Calculus: Help ASAP
Evaluate the integral of the quotient of the secant squared of x and the square root of the quantity 1 plus tangent x, dx.
Answer:
[tex]2\sqrt{1+tan(x)} +C[/tex]
Step-by-step explanation:
To start solving this you need to use substitution. I let u = 1+tan(x). Next you need to find du/dx, which is sec^2(x) using trigonometric properties. Solve for dx and get dx = du / sec^2(x). Next put the new dx back in. This gives you integral sec^2(x) / sqrt u * du / sec^2(x). The sec^2(x) cancels and the new expression is integral 1/sqrt u * du, which can be simplified to integral u^-1/2 * du. You then take the integral and get 2u^1/2. Lastly, substitute the original u back in and get 2 sqrt 1+tan(x) + C.
Does this figure have rotational symmetry?
A) No, pentagons cannot be rotated.
B) No, it has five lines of symmetry.
C) Yes, it has five lines of symmetry.
D) No, it only looks the same if it is rotated 360°.
Is the probability of contamination more than twice the mean of 14.4 unusual, or can it be considered typical variation? explain?
To determine if a probability of contamination more than twice the mean of 14.4 is unusual, the standard deviation must be considered. In a normal distribution, occurrences more than two standard deviations from the mean are typically unusual.
Whether a probability of contamination more than twice the mean of 14.4 is unusual or not depends on the standard deviation of the data. In a typical normal distribution, values more than two standard deviations away from the mean could be considered unusual. Considering a mean of 14.4, if the standard deviation is small, then a value twice as large would likely be an outlier. However, if the standard deviation is large, such a value could fall within the realm of normal variation.
To ascertain if a value is unusual, one would compare it to the range defined by a certain number of standard deviations from the mean. A common rule of thumb is the empirical rule, which states that for a normally distributed dataset, roughly 68% of data falls within one standard deviation of the mean, 95% within two standard deviations, and 99.7% within three standard deviations.
In this context, if a probability of contamination is more than twice the mean (greater than 28.8), and assuming a normal distribution, it would be considered unusual if it falls outside of two standard deviations from the mean.
All real numbers that are less than -3 or greater than it equal to 5
A function is given. Determine the average rate of change of the function between the given values of the variable.
h(t) = t2^2+ 2t; t = −1, t = 4
ALGEBRAAA
1. What is the average rate of change? How do you find it?
2. Whats the difference between recursive and explicit formulas?
1. The average rate of change is the slope of a line to find it divide the vertical change by the horizontal change
2. recursive is a formula to calculate the next term, depending on what the previous term was
Explicit is a formula to calculate any term depending on the term number
A certain mutual fund has net assets of $1,359,600. One share of this fund has a net asset value of $11.33. How many shares make up the fund?
Answer:
B
Step-by-step explanation:
Ari writes 2 + 4 on the left-hand side of his paper. Then he writes 6 to the right of the expression. Which symbol should Ari write between the two sets of numbers?
A.
+
B.
?
C.
=
Plz help will rate 19 pts
The correct symbol that Ari should write between the two sets of numbers is C. =.
When Ari writes "2 + 4" on the left-hand side of his paper and then writes "6" to the right of the expression, he is indicating that the sum of 2 and 4 is 6. The symbol "=" is used to denote equality, meaning that the value on the left side of the equation is the same as the value on the right side. In this case, the sum of 2 and 4 indeed equals 6, so the complete equation should be written as:
[tex]\[ 2 + 4 = 6 \][/tex]
This shows that the operation of adding 2 and 4 results in the number 6, which is a true statement. Therefore, the correct answer to the question is option C, the equals sign "=".
Erica sells magazine subscriptions and makes a flat rate of $5.35 for each subscription see cells if Erica man $42.80 on Monday $64.20 on Tuesday and $74.90 on Wednesday how many subscriptions did she sell in three days
C—34. Subscriptions
Hey Yo I needs some Help
Answer:
wow
Step-by-step explanation:
More than half of which climate type averages between 40 and 59 inches of precipitation a year?
Jill bought items costing $3.45 , $ 1.99, $6.59 , and $ 12.98 . she used a coupon worth $2. 50. if jill had $ 50.00 when she went into the store , how much did she have when she left
evaluate the expression if a=3 and b=5
4(a+2b)
What is the length of each side of a cube if its surface area is 486 in2?
Graph y-5 = -2/3 (x+9)
a family went on a vacation and used 5.4 gallons of gasoline to travel 150 miles. how many total gallons of gasoline will they need to travel 200 more miles?
Simplify the expression, if possible. (if the expression cannot be simplified, enter the given expression.) (k − 5)13 (k − 5)
5(1+4m)=2(3+10m)
Please help. Show work please
4x-8y=24 find the x-intercept and y- intercept on the graph
Can someone please help?
thanks :)
solving with systems of equations using elimination! please help me. thank u!
30 POINTS!!
Find the measure of angle B in isosceles triangle ABC.
