Answer:
1
Step-by-step explanation:
Formulas used:
[tex]sin^2 \theta + cos^2\theta = 1 => 1-sin^2 \theta = cos^2 \theta\\\\tan^2 \theta + 1 = sec^2 \theta[/tex]
[tex]Q) \ (1 + tan^2 \theta)(1-sin^2 \theta)\\\\= \ sec^2 \theta \times cos^2 \theta\\\\=\frac{1}{cos^2 \theta} \times cos^2 \theta\\\\= 1[/tex]
Answer:
[tex](1 + \tan {}^{2} ( \alpha ) )(1 - \sin {}^{2} ( \alpha ) ) \\ = \frac{1}{ \cos {}^{2} ( \alpha ) } \times \cos {}^{2} ( \alpha ) \\ = 1[/tex]
How much in earning can PNG make in a year in cocoa export of 400 000 tonnes at K2 353 per tonne ? (2 marks)
Answer: K941,200,000
Step-by-step explanation:
From the question, we are to calculate the amount of earning that PNG can make in a year in cocoa export of 400 000 tonnes at K2 353 per tonne.
This will be:
= Number of tonnes × Amount per ton
= 400000 × k2353
= K941,200,000
Therefore, the answer is K941,200,000
X^2+9x+20 divided by x+5
Answer:
x ≠ -5
Step-by-step explanation:
The easiest way is to factor the numerator.
x2 + 9x + 20 = (x + 4)(x + 5)
Then
(x2 + 9x + 20)/(x + 5) = (x + 4)(x + 5) / (x + 5) = x + 4,
with the restriction that x ≠ -5
when is 9+10 really equal to 21
Answer:
9 + 10 = 21
Step-by-step explanation:
9 + 10 = 21
Factor out 9 and 10
9 = 3 · 3 10 = 2 · 5
Next multiply 3 by 2
3 × 2 = 6
Then multiply 3 by 5
3 · 5 = 15
Finally add the products
15 + 6 = 21
HELP PLEASE ASAP What is the product of any integer and -1?
Answer:
A
Step-by-step explanation:
The product is opposite of the integer
For example
2 * -1 = -2
7/7q+21= x /5q^2-45 then x=?
Answer:
x = 5q - 15
Step-by-step explanation:
[tex]\frac{7}{7q+21}=\frac{x}{5q^{2}-45}\\\\\frac{7}{7(q+3)}=\frac{x}{5 (q^{2} -9)}\\\\frac{1}{q+3}=\frac{x}{5*(q^{2}-3^{2})}\\\\\frac{1}{q+3}=\frac{x}{5(q+3)(q-3)}\\\\\frac{1}{q+3}*5*(q+3)(q-3)=x\\\\5(q-3)=x\\\\x= 5q-15[/tex]
The number of incoming students at two campuses of a midwestern university have historically been normally distributed. The main campus incoming class has a mean of 3,507 and a standard deviation of 375, and the regional campus incoming class has a mean of 740 and a standard deviation of 114. If there were 3,838 incoming students on the main campus and 848 on the regional campus, which had the more successful year in student recruitment based on z scores
Answer:
Due to the higher z-score, the regional campus had the more successful year in student recruitment.
Step-by-step explanation:
Z-score:
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.
The main campus incoming class has a mean of 3,507 and a standard deviation of 375. There were 3,838 incoming students on the main campus.
We have to find Z, considering [tex]X = 3838, \mu = 3507, \sigma = 375[/tex]
So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{3838 - 3508}{375}[/tex]
[tex]Z = 0.88[/tex]
Regional campus incoming class has a mean of 740 and a standard deviation of 114. 848 students on the regional campus.
We have to find Z when [tex]X = 848, \mu = 740, \sigma = 114[/tex].
So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{848 - 740}{114}[/tex]
[tex]Z = 0.95[/tex]
Which had the more successful year in student recruitment based on z scores?
Due to the higher z-score, the regional campus had the more successful year in student recruitment.
From families with four children a family is chosen at random. Let X be the number of boys in the family. Calculate and sketch the distribution function of X. Assume that in a four-child family all gender distributions (for example, BBBB, BBBB, BBBB, BBBB, etc.) are equally probable.
Solution :
Given :
X = the number of boys in a family of four children
Families having four children are chosen randomly.
