Probability that the total weight for the two animals is 225 pounds or more is 0.17.
How to find the probability that the total weight for the two animals?We need to use the joint probability distribution for X and Y, where X and Y are the weights of the first and second animals, respectively. Let's denote the joint probability distribution as P(X=x, Y=y).
From the table given, we can see that the possible values of X and Y are 100, 120, and 140 pounds. To find the probability that the total weight is 225 pounds or more, we need to sum the joint probabilities for all pairs of (X,Y) that satisfy X+Y≥225.
These pairs are:
(120, 120)(100, 120)(120, 100)(100, 140)(140, 100)(120, 140)(140, 120)(140, 140)So, we have:
P(X+Y≥225) = P(X=120, Y=120) + P(X=100, Y=120) + P(X=120, Y=100) + P(X=100, Y=140) + P(X=140, Y=100) + P(X=120, Y=140) + P(X=140, Y=120) + P(X=140, Y=140)
Substituting the values from the table, we get:
P(X+Y≥225) = 0.04 + 0.03 + 0.03 + 0.01 + 0.01 + 0.02 + 0.02 + 0.01
P(X+Y≥225) = 0.17
Therefore, the probability that the total weight for the two animals is 225 pounds or more is 0.17.
So the response closest to 0.17 is 0.195.
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in a sample of 307 pop music selections, the key was identified correctly in 245 of them. in a sample of 347 new-age selections, the key was identified correctly in 304 of them. can you conclude that the method is more accurate for new-age songs than for pop songs?
find the general solution of the given higher-order differential equation. 16 d 4y dx4 40 d2y dx2 25y
The general solution of the given higher-order differential equation is y(x) = c1e[tex].^{x/2}[/tex]cos((1/2)√5x) + c2e[tex].^{x/2}[/tex]sin((1/2)√5x) + c3eˣ + c4e⁻ˣ.
The given higher-order differential equation is:
16(d⁴y/dx⁴) + 40(d²y/dx²) + 25y = 0
To find the general solution of this differential equation, we can assume that y(x) has the form:
y(x) = e[tex].^{rx}[/tex]
where r is a constant to be determined.
Differentiating y(x) four times with respect to x, we get:
d⁴y/dx⁴ = r⁴e[tex].^{rx}[/tex]
Differentiating y(x) two times with respect to x, we get:
d²y/dx² = r²e[tex].^{rx}[/tex]
Substituting these derivatives and y(x) into the differential equation, we get:
16(r⁴e[tex].^{rx}[/tex]) + 40(r²e[tex].^{rx}[/tex]) + 25e[tex].^{rx}[/tex] = 0
Simplifying this equation by dividing through by e[tex].^{rx}[/tex], we get:
16r⁴ + 40r² + 25 = 0
This is a quadratic equation in r². Solving for r² using the quadratic formula, we get:
r² = [-40 ± √(40² - 4(16)(25))] / 2(16)
r² = [-40 ± √(3600)] / 32
r² = [-40 ± 60] / 32
We get two possible values for r²:
r² = 5/4 or r² = 1
Taking the square root of each value, we get:
r = ±(1/2)i√5 or r = ±1
Thus, the general solution of the given higher-order differential equation is:
y(x) = c1e[tex].^{x/2}[/tex]cos((1/2)√5x) + c2e[tex].^{x/2}[/tex]sin((1/2)√5x) + c3eˣ + c4e⁻ˣ
where c1, c2, c3, and c4 are constants determined by the initial or boundary conditions of the specific problem.
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The complete question is :
find the general solution of the given higher-order differential equation : 16(d⁴y/dx⁴) + 40(d²y/dx²) + 25y = 0
draw the reflection of the triangle across the y axis
Answer:
Image
Step-by-step explanation:
2, 7, 4, 2, 3, 6, 11, 2
Mode:
What is the mode of all of these numbers??
Answer: 2
Step-by-step explanation: Mode is the most frequent number
List all of the possible outcomes for each experiment
The sample space for each experiment are as follow;
1. rolling a 12 sided fair die, the sample space is 12
2. flipping a coin, the sample space is 2
3. pulling a face card from a standard deck of cards is 12
4. A spin from the spinner, the sample space is 5
What is sample space?A sample space is a collection or a set of possible outcomes of a random experiment. The sample space is represented using the symbol, “S”.
For example the sample space of getting an odd number from a 6 sided fair die is 3, because the odd numbers between 1-6 are 1,3,5.
