Answers
Answer:
C
Step-by-step explanation:
Equation 1:
[tex]1+\frac{\cos^{2} \theta}{\cot^{2} \theta(1-\sin^{2} \theta)}\\ \\ 1+\frac{\sin^{2} \theta}{\cos^{2} \theta} \\ \\ 1+\tan^{2} \theta \\ \\ \sec^{2} \theta[/tex]
Equation 2:
[tex]15\cos \theta \left(\frac{1}{\cos \theta}-\frac{\cot \theta}{\csc \theta} \right) \\ \\ 15\cos \theta \left(\frac{1}{\cos \theta}-\frac{\cos \theta / \sin \theta}{1/\sin \theta} \right) \\ \\ 15\cos \theta \left(\frac{1}{\cos \theta}-\cos \theta \right) \\ \\ 15\cos \theta \left(\frac{1-\cos^{2} \theta}{\cos \theta} \right) \\ \\ 15(1-\cos^{2} \theta) \\ \\ 15\sin^{2} \theta[/tex]
Related Questions
For f(x) = 2x + 1 and g(x) = x² - 7, find (f+ g)(x).
Answers
Answer:
(f + g)(x) = x² + 2x - 6
Step-by-step explanation:
(f + g)(x)
= f(x) + g(x)
= 2x + 1 + x² - 7 ← collect like terms
= x² + 2x - 6 ← in standard form
The point (5,-9) is the image under the translation (x, y) → (x+3, y + 2). What is the
preimage?
1
Answers
Answer:
(2, -11)
Step-by-step explanation:
(x + 3, y + 2) = (5, -9)
x + 3 = 5
y + 2 = -9
x = 2
y = -11
A metallurgist has one alloy containing 30% copper and another containing 62% copper. How many pounds of each alloy must be used to make 50 pounds of a third alloy containing 32% copper?
Answers
The metallurgist would need 46.875 lb of an alloy containing 30 % copper and 3.125 lb of an alloy containing 62 % copper to produce 50 lb of a third alloy.
How to estimate proportions of ingredients for an alloy by weighted averages
In this question we must prepare a third alloy by using correct quantity of two alloys with different copper concentrations. Required weights can be determined by applying concept of weighted average:
(32/100) · (50 lb) = (30/100) · x + (62/100) · (50 - x)
32 · 50 = 30 · x + 62 · (50 - x)
32 · 50 = 30 · x + 62 · 50 - 62 · x
32 · x = 30 · 50
x = 46.875
The metallurgist would need 46.875 lb of an alloy containing 30 % copper and 3.125 lb of an alloy containing 62 % copper to produce 50 lb of a third alloy.
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Which point is a solution to the system?
Answers
Answer:
C. (2;9)
Step-by-step explanation:
for more details see the attachment.
How many interior angles does a 2D shape right arrow have and explain the answer?
Answers
The number of interior angles in a 2D shape right arrow is 8 because , the number of sides is also 8
How to determine the interior anglesIt is important that a 2D shape arrow is a shape with 8 sides
Sum of angles of a polygon = (n - 2) × 180
⇒ ( 8 - 2) × 180
⇒ 6 × 180
⇒ 1080
The number of interior angles are 8 and this is so because of the number of sides in the 2D shape right arrow
Thus, the number of interior angles in a 2D shape right arrow is 8 because , the number of sides is also 8
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Hellp please i need this super fast please
Answers
The surface area of the cone is 282.6 square centimeters.
How to get the surface area?
For a cone of radius R and height H, the surface area is given by:
[tex]A = pi*R^2 + pi*R*\sqrt{R^2 + H^2}[/tex]
Where pi = 3.14
In this case, we have:
R = 10cm/2 = 5cmH = 12 cm[tex]A = 3.14*(5cm)^2 + 3.14*5cm*\sqrt{(5cm)^2 + (12cm)^2} = 282.6 cm^2[/tex]
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A city mayor in Michigan is planning the number of new snow plows he must purchase to remove the snow next winter. The
average snowfall in the past 10 years has been normally distributed with a mean of 112 inches and a standard deviation of
14 inches. What amount, in inches, separates the lowest 20% of the means of yearly snowfall in the past 10 years from the
highest 80%?
Answers
The amount that separates the lowest 20% of the means of yearly snowfall in the past 10 years from the highest 80% is 23.57 inches.
Given mean of 112 inches, standard deviation of 14 inches.
