Using the unit circle, the coordinates of the terminal point corresponding to [tex]\theta = 120^\circ[/tex] is: (-0.5, 0.866).
What is the unit circle?For an angle [tex]\theta[/tex] the unit circle is a circle with radius 1 containing the following set of points: [tex](\cos{\theta}, \sin{\theta})[/tex].
In this problem, the angle is of [tex]\theta = 120^\circ[/tex], hence:
[tex]\cos{\theta} = \cos{120^\circ} = -0.5[/tex].[tex]\sin{\theta} = \sin{120^\circ} = 0.866[/tex].Hence the terminal point is:
(-0.5, 0.866).
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Subject
mathematics, 06.11.2020 05:30 tonya3498
2. (15 points) sheila needs to hire a babysitter for the evening. the babysitter charges $10 for each
hour and also charges for the time she spends driving to and from the house. she thinks it will take
1.5 hours of total driving time. sheila is willing to spend $80 for the night for babysitting.
a. write an equation to determine for how many hours sheila can afford to hire the babysitter.
b. use the guess-and-check method to determine how many hours of babysitting sheila can
afford.
c. sheila finds another babysitter that lives much closer to her and would only need 1 hour of
driving time. however, she charges $15 per hour. write an equation to determine how many hours
of babysitting sheila could buy from her.
d. can sheila afford the same amount of babysitting from the second sitter as she could from the
first sitter?
a. The equation we get is 10(1.5 + x) = 80, where x is the number of hours Sheila can afford to hire the babysitter.
b. Sheila can afford the babysitter for 6 hours and 30 minutes.
c. The equation we get is 15(1 + x) = 80, where x is the number of hours Sheila can afford to hire the new babysitter.
d. Sheila can afford to hire the new babysitter for 4 hours and 20 minutes, while the first babysitter was hired for 6 hours and 30 minutes.
Thus, Sheila can't afford the same amount of babysitting from the second sitter as she could from the first sitter.
a. We assume the hours affordable to Sheila be x hours.
Per hour charge of the babysitter = $10.
Time taken by the babysitter traveling = 1.5 hours.
Therefore, total chargeable time = 1.5 + x.
Therefore, the total charge by the babysitter = $10(1.5 + x).
This needs to be equal to the amount Sheila is willing to spend, that is, $80.
Thus, the equation we get is: 10(1.5 + x) = 80.
b. We are asked to determine the hours Sheila can afford to hire the babysitter.
We have got the equation 10(1.5 + x) = 80, where x is the hours Sheila can afford to hire the babysitter.
Thus, by solving this equation, we can determine the hours Sheila can afford to hire the babysitter.
10(1.5 + x) = 80,
or, 1.5 + x = 8,
or, x = 8 - 1.5 = 6.5 = 6 hours and 30 minutes.
Thus, Sheila can afford the babysitter for 6 hours and 30 minutes.
c. Per hour charge of the new babysitter = $15.
Time taken by the new babysitter traveling = 1 hour.
Therefore, total chargeable time = 1 + x.
Therefore, the total charge by the new babysitter = $15(1 + x).
This needs to be equal to the amount Sheila is willing to spend, that is, $80.
Thus, the equation we get is: 15(1 + x) = 80.
d. We are asked whether Sheila affords the same amount of babysitting from the second sitter as she could from the first sitter.
To determine this, we need to find the hours she affords from the second babysitter, for which, we solve the equation 15(1 + x) = 80 as follows:
15(1 + x) = 80,
or, 1 + x = 80/15,
or, x = 80/15 - 1 = 65/15 = 13/3 = 4 hours and 20 minutes.
Sheila can afford to hire the new babysitter for 4 hours and 20 minutes, while the first babysitter was hired for 6 hours and 30 minutes.
Thus, Sheila can't afford the same amount of babysitting from the second sitter as she could from the first sitter.
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If p= the motorcycle's original price in dollars, which algebraic expression
represents the reduced price?
A. 275-p
B. 275p
C. 275+ p
D. p - 275
Answer: D
Step-by-step explanation:
If the original price was p, a price reduction would be p- the amount. Per the given answers, $275 is used for the reduction amount.
