Answers
Answer:
When Ø = 300°, Ø = 60 degrees.
When Ø = 225°, Ø = 45 degrees.
When Ø = 480°, Ø = 60 degrees.
When Ø = -210°, Ø = 30 degrees.
Step-by-step explanation:
Reference angles are in Quadrant I (0° to 90°).
1. Find 300° (Quadrant IV) on the unit circle. Since it's in Quadrant IV, you use 360 - 300 = 60° to get your answer.
2. Find 225° (Quadrant III) on the unit circle. Since it's in Quadrant III, you use 225 - 180 = 45° to get your answer.
3. The angle 480° is not on the unit circle. To find its corresponding angle between 0° and 360°, use 480 - 360 = 120°. Then, find 120° (Quadrant II) on the unit circle. Since it's in Quadrant II, you use 180 - 120 = 60° to get your answer.
4. The angle -210° is not on the unit circle. To find its corresponding angle between 0° and 360°, use -210 + 360 = 150°. Then, find 150° (Quadrant II) on the unit circle. Since it's in Quadrant II, you use 180 - 150 = 30° to get your answer.
Related Questions
Find the common difference of the arithmetic sequence. 4, 10, 16, 22, . . .
Answers
Answer:
6
Step-by-step explanation:
10 - 4 = 6
16 - 10 = 6
22 - 16 = 6
Answer:6
Step-by-step explanation:
1) 10-4=6
2) 16-10=6
3) 22-16=6
find the total number of terms.32,256,2048,16384,......,2⁵⁰
Answers
Answer:
16 termsStep-by-step explanation:
32,256,2048,16384,......,2⁵⁰
32=2⁵
256=2⁸
2048=2¹¹
16384=2¹⁴
2⁵, 2⁸, 2¹¹,2¹⁴, ….,2⁵⁰
[tex]t_{1}[/tex]=2⁵; [tex]t_{2}[/tex]=2⁸
r=2⁸:2⁵=2³
[tex]t_{n}[/tex]=[tex]t_{1}[/tex]*[tex]r^{n-1}[/tex]
2⁵*[tex]2^{3(n-1)}[/tex] =2⁵⁰
5+3(n-1)=50
3n-3=45
3n=48
n=48:3
n=16
So, 16 terms
Find a power series for the function, centered at c. f(x) = 1 9 − x , c = 4 f(x) = [infinity] n = 0 Incorrect: Your answer is incorrect. Determine the interval of convergence. (Enter your answer using interval notation.)
Answers
Looks like the given function is
[tex]f(x)=\dfrac1{9-x}[/tex]
Recall that for |x| < 1, we have
[tex]\displaystyle\frac1{1-x}=\sum_{n=0}^\infty x^n[/tex]
We want the series to be centered around [tex]x=4[/tex], so first we rearrange f(x) :
[tex]\dfrac1{9-x}=\dfrac1{5-(x-4)}=\dfrac15\dfrac1{1-\frac{x-4}5}[/tex]
Then
[tex]\dfrac1{9-x}=\displaystyle\frac15\sum_{n=0}^\infty\left(\frac{x-4}5\right)^n[/tex]
which converges for |(x - 4)/5| < 1, or -1 < x < 9.
I need help for this problem!
Answers
Answer:
[tex] a = 2.7 [/tex]
Step-by-step explanation:
Distributive property can be used to solve the equation, by multiplying [tex] \frac{2}{3} [/tex] with [tex] 6a, [/tex] and [tex] 9 [/tex]
Thus,
[tex] (\frac{2}{3}*6a) + (\frac{2}{3}*9) = 16.8 [/tex]
[tex] 2*2a + 2*3 = 16.8 [/tex]
[tex] 4a + 6 = 16.8 [/tex]
Subtract 6 from both sides.
