The value of T is 428°C.
How to calculate temperature from resistance?To solve the problem, we can start by substituting the given value of R = 13946 into the equation R = 10000 + (4124 x 10^-2)T – (1779 x 10^-5)T^2 and solving for T. This gives us a quadratic equation in T which can be solved using the quadratic formula.
After simplifying, we get T = 427.67°C or T = -88.22°C. However, we know that the thermometer is only used if T ≤ 600°C, so the only valid solution is T = 427.67°C.Therefore, the temperature corresponding to a resistance of 13946 ohms is approximately 428°C.
It's important to note that this assumes the thermometer is operating within its specified range and that the resistance-temperature relationship remains linear over the given temperature range.
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Jenny and Kera are playing a game. Jenny has -10 points and loses 5 more points. How many points does Jenny have now? Kera has 22 points and loses 14 points. How many points does Kera have now? Make sure that you type each name with her current score
The current scores of both Jenna and Kera in the game they were playing are
Jenny's current score is -15.
Kera's current score is 8.
How many points does Jenny have now?In the given problem, we are given two players, Jenny and Kera, playing the game.
Jenny has -10 points, which means she already has negative points. He has since lost 5 more points. So his current score would be:
-10 - 5 = -15
So now Jenny has a score of -15.
Kera, meanwhile, has 22 points and 14 points to lose. So his current score would be:
22 - 14 = 8
So now Kera has 8 points.
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Please help! This is part of my grade, please make sure to read the question before answering because I need this to be correct (35 points)
Answer:
u = -2.34 or u = 18.34
Step-by-step explanation:
You want to solve u² -16u = 43 by completing the square.
Completing the squareTo complete the square, add the square of half the coefficient of the linear term to both sides.
u² -16u +(-16/2)² = 43 +(-16/2)²
u² -16u +64 = 107 . . . . . . . simplify
(u -8)² = 107 . . . . . . . . . write as a square
u -8 = ±√107 . . . . . . square root
u = 8 ± √107 . . . add 8
u = -2.34 or u = 18.34 . . . . . find the decimal values
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Omar cuts a piece of wrapping paper with the shape and dimensions as shown.Find The Area Of The Wrapping Paper.Round Your Answer To The Nearest Tenth If Needed
The total area of the wrapping paper is 72.5 in².
In the given figure (attached below), we have two shapes one is a triangle and the other one is a rectangle. To find the total area of the wrapping paper we have to add the area of the rectangle part and the area of the trianglular part.
Total area = Area of the rectangular part + area of the triangular part.
Area of the rectangular part = length x breadth
from the below figure, length = 15 in
breadth = 4 in
So, area of the rectangular part = 15 in x 4 in = 60 in²
Similarly, area of the triangular part = 1/2 x base x height
from the below figure, base of the triangle = 15 in -10 in = 5 in
height of the triangle = 9 in - 4 in = 5 in
So, area of the triangular part = 1/2 x 5 in x 5in = 12.5 in²
Now, the total area of the wrapping paper = area of the rectangular part + area of the triangular part = 60 in² + 12.5 in² = 72.5 in².
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Use the prescribed Testing Method if it is stated, to determine
whether the
following series is convergent or divergent.
Apply the Integral Test to:
[infinity]X
n=1
1
5√n
To apply the Integral Test, we need to find a function f(x) that is continuous, positive, and decreasing such that f(x) = 1/(5√x).
Taking the integral of f(x) from 1 to infinity, we get:
∫1 to infinity (1/(5√x)) dx = 2/5
Since this integral is a finite number, the series is convergent by the Integral Test.
To determine whether the series is convergent or divergent, we will apply the Integral Test as requested. The given series is:
Σ (from n=1 to infinity) of (1 / (5√n))
First, let's consider the function f(x) = 1 / (5√x). This function is positive, continuous, and decreasing for x ≥ 1, which are the necessary conditions for applying the Integral Test.
