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
the chairs in a hall are about to be arranged in a row. if i put 6 chairs in a row there will be 4 left if i put 7 chairs in a row there will be 3 short how many chairs are there
Answers
Step-by-step explanation:
THERE WILL BE
6+4+3+7= 23
Find the volume of the composite figure. Round to the nearest tenth. 3cm 4cm 10cm 5 cm
Answers
The volume of the composite figure is 655.44 unit³.
How to illustrate the volume?The information is incomplete. An overview will be given. Let's assume that the shape is a cylinder.
The volume of a cylinder is πr²h
Assumed radius = 7
Assumed height = 4
The volume will be:
= πr²h
= 3.14 × 7² × 4
= 615.44 unit³
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Solve for x.
x-2.13 = 5.3
Answers
+2.13
Process:
Start by isolating the variable by itself, in this case we add 2.13 to the -2.13 as whatever we do to one side of the equation we do to the other hence we add 2.13 to 5.3 which will become x = 7.43 and we can verify our answer by substituting our answer for x
7.43 - 2.13 = 5.3
Answer:
x = 7.43
Step-by-step explanation:
X - 2.13 = 5.3
add -2.13 to both sides
x -2.13+2.13 = 5.3 + 2.13
-2.13 + 2.13 cancel out and 5.3 +2.13 equals 7.43
therefore x =7.43
check your work by substituting 7.43 for x
7.43 - 2.13 = 5.3
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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A sweater is selling for ½ off the original
price. Which number is equivalent to
A 0.23
B 33.3%
C 6.6
D 66.6%
Answers
Answer:
Step-by-step explanation:
it would be D
Assume that Hogan Surgical Instruments Co. has $2,500,000 in assets. If it goes with a low-liquidity plan for the assets, it can earn a return of 18 percent, but with a high-liquidity plan, the return will be 14 percent. If the firm goes with a short-term financing plan, the financing costs on the $2,500,000 will be 10 percent, and with a long-term financing plan, the financing costs on the $2,500,000 will be 12 percent.
Answers
The the anticipated return after financing cost with the most aggressive asset financing mix is $200000.
Most aggressive
Low liquidity = $2,500,000 *18%
Low liquidity = $450,000
Short-term financing = -$2,500,000*10%
Short-term financing = -$250,000
Anticipated return = $450,000 + (-$250,000)
Anticipated return = $200,000
Most conservative
High liquidity = $2,500,000 *14%
High liquidity = $350,000
Long-term financing = –$2,500,000 * 12%
Long-term financing = -$300,000
Anticipated return = $350,000 + (-$300,000)
Anticipated return = $50,000
Moderate approach
Low liquidity = $2,500,000 *18%
Low liquidity = $450,000
Long-term financing =–$2,500,000 * 12%
Long-term financing = -$300,000
Anticipated return = $450,000 + (-$300,000)
Anticipated return = $150,000
Moderate approach
High liquidity = $2,500,000 *14%
High liquidity = $350,000
Short-term financing = -$2,500,000*10%
Short-term financing = -$250,000
Anticipated return = $350,000 + (-$250,000)
Anticipated return = $100,000
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Complete question:
a. Compute the anticipated return after financing cost with the most aggressive asset financing mix.
b. Compute the anticipated return after financing cost with the most conservative asset financing mix.
c. Compute the anticipated return after financing cost with the two moderate approaches to the asset financing mix.
“The length of a rectangle is two feet greater than twice it’s width. If the perimeter is 25 feet, find the width.” Which of the following translations is correct
Answers
The width of the rectangle is 3.5 feet
Solving for the missing sides of a rectangle
The width of the rectangle = w
The length of the rectangle = l
The perimeter = p
Length of the rectangle is two feet greater than twice it’s width
l = 2w + 2
p = 2(l + w)
p = 2(2w + 2 + w)
p = 2(3w + 2)
p = 6w + 4
The perimeter of the rectangle is 25 ft
25 = 6w + 4
This can be rewritten as:
6w + 4 = 25
6w = 25 - 4
6w = 21
w = 21/6
w = 3.5
Therefore, the width of the rectangle is 3.5 feet
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FRAME AN EQUATION AND SOLVE IT .NEED ASAP
3 is added to a number and the result is multiplied by 4 to get 20.
