reversed, express the limits of integration and functions appropriately.
Reversed integral:
[tex]\int\limits^b_a \int\limits^{g(y)}_{f(y)} {F(x,y)} \ dxdy + \int\limits^c_b \int\limits^{h(y)}_{k(y)} {F(x,y)} \ dxdy \\[/tex]
Now, let's determine the values of the variables:
a = 0: The lower limit of the outer integral remains the same as the original integral.
b = 1: The upper limit of the outer integral also remains the same as the original integral.
c = 1: The upper limit of the second inner integral is determined by the limits of integration of the original integral, which is 1.
f(y) = y: The lower limit of the first inner integral is the same as the original integral, which is y = x.
g(y) = 2 - y: The upper limit of the first inner integral is determined by the limits of integration of the original integral, which is 2 - x.
h(y) = 0: The lower limit of the second inner integral remains the same as the original integral.
k(y) = y: The upper limit of the second inner integral remains the same as the original integral.
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50 POINTS ASAP Triangle 1 and triangle 2 are similar right triangles formed from a ladder leaning against a building.
Triangle 1 Triangle 2
The distance, along the ground, from the bottom of the ladder to the building is 12 feet. The distance from the bottom of the building to the point where the ladder is touching the building is 18 feet. The distance, along the ground, from the bottom of the ladder to the building is 8 feet. The distance from the bottom of the building to the point where the ladder is touching the building is unknown.
Determine the distance from the bottom of the building to the point where the ladder is touching the building for triangle 2.
27 feet
18 feet
12 feet
5 feet
The distance where the ladder is touching the building for triangle 2 is 12 ft
Determining the distance from the bottom of the building to the pointFrom the question, we have the following parameters that can be used in our computation:
Ladder 1
Distance along the ground = 12 ft
Distance touching the ladder = 8 ft
Ladder 2
Distance along the ground = 18 ft
Distance touching the ladder = x
Using proportion of similar triangles, we have
x : 18 = 8 : 12
Express as fraction
x/18 = 8/12
So, we have
x = 18 * 8/12
Evaluate
x = 12
Hence, the distance where the ladder is touching the building for triangle 2 is 12 ft
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Answer:
12?
Step-by-step explanation:
Not too sure! I am in the middle of taking the test right now though
5.2 cm
4 cm
V = bh
V = ______ x 4
V=
3 cm
Area of base:_________x
cubic cm
11
sq. cm
How do I do this step by step
Answer:
Step-by-step explanation:
Let's call the total volume of the container "V".
We know that the container was originally 15% full, so the amount of water in the container was 0.15V.
When 48 litres of water was added, the new volume of water in the container became 0.15V + 48.
We also know that the container is now 75% full, so the new volume of water in the container must be 0.75V.
We can set up an equation to solve for V:
0.15V + 48 = 0.75V
Subtracting 0.15V from both sides:
48 = 0.6V
Dividing both sides by 0.6:
V = 80
So the container can hold 80 litres of water when it is full.
Find the product. Assume that no denominator has a value of 0.
6r+3/r+6 • r^2 + 9r +18/2r+1
Answer:
Step-by-step explanation:
We can simplify the fractions first:
(3r + 9)(r+6) / (r+6) = 3r + 9
6r + 3 / (r + 6) = 3(2r + 1) / (r + 6)
(r^2 + 9r + 18) / (2r + 1) = (r^2 + 6r + 3r + 18) / (2r + 1) = [(r+3)(r+6)] / (2r + 1)
So the expression becomes:
[3(2r + 1) / (r + 6)] * [(r+3)(r+6) / (2r + 1)]
We can now cancel out the common factors:
[3 * (r+3)] = 3r + 9
Therefore, the simplified product is:
(3r + 9)(r+6) / (r+6) = 3r + 9
Cleo bought a computer for
$
1
,
495
. What is it worth after depreciating for
3
years at a rate of
16
%
per year?
The worth of the computer after depreciating for 3 years is $749.77, under the condition that a rate of 16% per year was applied.