N=
Help me please!!! Asap thanks so much :)
Answer:
n = 100
Step-by-step explanation:
the area (A) of the sector is calculated as
A = area of circle × fraction of circle
given A = 40π , then
πr² × [tex]\frac{n}{360}[/tex] = 40π
π × 12² × [tex]\frac{n}{360}[/tex] = 40π
144π × [tex]\frac{n}{360}[/tex] = 40π ( divide both sides by π )
144 × [tex]\frac{n}{360}[/tex] = 40 ( multiply both sides by 360 to clear the fraction )
144n = 14400 ( divide both sides by 144 )
n = 100
A sample of bacteria is growing at an hourly rate of 15% according to the continuous exponential growth function. The sample began with 11 bacteria. How many bacteria will be in the sample after 21 hours
If the sample of bacteria is growing at an hourly rate of 15% continuously and the bacteria began with 11 bacteria then there will be 244.178 samples bacteria after 21 hours.
Given growth of bacteria 15% ,bacteria at beginning 11.
We have to find the number of sample of bacteria after 21 hours.
We have to first form exponential function which shows the growth of bacteria in variable t.
Exponential function which shows the sum is y=P[tex]e^{rt}[/tex]
where P is initial amount ,
r is rate and
y is the sum
So in our problem P=11 and r=0.15
y=11*[tex]e^{0.15t}[/tex]
To find the samples after 21 hours we have to put t=21.
y=11[tex]e^{0.15*21}[/tex]
y=11*[tex]e^{3.1}[/tex]
y=11*22.198 ([tex]e^{3.1}[/tex]=22.198 from e table)
y=244.178
Hence the samples after 21 hours will be 244 approximately.
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[tex]\frac{2x}{x+1} +\frac{3(x-1)}{x} =5[/tex]
Answer:
[tex]x=-3[/tex]
Step-by-step explanation:
Given equation:
[tex]\dfrac{2x}{x+1}+\dfrac{3(x+1)}{x}=5[/tex]
Make the denominators the same:
[tex]\implies \dfrac{2x}{x+1} \cdot\dfrac{x}{x}+\dfrac{3(x+1)}{x} \cdot \dfrac{x+1}{x+1}=5[/tex]
[tex]\implies \dfrac{2x^2}{x(x+1)}+\dfrac{3(x+1)^2}{x(x+1)} =5[/tex]
Combine the fractions:
[tex]\implies \dfrac{2x^2+3(x+1)^2}{x(x+1)} =5[/tex]
Multiply both sides by x(x+1):
[tex]\implies 2x^2+3(x+1)^2 =5x(x+1)[/tex]
Expand the brackets:
[tex]\implies 2x^2+3(x^2+2x+1) =5x^2+5x[/tex]
[tex]\implies 2x^2+3x^2+6x+3 =5x^2+5x[/tex]
Combine like terms:
[tex]\implies 5x^2+6x+3=5x^2+5x[/tex]
Subtract 5x² from both sides:
[tex]\implies 6x+3=5x[/tex]
Subtract 5x from both sides:
[tex]\implies x+3=0[/tex]
Subtract 3 from both sides:
[tex]\implies x=-3[/tex]
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Using the order of operations, what should be done first to evaluate 12 divided by (negative 6) (3) + (negative 2)?
According to the order of operations, brackets are solved first which contains the division operation. Hence, 12 is divided by -6 first.
Order of Operations
Given expression is,
(12 ÷ (-6))(3) + (-2)
According to the BODMAS rule of operations, the precedence order of operations is as follows,
Brackets > Of > Division > Multiplication > Addition > Subtraction
Hence, we will start by solving the brackets first, then solve the division and then the addition.
Evaluation
Solving the given expression as per the order of operations,
Brackets are solved first, then division followed by multiplication and then addition. Division is always of the highest precedence among all operations after brackets and of.