1. The sample space of rolling a 12 sided fair die is 12, because it will have 12 faces.
2. A coin has two faces, therefore the sample space of flipping a coin is 2
3. There are 12 face cards in a standard deck, therefore, the sample space to pull a face card out of a standard deck is 12.
4. The spinner has 5faces, therefore the sample space for a spin is 5.
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Divide using long division. Check your answer
(x3+3x2-x+2)/(x-1)
After performing long division on (x3+3x2-x+2)/(x-1) we get x² + 4x +3 leaving a remainder of 5.
Long division refers to the method of performing a division of two numbers or polynomials by hand. Furthermore, it involves several steps to evaluate in order to find a quotient and a remainder. It is considered an important and crucial form of practice in the branch of mathematics.
In the subject of dividing a polynomial, first, we divide the highest degree term of the dividend by the highest degree term of the divisor, and the remaining result is subtracted from the dividend. The calculation is as follows in the picture
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Help?
You are interested in studying the proportion of people 65 years or older that have an active Netflix subscription. You interview 65 random people that are 65 years or older that live in the United States. 23 of them claim to have an active Netflix subscription.
a) Define the parameter of interest.
b) State and check if the assumptions needed for constructing the appropriate CI for the parameter of interest are satisfied.
c) Find a 90% confidence interval for the parameter defined in part a). (Use the provided table, not the calculator to find the appropriate critical value. )
d) Write a sentence to interpret the CI computed in part c)
a) The parameter of interest is the proportion of people 65 years or older in the United States.
b) The assumptions include the sample is random, the sample size is large and observations are independent.
c) The 90% confidence interval lie in (0.198, 0.51).
d) We are 90% confident that the true proportion of people 65 years or older lies between 0.198 and 0.51.
a) The parameter of interest is the proportion of people 65 years or older in the United States who have an active Netflix subscription.
b) The assumptions needed for constructing the appropriate confidence interval for the proportion include: 1) the sample is random, 2) the sample size is sufficiently large (at least 10 times the number of successes and failures), and 3) the observations are independent.
To check these assumptions, we need to verify that the sample is indeed random, and that the sample size is large enough. Since the sample size is 65 and the number of successes (i.e., those with an active Netflix subscription) is 23, we can assume that the sample size is sufficiently large.
Additionally, we assume that each person in the sample has an independent probability of having an active Netflix subscription.
c) To find a 90% confidence interval for the proportion of people 65 years or older in the United States with an active Netflix subscription, we can use the normal approximation to the binomial distribution. The formula for the confidence interval is:
p' ± z*(√(p'(1-p'))/n)
where p' is the sample proportion (23/65), z* is the critical value from the standard normal distribution corresponding to a 90% confidence level (1.645), and n is the sample size (65).
Plugging in the values, we get:
0.354 ± 1.645*(√(0.354*(1-0.354))/65)
This simplifies to:
(0.198, 0.51)
d) We are 90% confident that the true proportion of people 65 years or older in the United States with an active Netflix subscription lies between 0.198 and 0.51. This means that if we were to repeat this study many times and construct a 90% confidence interval for each study, we would expect that 90% of these intervals would contain the true proportion.
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Sam is stacking cans of vegetables at the Store His shelf is 10 inches tall, 10 inches deep, and 50 inches wide The cans are 4 inches tall and each has a volume of 50 24 in³ How many cans will fit on the shelf?
Answer:
48
Step-by-step explanation:
You want to know the number of cans 4 inches tall with a volume of 50.24 in³ that will fit on a shelf with a height and depth of 10 inches and a length of 50 inches.
DiameterThe diameter of the can will be found from the volume formula:
V = (π/4)d²h
d = √(4V/(πh)) = √(4·50.24/(4·3.14)) = √16 = 4 . . . inches
The cans are 4 inches in diameter.
NumberThe number of cans that will fit in each dimension will be the integer part of the dimension divided by the size of the can in that dimension.
Height: (10 in)/(4 in/can) = 2.5 cans . . . . cans will fit 2 cans high
Depth: (10 in)/(4 in/can) = 2.5 cans . . . . cans will fit 2 cans deep
Length: (50 in/4 in/can) = 12.5 cans . . . . cans will fit 12 cans long
A total of 2 × 2 × 12 = 48 cans will fit on the shelf.
__
Additional comment
There will be 2 inches of empty space in each direction.
