(a) The probability that a person owns fewer than 3 calculators is 0.95.
(b) The expected number of calculators that a person owns is 1.4.
(c) The expected value of X (the number of calculators a person owns) is 1.4.
(d) The standard deviation for the number of calculators a person owns is 0.8.
(a) To find the probability that a person owns fewer than 3 calculators, we need to calculate the cumulative probability up to X = 2. This includes the probabilities P(X = 0), P(X = 1), and P(X = 2). Adding these probabilities together, we have 0.15 + 0.40 + 0.40 = 0.95. Therefore, the probability that a person owns fewer than 3 calculators is 0.95.
(b) To find the expected number of calculators that a person owns, we multiply each possible number of calculators by its respective probability and sum them up. So, we have (0 × 0.15) + (1 ×0.40) + (2 × 0.40) + (3 × 0.05) = 1.4. Therefore, the expected number of calculators that a person owns is 1.4.
(c) The expected value of X, denoted E[X], represents the average number of calculators that a person owns. In this case, we have already calculated E[X] in part (b), which is 1.4.
(d) The standard deviation of X, denoted as σX, measures the spread or variability of the number of calculators a person owns. To calculate it, we need to find the variance of X and then take the square root. The variance of X is calculated as the sum of each value of (X - E[X]) squared multiplied by its respective probability. So, we have [tex](0 - 1.4)^{2}[/tex] ×0.15 + [tex](1 - 1.4)^{2}[/tex]× 0.40 +[tex](2 - 1.4)^{2}[/tex] × 0.40 + [tex](3 - 1.4)^{2}[/tex] × 0.05 = 0.8. Taking the square root of the variance, we find that the standard deviation for the number of calculators a person owns is 0.8.
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consider two concentric spheres with diameters 12cm and 18cm forming an enclosure. The view factor, from the inner surface of the outer sphere to its own , is
A
4
9
B
1
C
5
9
D
0
The view factor from the inner surface of the outer sphere (Sphere B) to its own surface is 9/4.
In this case, we have two concentric spheres with diameters of 12 cm and 18 cm. Let's denote the inner sphere as Sphere A and the outer sphere as Sphere B.
The view factor from the inner surface of Sphere B to its own surface (F_AB) can be calculated using the formula:
F_AB = (A_AB) / (A_A)
where A_AB is the area of the surface on Sphere B that can "see" the inner surface of Sphere B, and A_A is the total surface area of Sphere A.
In this case, since the spheres are concentric, the view factor from the inner surface of Sphere B to its own surface is simply the ratio of the surface area of Sphere B that faces the inner surface of Sphere B to the total surface area of Sphere A.
The surface area of Sphere B that faces the inner surface of Sphere B is the same as the surface area of Sphere B itself, which is given by:
A_AB = 4πr_B²
where r_B is the radius of Sphere B (which is half of its diameter).
The total surface area of Sphere A is given by:
A_A = 4πr_A²
where r_A is the radius of Sphere A (which is half of its diameter).
Let's calculate the view factor (F_AB):
Radius of Sphere B (r_B) = 9 cm (since the diameter is 18 cm)
Radius of Sphere A (r_A) = 6 cm (since the diameter is 12 cm)
A_AB = 4π(9²) = 324π
A_A = 4π(6²) = 144π
F_AB = A_AB / A_A
= (324π) / (144π)
= 9/4
Therefore, the view factor from the inner surface of the outer sphere (Sphere B) to its own surface is 9/4.
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the following histogram shows the distribution of serum cholesterol level (in milligrams per deciliter) for a sample of men. use the histogram to answer the following questions. The percentage of men with cholesterol levels above 220 is closest to (Choose one)
Based on the histogram, it seems that the percentage of men with cholesterol levels above 220 is around 15%. To calculate this, we can look at the total area of the bars to the right of 220 and divide it by the total area of the entire histogram.
To be more specific, we can count the number of bars to the right of 220, which is 3. Each of these bars has a width of 5 and a height (frequency) of 4, 6, and 2 respectively. So the total area of these bars is 5 x (4 + 6 + 2) = 60.
The total area of the entire histogram is 5 x 20 = 100. Therefore, the percentage of men with cholesterol levels above 220 is (60/100) x 100 = 60%.
So the answer is not provided in the answer choices, but it would be closest to 60% based on the given histogram.