12 ÷ (-6)(3) + (-2)
= 12 ÷ (-6)(3) - 2 [∵ +(-n) = -n]
= (-2)(3) -2
= -6 - 2
= -8
Thus, solving the +(-2) and then division of 12 by (-6) are the first operations to be performed in order to evaluate the given expression.
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3. Assume that the likelihood of a child under the age of ten watching PBS is 0.76. Three children are
chosen at random. Use the binomial formula to calculate the following probabilities: (You must show
your work and round the solution to the nearest thousandths place.)
a. exactly two children will watch PBS
b. at most two children will watch PBS
C. at least 2 children will watch PBS
Using the binomial distribution, the probabilities are given as follows:
a) 0.4159 = 41.59%.
b) 0.5610 = 56.10%.
c) 0.8549 = 85.49%.
What is the binomial distribution formula?The formula is:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
The parameters are:
x is the number of successes.n is the number of trials.p is the probability of a success on a single trial.For this problem, the values of the parameters are:
n = 3, p = 0.76.
Item a:
The probability is P(X = 2), hence:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 2) = C_{3,2}.(0.76)^{2}.(0.24)^{1} = 0.4159[/tex]
Item b:
The probability is P(X < 3), hence:
P(X < 3) = 1 - P(X = 3)
In which:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 3) = C_{3,3}.(0.76)^{3}.(0.24)^{0} = 0.4390[/tex]
Then:
P(X < 3) = 1 - P(X = 3) = 1 - 0.4390 = 0.5610 = 56.10%.
Item c:
The probability is:
[tex]P(X \geq 2) = P(X = 2) + P(X = 3) = 0.4159 + 0.4390 = 0.8549[/tex]
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Quick algebra 1 question for 50 points!
Only answer if you know the answer, quick shout-out to Yeony2202, tysm for the help!
Answer:
Yes.
Step-by-step explanation:
Yes, the given line can be used to make reasonable predictions of the number of cheese pizzas that will be sold, since the scatter points clearly show a trend.
As time goes on, the number of pizzas sold is getting bigger, and the trend is what created the line.
The data was taken over 8 consecutive weeks, so we can assume that it can be used in our prediction.
Since the trend has been pretty consistent over periods of time, we can expect it to continue in the upcoming weeks.
If there are 4 green apple and 3 red apples, what's the probability that a red apple is picked?
Answer: 3/7
Step-by-step explanation:
Leticia was driving 45 miles per hour. after traveling for four hours she found that she was to 250 miles east of albertville
Answer:
can you give the question?
Step-by-step explanation:
didnt ask a question
Are the ratios 2:1 and 14:6 equivalent?
yes
no
Answer:
Step-by-step explanation:
To check this, we need to know whether
2
1
=
3
2
We have,
2
1
=
2×3
1×3
=
6
3
and
3
2
=
3×2
2×2
=
6
4
We find that
6
3
<
6
4
, which means that
2
1
<
3
2
.
Therefore, The ratio 1:2 is not equivalent to the ratio 2:3
Answer:
No, they aren't equal.
Step-by-step explanation:
solve for x
A)8
B)9
C)-9
D)-8
Answer:
C) -9
Step-by-step explanation:
x + 19 must be half x + 29 because triangles RBC and RST are similar by SAS and RB is half of RS and RC is half of RT.
2(x + 19) = x + 29
2x + 38 = x + 29
x + 38 = 29
x = -9
Which of the following is the graph of f(x) = x2 − 5x + 4? WILL MARK BRAINLIEST
A graph of a quadratic function with a minimum at 2, negative 9 and x intercepts at negative 1 and 5
B graph of a quadratic function with a minimum at 3, negative 4 and x intercepts at 1 and 5
C graph of a quadratic function with a minimum at 2.5, negative 2.4 and x intercepts at 1 and 4
D graph of a quadratic function with a minimum at negative 1.5, negative 6.2 and x intercepts at 1 and negative 4
C) graph of a quadratic function with a minimum at 2.5, negative 2.25 and x intercepts at 1 and 4
Step-by-step explanation:Standard Form of a Quadratic Function: ax² + bx + c = 0, where a ≠ 0
Given function: x² - 5x + 4
⇒ a = 1, b = -5, c = 4
The minimum of a function is the lowest point of its parabola. We can use the following formula to find the vertex or the minimum of the function: [tex]x=\dfrac{-b}{2a}[/tex] . This will give us the x-value of the vertex, and we will need to solve for the y-value.
