Hello, I really need help solving this. It is a practice problem from my ACT prep guide. The subject is trigonometry. The answer options are at the bottom, *one answer per box*
Answers
Answer:
To find the domain of the function f(x)=tanx restricted so that its inverse function exists
we know that,
Since the range of tan inverse x is (-π/2, π/2), the answer should lie in this interval. Assume that y = tan -1 x. Then by the definition of inverse tan, tan y = x. The value of y in the interval (-π/2, π/2) that satisfies the equation tan y = x .
The domain of tanx is restricted to (-π/2, π/2). The range of tanx is always real numbers.
we get that,
The domain of f(x)=tanx is restricted to (-π/2, π/2) so that the inverse function exists. This means that all functional values of f(x)=tan^-1 x are on the interval (-π/2, π/2).
Related Questions
The distribution of sale prices (online) for four-year-old Harley Davidson touring motorcycles is approximately Normally distributed with a mean
of $14,000 and a standard deviation of $4,000.
8. What proportion of available motorcycles are priced at or below $9,000? Show your work.
9. What proportion of available motorcycles are priced at or below $12,000? Show your work.
10. Mr. Kawasaki plans to spend between $9,000 and $12,000 on a motorcycle. What proportion of the available motorcycles of this type can he
afford?
11. What is the approximate z-score for the 30th percentile in the standard Normal distribution?
12. Hence, what is the 30th percentile for the prices of motorcycles of this type? Show your work.
Answers
Answer:
$2000
Step-by-step explanation:
you subtract 4000-2000=2000
HELP ASAP PLEASE
Determine all real values of a.
a2 = 225
a = 112.5
a = ±112.5
a = 15
a = ±15
Answers
The real value of a is 15.
Given,
[tex]a^2 = 225[/tex]
Determine the real value of a
What is Perfect Square?
An integer that can be expressed as the square of another integer is called a perfect square. In other words, it is defined as the product of some integer with itself.
Here, find the square root of 225
Now,
[tex]a^2 = 225 \\\\a = \sqrt{225}[/tex]
a = 15 x 15 = 225
Hence, The real value of a is 15.
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Answer: the answer is the last option
Step-by-step explanation: I took the test and got it right
Here is a graph of the function g.4-3-2-1Use the graph to find the following.If there is more than one answer, separate them with commas.(a) All local maximum values of g:(6) All values at which g has a local maximut:X
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Graphically, the local maximum can be localized by spotting the "highest value" inside a range. A local maximum point on a function is a point (x,y) on the graph of the function whose y coordinate is larger than all other y coordinates on the graph at points "close to'' (x,y).
We can see that in our g function at x= -2 and x = 3, with respective values y = 3 and y = -1.
The answer for item (a) is: -1, 3
For item (b): -2, 3
6.75 +3/8x=13 1/4 solve please
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To solve this equation, we can proceed as follows:
[tex]6.75+\frac{3}{8}x=13\frac{1}{4}[/tex]1. Subtract 6.75 to both sides of the equation:
[tex]6.75-6.75+\frac{3}{8}x=13\frac{1}{4}-6.75\Rightarrow\frac{3}{8}x=13\frac{1}{4}-6.75[/tex]We can solve the right part of the equation using fractions as follows:
[tex]6.75=6+\frac{3}{4}[/tex]We also know that
[tex]13\frac{1}{4}=13+\frac{1}{4}[/tex]Then, we have:
[tex]\frac{3}{8}x=13+\frac{1}{4}-(6-\frac{3}{4})=13-6+\frac{1}{4}-\frac{3}{4}=7+\frac{1-3}{4}_{}[/tex][tex]\frac{3}{8}x=7+(-\frac{3}{4})=7-\frac{3}{4}=\frac{7\cdot4-3}{4}=\frac{28-3}{4}_{}=\frac{25}{4}[/tex]Now, the equation is:
[tex]\frac{3}{8}x=\frac{25}{4}[/tex]We need to multiply by 8/3 to both sides to solve for x as follows:
[tex]\frac{8}{3}\cdot\frac{3}{8}x=\frac{8}{3}\cdot\frac{25}{4}\Rightarrow x=\frac{8}{4}\cdot\frac{25}{3}\Rightarrow x=2\cdot\frac{25}{3}\Rightarrow x=\frac{50}{3}=16.6666666\ldots=16\frac{2}{3}[/tex]Therefore, the value for x is equal to:
[tex]x=16\frac{2}{3}=\frac{50}{3}=16.6666666\ldots[/tex]Answer:
The exact form, decimal form, and the mixed number form are down
Step-by-step explanation:
exact form ; x = 208/3
decimal form ; 69.33333..