Now, we evaluate the improper integral:
∫ (from x=1 to infinity) of (1 / (5√x)) dx
To solve this integral, we'll first rewrite the integrand:
1 / (5√x) = 1 / (5x^(1/3))
Now integrate:
∫(1 / (5x^(1/3))) dx = (3/2) * (1/5) * x^(2/3) + C = (3/10) * x^(2/3) + C
Evaluate the improper integral:
lim (t -> infinity) [∫(from x=1 to t) of ((3/10) * x^(2/3)) dx]
= lim (t -> infinity) [(3/10) * (t^(2/3) - 1)]
Since the exponent (2/3) is less than 1, the limit converges to a finite value:
lim (t -> infinity) [(3/10) * (t^(2/3) - 1)] = -(3/10)
Since the improper integral converges, by the Integral Test, the given series is convergent as well.
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Qn in attachment. ..
Answer:
pls mrk me brainliest (´(ｪ)｀）
Verify that the sample standard deviations use of ANO\A allow the the means to compare the population means. What do the suggest about the effect of the subject’s gender and attractiveness of the confederate on the evaluation of the product?
On performing an ANOVA test the p-value obtained is less than the chosen significance level, hence it is verified that the sample standard deviations use of ANOVA allow the the means to compare the population means. Since ANOVA test shows significant difference therefore, it suggests that these factors play a role in influencing the evaluation of the product.
To verify that the sample standard deviations use of ANOVA allows means to compare the population means, discuss the terms ANOVA, sample standard deviation, population means.
1. ANOVA (Analysis of Variance): ANOVA is a statistical method used to compare the means of multiple groups to determine if there's a significant difference between them.
2. Sample Standard Deviation: Sample standard deviation is a measure of how spread out the values in a sample are. It helps estimate the population standard deviation, which is necessary for calculating the F statistic in ANOVA.
a. Calculate the sample means and standard deviations for each group.
b. Perform an ANOVA test using calculated means and standard deviations.
c. Interpret results: If p-value obtained from the ANOVA test is less than the chosen significance level (e.g., 0.05), it means there is a significant difference between population means.
Regarding the effect of the subject's gender and attractiveness of the confederate on the evaluation of the product, if the ANOVA test shows a significant difference, it suggests that these factors play a role in influencing the evaluation of product. You can further analyze the data by performing post-hoc tests to identify which specific groups differ significantly.
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You're at a clothing store that dyes your clothes while you wait. The store offers
4 different articles of clothing and
3 colors.
If you randomly choose the article of clothing and the color, which of these diagrams can be used to find all of the possible outcomes?
The probability of randomly selecting an orange hat is 1/12 or 0.0833.
What is the probability of randomly selecting an orange hat?In the sample, there are total of 4 pieces of clothing and 3 colors.
The possible outcomes is:
= 4 x 3
= 12
So, the outcomes when randomly selecting a piece of clothing and a color is 12.
From 12 possible outcomes, there is only one outcome where you end up with an orange hat.
So, the probability of randomly selecting an orange hat is:
= 1/12
= 0.0833.
Correct question "You're at a clothing store that dyes your clothes while you wait. You get to pick from 4 pieces of clothing (shirt, pants, socks, or hat) and 3 colors (purple, blue, or orange). If you randomly pick the piece of clothing and the color, what is the probability that you'll end up with an orange hat?"
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Pls answer this, 5 points and brainliest for the one who answers first.
Answer: A
Step-by-step explanation:
It's A because our function of f is multiplied by 3.
Since our y intercept is 1, and we are multiplying the function f by 3,
our new y intercept is 3, meaning it is A.
Another way to check this is by using the other two points on your graph.
Please give brainliest + have a good afternoon.
Answer:
Step-by-step explanation:
Your original function has points at
0, 1
1, 2
2,4
if you stretched it by 3, multiply your y by 3
new function:
0, 3
1, 6
2, 12
How would the equation for the blade of the wind turbine change if the point starts at the π2
position?
If the point starts at the π/2 position, the equation for the blade of the wind turbine will be sin(θ + π/2) = sin(θ - π/2)cos(β) + cos(θ - π/2)sin(β).
The equation for the blade of the wind turbine is given by the expression sin(θ) = sin(θ - β)cos(α) + cos(θ - β)sin(α), where θ represents the angle of the blade, β represents the angle between the wind direction and the blade, and α represents the pitch angle of the blade.
If the point starts at the π/2 position, we need to substitute θ + π/2 for θ in the equation. This gives us sin(θ + π/2) = sin(θ - β + π/2)cos(α) + cos(θ - β + π/2)sin(α).
Using trigonometric identities, we can simplify this expression to sin(θ + π/2) = cos(θ - β)cos(α) - sin(θ - β)sin(α).
