Claire runs 100 meters in 17 seconds what is her speed in meters per second?
Find the solution to the initial value problem (1 + x^{5}) y' + 5 x^{4} y = 5 x^{8}
Graph 24x+25=−6y+7 .
How would I go about doing this? can someone give me a step by step process?
Answer:
Graph is attached below
Step-by-step explanation:
[tex]24x+25=-6y+7[/tex]
To graph the given equation , first we need to solve the equation for y
[tex]24x+25=-6y+7[/tex]
Subtract 7 on both sides
[tex]24x+18=-6y[/tex]
Divide both sides by -6
[tex]y=-4x-3[/tex]
To graph the given equation , make a table.
Assume some random number for x and find out y
x y=-4x-3
-1 1
0 -3
1 -7
Now graph all the points and join it by a line
(-1,1)(0,-3)(1,-7)
The graph is attached below
Suppose that you add 10 to all of the observations in a sample. how does this change the sample mean? how does it change the sample standard deviation?
Adding 10 to every observation in a sample, the sample mean would be 10 more the precious one and the standard deviation will remain the same.
What is mean of sample?"It is an average of a set of data."
What is formula of mean of sample?"For a sample of observation [tex]x_1,x_3,x_2,...,x_n[/tex] the mean of the sample is,
[tex]\Rightarrow \bar{X}=\frac{x_1+x_3+x_2+...+x_n}{n}[/tex]"
What is standard deviation?"It is a measure of how dispersed the data from the mean."
Formula for standard deviation?[tex]\Rightarrow \sigma=\sqrt{\frac{\Sigma(x_i-\bar{X})^2}{N}}[/tex]
where, [tex]\bar{X}[/tex] is the mean of sample and N is the size of sample
For given question,
Let [tex]x_1,x_3,x_2,...,x_n[/tex] be a sample observation.
We need to check if we add 10 to all of the observations in a sample, then does this change the sample mean. Also we have to check how does it change the sample standard deviation.
Let [tex]\bar{X}[/tex] be the mean of [tex]x_1,x_3,x_2,...,x_n[/tex]
[tex]\Rightarrow \bar{X}=\frac{x_1+x_3+x_2+...+x_n}{n}[/tex]
We add 10 to all of the observations in a sample.
[tex]\Rightarrow x_1+10,x_3+10,x_2+10,...,x_n+10[/tex]
The mean of above sample would be,
[tex]=\frac{(x_1+10)+(x_3+10)+(x_2+10)...+(x_n+10)}{n}\\\\=\frac{10n + (x_1+x_3+x_2+...+x_n)}{n}\\\\ =\frac{10n}{n} +\frac{x_1+x_3+x_2+...+x_n}{n}\\\\ =10 + \bar{X}[/tex]
This means, if we add 10 to every observation in a sample then the sample mean we 10 more the precious one.
In case of standard deviation,
adding 10 to every observation will not change the [tex](x_i-\bar{X})[/tex] factor.
This means, the standard deviation will remain the same.
Therefore, adding 10 to every observation in a sample, the sample mean would be 10 more the precious one and the standard deviation will remain the same.
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Final answer:
Adding 10 to each observation in a sample raises the sample mean by 10 but does not change the sample standard deviation, which measures the variability or spread of the data from the mean.
Explanation:
When you add 10 to all of the observations in a sample, you increase the sample mean by 10. This is because the mean is the average of all the values, and increasing each value by 10 raises the average by the same amount. However, this adjustment does not affect the sample standard deviation because standard deviation is a measure of variability or spread of the data from the mean, and adding a constant to each data point does not change the spread of the data relative to each other.
To understand how this works, suppose we have a sample with observations such as 3, 7, and 4. The sample mean is (3+7+4)/3 = 4.67.
If we add 10 to each observation, we get 13, 17, and 14. The new mean is,
(13+17+14)/3 = 14.67,
which is the original mean plus 10. However, the differences between each observation and the mean remain the same
(13-14.67 = -1.67, 17-14.67
= 2.33, and
14-14.67 = -0.67),
Meaning the spread has not changed, and thus the standard deviation remains the same.