Answers
Answer:
[tex]\fbox {Required equation : 4(x + 3) = 20}[/tex]
[tex]\fbox {Result : x = 2}[/tex]
Step-by-step explanation:
Let our number be x.
1) 3 is added to this number.
x + 32) It is multiplied by 4.
4(x + 3)3) It is equated to 20.
4(x + 3) = 20∴ This is our framed equation.
Steps to solve :
1) Divide by 4 on both sides.
1/4 x 4(x + 3) = 20/4x + 3 = 52) Subtract 3 on both sides.
x + 3 - 3 = 5 - 2x = 2∴ The number is 2.
Which of the following are equations for the line shown below? Check all that
apply.
(-4,3)
(4,-5)
A. y=-x-1
B. y+ 5=-(x-4)
C. y-3 = -(x+4)
D. y=-x-9
Answers
Answer: A, B, C
Step-by-step explanation:
[tex]m=\frac{-5-3}{4-(-4)}=-1[/tex]
Substituting into point-slope form, we get [tex]y-3=-(x+4)[/tex] and [tex]y+5=-(x-4)[/tex]. Rearranging this into slope-intercept form,
[tex]y-3=-(x+4)\\\\y-3=-x-4\\\\y=-x+1[/tex]
find the interest accrued on a $7500 loan with a 2.5% interest rate over 4 years
Answers
The interest obtained after 4 years from a loan of $7500 is = $750
Calculation of generated interestThe principal amount of the loan = $7500
The rate at which the interest is paid is = 2.5%
The time that it will take to pay the interest = 4 years
Using the formula for Simple interest;
SI= P×T×R/100
SI = 7500×4 × 2.5/100
SI= 75000/100
SI=$750
Therefore, the interest accrued on a $7500 loan with a 2.5% interest rate over 4 years is = $750
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find the slope of this line.
Answers
Answer:
4/5
Step-by-step explanation:
SImply use slope formula. We see the graph has defined points at (5, 4), and (-5, -4).
m=(Y2-Y1)/(X2-X1)
(4-(-4))/(5-(-5))=8/10
Simplify 8/10
=4/5
write the explicit formula for this geometric sequence.
81,27,9,3, …
Find the common ratio, r.
Answers
The explicit formula for this geometric sequence 81, 27, 9, 3, … is aₙ = 81(1/3)ⁿ⁻¹. It has common ratio of 1/3 and first term of 81.
What is an equation?An equation is an expression that shows the relationship between two or more variables and numbers.
A geometric sequence is in the form aₙ = ar⁽ⁿ⁻¹⁾, where a is the first term and r is the common ratio.
The geometric sequence 81, 27, 9, 3, … has common ratio:
r = 27/81 = 1/3
The explicit formula for this geometric sequence 81, 27, 9, 3, … is aₙ = 81(1/3)ⁿ⁻¹. It has common ratio of 1/3 and first term of 81.
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Multiply.
x²+3x+2
x 2x²+3x-1
OA. 2x¹ +9x² + 12x² + 3x-2
OB. 2x¹ +9x2 - 2
OC. 3x2 + 6x +1
OD. 2x¹ +21x² + 3x-2
Answers
The multiplication of the expression (x² + 3x + 2) (2x² + 3x + 1) is 2x⁴ + 9x³ + 14x² + 9x + 2
Multiplication(x² + 3x + 2) (2x² + 3x + 1)
= 2x⁴ + 3x³ + x² + 6x³ + 9x² + 3x + 4x² + 6x + 2
collect like terms= 2x⁴ + 3x³ + 6x³ + x² + 9x² + 4x² + 3x + 6x + 2
= 2x⁴ + 9x³ + 14x² + 9x + 2
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Determine the number of solutions for the equation shown below.
