From the given information , the brand which is a "better-buy" is (c) Brand C .
To determine which brand is the better buy, we calculate the "price-per-ounce" for each brand.
To find the "price-per-ounce" we divide "the cost" by "the number of ounces",
On dividing cost by ounces,
We get,
⇒ For Brand A: $2.16 for 18 ounces,
The "price-per-ounce" is = $2.16/18 = $0.12 per ounce.
⇒ For Brand B: $1.50 for 12 ounces,
The "price-per-ounce" is = $1.50/12 = $0.125 per ounce.
⇒ For Brand C: $2.26 for 20 ounces,
The "price-per-ounce" = $2.26/20 = $0.113 per ounce.
⇒ For Brand D: $1.95 for 16 ounces,
The "price-per-ounce" is = $1.95/16 = $0.122 per ounce.
On comparing the price per ounce, we see that "Brand C" has the lowest price per ounce at $0.113, which makes it the better buy among the options given.
Therefore, the correct answer is (c) Brand C.
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The given question is incomplete, the complete question is
Given the following information, choose the brand that is the better buy.
Brand A: $2.16 for 18 ounces
Brand B: $1.50 for 12 ounces
Brand C: $2.26 for 20 ounces
Brand D: $1.95 for 16 ounces
(a) Brand A
(b) Brand B
(c) Brand C
(d) Brand D
‼️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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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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Find the missing measure.
The missing angles in the given pair of lines AB and CD with transversals EF & GH intersecting at O & missing sides on the basis of similarity of triangles are:
∠IKF=w°=109°
JO=z=2.7 units
∠JLO=x°=39°
∠DLO=y°=141°
What is similarity?
If two forms or figures have an equal number of comparable sides and angles, they are said to be similar. Similar figures are those when two or more figures share the same shape but have varied sizes.
Given that
∠KIO=39°
∠IKO=71°
∠IOK=70°
IO=12 units
KO=8 units
LO=4 units
a)We know that ∠KIO=∠OLJ {alternate interior angles}
∠KIO=∠OLJ=39°
∴x° = 39°
b)We know that ∠OLJ+∠OLD=180° {linear pair}
x°+y°=180°
39°+y°=180°
y°=180-39
y°=141°
c)We know that ∠IKO+∠IKF=180° {angles on straight line}
71°+w°=180°
w°=180-71
w°=109°
d)In ΔOKI and ΔOJL, we can see that
∠OIK=∠OLJ=39°
∠OKI=∠OJL=71°
∠KOI=∠JOL=70°
as the angles are congruent, we can say that ΔOKI and ΔOJL are similar.
∴Sides will be in same ratio
[tex]\frac{OI}{OL}[/tex] = [tex]\frac{OK}{OJ}[/tex] = [tex]\frac{KI}{JL}[/tex]
Taking [tex]\frac{OI}{OL}[/tex] = [tex]\frac{OK}{OJ}[/tex]
[tex]\frac{12}{4} = \frac{8}{z}[/tex]
3z = 8
z =2.667
z≈2.7 units
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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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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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The circumference of a circle is 176 mm. Find the diameter, radius and area. Show your working.
Step-by-step explanation:
Given :
Circumstance = 176 mm
We know that,
C = 2πr
r = C / 2π
r = 176 × 7/ 22 × 2
r = 1232/44
r = 28 mm
Now,
d = 2r = 2(28) = 56 mm
Now,
A = π r²
A = 22/7 × (28)²
A = 22/7 × 784
A = 17248/7
A = 2464 mm²
Answer:
Step-by-step explanation:
Circumference, C = 2πr
given: c=176mm, π=[tex]\frac{22}{7}[/tex]
c = 2 x [tex]\frac{22}{7}[/tex] x r
176 = [tex]\frac{44}{7}[/tex]r
r = [tex]\frac{7 *176}{44}[/tex]
r = 28
Area, A = π[tex]r^{2}[/tex]
A = [tex]\frac{22}{7}[/tex] x [tex]28^{2}[/tex]
A = 2464[tex]mm^{2}[/tex]
Need help ASAP
there are 600 poetry books at the library.Of the poetry books,8.5 are for children.How many poetry books at the library are for children
The number of poetry books at the library that are for children is 510
How many poetry books at the library are for childrenfrom the question, we have the following parameters that can be used in our computation:
Books = 600
If 8.5/10 of the poetry books are for children, we can calculate the number of poetry books for children as follows:
Number of poetry books for children = (8.5/10) x 600
Number of poetry books for children = 510
Therefore, there are 510 poetry books at the library for children.
