Answer:
The probability of randomly selecting a queen or club from a deck of cards = 17/52
Step-by-step explanation:
Here in this question, we are concerned with computing the probability of randomly selecting a queen or club form a deck of cards
Mathematically, the probability is;
Probability of selecting a queen + Probability of selecting a club
Probability of selecting a queen = number of queens/total card number
The number of queens = 4
Probability of selecting a queen = 4/52
Probability of selecting a club card = number of club cards/ total number of cards
Number of club cards = 13
Probability of selecting a club card = 13/52
The probability of selecting a queen or club from a deck of cards = 4/52 + 13/52 = 17/52
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Answer:
D. the bottom one is the answer, because hyperbola is two curves that curve infinitely
An observer standing on a cliff 320 feet above the ocean measured angles of depression of the near and far sides of an island to be 16.5 and 10.5 respectively. How long is the island ?
Answer:
154.10 Feets
Step-by-step explanation:
Given the following :
Height (h) of cliff = 320 feet
Angle of depression of near side = 16.5°
Angle of depression of far side = 10.5°
Using trigonometry :
We can obtain x and y as shown in the attached picture :
Tanθ = opposite / Adjacent
Adjacent = height of cliff = 320 Feets
For the near side :
Tanθ = opposite / Adjacent
Tan (16.5°) = x / 320
0.2962134 = x / 320
x = 0.2962134 * 320
x = 94.788318 Feets
For the far side :
Tanθ = opposite / Adjacent
Tan (10.5°) = x / 320
0.1853390 = x / 320
x = 0.1853390 * 320
x = 59.308494 Feets
Length of island = (59.308494 + 94.788318) feet
= 154.10 Feets
If m(x) =x+5/x-1 and n(x) = x - 3, which function has the same domain as (mºn)(x)?
We have
M(X) = (X + 5)/(X - 1)
N(X) = X - 3
So,
M(N(X)) = [(X - 3) + 5]/[(X - 3) - 1]
M(N(X)) = [X + 2]/[X - 4]The M(N(X)) domain will be:
D = {X / X ≠ 4}
4 ∉ to the M(N(X)) domain, otherwise we would have a/0, which is not possible (a denominator with zero). An equivalent function would be
H(X) = 1/(X - 4)
Evaluate 1 + (-2/3) - (-m) where m = 9.2.
Answer:
9.533
Step-by-step explanation:
1+(-2/3)-(-9.2)
1-2/3--9.2
1-2/3+9.2=9.533
Simply. Who ever answers this will be marked Brainlist.
Answer:
Step-by-step explanation:
Hello,
[tex]r^3s^{-2}\cdot 8r^{-3}s^4\cdot 4rs^5\\\\=r^{3-3+1}s^{-2+4+5}\cdot 8\cdot 4\\\\\boxed{=32\cdot r\cdot s^7}[/tex]
Hope this helps.
Do not hesitate if you need further explanation.
Thank you
(Algebra) PLZ HELP ASAP!
Answer: Its everthing except irrational
Step-by-step explanation:
PLEASE HELP!!! The question is.. [tex]163-y=-5[/tex] ANSWER GETS BRAINLIEST
Answer:
y = 168Step-by-step explanation:[tex]163 -y =-5\\Collect\:Like\:terms\\163+5 = y\\Simplify\\168 =y\\\\y = 168[/tex]
Hello There!
Answer: [tex]163-168=-5[/tex]Explanation:[tex]163-y=-5[/tex]
To solve your equation, you can just change the -5 to 5 and move it to where y is. After that, change the minus sign to addition.
[tex]163+5=y[/tex]
Now all you have to do is sum it up.
[tex]163+5=168[/tex]
So y = to 168
So your answer is
[tex]163-168=-5[/tex]
Hope this Helps!
What is the range of g?
Answer:
R: {y∈R | -1 ≤ y ≤ 5}
Step-by-step explanation:
the lowest point is -1 and the highest point is 5.
A professional soccer player kicked a ball across the field. The ball’s height, in meters, is modeled by the function graphed below. What's the average rate of change between the point when the ball reached its maximum height and the point where it hit the ground?