The histogram displays the distribution of serum cholesterol levels in milligrams per deciliter (mg/dL) for a sample of men. To determine the percentage of men with cholesterol levels above 220 mg/dL, you should examine the histogram and identify the relevant bars that represent cholesterol levels above 220 mg/dL. Then, calculate the number of men in these bars and divide it by the total number of men in the sample, and finally multiply the result by 100 to obtain the percentage.
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Which choices are equivalent to the fraction below
Answer:
E and F
Step-by-step explanation:
(16/20 = 0.80)
14/8 = 1.75
9/10 = 0.90
8/5 =1.60
13/10 = 1.30
4/5 = 0.80
8/10 = 0.80
You have to to put the reduce the fractions and then put them in to decimal form then see if they are the same as the one you want it to be.
Is the area of a square with side length 2 inches greater than or less than the area of a circle with radius 1. 2 inches? How do you know?
A square has sides of equal lengths and four right angles while a circle is a geometric shape that has a curved line circumference and radius and are measured in degrees.
The area of a square is found by multiplying the length by the width.
The area of a circle, on the other hand, is found by multiplying π (3.14) by the radius squared.
To find out whether the area of a square with a side length of 2 inches is greater than or less than the area of a circle with a radius of 1.2 inches, we must first calculate the areas of both figures.
Using the formula for the area of a square we get:
Area of a square = side length × side length
Area of a square,
= 2 × 2
= 4 square inches.
Now let's calculate the area of a circle with radius of 1.2 inches, using the formula:
Area of a circle = π × radius squared
Area of a circle,
= 3.14 × (1.2)²
= 4.523 square inches
Since the area of the circle (4.523 square inches) is greater than the area of the square (4 square inches), we can say that the area of the square with a side length of 2 inches is less than the area of a circle with a radius of 1.2 inches.
Therefore, the answer is less than (the area of a circle with radius 1.2 inches).
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3. A businesswoman bought a personal computer for $108 000.
a) Calculate her selling price on the personal computer if she wants to make a profit of
25%
b) During transporting the personal computer to the customer, it was damaged. Calculate
her selling price if she incurred a loss of 5%.
According to he solving the selling price of the personal computer, if the businesswoman incurred a loss of 5%, would be $102,600
(a) Calculation of the selling price of the personal computer for 25% profit:
As per the given question, a businesswoman bought a personal computer for $108,000. Now, she wants to sell it to make a profit of 25%.
Thus, the selling price of the personal computer would be equal to the cost price of the computer plus the 25% profit.Using the formula of cost price, we can calculate the selling price of the computer as follows:
Selling Price = Cost Price + Profit
Since the profit required is 25%, we can represent it in decimal form as 0.25.
Therefore, Selling Price = Cost Price + 0.25 × Cost Price
= Cost Price (1 + 0.25)
= Cost Price × 1.25
= $108,000 × 1.25
= $135,000
Therefore, the selling price of the personal computer, if the businesswoman wants to make a profit of 25%, would be $135,000.
(b) Calculation of the selling price of the personal computer if the businesswoman incurred a loss of 5%:Now, let's suppose that during the transportation of the personal computer to the customer, it was damaged, and the businesswoman incurred a loss of 5%.
Therefore, the selling price of the personal computer would be equal to the cost price of the computer minus the 5% loss.As per the given question, the cost of the personal computer is $108,000.
Using the formula of cost price, we can calculate the selling price of the computer as follows:
Selling Price = Cost Price - Loss
Since the loss incurred is 5%, we can represent it in decimal form as 0.05.
Therefore, Selling Price = Cost Price - 0.05 × Cost Price
= Cost Price (1 - 0.05)
= Cost Price × 0.95
= $108,000 × 0.95
= $102,600
Therefore, the selling price of the personal computer, if the businesswoman incurred a loss of 5%, would be $102,600
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If you can please show your work. Thanks!
The equation of this circle in standard form is (x + 1)² + (y - 3)² = 4².
What is the equation of a circle?In Mathematics and Geometry, the standard form of the equation of a circle is modeled by this mathematical equation;
(x - h)² + (y - k)² = r²
Where:
h and k represent the coordinates at the center of a circle.r represent the radius of a circle.Based on the information provided in the graph above, we have the following parameters for the equation of this circle:
Center (h, k) = (-1, 1)
Radius (r) = 4 units.