Finally, substituting β for (π/2 - β) in the above equation, we get sin(θ + π/2) = sin(θ - π/2)cos(β) + cos(θ - π/2)sin(β). This is the required equation for the blade of the wind turbine if the point starts at the π/2 position.
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A windshield wiper is 45 cm long and
creates a central angle of 120° in one
wipe. what is the sector area?
The windshield sector area is 706.86 cm².
To calculate the sector area of the windshield wiper, we need to use the formula for the area of a sector of a circle. The formula is:
A = (θ/360°) x πr²
where A is the area of the sector, θ is the central angle of the sector in degrees, and r is the radius of the circle.
In this problem, we are given that the windshield wiper has a length of 45 cm, which means that the radius of the circle traced by the wiper is 45 cm/2 = 22.5 cm.
We are also given that the wiper creates a central angle of 120° in one wipe. Substituting these values into the formula, we get:
A = (120°/360°) x π(22.5 cm)²
A = (1/3) x π x (22.5 cm)²
A ≈ 706.86 cm²
Therefore, the sector area of the windshield wiper is approximately 706.86 square centimeters.
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WORK OUT THE SIZE OF AN EXTERIOR ANGLE OF A REGULAR HEXAGON
Answer:
60°
Step-by-step explanation:
A hexagon has 6 angles
The sum of the measures of the exterior angles of a hexagon is equal to 360°
So, measure of each exterior angle = 360∘ / 6 = 60∘
A newspaper for a large city launches a new advertising campaign focusing on the number of digital subscriptions. The equation S(t)=31,500(1. 034)t approximates the number of digital subscriptions S as a function of t months after the launch of the advertising campaign. Determine the statements that interpret the parameters of the function S(t)
The parameters of the function S(t)=31,500(1.034)t are the initial number of digital subscriptions, which is 31,500, and the monthly growth rate, which is 3.4%.
How to find the parameters of the function?
The given function S(t)=31,500(1.034)t is a exponential growth function that models the number of digital subscriptions S as a function of t months after the launch of the advertising campaign. The parameters of the function are the initial number of digital subscriptions, which is 31,500, and the monthly growth rate, which is 3.4%.
The initial value of 31,500 represents the number of digital subscriptions at the start of the advertising campaign. This means that the campaign began with 31,500 digital subscribers.
The monthly growth rate of 3.4% represents the rate at which the number of digital subscriptions is increasing each month due to the advertising campaign. This means that for each month after the launch of the campaign, the number of digital subscribers is increasing by 3.4% of the previous month's total.
For example, after one month, the number of digital subscribers would be:
S(1) = 31,500(1.034)1 = 32,687
After two months, the number of digital subscribers would be:
S(2) = 31,500(1.034)2 = 33,912
And so on...
Therefore, the initial value and monthly growth rate are important parameters that help us understand how the number of digital subscriptions is changing over time due to the advertising campaign.
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8. The table shows the number of different
kinds of sodas sold at a gas station on a
Monday.
A.
B.
Kind of Soda
18
If the gas station had 80 customers on
Tuesday, how many customers can be
predicted to get a Dr. Pepper?
C. 45
Coks
Sprite
Dr. Papper
7-Up
36
Number of
Bottles Sold
11
D. Not Here
One salt solution is 20% salt and another is 60% salt. How many cubic centimeters of each solution must be mixed to obtain 100 cubic centimeters of a 30% salt solution?
Answer: Let's denote the number of cubic centimeters of the 20% salt solution as x and the number of cubic centimeters of the 60% salt solution as y.
We know that the total volume of the mixture is 100 cubic centimeters, so we have:
x + y = 100
We also know that the final solution should be a 30% salt solution. This means that the amount of salt in the final solution should be 0.3 times the total volume of the solution:
0.3(100) = 0.20x + 0.60y
where 0.20x represents the amount of salt in the 20% salt solution and 0.60y represents the amount of salt in the 60% salt solution.
We now have two equations with two unknowns:
x + y = 100
0.20x + 0.60y = 30
We can solve for x and y by using any method of linear equations, such as substitution or elimination.
