Given that sec(x) = 10/9 and that 270° < x < 360°, we want to complete:
sin x/2 = cos x/2 = tan x/2 =We will find that x = 334.16°
The solutions are:
sin(334.16°/2) = 0.221cos(334.16°/2) = -0.975tan(334.16°/2) = -0.229Remember that sec(x) = 1/cos(x)
Then:
sec(x) = 10/9 = 1/cos(x)
so we can write:
cos(x) = 9/10
If we apply the inverse cosine function, we get:
Acos(cos(x)) = Acos(9/10)
x = 25.84°
But this is not in the wanted interval, because the cosine function is even, we have that:
cos(25.84°) = cos( -25.84°)
And it has a periodicity of 360°, then:
cos(-25.84°) = cos(-25.84° + 360°) = cos(334.16°)
Then our angle is x = 334.16°.
Now we replace that in the wanted expressions:
sin(334.16°/2) = 0.221cos(334.16°/2) = -0.975tan(334.16°/2) = -0.229If you want to learn more, you can read:
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D. Directions: Write the equation for line in any form) for the following points
(0,4) and (-3,12)
Answer:
y = -8/3x + 4
Step-by-step explanation:
Can someone please help me on this one ?
You are considering different investment strategies to save for your retirement.
Option 1: You invest $50/ month at a rate of 3.5% APR compounded monthly for 35 years.
Option 2: You invest $150/ quarter at a rate of 4.15% APR compounded monthly for 35 years.
Option 3: You invest $4,000 at a rate of 5.5% APR compounded monthly for 35 years.
Complete the table below and answer the questions below it.
You may use this calculator http://www.mycalculators.com/ca/savecalcm.html to help you.
(Hint: The “Present Value” for options 1 and 2 is 0 while for option 3 it is $4,000.00. Also, the
top radio button in the Contributions box should be selected so that contributions are made at the beginning of the period.)
Table:
Option # | Contributions | Final Balance | Total Interest Earned
1
2
3
1) How did you calculate the contribution for each option? In which option would you
contribute the least?
2) Which option yielded the highest amount at the end of the 35 years and what was the basis of the plan?
3) What is the difference in the principal invested for the highest and lowest final
balances? What is the difference in the interest earned?
4) What plan would you recommend for the largest return on investment? (This means
the most interest for the least amount invested)
5) How does the differing interest rates in each option play into your recommendation?
I would appreciate full feedback! Thank you :)
Return on investment increases as the interest rate applied, the duration of investment, and the principal invested increases.
The responses are as follows;
1) Total contribution = Single contribution Value × Number of contributions2) Option 23) $-4,0004) Option 35) The higher interest rate increases the return on investmentReasons:
Option 1: Investment
The present value = 0
The contributions made = $50 monthly
APR of investment = 3.5%
Number of years of investment = 35 years
The contribution = $50 × 12 × 35 = $21,000
Future value (final balance) = $41,230.22
Interest Earned = $41,230.22 - $21,000 = $20,230.22
Option 2: Investment
The present value = 0
The contributions made = $150 per quarter
APR on investment = 4.15%
Number of years of investment = 35 years
The contribution = $150 × 4 × 35 = $21,000
Future value = $47,503.88
Interest Earned = $47,503.88 - $21,100
Option 3: Investment
Present value = $4,000
APR on investment = 5.5%
Number of years of investment = 35 years
The contribution = $4,000
Future value = $27,300.26
Interest Earned = $27,300.26 - $4,000 = $23,300.26
[tex]\begin{array}{|c|c|c|c|}Option \ number&Contributions&Total \ Interest \ Earned&Final \ Balance\\1&\$50&\$20,230.22&\$41,230.22\\2&\$150&\$26,403.88&\$47,503.88\\3& \$4,000 &\$23,300.26 &\$27,300.26 \end{array}\right][/tex]
1) The total contribution is given by the product of the monthly contribution and the number of timer units.
2) The option that yielded the highest amount at the end of 35 years is the option 2.
The basis of the plan is quarterly investment of $150 and an annual interest rate of 4.15% compounded monthly.
3) The principal with the highest final balance is the principal for Option 2. which is 0
The principal that has the lowest final balance is the principal for option 3 which is $4,000
The difference in the principal for the highest and lowest final balances is
$0 - $4,000 = $-4,000
4) The plan recommended for the largest return on investment is option 2, in which the amount invested increased by more than 600%
5) The higher the interest rate, the higher the return on the amount invested.
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what is 250% of 5
please help
Answer:
12.5
Step-by-step explanation:
You can read this problem as ...