[tex] 4a + 6 - 6 = 16.8 - 6 [/tex]
[tex] 4a = 10.8 [/tex]
Divide both sides by 4 to solve for a
[tex] \frac{4a}{4} = \frac{10.8}{4} [/tex]
[tex] a = 2.7 [/tex]
HELP!!! Evaluate 8^P7
Answers
The correct answer is B. 40,320
Explanation:
In mathematics, a permutation refers to all the possible ways of arranging objects or elements in a set, while still considering an order. For example, you can calculate all the possible ways 5 athletes can end in a race as one athlete cannot have both the first and third place. The expression [tex]{8}[/tex][tex]P_{7}[/tex] shows a permutation because the P indicates the expression refers to a permutation. Additionally, this can be solved by using the formula [tex]{n}[/tex][tex]P_{r}[/tex] =[tex]\frac{n!}{(n-r)!}[/tex]. This means, in the expression presented n = 8 while r = 7. Also, the symbol (!) indicates the number should be multiplied using all whole numbers minor to the given number until you get to 1, which is known as factorial functions. The process is shown below:
[tex]{n}[/tex][tex]P_{r}[/tex] =[tex]\frac{n!}{(n-r)!}[/tex] [tex]{8}[/tex][tex]P_{7}[/tex] = [tex]\frac{8!}{(8-7) !}[/tex][tex]{8}[/tex][tex]P_{7}[/tex] = [tex]\frac{8!}{1!}[/tex][tex]{8}[/tex][tex]P_{7}[/tex] = [tex]\frac{8 x 7 x 6 x 5 x 4 x 3 x 2 x 1}{1}[/tex] or 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 / 1
[tex]{8}[/tex][tex]P_{7}[/tex] = 40320
If a line with the slope of -1 goes through the point (-2,-2), then solve for b: y=mx+b
Answers
Answer:
b = -4
Step-by-step explanation:
Well we already have m which is slope which is -1.
And if we start at (-2,-2) and go down using the slope we get -4 as the y intercept or b.
Thus,
-4 is the y intercept or b.
Hope this helps :)
Answer:
b = -4.
Step-by-step explanation:
In this case, y = -2, m = -1, and x = -2.
-2 = (-1) * (-2) + b
-2 = 2 + b
b + 2 = -2
b = -4
Hope this helps!
please I need help with this question!
The weight of adult males in Boston are normally distributed with mean 69 kilograms and variance 25 kilograms.
I. what percentage of adult male in Boston weigh more than 72 kilograms?
ii. what must an adult male weigh in order to be among the heaviest 10% of the population?
Thank you in advance!
Answers
Answer:
I. 60%
II. 75.4 kg
Step-by-step explanation:
We will use the z-scores and the standard normal distribution to answer this questions.
We have a normal distribution with mean 69 kg and variance 25 kg^2 (therefore, standard deviation of 5 kg).
I. What percentage of adult male in Boston weigh more than 72 kg?
We calculate the z-score for 72 kg and then calculate the associated probability:
[tex]z=\dfrac{X-\mu}{\sigma}=\dfrac{72-69}{5}=\dfrac{3}{5}=0.6\\\\\\P(X>72)=P(z>0.6)=0.274[/tex]
II. What must an adult male weigh in order to be among the heaviest 10% of the population?
We have to calculate tha z-score that satisfies:
[tex]P(z>z^*)=0.1[/tex]
This happens for z=1.28 (see attachment).
Then, we can calculate the weight using this transformation:
[tex]X=\mu+z^*\cdot\sigma=69+1.28\cdot 5=69+6.4=75.4[/tex]
i will give brainliest and 50 points pls help ASP
Answers
Answer:
2064 cm squared
Step-by-step explanation:
First I will try to solve for the area of each side:
Side #1(trapezoid): Area of a Trapezoid = half of sum of bases*height
A= (6+27)/2*8 = 33/2 *8 =132
Side #2(opposite trapezoid): Same area as theother one...
A= 132
Side#3(Top):
A=6*30=180
Side #4(Bottom):
A=27*30=810
Side #5(Left side):
A=10*30=300
Side #6(Right Side):
A=30*17=510
After solving for all the areas we just need to add them all up:
SA=132+132+180+810+300+510=2064 cm squared
Hope this helps!
Answer:
total surface area = 2064 cm^2
Step-by-step explanation:
Given prism with trapezoidal bases.