Here, we will use substitution. Solving the first equation for x, we get:
x = 100 - y
Substituting this expression for x in the second equation, we get:
0.20(100 - y) + 0.60y = 30
Simplifying and solving for y, we get:
20 - 0.20y + 0.60y = 30
0.40y = 10
y = 25
So, we need 25 cubic centimeters of the 60% salt solution.
To find the amount of the 20% salt solution, we can substitute this value of y back into either equation:
x + y = 100
x + 25 = 100
x = 75
So, we need 75 cubic centimeters of the 20% salt solution.
Therefore, we need to mix 75 cubic centimeters of the 20% salt solution and 25 cubic centimeters of the 60% salt solution to obtain 100 cubic centimeters of a 30% salt solution.
Wes has 20 feet of garden fencing. If he
wants the smallest side of his garden
to be 3 feet or longer, what possible
rectangles can he make?
The possible rectangles that Wes can make with his 20 feet of fencing are:
L = 3, W = 7
L = 4, W = 6
L = 5, W = 5
L = 6, W = 4
L = 7, W = 3
How to find the possible rectangles?Let L be the length of the rectangular garden and W be the width of the garden. Since the garden is enclosed by four sides, Wes will need 2L+2W feet of fencing to enclose it. We know that he has 20 feet of fencing, so we have the equation:
2L + 2W = 20
We also know that the smallest side of the garden should be 3 feet or longer, so:
L >= 3
W >= 3
To find the possible rectangles Wes can make, we can solve the equation for one variable in terms of the other:
2L + 2W = 20
2L = 20 - 2W
L = 10 - W
Now we can substitute this expression for L into the inequality L >= 3 to get:
10 - W >= 3
W <= 7
Similarly, we can substitute L = 10 - W into the inequality W >= 3 to get:
10 - L >= 3
L <= 7
Therefore, the possible values for L and W are:
3 <= L <= 7
3 <= W <= 7
We can also use the equation 2L + 2W = 20 to find the combinations of L and W that add up to 10, since the total length of fencing is 20 feet:
L = 3, W = 7
L = 4, W = 6
L = 5, W = 5
L = 6, W = 4
L = 7, W = 3
These are the possible rectangles that Wes can make with his 20 feet of fencing, where the smallest side is 3 feet or longer.
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2. 7.G.1.2 Can a quadrilateral be drawn that meets the conditions described below? Select Yes or No by placing a check or X in the appropriate box. Conditions Two pairs of parallel sides and at least two right angles One pair of parallel sides and no right angles One pair of parallel sides and three right angles No parallel sides and four right angles Yes No
The complete conditions are
Two pairs of parallel sides and at least two right angles : YesOne pair of parallel sides and no right angles :YesOthers are NoChecking if a quadrilateral can be drawn from the conditionsBy definition a quadrilateral is a shape that has four sides and four angles
Next, we test the conditions
Two pairs of parallel sides and at least two right angles
This is true because quadrilaterals like rectangles and squares have two pair of parallel sides and right angles
One pair of parallel sides and no right angles
This is also true because quadrilaterals like trapezoid have one pair of parallel sides and may or may not have right angle
One pair of parallel sides and three right angles
This is false because a quadrilateral cannot be drawn with this condition
No parallel sides and four right angles
This is false because a quadrilateral cannot be drawn with this condition
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A sample size a 28 produced test statistic is T equals 2. 51
The mathematical probabilities of p values lies between range from 0 to 1 and using technology, p-value is 0.050086.
Sample = n = 28.
t = 2.051
P value by the means of the technology is 0.050086.
The likelihood of receiving outcomes from a statistical hypothesis test that are at least as severe as the actual results, provided the null hypothesis is true, is known as the p-value in statistics. The p-value provides the minimal level of significance at which the null hypothesis would be rejected as an alternative to rejection points. The alternative hypothesis is more likely to be supported by greater evidence when the p-value is lower.
P-value is frequently utilised by government organisations to increase the credibility of their research or reports. The U.S. Census Bureau, for instance, mandates that any analysis with a p-value higher than 0.10 be accompanied by a statement stating that the difference is not statistically significant from zero.
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Complete question:
A significance test was performed to test H o : u = 2 versus the alternative He: u # 2. A sample of size 28 produced a standardized test statistic of t = 2.051. Assume all conditions for inference are met. Using Table B, the P-value falls between and . (Do not round) Using technology the P-value is . (Round to 4 decimal places)
salvador recorded in this list the heights in millimeters of each of his bean plants.