4x+6= 4x+6
Ο Α. 0
OB. Infinitely many
* O C. 1
OD. 2
Answers
A concert manager counted 525 ticket receipts the day after a concert. The price for a student ticket was $10.50, and the price for an adult ticket was $18.00. The register confirms that $8,325.00 was taken in. How many student tickets and adult tickets were sold?
Answers
Answer:
150 student tickets and 375 adult tickets
Step-by-step explanation:
Let x = # of student tickets sold, and y = # of adult tickets sold.
Total of 525 tickets were sold, so the first equation is x + y = 525. The register gained $8325, so 10.50x + 18y = 8235 is the second equation.
x + y = 525
10.50x + 18y = 8325
18x + 18y = 9450
10.50x + 18y = 8325
7.5x = 1125
x = 150
150 + y = 525
y = 375
A line is parallel to the line y = x and passes
through the parabola y = x² - 3 at
(4, 13). What is the other point at which the two
functions intersect?
Answers
Answer:
Step-by-step explanation:
hello here is an solution
Simplify the following
Answers
Answer:
29/12
Step-by-step explanation:
hello :
2/3 +5/6 +11/12 = (2×4)/(3×4) + (5×2)/(6×2) + 11/12
2/3 +5/6 +11/12 = 8/12 +10/12 +11/12 = (8+10+11)/12
2/3 +5/6 +11/12 = 29/12
Answer:
[tex]2\frac{5}{12}[/tex]
Step-by-step explanation:
To add fractions, we have to make sure that they have the same denominators. To do that, we have to find their lowest common multiple (LCM).
The LCM of 3, 6, and 12 is 12.
Then we have to multiply the numerator and denominator of each fraction by a number so that the denominator becomes the LCM (12).
[tex]\frac{2}{3} + \frac{5}{6} + \frac{11}{12}[/tex]
⇒ [tex]\frac{2 \times 4}{3 \times 4} + \frac{5 \times 2}{6 \times 2} + \frac{11 \times 1}{12 \times 1}[/tex]
⇒ [tex]\frac{8}{12} + \frac{10}{12} + \frac{11}{12 }[/tex]
⇒ [tex]\frac{8+10+11}{12}[/tex]
⇒ [tex]\frac{29}{12}[/tex]
⇒ [tex]\bf 2\frac{5}{12}[/tex]
Help again please. 10 points for help!! Thanks
Answers
Answer: 23 inches by 7 inches
Step-by-step explanation:
161 = 7 x 23 (or 1 x 161 but that doesn't help...)
And to check:
7 x 3 + 2 = 23
Answer:
23inches by 7inches
Step-by-step explanation:
7 ×3+2=23
Suppose that $6500 is placed in an account that pays 12% interest compounded each year.
Assume that no withdrawals are made from the account.
Follow the instructions below. Do not do any rounding.
Answers
The amount after 1 year is $7280 and the amount after two year is $8153.
Given that $6500 is placed in an account that pays 12% interest compounded each year.
Compounding is the addition of interest to the principal of a loan or deposit, or in other words, interest on principal plus interest.
Compounded interest=12%
Principal amount=$6500
Time period = 1 year
[tex]A=P\left(1+\frac{r}{n}\right)^{nt}[/tex]
where P is Principle amount, r is annual interest, n is number of times the interest compounded monthly, t is number of years
Here P=6500, r=12%, n=1, t=1
Substitute these values in the formula, we get
A=6500(1+(0.12/1))¹⁽¹⁾
A=6500(1+0.12)¹
A=6500×1.12
A=7280
Now we have to calculate for two years.