2.5 × 5 = 12.5
__
You can think of % as meaning /100. You can think of "of" as meaning "times". Then the expression
250% of 5
can be thought of as ...
250/100 × 5
= 1250/100 = 12.5
A scientist needs 180 milliliters of a 20% acid solution for an experiment. The lab has available a 25% and a 10% solution. How many milliliters of the 25% solution and how many milliliters of the 10% solution should the scientist mix to make the 20% solution
9514 1404 393
Answer:
120 mL of 25% solution60 mL of 10% solutionStep-by-step explanation:
Let q represent the quantity of 25% solution in the mix. Then 180-q is the quantity of 10% solution. The quantity of acid in the mix is ...
0.10(180 -q) +0.25(q) = 0.20(180)
18 +0.15q = 36 . . . . simplify
0.15q = 18 . . . . . . . . subtract 18
q = 18/0.15 = 120 . . . . divide by the coefficient of q
180-q = 60
The scientist should mix 120 mL of 25% solution with 60 mL of 10% solution.
WHAT IS 159 DIVIDED BY 3 (ITS NOT HARD PLEASE ANSWER I DON'T HAVE A CACULATER)
Answer:
Step-by-step explanation:
The asked quotient of 159 divided by 3 is the number 51.
What is divide?It is the inverse of multiplication, and it is used to find out how many times one number can be divided by another. In mathematics, the division is an arithmetic operation that involves splitting a quantity into equal parts or groups.
Here,
As mentioned in the question, we have to determine the quotient of 159 divided by 3
So let the quotient be y,
y = 159/3
y = 51
Thus, the asked quotient of 159 divided by 3 is number 51.
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The population of a hornet nest experienced growth at a 20% monthly rate, compounded
continuously. At the end of a 5 month period, the population reached a size of 815
hornets.
Assuming that every month has 30 days, how many hornets were in the nest at the
beginning of the 5 months according to the exponential growth function? Round your
answer to the nearest whole number, and do not include units.
Using an exponential function, it is found that at the beginning, there were 328 hornets.
An increasing exponential function has the following format:
[tex]A(t) = A(0)(1 + r)^t[/tex]
In which:
A(0) is the initial value.r is the growth rate, as a decimal.In this problem, there is a growth of 20%, hence [tex]r = 0.2[/tex].
After 5 months, the size is of 815, hence, when [tex]t = 5, A(t) = 815[/tex], and this is used to find A(0).
[tex]A(t) = A(0)(1 + r)^t[/tex]
[tex]815 = A(0)(1 + 0.2)^5[/tex]
[tex]A(0) = \frac{815}{(1.2)^5}[/tex]
[tex]A(0) = 328[/tex]
At the beginning, there were 328 hornets.
A similar problem is given at https://brainly.com/question/22733028
WILL GIVE BRAINLIEST!!
Which graph shows the following system of equations and it’s solution?
{ -2x -y = -5
{ 2x - 3y = 1
Answer:
Step-by-step explanation:
These two lines will intersect at (-4, -3). The top equation will have a slope of 1/4 and the bottom one a slope of 7/4.
Which function has an inverse this is a function?
b(x)=x^2 + 2x
d(x)=-4x
m(x)=-3
p(x)=|x|
Answer :-
Option 2
Step by step explanation :-
d (x) = -4x has an inverse .
!!! Help im failing math !
Answer:
So am I lol btw I think it’s C
Step-by-step explanation:
Aaron creates a stacked cake comprised of three cylindrical sections as pictured below, and plans to cover the top of each section with a different color icing. Each lower section is a total of two inches wider than the section above it. If the yellow top of the upper section has an area of 12.56 square inches, what is the approximate area of the green visible portion of the bottom section which he will need to cover with icing?
Answer:
Step-by-step explanation:
A = πR²
top layer has a radius of
R = √(12.56/π) = 2 inches
The middle layer has a radius of 3 inches and an area of
A₂ = π3² = 9π in²
The bottom layer has a radius of 4 inches and an area of
A₃ = π4² = 16π in²
so the visible area on the bottom layer has an area of
16π - 9π = 7π in² or about 22 in²
PLZZZ HELP MEEEeeeeeeeeeeeeeeeeeee
Answer:
I am a professional, worry not
-1.6 < -1.55 < -0.4 < 1.35 < 1.7
WILL GIVE BRAINLIEST
These two triangles are congruent by ....
O SSS
O SAS
O HL
O ASA
O AAS
O the triangles are NOT congruent
SAS postulate states that if two sides and one angle of the two triangles are congruent then the corresponding triangles are congruent.
