By using the concepts of unit circle and trigonometric functions, we find that the angle OA, whose x-coordinate is 0.222, has a measure of approximately 77.173°.
How to find an angle in an unit circle
Unit circles are circles with radius of 1 and centered at the origin of a Cartesian plane, which are used to determine angles and trigonometric functions related to them. If we use rectangular coordinate system and the definition of the tangent function, we find that the angle OA is equal to:
[tex]\tan \theta = \frac{\sqrt{1 - x^{2}}}{x}[/tex]
[tex]\tan \theta = \frac{\sqrt{1-0.222^{2}}}{0.222}[/tex]
tan θ ≈ 77.173°
By using the concepts of unit circle and trigonometric functions, we find that the angle OA, whose x-coordinate is 0.222, has a measure of approximately 77.173°.
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The measures of the angles In alinear pair are x degree and (x+25) degree. Find the measures of each of them
Answer:
77.5° and
102.5°
Step-by-step explanation:
Angles in a linear pair sum up to 180°
Therefore, x + (x +25) = 180
x + x +25 = 180
2x + 25 = 180
2x = 180- 25
2x 155°
dividing bothsides by 2
x = 155/2
x = 77.5
Therefore,
x = 77.5°
(x+25) = 77.5 + 25 = 102.5°
are the two figures similar? if so give the similarity ratio of the smaller figure to the larger figure.
explain why or why not
Answer:
Not similar
Step-by-step explanation:
They are not similar because the ratio is not the same. 42/35 = 1.2 and 14/10=1.4
Sketch the graph of f(x) = log2x
7.1 Write down the domain of f.
7.2 Write down the equation of f^-1 in the form y=_
7.3 Write down the equation of the asymptote of f^-1
7.4 Explain how, using the graph of f, you would sketch
7.4.1 g(x) = log2 x
The graph of the functions f(x) and g(x) are the same
The sketch of the graph of the functionThe function is given as:
f(x) = log₂(x)
See attachment for the sketch of the graph.
The domain of fFrom the graph, we can see that the x values are greater than 0
This means that the domain of f is x > 0
The equation of f⁻¹(x)We have:
f(x) = log₂(x)
Rewrite as:
y = log₂(x)
Swap x and y
x = log₂(y)
Express as an exponential function
y = 2ˣ
So, we have:
f⁻¹(x) = 2ˣ
Hence, the equation of f⁻¹(x) is f⁻¹(x) = 2ˣ
The asymptote of f⁻¹(x)We have:
f⁻¹(x) = 2ˣ
Set the function to 0
f⁻¹(x) = 0
Rewrite as:
y = 0
Hence, the asymptote of f⁻¹(x) is y = 0
How to plot the graph of g(x)?We have:
f(x) = log₂(x)
g(x) = log₂(x)
Both equations are the same.
Hence, the graph of f(x) and g(x) are the same
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What is the extraneous solution found in solving the equation log2 4x + log₂ (x + 1) = 3
Answer:
x = -2
Step-by-step explanation:
We are given the logarithmic base 2 equation of:
[tex]\displaystyle{\log_2 (4x) + \log_2 (x+1) = 3}[/tex]
Apply logarithm property of addition where:
[tex]\displaystyle{\log_a M + \log_a N = \log_a MN}[/tex]
Therefore, we will write new equation as:
[tex]\displaystyle{\log_2 [4x(x+1)] = 3}[/tex]
Apply logarithm to exponential form using:
[tex]\displaystyle{\log_a M = N \to a^N = M}[/tex]
Thus, another new rewritten equation is:
[tex]\displaystyle{2^3 = 4x(x+1)}\\\\\displaystyle{8 = 4x(x+1)}\\\\\displaystyle{2=x(x+1)}[/tex]
Expand the expression in and arrange the terms in quadratic expression:
[tex]\displaystyle{2=x^2+x}\\\\\displaystyle{0=x^2+x-2}\\\\\displaystyle{x^2+x-2=0}[/tex]
Solve for x:
[tex]\displaystyle{(x+2)(x-1)=0}\\\\\displaystyle{x=-2,1}[/tex]
These are potential solutions to the equation. To find extraneous solution, you’ll have to know the domain of logarithm function. We know that logarithm’s domain is defined to be greater than 0. Henceforth, anti-logarithm must be greater than 0.