The vertex or minimum.
Step 1: Find the x-value of the vertex.
[tex]\\\implies x=\dfrac{-(-5)}{2(1)}\\\\\implies x=\dfrac{5}{2}=2.5[/tex]
Step 2: Find the y-value of the vertex by substituting 2.5 as the value of x in the given function.
[tex]\\\implies x^2 - 5x + 4\\\\\implies 2.5^2-5(2.5)+4\\\\\implies 6.25-12.5+4\\\\\implies -2.25[/tex]
Vertex: (2.5, -2.25)
The x-intercepts (roots).
We can use the Quadratic Formula to find the roots of this function.
Quadratic Formula: [tex]x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex] when [tex]ax^2+bx+c=0[/tex]
Equation: x² - 5x + 4 = 0
⇒ a = 1, b = -5, c = 4
Step 1: Substitute the values of a, b, and c into the formula.
[tex]\\\implies x=\dfrac{\bold{-(-5)}\pm\sqrt{\bold{(-5)^2}\bold{-4(1)(4)}}}{\bold{2(1)}}\\\\\implies x=\dfrac{5\pm\sqrt{\bold{25-16}}}{2}\\\\\implies x=\dfrac{5\pm\sqrt{\bold{9}}}{2}\\\\\implies x=\dfrac{5\pm3}{2}[/tex]
Step 2: Separate into two possible cases.
[tex]x_1=\dfrac{5-3}{2}\implies \dfrac{2}{2}\implies \boxed{1}\\\\x_2=\dfrac{5+3}{2}\implies \dfrac{8}{2}\implies \boxed{4}[/tex]
The x-intercepts of the given function are 1 and 4.
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Find the cube of (x-1/3x)
Answer:
2/3x
Step-by-step explanation
Answer:
(x³-3x²-3x-1) / (27x³)
Step-by-step explanation:
((x-1) / (3x))³
= (x-1)³ / /3x)³
(x-1)³ = (x-1)(x-1)(x-1) = x³ - 3x² - 3x - 1
then:
(x-1)³ / (3x³) = (x³-3x²-3x-1) / (27x³)
Ali and Baba discovered an underground palace and set out to map all the treasure in it. After carefully mapping the interior, they found that the palace had a vault filled with treasure chests. In each chest, they found either 7 gold bars or 11 silver bars. There were 90 bars in total. How many of them were gold bars?
Answer:
396 gold bars
Step-by-step explanation:
first of all we will find numbers of gold bar 7*99
which is 693 and
we will find number of silver bars 11*99
which is 1089
then 1089-693=
396
what is the
area of
Rectangle with the length 3 XY
and width
14X2y
Answer: [tex]42x^3 y^2[/tex]
Step-by-step explanation:
[tex]A=(3xy)(14x^2 y)=42x^3 y^2[/tex]
Line a is perpendicular to line b. if the slope of line a is 7 what is the slope of line b
Answer:
1/7
Step-by-step explanation:
When 2 lines are perpendicular the gradient of one is the reciprocal of the other :
If the gradient of A was 2 the gradient of B would be 1/2.
If the gradient of a is 7 the gradient of b would be 1/7 .
Hope this helped and have a good day
Rule 1: Multiply by 2 then add 1 starting from 1.
Rule 2: Divide by 2 then add 4 starting from 40.
I need to make a sequence and I need help :)
PLease dont delete my question :(
Rule 1:
1, 3, 7, 15, 31, 63, 127, 255, 511, 1023 etc
Rule 2:
40, 24, 16, 12, 10, 9, 8.5, 8.25, 8.125, 8.0625 etc
Hope this helps!