<95141404393>
Question A scale model of a ramp is a right triangular prism as given in this figure. In the actual ramp, the triangular base has a height of 0.6 yards. What is the surface area of the actual ramp, including the underside? Enter your answer as a decimal in the box. yd² Right triangular prism. Each base is a triangle whose legs are 8 in, 5 in, and 5 in. The height of the triangles is 3 in. The prism is oriented so that the side labeled 8 in is on the bottom. The distance between the bases is labeled 4 in.
The surface area of the actual ramp, including the underside, is approximately 15.38 yd².
What is triangle?
A triangle is a three-sided polygon with three angles. It is a fundamental geometric shape and is often used in geometry and trigonometry.
To find the surface area of the actual ramp, we need to first find the dimensions of the ramp.
We are given that the scale model of the ramp is a right triangular prism with legs of 8 in, 5 in, and 5 in, and a height of 3 in. We can use these dimensions to find the dimensions of the actual ramp.
Since the ramp is a scale model, the ratio of the dimensions of the model to the actual ramp is the same for all corresponding dimensions. The height of the triangular base in the actual ramp is given as 0.6 yards, which is equal to 21.6 inches. So, we have:
height of actual ramp / height of model = 21.6 in / 3 in = 7.2
We can use this ratio to find the dimensions of the actual ramp:
height of actual ramp = 7.2 * 3 in = 21.6 in
length of actual ramp = 7.2 * 8 in = 57.6 in
width of actual ramp = 7.2 * 5 in = 36 in
Now we can find the surface area of the actual ramp. The surface area of the top and bottom of the ramp is the area of the triangular base plus the area of the rectangle formed by the length and width of the ramp:
Area of triangular base = (1/2) * base * height = (1/2) * 5 in * 5 in = 12.5 in²
Area of rectangular top and bottom = length * width = 57.6 in * 36 in = 2073.6 in²
Total surface area of top and bottom = 2 * (Area of triangular base + Area of rectangular top and bottom) = 2 * (12.5 in² + 2073.6 in²) = 4153.2 in²
The surface area of the sides of the ramp is the area of the three rectangles formed by the height and width of the ramp:
Area of one side rectangle = height * width = 21.6 in * 36 in = 777.6 in²
Total surface area of sides = 3 * Area of one side rectangle = 3 * 777.6 in² = 2332.8 in²
Finally, we add the surface area of the top and bottom to the surface area of the sides to get the total surface area of the ramp:
Total surface area of ramp = Surface area of top and bottom + Surface area of sides = 4153.2 in² + 2332.8 in² = 6486 in²
Converting to yards and rounding to two decimal places, we get:
Total surface area of ramp = 6486 in² / (36 in/yd)² = 15.38 yd² (rounded to two decimal places)
Therefore, the surface area of the actual ramp, including the underside, is approximately 15.38 yd².
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Which answer choice correctly identifies the missing length of the polygon if the perimeter is 137 m?
a(26
b(25
c(24
d(23
Answer:
a
Step-by-step explanation:
to find the missing side x , subtract the sum of the 5 given sides from the given perimeter.
x = 137 - (39 + 37 + 12 + 10 + 13) = 137 - 111 = 26 m
Solve this proportion 12/m = 18/9
Answer:
m = 6
Step-by-step explanation:
We have the proportion:
12/m = 18/9
To solve for m, we can cross-multiply the terms in the proportion:
12 × 9 = 18 × m
Simplifying both sides of the equation, we get:
108 = 18m
Dividing both sides by 18, we get:m = 6
Therefore, the solution to the proportion 12/m = 18/9 is m = 6.
Answer: m = 6
Step-by-step explanation:
First, we will rewrite this proportion:
[tex]\displaystyle \frac{12}{m} =\frac{18}{9}[/tex]
Next, we will cross-multiply:
12 * 9 = 18 * m
108 = 18m
Lastly, we will divide both sides of the equation by 18:
m = 6
We can also solve this proportion another way.
We know that 18/9 = 2, so 12/m must equal 2 as well.
12/6 = 2, so m = 6.
A teacher was interested in the subject that students preferred in a particular school. He gathered data from a random sample of 100 students in the school and wanted to create an appropriate graphical representation for the data.
Which graphical representation would be best for his data?
Stem-and-leaf plot
Histogram
Circle graph
Box plot
The graphical representation that would be the best for this data would be a circle graph. That is option C.