3 angles inside a triangle = 180 degrees
since the 2 sides are equal
angle B and C are the same
180 - 50 = 130 degrees
130 / 2 =65
Angle B is 65 degrees
in a experiment investigating the growth of spores in varying soil conditions a certain spore colony grew an average of 3 times larger during each 24 hours period.if the colony contained 50 spores at the beginning of the experiment how many spores were there at the end of the 4th day?
Given that the certain type of spore colony having 50 spores and a rate of growth of 3 times in 24 hour or one day period, it would grow to (3 times 50) 150 spores at the end of the first day, (3 times 150) 450 in the 2nd day, (3 times 450) 1350 in the third day, and (3 times 1350) 4050 spores at the end of the fourth day.
The spore colony, which triples in size each day, will contain 4050 spores at the end of the 4th day starting from an initial count of 50 spores.
This question involves exponential growth, where the size of the spore colony triples every day.
To solve this, we will calculate the number of spores at the end of each day:
Initial spores= 50
End of Day 1,
50 * 3 = 150
End of Day 2,
150 * 3 = 450
End of Day 3,
450 * 3 = 1350
End of Day 4,
1350 * 3 = 4050
Therefore, at the end of the 4th day, the spore colony would contain 4050 spores.
Three consecutive integers have a sum of 114. what are the three integers
Our three consecutive integers are 37, 38, and 39.
Work is provided in the image attached.
One 10-ounce soft drink contains about 8 teaspoons of sugar. How much sugar would be in three 10-ounce drinks ?
In a class of 20 students ,40% are boys.25% of theboys and 50% of the girls were glasses.how many students were glassses. show work
the angles formed by two perpendicular lines have a measure of _______.
A.45°
B.90°
C.135°
D.180°
thank in advance!! ☺
In a country where prices are rising quickly, bread that now costs $1.39 will cost 2.4 times as much next year. How much will the bread cost next year
multiply the current price by the increase
1.39 * 2.4 = $3.34 ( price next year)
Mrs. Reid is going on a trip. She has 9 books that she hasn't read yet, but she wants to bring only 3 on the trip. In how many ways can she choose 3 books to bring on the trip?
♦27
♦84
♦504
♦60,480
Answer:
Option B is right.
Step-by-step explanation:
Given that there are totally 9 books unread by Mrs. Reid. OUt of these she wants to take only 3 books on the trip.
For books order does not count.
Hence combinations would be appropriate to calculate.
3 books out of 9 can be selected in
9C 3 ways
No of ways of selecting 3 books for the trip out of 9 = [tex]\frac{9(8)(7)}{1(2)(3)} =84[/tex]
There are just 84 ways of choosing 3 books to bring on the trip out of 9 unread books.
Option B is right.
The correct answer is 84.
To solve this problem, we can use the concept of combinations from combinatorics. A combination is a way of selecting items from a collection, such that the order of selection does not matter. In this case, Mrs. Reid wants to select 3 books out of 9 without regard to the order in which they are chosen.
The number of ways to choose 3 books from 9 is given by the combination formula:
[tex]\[ C(n, k) = \frac{n!}{k!(n-k)!} \][/tex]
where[tex]\( n \)[/tex] is the total number of items to choose from, [tex]\( k \)[/tex]is the number of items to choose, and [tex]\( ! \)[/tex] denotes factorial, which is the product of all positive integers up to that number.
For Mrs. Reid's situation:
[tex]\[ n = 9 \] \[ k = 3 \][/tex]
So we plug these values into the formula:
[tex]\[ C(9, 3) = \frac{9!}{3!(9-3)!} \][/tex]
Calculating the factorials:
[tex]\[ 9! = 9 \times 8 \times 7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1 \] \[ 3! = 3 \times 2 \times 1 \] \[ (9-3)! = 6! = 6 \times 5 \times 4 \times 3 \times 2 \times 1 \][/tex]
Now we simplify the expression by canceling out the common terms in the numerator and the denominator:
[tex]\[ C(9, 3) = \frac{9 \times 8 \times 7 \times 6!}{3! \times 6!} \] \[ C(9, 3) = \frac{9 \times 8 \times 7}{3 \times 2 \times 1} \][/tex]
Divide out the common factors:
[tex]\[ C(9, 3) = \frac{9}{3} \times \frac{8}{2} \times \frac{7}{1} \] \[ C(9, 3) = 3 \times 4 \times 7 \][/tex]
Now we multiply the remaining numbers [tex]\[ C(9, 3) = 3 \times 4 \times 7 = 84 \][/tex]
Therefore, Mrs. Reid can choose 3 books to bring on the trip in 84 different ways.
What is the reciprocal of each mixed number? Drag and drop the answer into the box to match each number.
10 1/3
2 2/3
5 1/3.
Answer:
10 1/3 = 3 /31. 2 2/3 = 3/8. 5 1/3 = 3/16.
Step-by-step explanation:
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