By substituting the given parameters, we have:
(x - h)² + (y - k)² = r²
(x - (-1))² + (y - 3)² = 4²
(x + 1)² + (y - 3)² = 4²
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Complete Question:
Find the equation of this circle in standard form.
If the sum of the parallel sides of a trapezium shaped field is 32m and the distance the two parallel sides is 10m then its area is
The area of the trapezium is 160 + 5b/2 square meters.
Given data:
The sum of the parallel sides of a trapezium-shaped field is 32 m.
Distance between the two parallel sides is 10 m.
To find: The area of the trapezium
Formula: Area of a trapezium is given by the formula,
A = 1/2 (a+b)h,
Where, a and b are the length of parallel sides,
h is the perpendicular distance between two parallel sides.
Calculation:
Given that the sum of parallel sides is 32 m, a+b = 32 (Equation 1)
And, distance between two parallel sides is 10 m, h = 10 m.
Now, we can calculate the length of one of the parallel sides.
Substituting the value of a from equation (1) in the above formula we get,
32-b/2 × 10 = A
Which gives, 160 - b/2 = A
Thus, we get the area of the trapezium by putting the values in the formula,
A = 1/2 (a+b)h
A = 1/2 (32+b)×10
A = 160 + 5b/2
So, the area of the trapezium is 160 + 5b/2 square meters.
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I need help pls.
MULTIPLE CHOICE Kala is making a tile
design for her kitchen floor. Each tile has sides that are 3 inches less than twice the side length of the smaller square inside
the design.
Select the polynomial that represents the
area of the tile.
(A) 2x²-3x
(B) 4x² - 12x +9
(C) 4x² + 12x + 9
(D) 4x² - 9
Answer: b
Step-by-step explanation:
took the test
Julia grows the same yeast colonies in 20 test tubes. She places 10 of the tubes in a fume hood with a normal atmosphere and labels them "Group A". The remaining tubes she places in a closed system in which the oxygen level is double the normal level and labels them "Group B". Which of the following best describes the groups?
Question 3 options:
Group A is the experimental group and Group B is the control
Group A is the control and Group B is the experimental group
Group A is hypothesis and Group B is the variable
Group A is the theory and Group B is the dependent variable
Julia is conducting an experiment to observe the effect of oxygen levels on the growth of yeast colonies. To do this, she grows the same yeast colonies in 20 test tubes and splits them into two groups: Group A with a normal oxygen level and Group B with double the normal oxygen level.
In an experiment, the control group is the group that is kept under normal or standard conditions, and the experimental group is the group that is exposed to the variable being tested. In this case, Group A is kept under normal conditions, and Group B is exposed to the variable (double the normal oxygen level).
Therefore, the best description of the groups would be: Group A is the control and Group B is the experimental group. This is because the control group is used as a baseline to compare the results with the experimental group.
In summary, Group A is used as a standard or control group, while Group B is used as an experimental group to test the effect of the variable (double the normal oxygen level) on the growth of yeast colonies.
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show that each wff is a tautology by using equivalences to show that each wff is equivalent to true.A → Ꞁ (Ꞁ A v ¬ B) v Ꞁ B
The given WFF is equivalent to "true" using logical equivalences. Therefore, it is a tautology.
To show that a well-formed formula (WFF) is a tautology, we need to demonstrate that it is logically equivalent to the statement "true" regardless of the truth values assigned to its variables. Let's analyze the given WFF step by step and apply logical equivalences to show that it is equivalent to "true."
The given WFF is:
A → (¬A v ¬B) v B
We'll use logical equivalences to transform this expression:
Implication Elimination (→):
A → (¬A v ¬B) v B
≡ ¬A v (¬A v ¬B) v B
Associativity (v):
¬A v (¬A v ¬B) v B
≡ (¬A v ¬A) v (¬B v B)
Negation Law (¬P v P ≡ true):
(¬A v ¬A) v (¬B v B)
≡ true v (¬B v B)
Identity Law (true v P ≡ true):
true v (¬B v B)
≡ true
Hence, we have shown that the given WFF is equivalent to "true" using logical equivalences. Therefore, it is a tautology.