That is if n=2 , then
A=6500(1+(0.12/1))¹⁽²⁾
A=6500(1+0.12)
A=6500×1.2544
A=8153.6
Hence, the amount for one year and two year when $6500 is placed in an account that pays 12% interest compounded is $7280 and $8153.60.
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Practise the Skill
A container holds 4 yellow balls, 3 blue balls and 1 red ball.
Luke chooses a ball at random.
What is the probability that Luke will pick a blue ball?
Give your answer as a fraction in its lowest terms.
Answers
The probability that Luke will pick a blue ball is 3/8.
We have,
To find the probability of Luke picking a blue ball, we need to determine the total number of balls in the container and the number of blue balls.
Total number of balls
= 4 (yellow balls) + 3 (blue balls) + 1 (red ball)
= 8 balls
Number of blue balls = 3
Now, the probability (P) of picking a blue ball is given by:
P = Number of favorable outcomes (picking a blue ball) / Total number of possible outcomes
P = 3 (number of blue balls) / 8 (total number of balls)
Now, we can simplify the fraction to its lowest terms:
P = 3/8
Thus,
The probability that Luke will pick a blue ball is 3/8.
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If f(x) = 4x, which statements are true of g(x)? Select two options.
Answers
The two statements that are true for g(x ) are:
g(x) = [tex]4^{x}[/tex] - 1
g(x) is translated both vertically and horizontally.
What is a function?A function is a relation showing the relationship between two or more variables.
A function produces a unique output when a unique input is given to it. The input is called the domain and the output is called the Range.
Analysis:
If we use the values of x as 0,1,2,3
for x = 0
g(0) = [tex]4^{0}[/tex] -1 = 1 -1 = 0
for x = 1
g(1) = [tex]4^{1}[/tex] -1 = 4 - 1 = 3
for x = 2
g(2) = [tex]4^{2}[/tex] - 1 = 16 - 1 = 15
for x = 3
g(3) = [tex]4^{3}[/tex] - 1 = 64 - 1 = 63
Therefore g(x) = [tex]4^{x}[/tex] - 1
Also since the values of g(x) changes along the y - axis and x-axis also changes, therefore, g(x) is translated along both axes.
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NEED FAST AND CORRECT!! Use the box plots comparing the number of males and number
of females attending the latest superhero movie each day for a
month to answer the questions.
Males
10
H
Females
20
30
Part A: Describe the shape of each plot
Part B: What is the best measure of center for Males? Females?
How do you know?
Part C: What is the best measure of spread for Males? Females?
How do you know?
Part D: Provide a possible reason for the outlier in the data set. Table
Answers
The description of the box plots are as follows:
The Interquartile Range is given as 23; and the difference between the median values is 14What is the calculation for the above?IQR = 25 - 2
= 23
The difference between the median values
= 20 - 6
= 14
What are the respective best measure of center for males? females?The mean would be a better measure of center for Females because the data has no outliers.The median would be a better measure of center for Males because the data has outliers.What is the reason for the outlier in the data set?That female admires those movie stars and has a large group of pals with whom she goes out on a regular basis to keep them company.
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I need help to this it would be awesome if you could help.
Answers
In the given diagram, the value of JI is 6
Solving equations
From the question, we are to determine JI
From the given diagram, we can write that
JI + IH = x + 22
Also,
JI = 2x + 28
and
IH = 5
Then, we can write that
2x + 28 + 5 = x + 22
Collect like terms
2x - x = 22 -28 -5
x = -11
Now, substitute the value of x into the equation
JI = 2x + 28
JI = 2(-11) + 28
JI = -22 +28
JI = 6
Hence, the value of JI is 6
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10 8 12 10 14 ? sequence
Answers
Answer:
The Sequence
Step-by-step explanation:
the Sequence is a decrease by 2 and a increase of 4. So subtract 2 by 10 to get 8 then add 4 to get 12 and so on.