The gender distribution in the four child family are equally probable.
Thus,
X P(X) CDF
0 [tex]^4C_0 (1/2)^{4}[/tex] = 1/16 [tex]\frac{1}{16}[/tex]
1 [tex]^4C_1 (1/2)^{4}[/tex] = 1/4 [tex]\frac{5}{16}[/tex]
2 [tex]^4C_2 (1/2)^{4}[/tex] = 3/8 [tex]\frac{11}{16}[/tex]
3 [tex]^4C_3 (1/2)^{4}[/tex] = 1/4 [tex]\frac{15}{16}[/tex]
4 [tex]^4C_4 (1/2)^{4}[/tex] = 1/16 1
DJ Jacqueline is making a playlist for work; she is trying to decide what 9 songs to play and in what order they should be played. If she has her choices narrowed down to 6 jazz, 19 reggae, and 7 blues songs, and she wants to play an equal number of jazz, reggae, and blues songs, how many different playlists are possible
Write an explicit formula for an, the nth term of the sequence 63,21,7
Answer:
63/3=2121/3=77/3=7 -3
Which of the following pairs consists of equivalent fractions? .4/6 and 3/5 or 9/16 and 3/32 or 18/48 and 15/40 or 7/10 and 10/7
Answer:
18/48 and 15/40
Step-by-step explanation:
The function h(x) is defined as shown.
What is the range of h(x)?
h(x) =
x + 2, x <3
- x +8. X23
0-00
Oh(x) s 5
Oh(x) 25
Oh(x) 23
PLEASE HELOOOOODOOOOODIEIE
9514 1404 393
Answer:
(b) h(x) ≤ 5
Step-by-step explanation:
The maximum vertical extent of the graph is h(x) = 5 at x = 3. The range is all values of h(x) less than or equal to that:
h(x) ≤ 5
Answer: Choice B
The range is [tex]h(x) \le 5[/tex]
==============================================================
Explanation:
If we graph y = x+2, but only draw the line for x values smaller than 3, then we'll end up with the red line shown in the diagram below.
The blue line is the graph of y = -x+8, but it's only drawn when [tex]x \ge 3[/tex]
The two lines form an upside down V shape. This is an absolute value graph.
The highest point is at the vertex (3,5). The y coordinate is y = 5. This tells us that the largest h(x) can get is h(x) = 5.
Therefore, the range is [tex]h(x) \le 5[/tex]
This is the same as saying [tex]y\le 5[/tex] since y and h(x) are both outputs of a function.
The set (AB) (B-C) is equal to
Answer:
AB^2- AC.
Step-by-step explanation:
I'm not sure if this question is complete, but when two separate variables are placed in brackets side by side, then it means they need to be expanded.
Therefore, expanding the bracket gives us:
(AB) (B-C)=
AB^2- AC.
This is the answer, if the only task needed is to expand the brackets.
The moment generating function for health care costs experienced by a policyholder is given as follows:
Mx(t)= (4/4-t)^3
An insurer reimburses the policyholder for 70% of health care costs experienced by the policyholder. Calculate the expected reimbursement by the insurer for a policyholder.
Answer:
0.525 = 52.5%
Step-by-step explanation:
Moment generating function ( Mx(t) ) = ( 4 / 4-t)^3
Reimbursement by Insurer = 70%
Determine the expected reimbursement by insurer for policyholder
d/dx (Mx(t) ) = d/dt ( 4 / 4-t)^3 = d/dt (1 - t/4 )^-3
= 3/4 ( 1 - t/4 )^-4 = 3/4
as t → 0
Given that the insurer reimburses 70% = 0.7
expected reimbursement = 0.7 * 3/4 = 0.7 * 0.75 = 0.525
Câu 1 (2 điểm). Cho hệ các vector
U = {(1,2,2); (0,-1,-1);(2,3,3);(1,0,0).
a) tìm số chiều và một cơ sở W của không gian con sinh bởi hệ vector U
b) tìm tham số k để u=(2,3,k^2 +1) là một tổ hợp tuyến tính cảu W, và suy ra [u]w
giải hộ mình với
Answer:
Step-by-step explanation:
Complete the table of inputs and outputs for the given function. g(x) = 3 - 8x g() 0 -5 3 Reset
Answer:
Step-by-step explanation:
how can two different rectangles both have a perimeter of 24 cm
Explanation:
Perimeter is simply the sum of all the edges. The same way 10 can be made of 4+6 or 3+7, the perimeter can be made by many combinations. if you know the 2 must equal 24cm, then we can create numerous combinations.