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let r be a partial order on set s, and t ⊆ s. suppose that a,a′ ∈ t, where a is greatest and a′ is maximal. prove that a = a′
Let r be a partial order on set S, and let t be a subset of S. If a and a' are both elements of t, where a is the greatest element and a' is a maximal element, then it can be proven that a = a'.
To prove that a = a', we consider the definitions of greatest and maximal elements. The greatest element in a set is an element that is greater than or equal to all other elements in that set. A maximal element, on the other hand, is an element that is not smaller than any other element in the set, but there may exist other elements that are incomparable to it.
Given that a is the greatest element in t and a' is a maximal element in t, we can conclude that a' is not smaller than any other element in t. Since a is the greatest element, it is greater than or equal to all elements in t, including a'. Therefore, a is not smaller than a'.
Now, to prove that a' is not greater than a, suppose by contradiction that a' is greater than a. Since a' is not smaller than any other element in t, this would imply that a is smaller than a'. However, since a is the greatest element in t, it cannot be smaller than any other element, including a'. This contradicts our assumption that a' is greater than a.
Hence, we have shown that a is not smaller than a' and a' is not greater than a, which implies that a = a'. Therefore, if a is the greatest element and a' is a maximal element in t, then a = a'.
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PLEASE SOMEONE ANSWER THIS ASAP PLS I NEED IT
The required exponential regression equation is y = 6682 · 0.949ˣ
Given is a table we need to create an exponential regression for the same,
The exponential regression is give by,
y = a bˣ,
So here,
x₁ = 4, y₁ = 5,434
x₂ = 6, y₂ = 4,860
x₃ = 10, y₃ = 3963
Therefore,
Fitted coefficients:
a = 6682
b = 0.949
Exponential model:
y = 6682 · 0.949ˣ
Hence the required exponential regression equation is y = 6682 · 0.949ˣ
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evaluate the integral by reversing the order of integration. 27 0 3 6ex4 dx dy 3 y
The value of the integral by reversing the order of integration is (81/4)(96e^(12) - 1).
We need to evaluate the integral of 3y over the region R bounded by x=0, x=3, y=27, and y=6e^(4x) by reversing the order of integration.
To reverse the order of integration, we first draw the region of integration, which is a rectangle. Then, we integrate with respect to x first. For each value of x, the limits of integration for y are from 27 to 6e^(4x). Thus, we have:
∫(0 to 3) ∫(27 to 6e^(4x)) 3y dy dx = ∫(27 to 6e^(12)) ∫(0 to ln(y/6)/4) 3y dx dy
To find the new limits of integration for x, we solve y=6e^(4x) for x to get x=ln(y/6)/4. The limits of integration for y are still from 27 to 6e^(12).
Now, we can evaluate the integral using the reversed order of integration:
∫(27 to 6e^(12)) (∫(0 to ln(y/6)/4) 3y dx) dy = ∫(27 to 6e^(12)) (3y/4 ln(y/6)) dy
Integrating this expression gives:
(3/4)(y ln(y/6) - (9/4)y) from y=27 to y=6e^(12) = (81/4)(96e^(12) - 1)
Therefore, the value of the integral by reversing the order of integration is (81/4)(96e^(12) - 1).
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Correct answer gets brainliest!!
The longest line segment is line segment A.
option A.
What is the length of the longest line?The length of the longest line is calculated by converting the unit measurement of both lines to the same units as shown below.
the length of line A = 8.3 feet
the length of line B = 2 m
The given conversion factor is;
3.28 ft = 1 m
The length of line B is feet is calculated as follows;
Length of line B (ft) = length in meters x conversion factor
the length of line B = 2 m x 3.28 ft / 1 m
the length of line B = 6.56 feet
Thus, we can conclude that the length of line A is greater than the length of line B.
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Find the x
For 15 points
Step-by-step explanation:
So the measure of angle O is 360°- 230°
<O= 360°- 230°
= 130°
And to get <X it is intrusive angle is the half of suspended arc.
< X = 230°/ 2
< X = 115°
Answer: x=1115
Step-by-step explanation:
the first step in testing a hypothesis is: formulate h0 and h1 collect data and calculate test statistics select appropriate test choose level of significance
The correct answer is "formulate H0 and H1." This comparison helps determine whether there is sufficient evidence to reject the null hypothesis and support the alternative hypothesis.