( 1 ) 4x > 0, x > 0
( 2 ) x + 1 > 0, x > -1
Therefore, our anti-log must be greater than 0, so any solutions that are equal or less than 0 will be considered as extraneous solution.
Hence, x = -2 is the extraneous solution.
You want to be able to withdraw $45,000 each year for 20 years. Your account earns 6% interest. a) How much do you need in your account at the beginning? $ b) How much total money will you pull out of the account? $ c) How much of that money is interest?
Step-by-step explanation:
gd seek is sssa eh uiiio if fsssw we to i if i jobs sss
A fence company is measuring a rectangular area in order to install a fence around its perimeter. If the length of the rectangular area is 140 yards and the width is 75 feet what is the total distance to be fenced in feet?
Answer:
990 ft
Step-by-step explanation:
1 yard = 3 feet, using this we can multiply 140 by 3 to convert it from yards to feet.
140 yd * 3 = 420 ft.
Next, to find the perimeter we need to follow this formula:
l + l + w + w.
420 ft + 420 ft + 75 ft + 75 ft = 990 ft
The total distance that needs to be fenced in feet is;
990 ft.
What is the solution to this system of linear equations? 3x + 4y = 11, x+4y=9
Five years ago, you invested $475 in corporate stock. You received dividends of $10 at the end of each quarter for two years. You then received quarterly dividends of $15 for the following three years. You just sold the stock for $1,700, immediately after receiving your 20th quarterly dividend check. What is your rate of return?
Group of answer choices
32.43%
31.03%
93.09%
9.73%
The rate of return earned on the investment of $475 five years ago in the corporate stock is 312.63%.
What is the rate of return?The rate of return is the net gain or loss of an investment expressed as a percentage of the investment's initial cost.
It is given by the formula, R= {Vf - Vi}/{Vi} x 100.
Where:
R = Rate of return
Vf = final value, including dividends and interest
Vi = initial value
Data and Calculations:Investment cost = $475
Dividends received:
1st two years = $80 ($10 x 8)
Three years = $180 ($15 x 12)
Total dividends received = $260 ($80 + $180)
Total revenue from sale = $1,700
Total proceeds = $1,960 ($1,700 + $260)
Total return = $1,485 ($1,960 - $475)
Rate of return = 312.63% ($1,485/$475 x 100)
Thus, the rate of return is 312.63%.
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which liner equality will not have a shared solution set with the graphed liner inequality
The linear inequality wthat will not have a shared solution set with the graphed linear inequality is C. y > 5/3x + 2.
How to illustrate the information?It should be noted that the graph shows the shaded area as y < 5/3x + 1.. The slope of the line will be 5/3.
The two parallel lines are the same. The graph of the inequality is also attached.
The complete question is:
Which linear inequality will not have a shared solution set with the graphed linear inequality?
A. y < 5/3x – 2
B. y < -5/3x + 1
C. y > 5/3x + 2
D. y > -5/3x + 2
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Find the surface area
Answer:
17038.94mm
Step-by-step explanation:
someone help me understand this
Answer:
Step-by-step explanation:
for reflection around x-axis.
(x,y)→(x,-y)
so P' is (-7,4)
What is the slope of the equation Y = 5/4x - 7/4?
Hello,
Y = ax + b (where a is the slope) si here the slope is 5/4
Answer:
5/4
Step-by-step explanation:
• Compare the given equation with the general equation of a straight line:
y = 5/4 x - 7/4
y = m x + c [m = slope, c = y-intercept]
As we can see, m in the general equation corresponds to 5/4 in the given equation. This means the slope is 5/4.
(We can also see that the y-intercept is -7/4.)
Two particles are on a spinning disk. Particle A is 12 cm away from the center, while particle B is 15 cm away from the center. If it takes 6 seconds to make a rotation, what is the linear velocity of each particle, in centimeters per second?
