plt.plot(x, y_sine)
plt.plot(x, y_cosine)
To compute the x and y coordinates for points on sine and cosine curves, you need to use the trigonometric functions sine and cosine. To plot the sine and cosine graphs in the same figure, you need to create a subplot grid using the plt.subplot() function. This function takes in the number of rows, columns and the active plot you want to plot the graphs in.
To create a subplot grid that has height 2 and width 1 and set the first subplot as active, the code will look like this:
plt.subplot(2, 1, 1)
You can then plot the sine and cosine graphs by using the x and y coordinates calculated from the sine and cosine functions. The code for plotting the graphs will look like this:
plt.plot(x, y_sine)
plt.plot(x, y_cosine)
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What equals $15,737.50?
Answer: 1rubber band + 15,736.50 rubber bands
Step-by-step explanation:
Well I'm not sure how advanced you wanted this but you could say that it equals to 15,737.50x1
1) Find a value of theta????[0,????/2] that satisfies the statement. Solve for theta WITHOUT using csc^-1 x.
Show all steps and provide the exact answer.
cos(????/2−theta)=1/7
2) Find all values of theta????[0,2????) such that sintheta=−√3/2. Work in radians, solution(s) should be in radians.
Trigoometric function
1) To find a value of theta that satisfies the statement, we can rearrange the equation and use the double angle formula for cosine:
cos(π/2-theta)=1/7
cos(π/2)cos(theta)+sin(π/2)sin(theta)=1/7
0cos(theta)+1sin(theta)=1/7
sin(theta)=1/7
theta=sin^-1(1/7)
theta=8.213 degrees or 0.143 radians
Therefore, a value of theta that satisfies the statement is 0.143 radians.
2) To find all values of theta that satisfy the statement, we can use the fact that sin(theta) is negative in the third and fourth quadrants:
sin(theta)=-√3/2
theta=sin^-1(-√3/2)
theta=4π/3 or 5π/3
Therefore, the values of theta that satisfy the statement are 4π/3 and 5π/3.
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O RATIOS, PROPORTIONS, AND PERCENTS Solving a word problem on proportions using a unit rate Suppose that 18 inches of wire costs 72 cents. At the same rate, how much (in cents ) will 13 inches of wire cost?
13 inches of wire will cost 52 cents at the same rate as 18 inches of wire costs 72 cents.
Determine the number of costTo solve this word problem on proportions using a unit rate, we need to first find the unit rate for the cost of the wire. The unit rate is the cost per one inch of wire.
We can find this by dividing the cost by the number of inches:
Unit rate = 72 cents / 18 inches = 4 cents per inch
Now that we have the unit rate, we can use it to find the cost of 13 inches of wire.
We simply multiply the unit rate by the number of inches:
Cost = 4 cents per inch × 13 inches = 52 cents
Therefore, 13 inches of wire will cost 52 cents at the same rate as 18 inches of wire costs 72 cents.
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When does Percy start to realize the casino is a trap? Use text evidence to support your answer.
Answer:
He realizes the casino is a trap when he found out people from 1977 are in the casino. They wasted five days in the casino.
2. Express the following decimal fractions as a sum of fractions. The denominator should be a power of 10. a)0,32 b)3,003 c)13, 134 d)5,2303
Answer:
a) 0.32 = 32/100 = 8/25
b) 3.003 = 3 + 3/1000 = 3000/1000 + 3/1000 = 3003/1000
c) 13.134 = 13 + 134/1000 = 13000/1000 + 134/1000 = 13134/1000
d) 5.2303 = 5 + 2303/10000
Which measurement of variability would be best to use for this distribution?
A. Median
B. Interquartile range
C. Mean
D. Mean absolute deviation
The measurement of variability that would be best to use for the distribution is Interquartile Range, the correct option is (b).
The best measurement of variability to use depends on the distribution of the data and the purpose of the analysis.
If the distribution is skewed or contains outliers, the median and interquartile range would be better measures of variability than the mean and standard deviation.
The median is less affected by extreme values, and
The interquartile range is a robust measure of spread that is not influenced by outliers.
The mean and mean absolute deviation may be appropriate if the data are approximately symmetric and do not contain outliers.
Therefore, The best measurement of variability is (b) Interquartile range.
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439 crates/hour equals how many crates/
week
Answer: 73,752 crates/ week
We can get to the answer by multiplying 439 by 24 by 7
Hope this helps!!