What is a circle graph?A circle graph, which is also called a pie chart, is defined as a type of data representation where by the information concerning a data set is displayed in a circular form and in a way that the various information displayed is a percentage of the total data set involved.
Now, the number of students that were surveyed = 100 students.
The number of subjects that are preferred by the students would be represented as x,y,z.
Therefore to represent the number of students that preferred a particular subject on the circle graph the following is carried out;
For subject x = Number of X/100 × 360/1
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I need the answer I do not understand this problem
The possible estimation of the acute angle will be 14.5⁰, 14.6⁰, 14.7⁰, 14.8⁰, 14.9⁰ or 15⁰.
What is the measure of the acute angle?An acute angle is an angle that measures less than 90 degrees. In other words, it is an angle that is smaller than a right angle. A right angle measures exactly 90 degrees, while an acute angle measures less than that.
The measure of the given angle is less than 90 degrees, and the measure can range from 0⁰ to 90 degrees.
If we are to estimate within 15⁰, then the possible measure will be 14.5⁰, 14.6⁰, 14.7⁰, 14.8⁰, 14.9⁰ or 15⁰
All the estimation of the angle given above is less than 90 degrees and can be considered an acute angle.
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what is the average size of a customer's bill at a restaurant that earns daily $3,250 for the meals that it sells to 200 customers? $32.50 $20.00 $16.25 $15.84
The average size of a customer's bill at a restaurant that earns daily $3,250 for the meals that it sells to 200 customers is $16.25. Therefore, the right answer is option (c).
The average or mean is calculated by taking the ratio of the total sum of the outcomes of an event to the frequency or the number of times the event occurs.
It can be written as [tex]\frac{n_1+n_2+.....+n_a}{a}[/tex].
In the given question, the sum of the customer bill is given as $3,250.
And the number of customers served is given to be 200.
Therefore, the average size of a customer's bill is calculated by [tex]\frac{3250}{200}[/tex]
Which turns out to be $16.25.
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The answer is $16.25. To find the average size of a customer's bill, you would divide the total earnings by the number of customers.
$3,250 / 200 customers = $16.25 per customer.
To find the average size of a customer's bill at the restaurant, you need to divide the total daily earnings by the number of customers. Here's a step-by-step explanation:
1. The restaurant earns $3,250 daily from the meals it sells.
2. The restaurant serves 200 customers daily.
Now, calculate the average bill size:
3. Divide the total daily earnings ($3,250) by the number of customers (200).
$3,250 ÷ 200 = $16.25
The average size of a customer's bill at the restaurant is $16.25.
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a repairable product with a constant failure rate of 0.0078 failures per hour has mean time to repair of 40 hours. find its availability
The availability of this repairable product is approximately 0.762, or 76.2%.
In order to find the availability of a repairable product, we need to consider its failure rate and mean time to repair. The formula for availability (A) is:
A = MTBF / (MTBF + MTTR)
Where MTBF is Mean Time Between Failures and MTTR is Mean Time To Repair.
Since we have a constant failure rate (λ), we can calculate the MTBF as the inverse of the failure rate:
MTBF = 1 / λ
In this case, the failure rate (λ) is 0.0078 failures per hour. Let's calculate the MTBF:
MTBF = 1 / 0.0078 = 128.205 hours
Now, we know the MTTR is 40 hours. We can use the availability formula to find the answer:
A = MTBF / (MTBF + MTTR)
A = 128.205 / (128.205 + 40)
A = 128.205 / 168.205
A ≈ 0.762
So, the availability of this repairable product is approximately 0.762, or 76.2%.
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this lesson will focus on finding the perimeter of rectangles. truefalse\
Answer:
Step-by-step explanation:
false
Which relation shows y as a function of x
The relation that shows y as a function of x is an equation.
What is an equation?An equation is a mathematical statement that two or more algebraic expressions share equality or equivalence.
Equations are depicted using the equation symbol (=), unlike mathematical expressions, which combine variables, numbers, constants, and values with mathematical operands but without the symbol of equality.
Thus, the relation, y is the dependent variable while x is the independent variable.
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i need to make this 20 characters so this is the question in the photo please help
The combined fraction in the context of this problem is given as follows:
(4x² + 12x - 9)/(x² + 8x + 15).
How to obtain the combined fraction?The fractional expression in the context of this problem is given as follows:
(x + 6)/(x² + 8x + 15) + 3x/(x + 5) - (x - 3)/(x + 3).