Answer:
Hey there!
You can think of the rate of change as the slope of a quadratic function- here we see that it is 9/-3, or - 3.
Let me know if this helps :)
Answer:
–3 meters per second
Step-by-step explanation:
An architectural drawing lists the scale as 1/4" = 1'. If a bedroom measures 6 3/4" by 4 1/2" on the drawing, how large is the bedroom? Please Help! (No other information was given.)
1 inch = four 1/4’s
1 inch = 4 feet
6 X 4 = 24 feet
3/4 inches = 3 feet.
6 3/4 inches = 27 feet
4 x 4 = 16
1/2 inch = 2 feet
4 1/2 inches = 18 feet
Room is 27 feet x 18 feet
For some postive value of Z, the probability that a standardized normal variable is between 0 and Z is 0.3770. The value of Z is
Answer:
1.16
Step-by-step explanation:
Given that;
For some positive value of Z, the probability that a standardized normal variable is between 0 and Z is 0.3770.
This implies that:
P(0<Z<z) = 0.3770
P(Z < z)-P(Z < 0) = 0.3770
P(Z < z) = 0.3770 + P(Z < 0)
From the standard normal tables , P(Z < 0) =0.5
P(Z < z) = 0.3770 + 0.5
P(Z < z) = 0.877
SO to determine the value of z for which it is equal to 0.877, we look at the
table of standard normal distribution and locate the probability value of 0.8770. we advance to the left until the first column is reached, we see that the value was 1.1. similarly, we did the same in the upward direction until the top row is reached, the value was 0.06. The intersection of the row and column values gives the area to the two tail of z. (i.e 1.1 + 0.06 =1.16)
therefore, P(Z ≤ 1.16 ) = 0.877
Calcule o valor de x nas equações literais: a) 5x – a = x+ 5a b) 4x + 3a = 3x+ 5 c) 2 ( 3x -a ) – 4 ( x- a ) = 3 ( x + a ) d) 2x/5 - (x-2a)/3 = a/2 Resolva as equações fracionárias: a) 3/x + 5/(x+2) = 0 , U = R - {0,-2} b) 7/(x-2) = 5/x , U = R - {0,2} c) 2/(x-3) - 4x/(x²-9) = 7/(x+3) , U = R - {-3,3}
Answer:
1) a) [tex]x = \frac{3}{2}\cdot a[/tex], b) [tex]x = 5-3\cdot a[/tex], c) [tex]x = -a[/tex], d) [tex]x = \frac{5}{2}\cdot a[/tex]
2) a) [tex]x = -\frac{3}{4}[/tex], b) [tex]x = -5[/tex], c) [tex]x = 3[/tex]
Step-by-step explanation:
1) a) [tex]5\cdot x - a = x + 5\cdot a[/tex]
[tex]5\cdot x - x = 5\cdot a + a[/tex]
[tex]4\cdot x = 6\cdot a[/tex]
[tex]x = \frac{3}{2}\cdot a[/tex]
b) [tex]4\cdot x + 3\cdot a = 3\cdot x + 5[/tex]
[tex]4\cdot x - 3\cdot x = 5 - 3\cdot a[/tex]
[tex]x = 5-3\cdot a[/tex]
c) [tex]2\cdot (3\cdot x - a) - 4\cdot (x-a) = 3\cdot (x+a)[/tex]
[tex]6\cdot x -2\cdot a -4\cdot x +4\cdot a = 3\cdot x +3\cdot a[/tex]
[tex]6\cdot x -4\cdot x -3\cdot x = 3\cdot a -4\cdot a +2\cdot a[/tex]
[tex]-x = a[/tex]
[tex]x = -a[/tex]
