The minimum value of both sine and cosine is -1. However the angles that produce the minimum values are different, [tex]-\pi/2, \pi[/tex] for sine and cosine respectively.
The question is, can we find an angle for which the sum of sine and cosine of such angle is less than the sum of values at any other angle.
Here is a procedure, first take a derivative
[tex]\frac{d}{dx}(\sin x+\cos x)=\cos x -\sin x[/tex]
Then compute critical points of a derivative
[tex]\cos x-\sin x=0\implies x_1=\frac{\pi}{4},x_2=\frac{5\pi}{4}[/tex].
Then evaluate [tex]\sin x +\cos x[/tex] at [tex]x_1,x_2[/tex].
You will obtain global maxima and global minima [tex]\sqrt{2}, -\sqrt{2}[/tex] respectively.
The answer is [tex]-\sqrt{2}[/tex].
Hope this helps.
here are the approximate population of three countries, expressed in scientific notation: panama: 4 x 10^6 ; peru: 3.2 x 10^7 ; thailand: 7 x 10^7. Lin says that more than 20 times as many people live in thailand than in panama. Is this correct
Answer:
No, Lin assumption is wrong
Step-by-step explanation:
Given
Population of panama = 4 x 10^6
population of thailand = 7 x 10^7.
Taking their ratios
thailand/panama = 7x 10^7/4 x 10^6
thailand/panama = 7/4 * 10^7-6}
thailand/panama = 1.75 * 10^1
thailand/panama = 17.5
thailand = 17.5 * panama
Hence the amount of people in thailand is not up to 20times those in panama. Hence Lin assumption is wrong
Using proportions, it is found that the ratio is of 17.5, hence Lin is not correct.
What is a proportion?A proportion is a fraction of a total amount.
In this problem:
Thailand's population is of 7 x 10^7.Panama's population is of 4 x 10^6.The ratio between the populations is given by:
r = 7 x 10^7/(4 x 10^6) = 1.75 x 10^1 = 17.5.
The ratio is of 17.5, hence Lin is not correct.
More can be learned about proportions at https://brainly.com/question/24372153
altitudes of right triangle
Suppose a family has three children. Find the probability they have at
most one boy. (Enter as a decimal)?
Answer:
33.333333percent or .333333
Step-by-step explanation:
Suppose the mean income of firms in the industry for a year is 90 million dollars with a standard deviation of 15 million dollars. If incomes for the industry are distributed normally, what is the probability that a randomly selected firm will earn less than 109 million dollars? Round your answer to four decimal places.
Answer:
0.8980 = 89.80% probability that a randomly selected firm will earn less than 109 million dollars
Step-by-step explanation:
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Distributed normally, mean of 90 million, standard deviation of 15 million.
This means that [tex]\mu = 90, \sigma = 15[/tex]
What is the probability that a randomly selected firm will earn less than 109 million dollars?
This is the pvalue of Z when X = 109. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{109 - 90}{15}[/tex]
[tex]Z = 1.27[/tex]
[tex]Z = 1.27[/tex] has a pvalue of 0.8980
0.8980 = 89.80% probability that a randomly selected firm will earn less than 109 million dollars
4 + 62 + 9 ∙ 3 - 10 asap for brainliest
[tex]215.[/tex]
Step-by-step explanation:
[tex]4 + 62 = 66.[/tex]
[tex]66 + 9 = 75.[/tex]
[tex]75 \times 3 =225.[/tex]
[tex]225 - 10 = 215.[/tex]
Which function is the inverse of f(x) = -5x - 4
Answer:
f-¹(x) = -⅕x - ⅘
Step-by-step explanation:
f(x) = -5x - 4 → x = -5y - 4 → 5y = - x - 4 → y = -⅕x - ⅘ → f-¹(x) = -⅕x - ⅘
Interior exterior angles triangles
Answer:
The interior angles of a triangle are inside the triangle and add up to 180 degrees. The exterior angles are angles between any side of the triangle, and the line extended from the side. The sum of an exterior angle and its adjacent interior angle is also 180 degrees.
James m
Lou 2 m
Rob 3 m
Teri 4 m
Shawn 4 m
Skip 3 m
Art 2 m
Jim m
Eight students in a small class made the test scores shown in the table. What was the mean absolute deviation for the class?