(x + 5)(x + 3) = x² + 8x + 15, hence the denominator of the simplified expression is given as follows:
x² + 8x + 15.
Applying the least common factor, the numerator of the simplified expression is given as follows:
x + 6 + 3x(x + 3) + (x - 3)(x + 5) = x + 6 + 3x² + 9x + x² - 3x + 5x - 15
x + 6 + 3x(x + 3) + (x - 3)(x + 5) = 4x² + 12x - 9
Hence the combined expression is given as follows:
(4x² + 12x - 9)/(x² + 8x + 15).
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If cosθ=-3/4 and tanθ is negative find sinθ
If cosθ=-3/4 and tanθ is negative, then sinθ= √(7)/4.
Since cosθ = -3/4 and θ is an angle in the second quadrant where cosθ is negative, we know that sinθ must be positive.
The Pythagorean identity is a trigonometric identity that relates the three basic trigonometric functions: sine, cosine, and tangent
To find sinθ, we can use the Pythagorean identity
sin^2θ + cos^2θ = 1
Substituting the value of cosθ we get
sin^2θ + (-3/4)^2 = 1
Simplifying
sin^2θ + 9/16 = 1
sin^2θ = 7/16
Taking the square root of both sides, we get
sinθ = ±√(7)/4
Since we know that sinθ is positive in the second quadrant, we take the positive value
sinθ = √(7)/4
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‼️WILL MARK BRAINLIEST‼️
Jamal ought to utilize a histogram to display the information regarding the amount of steps he takes each day.
What is sample and population?The complete set of people or things that we are interested in investigating is referred to as a population in statistics. We want to examine and draw conclusions from the entire set of facts. For instance, all adult women in a country would represent the population if we were interested in measuring the average height of adult women there.
In contrast, a sample is a smaller portion of the population that is chosen for analysis. When measuring the entire population is neither practicable or practical, this method is utilised.
Jamal ought to utilise a histogram to display the information regarding the amount of steps he takes each day. A histogram is a form of graph that shows how continuous data, such the number of steps, are distributed. It divides the data into intervals or "bins" and displays how frequently data points fall into each bin. Jamal may detect the usual or central trend of his daily step count as well as any fluctuation or outliers in the data by examining the shape of the histogram.
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A pre -image has coordinates N(2,3), U(5,-1) and M(4,1) it is reflected over the x-axis what is the y-coordinate of point U’?
Answer:
U' (5, 1 )
Step-by-step explanation:
under a reflection in the x- axis
a point (x, y ) → (x, - y ) , then
U (5, - 1 ) → U' (5, - (- 1) ) → U' (5, 1 )
3. In a box of phones, 48 are apple phones out of 100. Give a reduced ratio of non-apple phones to apple phones.
Answer: 13 non-apple phone to 12 apple phone
Step-by-step explanation:
48 are apple phone
100-48=52 52 are non-apple phones
52:48
simplify
13:12
a travel agent says that the mean hotel room rate for a family of 4 in a certain resort town is at most $170. A random sample of 33 hotel room rates for families of 4 has a mean of $179 and a standard deviation of $19. At a=0.01, is there enough evidence to reject the agent's claim
In a particular vacation town, the average cost of a hotel room for a family of four is more than $170 at a=0.01.
WHAT ARE AVERAGE COSTS?The term "average cost" refers to the production cost per unit, which is determined by dividing the overall production cost by the overall number of units produced. In other words, it calculates the cost for each unit of output that the company must incur.
The null hypothesis states that a family of four can only pay a maximum of $170 for a hotel room in a certain vacation town. The alternative premise is that a particular resort town's average hotel room cost for a family of four is higher than $1701.
There are 33 participants in the sample, and the mean value is $179 with a $192 standard deviation.
This hypothesis test's test statistic is computed as follows:
t =√(sample size) / (sample standard deviation / hypothesized mean) / (sample mean - hypothesized mean)
t = (179 - 170) / (19 /√(33)) = 3.02
This test's p-value, which is less than the significance level of 0.012, is 0.0026.. We conclude that there is enough evidence to show that the average hotel room price for a family of four in a particular resort town is more than $1701 and reject the null hypothesis as a result.