A toy factory makes an average of 528 toys during a 12-hour shift when it is operating during
its 2-month long busy season. The same factory averages 304 toys during an 8-hour shift
during the remainder of the year.
How many more toys does the factory produce in an hour during the busy season than during
the regular season?
Blank more toys per hour
Answer:
6
Step-by-step explanation:
First, we need to calculate the average number of toys produced per hour during the busy season and the regular season.
During the busy season, the factory operates for 2 x 30 = 60 days or 60 x 12 = <<2*30=60>>720 hours.
The average number of toys produced during this time is 528 toys per 12-hour shift, or 528/12 = <<528/12=44>>44 toys per hour.
During the regular season, the factory operates for the rest of the year, which is 12 - 2 = 10 months, or 10 x 4 = 40 weeks, or 40 x 5 = <<1045=200>>200 days, or 200 x 8 = <<200*8=1600>>1600 hours.
The average number of toys produced during this time is 304 toys per 8-hour shift, or 304/8 = <<304/8=38>>38 toys per hour.
The difference between the average number of toys produced per hour during the busy season and the regular season is:
44 - 38 = <<44-38=6>>6 toys per hour.
Therefore, the factory produces 6 more toys per hour during the busy season than during the regular season. Answer: 6.
Answer:
To calculate the number of more toys the factory produces in an hour during the busy season than during the regular season, we can divide the difference between the two shifts by the total hours of each shift:
More toys per hour = (528-304)/(12-8) = 224/4 = 56 toys per hour
Question content area top Part 1 Challenge A movie theater sends out a coupon for 20% off the price of a ticket. Write an equation for the situation, where y is the price of the ticket with the coupon, and x is the original price of the ticket. Use pencil and paper. Draw a graph of the equation and explain why the line should only be in the first quadrant. Question content area bottom Part 1 The equation is y enter your response here. (Use integers or decimals for any numbers in the expression).
Answer:
y = 0.8x
Step-by-step explanation:
y = x-0.2x
y=x(1-0.2)
y=x(0.8)
hence y = 0.8x
With these informations you can now do a graph !
Assume that the sales of automobiles in Brandon follow a Poisson distribution with a mean of 3 per day.
a. What is the probability that none is sold on a particular day?
b. What is the probability that at least 2 automobiles are sold on a particular day?
c. What is probability that for five consecutive days at least one automobile is sold?
Therefore, the answers are:
a. 0.0498
b. 0.8008
c. 0.7745
The Poisson distribution is a discrete probability distribution that expresses the probability of a given number of events occurring in a fixed interval of time or space if these events occur with a known constant mean rate and independently of the time since the last event.
a. The probability that none is sold on a particular day can be calculated using the formula:
P(X = 0) = (e^-λ)(λ^0) / 0!
Where λ is the mean and e is the base of the natural logarithm.
Substituting the values, we get:
P(X = 0) = (e^-3)(3^0) / 0!
P(X = 0) = (0.0498)(1) / 1
P(X = 0) = 0.0498
b. The probability that at least 2 automobiles are sold on a particular day can be calculated using the formula:
P(X ≥ 2) = 1 - P(X < 2)
P(X ≥ 2) = 1 - (P(X = 0) + P(X = 1))
P(X ≥ 2) = 1 - ((e^-3)(3^0) / 0! + (e^-3)(3^1) / 1!)
P(X ≥ 2) = 1 - (0.0498 + 0.1494)
P(X ≥ 2) = 1 - 0.1992
P(X ≥ 2) = 0.8008
c. The probability that for five consecutive days at least one automobile is sold can be calculated using the formula:
P(X ≥ 1) = 1 - P(X = 0)
P(X ≥ 1) = 1 - (e^-3)(3^0) / 0!
P(X ≥ 1) = 1 - 0.0498
P(X ≥ 1) = 0.9502
The probability that for five consecutive days at least one automobile is sold is:
P(X ≥ 1)^5 = 0.9502^5 = 0.7745
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the red outer shape is a regular hexagon. Decide whether the hexagons are similar.
Answer:
Yes they are similar since it is a regular shape
Yes, the red outer shape is a regular hexagon. the hexagons are similar. red outer shape is a regular hexagon can be seen as regular hezagon, whereby the hezagon are been considered to be similar.
What is regular hexagon ?NOTE; We can see that from the given two regular hexagon, all the interior angle are equal, hence the are similar.