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Please help me with this homework
Answer: 10
Step-by-step explanation:
10
What is 1.8 million divided by 400
Answer: 4,500 i got this answer
:)
Step-by-step explanation:
Answer:
Step-by-step explanation:
1.8million/400
[tex]18 * 10 ^{-1} *10^{6}*10^{-2} /4[/tex]
=4.5*10^3
=4.5*1000
=4500
set the number of flips per sample to 30, and adjust the proposed proportion of heads to 0.50. click flip so you have numbers to look at. you can ignore the shading on the graph for this question. the possible sample proportions are multiples of 1/30, such as 0/30, 1/30, 2/30, etc. (from observing 0, 1, 2, etc. heads out of 30 flips). the probability of observing a proportion of 10/30 or lower (10 or fewer heads) is 0.0494. a. use the binomial distribution to calculate the probability of observing exactly 11 heads (a sample proportion of 0.3667). b. then, calculate the probability of observing exactly 12 heads (a sample proportion of 0.4). c. finally, calculate the cumulative probability of observing 12 or fewer heads (a sample proportion of 0.4 or lower).
(a) The probability of observing exactly 11 heads is 0.1020.
(b) The probability of observing exactly 12 heads is 0.0687.
(c) The cumulative probability of observing 12 or fewer heads is 0.9531.
How find the probability of observing exactly 11 heads in 30 flips?a. To calculate the probability of observing exactly 11 heads in 30 flips, we can use the binomial distribution with parameters n = 30 (number of flips) and p = 0.50 (proportion of heads):
P(X = 11) = (30 choose 11) * (0.50)^11 * (1 - 0.50)^(30 - 11)
P(X = 11) = 0.1020 (rounded to four decimal places)
Therefore, the probability of observing exactly 11 heads is 0.1020.
How find the probability of observing exactly 12 heads in 30 flips?b. To calculate the probability of observing exactly 12 heads in 30 flips, we can use the same formula:
P(X = 12) = (30 choose 12) * (0.50)^12 * (1 - 0.50)^(30 - 12)
P(X = 12) = 0.0687 (rounded to four decimal places)
Therefore, the probability of observing exactly 12 heads is 0.0687.
How find the cumulative probability of observing 12 or fewer heads?c. To calculate the cumulative probability of observing 12 or fewer heads (a sample proportion of 0.4 or lower), we can sum the probabilities of observing 0, 1, 2, ..., 12 heads:
P(X <= 12) = P(X = 0) + P(X = 1) + ... + P(X = 12)
We can use software or a binomial probability table to calculate these probabilities and then sum them up. Alternatively, we can use the complement rule and subtract the probability of observing 13 or more heads from 1:
P(X <= 12) = 1 - P(X >= 13)
P(X <= 12) = 1 - [P(X = 13) + P(X = 14) + ... + P(X = 30)]
Using a binomial probability table or software, we can find that:
P(X >= 13) = 0.0469 (rounded to four decimal places)
Therefore,
P(X <= 12) = 1 - P(X >= 13) = 1 - 0.0469 = 0.9531
So the cumulative probability of observing 12 or fewer heads is 0.9531.
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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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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
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.
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>
which equation represents y as a function of x?
to get the equation of any straight line, we simply need two points off of it, let's use those two in the picture below
[tex](\stackrel{x_1}{40}~,~\stackrel{y_1}{30})\qquad (\stackrel{x_2}{100}~,~\stackrel{y_2}{75}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{75}-\stackrel{y1}{30}}}{\underset{\textit{\large run}} {\underset{x_2}{100}-\underset{x_1}{40}}} \implies \cfrac{ 45 }{ 60 } \implies \cfrac{ 3 }{ 4 }[/tex]
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{30}=\stackrel{m}{ \cfrac{ 3 }{ 4 }}(x-\stackrel{x_1}{40}) \\\\\\ y-30=\cfrac{ 3 }{ 4 }x-30\implies {\Large \begin{array}{llll} y=\cfrac{ 3 }{ 4 }x \end{array}}[/tex]
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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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?