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What is the relationship between educational achievement and home ownership? A random sample of 500 U.S. adults was selected. Each member of the sample was identified as a high school graduate (or not) and as a homeowner (or not). Define event G as being a high school graduate and event H as being a homeowner. The Venn diagram summarizes the data based on these two events. What’s the probability that a randomly selected person who owns a home is also a high school graduate?
image wasnt working so: venn diagram G=89, H=119, G and H=221, and 71 outside
The probability of a randomly selected person who owns a home also being a high school graduate is approximately 0.442 or 44.2%.
How to find the probabilityBased on the information provided, we know that there are:
A random sample of 500 U.S. adults was selected221 individuals who are both high school graduates and homeowners (the intersection of events G and H). a total of 119 individuals who are homeowners (event H).Therefore, the probability of a randomly selected person who owns a home also being a high school graduate is:
P(G|H) = P(G and H) / Total number = 221/500 ≈ 0.442
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A pebble falls off a cliff at a height of
256 ft. If the equation for height as a
function of time is
h(t)=-16t2+ initial height where t is time
in seconds and h(t) is height in feet, how
many seconds will it take for the pebble
to hit the ground?
Check the picture below.
so the pebble will hit the ground when h(t) = 0.
It's noteworthy that the pebble is falliing off a cliff, so it was at rest, so its initial velocity is 0, so in essence is falling as fast as gravity can drop it.
[tex]~~~~~~\textit{initial velocity in feet} \\\\ h(t) = -16t^2+v_ot+h_o \quad \begin{cases} v_o=\textit{initial velocity}&0\\ \qquad \textit{of the object}\\ h_o=\textit{initial height}&256\\ \qquad \textit{of the object}\\ h=\textit{object's height}&\\ \qquad \textit{at "t" seconds} \end{cases} \\\\\\ h(t)=-16t^2+256\implies 0=-16t^2+256\implies 16t^2=256 \\\\\\ t^2=\cfrac{256}{16}\implies t^2=16\implies t=\sqrt{16}\implies t=4 ~~ seconds[/tex]
mateo has drawn a line to represent the parallel cross-section of the triangular prism. is he correct? explain. riangular prism lying on a rectangular face and a line drawn along the length of a rectangular face
Based on the information provided, Mateo has drawn a line to represent the parallel cross-section of the triangular prism. Is he correct? Yes, he is correct. Here's an explanation:
A triangular prism has two triangular bases and three rectangular faces. When a triangular prism is lying on a rectangular face, it means that one of its rectangular faces is on the bottom. If Mateo draws a line along the length of this rectangular face, he is creating a parallel cross-section of the triangular prism.
This is because the line he drew is parallel to the triangular base of the prism, and the two bases are also parallel to each other. A parallel cross-section is created when a plane cuts through a solid parallel to its base, and in this case, Mateo's line fulfills this condition.
Therefore, Mateo is correct in representing the parallel cross-section of the triangular prism by drawing a line along the length of a rectangular face.
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The set B = {1 + t2, t + t2, 1 + 2t + t2} is a basis for P2.
Find the coordinate vector of p(t) = 1 + 4t + 7t2 relative to B
The coordinate vector of p(t) relative to the basis B is:
[ -1 ]
[ 2 ]
[ 2 ]
To find the coordinate vector of p(t) = 1 + 4t + 7t2 relative to the basis B = {1 + t2, t + t2, 1 + 2t + t2}, we need to express p(t) as a linear combination of the basis vectors and then write down the coefficients as a column vector.
We have:
p(t) = a(1 + t2) + b(t + t2) + c(1 + 2t + t2)
Expanding this out, we get:
p(t) = (a + c) + (b + 2c)t + (a + b + c)t2
Comparing coefficients with the polynomial 1 + 4t + 7t2, we get the following system of equations:
a + c = 1
b + 2c = 4
a + b + c = 7
Solving this system, we find:
a = -1
b = 2
c = 2
Therefore, the coordinate vector of p(t) relative to the basis B is:
[ -1 ]
[ 2 ]
[ 2 ]
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a population of men has a mean weight of 182 lbs. and std dev. of 23 lbs. find the probability that a randomly selected man will have a weight of greater than 251 lbs.
The probability of picking a male from the population whose weight will be greater than 251 lbs is 0.13%.
In order to calculate the probability we need to use the formula of z-score
z = (x -μ)/ σ
here,
x = value of interest
μ = population mean
σ = population standard deviation
now adding the values into the given formula
z = ( 251 -182)/23
z = 69/23
z = 3
now after using the standard distribution table the probability of a z-score greater than 3 is 0.13%
The probability of picking a male from the population whose weight will be greater than 251 lbs is 0.13%.