Then the derived formula for evaluating depreciation
Depreciation = (Asset Cost – Residual Value) / Life-Time Production × Units Produced
Then,
Asset Cost = $1,495
Residual Value = 0 (assuming the computer has no resale value after 3 years)
Life-Time Production = 3 years
Units Produced = 1
Hence, the depreciation rate
[tex]Depreciation Rate = (1 - (Residual Value / Asset Cost)) ^{ (1 / Life-Time Production) - 1}[/tex]
[tex]Depreciation Rate = (1 - (0 / 1495))^{(1/3-1)}[/tex]
Depreciation Rate = 16%
Now to evaluate the value of the computer after three years of depreciation at a rate of 16% per year, we can apply the derived formula
Value of Asset After Depreciation = Asset Cost × (1 - Depreciation Rate) ^ Life-Time Production
Value of Asset After Depreciation = $1,495 × (1 - 0.16)³
Value of Asset After Depreciation = $749.77
Hence, the computer is worth $749.77 after three years of depreciation at a rate of 16% per year.
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The complete question is
Cleo bought a computer for $1,495. What is it worth after depreciating for 3 years at a rate of 16% per year?
The faces of a rectangular prism have areas of 9, 9, 25, 25, 49, and 49 square meters. Find the volume of the rectangular prism, in cubic meters
The volume of the rectangular prism is 105 cubic meters.
To find the volume of the rectangular prism, we can use the formula V = lwh, where V is the volume, l is the length, w is the width, and h is the height.
Since there are three pairs of congruent faces, we can deduce that the areas of the three pairs of faces represent the three dimensions of the rectangular prism. The areas are 9, 25, and 49 square meters, which are the squares of the sides' lengths.
Take the square root of each area to find the corresponding side lengths:
√9 = 3 meters
√25 = 5 meters
√49 = 7 meters
Now, apply the formula to find the volume:
V = lwh = 3 × 5 × 7 = 105 cubic meters.
The volume of the rectangular prism is 105 cubic meters.
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A farmer sell 7. 9 kilograms of pears and apples at the farmers market. 3/5 of this wieght is pears,and the rest is apples. How many apples did she sell at the farmers market?
The farmer sold 3.16 kilograms of apples at the farmers market.
What is division?
A division is one of the fundamental mathematical operations that divides a larger number into smaller groups with the same number of components. How many total groups will be established, for instance, if 20 students need to be separated into groups of five for a sporting event? The division operation makes it simple to tackle such issues. Divide 20 by 5 in this case. 20 x 5 = 4 will be the outcome. There will therefore be 4 groups with 5 students each. By multiplying 4 by 5 and receiving the result 20, you may confirm this value.
Let's start by finding out the weight of pears the farmer sold.
Weight of pears = 3/5 x 7.9 kg = 4.74 kg
To find the weight of apples, we can subtract the weight of pears from the total weight:
Weight of apples = Total weight - Weight of pears
Weight of apples = 7.9 kg - 4.74 kg
Weight of apples = 3.16 kg
Therefore, the farmer sold 3.16 kilograms of apples at the farmers market.
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solve quadratic equation 6x²-11x-35= 0 pls needed urgently
Answer:
Step-by-step explanation:To solve the quadratic equation 6x²-11x-35= 0, we can use the quadratic formula:
x = (-b ± sqrt(b² - 4ac)) / 2a
where a, b, and c are the coefficients of the quadratic equation.
In this case, we have:
a = 6
b = -11
c = -35
Substituting these values into the quadratic formula, we get:
x = (-(-11) ± sqrt((-11)² - 4(6)(-35))) / 2(6)
Simplifying this expression:
x = (11 ± sqrt(121 + 840)) / 12
x = (11 ± sqrt(961)) / 12
x = (11 ± 31) / 12
So, we have two solutions:
x = (11 + 31) / 12 = 3
and
x = (11 - 31) / 12 = -5/2
Therefore, the solutions to the equation 6x²-11x-35= 0 are x = 3 and x = -5/2.
Please upload a picture of a piece of paper with the problem worked out, and draw the graph for extra points, there will be 6 of these, so go to my profile and find the rest, and do the same, for extra points. for this one, use substitution method.
The value of X and y when substitution method is used to solve the given quadratic equation would be = 8 and 2 respectively.
How to calculate the unknown values using the substitution method?The equations that are given is listed below:
X - 3y = 2 ---> equation 1
2x - 6y = 6 ----> equation 2
In equation 1, make X the subject of formula;
X = 2 + 3y
Substitute X = 2 + 3y into equation 2,
2( 2 + 3y) - 6y = 6
4 + 6y - 6y = 6
y = 6-4
y = 2
Substitute y = 2 into equation 1;
x - 3(2) = 2
X = 2 + 6
X= 8
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expanded form 6.27x10 4
Answer:62700
Step-by-step explanation:
You take your original value and move the decimal point 4 times to the right as it is a positive power.