A classroom contains an equal number of boys and girls. if 10 girls leave, twice as many boys as girls remain. what was the original number of students present?
the answer of this question is 38 and i hope it s correct
7 cm
Intro
5 cm
A
5 cm
D
4 cm
B
E
3 cm
3 cm
C
7 cm
Which face has an area of 28 cm²?
Face
4 of 10
Done
Answer:
Step-by-step explanation:
Solution
The length of all the rectangles is 7
You need the width to be 4
Area rectangle = L*w
Area rectangle = 7*4
Area rectangle = 28
Answer: B
verify commutative property of multiplication and addition 5 4
- -
2 5
then what will the answer of this with prof and detaling
The commutative property of multiplication addition is illustrated below.
How to illustrate the information?The commutative property implies that the changing of orders of the numbers doesn't have a effect on the value.
In this case, 5 × 4 = 20. Also, changing them to 4 × 5 is still 20.
Likewise 2 + 5 as 5 + 2 gives 7.
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Determine if the following lines are parallel (never intersect), perpendicular (intersect at a 90 degree angle), intersecting (intersect at just one point), or coinciding (intersect at all points)?
y = -6x − 8, -x + 6y = 12
Answer:
These lines are perpendicular.
Step-by-step explanation:
Put both equations in the slope intercept form of a line.
y = -6x - 8 This is already in the slope intercept form for a line
-x + 6y = 12 Add x to both sides of the equation
6y = x + 12 Divide through the whole equation by 6
y = 1/6x +2
Now we compare the two slopes of -6 and 1/6. They are negative reciprocals of each other. That means that the line are perpendicular.
The number of bacteria in a certain population increases according to a continuous exponential growth model with a growth rate parameter of 4.9% per hour how many hours does it take for the size of the sample to double
Answer:
14.5 hours to the nearest tenth.
Step-by-step explanation:
4.9% = 0.049.
If the original number is 50 it will double to 100 so
100 = 50(1.049)^t
1.049^t = 2
t * log 1.049 = log 2
t = log 2 / log 1.049
= 14.49 hours,
You are _____ to commit a Type I error using the 0.05 level of significance than using the 0.01 level of significance. Group of answer choices more likely less likely equally likely twice as likely
More likely -You are more likely to commit a Type I error
According to statement
we have to find the type 1 error by using the significant levels.
we are commit a MORE LIKELY to find the error by rejecting a true null hypothesis using the 0.05 level of significance than using the 0.01 level of significance.
So, More likely -You are more likely to commit a Type I error
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Quick algebra 1 question for 25 points!
Only answer if you know the answer, quick shout-out to Dinofish32, tysm for the help!
Yes
It's inverse variationSee
3 contractors took 8hours
4 contractors took 6hours
We observe
No of contracter increases hence time decreasesSo it's inverse variation
Answer:
[tex]\fbox {Yes}[/tex]
Step-by-step explanation:
An inverse variation can be seen when two factors are compared, if one factor is seen to be increasing, then naturally the factor should be decreasing.
Here, as the number of contractors increase, the time taken to complete the work decreases.
∴ Hence, this represents an inverse variation.
On a coordinate plane, line k l goes through (negative 6, 8) and (6, 0). point m is at (negative 4, negative 2). which point could be on the line that is parallel to line kl and passes through point m?
The equation of the line parallel to the line KL passing through the points (-6, 8) and (6, 0), and going through the point M (-4, -2) is 2x + 3y = -6. The point satisfying this equation is (-6, 2). Thus, the 2nd option is the right choice.
Slope of the line KL = (8 - 0)/(-6 - 6) = 8/(-12) = -2/3.
Using the formula of the slope of the line passing through the points (x₂, y₂) and (x₁, y₁), as m = (y₂ - y₁)/(x₂ - x₁).
The slope of the line parallel to the line KL will be equal to the slope of KL.
Thus, the slope of the required line is m = -2/3.
The required line also passes through point M (-4, -2).
Thus, the equation of the required line will be,
y - (-2) = (-2/3)(x - (-4)) {Using the equation of the line passing through the point (x₁, y₁) and a slope m, as y - y₁ = m(x - x₁)},
or, y + 2 = (-2/3)(x + 4),
or, 3(y + 2) = -2x - 8,
or, 2x + 3y = -6.