We are required to find the amount that separates the lowest 20% ofthe means of yearly snowfall in the past 10 years from the highest 80%.
a) Bottom 20% would have a z score of -0.8416.
b) Top 80% would have a z score of 0.842.
Use the z formula to find the raw score.
z=(X-m)/sd
X=the raw score
m= mean
sd=standard deviation
Putting the value of low score.
-0.8416=(X-112)/14
X=-11.7824+112
=100.2176
Putting the values of high score.
0.842=(X-112)/14
X=123.788
The amount that seprates the lowest from highest is 123.788-100.2176
=23.57 inches.
Hence the amount that separates the lowest 20% of the means of yearly snowfall in the past 10 years from the highest 80% is 23.57 inches.
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For f(x) = 3x+1 and g(x) = x2 - 6, find (F/g)
Answers
Answer: [tex]\frac{3x+1}{x^{2}-6}[/tex]
Step-by-step explanation:
(f/g) represents the division of function f by function g.
Find the measure of a when b=74 and c=165
Answers
Answer:
121°
Step-by-step explanation:
Angles around a point add to 360°.
[tex]a=360-74-165=\boxed{121^{\circ}}[/tex]
Which of the following will form the composite function G(F(x)) shown
below?
G(F(x)) = x² + 4
OA. F(x) = x + 4 and G(x) = x²
OB. F(x)= x and G(x) = x²
O C. F(x)=x² and G(x) = 4
OD. F(x) = x² and G(x) = x + 4
Answers
The composite function G(F(x)) = x² + 4 is formed with these following original functions:
D. F(x) = x² and G(x) = x + 4.
How to find the composite function of f(x) and g(x)?The composite function of f(x) and g(x) is given as follows:
[tex](f \circ g)(x) = f(g(x))[/tex]
For g of f(x), we have that:
[tex](g \circ f)(x) = g(f(x))[/tex]
For this problem, we have that:
G(F(x)) = x² + 4.
Which is possible with option D, as:
[tex]G(F(x)) = G(x^2) = x^2 + 4[/tex]
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16) Write the scientific notation.
5.5 billion
Answers
So basically it’s like your just adding the zeros at the end except this preference as opposed to seeing all those zeros so scientists chose this method .
anybody answer me please with step by step explanation need complete detailed answer
Answers
Answer:
A = 55
Step-by-step explanation:
take the two identical triangles and join them so that you get a rectangle wih sides 5 and 11. now multiply them togeter to get the are of the polynom
The area of triangle is 55 square centimeters.
What is area?Area is the amount of space occupied by a two-dimensional figure.
What is the formula for the area of triangle?The formula for the area of triangle is
[tex]Area = \frac{1}{2} \times base\times height[/tex]
According to the given question.
We have a figure of a quadrilateral which is made up of four right angled tringles.
Now,
The area of a triangle with base 5cm and height 7 cm
= [tex]\frac{1}{2} \times 5\times 7[/tex]
[tex]=\frac{35}{2}[/tex]
[tex]= 17.5[/tex] square centimeters
And, the area of triangle with base 4cm and height 5cm
= [tex]\frac{1}{2} \times 4\times 5[/tex]
[tex]= 10[/tex] square centimeters
Since, the quadrilateral is made up of 2 right angled triangle with base 5cm and height 7cm and 2 right angled triangle with base 4cm and height 5cm.
Therefore, the area of quadrilateral or the given fiure
= 2( area of triangle with height 7cm and base 5cm + area of triangle with base 4cm and height 5cm )
= 2(17.5 + 10) square centimeter
= 2 × 27.5
= 55 square centimeters
Hence, the area of triangle is 55 square centimeters.
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solve this equation -1/2 ( -3y + 10)
Answers
Answer:
3/2y-5
Step-by-step explanation:
Find the area of the region enclosed by the curves yequals
xsquaredminus2x
and yequals
minusxsquaredplus2
x.
Answers
The area enclosed by the given 2 curves is; 8/3 or 2.67
How to Solve Integration with Limits?We want to find the area enclosed by the curves;
y = x² - 2x
y = -x² + 2x
The point of intersection of the parabola and the line is given by;
x² - 2x = -x² + 2x
2x² - 4x = 0
Solving this gives;
x = 0, 2
Therefore, the area bounded by the parabola and the line between x = 0 and x = 2 is given as;
A = ∫₀² (-x² + 2x - x² + 2x)
A = ∫₀² (-2x² + 4x)
Using online integration calculator here gives;
A = 2.67
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Which of the following functions has a vertical asymptote at x=−1, a horizontal asymptote at f(x)=5, and a root at x=−3?