When testing a hypothesis, the first step is to clearly define the null hypothesis (H0) and the alternative hypothesis (H1). The null hypothesis represents the assumption of no effect or no difference, while the alternative hypothesis represents the hypothesis you are trying to support, which typically suggests the presence of an effect or a difference.
After formulating the hypotheses, the subsequent steps in hypothesis testing are as follows:
Collect data and calculate test statistics: Gather relevant data through observations, experiments, or surveys. Then, analyze the data and calculate the appropriate test statistic based on the nature of the hypothesis being tested. The test statistic depends on the specific hypothesis test being used.
Select an appropriate test: Choose a statistical test that is most suitable for the type of data and the research question at hand. The selection of the test depends on factors such as the nature of the data (continuous or categorical), the number of groups being compared, and the assumptions associated with the test.
Choose the level of significance: Determine the desired level of significance (alpha level) for the hypothesis test. The level of significance represents the maximum probability of incorrectly rejecting the null hypothesis. Commonly used alpha levels are 0.05 (5%) or 0.01 (1%), but it can vary depending on the context and the consequences of making Type I errors.
After completing these steps, further analysis involves comparing the calculated test statistic to the critical value or p-value associated with the chosen level of significance. This comparison helps determine whether there is sufficient evidence to reject the null hypothesis and support the alternative hypothesis.
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e accompanying data set lists full IQ scores for a random sample of subjects with medium lead levels in their blood and another random sample of subjects with high lead levels in their blood. Use a 0.01 significance level to test the claim that IQ scores of subjects with medium lead levels vary more than IQ scores of subjects with high lead levels. A. H 0
:σ 1
2
=σ 2
2
B. H 0
:σ 1
2
=σ 2
2
H 1
:σ 1
2
<σ 2
2
H 1
:σ 1
2
>σ 2
2
c. H 0
:σ 1
2
=σ 2
2
D. H 0
:σ 1
2
=σ 2
2
H 1
:σ 1
2
=σ 2
2
H 1
:σ 1
2
=σ 2
2
Identify the test statistic. The test statistic is
To test the claim that IQ scores of subjects with medium lead levels vary more than IQ scores of subjects with high lead levels, we can use the F-test for comparing variances.
The appropriate null and alternative hypotheses for this test are:
H0: σ1^2 = σ2^2 (The variances of the two populations are equal)
H1: σ1^2 > σ2^2 (The variance of the population with medium lead levels is greater than the variance of the population with high lead levels)
The test statistic for this test is the F-statistic, which is calculated as the ratio of the sample variances:
F = s1^2 / s2^2
where s1^2 is the sample variance of the group with medium lead levels and s2^2 is the sample variance of the group with high lead levels.
To determine the critical value and make a decision about the null hypothesis, we would compare the calculated F-statistic to the critical value from the F-distribution table at a significance level of 0.01. If the calculated F-statistic is greater than the critical value, we would reject the null hypothesis in favor of the alternative hypothesis.
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What are the coordinates of the point on the directed line segment from ( − 3 , − 5 ) (−3,−5) to ( 7 , 10 ) (7,10) that partitions the segment into a ratio of 2 to 3?
The coordinates of the point on the directed line segment from (−3,−5) to (7,10) that partitions the segment into a ratio of 2 to 3 are (1 + √3, 4 + √6) and (1 - √3, 4 - √6).
To find the coordinates of the point that partitions the segment from (−3,−5) to (7,10) into a ratio of 2:3, we can use the ratio formula.
Let (x, y) be the coordinates of the point we're looking for. Then the distance from (−3,−5) to (x,y) is 2/5 of the total distance, and the distance from (x,y) to (7,10) is 3/5 of the total distance.
Using the distance formula, we can find the total distance between the two points:
d = √[(7 - (-3))² + (10 - (-5))²] = √[(10)² + (15)²] = √325
The distance from (−3,−5) to (x,y) is (2/5)√325, and the distance from (x,y) to (7,10) is (3/5)√325.