d) [tex]\frac{2\cdot x}{5} - \frac{x-2\cdot a}{3} = \frac{a}{2}[/tex]
[tex]\frac{6\cdot x-5\cdot (x-2\cdot a)}{15} = \frac{a}{2}[/tex]
[tex]\frac{6\cdot x - 5\cdot x+10\cdot a}{15} = \frac{a}{2}[/tex]
[tex]2\cdot (x+10\cdot a) = 15 \cdot a[/tex]
[tex]2\cdot x = 5\cdot a[/tex]
[tex]x = \frac{5}{2}\cdot a[/tex]
2) a) [tex]\frac{3}{x} + \frac{5}{x+2} = 0[/tex]
[tex]\frac{3\cdot (x+2)+5\cdot x}{x\cdot (x+2)} = 0[/tex]
[tex]3\cdot (x+2) + 5\cdot x = 0[/tex]
[tex]3\cdot x +6 +5\cdot x = 0[/tex]
[tex]8\cdot x = - 6[/tex]
[tex]x = -\frac{3}{4}[/tex]
b) [tex]\frac{7}{x-2} = \frac{5}{x}[/tex]
[tex]7\cdot x = 5\cdot (x-2)[/tex]
[tex]7\cdot x = 5\cdot x -10[/tex]
[tex]2\cdot x = -10[/tex]
[tex]x = -5[/tex]
c) [tex]\frac{2}{x-3}-\frac{4\cdot x}{x^{2}-9} = \frac{7}{x+3}[/tex]
[tex]\frac{2}{x-3} - \frac{4\cdot x}{(x+3)\cdot (x-3)} = \frac{7}{x+3}[/tex]
[tex]\frac{1}{x-3}\cdot \left(2-\frac{4\cdot x}{x+3} \right) = \frac{7}{x+3}[/tex]
[tex]\frac{x+3}{x-3}\cdot \left[\frac{2\cdot (x+3)-4\cdot x}{x+3} \right] = 7[/tex]
[tex]\frac{2\cdot (x+3)-4\cdot x}{x-3} = 7[/tex]
[tex]2\cdot (x+3) -4\cdot x = 7\cdot (x-3)[/tex]
[tex]2\cdot x + 6 - 4\cdot x = 7\cdot x -21[/tex]
[tex]2\cdot x - 4\cdot x -7\cdot x = -21-6[/tex]
[tex]-9\cdot x = -27[/tex]
[tex]x = 3[/tex]
3. Solve for x2=81 C. 10
Answer:
9
Step-by-step explanation:
9 x 9 = 81
Answer:
x = ±9
Step-by-step explanation:
x^2 = 81
Take the square root of each side
sqrt(x^2 ) = ±sqrt(81)
x = ±9
I don’t understand this, may I get some help?
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Hi my lil bunny!
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80,023 written in scientific notation is [tex]8,0023[/tex] x [tex]10^4[/tex].
Step 1
To find a, take the number and move a decimal place to the right one position.
Original Number: 80,023
New Number: 8.0023
Step 2
New Number: 8 . 0 0 2 3
Decimal Count: 1 2 3 4
Now, to find b, count how many places to the right of the decimal.
There are 4 places to the right of the decimal place.
Step 3
Building upon what we know above, we can now reconstruct the number into scientific notation.
Remember, the notation is: a x 10^b
a = 8.0023
b = 4
Now the whole thing:
8.0023 x 104
Step 4
Check your work:
10^4 = 10,000 x 8.0023 = 80,023
❧⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯☙
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Have a great day/night!
❀*May*❀
A population has a standard deviation of 16. If a sample of size 64 is selected from this population, what is the probability that the sample mean will be within 2 of the population mean?
a. Since the mean is not given, there is no answer to this question.