Find the area of the shaded region.
round to the nearest tenth.
1230
18.6 m
area = [ ? ] m2
The area of the shaded region is 422.8 m², rounded to the nearest tenth.
To find the area of the shaded region, we first need to determine the areas of the two shapes that make up the region. The first shape is a rectangle with dimensions of 18.6 m by 30 m, which has an area of:
Area of rectangle = length x width = 18.6 m x 30 m = 558 m²
The second shape is a semi-circle with a diameter of 18.6 m, which has a radius of 9.3 m. The area of a semi-circle is half the area of a full circle, so we can use the formula for the area of a circle to find the area of the semi-circle:
Area of semi-circle = (1/2) x π x r² = (1/2) x π x 9.3² = 135.2 m²
To find the area of the shaded region, we need to subtract the area of the semi-circle from the area of the rectangle:
Area of shaded region = Area of rectangle - Area of semi-circle
Area of shaded region = 558 m² - 135.2 m²
Area of shaded region = 422.8 m²
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Kendrick is trying to determine if a painting he wants to buy will fit in the space on his wall. If the rectangular frame's diagonal is 50 inches and forms a 36.87° angle with the bottom of the frame, what is its height? Round your answer to the nearest inch.
The height of the rectangular frame is 30 inches.
How to find the height of the frame?Kendrick is trying to determine if a painting he wants to buy will fit in the space on his wall. The rectangular frame's diagonal is 50 inches and forms a 36.87° angle with the bottom of the frame.
Hence, the height of the frame can be represented as follows:
using trigonometric ratios,
sin 36.87 = opposite / hypotenuse
sin 36.87 = h / 50
cross multiply
h = 50 sin 36.87
h = 50 × 0.60000142913
h = 30.0000714566
Therefore,
height of the frame = 30 inches
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PLEASE HELP I NEED THIS QUICK!!!
The number of ways to travel the route is given as follows:
18 ways.
What is the Fundamental Counting Theorem?The Fundamental Counting Theorem states that if there are m ways to do one thing and n ways to do another, then there are m x n ways to do both.
This can be extended to more than two events, where the number of ways to do all the events is the product of the number of ways to do each individual event, according to the equation presented as follows:
[tex]N = n_1 \times n_2 \times \cdots \times n_n[/tex]
The options for this problem are given as follows:
Providence to Boston: 3 ways.Boston to Syracuse: 3 ways.Syracuse to Pittsburgh: 2 ways.Hence the total number of ways is given as follows:
3 x 3 x 2 = 18 ways.
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the chance of rain on a random day in May in Gwinnett is about 30%. Using this empirical probability, what would you estimate the probability of having NO rain for an entire week (7 days)?
The probability of having NO rain for an entire week (7 days) is 0.9998
Estimating the probability of having no rainFrom the question, we have the following parameters that can be used in our computation:
P(Rain) = 30%
Given that the number of days is
n = 7
The probability of having no rain for an entire week is calculated as
P = 1 - P(Rain)ⁿ
Where
n = 7
Substitute the known values in the above equation, so, we have the following representation
P = 1 - (30%)⁷
Evaluate
P = 0.9998
Hence, the probability is 0.9998
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The smaller of two similar rectangles has dimensions 4 and 6. Find the dimensions of the larger rectangle if the ratio of
the perimeters is 2 to 3.
O 6 by 9
2/3
by 4
12 by 12
O8 by 18
Answer:
The smaller rectangle has perimeter
2(4 + 6) = 2(10) = 20, so the larger rectangle will have perimeter 30. The dimensions of the larger rectangle are 6 by 9 since 2(6 + 9) = 2(15) = 30.
A rectangle is changing in such a manner that its length is increasing 5 ft/sec and its width is decreasing 2 ft/sec. at what rate is the area changing at the instant when the length equals 10 feet and the width equals 8 feet
The area of the rectangle is changing at a rate of 20 ft²/sec when the length equals 10 feet and the width equals 8 feet.
How to find the length and width?Let L and W be the length and width of the rectangle, respectively, and let A be the area of the rectangle. Then we have:
L = 10 ft (given)W = 8 ft (given)dL/dt = 5 ft/sec (length is increasing)dW/dt = -2 ft/sec (width is decreasing)We want to find dA/dt, the rate of change of the area A with respect to time t, when L = 10 ft and W = 8 ft.