A regular hexagon is a polygon with six equal sides and six equal angles. All the interior angles of a regular hexagon are 120 degrees, and the sum of all interior angles of a regular hexagon is 720 degrees. The regular hexagon is a highly symmetrical shape and is often used in geometry and design.
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Mrs. Nelson had to wait 4 minutes in line at her bank's automated teller machine. This was 3 minutes less than one-half of the time she waited in line at the grocery store. How long in minutes did she wait in line at the grocery store?
Mrs. Nelson waited 14 minutes in line at the grocery store.
Mrs. Nelson had to wait 4 minutes in line at her bank's automated teller machine. This was 3 minutes less than one-half of the time she waited in line at the grocery store. To find out how long in minutes did she wait in line at the grocery store, we can use the following equation:
4 = (x/2) - 3
Where x is the time she waited in line at the grocery store. To solve for x, we can first add 3 to both sides of the equation:
4 + 3 = (x/2) - 3 + 3
7 = x/2
Then, we can multiply both sides of the equation by 2 to isolate x:
7 * 2 = (x/2) * 2
14 = x
Therefore, Mrs. Nelson waited 14 minutes in line at the grocery store.
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Add. (z)/(z^(2)+8z+12)+(2)/(z^(2)+8z+12) Simplify your answer as much as possible.
The simplification form of the expression "(z)/(z^(2)+8z+12)+(2)/(z^(2)+8z+12)" is = "1/(z+6)".
To add the two fractions, we need to have a common denominator. Since both fractions already have the same denominator of z^(2)+8z+12, we can simply add the numerators together and keep the same denominator.
So, (z)/(z^(2)+8z+12)+(2)/(z^(2)+8z+12) = (z+2)/(z^(2)+8z+12)
Now, we need to simplify the fraction as much as possible. We can do this by factoring the denominator and seeing if there are any common factors that can be canceled out.
The denominator can be factored as (z+6)(z+2).
So, (z+2)/(z^(2)+8z+12) = (z+2)/(z+6)(z+2)
Now, we can see that there is a common factor of (z+2) in both the numerator and denominator, so we can cancel them out.
So, the final simplified answer is 1/(z+6).
Therefore, (z)/(z^(2)+8z+12)+(2)/(z^(2)+8z+12) = 1/(z+6).
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Jane wants to buy 15 tomatoes. She asks for 1 kg of tomatoes at a shop. Jane assumes that each tomato has a weight of 75 g. (b) (i) If Jane's assumption is correct, will she get 15 tomatoes? You must show how you get your answer. (ii) If Jane's assumption is not correct, could she get 15 tomatoes? Justify your answer.
(i) If Jane's assumption is correct, she will not get 15 tomatoes.
(ii) If Jane's supposition about the body mass of the each tomato is wrong, she could not obtain 15 tomatoes to 1 kg of tomatoes.
What types of things are assumptions?
An presumption is something you believe to be true despite the lack of evidence. People might presume, for instance, that you are a geek if you wear spectacles, even though that is untrue.
(b) (i) If Jane's assumption is correct, then the weight of 15 tomatoes would be:
15 tomatoes × 75 g/tomato = 1125 g
Since 1 kg is equal to 1000 g, Jane would need to buy at least:
1125 g / 1000 g/kg = 1.125 kg of tomatoes
Therefore, Jane would need to ask for at least 1.125 kg of tomatoes to get 15 tomatoes if her assumption about the weight of each tomato is correct.
(b) (ii) If Jane's assumption about the weight of each tomato is not correct, it is possible that she could get 15 tomatoes with 1 kg of tomatoes, depending on the actual weight of each tomato.
For example, if each tomato actually weighs 67 g, then 15 tomatoes would weigh:
15 tomatoes × 67 g/tomato = 1005 g
This is less than 1 kg, so Jane would get 15 tomatoes with 1 kg of tomatoes.
On the other hand, if each tomato actually weighs 100 g, then 15 tomatoes would weigh:
15 tomatoes × 100 g/tomato = 1500 g
This is more than 1 kg, so Jane would not get 15 tomatoes with 1 kg of tomatoes if her assumption about the weight of each tomato is incorrect.
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From a pool of six juniors and twelve seniors, four co-captains will be chosen for the football team. How many different combinations are possible if two juniors and two seniors are chosen?