Select the correct answer below:
Linear velocity of particle A is 2 cm/sec, and particle B is 2.5 cm/sec.
Linear velocity of particle A is 2π cm/sec, and particle B is 5π2 cm/sec.
Linear velocity of particle A is 4 cm/sec, and particle B is 5 cm/sec.
Linear velocity of particle A is 4π cm/sec, and particle B is 5π cm/sec.
Answer:
Step-by-step explanation:
circumference for A=2π×12=24π
linear velocity=24π÷6=4π cm/sec
circumference for B=2π×15=30π
linear velocity=30π÷6=5π cm/sec
Find the value of Y to nearest tenth...
cos 64degrees = y/8
Step-by-step explanation:
what is the problem ? this is very straight forward with a calculator :
cos(64°) = y/8
y = 8×cos(64°) = 8×0.438371147... = 3.506969174... ≈
≈ 3.5
Trinity has 12 ounces of tea leaves. If
each cup of tea requires 3 ounce
of tea leaves, how many cups of tea
can Trinity make?
cups of tea
Answer:
4 cups of tea
Step-by-step explanation:
12 ounces ÷ 2/3 ounces = 18 cups of tea.
12/1 ÷ 2/3
12/1 x 3/2
= 36/2
=18
Answer:
4 cups of tea
Step-by-step explanation:
Given Trinity has 12 ounces of tea leaves, and 1 cup of tea requires 3 ounce of tea leaves,
No. of cups of tea = Total amount of tea leaves / Tea leaves required per cup of tea
= 12 / 3
= 4 cups of tea.
REALLY need help on this question
The values of the composite functions can be derived from the given tables as follows;
(g•f)(0) = -2(g•f)(1) = 1The domain of f(x) are; -2, -1, 0, 1The range of g(x) are; 2, 0, 1, 5How can the composite functions be evaluated?By composite functions definition, we have;
(g•f)(0) = g(f(0))
From the given tables, we have;
f(0) = 1
g(1) = -2
Therefore;
(g•f)(0) = g(f(0)) = g(1) = -2Similarly, we have;
(g•f)(1) = g(f(1))
From the given tables, we have;
f(1) = 0
g(0) = 1
Therefore;
(g•f)(1) = g(f(1)) = g(0) = 1The domain of f(x) are the possible x-values of f(x).
From the given table the domain of f(x) is; -2, -1, 0, 1The range of g(x) are the possible y-values of g(x).
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What types of Functions will left endpoint lead to an under approximation and right endpoints lead to and over approximation?
What types of Functions will left endpoint lead to an over approximation and right endpoints lead to and under approximation?
The functions that the left endpoint lead to an under approximation and right endpoints lead to and over approximation is the positive and increasing function.
How to illustrate the function?It should be noted that function simply means the illustration that shows the relationship between the variables.
In this case, the functions that the left endpoint lead to an under approximation and right endpoints lead to and over approximation is the positive and increasing function.
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Solve the following equation by first writing the equation in the form ax² = c
²-49-0
a.
b.
C.
d.
-49
- 149
= 7
:= ±7
The solution to the given equation is x = ±7. The correct option is d. x = ±7
Solving quadratic equationsFrom the question, we are to determine the solution to the given equation
The given equation is
x²-49 = 0
NOTE: I assumed the variable is x
Solving the equation
x²-49 = 0
Writing in the form ax²= c
x² = 49
∴ x = ±√49
x = ±7
Hence, the solution to the given equation is x = ±7
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Write the nth term of the arithmetic sequence 2,6,18,54 find the 10th term of the sequence
Answer:
Step-by-step explanation:
Givens
t1 = 2
r = 3
n = 10
Formula
tn = a*r^(n -1) Substitute the givens into the this formula
Solution
t10 = 2 * 3^(10 - 1)
t10 = 2 * 3^9
t10 = 2 * 19683
t10 = 39366
Answer: 39366
Please answer all parts as I know the answers but need the work to go with them. Thus, I believe the below answers are correct. Thank you!