H=8
B1 = 27
B2 = 6
slant sides = 10, 17 cm
H = 30
Area of bases
A1 = 2 * (B1+B2)/2 * h
= 2* ( (27+6)/2 * 8 )
= 264
Area of sides
A2 = perimeter * H
= (6+17+27+10)*30
= 1800
Total area = A1+A2 = 264+1800 = 2064 cm^2
2 lines connect to form a right angle. A third line extends between the 2 lines to form 2 angles which are labeled 1 and 2. Angles 1 and 2 are complementary and congruent. What is the measure of angle 1? 30° 45° 50° 75°
Answers
Answer:
the correct answer is 45°
Answer:
45 degrees.
Explanation: This is the correct answer on Edge 2021, just took the Unit test and made a 100%. Hope this helps ^-^.
The following are the weekly amounts of welfare payments made by the federal government to a sample of six families: $139, $136, $130, $136, $147, and $136. What is the range
Answers
Answer:
$17
Step-by-step explanation:
data:
$139 $136 $130 $136 $147 $136In statistics, the range is the difference between the highest value and the lowest value of the data set.
Highest value = $147
Lowest value = $130
Range = $17
Dimitri is solving the equation x2 – 10x = 21. Which value must be added to both sides of the equation to make the left side a perfect-square trinomial?
Answers
Answer:
[tex]\boxed{\sf \ \ 25 \ \ }[/tex]
Step-by-step explanation:
Hello,
we can see that
[tex]x^2-10x = x^2-2*5x[/tex]
is the beginning of
[tex]x^2-2*5x+5^2=(x-5)^2[/tex]
so we must add 5*5=25 to both sides of the equation to make the left side a perfect square trinomial
hope this helps
Answer:
25.
Step-by-step explanation:
To find the value that will make the left side a perfect-square trinomial, you need to find (b/2)^2. In this case, b = -10.
(-10 / 2)^2
= (-5)^2
= (-5) * (-5)
= 25
Once you add 25 to both sides, the left side becomes x^2 - 10x + 25, which is equal to (x - 5)^2.
Hope this helps!
Suppose , varies jointly with g and v, and j = 2 when g = 4 and v= 3.
Find j when g = 8 and v= 11.
Answers
Answer:
j = 44/3
Step-by-step explanation:
j varies jointly as g and v. This can be represented mathematically as:
[tex]j \alpha gv\\j = kgv[/tex].............(1)
Where k is a constant of proportionality
j = 2 when g = 4 and v = 3
Substitute these values into equation (1)
2 = k * 4 * 3
2 = 12 k
k = 1/6
when g = 8 and v = 11:
j = (1/6) * 8 * 11
j = 44/3
About 9% of the population has a particular genetic mutation. 600 people are randomly selected.
Find the standard deviation for the number of people with the genetic mutation in such groups of 600.
Answers
Answer:
The mean for all such groups randomly selected is 0.09*800=72.
Step-by-step explanation:
The value of the standard deviation is 7.
What is the standard deviation?Standard deviation is defined as the amount of variation or the deviation of the numbers from each other.
The standard deviation is calculated by using the formula,
[tex]\sigma = \sqrt{Npq}[/tex]
N = 600
p = 9%= 0.09
q = 1 - p= 1 - 0.09= 0.91
Put the values in the formulas.
[tex]\sigma = \sqrt{Npq}[/tex]
[tex]\sigma = \sqrt{600 \times 0.09\times 0.91}[/tex]
[tex]\sigma[/tex] = 7
Therefore, the value of the standard deviation is 7.
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Determine if the field Bold Upper F equals 10 yz Bold i plus 10 xz Bold j plus 10 xy Bold k is conservative or not conservative.
Answers
F is conservative if we can find a scalar funciton f such that grad(f) = F.