Mixed number form ; 69 1/3
A coin is flipped 2,500 times. It lands on heads 1,223 times and tails 1,277 times. What is the empirical probability of getting tails on this coin
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Answer:
The empirical probability of getting tails on this coin is 50.08%.
Step-by-step explanation:
If the measure of arc AB is 64 degrees, what is the measure of angle ADB?
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Answer:
the answer is AB multi
Step-by-step explanation:
Is AB degrees
Water drips from a faucet at a rate of 41 drops a minute assuming there is a 15,000 drop in a gallon. How many minutes will it take for the dripping faucet to fill a 1 gallon bucket?
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PLS HELP ASAP!!!!!!!!!!!!!!!!!!!!!!!!!!!!!Which statement is true?A. 25-15×4-3×2=30B. 24-15×(4-3)×2=30C. (24-15)×4-3×2=30D. (24-15)×4-3×2=66
Answers
The correct statement is C.
To notice this, we need to remember the correct order of operations:
• Parentheses
,• Powers and roots
,• Multiplications and divisions
,• Additions and subtractions.
Using this ordering we have for each operation:
A.
[tex]\begin{gathered} 25-15\times4-3\times2=25-60-6 \\ =-41 \end{gathered}[/tex]B.
[tex]\begin{gathered} 24-15\times(4-3)\times2=24-15\times1\times2 \\ =24-30 \\ =-6 \end{gathered}[/tex]C.
[tex]\begin{gathered} (24-15)\times4-3\times2=9\times4-3\times2 \\ =36-6 \\ =30 \end{gathered}[/tex]D.
[tex]\begin{gathered} (24-15)\times4-3\times2=9\times4-3\times2 \\ =36-6 \\ =30 \end{gathered}[/tex]Hence the only correct result in the operations is the one given in option C.
i have to find out if the triangles are similar and if so y
Answers
We will determine the height of the tree as follows:
*First: We take the height of Dave to just ft, that is:
We know that one feet has 12 inches, so:
[tex]x=\frac{4\cdot1}{12}\Rightarrow x=\frac{1}{3}[/tex]Now, we add that to the 6 feet:
[tex]6+\frac{1}{3}=\frac{19}{3}=6.333\ldots[/tex]So, his height is 19/3 ft.
Now, we determine the height of the tree as follows:
[tex]\frac{15}{(\frac{19}{3})}=\frac{y}{66+15}[/tex]Here y represents the height of the tree, now we solve for it:
[tex]\frac{45}{19}=\frac{y}{81}\Rightarrow y=\frac{45\cdot81}{19}\Rightarrow y=\frac{3645}{19}[/tex][tex]\Rightarrow y\approx191.8[/tex]So, the height of the tree is approximately 191.8 feet.
So can y’all help me please this is due at 5pm
Answers
Answer:
Variable terms: 4a and 6a
Constant terms: 4 and 11
Step-by-step explanation:
A constant term is one that is NOT multiplied by any variables.
At this level of math, think of constants as terms that are only numbers.
(for example: 1, 68.9, -42, etc.)
Note that a term in « a + bi » form can also be a constant.
A variable term is a one that IS multiplied by a variable.
(for example x, -3y, 8z, etc.)
In question 1, the variable terms are:
4a and 6a because they are multiplied by the variable a
The constant terms are:
4 and 11 because they are simply integers
Note that the constant terms could also be written as -4 and -11 depending on how the operations are viewed (subtracting vs adding a negative)
Can anyone answer either of these questions with an explanation please I really need it thanks!
Answers
Answer:
6. 4
7. 8.25
Step-by-step explanation:
all the explanation for both questions is in the pics below please check it out also I am sorry if it's wrong I am only in middle school
Have a wonderful day:)
Marian purchased a home valued at $465,000. She purchased homeowner insurance for 75% of the value of the home. If the annual premium on the policyhundred-dollar unit, how much did she pay to the nearest whole cent)?$2,875.50$2,695.00$2,580.75$3,050.74None of these choices are correct.
Answers
Ok, so
Marian purchased a home valued at $465,000. If She purchased homeowner insurance for 75% of the value of the home, she paid:
$(465,000)*(75) / (100)
$348,750.
Now, we know that the annual premium on the policy was $0.74 per hundred-dollar unit. Then, this is:
0.74/100 dollar unit.