Answers
Answer:
Step-by-step explanation:
B :10/(x+1) +5
Nikos, a 39-year old male, bought a 300,000, 20-year life insurance policy.
What is the total amount he will pay for 20 years of coverage.
13,650
27,300
30,990
61,980
Answers
The total amount he will pay for 20 years of coverage is $61,980. Option D
How to determine the total amount
To find the total amount, we use the expression
First, we multiply the value per $1,000.00 by the number of thousands of face value coverage. This gives an estimate of the annual premium for life insurance policy.
Nikos's premium per year = [tex]\frac{300000}{1000} * 10. 33[/tex]
Niko's premium per year = [tex]300 * 10. 33[/tex]
Niko's premium per year = $3, 099
To find the total amount, we need to multiply by the number of years
= $3,099 x 20
= $61,980
Thus, the total amount he will pay for 20 years of coverage is $61,980. Option D
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IM IN A HURRY PLEASE HELP ME QUESTION IS DOWN BELOW WORTH 15 POINTS each
Answers
Answer: x = 6
NS = 8.5
Step-by-step explanation:
JK = KL= KP + LP
26 = 13 + 2x + 1
2x = 12
x = 6
NS = PS
PS = 8.5
NS = 8.5
Nicky opened a savings account with a single deposit of R1 000 on 1 April 2011. She
then makes 18 inonthly deposits of R700 at the end of every month. Her first payment
is made on 30 April 2011 and her last payment on 30 September 2012. The account
earns interest at 15% per annum compounded monthly.
Determine the amount that should be in her savings account inmediately after her last
deposit is made (that is on 30 September 2012).
Answers
The amount that should be in Nickey's savings account immediately after her last deposit on September 30, 2012, using the future value concept, is R15,282.91.
What is the future value?The future value refers to the compounded value (at an interest rate) of the present value, including the periodic cash investments, over a period.
The future value can be determined using either the future value formula, future value table, or an online finance calculator, as below.
Data and Caluclations:N (# of periods) = 18 months
I/Y (Interest per year) = 15%
PV (Present Value) = R1,000
PMT (Periodic Payment) = R 700
Results
FV = R15,282.91 (R12,600 + R1,000 + R1,682.91)
Sum of all periodic payments = R12,600 (R700 x 18)
Total Interest = R1,682.91
Thus, the amount that should be in Nickey's savings account immediately after her last deposit on September 30, 2012, using the future value concept, is R15,282.91.
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A sample of a radioactive isotope had an initial mass of 440 mg in the year 1990 and decays exponentially over time. A measurement in the year 1998 found that the sample's mass had decayed to 40 mg. What would be the expected mass of the sample in the year 2001, to the nearest whole number?
Answers
Using an exponential function, the expected mass of the sample in the year 2001 would be of 16 mg.
What is the exponential function for the amount of a substance?The function is:
[tex]A(t) = A(0)e^{-kt}[/tex].
In which:
A(0) is the initial amount.k is the decay rate.The information given is as follows:
A(0) = 440, A(8) = 40.
Hence:
[tex]A(t) = A(0)e^{-kt}[/tex].
[tex]40 = 440e^{-8k}[/tex].
[tex]e^{-8k} = 0.09090909[/tex]
[tex]\ln{e^{-8k}} = \ln{0.09090909}[/tex]
[tex]-8k = \ln{0.09090909}[/tex]
[tex]k = -\frac{\ln{0.09090909}{8}[/tex]
k = 0.29973691
Then the function is:
[tex]A(t) = 440e^{-0.29973691t}[/tex]
2001 is 11 years after 1990, hence the amount is:
[tex]A(11) = 440e^{-0.29973691 \times 11} = 16[/tex]
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PLEASE FAST!!! Explain why, given a large unit A and a small unit B, it is wise to leave the conversion factor in fractional form if the decimal form goes on forever.
Answers
Numbers whose decimals form goes on forever are best represented as fractions because they are non-terminating decimals
How to determine the reasons?The decimal numbers are represented as:
A and B
Where
A > B
Numbers whose decimals form goes on forever are non-terminating numbers, and the complete form cannot be represented using decimals except with the sign .......
Because non-terminating decimals have no end, it is best to represent them as fractions
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x-4[x-2(x+6)]=5x+3
[tex]x - 4 [ x - 2(x + 6)] = 5x + 3[/tex]
Answers
The equivalence of the equation is 5x + 48 = 5x + 3.