This would entail
[tex]\dfrac{\partial f}{\partial x}=10yz[/tex]
[tex]\dfrac{\partial f}{\partial y}=10xz[/tex]
[tex]\dfrac{\partial f}{\partial z}=10xy[/tex]
Integrate both sides of the first equation with respect to x :
[tex]f(x,y,z)=10xyz+g(y,z)[/tex]
Differentiate both sides with respect to y :
[tex]\dfrac{\partial f}{\partial y}=10xz=10xz+\dfrac{\partial g}{\partial y}[/tex]
[tex]\implies\dfrac{\partial g}{\partial y}=0\implies g(y,z)=h(z)[/tex]
Differentiate both sides with respect to z :
[tex]\dfrac{\partial f}{\partial z}=10xy=10xy+\dfrac{\mathrm dh}{\mathrm dz}[/tex]
[tex]\implies\dfrac{\mathrm dh}{\mathrm dz}=0\implies h(z)=C[/tex]
So we have
[tex]f(x,y,z)=10xyz+C[/tex]
that satisfies
[tex]\nabla f(x,y,z)=\mathbf F(x,y,z)[/tex]
and so F is indeed conservative.
Subtracting polynomials
Answers
Answer:
The third side of the triangle is 10x + 3
Step-by-step explanation:
x + 1 + 2x + 4 = 3x + 5
( 13x + 8 ) - ( 3x + 5 ) = 13x + 8 - 3x - 5
= 10x + 3
You work at a coffee house. Roasted coffee beans retain approximately 3/5 of their initial weight. Approximately what percent of their inital weight do they retain?
Answers
Answer:
60%
Step-by-step explanation:
We need convert 3/5 into a percent in order to find the answer.
We can convert by first dividing 3 by 5 to find the decimal value.
3/5= .6
Now we need to multiply by 100 to make it a percentage
.6 x 100= 60
60%
1. find x and y 2. find the measure of each side of LMN
Answers
Answer:
X= 3
Y= 18
Each side of the triangle= 10 units
Step-by-step explanation:
LMN is equilateral so
LM = MN
3x+1= 4x-2
3x-4x = -2-1
-x = -3
X= 3
MP is the perpendicular bisector of line LN
so definitely angle lpm =90.
And lpm = 5y = 90
5y = 90
Y= 90/5
Y = 18°
For the side of the triangle
3x+1
But x= 3
3(3)+1
9+1
10
Each side of the triangle= 10 units
About 30% of babies born with a certain ailment recover fully. A hospital is caring for five babies born with this ailment. The random variable represents the number of babies that recover fully. Decide whether the experiment is a bnomial experiment. If it is identify a success, specify the values of n,p, and q and list the possible values of hte random variable x.
1. Specigy the value of n. Select the correct choice bellow and fill in any answer boxes in your choice.
A. n=
B. This is not a binomial experiment
2. Specify the value of p. Select the correct choice below and fill in any answer boxes in your choice
A p=
B. This is not a binomial experiment.
3. Specify the value of q. Select the correct choice below and fill in any answer boxes in your choice.
A. q=
B. This is not a binomial experiment
Answers
Answer:
n = 5 (a)p = 0.3 (a)q = 0.7 (a)Step-by-step explanation:
From the Given data in the above question it can be said that the experiment is a Binomial experiment because there is a success rate and a failure rate involved and the success rate is about 30% of the babies recovering from the ailment while the failure rate is about 70% of the babies not recovering from the ailment
The number of babies (n) = 5
success rate (p) = 30% = 0.3
failure rate (q) = 100% - 30% = 70% = 0.7
The possible values of the random value x = from 0 to 5
the substitution method solve 6x-y=3 4x+3y=1
Answers
4x+3y=1
4x+3(-3 + 6x) = 1
4x-9+18x-1=0
22x= 0
22x= -8
x = -8/22 = -4/11
Answer:
[tex]( \frac{5}{11} \:, - \frac{3}{11} )[/tex]Step-by-step explanation:
6x - y = 3
4x + 3y = 1
Solve the equation for y
y = -3 + 6x
4x + 3y = 1
Substitute the given value of y into the equation
4x + 3y = 1
plug the value
[tex]4x + 3( - 3 + 6x) = 1[/tex]
Distribute 3 through the parentheses
[tex]4x - 9 + 18x = 1[/tex]
Collect like terms
[tex]22x - 9 = 1[/tex]
Move constant to R.H.S and change its sign
[tex]22x = 1 + 9[/tex]
Calculate the sum
[tex]22x = 10[/tex]
Divide both sides of the equation by 22
[tex] \frac{22x}{22} = \frac{10}{22} [/tex]
Calculate
[tex]x = \frac{5}{11} [/tex]
Now, substitute the given value of x into the equation
y = -3 + 6x
[tex]y = - 3 + 6 \times \frac{5}{11} [/tex]
Solve the equation for y
[tex]y = - \frac{3}{11} [/tex]
The possible solution of the system is the ordered pair ( x , y )
[tex](x ,\: y) = ( \frac{5}{11} ,\: - \frac{3}{11} )[/tex]-----------------------------------------------------------
Check if the given ordered pair is the solution of the system of equations
[tex]6 \times \frac{5}{11} - ( - \frac{3}{11} ) = 3[/tex]
[tex]4 \times \frac{5}{11 } + 3 \times ( - \frac{3}{11} ) = 1[/tex]
Simplify the equalities
[tex] 3 = 3[/tex]
[tex]1 = 1[/tex]
Since all of the equalities are true , the ordered pair is the solution of the system
[tex]( \: x ,\: y \: ) = ( \frac{5}{11} \:, - \frac{3}{11} )[/tex]Hope this helps..