b. -0.6826
c. 0.3413
d. 0.6826
e. -0.3413
Answer:
The correct option is D
Step-by-step explanation:
From the question we are told that
The standard deviation is [tex]\sigma = 16[/tex]
The sample size is n = 64
The standard error of mean is mathematically evaluated as
[tex]\sigma _{\= x } = \frac{\sigma }{\sqrt{n} }[/tex]
substituting values
[tex]\sigma _{\= x } = \frac{16 }{\sqrt{64} }[/tex]
[tex]\sigma _{\= x } = 2[/tex]
Generally the probability that the sample mean will be within 2 of the population mean is mathematically represented as
[tex]P( \mu - 2 < \= x < \mu + 2) = P(\frac{( \mu - 2 ) - \mu }{\sigma_{\= x }} < \frac{ \= x - \mu }{\sigma_{\= x }} < \frac{( \mu +2 ) - \mu }{\sigma_{\= x }} )[/tex]
Generally [tex]\frac{ \= x - \mu }{\sigma_{\= x }} = Z (The \ standardized \ value \ of \ \= x )[/tex]
So
[tex]P( \mu - 2 < \= x < \mu + 2) = P(\frac{( \mu - 2 ) - \mu }{\sigma_{\= x }} < Z< \frac{( \mu +2 ) - \mu }{\sigma_{\= x }} )[/tex]
[tex]P( \mu - 2 < \= x < \mu + 2) = P(\frac{( -2 }{\sigma_{\= x }} < Z< \frac{ 2 }{\sigma_{\= x }} )[/tex]
substituting values
[tex]P( \mu - 2 < \= x < \mu + 2) = P(\frac{-2 }{2} < Z< \frac{ 2 }{2} )[/tex]
[tex]P( \mu - 2 < \= x < \mu + 2) = P(-1< Z< 1 )[/tex]
=> [tex]P( \mu - 2 < \= x < \mu + 2) = P(Z < 1) - P(Z < -1)[/tex]
From the normal distribution table [tex]P(Z < 1 ) = 0.84134[/tex]
[tex]P(Z < - 1) = 0.15866[/tex]
=> [tex]P( \mu - 2 < \= x < \mu + 2) = 0.84134 - 0.15866[/tex]
=> [tex]P( \mu - 2 < \= x < \mu + 2) = 0.6826[/tex]
The mean salary of federal government employees on the General Schedule is $59,593. The average salary of 30 state employees who do similar work is $58,800 with \sigmaσσ= $1500. At the 0.01 level of significance, can it be concluded that state employees earn on average less than federal employees? What is the critical value? Round your answer to the nearest hundredths.
Answer:
Yes it can be concluded that state employees earn on average less than federal employees
The critical value is [tex]Z_{\alpha } = - 2.33[/tex]
Step-by-step explanation:
From the question we are told that
The population mean is [tex]\mu = \$ 59593[/tex]
The sample size is n = 30
The sample mean is [tex]\= x = \$ 58800[/tex]
The standard deviation is [tex]\sigma = \$ 1500[/tex]
The significance level is [tex]\alpha = 0.01[/tex]
The null hypothesis is [tex]H_o : \mu = \$ 59593[/tex]
The alternative hypothesis is [tex]H_a : \mu < \$ 59593[/tex]
The critical value of [tex]\alpha[/tex] from the normal distribution table is [tex]Z_{\alpha } = - 2.33[/tex]
Generally the test statistics is mathematically evaluated as
[tex]t = \frac{\= x - \mu}{ \frac{ \sigma }{ \sqrt{n} } }[/tex]
=> [tex]t = \frac{ 58800 - 59593 }{ \frac{ 1500 }{ \sqrt{30} } }[/tex]
=> [tex]t = -2.896[/tex]
The p-value is obtained from the z-table
[tex]p-value = P(t < -2.896) = 0.0018898[/tex]
Since [tex]p-value < \alpha[/tex] , we reject the null hypothesis, hence it can be concluded that state employees earn on average less than federal employees
A father is three times as old as his son. After fifteen years the father will be twice as old as his son's age at that time. Hence the father's present age is
Answer:
Step-by-step explanation:
let present age of father=y
present age of son=x
then y=3x
after 15 years age of father=y+15
and age of son=x+15
∴y+15=2(x+15)
y+15=2x+30
y-2x=30-15
y-2x=15
∴3x-2x=15
x=15
y=3x=15×3=45
father's present age=45 years
60feet to meters plaese with work
Answer:
60 Feet = 18.288 Meters
Step-by-step explanation:
foot = 12 inch = 0.3048 m
0.3047 × 60
18.288 meters
Which point is located at (5, –2)?