I will get my points but answer it correctly and no LINKS!!! (factotise by using a suitable identity X5-X)
x(x-1)(x+1)(x²+1)=0
Hope it helps you
You have an employee who copes with stressful demands by working overtime and weekends. You are concerned this will eventually burn him out, and want him to cope in a way that better addresses the emotions he is feeling head on. Which of the following would be an emotion-focused coping strategy?
a. Ask a coworker to help lighten the load
b. Go for a run to clear his mind
c. Increase the hours he works, but decrease the number of days (e.g., Four 12-hour days)
d. Coming up with a strategy to fix the stressful demand
Answer:
b. Go for a run to clear his mind.
Step-by-step explanation:
Emotion focused coping strategy is one in which a person goes for self isolation to release his stress. The person focuses on emotional distance from people because he believes the stress can increase if other people stays around him. When an employee suffers from stressful demand at work the best for him is to go for a run or walk and release stress.
can anyone pls answer this! it's really urgent!
Answer:
The answer is C
Step-by-step explanation:
You need to find a common denominator and in this case its 20. SO you change 3/4ths to 15/20 and 4/5ths to 16/20ths and 19/20 stays the same. Then you cancel out the 20 because its all the same number (I think) and you have your answer.
Can someone please answer this please
Answer: I don't know but i have the formula.
Step by Step: [tex]A=\frac{1}{2}b h[/tex]
5)
I
6
50°
16x + 2
B) 9
A) -10
C) 4
D) 8
Answer:
c is answer
Step-by-step explanation:
c is ans because it is simple c only serves the need of questions and satisfy it
Answer:
D) 8
Step-by-step explanation:
Liner pair meaning that the angles have a sum of 180. So you add them together to get the equation 16x+52=180 an16x=128 and then you divide both sides by 16 to get x equal to 8. Hope I helped and post more questions :)
Karl wants to fertilize his 6 acres. If it takes 7 StartFraction 2 Over 3 EndFraction bags of fertilizer for each acre, how much fertilizer does Karl need to buy?
Answer:
46
Step-by-step explanation:
Just multiply 6 by 7 2/3 to get 46.
Answer:
The answer is 46 bags
Step-by-step explanation:
Have a good summer!!!
Simplify 3/4 X 14/ 15 .
Please answer this!!! WILL GIVE BRAINLIEST
Answer:
p > 9
Step-by-step explanation:
First let's note down-
George- has 23$
Total cost of m+p= more than $14
Second, let's subtract 23 and 14 to get what the glue costs.
23 - 14 = 9
So now we can cross out choice A and D.
Third, now earlier I said more than $14, this is the key part to find what we are going to choose.
more than = >
now we just plug in the variable,
p > 9
Hope this helps!
Please reach out to me if you still don't understand :)
9,16,25,36 arithmetic or geometric?
24,18,12,arithmetic or geometric?
500,100,20 ,4 arithmetic or geometric?
Answer:
9,16,25,36 neither, 24,18,12 arithmetic, 500,100,20 ,4 geometric
Step-by-step explanation:
1. has no common number
2. goes down by 6 each time
3. is divided by 5 each time
Whoever helps gets Brainliest!!! PLEASE HELP!!!
The length of the longer leg of a right triangle is 6 inches more than twice the length of the shorter leg. The length of the hypotenuse is 9 inches more than twice the length of the shorter leg. Find the side lengths of the triangle.
9514 1404 393
Answer:
15 in, 36 in, 39 in
Step-by-step explanation:
The Pythagorean theorem tells us that for short side x, the relation is ...
(2x +9)² = (2x +6)² +x²
4x² +36x +81 = 4x² +24x +36 +x²
x² -12x -45 = 0 . . . . . subtract the left-side expression
(x -15)(x +3) = 0 . . . . factor
x = 15 . . . . . . . . . . . the positive value of x that makes a factor zero
The side lengths of the triangle are 15 inches, 36 inches, and 39 inches.