Best regards!!
Solve for x: [X - 3] + [x + 5]= 10
Answers
Answer:
x = 4Step-by-step explanation:
[X - 3] + [x + 5]= 10
Remove the parenthesis
That's
x - 3 + x + 5 = 10
Simplify
2x + 2 = 10
2x = 10 - 2
2x = 8
Divide both sides by 2
x = 4Hope this helps you
What scenario depicts two independent events
Answers
Step-by-step explanation:
A t
eacher is calling on students to present their reports. He calls on Mario first and then chooses the next presenter from the remaining students. The girls’ basketball team is playing against the boys’ basketball team. The coach chooses a captain for the girls’ team and then chooses a captain for the boys’ team. Yasmin is picking flowers from a garden to create a bouquet. She picks a flower, keeps it for the bouquet, and then she picks another. Felipe is making a dentist appointment. First he chooses the day for his appointment, and then he chooses the time from the available openings.
Answer:
A.The school play opens tonight and it is raining.
B.Neva is hungry and she buys a snack from the concession stand.
C. Ari chooses a partner for a group project and then Ezekial chooses a partner from the remaining classmates.
D.Luka paints during school and he stains his shirt.
Suppose that your uncle is decorating his house for christmas.He uses 300 strands of lights each containing 150 light bulbs.Each light bulb consumes 4 watts of power. If he illuminates his light for 5 hours a day for 30 days and power in his area sells for $0.08/kWh, how much will he end up paying to light his home for the holidays?
Answers
Answer:
$14.4
Step-by-step explanation:
From the question;
There are 300 strands of light each containing 150 light bulbs. Altogether, there are;
300 x 150 light bulbs = 45000 light bulbs.
Also;
Each bulb consumes 4 watts of power. Since there are 45000 light bulbs, the total power consumed by all the bulbs is;
45000 x 4 watts = 180000watts
Next convert the total power consumed to kW by dividing by 1000. i.e
180000watts = 180kW
Therefore, total power consumed is 180kW
He lights up for 5 hours a day for 30 days. This means that the total number of hours he lights his home for those 30 days is:
30 x 5 hours = 150 hours.
Now since power in his area sells for $0.08/kWh, this means that;
1kWh costs $0.08
Then;
180kWh will cost [180kWh x $0.08 / 1kWh] = $14.4
Therefore, he will end up paying $14.4 to light his home for the holidays.
Over what interval is the function in this graph increasing?
5
-6
-5
Answers
In a large university, 20% of the students are business majors. A random sample of 100 students is selected, and their majors are recorded. a) Compute the standard error of the proportion. b) What is the probability that the sample contains at least 12 business majors
Answers
Answer:
a. 0.04
b. 0.9772
Step-by-step explanation:
Please check attachment for complete solution and step by step explanation
Determine the height of the tree to the nearest foot
Answers
Answer:
80 ft
Step-by-step explanation:
in similar triangles sides are proportional.
[tex]\frac{176}{h} =\frac{120+100}{100} =\frac{220}{100} =\frac{22}{10} \\h=\frac{10}{22} \times 176=80[/tex]
h=80 ft
find the value of a. A: 15, B: 19
Answers
Answer:
A: 15
Step-by-step explanation:
The angles are opposite to each other.