A) m
B) 2.5m
C) 4m
D) 8m
Answer:
A) = m
Step-by-step explanation:
Enter the number that makes the equation true
0.02 + 5/100= ______ / 100 + 5/100
Answer:
2
Step-by-step explanation:
0.02 = 2/100 so the answer is 2
These are numbers that cannot be written as fractions, numbers with decimals that do not end or repeat. Example: π, 2.345643.....,
Answer:
These types of numbers are commonly referred to as "irrational numbers".
Step-by-step explanation:
Please help ! I'll give brainliest as well.
Answer:
390 Millions of bacteria particles by the end of one week.
Step-by-step explanation:
The Bacteria Growth Rate Formula is: ---> N (T) = N (0) * (1 + R) ^tT
N (0) = # of bacteria present during the beginning of the experiment
Variable R= Growth rate
Variable T= Time taken / elapsed.
Substitute the #'s for N (T)
N (0) and T from the given description
We then get the value of variable R.
220 = 20 * (1+R) ^ (24 hrs)
When solving for R, we get R = 0.105074
1 week= (7 x 24 = 168) hrs
We need to plug in the solutions
Therefore
N (168 hours) = 20 * (1+0.105074) ^168
Which is around 390 millions.
So now we know that there will be 390 millions of bacteria particles at the end of 1 week
Nathan inherited $100,000 from a wealthy uncle and invested the money in an account that earns 4% interest compounded annually.
How much interest will this money earn if Nathan leaves it in the account for 10 years?
A: 49
B: 33
C: 57
D: 16
Answer:
d
Step-by-step explanation:
i believe its 49 - 33= answer bc 49=49
Answer:
16°
Step-by-step explanation:
The two angles are vertical, meaning that they are the same
33 + 16 = 49
Simplify the following fraction: 12/16
[tex]\huge\text{Hey there!}[/tex]
[tex]\large\text{SIMPLIFY THE following FRACTION: } \mathsf{\dfrac{12}{16}}[/tex]
[tex]\large\text{FINDING the numerator GCF (Greatest Common Factor)}[/tex]
[tex]\large\text{12: 1,2,3,4,6,12}[/tex]
[tex]\large\text{16: 1, 2, 4, 8, 16}[/tex]
[tex]\large\text{GCF (Greatest Common Factor): 4}[/tex]
[tex]\large\text{So, we will DIVIDE the numerator and the denominator from 4.}\\\bullet\large\text{Numerator}\rightarrow\large\text{\bf TOP NUMBER}\\\bullet\large\text{Denominator}\rightarrow\large\text{\bf BOTTOM NUMBER}[/tex]
[tex]\mathsf{\dfrac{12\div4}{16\div4}}[/tex]
[tex]\mathsf{12 \div 4 = \bf 3}\leftarrow\large\text{NUMERATOR}[/tex]
[tex]\mathsf{16\div 4 = \bf 4}\leftarrow\large\text{DENOMINATOR}[/tex]
[tex]\boxed{\boxed{\large\text{Answer: }\mathsf{\bf \dfrac{3}{4}}}}\huge\checkmark[/tex]
[tex]\text{Good luck on your assignment and enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
PLEASE DO AS MUCH AS YOU CAN! THANKS!
Answer:
1. 2x+20
2. 8x-40
3. 7x+21
4. 8x-4
5. 15x+5
6. 12x+15
7. 20x-50
8. 21x+14
9. 24x-6
10. 45x-18
11. 18x-8
12. 30x+9
Explanation: Distributive Property
6. 10-2 is how many times as large as 2 . 10-8?
Answer:
105 I think i might have did it wrong
Step-by-step explanation:
3.25 ÷ 10. 2) 685.34 ÷ 102. 3) 87 * 105.
Can you help me please I’m desperate.
Answer:
The answer would be A, and she can make 15 bows.
Step-by-step explanation:
Answer:
A, C and she can make 15 bows.
Complete the following statement. Round your answer to the nearest cent.
5% of $585.26 = $
Jay has 6,200 beads. He is making bracelets with 9 beads each. How many bracelets can he make? How many beads will be left?
Answer: He can make 688 beads, and 8 beads will be left.
Step-by-step explanation:
First, you need to divide 6,200 by 9.
6,200 ÷ 9 = 688 R8.
688 will be the number of bracelets he can make, and the remainder, 8, will be the leftover beads because he doesn't have enough to make another bracelet.
For the labels, it says, "How many bracelets can he make?" and," How many beads will be left?"