And, if we multiply, we obtain:
$348,750 * (0.74/100) = $2,580.75
Therefore, she paid $2,580.75
how do I do this question
Answers
The value of x can be determined as,
[tex]\begin{gathered} \tan 39^{\circ}=\frac{x}{15} \\ x=15\tan 39^{\circ} \\ x=12.15 \end{gathered}[/tex]Thus, the required value of x is 12.15.
Equation A matches graph __ because …….I need some help on this
Answers
Answer:
The function A is given below as
[tex]y=x^2-6x+8[/tex]Using a graphing tool, we will have the graph be
Hence,
Equation A matches graph 3 because the x-intercepts are on the positive x-axis and it has a y-intercept of 8(on the positive y-axis)
Step 2:
Equation B is given below as
[tex]y=(x-6)(x+8)[/tex]Using the graphing tool, we will have the graph as
Hence,
Equation B matches graph 4
The x-intercepts cuts at the negative x and positive x-axis and the y-intercepts is on the negative y-axis
Step 3:
Equation C is given below as
[tex]y=(x-6)^2+8[/tex]Hence,
Using a graphing calculator, we will have the graph as
Hence,
Equation C matches Graph 1, because its vertex is (6,8) and it has a y-intercept on the positive y-axis
a Find the volume of the specified cone. Use 3.14 for x, and round your answer to the nearest whole number. Radius = 4 in., Height = 9 in. 301 cu. in. b. 226 cu. in. 75 cu. in. d. 151 cu. in. Please select the best answer from the choices provided ΟΑ OB с OD
Answers
volume of cone approximately is 151 cubic inch
an astronsut weighs 174 pounds on earth and 29 pounds on the moon if his daughter weighs 108 pounds on earth what is the daughters weight on the moon in pounds
Answers
Answer:
Step-by-step explanation:
18 pounds
A particular fruit's weights are normally distributed, with a mean of 598 grams and a standard deviation of 22 grams.
If you pick 9 fruits at random, then 16% of the time, their mean weight will be greater than how many grams?
Give your answer to the nearest gram.
Answers
If a particular fruit's weights are normally distributed, with a mean of 598 grams and a standard deviation of 22 grams and I pick 9 fruits at random, then their mean weight will be greater than 605.29263 grams 16% of the time.
As per the question statement, a particular fruit's weights are normally distributed, with a mean of 598 grams and a standard deviation of 22 grams and I pick 9 fruits at random.
We are required to calculate their mean weight will be greater than how many grams for 16% of the time.
Given (μ = 598), (σ = 22), and (n = 9)
Therefore, the standard deviation of the distribution of sample, otherwise know as the standard error, will be [s = (sdp)/√(ss)]
Where, "s" is the standard error, "sdp" is the standard deviation of the population and "ss" is the sample size.
Therefore, [s = (22/√9) = (22/3) = 7.33...
Now, we need to look up the z-score for an area to the right of it being equal to (0.16) since we are concerned about (16%) times among the random selection, and [16% = (16/100) = 0.16]
That is, we need to look up the z-score for an area of [(1 - 0.16) = 0.84] to the left of it.
Hence, a z-score with an area of 0.84 to the left of it will be equal to 0.99445.
Now to find the raw score associated with this, we will have to use the formula to calculate z-score which goes as [(x - m)/s].
Where, "z" is the z-score, "x" is the raw score, "m" is the mean and "s" is the standard error.
Therefore, with a mean of 598 and a standard error of 7.333 and a z-score of 0.99445, applied to the above mentioned formula to calculate z-score, we get:
[0.99445 = (x - 598)/7.33]
Or, (x - 598) = (0.99445 * 7.33)
Or, (x - 598) = 7.29263
Or, x = (598 + 7.29263)
Or, [x = 605.29263]
That is, if I pick a sample of 9 fruits at random, then their mean weight will be greater than 605.29263 grams 16% of the time.
Mean: In Mathematics and Statistics, the mean refers to the average of a set of values in a sample or observation.To learn more about Mean, click on the link below.
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A computer is normally $500, but is discounted to $200. By what percentage did the computer decrease?
Answers
Answer:
60%
Step-by-step explanation:
What should be done to both sides of the equation in order to solve x = 4?Divide by 4.Multiply by 4.Divide by 1/3.Multiply by 1/3.
Answers
Given:
There are given that the equation:
[tex]\frac{1}{3}x=4[/tex]Explanation:
According to the question:
We need to find the value that orders to solve both sides of the equationn.