Sam used 4 gallons of gas to drive 108 miles and 7 gallons of gas to drive 189 miles. Is this a proportional relationship? Explain your reasoning.
The 2011 super bowl had an attendance of 103,219 people. If the headline in the newspaper the next day read, about 200,000 people attend super bowl, is the newspapers estimate reasonable? Use rounding to explain your answer
The price of a pair of shoes is $63.20. The sales tax rate is 4.5 percent. How much sales tax would you pay if you bought these shoes?
You would end up paying $2.84 in sales tax.
63.20*0.45=$2.84.
Hope this helps!
4.5% = 0.045
63.20 x 0.045 = 2.844
tax = $2.84
"most humans find it easier to remember words, rather than numbers. if you tell someone to go to www.icann.org, they can probably remember that. if you told them to go to 192.0.32.7, they would have a difficult time remembering an ip address. computers process in numbers. dns is the process of translating words into numbers. there is a second translation that takes place. humans think in base 10 numbers. computers process in base 2 numbers. the base 10 ip address 192.0.32.7 in base 2 numbers is 11000000.00000000.00100000.00000111. what happens if you cut and paste these base 2 numbers into a browser?"
If you were to cut and paste the base 2 numbers 11000000.00000000.00100000.00000111 into a browser, it would not work as expected.
Why is this so?Browsers expect IP addresses to be provided in the standard base 10 format, not in base 2.
The base 2 representation you mentioned is the binary representation of the IP address 192.0.32.7, but browsers require the IP address to be in decimal format to establish a successful connection.
A browser is a software application used to access and view information on the World Wide Web, displaying webpages and supporting various internet activities.
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what is another pattern in the numbers? Rule: add 1, multiply by 2 first term: 2
What is the percent grade of a hill with a gradient of 65 ft/mile?
six Bakers share 7.5 kg of flour equals how much flour did they each receive
At oxnard university, a student id consists of one letter (26 possibilities) followed by eight digits (10 possibilities). (a) how many unique student ids can be created? number of student ids (b) would one letter followed by three digits suffice for a university with 43,000 students? yes no
A. We are given that the combination is 1 letter and 8 digits, so the total number of unique combinations would be the product of each possibilities.
Total unique ID’s = 26 * 10 * 10 * 10 * 10 * 10 * 10 * 10 * 10
or can also be written as
Total unique ID’s = 26 * 10^8
Solving:
Total unique ID’s = 2.6 x 10^9
B. Let us now calculate the total unique ID’s if there is only 1 letter followed by 3 digits.
Total unique ID’s = 26 * 10^3
Total unique ID’s = 26,000
Since there are 48,000 students and only 26,000 unique ID’s, therefore it is not enough.
NO.
Final answer:
The answer explains the calculation of unique student IDs at a university and determines if a specific ID format is sufficient for a given student count.
Explanation:
(a) To calculate the number of unique student IDs, we multiply the possibilities for each part: 26 possibilities for a letter and 10 possibilities for each of the eight digits:
Total unique student IDs = 26 x (10)^8 = 26 x 100,000,000 =26 x 10^8
(b) For a university with 43,000 students, one letter followed by three digits would have:
Total unique IDs = 26 x (10)^3 = 26 x 1,000 = 26,000, which is more than 43,000 students - so no, it would not suffice.
Consider (test a - test b). use a 0.05 significance level to test the claim that people do better on the second test than they do on the first. (note: you may wish to use software.)
Find the maximum value of the function
The points (6,8) and (5,5) fall on a particular line.
what is the slope of the line passing through those points? show your work?
Answer:
The slope of the line passing through these points is 3.
Step-by-step explanation:
A first order function is given by the following formula:
[tex]y = ax + b[/tex]
In which a is the slope.