These two triangles are congruent by SAS postulate
Proof
Statements Reasons
In ΔNHJ ↔ ΔKHJ
mHJ≅mHJ common to both Δs∠N≅∠K right anglesmHN≅mHK givenFrom 1,2, and 3 ΔNHJ ≅ ΔKHJ SAS≅SAS
For more explanation click
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1. Which of the following is an example of acceleration? A. 10m/s B. 64km/h/min C. 50 cm2/s2 D. 46 km/h
Answer:
i beleive c for the proper answer form is m/s 2 c is the only one to show to square anything. if that's wrong the a but there is no square symbol.
Subtract (7u2+10u+6) from (3u2−5u+4).
The solution to simplifying the algebraic expression is: -4u² - 15u - 2
How to solve Algebraic Expressions?Algebraic expressions are defined as the idea of expressing numbers using letters or alphabets without specifying their actual values
The algebraic expression we want to simplify is:
3u² - 5u + 4 - (7u² + 10u + 6 )
Simplifying the bracket gives us:
3u² - 5u + 4 - 7u² - 10u - 6
Arranging like terms gives us:
3u² - 7u² - 5u - 10u + 4 - 6
= -4u² - 15u - 2
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The simple interest charged on a 12-month loan of $82,000 is $631. Find the simple interest rate. (Round your answer to one decimal place.)
Step-by-step explanation:
631/82000×100
=0.8
MARK ME BRAINLIEST PLSS!
Find the value of y for the given value of x.
y = x/2 + 9;x = -12
Step-by-step explanation:
x = -12
y = x/2 + 9
y = -12/2 + 9
y = -6 + 9
y = 3
Find the inequality represented by the graph?
Answer:
[tex]y \geqslant - 2x - 5[/tex]
Step-by-step explanation:
Since the shaded area is above the line and the line is solid, you will use the greater-than-or-equal-to sign.
Not to mention inequalities still have a slope and y-intercept. (In this case, the y-intercept will be -5, since the line crosses the y-axis at that point, and the slope will be -2 because the line is going down 2 units and to the right 1 unit.)
Hope this helps :)
Customers at a gym pay a membership fee to join and then a fee for each class they attend. Here is a graph that represents the scenario.
What is the slope of the line?
Find the volume of the following prism.
Answer:
[tex]4860[/tex] cubic units
Step-by-step explanation:
First, we use the formula of the triangle prism to solve the question
[tex]v=\frac{1}{2}b*h*l[/tex]
[tex]v=\frac{1}{2} 18*12*45[/tex]
[tex]v=4860 cm^{3}[/tex]
A microscope shows you an image of an object that is 80 times the object's actual size. Therefore, the scale factor of the enlargement is 80. An insect has a body length of 7 millimeters. What is the body length of the insect under the microscope?
A. 56 millimeters
B. 560 centimeters
C. 5,600 millimeters
D. 560 millimeters
Answer:
560 mm (Answer D)
Step-by-step explanation:
Multiply the 7 mm measurement by 80; the result is 560 mm (Answer D).
Can someone help me? I still don't understand this question.
[tex]f(x) = -6x^2 + 7x + 4[/tex]
Step-by-step explanation:
For x = 1
[tex]a(1)^2 + b(1) + c = 5 \Rightarrow a + b + c = 5[/tex] (1)
For x = -3,
[tex]a(-3)^2 + b(-3) + c = -71[/tex]
[tex]\Rightarrow 9a - 3b + c = -71[/tex] (2)
For x = 3,
[tex]a(3)^2 + b(3) + c = -29[/tex]
[tex]\Rightarrow 9a + 3b + c = -29[/tex] (3)
Let's add Eqn(2) and Eqn(3) together to eliminate b:
[tex]\Rightarrow 18a + 2c = -100[/tex] (4)
Next, multiply Eqn(1) by 3 and then add to Eqn(2) to get
[tex]\Rightarrow 12a + 4c = -56[/tex] (5)
Then we want to eliminate c by multiplying Eqn(4) by -2 and then adding to Eqn(5) and we will get
[tex]-24a = 144 \Rightarrow a = -6[/tex]
Now that we have the value for a, we can use either Eqn(4) or Eqn(5) to solve for c and we will get
[tex]12(-6) + 4c = -56 \Rightarrow c = 4[/tex]
Using the values of a and c on Eqn(1), we find that [tex]b = 7[/tex] so therefore, our function f(x) has a form
[tex]f(x) = -6x^2 + 7x + 4[/tex]
1. You are interested in recycling behavior and whether it varies between urban and
rural residents. You know that the statewide recycling rate is 48.89%, and you
survey 140 rural residents and 310 urban residents to find out if they recycle.