Since 48 cannot be equal to 3, hence there are no solution.
What is the value of x?Given the equation; x-4[ x - 2( x + 6) ] = 5x + 3
We remove the parentheses
x-4[ x - 2( x + 6) ] = 5x + 3
x-4[ x - 2x - 12 ] = 5x + 3
x - 4x + 8x + 48 = 5x + 3
5x + 48 = 5x + 3
We can go further and collect like terms
5x - 5x + 48 = 3
48 ≠ 3
Since 48 cannot be equal to 3, hence there are no solution.
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If you horizontally stretch the quadratic parent function, f(x) = x², by a factor
of 5, what is the equation of the new function?
A. g(x) = (5x)2
B.
B. g(x) = (x)²
C. g(x) = 5x²
OD. g(x)=x²2
Answers
Answer: [tex]g(x)=\left(\frac{x}{5} \right)^2[/tex]
Step-by-step explanation:
See attached image.
HELP PLS!!! I GIVE BRAINLIEST
Answers
Based on the multiplication property of equality, the statement that completes the proof is: C. CD = b(sin A) and CD = a(sin B).
What is the Multiplication Property of Equality?The multiplication property of equality is given as, if a/b = y, then a = yb. Both sides of the equation is multiplied by the same value.
In step 5 where the multiplication property of equality is applied, we would have:
sin(A) = CD/b
Multiply both sides by b
sin(A) × b = CD/b × b
b(sin A) = CD
CD = b(sin A)
This same property is applied to sin B = CD/a to get CD = a(sin B).
Therefore, the missing statement is: C. CD = b(sin A) and CD = a(sin B).
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Which number line represents the solutions to |x + 4| = 2?
Answers
Answer: Option 1
Step-by-step explanation:
[tex]|x+4|=2\\\\x+4=\pm 2\\\\x=-4\pm 2\\\\x=-6, -2[/tex]
Solve Absolute Value.
| x + 4 | = 2
We know either x + 4 = 2 or x + 4 = −2
x + 4 = 2 (Possibility 1)
x + 4 - 4 = 2 - 4 (Subtract 4 from both sides)
x = -2
x + 4 = −2 (Possibility 2)
x + 4 - 4 = - 2 - 4 (Subtract 4 from both sides)
x = -6
Answer: x = - 2 or x = -6
Therefore we conclude that the solution of the exercise | x + 4 | = 2, is the first number line, since both results are negative.
7. The exam scores of MBA students are normally distributed with a mean of 950 and a standard deviation of 200. (Also explain all your answers using Graphical work)
a) if your score was 1390 what percentage of students have scored more than you ?
b) What are the minimum and the maximum values of the middle 87.4% of the scores?
c) If there were 165 students who scored above 1432. How many students took the exam?
Answers
The percentage of students that have scored more than you is 1.39%
How to illustrate the probability?a) Probility that people scored more than Nancy = P(X>1390) = 1- P(X<1390).
Now z= (1390-950)/200
z= 2.2
P(Z<2.2) = 0.9861
So 1- P(X<1390) = 1 - P(Z<2.2) = 1 - 0.9861 = 0.0139
= 1.39 %
Let P1 be the % of people who score below 1100 and P2 be the % of people who scored below 1200
Then % of students between scores of 1100 and 1200 = P2 - P1
Z (X=1100) =0.75 and Z (X=1200) = 1.25
P1 = P(X<1100)= P (Z< 0.75) =0.7734
P2 = P(X<1200)= P (Z< 1.25) =0.8944
Then % of student between score of 1100 and 1200 = P2 - P1 = 0.8944 - 0.7734 = 0.121 = 12.10%
Middle 87.4 % score means that a total of 12.6 % of the population is excluded. That is 6.3% from both sides of the normal curve. So the minimum value for the middle 87.4% will the one which is just above 6.3% of the population i.e. it will have value x such that P(X<x)= .063.
z value (for P(X<x)= .063) = (-1.53)
But Z= (x-u)/ \sigma from here calculating x, x=644
The minimum value of the middle 87.4% score is 644
The maximum value for the middle 87.4 % of the scores will be the one that has 6.3% scores above it, i.e. it will have value x such that P(X>x)= .063.
P(X<x)= 1 -P(X>x)= 1 - 0.063 = 0.937.