Please help and show work
1 and 3
Step-by-step explanation:
pick one from the junior side and 3 from seniors because the senior is more that the junoir
Answer:
990 different combinations
Step-by-step explanation:
There are 6 juniors and 12 seniors for a total of 16 students
Out of 6 juniors we have to pick 2 juniors
Out of 12 seniors we have to pick 2 seniors
The number of items r that we can pick from a larger set of n items is given by C(n, r) pronounced n choose r.. This is sometimes written as nCr
The formula forC(n, r) is
[tex]\boxed{C(n,r) = \dfrac{n!}{r! (n - r)! }}[/tex]
where n! = n factorial = n x (n-1) x (n-2) x .... x 3 x 2 x 1
We can choose 2 juniors out of 6 juniors in C(6, 2) ways
and
2 seniors out of 12 seniors in C(12, 2) ways
[tex]C(6, 2) = = \dfrac{6!}{ 2! (6 - 2)! }\\\\= \dfrac{6!}{2! \times 4! }\\\\= 15[/tex]
[tex]C(12, 2) = \dfrac{12!}{ 2! (12 - 2)! }\\\\ = \dfrac{12!}{2! \times 10! }\\\\= 66[/tex]
Therefore the total number of ways you can select 2 juniors and 2 seniors from a pool of 6 juniors and 12 juniors
= 15 x 66 = 990
O.
Ob
Oc
Od
31 40 50 54
70
84 87 90
Referring to the figure above, which numbers are considered
possible outliers?
40, 84
31, 87, 90
84, 87, 90
31, 40, 50
31, 87, 90 are the numbers which are considered possible outliers.
How to determine which numbers are considered possible outliers?An outlier is an observation or data point that is significantly different from other observations in a dataset. In other words, it is an unusual or extreme value that is much higher or lower than most other values in the data.
A box and whisker plot is used to easily detect outliers. In this figure, the outliers are shown as black circles or dots. These are the data points that are distant from other observations.
Therefore, the numbers which are considered possible outliers are 31, 87, and 90.
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Simplify. Remove all perfect squares from inside the square root. Assume y is positive. √39y⁹
The solution of the radical expression will be y⁴√(39y).
What is a radical expression?Algebraic expressions involving radicals are known as radical expressions. The root of an algebraic expression makes up the radical expressions (number, variables, or combination of both). The root can be an nth root, a square root, or a cube root.
The given expression is √39y⁹. The radical expression can be simplified as below,
E = √39y⁹
E = √( 39 x y² x y² x y² x y² x y )
E = y⁴√39y
Therefore, the expression will have the simplified solution as E = y⁴√39y.
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Find the slope-intercept form of the equation of the line that passes through the point P and makes angle 0 with the positive x-axis.
P = (5.4) theta = 30 deg
A. y = (sqrt(3))/3 * x - ((5sqrt(3))/3 - 4)
B. y = (sqrt(3))/3 * x + ((12sqrt(3))/3 - 5)
c. y = sqrt(3) * x - (5sqrt(3) + 4)
D. y = 1/3 * x + ((5sqrt(3))/3 + 12)
The slope-intercept form of the equation of the line that passes through the point P (5, 4) and makes an angle, θ = 30°, with the x-axis is the option A.
A. y = ((sqrt(3))/3)·x - ((5·sqrt(3))/3 - 4)
What is the slope-intercept form of linear equation?The slope-intercept form of linear equation is an equation of the form; y = m·x + c, where;
m = The slope of the graph of the equation
c = The y-intercept of the graph of the equation.
The point through which the line passes, P = (5, 4)
The angle θ the line makes with the positive x-axis = 30°
The slope of the line = The tangent of the angle the line makes with the positive x-axis, therefore;
(y - 4)/(x - 5) = tan(30°) = 1/√3
y - 4 = (x - 5)/√3 = (x - 5)/√3 × (√3/√3) = (x - 5)·√3/3
y = (x - 5)·√3/3 + 4
The above equation can be converted into the slope-intercept form of a linear equation; y = m·x + c by simplifying the equation and rearranging the equation, into the required form;
y = (x - 5)·√3/3 + 4
y = (√3/3)·x - 5·√3/3 + 4 = (√3/3)·x - (5·√3/3 - 4)
y = (√3/3)·x - (5·√3/3 - 4)
The equation in slope-intercept form, is therefore;
A. y = (sqrt(3))/3)·x - (5·sqrt(3))/3 - 4)
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Mr. Morris is a librarian at Eastside Library. In examining a random sample of the library's book collection, he found the following. 737 books had no damage, 67 books had minor damage, and 31 books had major damage. Based on this sample, how many of the 34,000 books in the collection should Mr. Morris expect to have minor damage or major damage? Round your answer to the nearest whole number. Do not round any intermediate calculations.