We can set up two equations based on the coordinates:
(x - (-3))² + (y - (-5))² = (2/5)√325)²
(x - 7)² + (y - 10)² = (3/5)√325)²
Expanding and simplifying these equations, we get:
(x + 3)² + (y + 5)² = 52
(x - 7)² + (y - 10)² = 117
Solving these equations simultaneously will give us the coordinates of the point that partitions the line segment into a 2:3 ratio. One possible method is to solve for y in terms of x in both equations, and then set the two expressions equal to each other:
(x + 3)² + (y + 5)² = 52
(x - 7)² + (y - 10)² = 117
y = -5 ± √(52 - (x + 3)²)
y = 10 ± √(117 - (x - 7)²)
-5 ± √(52 - (x + 3)²) = 10 ± √(117 - (x - 7)²)
Squaring both sides of the equation and simplifying, we get:
x² - 2x + 28 = 0
This quadratic equation has two solutions:
x = 1 ± √3
Substituting each value of x into either equation for y, we get the coordinates of the two points that partition the segment into a 2:3 ratio:
(1 + √3, 4 + √6) and (1 - √3, 4 - √6)
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The shape of this particular section of the rollercoaster is a half of a circle. Center the circle at the origin and assume the highest point on this leg of the roller coaster is 30 feet above the ground
The equation of the circle that forms the section of the rollercoaster is:x² + y² = 900
The shape of this particular section of the rollercoaster is a half of a circle. Center the circle at the origin and assume the highest point on this leg of the roller coaster is 30 feet above the ground.To find the equation of the circle that forms the section of the rollercoaster, we can use the standard form equation of a circle which is:(x - h)² + (y - k)² = r²Where (h, k) is the center of the circle and r is the radius. Since the center is at the origin, h = 0 and k = 0. We only need to find the value of the radius, r.The highest point on the rollercoaster is at the center of the circle. Since it is 30 feet above the ground, it means that the distance from the center to the ground is also 30 feet. Thus, the radius is equal to 30 feet.
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Find a counterexample, if possible, to these universally quantified statements, where the domain for all variables consists of all integers.
A) ∀x(x2≥x)
B) ∀x(x>0∨x<0)c)∀x(x=1)
A) A counterexample for ∀x(x² ≥ x) is x = -1.
B) A counterexample for ∀x(x > 0 ∨ x < 0) is x = 0.
C) No counterexample exists for ∀x(x = 1).
A) The statement claims that for all integers x, x² is greater than or equal to x. However, when x = -1, we get (-1)² = 1, which is not greater than or equal to -1.
B) The statement claims that for all integers x, x is either greater than 0 or less than 0. However, when x = 0, it is not greater than 0 nor less than 0, disproving the claim.
C) The statement is not universally quantified, as it claims that every integer x is equal to 1. This is clearly false, as there are many other integers besides 1.
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The area of the region in the first quadrant enclosed by the graph of y = x(1 – x) and the x axis is A. 2/3 B. 1/3 C. 5/6 D. 1/6
Answer:
D. 1/6
Step-by-step explanation:
You want the area enclosed by the graph of y = x(1 -x) and the x-axis.
IntegralThe area is the integral of the function value over the interval in which it is non-negative.
The zeros are at x=0 and x=1, so those are the limits of integration.
[tex]\displaystyle \int_0^1{(x-x^2)}\,dx=\left[\dfrac{x^2}{2}-\dfrac{x^3}{3}\right]_0^1=\dfrac{1}{2}-\dfrac{1}{3}=\dfrac{1}{6}[/tex]
The enclosed area is 1/6 square units.
<95141404393>
An airplane takes 8 hours to fly an 8000 km trip with the wind. The return trip (against the wind) takes 10 hours. Determine the speed of the plane and the speed of the wind
The speed of the plane is 900 km/h, and the speed of the wind is 100 km/h.
Let's denote the speed of the plane as P and the speed of the wind as W.
When the airplane is flying with the wind, the effective speed of the plane is increased by the speed of the wind. Conversely, when the airplane is flying against the wind, the effective speed of the plane is decreased by the speed of the wind.
We can set up two equations based on the given information:
With the wind:
The speed of the plane with the wind is P + W, and the time taken to cover the 8000 km distance is 8 hours. Therefore, we have the equation:
(P + W) * 8 = 8000
Against the wind:
The speed of the plane against the wind is P - W, and the time taken to cover the same 8000 km distance is 10 hours. Therefore, we have the equation:
(P - W) * 10 = 8000
We can solve this system of equations to find the values of P (speed of the plane) and W (speed of the wind).