52, 46, 51, 32,50
which 2 inequalities best describe, h, the plant heights in millimeters?
h < 32, h > 52
h> 32, h < 52
h < 46, h > 52
h < 46, h > 52
The two inequalities that best describe the plant heights in millimeters are: h > 32 and h < 52. This is because all the recorded heights fall within this range. The other options do not include all the recorded heights or include heights that are not recorded.
To find the best inequalities that describe the plant heights (h) in millimeters, we need to determine the minimum and maximum heights from the given list.
List of plant heights: 52, 46, 51, 32, 50
Minimum height: 32 mm
Maximum height: 52 mm
Now we can write the inequalities that best describe the plant heights:
h > 32 (heights are greater than 32 mm)
h < 52 (heights are less than 52 mm)
Your answer: h > 32, h < 52
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Write an equation for the circle graphed below.
-4
-2
6
4
2
-2
-4
-6
2
Answer:
[tex]\left(x\:+\:1\right)^2\:+\:y^2=25[/tex]
Step-by-step explanation:
The equation of a circle with radius r and center at (a, b) is given by
(x - a)² + (y - b)² = r²
Let's first find the radius
The circle intersects the x axis at two points (-6, 0) and (4, 0)
The diameter is therefore the absolute difference between the x values:
|-6 - 4| same as |4 - (-6)| = 10
The radius r = 5 (half of diameter)
Now, let's find the center point of the circle. This will lie midway between (-6, 0) and (4, 0)
Midpoint (xm, ym) between two points(x1, y) and (x2, y2) :
xm = (x1 + x2)/2 = (-6 + 4)/2 = -1
ym = (y1 + y2)/2 = (0 + 0)/2 = 0
So the center (a, b) = (-1, 0) with a = -1, b = 0
The equation of the circle therefore is
(x - a)² + (y - b)² = r²
( x - (-1) )² + (y - 0)² = 25
(x + 1)² + y² = 25
To find a and b take any point (x, y) and plug these
Find the first four nonzero terms of the Taylor series for the function cos (20²) about 0. f(0) = NOTE: Enter only the first four non-zero terms of the Taylor series in the answer field. Coefficients must be exact. f(0) = Find the first four nonzero terms of the Taylor series for the function f(y) = ln(1 - 4y¹) about 0. f(y) NOTE: Enter only the first four non-zero terms of the Taylor series in the answer field. Coefficients must be exact. = +.. +...
The first four nonzero terms for cos(20x²) are:
1
The first four nonzero terms for ln(1 - 4y) are:
-4y + 8y² - 32y³ +...
Taylor series:
To find the first four nonzero terms of the Taylor series for the function cos(20x²) about 0,
we need to find the first few derivatives of the function, and evaluate them at x = 0.
f(x) = cos(20x²)
f'(x) = -40x * sin(20x²)
f''(x) = -40(40x² * cos(20x²) + 20sin(20x²))
f'''(x) = 40(1600x³ * sin(20x²) + 120x * cos(20x²))
Now, evaluate these at x = 0:
f(0) = cos(0) = 1
f'(0) = 0 (since sin(0) = 0
f''(0) = -40(0) = 0
f'''(0) = 0 (since cos(0) = 1
The first four nonzero terms for cos(20x²) are:
1
Now, let's find the first four nonzero terms of the Taylor series for the function f(y) = ln(1 - 4y) about 0.
f(y) = ln(1 - 4y)
f'(y) = -4 / (1 - 4y)
f''(y) = 16 / (1 - 4y)²
f'''(y) = -96 / (1 - 4y)³
Evaluate these at y = 0:
f(0) = ln(1) = 0
f'(0) = -4 / (1) = -4
f''(0) = 16 / (1)² = 16
f'''(0) = -96 / (1)³ = -96
The first four nonzero terms for ln(1 - 4y) are:
-4y + 8y² - 32y³ +...
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Please help!
For each problem approximate the area under the curve under the given interval using five trapezoids.
Answer:
area ≈ 9.219 square units
Step-by-step explanation:
You want the approximate area under the curve y = -1/2x² +x +5 on the interval [1.5, 4] using 5 trapezoids.
Trapezoid areaThe interval can be divided into 5 intervals of width ...