The problem proves that the distributor's claim is true and he has a right to complain.
But when the confidence interval is changed from 95% to 90% the distributor's claim proves to be false.
The Confidence Interval for 95% is 0.9687;0.98532
For a sample size of n>30 the central limit theorem allows us to assume that the sampling distribution of x~ is approximately normal.
The critical region is Z ≥ 1.28 therefore the 1.877 lies in the rejection region that the distributor's claim is not true.
The Confidence Interval for 90% is 0.97156;0.982431
Here
μ = 0.977
s= σ= 0.03
95 % confidence interval is given by
x~± z∝/2 (s/√n)
Putting the values
0.977 ± 1.96 (0.03/√50)
=0.977 ± 0.008315
0.9687;0.98532
Part B:
x~+ 0.95= 0.977+0.95= 1.927
The critical region is Z ≥ 1.96 therefore the 1.927 lies in the acceptance region that the distributor's claim is true.
Part C:
For a sample size of n>30 the central limit theorem allows us to assume that the sampling distribution of x~ is approximately normal.
Part D:
μ = 0.977
s= σ= 0.03
90 % confidence interval is given by
x~± z∝/2 (s/√n)
Putting the values
0.977 ± 1.28 (0.03/√50)
=0.977 ± 0.005431
0.97156;0.982431
Part D:
x~+ 0.90= 0.977+0.90= 1.877
The critical region is Z ≥ 1.28 therefore the 1.877 lies in the rejection region that the distributor's claim is not true.
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The mean annual cost of an automotive insurance policy is normally distributed with a mean of $1140 and standard deviation of $310.
a. What is the probability that a random sample of 16 policyholders will have a mean insurance policy cost between $1000 and $1250?
Round your z value(s) to two decimal places. Do not round any other intermediate calculations. Round your answer to four decimal places.
Probability =
b. What is the probability that a random sample of 16 policyholders will have a mean insurance policy cost which exceeds $1250?
Round your z value(s) to two decimal places. Do not round any other intermediate calculations. Round your answer to four decimal places.
Probability =
c. What is the probability that a random sample of 16 policyholders will have a mean insurance policy cost below $1220?
Round your z value(s) to two decimal places. Do not round any other intermediate calculations. Round your answer to four decimal places.
Probability =
Using the normal distribution, it is found that the probabilities are given as follows:
a) 0.8871 = 88.71%.
b) 0.0778 = 7.78%.
c) 0.8485 = 84.85%.
Normal Probability DistributionThe z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score measures how many standard deviations the measure is above or below the mean. Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.By the Central Limit Theorem, the sampling distribution of sample means of size n has standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].The parameters in this problem are given as follows:
[tex]\mu = 1140, \sigma = 310, n = 16, s = \frac{310}{\sqrt{16}} = 77.5[/tex]
Item a:
The probability is the p-value of Z when X = 1250 subtracted by the p-value of Z when X = 1000, hence:
X = 1250:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{1250 - 1140}{77.5}[/tex]
Z = 1.42
Z = 1.42 has a p-value of 0.9222.
X = 1000:
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{1000 - 1140}{77.5}[/tex]
Z = -1.81
Z = -1.81 has a p-value of 0.0351.
0.9222 - 0.0351 = 0.8871 = 88.71% probability.
Item b:
The probability is one subtracted by the p-value of Z when X = 1250, hence:
1 - 0.9222 = 0.0778 = 7.78%.
Item c:
The probability is the p-value of Z when X = 1220, hence:
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{1220 - 1140}{77.5}[/tex]
Z = 1.03
Z = 1.03 has a p-value of 0.8485.
0.8485 = 84.85% probability.
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The binary operation* is defined on the set R of real numbers by X*Y = 3x + 3y - xy for all X , y E R. determine on the terms of X, the identity element.
Pls I need this answer with explanations( deep). pls help me.
Will mark the brainliest.
Answer:
This is the Answer
Step-by-step explanation:
Pls mark as brainliest
4 If 2² = 4x₁ find x.
Answer:
x = 1
Step-by-step explanation:
The value of x can be found in this one-step linear equation by dividing by its coefficient.