So,
From the equation:
[tex]\frac{1}{3}x=4[/tex]Then,
For the equation, divide by 1/3 on both sides of the equation:
So,
From the properties:
If,
[tex]\frac{a}{\frac{b}{\frac{c}{d}}}=\frac{a}{b}\times\frac{d}{c}[/tex][tex]\begin{gathered} \frac{1}{3}x=4 \\ \frac{\frac{1}{3}x}{\frac{1}{3}}=\frac{4}{\frac{1}{3}} \\ \frac{\frac{1}{3}x}{\frac{1}{3}}=4\times3 \\ \frac{1}{3}x\times3=12 \\ x=12 \end{gathered}[/tex]Final answer:
Hence, the correct option is C.
Can you help and explain what to do with practice question below?
Answers
Solution:
Given the figure below:
To solve for the missing angles,
Step 1: Solve for c.
The sum of the interior angles of a triangle equals 180 degrees.
Thus,
[tex]\begin{gathered} 48+58+c=180(sum\text{ of interior angles in a triangle\rparen} \\ \Rightarrow106+c=180 \\ subtract\text{ 106 from both sides,} \\ 106-106+c=180-106 \\ \Rightarrow c=74\degree \end{gathered}[/tex]Step 2: Solve for d.
The sum of angles on a straight line gives 180 degrees.
[tex]\begin{gathered} 58+d=180\text{ \lparen sum of angles on a straight line\rparen} \\ subtract\text{ 58 from both sides,} \\ 58-58+d=180-58 \\ \Rightarrow d=122\degree \end{gathered}[/tex]Step 3: Solve for a.
From the figure,
[tex]a=58\degree\text{ \lparen alternate angles\rparen}[/tex]Step 4: Solve for b.
From the figure,
[tex]\begin{gathered} b+c=d\text{ \lparen alternate angles\rparen} \\ \Rightarrow b+74=122 \\ subtract\text{ 74 from both sides,} \\ b+74-74=122-74 \\ \Rightarrow b=48\degree \end{gathered}[/tex]Hence, we have
[tex]\begin{gathered} a=58\degree \\ b=48\degree \\ c=74\degree \\ d=122\degree \end{gathered}[/tex]The first 19 terms of the arithmetic sequence 9, 2, -5, -12,...
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9, 2, -5, -12,...
First let's find the common difference
Common difference= 2 - 9 = -7
So we will add - 7 to get the next term
9, 2, -5, -12, -19, -26, -33,-40, -47, -54, -61, -68, -75, -82, -89, -96, -103, -110, -117
Sharon baked 72 cookies for herclassmates. Her brothers ate some ofthe cookies and 54 cookies remain.Find the percent of decrease.
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Answer
Percent decrease = 25%
Explanation
Percent decrease is given as
[tex]\text{Percent decrease = }\frac{Amount\text{ decreased}}{\text{Original amount}}\times100\text{ percent}[/tex]For this question,
Amount decreased = (Original amount) - (Amount remaining)
Amount decreased = 72 - 54 = 18 cookies
Original amount = 72 cookies
Percent decrease = (18/72) × 100%
Percent decrease = 25%
Hope this Helps!!!
a.H1. Determine if the given points are collinear or not collinear.|points E, H, and J:b. points F, J, and E:points G, J, and E:points G, H, and J:C.d.J
Answers
Collinear means that the points all lie on a straight line
From the picture, we will see that:
I. points E, J & F all lie on a straight line (Line y)
II. points G, J & H all lie on a straight line (Line t)
a. Points E, H & J do no lie on a straight line; point E lies on line y while point H lies on line t
b. Points F, J & E all lie on the straight line y
c. Point G, H & J all lie on a straight line t
Which expression equals the expression 5x-3y?
Answers
Answer
Options A, C and D are all correct.
They simplify to give 5x - 3y
Explanation
We are asked to pick the expressions which simplify to give 5x - 3y
Taking the statements one at a time,
Option A
5x + -8y + 5y
= 5x - 8y + 5y
= 5x - 3y
This option is correct.
Option B
15xy ≠ (5x - 3y)
This option is not correct.
Option C
5 (x + y) + -8y
= 5x + 5y - 8y
= 5x - 3y
This option is correct.
Option D
-2 (2y - x) + x + x + x + y
= -4y + 2x + 3x + y
= 5x - 3y
This option is correct.
Hope this Helps!!!
lynn is tracking the progress of her plants growth. today the plant is 5 cm high. the plant grows 1.5 cm per day. suppose Lynn's plant grewn to a height of 30.5 inches how many days will have passed
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We have that the plant start with 5 cm high and it grows 1.5 cm per day, then the equation to model this situation is:
[tex]y=1.5x+5[/tex]where x represents the days that passes and y represents the height of the plant.