(4 -1.5)/5 = 2.5/5 = 0.5
The "bases" of each trapezoid will be the function values at the ends of the intervals, for example, at x=1.5 and x=2. The "height" of each trapezoid is the width of the sub-interval, 0.5.
The area formula for a trapezoid applies:
A = 1/2(b1 +b2)h
A = 1/2(f(x) +f(x +0.5))·0.5 . . . . . for x = 1.5, 2, 2.5, 3, 3.5
Approximate total areaThe sum of the areas is computed in the attachment as ...
area under the curve = 9.21875
__
Additional comment
The value of the integral is 445/48 ≈ 9.2708333...
If a triangle given by the matrix [235-102] is dialed by a scale factor of 2, what will will happened to the side lengths and angle measure of triangle?
If the triangle given by the matrix [235-102] is scaled by a factor of 2, the side lengths of the triangle will be doubled. The angle measures of the triangle will remain the same since scaling does not affect the angles.
When a triangle is scaled by a factor of 2, the side lengths will be doubled, but the angle measures will remain the same. Here's a step-by-step explanation:
1. The original matrix is [2 3 5; -1 0 2].
2. Apply the scale factor of 2 to each of the side lengths by multiplying the matrix by 2: [4 6 10; -2 0 4].
3. The side lengths of the triangle have been doubled, but the angle measures remain the same.
So, after scaling the triangle by a factor of 2, the side lengths will be doubled while the angle measures will stay the same.
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moving company is using a large shipping container to pack up several smaller boxes. The smaller boxes are cubes with each side length measuring
The larger container will hold 20 smaller boxes along its width, 40 boxes along its length, and 20 boxes along its height.
e this information to fill in the blanks below.
please look at the photo:(
The volume of one smaller box is 1 cubic foot.
Solution to Shipping Container ProblemThe volume of one smaller box is calculated by raising the length of its sides to the power of 3, so the volume of one smaller box is:
Volume (smaller box) = (1 foot)³ = 1 cubic foot
The number of smaller boxes that fit into a shipping container is obtained by multiplying the number of boxes that fit along each dimension, so the number of smaller boxes that fit into a shipping container is:
Number of smaller boxes = 20 boxes (width) × 40 boxes (length) × 20 boxes (height) = 16,000 boxes
To calculate the volume of the large shipping container, we need to multiply the length, width, and height of the container. Since each dimension is given in terms of the number of boxes it can hold, we need to multiply each dimension by the length of one smaller box (1 foot) to obtain the dimensions in feet. Therefore, the volume of the large shipping container is:
Volume of the large shipping container = 20 boxes (width) × 1 foot (length of one smaller box) × 40 boxes (length) × 1 foot (length of one smaller box) × 20 boxes (height) × 1 foot (length of one smaller box) = 16,000 cubic feet
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During the period 2000-2016, the average costs B (in dollars) for a new boat and the average costs H (in dollars) for a hovercraft can be modeled
by the following functions:
B = 30 +140 and H=-1012 +350 + 400
where t is the number of years since 2000
(a) How can the difference of the costs of a hovercraft and the costs of a boat be expressed? (4 points)
(b) About how much was the difference in the year 2010? (2 points)
The difference between the costs of a hovercraft and a boat in the year 2010 was approximately $1,558.
(a) The difference in costs between a hovercraft and a boat can be expressed as follows:
Cost difference = Hovercraft cost - Boat cost
Cost difference = (-1012 + 350t + 400) - (30 + 140t)
Cost difference = -1012 + 350t + 400 - 30 - 140t
Cost difference = 220t - 642
Therefore, the difference in costs between a hovercraft and a boat can be expressed as 220t - 642.
(b) To find the difference in the year 2010, we need to substitute t = 10 in the expression we derived in part (a):
Cost difference = 220t - 642
Cost difference = 220(10) - 642
Cost difference = 2200 - 642
Cost difference = 1558
Therefore, the difference between the costs of a hovercraft and a boat in the year 2010 was approximately $1,558.
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Tim can paint a room for 6 hours. Bella can paint the same room for 4 hour. How many hours would it take Tim and Bella to paint the room while working together?
Tim and Bella working together can paint the room in 2.4 hours.
We can use the formula:
1/Total Work = 1/Time1 + 1/Time2
where Total Work is the work to be done (in this case, painting the room), Time1 is the time taken by Tim to complete the work, and Time2 is the time taken by Bella to complete the work.