The answers will be: 688 bracelets;8beads
Equation : 6,200÷9=x 6,200÷9=688 R8 x=688 bracelets;8 beads
With one method of a procedure called acceptance sampling, a sample of items is randomly selected without replacement and the entire batch is accepted if every item in the sample is okay. The ABC Electronics Company has just manufactured 2100 write-rewrite CDs, and 60 are defective. If 3 of these CDs are randomly selected for testing, what is the probability that the entire batch will be accepted
Answer:
0.9167 = 91.67% probability that the entire batch will be accepted
Step-by-step explanation:
The CDs are chosen without replacement, which means that the hypergeometric distribution is used.
Hypergeometric distribution:
The probability of x sucesses is given by the following formula:
[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}[/tex]
In which:
x is the number of sucesses.
N is the size of the population.
n is the size of the sample.
k is the total number of desired outcomes.
Combinations formula:
[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
2100 write-rewrite CDs, and 60 are defective.
This means, respectively, that [tex]N = 2100, k = 60[/tex]
3 of these CDs are randomly selected for testing
This means that [tex]n = 3[/tex]
What is the probability that the entire batch will be accepted?
Probability of none defective, so P(X = 0).
[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}[/tex]
[tex]P(X = 0) = h(0,2100,3,60) = \frac{C_{60,0}*C_{2040,3}}{C_{2100,3}} = 0.9167[/tex]
0.9167 = 91.67% probability that the entire batch will be accepted
Evaluate the expression: 2 ⋅ 6^2 *
Answer:
72
Step-by-step explanation:
First square 6.
6^2=36
Then multiply 26 by 2.
2*36=72
10 is 20% of which number
Answer:
50
Step-by-step explanation:
100/20 = 5
5 x 10 = 50
taka is playing a game of darts. she scores 52 points. in the game she is playing, she gets a -3 score each time she misses the board. her final point total is 37. write and solve an equation to find out how many times she missed the board
Answer:
5
Step-by-step explanation:
52-37 is 15 . divide by 3 and u get five
A cookie jar contains 3 vanilla, 2 chocolate chip, and 7 gingersnap cookies. If one cookie is taken at random from the jar, what is the probability that it will be a vanilla cookie?
Answer:
3/12= 1/4
Step-by-step explanation: because you would add the all up for 12 and you have a 3 vanilla's so 3/12= 1/4
Oldwick High School has a population of 2345
students. A survey showed that 34% of the student
population would like to have hamburgers as a
daily choice for lunch. Which of the following is
closest to 34% of the student population?
A.340 students
B.800 students
C.1,200 students
D.1600 students
Answer:
B
Step-by-step explanation:
To find your answer, simply multiply 2345 by 0.34. As 34% in decimal form is 0.34 and to find the percentage of a number, you must multiply the number with the percentage. When you do so, you get 797.3 exactly which is closest to 800 students, resulting in B being the answer. PS. Hamburgers every day would be disgusting and boring!!!!
Which of the following is the correct Pythagorean Formula?
a? – 62 + c = 0
a² + 6² = ²
6² + c = a²
a + b = c
hi, i need help with this lol, i'm bad at math
Answer:
-44
Step-by-step explanation:
Since a is -2 and y equals 7 we can plug them both into the expression to get -2 - 6(7) which after simple math results in the answer of -44.
WILL MARK BRAINLIEST WILL REPORT IF U GIVE ME A LINK TO UKNOWN THING
Answer:
I think the answer will be x⩽4
Noah is going to invest in an account paying an interest rate of 3.7% compounded annually. How much would Noah need to invest, to the nearest hundred dollars, for the value of the account to reach $1,110 in 13 years?
Answer:700
Step-by-step explanation:
A rectangular pool is drained of water until it is only half full.
If the length of the pool is 5.5m,
the breadth is 12m and the height is 18m, find the volume of water drained in liters.
Answer:
[tex]Volume = 594m^3[/tex]
Step-by-step explanation:
Given
[tex]Length = 5.5m[/tex]
[tex]Breadth = 12m[/tex]
[tex]Height =18m[/tex]
Required
The volume when it is half full
The height, when half full is:
[tex]h = 0.5 *Height[/tex]
[tex]h = 0.5 *18m[/tex]
[tex]h = 9m[/tex]
So:
The volume is:
[tex]Volume = Length * Breadth*h[/tex]
[tex]Volume = 5.5m * 12m * 9m[/tex]
[tex]Volume = 594m^3[/tex]