Let's start by simplifying the equations:
(P + W) * 8 = 8000
8P + 8W = 8000
(P - W) * 10 = 8000
10P - 10W = 8000
Now, we can solve these equations simultaneously. One way to do this is by using the method of elimination:
Multiply the first equation by 10 and the second equation by 8 to eliminate W:
80P + 80W = 80000
80P - 80W = 64000
Add these two equations together:
160P = 144000
Divide both sides by 160:
P = 900
Now, substitute the value of P back into either of the original equations (let's use the first equation):
(900 + W) * 8 = 8000
7200 + 8W = 8000
8W = 8000 - 7200
8W = 800
W = 100
Therefore, the speed of the plane is 900 km/h, and the speed of the wind is 100 km/h.
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Atong needs to make a square pyramid for his project. His brother helped him with the geometric net, and it shows four triangles. Will he be able to gorm the square pyramid out of the net that his brother made?
Yes, Atong will be able to form a square pyramid out of the net that his brother made.
A geometric net is a two-dimensional representation of a three-dimensional shape that can be folded to create the shape. In the case of a square pyramid, the net consists of four triangles and a square base.
To form a square pyramid, the triangles need to be folded along their edges and connected to create the four sides of the pyramid, with the square base closing the bottom.
Since the net provided by Atong's brother consists of four triangles, it aligns with the requirements for constructing a square pyramid. Each triangle represents one of the four sides of the pyramid. By folding along the edges of the triangles and connecting them, Atong will be able to form the desired square pyramid shape.
It is important to ensure that the dimensions of the triangles and the square base match and align correctly when folding the net. If the measurements are accurate and the edges are properly connected, Atong will successfully create a square pyramid.
Therefore, based on the information provided, Atong will be able to form the square pyramid using the net that his brother made, as the net contains the necessary components to construct the desired shape.
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Two angels of a quadrilateral measures 260 and 30. The other two angels are in a ratio of 3:4. What are the measures of those two angels?
Given,Two angles of a quadrilateral measures 260 and 30.The other two angles are in a ratio of 3:4.
Let the measures of other two angles be 3x and 4x (in degrees).Since the sum of all angles in a quadrilateral is 360°, we can write the equation as follows;
Sum of all the angles of the quadrilateral = 260 + 30 + 3x + 4x =360
= 290 + 7x = 360
= 70x = 10°
= x = 7°
Now, measure of other two angles = 3x and 4x = 3(10°) and 4(10°)= 30° and 40°
Hence, the measures of those two angles are 30° and 40°.
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Cynthia had a credit card with a 17% APR and a $3,265 balance. She had budgeted to have the credit card paid off in 24 months. But after missing a single monthly payment, Cynthia’s credit card company has increased her interest rate to 21%. How much extra will Cynthia have to pay in finance charges (interest) because of the increase in her APR if she still pays off the credit card in 24 months? a. $152. 16 b. $272. 08 c. $609. 32 d. $761. 48 Please select the best answer from the choices provided A B C D.
The extra amount Cynthia will have to pay in finance charges (interest) due to the increase in her APR is $761.48.
In summary, Cynthia will have to pay an additional $761.48 in finance charges because of the increase in her APR.
To calculate the extra finance charges, we need to compare the finance charges under the original APR and the new APR.
Under the original APR of 17%, Cynthia's monthly interest rate would be (17%/12) = 1.42%. With a balance of $3,265 and a repayment period of 24 months, the total finance charges would be ($3,265 * 1.42% * 24) = $1,169.47.
After missing a payment, Cynthia's APR increases to 21%. The new monthly interest rate would be (21%/12) = 1.75%. Using the same balance and repayment period, the total finance charges under the new APR would be ($3,265 * 1.75% * 24) = $1,930.95.
The difference in finance charges between the two APRs is ($1,930.95 - $1,169.47) = $761.48. Therefore, Cynthia will have to pay an additional $761.48 in finance charges due to the increase in her APR.
Thus, the correct answer is d. $761.48.
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The transport of a substance across a capillary wall in lung physiology has been modeled as (dh)/(dt)=((-R)/(v))((h)/(R+h)) where h is the hormone concentration in the bloodstream, t is the time, R is the maximum transport rate, v is the volume of the capillary, and k is a constant measuring the affinity between the hormones and the enzymes that assist the process. Solve the differential equation and find h(t).