Let x be the time taken by Tim and Bella working together to complete the work. Then we can write:
1/1x = 1/6 + 1/4
Simplifying this equation, we get:
1/1x = 5/12
Multiplying both sides by x, we get:
x = 12/5 = 2.4 hours.
Therefore, Tim and Bella working together can paint the room in 2.4 hours.
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Create a bucket by rotating around the y axis the curve y = 4 ln(x - 4) from y = 0 to y = 3. If this bucket contains a liquid with density 860 kg/m filled to a height of 2 meters, find the work required to pump the liquid out of this bucket (over the top edge). Use 9.8 m/s2 for gravity. Work = Preview Joules License Points possible: 1 This is attempt 1 of 3.
The work required to pump the liquid out of the bucket is approximately 2.482 x 10⁷ Joules.
How to find the work requiredTo create a bucket by rotating around the y-axis, we will use the formula for volume of revolution:
V = π ∫[a,b] (f(y))² dy where f(y) is the function being rotated, and a and b are the limits of integration.
In this case, the limits of integration are y = 0 and y = 3, and the function being rotated is y = 4 ln(x - 4), or x = e⁽y/⁴⁾ + 4.
So, we have:
V = π ∫[0,3] ((e⁽y/⁴⁾ + 4))² dy
V = π ∫[0,3] (e⁽y/²⁾ + 8e⁽y/⁴⁾+ 16) dy
V = π (2e⁽³/²⁾ + 32e⁽³/⁴⁾ + 48)
Now, to find the work required to pump the liquid out of the bucket, we need to use the formula:
W = ∫[h1,h2] ρgV(y) dy
where h1 is the height of the liquid (2 meters in this case), h2 is the height of the top edge of the bucket, ρ is the density of the liquid (860 kg/m^3), g is the acceleration due to gravity (9.8 m/s²), and V(y) is the volume of the liquid at height y.
To find V(y), we need to first find the radius of the bucket at height y.
The radius is given by: r(y) = e⁽y/⁴⁾+ 4
So, the volume of the liquid at height y is:
V(y) = π(r(y))² (h2 - y)
Plugging in the values, we have:
W = ∫[0,2] 860×9.8×π((e⁽y/⁴ + 4)²)×(2-y) dy
W = 2.482 x 10⁷J
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At a high school with 900 total students, the true opinions of the entire student body on whether they approve of the student council president are shown below. Follow the directions below to determine a confidence interval for a sample of size 109.
Based on the above, the proportion of the population who said yes is 78%.
What is the Population size?To be able to calculate the population proportion who said yes, you have to divide the number of students who said "Yes" by the total amount or number of students in the whole population:
Hence it will be:
Population proportion who said yes = 741/950
= 0.78
= 78%
So, the proportion of the population who said yes is 0.78 or 78%.
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See text below
At a high school with 950 total students, the true opinions of the entire student body on whether they approve of the student council president are shown below. Follow the directions below to determine a confidence interval for a sample of size 125.
Population Yes 741, Population No 209, Population Size 950
Population proportion who said yes: ---
Two random samples 4. 49, 7. 68, 5. 97, 0. 97, 6. 88, 6. 07, 03. 08, 04. 02, 03. 83, 6. 35, and 4. 59, 3. 39, 3. 79, 6. 89, 5. 07, 07. 41, 0. 44, 2. 47, 4. 80, 7. 23 were obtained independently from distributions with the same mean. Perform a permutation test to test the hypothesis that the variability in both populations is the same against the alternative that it is larger in the second population. As a test statistic use: (i) The difference of sample ranges. (ii) The ratio of sample variances. (iii) Compare both results
A. Main Answer:
The hypothesis that the variability in both populations is the same against the alternative that it is larger in the second population, we can perform a permutation test using two different test statistics:
(i) the difference of sample ranges and
(ii) the ratio of sample variances. By comparing the results of both test statistics, we can draw conclusions about the variability in the populations.
(i) Difference of Sample Ranges:
1. Calculate the sample range for each sample. The sample range is the difference between the maximum and minimum values in the sample.
Sample 1 Range = Maximum value - Minimum value for Sample 1
Sample 2 Range = Maximum value - Minimum value for Sample 2
2. Calculate the observed difference of sample ranges, which is the difference between the sample range of Sample 2 and Sample 1.