Mr. Morris should expect around 3672 books in the collection to have minor or major damage.
What is proportion ?
Proportion is a relationship between two quantities that expresses the fraction of one quantity in terms of the other. In other words, a proportion is a statement that two ratios are equal.
To estimate the number of books in the collection that have minor or major damage, we first need to find the proportion of books in the sample that have such damage. We can then use this proportion to estimate the number of damaged books in the entire collection.
The total number of books in the sample is:
Total number of books = 737 + 67 + 31 = 835
The proportion of books in the sample that have minor or major damage is:
Proportion of damaged books = (67 + 31) / 835 = 0.108
To estimate the number of damaged books in the entire collection, we can multiply the proportion of damaged books by the total number of books in the collection:
Number of damaged books in collection = 0.108 x 34,000 = 3672
Rounding this answer to the nearest whole number, we get:
Therefore, Mr. Morris should expect around 3672 books in the collection to have minor or major damage.
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Question 1 1 pts Use the following functions to evaluate each expression f(x) = 1 x + 2 \
g(x) = 3x + 7 a.) f (g(-2)) = [ Select] b.) g (f (1)) = [Select ]
So, the final answers are:
a.) f(g(-2)) = 1/3
b.) g(f(1)) = 8
Question 1: Use the following functions to evaluate each expression f(x) = 1/(x + 2) and g(x) = 3x + 7.
a.) f(g(-2)) = f(3(-2) + 7) = f(1) = 1/(1 + 2) = 1/3
b.) g(f(1)) = g(1/(1 + 2)) = g(1/3) = 3(1/3) + 7 = 1 + 7 = 8
So, the final answers are:
a.) f(g(-2)) = 1/3
b.) g(f(1)) = 8
In summary, to evaluate the expression f(g(x)) or g(f(x)), we need to first find the value of the inner function and then substitute it into the outer function. This process is called function composition. It is important to follow the order of operations and simplify the expression as much as possible.
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Help! I need new dish soap. Which
one is the better price? Should I buy
the Method brand that is $5. 49 for 36
oz. Or the Seventh Generation brand
that is $3. 39 for 25 oz? Use math to solve
The soap from Seventh Generation brand cost less than Method brand.
What is Unitary Method?The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units.
For Example, Let's say Ram spends 36 Rs. for a dozen (12) bananas.
12 bananas will set you back 36 Rs. 1 banana costs 36 x 12 = 3 Rupees.
As a result, one banana costs three rupees. Let's say we need to calculate the price of 15 bananas.
This may be done as follows: 15 bananas cost 3 rupees each; 15 units cost 45 rupees.
The Method brand that is $5. 49 for 36 oz
So, the unit rate of soap
= 5.49 / 36
= $ 0.1525
and, The Seventh Generation brand that is $3. 39 for 25 oz
So, the unit rate of soap
= 3.39/ 25
= $0.1356
So, the soap from Seventh Generation brand is cheaper.
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A locker requires a three-digit code to open the lock. The code must contain one letter and two numbers, and no letter or number can be repeated. You can choose from among four letters, A, B, C, and D, and two numbers, 5 and 6.
The size of the sample space is
.
If a code is chosen at random, the probability that it has a letter that immediately follows an odd number is
.
If a code is chosen at random, the probability that D is in the code but is not in the first position is
.
The probability that this really contains a letter just after an odd number is one-half. D's likelihood of being in the program but not at the first place is 1/4.
What is the likelihood?A possibility which deals with the possibility of random occurrences is referred to as probability. All occurrences must have a chance of occuring at least once, or 1.
Describe probability with an example.The possibility or possibility of an incident occurrence is known as probability. For instance, there is only one method to receive a head and there are a total of two possible outcomes, hence the chance of coin flipping and receiving heads is 1 in 2. (a head or tail). P(heads) = 12 is what we write.
You can choose from among four letters, A, B, C, and D, and two numbers, 5 and 6.