We start by rearranging the given differential equation into the standard form of a separable differential equation:
[tex]\frac{dh}{dt} = (\frac{-R}{v}) (\frac{h}{R+h})[/tex]
=> [tex](\frac{v}{R+h)} \frac{dh}{h} = \frac{-R}{v} dt[/tex]
Integrating both sides with respect to their respective variables, we get:
[tex]ln|h+R| - ln|R| = (\frac{-R}{v}) t + C[/tex]
where C is the constant of integration. Simplifying, we have:
[tex]ln|h+R| = (\frac{-R}{v})t + ln|CR|[/tex]
where CR is a positive constant obtained by combining R and the constant of integration.
Taking the exponential of both sides, we get:
[tex]|h+R| = e^{(\frac{-R}{v}) t} + ln|CR|)[/tex]
=> [tex]|h+R| = e^{(\frac{-R}{v}) t} CR[/tex]
We take cases for h+R being positive and negative:
Case 1: h+R > 0
Then we have: [tex]|h+R| = e^{(\frac{-R}{v}) t} CR[/tex]
[tex]h = (e^{(\frac{-R}{v}) t} CR) - R[/tex]
Case 2: h+R < 0
Then we have:
[tex]|h+R| = e^{(\frac{-R}{v}) t} CR[/tex]
=>[tex]h =- ((e^{(\frac{-R}{v}) t} CR)+R[/tex]
Therefore, the general solution to the given differential equation is:
[tex]h(t)=e^{(\frac{-R}{v}) t} CR)-R[/tex] if h+R > 0,
[tex]- (e^{\frac{-R}{v} }t ) CR)+R[/tex]if h+R < 0}
where CR is a positive constant determined by the initial conditions.
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Verify(-5/9)+7/21=7/21+(-5/9)
The expressions (-5/9) + 7/21 and 7/21 + (-5/9) are equivalent by the commutative property of addition
Verifying if the expressions are equivalentFrom the question, we have the following parameters that can be used in our computation:
(-5/9)+7/21=7/21+(-5/9)
Express properly
So, we have
(-5/9) + 7/21 = 7/21 + (-5/9)
The commutative property of addition states that
a + b = b + a
In this case, we have
a = -5/9
b = 7/21
Using the above as a guide, we have the following conclusion
This means that the expressions are equivalent by the commutative property of addition
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A triangular prism has a base that is 12cm2. Its height is 5cm. What is its volume
Volume of the triangular prism is = [tex]60cm^3[/tex]
We have the information from the question:
A triangular prism has a base area is : [tex]12cm^2[/tex]
A triangular prism has height is 5 cm
We have to find the volume of the triangular prism.
We know that :
The formula of volume of the triangular prism:
Volume of the triangular prism is = [tex]A_b.h[/tex]
Volume of the triangular prism = 12 × 5
Volume of the triangular prism = [tex]60cm^3[/tex]
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The point P is on the unit circle. If the y-coordinate of P is -3/8 , and P is in quadrant III , then x= what ?
The value of x is -sqrt(55)/8.
Let's use the Pythagorean theorem to find the value of x.
Since P is on the unit circle, we know that the distance from the origin to P is 1. Let's call the x-coordinate of P "x".
We can use the Pythagorean theorem to write:
x^2 + (-3/8)^2 = 1^2
Simplifying, we get:
x^2 + 9/64 = 1
Subtracting 9/64 from both sides, we get:
x^2 = 55/64
Taking the square root of both sides, we get:
x = ±sqrt(55)/8
Since P is in quadrant III, we know that x is negative. Therefore,
x = -sqrt(55)/8
So the value of x is -sqrt(55)/8.
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What is the simplified form of the expression x^2-4x-21 over 4(x-7)
The simplified form of the expression (x² - 4x -21)/4(x-7) is (x + 3)/4
How to determine the simplified form of the expressionFrom the question, we have the following parameters that can be used in our computation:
x²-4x-21 over 4(x-7)
Express properly
So, we have
(x² - 4x -21)/4(x-7)
Factor the numerator
This gives
(x + 3)(x - 7)/4(x-7)
Cancel out the common factors
This gives
(x + 3)/4
Hence, the simplified form of the expression is (x + 3)/4
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