3. Pool the data from both samples and shuffle them randomly, keeping the same sample sizes.
4. Calculate the difference of sample ranges for the shuffled data.
5. Repeat steps 3 and 4 many times (e.g., 1000 permutations) to obtain a distribution of the difference of sample ranges under the null hypothesis (where variability is the same in both populations).
6. Compare the observed difference of sample ranges from step 2 with the distribution obtained from the permutations.
(ii) Ratio of Sample Variances:
1. Calculate the sample variance for each sample.
2. Calculate the observed ratio of sample variances, which is the ratio of the sample variance of Sample 2 to the sample variance of Sample 1.
3. Pool the data from both samples and shuffle them randomly, keeping the same sample sizes.
4. Calculate the ratio of sample variances for the shuffled data.
5. Repeat steps 3 and 4 many times (e.g., 1000 permutations) to obtain a distribution of the ratio of sample variances under the null hypothesis.
6. Compare the observed ratio of sample variances from step 2 with the distribution obtained from the permutations.
By comparing the results of both test statistics, we can assess whether the variability in the second population is significantly larger than the first population. If both test statistics consistently indicate larger variability in the second population, it provides evidence against the null hypothesis and suggests that the variability in the second population is indeed larger.
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Question 3 B0/5 pts 100 Details If the eighth term of a geometric sequence is 81920, and the eleventh term of an geometric sequence is 5242880 its first term a and its common ratio r = Question Help:
To find the first term and common ratio of a geometric sequence, we can use the formula for the nth term:
a_n = a_1 * r^(n-1)
We are given the eighth and eleventh terms, so we can set up two equations:
a_8 = a_1 * r^(8-1) = 81920
a_11 = a_1 * r^(11-1) = 5242880
After dividing the second with by the first equation, we get:
(a_1 * r^(11-1)) / (a_1 * r^(8-1)) = 5242880 / 81920
Simplifying, we get:
r³ = 64
Doing the root of cube both sides, we get:
r = 4
Substituting this into the first equation, we get:
a_1 * 4^(8-1) = 81920
a_1 * 4^7 = 81920
a_1 = 5
Therefore, the first term is 5 and the common ratio is 4.
In a geometric sequence, each term is obtained by multiplying the previous term by a constant factor called the common ratio (r). The formula for the nth term of a geometric sequence is:
an = a * r^(n-1)
Given that the 8th term (a8) is 81,920 and the 11th term (a11) is 5,242,880, we can set up the following equations:
81920 = a * r^(8-1) => 81920 = a * r⁷ (1)
5242880 = a * r^(11-1) => 5242880 = a * r¹⁰ (2)
Now, we need to find the values of a (the first term) and r (the common ratio). Divide equation (2) by equation (1):
(5242880 / 81920) = (a * r¹⁰) / (a * r⁷)
64 = r^3
Now, we can find the common ratio r:
r = 4 (since 4³ = 64)
Next, substitute r back into equation (1) to find the first term a:
81920 = a * 4⁷
a = 81920 / 16384
a = 5
So, the first term (a) is 5, and the common ratio (r) is 4.
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A rectangle with length n is inscribed in a circle of radius 9. Find an expression for the area of the rectangle in terms of n
The expression for the area of the rectangle inscribed in a circle of radius 9, in terms of n, is:
Area = n * √(81 - n^2)
To find an expression for the area of a rectangle inscribed in a circle of radius 9, we need to use the terms "rectangle" and "circle."
First, let's denote the length of the rectangle as "n" and the width as "w." Since the rectangle is inscribed in a circle with a radius of 9, its diagonal is equal to the diameter of the circle, which is 2 * 9 = 18.
Using the Pythagorean theorem for the right triangle formed by half of the diagonal, the length, and the width, we can write the equation:
(1/2 * 18)^2 = n^2 + w^2
81 = n^2 + w^2
Now, we need to express w in terms of n. To do this, we'll isolate w from the equation:
w^2 = 81 - n^2
w = √(81 - n^2)
The area of the rectangle can be calculated as the product of its length and width:
Area = n * w
Area = n * √(81 - n^2)
So, the expression for the area of the rectangle inscribed in a circle of radius 9, in terms of n, is:
Area = n * √(81 - n^2)
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