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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Find the value of the missing angle. Round to the nearest degree.
1. 71 degrees
2. 19 degrees
3. 43 degrees
4. 90 degrees
Answer:
1. 71°
Step-by-step explanation:
SohCahToa
use sin
sin^-1(51/54)
=70.81186355
=71°
draw the reflection of the triangle across the y axis
Answer:
Image
Step-by-step explanation:
In parallelogram EFGH EJ =5x-3 and JG = 3x +9
What is EG?
The calculated value of the length of the segment EG is 54 units.
Calculating the length of the segments EGSince J is the midpoint of EG, we know that EJ = JG.
So, we can set the two expressions equal to each other and solve for x:
5x - 3 = 3x + 9
Subtracting 3x from both sides, we get:
2x - 3 = 9
Adding 3 to both sides, we get:
2x = 12
Dividing both sides by 2, we get:
x = 6
Now that we have x, we can substitute it back into either EJ or JG to find its value:
EJ = 5x - 3 = 5(6) - 3 = 27
JG = 3x + 9 = 3(6) + 9 = 27
Therefore, EG = EJ + JG = 27 + 27 = 54.
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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."--
If 55% of a number is 110 and 40% of the same number is 80, find 95% of that number.
Answer:
.40n = 80, so n = 200
.95 × 200 = 190
Answer:
190
Step-by-step explanation:
answer asap, 12 points !!!
Answer:
Step-by-step explanation:
domain is -infinity to positive infinity range is -3 to infinity. Increasing from -3 to infinity and decreasing from - infinity to -3 and it’s minimum
ecology: rocky mountain national park the following is based on information taken from winter wind studies in rocky mountain national park by d. e. glidden (rocky mountain nature association). at five weather stations on trail ridge road in rocky mountain national park, the peak wind gusts (in miles per hour) for january and april are recorded below. weather station 1 2 3 4 5 january 139 122 126 64 78 april 104 113 100 88 61 does this information indicate that the peak wind gusts are higher in january than in april? use a 5 0.01
Based on this analysis, it's clear that the peak wind gusts are generally higher in January than in April at these weather stations in Rocky Mountain National Park.
Yes, based on the provided information, the peak wind gusts in Rocky Mountain National Park are higher in January than in April.
Compare peak wind gusts for each weather station in January and April:
- Weather Station 1: January - 139 mph, April - 104 mph
- Weather Station 2: January - 122 mph, April - 113 mph
- Weather Station 3: January - 126 mph, April - 100 mph
- Weather Station 4: January - 64 mph, April - 88 mph
- Weather Station 5: January - 78 mph, April - 61 mph
Count the number of weather stations with higher peak wind gusts in January and April:
- Higher in January: 4 weather stations (1, 2, 3, and 5)
- Higher in April: 1 weather station (4)
Determine the overall trend:
- The peak wind gusts are higher in January at 4 out of 5 weather stations in Rocky Mountain National Park.
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Here's a comparison of the peak wind gusts at each weather station: Weather Station: 1 2 3 4 5 January: 139 122 126 64 78 April: 104 113 100 88 61 At all five weather stations, the peak wind gusts in January are higher than those in April.
Based on the information provided from winter wind studies in Rocky Mountain National Park by D.E. Glidden, it appears that the peak wind gusts are higher in January than in April.
The data shows that at all five weather stations on Trail Ridge Road, the peak wind gusts in January are higher than in April. To determine if this difference is statistically significant, a significance level of 0.01 can be used. Further statistical analysis would be needed to determine the significance of this difference.
Here's a comparison of the peak wind gusts at each weather station: Weather Station: 1 2 3 4 5 January: 139 122 126 64 78 April: 104 113 100 88 61 At all five weather stations, the peak wind gusts in January are higher than those in April.
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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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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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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
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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