Explanation:
The origin is the center of the grid. This is where the x and y axis meet. The location of this point is (0,0).
Start at the origin and move 5 places to the right. Note how the x coordinate is 5 which tells us how to move left/right. Positive x values mean we go right.
Then we go down 2 spots to arrive at point D. We move down because the y coordinate is negative.
You could also start at (0,0) and go down 2 first, then to the right 5 to also arrive at point D. Convention usually has x going first as (x,y) has x listed first.
Answer:
Point D is located at (5, -2)
Step-by-step explanation:
The coordinates are in the form of (x,y) so that means the point has the x value of 5 and the y value of -2
The domain of the following relation has how many elements?
[(1/2, 3.14/6), (1/2, 3.14/4), (1/2, 3.14/3), (1/2,3.14/2)]
a. 0
b. 1
c. 4
Answer:
b. 1
Step-by-step explanation:
All first coordinates are 1/2.
Answer: b. 1
Annie has 3/2 pounds of cookie dough. If she needs 1/16 of a pound of cookie dough to make one cookie, how many cookies can she make
Answer:
[tex]\boxed{\sf 24\ cookies}[/tex]
Step-by-step explanation:
1 cookie = 1/16 of a pound of cookie
If we want to find how many cookies can be made by 3/2 pounds ( 1.5 pounds) then we need to divide 3/2 pounds by 1/16
=> [tex]\frac{3}{2} / \frac{1}{16}[/tex]
=> [tex]\frac{3}{2} * 16[/tex]
=> 3*8
=> 24 cookies
Answer:
24 cookies
Step-by-step explanation:
3/2= 1.5 and 1/16= 0.0625
if you divide the amount of dough you have by the amount needed for each cookie you will have 24
1.5/0.0625=24
Megan’s room is expanded so the width is 150% of 3 meters. What is the new width?
Work Shown:
The keyword "of" means "multiply".
150% = 150/100 = 1.5
150% of 3 = 1.5*3 = 4.5
The percentage is calculated by dividing the required value by the total value and multiplying by 100.
Required percentage value = a
total value = b
Percentage = a/b x 100
100% = 3 meters
150% = 4.5 meters
The new width is 4.5 meters.
What is a percentage?The percentage is calculated by dividing the required value by the total value and multiplying by 100.
Example:
Required percentage value = a
total value = b
Percentage = a/b x 100
Example:
50% = 50/100 = 1/2
25% = 25/100 = 1/4
20% = 20/100 = 1/5
10% = 10/100 = 1/10
We have,
Megan’s room is expanded so the width is 150% of 3 meters.
This means,
100% = 3 meters
Multiply 150/100 on both sides.
150% = 150/100 x 3
150% = 4.5 meters
Thus,
The new width is 4.5 meters.
Learn more about percentages here:
https://brainly.com/question/11403063
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Will mark Brainliest! A stick has a length of $5$ units. The stick is then broken at two points, chosen at random. What is the probability that all three resulting pieces are longer than $1$ unit?
Answer:
0.16
Step-by-step explanation:
Length = 5 unitsNumber of broken sticks= 3Equal lengths = 5 units/3See the picture attached for reference.
As you see the best points are the green areas which covers 2 out of 5 zones.