In this problem, we have that:
The line passes through the point (5,5). This means that when x = 5, y = 5. So
[tex]5a + b = 5[/tex]
[tex]b = 5 - 5a[/tex]
The line also passes through the point (6,8). This means that when x = 6, y = 8. So:
[tex]6a + b = 8[/tex]
[tex]b = 5 - 5a[/tex]
So
[tex]6a + 5 - 5a = 8[/tex]
[tex]a = 3[/tex]
The slope of the line passing through these points is 3.
Translate to an algebraic expression
34 more than q
Which angles are corresponding angles?
Estimate 970,390+741,206
How do I
Simplify 8-13-(-4)
BODMAS stands for Brackets of Division, Multiplication, Addition, and Subtraction.
In the given equation, the simplified value is -1.
The given equation is:
[tex]8 - 13 - ( - 4)[/tex]
Step 1: In the equation, brackets are present. The brackets will open and the negative sign will be changed to a positive sign, (-) (-) = +.
The equation now becomes:
[tex]8 - 13 + 4[/tex]
Step 2: Based on the BODMAS, after division and multiplication, addition comes.
Solving for the same, we get:
[tex]8 - 9[/tex] [Becaue, -13 + 4 = -9 (+)(-) = (-)]
Step 3: The final value of subtracting -9 from 8, we get:
[tex]8 - 9[/tex] = -1.
Therefore, for the given equation, [tex]8 - 13 - ( - 4)[/tex], the simplified answer is -1.
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What is the amount of the tax per unit?
a. $3
b. $4
c. $2
d. $1?
The amount of the tax per unit imposed by the government, based on the examples provided, is $4 per unit. This specific tax impacts the supply curve and the market's equilibrium, affecting both the consumers' and suppliers’ prices.
The question you're asking about centers on the concept of tax per unit, which is a specific type of tax that governments impose on goods or services. In the information provided, various scenarios are described where a tax is imposed, which affects the prices and the quantity traded of the good. For instance, the imposition of a specific tax of $4 means the supply curve shifts vertically upwards by this amount. The resulting changes in market conditions illustrate how the tax burden is shared between consumers and suppliers.
In the most relevant example, both the government and supplier receive $4 per unit after the imposition of the tax. Therefore, the amount of the tax per unit imposed by the government is $4, which is option (b) in the context of your question.
The numbers on two consecutively numbered gym lockers have a sum of 143. What are the locker numbers
What is 7:9 to 48 states
Square 1 has a side length of x, and square 2 has a side length of y. Square 2 is formed by joining the midpoints of the sides of square 1 in order. If x = 2, find the ratio of the perimeter of square 1 to the perimeter of square 2.. . A. 2:1 . B. 1:2 . C. 1: Radical 2 . D. 2: radical 2 Ask for details Follow Report by Btie3oliv8iakram
Answer:
D. 2:√2
Step-by-step explanation:
Use properties of equality to simplify each of the following expressions so that you can simplify them in your head. Identify the properties used and describe how you used them.
1. 4 • (–3) • 5
2. (2.25 • 23) • 4
4. 5 • 12 • (–2)
5. 35(26)(0)
Miguel needs to fix a window screen that is 23 feet above the ground. The ladder he uses makes a 75° angle with the ground. What is the shortest possible length of the ladder if the top of it is 23 feet off the ground? Round to the nearest whole number.
Let L be the length of the ladder, and consider the 75 degree angle. Thinking in terms of trig, the "opposite side" of the triangle formed by the ladder, the ground and the wall is 23 ft. Your job is to determine the length of the ladder, which is the same as the length of the hypotenuse of the triangle.
The sine function relates these two lenths:
opp. side 23 ft
sin 75 deg = ---------------- = --------------
hyp hyp
23 ft 23 ft
Solving for hyp, hyp = ---------------------- = ------------ = 23.8 ft sin 75 deg 0.956
The minimum ladder length would be 23.8 ft, which rounds up to 24 ft.
Check: is (23.8 ft)(sin 75) = 23 ft? Yes.