180 urban residents respond that yes, they recycle. 130 do not. 40
rural residents recycle, and 100 do not.
a) Construct an expected frequencies crosstab, based on the sample size and the
statewide recycling rate.
b) Construct an observed frequencies crosstab, based on your actual data.
(NOTE for 1a and 16: Be sure to include both percentages and frequency values, in
Answer:
65
Step-by-step explanation:
A ruler 30 cm long is broken into two parts in the ratio 8:7. How long
are the two parts?
Answer:
Step-by-step explanation:
Length of each part of the ruler will be
8x and 7x
. Hence, 8x+7x=30 => 15x=30 =>x=2
Hence, the lengths will be
8x=8×2=16
7x=7×2=14
2y⁴×5y³
Send a message
Answer:
10y^7
Step-by-step explanation:
Answer:4+3=7
5×2=10
Step-by-step explanation:
help me someone please
Answer:4root3
Step-by-step explanation:
if you dont know what a equilateral triangle its just. a triangle basically
(im in 7th btw)
THIS ANSWER IS WORTH 20 PTS!!! WILL REWARD BRAINLIEST!!!
Convert the exponential equations into logarithmic form:
Answer:
a ) C = 81 and D = 4
b ) E = 625 and F = 4
c ) G = 1000 and H = 4
Step-by-step explanation:
Round to the nearest cent 0.2745
yooooooooooooooooooooooooo
Answer:
3/2
Step-by-step explanation:
Rise over run meaning how many up over how many over (would be a negative rise if the line was \ instead of /)
find where the line intersects with the corner of the graph lines and plot from there.
Mark me as brainliest if this helps!
[tex]▪▪▪▪▪▪▪▪▪▪▪▪▪ {\huge\mathfrak{Answer}}▪▪▪▪▪▪▪▪▪▪▪▪▪▪[/tex]
The slope of given line is ~
[tex] \boxed{ \frac{3}{2} }[/tex]
Let's find the slope of the given line by using the coordinates of points (3 , 0) and (1 , -3) ~
[tex] \sf{ \dfrac{y_2 - y_1}{x_2 - x_1} }[/tex][tex] \dfrac{0 - ( - 3)}{3 - 1} [/tex][tex] \dfrac{3}{2} [/tex]I need help with part a and b please
Answer:
The total answer should be 38 on the top
Step-by-step explanation:
a) So the first partial quotient would be equal to 30 as 31 x 30 = 930
b) Second partial quotient would be 8 as 31 x 8 = 248
Answer:
0
38
I hope it's help byeeee
Jerome makes and sells his own energy drinks. He mixes a liquid drink mix with water to create his own special blend. Jerome usually uses 8 cups of water and 3 cups of drink mix. Tomorrow, there is a road race in town, however, and Jerome thinks he’ll be able to sell a lot more of his energy drinks than usual. Jerome’s brother told him to add one cup of water for every one cup of drink mix he added to keep the ratio of water to drink mix the same and still increase the total amount of energy drink. Jerome’s sister told him to multiply both the amount of water and the amount of drink mix by the same number to keep the ratio the same and still increase the total amount of energy drink. Who is correct: Jerome’s brother or Jerome’s sister? As you complete the task, keep this question in mind: Based on what you know about ratios, what do you think the answer will be? Directions: Complete each task, reading the directions carefully as you do. You will be graded on the work you show, or your solution process, in addition to your answers. Make sure to show all your work and to answer each question as you complete the task. Type all of your work into this document so you can submit it to your teacher for a grade. You will be given partial credit based on the work you show and on the completeness and accuracy of your explanations. Your teacher will give you further directions on submitting your work. You may be asked to upload the document, e-mail it to your teacher, or hand in a hard copy. Now let’s get started! Step 1: Finding the part-to-part and part-to-whole ratios To make his special energy drink, Jerome uses 8 cups of water and 3 cups of drink mix. What is the ratio of water to drink mix? (2 points) What is the ratio of drink mix to water? (2 points) What is the ratio of drink mix to mixed energy drink? (2 points) What is the ratio of water to mixed energy drink? (2 points) Step 2: Testing Jerome’s brother’s approach Jerome’s brother told him to add one cup of water for every one cup of drink mix he add
Answer:
not well explained??
Step-by-step explanation:
?? explain it better bro.