Since it is same for both broken points, the probability of this is:
2/5*2/5 = 4/ 25 = 0.16Answer is 0.16
An economist is interested in studying the spending habits of consumers in a particular region. The population standard deviation is known to be $1,000. A random sample of 50 individuals resulted in an average expense of $15,000. What is the width of the 99% confidence interval for the mean of expense? a. 364.28 b. 728.55 c. 329.00 d. 657.99
Answer:
The width is [tex]w = \$ 729.7[/tex]
Step-by-step explanation:
From the question we are told that
The population standard deviation is [tex]\sigma = \% 1,000[/tex]
The sample size is [tex]n = 50[/tex]
The sample mean is [tex]\= x = \$ 15,000[/tex]
Given that the confidence level is 99% then the level of significance is mathematically represented as
[tex]\alpha = 100 - 99[/tex]
=> [tex]\alpha = 1\%[/tex]
=> [tex]\alpha = 0.01[/tex]
Next we obtain the critical value of [tex]\frac{\alpha }{2}[/tex] from the normal distribution table, the value is
[tex]Z_{\frac{\alpha }{2} } = Z_{\frac{0.01 }{2} } = 2.58[/tex]
Generally margin of error is mathematically represented as
[tex]E = Z_{\frac{\alpha }{2} * \frac{\sigma }{\sqrt{n} }[/tex]
substituting values
[tex]E = 2.58 * \frac{1000 }{\sqrt{50} }[/tex]
[tex]E = 2.58 * \frac{1000 }{\sqrt{50} }[/tex]
[tex]E = 364.9[/tex]
The width of the 99% confidence interval is mathematically evaluated as
[tex]w = 2 * E[/tex]
substituting values
[tex]w = 2 * 364.9[/tex]
[tex]w = \$ 729.7[/tex]
Suppose that prices of a certain model of new homes are normally distributed with a mean of $150,000. Use the 68-95-99.7 rule to find the percentage of buyers who paid: between $150,000 and $152,400 if the standard deviation is $1200.
A. 68%
B. 99.7%
C. 47.5%
D. 34%
Answer:
C. 47.5%
Step-by-step explanation:
The summary of the given statistics include:
mean =150000
standard deviation: 1200
The objective is to use tributed with a mean of $150,000. Use the 68-95-99.7 rule to find the percentage of buyers who paid: between $150,000 and $152,400
The z score formula can be use to calculate the percentage of the buyer who paid.
[tex]z = \dfrac{X - \mu}{\sigma}[/tex]
For the sample mean x = 150000
[tex]z = \dfrac{150000 - 150000}{1200}[/tex]
[tex]z = \dfrac{0}{1200}[/tex]
z = 0
For the sample mean x = 152400
[tex]z = \dfrac{152400 - 150000}{1200}[/tex]
[tex]z = \dfrac{2400 }{1200}[/tex]
z = 2
From the standard normal distribution tables
P(150000 < X < 152400) = P(0 < z < 2 )
P(150000 < X < 152400) =P(z<2) -P(z<0)
P(150000 < X < 152400) =0.9772 -0.5
P(150000 < X < 152400) = 0.4772
P(150000 < X < 152400) = 47.7% which is close to 47.5% therefore option C is correct
This question is based on concept of statistics. Therefore, correct option is C i.e. 47.5% of buyers who paid: between $150,000 and $152,400 if the standard deviation is $1200.
Given:
Mean is $150,000, and
Standard deviation is $1200.
We need to determined the percentage of buyers who paid: between $150,000 and $152,400 as per given mean and standard deviation.
By using z score formula can be use to calculate the percentage of the buyer who paid,
[tex]\bold{z=\dfrac{x-\mu }{\sigma}}[/tex]
As given in question sample mean i.e. X= 150,000
[tex]z=\dfrac{150000-150000}{1200} \\\\z= \dfrac{0}{1200}\\\\z=0[/tex]
Now for the sample mean X = 152,400 ,
[tex]z=\dfrac{152400-150000}{1200} \\\\\\z= \dfrac{24000}{1200}\\\\\\z=2[/tex]
By using standard normal distribution table,
P(150000 < X < 152400) = P(0 < z < 2 )
P(150000 < X < 152400) =P(z<2) -P(z<0)
P(150000 < X < 152400) =0.9772 -0.5
P(150000 < X < 152400) = 0.4772
P(150000 < X < 152400) = 47.7% which is close to 47.5%
Therefore, correct option is C that is 47.5%.
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Megan has 12 pounds of cheesecake. On Monday, she and her friends eat 4 pounds. On Tuesday, she and her friends eat another 3 pounds. On Wednesday, her friend Mark gives her some more cheesecake so that she has 3 times as much as she had at the end of Tuesday. On Thursday, some of her cheesecake goes bad, so she has the amount that she had at the end of Wednesday, but divided by 5. On Friday, she gives 3 pounds to her dog. On Saturday, her mom gives her one more pound. On Sunday, how many pounds of cheesecake does Megan have left?