Z value (for P(X<x)= 1.53
But Z= (x-u)/ \sigma from here calculating x, x=1256
The maximum value of the middle 87.4% score is 1256
Z value for (X=1432)= 2.41
P(Z<2.41) =0.9920
It means that 99.2 % of scores are less than 1432
So only 0.8% of scores are higher than 1432
but , 0.8% = 165
So 100% = 20625
20625 students took SAT
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The following data depicts the relationship between the Amount spent on insurance and the amount of inventory loss.
X = Amt spent on protection
Y = Amt of inventory lost or stolen
The least squared regression line : Y = 86.43 – 38.47 X
How much will the amount of loss in inventory be if the amount of protection is $6.39? Leave your answer to 2 decimal places.
Answers
Using the given regression line, it is found that the amount of loss in inventory will be of $159.39.
What is the regression line?The regression line is:
Y = 86.43 - 38.47X
In which:
X is the amount spent on protection.Y is the amount of inventory lost.In this problem, we have that X = $6.39, hence:
Y = 86.43 - 38.47 x 6.39 = -$159.39.
The amount of loss in inventory will be of $159.39.
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Find each of the following:
pls help me ASAP!!
Answers
Step-by-step explanation:
try this option, answer is marked with red colour.
find the slope of this line
Answers
Answer:
-3
Step-by-step explanation:
Select a point on the red line that crosses the graph at a corner like point (2,2). Start at the middle of the graph and go 2 spaces to the right on the x axis and then 2 spaces up. Now you will be a the point (2,2). Do you see how the right line is hitting at the top left corner of the square?
From this point, count how many spaces up and how many spaces to the left to get to the next spot that the red line touches a corner. If you go up 3 spaces and left 1, you have found the next corner. The slope is -3/1 or -3.
The slope is negative because the x and y's are going in different directions, as the x is getting bigger, the why is getting smaller, or another way of looking at it, is that I went up to the find slope and up is positive, but then I went left 1 and left is toward the negative numbers. A positive divided by a negative is a negative, so the slope is negative.
The weight of each “Golden Dairy’s Probiotic Yogurt with Fruit” cup is normally distributed with a mean of 170 grams and a standard deviation of 12 grams. One package contains six random cups and any package with an average weight per cup lower than 158 grams will be rejected.
Part A: What fraction of packages will be rejected because the average weight is too low?
Part B: In addition to original rejection criteria, suppose any packages that have an average weight per cup higher than 179 grams must be rejected as well. What is the total fraction of packages that will be accepted?
Answers
Using the normal distribution, it is found that:
A. 0.0071 = 0.71% of packages will be rejected because the average weight is too low.
B. 0.96 = 96% of packages that will be accepted.
Normal Probability DistributionThe z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score measures how many standard deviations the measure is above or below the mean. Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.By the Central Limit Theorem, the sampling distribution of sample means of size n has standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].For this problem, the parameters are given as follows:
[tex]\mu = 170, \sigma = 12, n = 6, s = \frac{12}{\sqrt{6}} = 4.9[/tex]
Item A:
The proportion is the p-value of Z when X = 158, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{158 - 170}{4.9}[/tex]
Z = -2.45
Z = -2.45 has a p-value of 0.0071.
0.0071 = 0.71% of packages will be rejected because the average weight is too low.
Item B:
The proportion that will be accepted is the p-value of Z when X = 179 subtracted by the p-value of Z when X = 158, hence:
X = 179:
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{179 - 170}{4.9}[/tex]
Z = 1.84
Z = 1.84 has a p-value of 0.9671.
X = 158:
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{158 - 170}{4.9}[/tex]
Z = -2.45
Z = -2.45 has a p-value of 0.0071.
0.9671 - 0.0071 = 0.96 = 96% of packages that will be accepted.
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The Royal Fruit Company produces two types of fruit drinks. The first type is 45% pure fruit juice, and the second type is 95% pure fruit juice. The company is attempting to produce a fruit drink that contains 65% pure fruit juice. How many pints of each of the two existing types of drink must be used to make 50 pints of a mixture that is 65% pure fruit juice?
Answers
The number of pints of each of the two existing types of drink must be used to make 50 pints of a mixture that is 65% pure fruit juice is: 32 pints of 95% juice, and 48 pints of 45% juice.
Number of pints neededLet x be the amount of 95% juice.
Let the amount of 65% juice be 80-x
Hence:
.95x+.45(80-x)=.65(80)
.5x+36=52
Collect like term
5x=16
Divide both side by 5x
x=16/5
x=32
Therefore the number of pints of each of the two existing types of drink must be used to make 50 pints of a mixture that is 65% pure fruit juice is: 32 pints of 95% juice, and 48 pints of 45% juice.
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