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how much of the variation in the sample values of weekly gross revenue does the model in part (a) explain? if required, round your answer to two decimal places.
The estimated regression equation with TV advertising as the independent variable is ycap = 53.586 + 25.957x. The model explains 19.8% of the variation in the sample values of weekly gross revenue.
The estimated regression equation with television advertising as the independent variable is ycap = 53.586 + 25.957x. This suggests that for each additional $100 spent on television advertising, there is an estimated increase of $25,957 in weekly gross revenue.
we have already calculated the regression equation as ycap = 53.586 + 25.957x. Using this equation, we can calculate the predicted values of y for each observation in the sample of total sum of squares (SST), sum of squares due to regression (SSR) and coefficient of determination (R-squared) as the ratio of SSR to SST
R² = SSR / SST.
To calculate the values of ycap and ybar, we first need to find the mean values of the variables
xbar = (4.9 + 4.2 + 4.5 + 3.6 + 3.5 + 5.0 + 6.8) / 7 = 4.93
ybar = (101.3 + 75.8 + 127.2 + 137.8 + 102.4 + 236.8 + 220.6) / 7 = 143.14
Using the regression equation ycap = 53.586 + 25.957x and the given data, we can calculate the predicted values of y
ycap(Mobile) = 53.586 + 25.957(1.4) = 91.08
ycap(Shreveport) = 53.586 + 25.957(1.5) = 92.04
ycap(Jackson) = 53.586 + 25.957(1.5) = 92.04
ycap(Birmingham) = 53.586 + 25.957(4.3) = 167.16
ycap(Little Rock) = 53.586 + 25.957(4.0) = 158.48
ycap(Biloxi) = 53.586 + 25.957(2.3) = 111.35
ycap(New Orleans) = 53.586 + 25.957(8.4) = 261.32
ycap(Baton Rouge) = 53.586 + 25.957(5.9) = 219.13
Thus, the values of ycap are 91.08, 92.04, 92.04, 167.16, 158.48, 111.35, 261.32, and 219.13.
The sum of squared residuals (SSR) can be calculated as
SSR = Σ(ycap - ybar)² = (91.08 - 143.14)² + (92.04 - 143.14)² + (92.04 - 143.14)² + (167.16 - 143.14)² + (158.48 - 143.14)² + (111.35 - 143.14)² + (261.32 - 143.14)² + (219.13 - 143.14)²
= 214,767.63
The total sum of squares (SST) can be calculated as
SST = Σ(y - ybar)² = (101.3 - 143.14)² + (75.8 - 143.14)² + (127.2 - 143.14)² + (137.8 - 143.14)² + (102.4 - 143.14)² + (236.8 - 143.14)² + (220.6 - 143.14)²
= 1,082,685.88
Finally, the coefficient of determination (R-squared) is the ratio of SSR to SST
R² = SSR / SST = 214,767.63 / 1,082,685.88 = 0.198
Multiplying by 100 to convert to a percentage, we get R² = 19.8%.
The coefficient of determination (R-squared) for the model is 0.198, indicating that approximately 19.8% of the variation in the sample values of weekly gross revenue is explained by the variation in television advertising.
This implies that the model is a reasonably good fit for the data, but there may be other factors that also influence the weekly gross revenue that are not accounted for in this model.
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--The given question is incomplete, the complete question is given
" Data for a sample of eight markets for a recent week follow. Weekly Gross Revenue ($100s) Television Advertising Newspaper Advertising ($100s) ($100s) Market Mobile 101.3 4.9 1.4 52.9 3.1 3.2 Shreveport Jackson 75.8 4.2 1.5 Birmingham 127.2 4.5 4.3 Little Rock 137.8 3.6 4.0 Biloxi 102.4 3.5 2.3 New Orleans 236.8 5.0 8.4 Baton Rouge 220.6 6.8 5.9 (a) Use the data to develop an estimated regression equation with the amount of television advertising as the independent variable. Let x represent the amount of television advertising. If required, round your answers to three decimal places. For subtractive or negative numbers use a minus sign even if there is a + sign before the blank. (Example: -300) ycap= ____ . (b) how much of the variation in the sample values of weekly gross revenue does the model in part (a) explain? if required, round your answer to two decimal places."--
Gina has a credit card balance of $5,820 and her minimum payment is $87.30. What rate is used to determine Gina’s minimum payment?