The size of the sample space is (8, 16, 20, and 24)
If a code is chosen at random,
The probability that it has a letter that immediately follows an odd number (1/8, 1/6, 1/3, 2/5, 2/3)
= 1/2
If a code is chosen at random,
The probability that D is in the code but is not in the first position (1/8, 1/6, 1/3, 2/5, 2/3)
= 1/4
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Which expressions are equivalent?
The equivalent expression to the given one is:
y⁸*y³*x⁰*x⁻² = y¹¹*x⁻²
Which expressions are equivalent?We start with the expression:
y⁸*y³*x⁰*x⁻²
Remember the exponent rule for products of powers with the same base, it says that we can write:
xᵃ*xᵇ = xᵃ⁺ᵇ
So we just add the two exponents.
Using exponent rules, we can rewrite the product as
y⁸*y³*x⁰*x⁻² = y³⁺⁸*x⁰⁻² = y¹¹*x⁻²
That is the equivalent expression.
Then we can write:
y⁸*y³*x⁰*x⁻² = y¹¹*x⁻²
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Heather decides to make monthly payments into her savings account in the amount of $75 paying 3.6% compounded monthly for 5 years. Use FV=P((1+i)n−1i)
to determine the amount Heather will have in her savings account after the 5 year period.
Responses
$29,922
$4,922
$4,500
$492
Answer:
First Option, (A) $29,922.
Step-by-step explanation:
To calculate the future value of Heather's savings account after 5 years, we can use the formula for compound interest:
FV = P((1+i)^n - 1)/i
where:
FV = future value
P = principal (the initial amount Heather deposits)
i = interest rate per period (monthly in this case)
n = number of periods (months in this case)
P = $75 (the amount of Heather's monthly payments)
i = 3.6% / 12 = 0.003 (the monthly interest rate, calculated by dividing the annual interest rate by 12)
n = 5 x 12 = 60 (the total number of months in 5 years)
Substituting these values into the formula, we get:
FV = $75((1+0.003)^60 - 1)/0.003
FV = $75(1.21879)/0.003
FV = $29,922.02 (rounded to the nearest cent)
Therefore, Heather will have approximately $29,922.02 in her savings account after the 5 year period. The answer is option A: $29,922.
Find all possible rational zeros for the polynomial fu P(x)=21x^(3)-38x^(2)+44x-10
The possible rational zeros for the polynomial function P(x)=21x^(3)-38x^(2)+44x-10 are ±1, ±2, ±5, ±10, ±1/3, ±2/3, ±5/3, ±10/3, ±1/7, ±2/7, ±5/7, ±10/7, ±1/21, ±2/21, ±5/21, ±10/21.
The possible rational zeros of a polynomial function can be determined using the Rational Zero Theorem. This theorem states that if a polynomial function has rational zeros, they will be in the form of p/q, where p is a factor of the constant term and q is a factor of the leading coefficient.
In the given polynomial function, P(x)=21x^(3)-38x^(2)+44x-10, the constant term is -10 and the leading coefficient is 21. The factors of -10 are ±1, ±2, ±5, ±10 and the factors of 21 are ±1, ±3, ±7, ±21.
Using the Rational Zero Theorem, the possible rational zeros are:
p/q = ±1/1, ±2/1, ±5/1, ±10/1, ±1/3, ±2/3, ±5/3, ±10/3, ±1/7, ±2/7, ±5/7, ±10/7, ±1/21, ±2/21, ±5/21, ±10/21
Simplifying these fractions gives us the possible rational zeros:
±1, ±2, ±5, ±10, ±1/3, ±2/3, ±5/3, ±10/3, ±1/7, ±2/7, ±5/7, ±10/7, ±1/21, ±2/21, ±5/21, ±10/21
Therefore, the possible rational zeros for the polynomial function P(x)=21x^(3)-38x^(2)+44x-10 are ±1, ±2, ±5, ±10, ±1/3, ±2/3, ±5/3, ±10/3, ±1/7, ±2/7, ±5/7, ±10/7, ±1/21, ±2/21, ±5/21, ±10/21.