Using trigonometry, the shortest possible length of the ladder given that the wall height is 23 feets and makes an angle of 23° with the ground ls 24 feets
Recall from trigonometry :
SOHCAHTOA The length of the ladder is the hypotenus ;Using :
Sinθ = opposite / hypotenus θ = 75°Sin(75°) = 23 / hypotenus
Cross multiply :
Hypotenus × 0.9659258 = 23
Divide both sides by 0.9659258
Hypotenus = (23 / 0.9659258)
Hypotenus = 23.81 feets
Therefore, the height of the ladder rounded to the nearest feet is 24 feets.
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The pattern of numbers below is an arithmetic sequence: 14, 24, 34, 44, 54, ... Which statement describes the recursive function used to generate the sequence? A. The common difference is 1, so the function is f(n + 1) = f(n) + 1 where f(1) = 14. B. The common difference is 4, so the function is f(n + 1) = f(n) + 4 where f(1) = 10. C. The common difference is 10, so the function is f(n + 1) = f(n) + 10 where f(1) = 14. D. The common difference is 14, so the function is f(n + 1) = f(n) + 14 where f(1) = 10.
Answer:
Option C is correct
The common difference is 10,
So, the function is f(n + 1) = f(n) + 10 , where f(1) = 14
Step-by-step explanation:
The recursive function for the arithmetic sequence is given by:
[tex]f(n+1) = f(n)+d[/tex] .....[1]
where, d is the common difference of the two consecutive terms.
Given the arithmetic sequence :
14, 24, 34, 44, 54, .......
First term f(1) = 14
Common difference(d) = 10
Since,
24 -14 = 10
34-24 = 10
44-34 = 10 and so on....
Substitute d = 4 in [1], we have;
[tex]f(n+1) = f(n) + 10[/tex]
Therefore, the recursive function used to generate the sequence is,
[tex]f(n+1) = f(n) + 10[/tex] and f(1) = 10
The common difference is 10, so the function is t(n + 1) = t(n) + 10. Option C is correct.
Given the sequence of numbers 14, 24, 34, 44, 54, ...
This can also be written as (4+10), (14+10) + (24+10), (34+10), (44+10)...
Since 10 is comon to all the terms, the recursive formula will be:
t(n+1) = t(n) + 10
t(n) is the nth term of the remaining sequence 4, 14, 24, 34...
t(n) = a+(n-1)d
t(n) = 4+(n-1)(10)
t(n) = 4 + 10n - 10
t(n) = 10n - 6
Hence the equivalent recursive function will be t(n + 1)= t(n) + 10 with a common difference of 10
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Divide. Write your answer as a fraction in simplest form.
9/10÷(−6/5)=
3. The formula to find the surface area of a sphere is to take the radius of the sphere and square it and multiply that amount by pi and then multiply that by 4. This is written algebraically as S=4πr 2 , where S is the surface area, r is the radius, and the value of π is 3.14. Rewrite the equation to solve for the radius of the sphere if you know the sphere’s surface area. Then estimate the radius of a sphere given a surface area of 500 meters2 .
Answer:
6.31 m
Step-by-step explanation:
The surface area (S) of a sphere is a function of its radius (r) according to the following expression.
[tex]S=4\pi r^{2}[/tex]
We can rewrite it to solve for the radius given the surface area.
[tex]S=4\pi r^{2}\\r^{2} =\frac{S}{4\pi} \\r=\sqrt{\frac{S}{4\pi}}[/tex]
When S = 500 m², the radius is
[tex]r=\sqrt{\frac{500m^{2} }{4\pi}}=6.31 m[/tex]
What is the value of n in the equation below? 12^n/12^5=12^4
If you sell 30 items at $200 a piece and your commission rate is 20%, how much commission do you earn
Answer:
$1200 a
Step-by-step explanation:
You sell 30 items at $200 a piece and your commission rate is 20%
Price of 30 items = 30 × 200 = $6,000
Your commission = 20% × 6,000
= [tex]\frac{20}{100}[/tex] × 6,000
= 0.20 × 6,000
= $1200
You earn $1200 as commission.