From the given points, only the point (-6, 2) satisfies the equation.
Thus, the equation of the line parallel to the line KL passing through the points (-6, 8) and (6, 0), and going through the point M (-4, -2) is 2x + 3y = -6. The point satisfying this equation is (-6, 2). Thus, the 2nd option is the right choice.
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The provided question is incomplete. The complete question is:
"On a coordinate plane, line K L goes through (negative 6, 8) and (6, 0). Point M is at (negative 4, negative 2). Which point could be on the line that is parallel to line KL and passes through point M?
(–10, 0)
(–6, 2)
(0, –6)
(8, –10)"
The volume of a cone is 37x³ cubic units and its height is x units.
Which expression represents the radius of the cone's base, in units?
3x
6x
О Злх2
97X2
The radius of the cone's base in the unit is 9*7x².
Which expression represents the radius of the cone's base, in units?Given:
The volume of a cone is 3*7x³ cubic units Its height is x units.To find:
The expression represents the radius of the cone's base, in units.Solution:
As we know, the volume of the cone formula is
V = πr²h/3
So, lets us compare the above formula with the given expression;
πr²h/3 = 3*7x³
Here, h is represented as x, we get;
πr²x/3 = 3*7x³
πr²/3 = 3*7x²
r²= 9*7x²
Hence, the radius of the cone's base, in units, is 9*7x².
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Solve for x and show your steps. Is the solution extraneous? Check your work to show how you determined if the solution is extraneous or not.
The square root of the quantity 3 x plus 12 end quantity equals 9.
The value of x from the given expression is 23
Radical equationsGiven the following equation
√3x+12 = 9
Square both sides
√3x+12)² = 9²
3x + 12. = 81
Subtract 12 from both sides
3x + 12 - 12 = 81- 12
3x = 69
x = 23
Hence the value of x from the given expression is 23
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Help please!!!!
Will give brainliest
The amplitude, Period, Horizontal Shift and Vertical Shift of both graphs are as detailed below.
How to interpret features of trigonometric Graphs?
3)a. Amplitude is the distance between the center line and the positive or negative peak of the graph. Thus, the amplitude is 0.5.
b. The period is the time it takes for the graph to repeat or complete one cycle and in this graph, it is 3.
c. Looking at the graph, ideally the coordinate (3, -1.5) should have been on the y-axis which is at (0, -1.5). This means it was shifted by 3 units to the right side.
d. The positive peak should be equal to the negative peak but in this case, it is not so and as such the center should be on the x-axis which means that the graph was shifted down vertically by 2 units.
4) a. Amplitude is the distance between the center line and the positive or negative peak of the graph. Thus, the amplitude is 3 - 1 = 2
b. The period is the time it takes for the graph to repeat or complete one cycle and in this graph, it is 6.
c. Looking at the graph, ideally the coordinate (4, -1) should have been on the y-axis which is at (0, -1). This means it was shifted by 4 units to the right side.
d. The positive peak should be equal to the negative peak but in this case, it is not so and as such the center should be on the x-axis which means that the graph was shifted up vertically by 1 unit.
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(‼️‼️I WILL MARK BRAINLIEST PLEASE HELP‼️‼️)Dilate the figure by the scale factor. Then enter
the new coordinates.
K = 5
(-3,-1)
A
(-1,-4) C
B(2,-2)
A' ([?], [ ])
B' ([ ], [ ])
C' ([ ], [ ])
Triangle ABC is dilated by a scale factor of 5 to get A'(-15, -5), B'(10, -10) and C'(-5, -20)
What is transformation?Transformation is the movement of a point from its initial location to a new location. Types of transformations are reflection, translation, rotation and dilation.
Rigid transformation preserves the shape and size of the figure. Reflection, translation, rotation are rigid transformations.
Triangle ABC has vertices at A(-3, -1), B(2, -2) and C(-1, -4). It is then dilated by a scale factor of 5 to get A'(-15, -5), B'(10, -10) and C'(-5, -20)
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