An ice chest contains 9 cans of apple juice6 cans of grape juice5 cans of orange juiceand 4 cans of pineapple juice Suppose that you reach the container and randomly select three cans in successionFind the probability of selecting no grape juice Select one 243 506 6 17/45; c * 5/506; d * 102/253
Answers
Answer:
243/506
Step-by-step explanation:
There are 24 total juice boxes.
18 of them are not grape
You have an 18/24 chance of picking not grape juice
The second time, 1 is removed, then another is removed. This creates:
(18/24)*(18/23)*(18/22) = 243/506
the ammount of time between interest payments is know as
Answers
The amount of time between interest payments is know as period.
What is period?Period is the time between when interests are paid. Period can vary depending on the terms of the investment. Periods can be yearly, quarterly, semi-annually, biweekly or weekly.
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Identify a horizontal or vertical stretch or compression of the function f(x) = x
by observing the equation of the function g(x) = 6x.
The base graph vertically stretched by a factor of 6.
The base graph horizontally stretched by a factor of 6.
The base graph vertically compressed by a factor of 6.
The base graph horizontally compressed by a factor of 6.
Answers
Answer: The base graph vertically stretched by a factor of 6.
Step-by-step explanation:
See attached image.
Using the following table, construct and interpret a 90% confidence interval for the population standard deviation of the carbon in metric tons.
Nation
Brazil
Germany
Mexico
Emissions
Canada
361
844
398
Great Britain 577
631
Answers
The 90 percent confidence interval for the data is given as 396.02, 727.98
First we have to find the meanThe formula is fx/n
= Mean, μ = 562.2
sum up the data and divide by 5
sd =
Σ(xi - μ)2/N
= (361 - 562.2)² + ... + (631 - 562.2)²/5
= 151806.8/5
= 30361.36
sd = √30361.36
= 174.24511470914
1 - confidence level
= 1 - 0.90
= 0.1
df = 4
Using excel
T.INV.2T(0.1, 4) = ±2.13
562 +- 2.13 x 174.245/√5
562- 165.98, 562+ 165.98
= 396.02, 727.98
Hence the confidence interval can be calculated to be 396.02, 727.98
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If the average work week was 43 hours in 2009 and 42 hours and 30 minutes in 2010, by what percentage did the average number of hours worked per week drop from 2009 to 2010?
Answers
The average number of hours worked per week drop from 2009 to 2010 dropped by 1.16%
How to determine the percentage change?The average work weeks are given as:
Year 2009 = 43 hours
Year 2010 = 42 hours 30 minutes
Rewrite as:
Year 2010 = 42.5 hours
The percentage change is then calculated as:
Percentage change= (Final - Initial)/Initial * 100%
So, we have:
Percentage change= (42.5 - 43)/43* 100%
Evaluate
Percentage change= -1.16%
Hence, the average number of hours worked per week drop from 2009 to 2010 dropped by 1.16%
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Officially, variable names in Python can be any length and can consist of uppercase and lowercase letters ( A-Z, a-z ), digits ( 0-9 ), and the underscore character ( _ ). An additional restriction is that, although a variable name can contain digits, the first character of a variable name cannot be a digit. Python’s most-followed style guide, PEP8 also suggests we limit each line to 79 characters, so, to be extra careful, we will assume variables can be of at most 7 characters in length.How many variable names can there be in Python if we abide by these two rules?
Answers
Abiding by the two rules, the number of variable names we can have in Python are; 63
How to name variables in Python Programming?The rules for python are given as;
1) Variable names in Python can be any length and can consist of uppercase and lowercase letters ( A-Z, a-z ), digits ( 0-9 ), and the underscore character ( _ ).
1b) An additional restriction is that, although a variable name can contain digits, the first character of a variable name cannot be a digit.
2) We limit each line to 79 characters, so, to be extra careful, we will assume variables can be of at most 7 characters in length.
Now, abiding by the two rules above, the number of variable names we can have in Python are;
26( A-Z) + 26(a-z) + 10(0-9) + 1 ( _ ) = 63 variable names
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