Answer:
Step-by-step explanation:
3 sinθ=3 cos 2θ
sin θ=cos 2θ
sinθ=1-2sin² θ
2sin²θ+sin θ-1=0
2sin²θ+2sinθ-sinθ-1=0
2sin θ(sin θ+1)-1(sin θ+1)=0
(sin θ+1)(2 sin θ-1)=0
sin θ=-1=-sin 90=sin (180+90)
θ=270
or sin θ=1/2=sin 30,sin (180-30)
θ=30,150
solution set is {30,150,270}
A box contains 7 blue socks, 13 yellow socks and 5 green socks. What is the probability of choosing a green sock at random?
1/5
1/7
5/21
5/20
Answer:
1/5
Step-by-step explanation:
7 + 13 =20
20 + 5 = 25
5 is a fifth of 25
Answer:
[tex]\frac{1}{5}[/tex]
Step-by-step explanation:
There are 25 socks in total, only 5 of these are green.
The proportion would look like this:
[tex]\frac{5}{25}=\frac{1}{5}[/tex]
9. Find the volume of the sphere if the radius is 12.4 in. Round to the nearest tenth.
Answer:
V=7982.4 in
Step-by-step explanation:
V=4/3pi*r^3
V=4/3pi*12.4^3
V=4/3pi*1906.62
V=7626.48/3pi
V=2542.16pi
V=2542.16*3.14
V=7982.4
find the value of x.
Answer:
5
Step-by-step explanation:
5y+155=180
5y=180-155=25
y=5
5y+13x=90
13x=90-25=65
x=5°
Solve -5x < -35. Enter your answer as an inequality.
Answer:
x > 7
Step-by-step explanation:
-5x < -35
(Divide by 5)
-x < -7
(When dividing by a negative number, you flip the sign)
x > 7
The answer of given inequality is x > 7 .
What is inequality?Inequality is the defined as mathematical statements that have a minimum of two terms containing variables or numbers is not equal.
Given,
-5x < -35
Divide by 5 in inequality
-x < -7
Multiply by (-1) in inequality [flip the sign of inequality]
So, x > 7
Learn more about inequalities
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If the area of a right-angled triangle is 47 56 cm and its height is 11.6 cm. finds its base.
Answer:
820
Step-by-step explanation:
Hi so if your area is 4756, the base would be 820
what is the y-intercept of the line that goes through (0, 0) (6, 3)
Answer:
QUESTION:
what is the y-intercept of the line that goes through (0, 0) (6, 3)
ANSWER:
Use the slope formula and the slope-intercept form to find the slope m and y-intercept b .
Slope: 1/2
y-intercept: (0,0)
Step-by-step explanation:
Hope that this helps you out! :)
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What is the angle of X
Answer:
∡x°=35°
Step-by-step explanation:
x° and 35° are vertical angles, so they are congruent to each other. Therefore, the measure of angle x° is also 35°
Graph the line with slope -1/2 passing through the point (-1,-2)
Answer:
See attachment for graph
Step-by-step explanation:
Given
[tex]m = -\frac{1}{2}[/tex]
[tex](x_1,y_1) = (-1,2)[/tex]
Required
Graph the line
First, is to determine the equation of the line using:
[tex]m = \frac{y - y_1}{x - x_1}[/tex]
So:
[tex]-\frac{1}{2} = \frac{y - 2}{x - -1}[/tex]
[tex]-\frac{1}{2} = \frac{y - 2}{x +1}[/tex]
[tex]\frac{-1}{2} = \frac{y - 2}{x +1}[/tex]
Cross multiply:
[tex](y -2) * 2 = -1 * (x + 1)[/tex]
[tex](y -2) * 2 = -x -1[/tex]
Solve for y - 2
[tex]y -2 = -\frac{x}{2} -\frac{1}{2}[/tex]
Solve for y
[tex]y = -\frac{x}{2} -\frac{1}{2} + 2[/tex]
[tex]y = -\frac{x}{2} +\frac{-1+4}{2}[/tex]
[tex]y = -\frac{x}{2} +\frac{3}{2}[/tex]
The above equation will then be plotted on the graph (See attachment)
Pls help 20 points !