Solution4 = 4x . . . . . simplify
1 = x . . . . . . . divide by 4
I need help with number 7 and 8 and 9!
Answer:
in the 8 is ADB, in the 7 I'm not sure about you need to do sorry, or maybe you need to classify what triangle it is think is a scalene triangle because has a different measurements
if (k-6)(k+2)-(k²-20)=2k+6, whatis tge value of k?
K=1/3
simplify each bracket, put all numbers on the left hand side, equal it to 0 and solve for k
Your child is prescribed amoxicillin (40mg/kg/day; not to exceed 1500 mg per 24 hour period) to be
given 3 times per day. If she weighs 81 pounds, what is the maximum dose that she should
receive? (round to the nearest milligram)
Answer:
491 mg per dose
Step-by-step explanation:
1 kg ≈ 2.2 lbs
81/2.2 36.82 kg
40*36.82 ≈ 1472.8 mg/day
1472.8/3 ≈ 490.93
to the nearest mg = 491 mg per dose
Which expression represents the fourth term in the binomial expansion of (e 2f)10?
The fourth term in the Binomial expansion of [tex](e + 2f)^{10}[/tex] is [tex]10C_{3} (e)^{3}(2f)^{7}[/tex]
In elementary algebra, The Binomial theorem (or binomial expansion) describes the algebraic expansion of powers of a binomial. According to the theorem, it is possible to expand the polynomial [tex](x + y)^{n}[/tex] into a sum involving terms of the form [tex]ax^{b}y^{c}[/tex], where the exponents b and c are nonnegative integers with b + c = n , and the coefficient a of each term is a specific positive integer depending on n and b.
The binomial theorem formula is [tex](x + y)^{n}[/tex] = ∑ [tex]nC_{r} x^{n-r}y^{r}[/tex], where n is a positive integer and x, y are real numbers, and 0 < r ≤ n.
The formula to find the nth term in the binomial expansion of [tex](x + y)^{n}[/tex] is [tex]T_{r+1} = nC_{r} x^{n-r}y^{r}.[/tex]
As question demands fourth term of the expansion we need to substitute
r = 3 in the formula of nth term
On substituting we get
[tex]T_{3+1} = 10C_{3} (e)^{10-3}(2f)^{3}.[/tex]
[tex]T_{4} =[/tex] [tex]10C_{3} (e)^{3}(2f)^{7}[/tex]
Hence the fourth term in the binomial expansion of [tex](e + 2f)^{10}[/tex] is [tex]10C_{3} (e)^{3}(2f)^{7}[/tex]
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3) How many whole 3s are there inside of 4½?
Answer:
1
Step-by-step explanation:
There is one whole 3 inside of 4 1/2 or 4.5.
Multiples of 3 are 3x1=3 3x2=6....
Only a single whole 3 can be inside of 4.5.
Answer:
One
Step-by-step explanation:
ONE
4.5 ÷ 3 = 1 . 5 <=====so there is one and a half 3's in 4.5
ANSWER THIS ASAP AND AS FAST AS POSSIBLE:
FUNCTION A FUNCTION B:
y=35x. (look at the linked image)
What is the difference in the rate of change between Function A and Function B? BE SURE TO INCLUDE THE RATE OF CHANGE OF EACH FUNCTION IN YOUR ANSWER!
PLEASE EXPLAIN THE ANSWER.
Answer: 15
Step-by-step explanation:
The rate of change of Function A is 35.
The rate of change of Function B is 50.
So, the difference in the rate of change is 50-35 = 15.
a group of 4 numbers have an average of 15, three of the numbers are 18,11 and 25. what is the other number??
Answer:
6
Step-by-step explanation:
The average of a set of numbers is their sum divided by their number. This fact lets us write an equation to find the missing number.
SetupLet x represent the missing number. The average of the 4 numbers is ...
(x +18 +11 +25)/4 = 15
SolutionMultiplying by 4 gives ...
x +54 = 60
Subtracting 54, we find the missing number:
x = 6
The other number is 6.