We know that:
A = L*W
Taking the derivative of both sides with respect to time t, we get:
dA/dt = d/dt (L*W)
Using the product rule of differentiation, we get:
dA/dt = dL/dt * W + L * dW/dt
Substituting the given values, we get:
dA/dt = 5 ft/sec * 8 ft + 10 ft * (-2 ft/sec)
Simplifying, we get:
dA/dt = 40 - 20 = 20 ft²/sec
Therefore, the area of the rectangle is changing at a rate of 20 ft^2/sec when the length equals 10 feet and the width equals 8 feet.
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Give an example of a Benchmark fraction and an example of a mixed number
The benchmark fractions are the most common fraction.
Such as 1/2, 0, 3/8 etc.
What is a mixed fraction?Mixed fractions are a type of fraction in which there is a whole number part and a fractional part. for example 17/3 would be 5 2/3 as a mixed fraction
Evaluate the integral.
∫(x^3+4x)/x^4+8x^2+1
To evaluate the integral ∫(x^3+4x)/x^4+8x^2+1, we can use the substitution u = x^2 + 1. Then, du/dx = 2x, which means that dx = du/(2x). Substituting these into the integral, we get:
∫(x^3+4x)/x^4+8x^2+1 dx = ∫(1/u)(x^2+1)(x^3+4x)/(2x) du
= 1/2 ∫(u-1)/u^2 du
= 1/2 ∫(u/u^2 - 1/u^2) du
= 1/2 ln|u| + 1/2 (1/u) + C
= 1/2 ln|x^2+1| + 1/2 (1/(x^2+1)) + C
Therefore, the final answer is ∫(x^3+4x)/x^4+8x^2+1 dx = 1/2 ln|x^2+1| + 1/2 (1/(x^2+1)) + C.
Hi! To evaluate the integral, we can rewrite the given expression as follows:
∫((x^3 + 4x) / (x^4 + 8x^2 + 1)) dx
Now, let's use substitution to solve this integral. Let's set:
u = x^2 + 4
Then, the derivative du/dx = 2x. So, dx = du / (2x).
Now, we can rewrite the integral in terms of u:
∫((x^3 + 4x) / (u^2 + 1)) (du / (2x))
Notice that x^3/x and 4x/x simplify, and we are left with:
(1/2) ∫(u / (u^2 + 1)) du
Now we can integrate this expression:
(1/2) * [ln(u^2 + 1) + C]
Now, substitute back x^2 + 4 for u:
(1/2) * [ln(x^2 + 4 + 1) + C] = (1/2) * [ln(x^2 + 5) + C]
So, the evaluated integral is:
(1/2) * [ln(x^2 + 5) + C]
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To gather information about the elk population, biologist marked 75 elk. later, they flew over the region and counted 250 elk, of
which 15 were marked. what is the best estimate for the elk population?
es -))
a)
1,200
b)
1,250
c)
1,300
d)
1,350
The best estimate for the elk population is b) 1,250.
To estimate the elk population, you can use the mark and recapture method. The proportion of marked elk to the total marked population should be equal to the proportion of marked elk observed in the sample to the total observed population.
So, (marked elk / total marked population) = (marked elk observed / total observed population)
In this case: (75 / total population) = (15 / 250)
Now, solve for the total population:
75 / total population = 15 / 250
Cross-multiply:
15 * total population = 75 * 250
total population = (75 * 250) / 15
total population = 18,750 / 15
total population = 1,250
The best estimate for the elk population is 1,250 (option b).
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Alexi sells apples in her garden at a stand sell each 3. 00 apples what is her total cost how many should she produce
Alexi to consider these factors before deciding how many apples to produce depends on the demand for apples in her area, the size of her garden, and her ability to produce apples efficiently.
How to determine Alexi's total revenue?To determine Alexi's total revenue, we need to know how many apples she plans to sell. Let's assume that Alexi plans to sell X apples.
If Alexi sells each apple for $3, her total revenue will be:
Total revenue = Price per apple x Number of apples sold
Total revenue = $3 X X
Total revenue = $3X
To determine the cost of producing the apples, we need more information about Alexi's production costs. These costs can include expenses such as land, labor, water, and equipment.
Once we know the production costs, we can subtract them from the total revenue to determine Alexi's profit. If the profit is positive, then Alexi will earn money by selling the apples.
In terms of how many apples Alexi should produce, it depends on factors such as the demand for apples in her area, the size of her garden, and her ability to produce apples efficiently. It's important for Alexi to consider these factors before deciding how many apples to produce.
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