100 POINTSSS! ASAP ANSWEERR PLS
The price of products may increase due to inflation and decrease due to depreciation. Marco is studying the change in the price of two products, A and B, over time.
The price f(x), in dollars, of product A after x years is represented by the function below:
f(x) = 0.69(1.03)x
Part A: Is the price of product A increasing or decreasing and by what percentage per year? Justify your answer.
Part B: The table below shows the price f(t), in dollars, of product B after t years:
t (number of years) 1 2 3 4
f(t) (price in dollars) 10,100 10,201 10,303.01 10,406.04
Which product recorded a greater percentage change in price over the previous year? Justify your answer.
PART A
Given:
f(x) = 0.69(1.03)x
To find:
If the price of the product is increasing or decreasing and by what percentage
Steps:
we know the formula to find the price of Product A per year, so
f(1) = 0.69 * 1.03 * 1
Price = $0.7107
f(2) = 0.69 * 1.03 * 2
Price = $1.4214
Here the Price of Product after 2 years is greater than the price of Product after one year. So the price of the product A is increasing.
Now to find percentage increase,
Percentage increase = [tex]\frac{FV-SV}{SV}*100[/tex] (FV = final value, SV = starting value)
Percentage increase = [tex]\frac{1.4214 - 0.7107}{0.7107}*100[/tex]
Percentage increase = [tex]\frac{0.7107}{0.7107}*100[/tex]
Percentage increase = 100 %
Therefore, the percentage increase of Product A is 100%
PART B
Given:
Price of product B in 1st year = $10,100
Price of product B in 2nd year = $10,201
Price of product B in 3rd year = $10,303.01
Price of product B in 4th year = $10,406.04
To find:
Which product recorded a greater percentage change over the previous year
Steps:
We need to find the percentage change of Product B and Product A of each year. We know that the percentage change of product A is 100 % for each year, so we only need to calculate for product B
PC of product B from 1st to 2nd year = [tex]\frac{10,201-10,100}{10,100}*100[/tex]
= [tex]\frac{101}{10,100}*100[/tex]
= 0.01 * 100
= 1 %
PC of product B from 2nd to 3rd year = [tex]\frac{10,303.01-10,201}{10,201} *100[/tex]
= 1%
PC of product B from 3rd to 4th year [tex]=\frac{10,406.04-10,303.01}{10,303.01}*100[/tex]
≈ 1%
So, percentage change of product B is 1% per year
Therefore, Product A has greater percentage change
Happy to help :)
If u need more help, feel free to ask
Answer:
A) The price of product A is increasing by 3% per year.
(B) The product A recorded a greater percentage change in price over the previous year.
Step-by-step explanation:
(A)
The function representing the price, in dollars, of product A after x years is:
FA(x)=0.69*(1.03)x
The function FA(x)can be written as:
FA(x)=0.69*1+(0.03)x
The function FA(x) is similar to the exponential growth function, y=a(1+r)x .
Here r is the growth rate.
Thus, it can be said that the price of product A is increasing by 3% per year.
(B)
Consider the data of product B for the year 3 and 4.
The price of product B for year 3 and 4 are 10,303.01 and 10,406.04.
Compute the percent price change from year 3 to 4 as follows:
10406.04-10303.01/10303.01*100
which is 0.999%
~1%
The price of product B is increasing by 1% per year.
Thus, the product A recorded a greater percentage change in price over the previous year.
99 students at a college were asked whether they had completed their required English 101 course, and 71 students said "yes". Find the best point estimate for the proportion of students at the college who have completed their required English 101 course. Round to four decimal places.
Answer: 0.070
Step-by-step explanation:
The question is asking you to estimate how many students completed the English 101 course.
1. Round 99 and 71 to 100 and 70
2. I am not completely sure but I believe the answer is 0.070?
3. Hope it helps! :)
The diameter of the circle below is 82cm. Work out the radius of the circle
Answer:
Radius = 41
Step-by-step explanation:
Diameter/2=radius
82/2 =41
Answer:
Radius=41
Step-by-step explanation:
Preamble
Diameter=82
Radius=?
Formula
Radius=diameter/2
Radius=82/2
reduce the fraction
82/2=82÷2/2÷2=41/1
therefore radius=41