Answer:
Step-by-step explanation:
First we start with 12 pounds
On Monday, she and her friends eat 4 pounds. So we have 8 now.
On Tuesday, she and her friends eat another 3 pounds. So we gave 5 now.
On Wednesday, her friend Mark gives her some more cheesecake so that she has 3 times as much as she had at the end of Tuesday. 5 * 3 = 15
On Thursday, some of her cheesecake goes bad, so she has the amount that she had at the end of Wednesday, but divided by 5. She had 15 at the end of Wednesday. 15/5 = 3.
On Friday, she gives 3 pounds to her dog. 5 - 3 = 2.
On Saturday, her mom gives her one more pound. 2 + 1 = 3.
On Sunday, she finally has 3 pounds.
Answer:
nnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnn
Step-by-step explanation:
EXAMPLE 5 If F(x, y, z) = 4y2i + (8xy + 4e4z)j + 16ye4zk, find a function f such that ∇f = F. SOLUTION If there is such a function f, then
If there is such a scalar function f, then
[tex]\dfrac{\partial f}{\partial x}=4y^2[/tex]
[tex]\dfrac{\partial f}{\partial y}=8xy+4e^{4z}[/tex]
[tex]\dfrac{\partial f}{\partial z}=16ye^{4z}[/tex]
Integrate both sides of the first equation with respect to x :
[tex]f(x,y,z)=4xy^2+g(y,z)[/tex]
Differentiate both sides with respect to y :
[tex]\dfrac{\partial f}{\partial y}=8xy+4e^{4z}=8xy+\dfrac{\partial g}{\partial y}[/tex]
[tex]\implies\dfrac{\partial g}{\partial y}=4e^{4z}[/tex]
Integrate both sides with respect to y :
[tex]g(y,z)=4ye^{4z}+h(z)[/tex]
Plug this into the equation above with f , then differentiate both sides with respect to z :
[tex]f(x,y,z)=4xy^2+4ye^{4z}+h(z)[/tex]
[tex]\dfrac{\partial f}{\partial z}=16ye^{4z}=16ye^{4z}+\dfrac{\mathrm dh}{\mathrm dz}[/tex]
[tex]\implies\dfrac{\mathrm dh}{\mathrm dz}=0[/tex]
Integrate both sides with respect to z :
[tex]h(z)=C[/tex]
So we end up with
[tex]\boxed{f(x,y,z)=4xy^2+4ye^{4z}+C}[/tex]
Explain the difference between using the sine ratio to solve for a missing angle in a right triangle versus using the cosecant ratio. You must use complete sentences and any evidence needed (such as an example) to prove your point of view. (10 points)
Answer:
The sine ratio is the ratio between the opposite side over hypotenuse. The cosecant ratio is the ratio between the hypotenuse over the opposite side, therefore cosecant is the reciprocal of sine.
To find a missing angle using sine, you would need to use the inverse of sine. For example, if the sine was [tex]\frac{30}{40}[/tex], to find the angle you would need to find sin⁻¹ of [tex]\frac{30}{40}[/tex] which is x = sin⁻¹ (0.75). Therefore x equals approximately 49°.
Construct a polynomial function with the following properties: fifth degree, 4 is a zero of multiplicity 3, −4 is the only other zero, leading coefficient is 4. setup problem so I can solve, thanks!!
Answer:
Step-by-step explanation:
Hello,
degree 5
4 is a zero of multiplicity 3 -> (x-4)^3 is a factor
-4 is the only other zero, so the multiplicity is 5-3=2 -> (x+4)^2 is a factor
leading coefficient is 4 so we can write
[tex]\boxed{4(x-4)^3(x+4)^2}[/tex]
If there is something that you do not understand or you are blocked somewhere let us know what / where.
Thank you.
Find the minimum and maximum values of 3 sin^2x – 2 cos^2x + 9