Answer:
the answer is 168 is the answer
Find the surface area of the cylinder and round to the nearest tenth.
What will be the coordinates of the point K' if the point K(-5,4) is translated 3 units down?
Answer:
(-5,1)
Step-by-step explanation:
Because if you graph the point and move it 3 units down then that is your awnser.
A culture of bacteria has an initial population of 470 bacteria and doubles every 8 hours. Using the formula P_t = P_0\cdot 2^{\frac{t}{d}}P t =P 0 ⋅2 d t , where P_tP t is the population after t hours, P_0P 0 is the initial population, t is the time in hours and d is the doubling time, what is the population of bacteria in the culture after 7 hours, to the nearest whole number?
Answer:
Step-by-step explanation:
The population of bacteria in the culture after 7 hours is approximately 883.
What is an exponential function?Several real-world phenomena, including population expansion, radioactive decay, compound interest, and the spread of diseases, are modeled using exponential functions. In calculus, where they are used to define the exponential and logarithmic functions—essential ideas in calculus and other fields of mathematics—they also play a significant role.
Using the formula [tex]P_t = P_0 \times 2^{\frac{t}{d}}[/tex], where P_t is the population after t hours, P₀ is the initial population, t is the time in hours and d is the doubling time, we can find the population of bacteria in the culture after 7 hours as follows:
Since the initial population is 470, we have P₀ = 470.
The doubling time is 8 hours, so we have d = 8.
Substituting these values into the formula, we get:
[tex]P_7 = 470 \times 2^{\frac{7}{8}}[/tex]
P₇≈ 882.77
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An online music store sells songs on its website. each song is the same price. The cost to purchase 8 songs is $10.
A. Create an equation to represent the relationship between the total cost, c, and the number of songs, s, purchased.
B. At this rate, how many songs can be purchased for $25
Answer 8 divide by 10 =0.8
0.8x 25=20
Step-by-step explanation: i hope this helps
The equation for the total cost, c, in terms of the number of songs, s, purchased is c = 1.25s and $25 can purchase 20 songs.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
Let x be the price of each song.
The cost to purchase 8 songs is given as $10, so we can write the equation:
8x = 10
To find the equation for the relationship between the total cost, c, and the number of songs, s, purchased, we can solve for x:
8x = 10
x = 10/8
x = 1.25
So the price of each song is $1.25, and the equation for the total cost, c, in terms of the number of songs, s, purchased is:
c = 1.25s
To find how many songs can be purchased for $25, we can use the equation:
c = 1.25s
Substitute c = $25, and solve for s:
25 = 1.25s
s = 25/1.25
s = 20
Therefore, at this rate, $25 can purchase 20 songs.
Hence, the equation for the total cost, c, in terms of the number of songs, s, purchased is c = 1.25s and $25 can purchase 20 songs.
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A) 120
B) 125
C) 50
D) 100
6.If Addison types at a constant rate of 2 pages per hour, how many hours will it take to
type a paper that is 5 pages long?Immersive Reader
(20 Points)
0.4 hour
2.5 hours
5 hours
10 hours
Answer:
2.5 hours
Step-by-step explanation
it takes 1/2 a hour to write one page so do
5 x 1/2 which is 2.5 since there are 5 pages
Simplify 1/4^-2 x 1/4^-7
On the unit circle, an arc of length 2 subtends an angle, β. What is the radian measure of β?