Vertically opposite angles are equal in size.
Put up an equation and solve for a.
6a + 10 = 3a + 55
Subtract 3a and 10 on both sides.
6a - 3a = 55 - 10
Combining like terms.
3a = 45
Divide both sides by 3.
a = 45/3
a = 15
The value of a is 15.
Answer:
a = 15
Step-by-step explanation:
=> 6a + 10 = 3a + 55 (Vertically Opposite Angles are congruent)
Combining like terms
=> 6a - 3a = 55 - 10
=> 3a = 45
Dividing both sides by 3
=> a = 15
What is the range of the function (-1,2) (3,6) (5,8)
Answers
Answer:
Range { 2,6,8}
Step-by-step explanation:
The domain is the input and the range is the output
Range { 2,6,8}
Answer:
2, 6, 8
Step-by-step explanation:
The range is the possible values of y, (x, y). So in this case, y could be 2, 6, or 8.
A city's population is currently 50,000. If the population doubles every 70 years, what will the population be 280 years from now?
Answers
Answer:
200,000
Step-by-step explanation:
The current population: 50,000
Doubling time:70
Population after 280 years=?
280/70=4
50,000*4=200,000
Hope this helps ;) ❤❤❤
Answer: 800,000
Step-by-step explanation: 50,000x2=100,000. That is after 70 years. 100,000x2=200,000. This is after 140 years. 200,000x2=400,000. This is after 210 years. 400,000x2=800,000. This is after 280 years.
The Stanford-Binet Intelligence Scale is an intelligence test, which, like many other IQ tests, is standardized in order to have a normal distribution with a mean of 100 and a standard deviation of 15 points.
As an early intervention effort, a school psychologist wants to estimate the average score on the Stanford-Binet Intelligence Scale for all students with a specific type of learning disorder using a simple random sample of 16 students with the disorder. Determine the margin of error, m, of a 99% confidence interval for the mean IQ score of all students with the disorder. Assume that the standard deviation IQ score among the population of all students with the disorder is the same as the standard deviation of IQ score for the general population, sigma = 15 points.
Answers
Answer:
The margin of error is [tex]MOE = 9.68[/tex]
Step-by-step explanation:
From the question we are told that
The sample size is [tex]n= 16[/tex]
The standard deviation is [tex]\sigma = 15[/tex]
The confidence level is [tex]C = 99[/tex]%
Generally the level of significance is mathematically evaluated as
[tex]\alpha = 100 - C[/tex]
[tex]\alpha = 100 - 99[/tex]
[tex]\alpha = 1%[/tex]%
[tex]\alpha = 0.01[/tex]
The critical value of [tex]\frac{\alpha }{2}[/tex] obtained from the normal distribution table is
[tex]Z_{\frac{\alpha }{2} } = 2.58[/tex]
The reason obtaining the critical value of [tex]\frac{\alpha }{2}[/tex] instead of [tex]\alpha[/tex] is because we are considering the two tails of the area normal distribution curve which is not inside the 99% confidence interval
Now the margin of error is evaluated as
[tex]MOE = Z_{\frac{\alpha }{2} } * \frac{\sigma}{\sqrt{n} }[/tex]
substituting values
[tex]MOE = 2.58 * \frac{15}{\sqrt{16} }[/tex]
[tex]MOE = 9.68[/tex]
In the diagram of RST, which term describes point U?
A.
Circumcenter
B.
Centroid
C.
Incenter
D.
Orthocenter
Answers
A triangle is a three-edged polygon with three vertices. It is a fundamental form in geometry. The correct option is C, Incenter.
What is a triangle?A triangle is a three-edged polygon with three vertices. It is a fundamental form in geometry. The sum of all the angles of a triangle is always equal to 180°.
In a triangle, the point at which all the angle bisectors of the triangle meet is known as the Incenter.
Since In ΔRST, all the angles are bisected by the angle bisector, and the point at which all the angle bisectors meet is represented by U. Thus, it can be concluded that the point U represents the incenter of the triangle.
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