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A Satellite orbits Earth at a rate of about 3,300 in 12 minutes. At this rate, how far does the satellite travel around Earth in 1 hour? Remember 1 hour = 60 minutes
Answer:
16,500 miles
Step-by-step explanation:
In 12 minutes, the satellite travels 3,300 miles around Earth. To find how far the satellite travels around Earth in 1 hour, we can use unit conversion:
1 hour = 60 minutes
So, the number of 12-minute intervals in 1 hour is:
1 hour / 12 minutes = 5 intervals
Therefore, in 1 hour, the satellite travels:
3,300 miles/interval × 5 intervals = 16,500 miles
So the satellite travels around Earth at a distance of 16,500 miles in 1 hour.
Triangle XYZ has vertices X(−2, −1), Y(0, 2), and Z(2, −1)
The image after the rotation would be X(2, 1) Y(0,-2) and Z(-2, 1) according to the graph below.
What is a Graph?An ordered graphical depiction of numbers or variables is how this is described.
180 degrees in each direction results in (x,y) becoming (-x,-y). The coordinates are thus inverted to either positive or negative values depending on their respective signs.
A graph is a mathematical structure made up of a set of lines linking some pairs of VERTICES that may or may not be empty and a collection of points called VERTICES. Graphs are a common method for displaying the relationships between data. Although taking up less space, a graph accomplishes the goal of presenting data that are either too many or complex to be adequately described in the text.
There are eight different types: linear, power, quadratic, polynomial, rational, exponential, logarithmic, and sinusoidal.
Hence, it means X(−2, −1), Y(0, 2), and Z(2, −1) = X(2, 1) Y(0,-2) and Z(-2, 1).
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Complete question -
The area of a circle is 615.44 sq. inches. what is the diameter of the circle? use 3.14 for π.
The diameter of the circle is 28 inches.
Formula for the area of a circle is:
A = πr²
Where A represents the area, r denotes the radius, and π is a mathematical constant approximately equal to 3.14.
To find the diameter of the circle, we can use the formula:
D = 2r
in the given formula D is the diameter and r is the radius.
We know that the area of the circle is 615.44 sq. inches. So, we can use the area formula to find the radius:
615.44 = πr²
615.44 = 3.14r²
r² = 615.44/3.14
r² = 196
r = √196
r = 14
Now that we know the radius is 14 inches, we can use the diameter formula to find the diameter:
D = 2r
D = 2(14)
D = 28
Therefore, the diameter of the given circle is 28 inches.
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Question 7(Multiple Choice Worth 2 points)
(Volume of Cylinders MC)
Bradenton Bakery is baking a cake for a customer's quinceañera. The cake mold is shaped like a cylinder with a diameter of 12 inches and height of 8 inches.
Which of the following shows a correct method to calculate the number of cubic units of cake batter needed to fill the mold? Approximate using pi equals 355 over 113.
V equals 355 over 113 times 12 squared times 8
V equals 355 over 113 times 6 squared times 8
V equals 355 over 113 times 8 squared times 6
V equals 355 over 113 times 8 squared times 12
The answer is V equals 355 over 113 times 6 squared times 8.
What is the volume of the cylinder?
The volume of a cylinder is given by the formula V = πr²h, where r is the radius of the base of the cylinder, and h is the height of the cylinder.
Alternatively, the volume of a cylinder can be found by multiplying the area of the base (πr²) by the height (h).
The correct method to calculate the number of cubic units of cake batter needed to fill the mold is:
[tex]V = \pi r^2h[/tex], where r is the radius and h is the height of the cylinder.
The diameter of the cake mold is 12 inches, so the radius is half of that, which is 6 inches.
Therefore, the volume of the cake batter needed is:
V = (355/113) x 6² x 8
V = (355/113) x 36 x 8
V = 904.96 cubic inches
So the answer is: V equals 355 over 113 times 6 squared times 8.
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Subtract the polynomials using the horizontal format. 3x^(3)+x^(2)+2 from 7x^(3)-x-8
Subtraction of the polynomials using the horizontal format (3x³ + x² + 2) from 7x³- x - 8 is 4x³ - x² - x - 10.
A polynomial is a mathematical statement made up of coefficients and indeterminates that uses only the operations addition, subtraction, multiplication, and powers of positive integers of the variables.
To subtract the polynomials using the horizontal format, we will first write the two polynomials next to each other with the subtraction sign in between, then subtract the corresponding terms.
7x³- x - 8 - (3x³ + x² + 2)
Next, we will distribute the negative sign to each term inside the parentheses:
7x³ - x - 8 - 3x³- x²- 2
Now we will combine like terms:
4x³ - x² - x - 10
So, the final answer is 4x³ - x² - x - 10.
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