Answer:
[tex](d)\ \beta = 2\ rad[/tex]
Step-by-step explanation:
Given
[tex]L =2[/tex] -- length of the arc
[tex]r = 1[/tex] --- radius of a unit circle
[tex]\beta =[/tex] the subtended angle
Required
Find [tex]\beta[/tex]
The length of an arc is:
[tex]L = r * \beta[/tex]
This gives:
[tex]2 = 1 * \beta[/tex]
[tex]2 = \beta[/tex]
Make [tex]\bets[/tex][tex]\beta[/tex] the subject
[tex]\beta = 2[/tex]
Hence:
[tex]\beta = 2\ rad[/tex]
Answer:
2rad
Step-by-step explanation:
Solve by elimination 4x - 4y = 8 -9x + 8y = -16
HELP PLZ!
The Fluffy Lump Cat Toy Company rents a warehouse facility. There
is a fixed cost of $1200 a month for rent and a variable cost of $5 per box of
toys that are stored. If the total cost for this month was $1315, how many boxes
of toys are being stored?
NO LINKS
Answer:
23 boxes of toys are being stored.
Step-by-step explanation:
There is a fixed cost of $1200 a month for rent and a variable cost of $5 per box of toys that are stored
This means that for x boxes of toys stored, the total cost is of:
[tex]C(x) = 1200 + 5x[/tex]
If the total cost for this month was $1315, how many boxes of toys are being stored?
This is [tex]x[/tex] for which [tex]C(x) = 1315[/tex]. So
[tex]C(x) = 1200 + 5x[/tex]
[tex]1315 = 1200 + 5x[/tex]
[tex]5x = 115[/tex]
[tex]x = \frac{115}{5}[/tex]
[tex]x = 23[/tex]
23 boxes of toys are being stored.
If one loaf of bread requires 450g of flour determine the maximum number of loaves of bread that can be baked from 12,5kg of flour
Aria recorded her daily lemonade stand profit during one week. Which data representation would you use to show her profit over the week? Explain how you would draw it and what you would expect to see
Answer:
Step-by-step explanation:
a line graph would show the data over time.I would plot the days along the horizontal axis and each daily profit at points on the vertical axis.I would connect the points with lines.If her profit increasing each day, I would expect the line height to increase over time.
Answer:
There is already another answer:
line graph or bar graph because it shows you what day of the week you sell more lemonade.
Step-by-step explanation:
gallon of
2
17. Mr. Jackson owns a vegetable juice stand. At the end of the day, he has
juice left. He pours an equal amount of the remaining juice mixture into 6 glasses.
What amount of juice does Mr. Jackson pour into each glass?
1
A.
gallon
12
B.
1
3
gallon
C. 3 gallons
D. 12 gallons
Answer:
12 gallons
Step-by-step explanation:
How many solutions exist for the system of equations below?
Answer Choices:
none
one
two
infinitely many
Answer:
None
Step-by-step explanation:
No solutions exist for the system of equations because the system is illogical: 3x+y=3x+y, but 18≠16.
Solve each of these equations. Explain or show your reasoning.
2(x+5)=3x+1
3y−4=6−2y
3(n+2)=9(6−n)
Convert the fraction 6/10 to a decimal.
Answer:
0.60
Step-by-step explanation:
Answer:
.60
Step-by-step explanation:
What does an individual's effective tax rate indicate?
A.
the average income earned
B.
the average tax rate
C.
the minimum tax rate
D.
the next year's tax rate
Answer:
d
Step-by-step explanation:
if the taxes raise each year
56,316 divided by 6 need step by step instructions
Answer:
9,386
Step-by-step explanation:
56,316 ÷ 6 = 9,386
Hope this Helps! :)
Have any questions? Ask below in the comments and I will try my best to answer.
-SGO
11x + x helppp plzzz
The product of 3m and 5r is 15mr True or False Explain...
Step-by-step explanation:
let's see....
3m × 5r = 15mr
15(m × r)
15mr.
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A graph shows the survey results for a group of students who
were asked how many honors classes they have taken and
how many elective classes:
Class Choices
Number of Elective Classes
0
lo 1 2 3
4
5 6 7 8
9 10 11
Number of Honors Classes
How many elective classes would students likely have taken if
they have taken 12 honors classes? (4 points)