Now, let's convert 30.5 inches to cm:
[tex]\begin{gathered} 1in=2.54\operatorname{cm} \\ \Rightarrow(30.5)\cdot(2.54)=77.47\operatorname{cm} \end{gathered}[/tex]then, suppose that Lynn's plant grew to a height of 77.47 cm, then we have to make y = 77.47 and solve for x to get the following:
[tex]\begin{gathered} y=77.47 \\ \Rightarrow77.47=1.5x+5 \\ \Rightarrow77.47-5=1.5x \\ \Rightarrow72.47=1.5x \\ \Rightarrow x=\frac{72.47}{1.5}=48.3 \\ x=48.3 \end{gathered}[/tex]therefore, it will take approximately 48 days to the plant to grow to a height of 30.5 inches
6x2 = x + 2Write the quadratic equation in standard form:( a )x2 + ( b )x + ( c ) = 0Identify the values of a, b, and c.a =-b =C=Substitute these values into the quadratic formula and simplify:x = -(b)£/( b )2 –4()()2( a )
Answers
6x² = x + 2
Subtracting x and 2 at both sides:
6x² - x - 2 = x + 2 - x - 2
6x² - x - 2 = 0
where
a: 6
b: -1
c: -2
Substituting these values into the quadratic formula:
[tex]\begin{gathered} x_{1,2}=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a} \\ x_{1,2}=\frac{1\pm\sqrt[]{(-1)^2-4(6)(-2)}}{2(6)} \\ x_{1,2}=\frac{1\pm\sqrt[]{49}}{12} \\ x_1=\frac{1+7}{12}=\frac{2}{3} \\ x_2=\frac{1-7}{12}=-\frac{1}{2} \end{gathered}[/tex]a) A paralegal bills a law firm for 19.5 hours of work at a rate of £240 per hour.
much money has the paralegal earned from this job? Include units in your
answer.
b) The paralegal splits her earnings between utilities and savings in a ratio of 2:3.
How much money will be allocated to her savings?
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1. The total earnings of the paralegal from this job was £4,680.
2. The amount of the earnings allocated to her savings, based on the allocation ratio, is £2,808.
What are the total earnings?The total earnings are a function of the unit hours worked and the hourly pay rate.
The total earnings are the product of the multiplication of the two variables.
What is a ratio?A ratio is a numerical relationship showing how much a value is contained in another value or variable.
Ratios are fractional values depicted in percentages, decimals, or fractions.
The total number of work hours = 19.5 hours
The work hour rate (per hour) = £240
The total earnings from the job = £4,680 (£240 x 19.5)
The ratio of utilities and savings = 2:3
The sum of the ratio = 5
The amount allocated to savings = 3/5 of £4,680 = £2,808.
The amount allocated to utilities = £1,872 or 2/5 (£4,680 - £2,808)
Thus, whereas, the paralegal earned £4,680 from the job, the amount allocated to her savings is £2,808, based on the subsisting allocation ratio.
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Sales are $500,00 and variable cost are $350,00. What is the contribution margin ratio
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If Sales are $500,000 and variable cost are $350,000. The contribution margin ratio is 30%.
What is contribution margin ratio?Contribution margin ratio can be determine or find by substracting or deducting the variables cost form the sales and then dividing it by the sales.
Now let find the contribution margin ratio using this formula
Contribution margin ratio = Sales - Variable cost / Sales
Where:
Sales = $500,000
Variable costs = $200,000
Let plug in the formula
Contribution margin ratio = $500,000 - $350,000 / $500,000
Contribution margin ratio = $150,000 / $500,000
Contribution margin ratio = 0.3 × 100
Contribution margin ratio = 30%
Therefore we can conclude that 30% is the contribution margin ratio .
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8. Suppose that A, B, and C are sets. Prove or disprove that
(A − B) − C = (A − C) − B.
Answers
The equation be (A − B) − C = (A − C) − B. Then results exists different, so we contain disproven the hypothesis by counterexample.
Is (A − B) − C = (A − C) − B exists equivalent?Given: (A − B) − C = (A − C) − B.
First, we will attempt to show [tex]$A-(B-C) \subseteq(A-C)-C$[/tex]. Let [tex]$x \in A-(B-C)$[/tex]. Then [tex]$x \in A$[/tex] and [tex]$x \notin(B-C)$[/tex].
By De Morgan's law we have that
[tex]$$x \notin(B-C)=x \notin B \vee x \in C .$$[/tex]
We have that [tex]$x \in A \wedge(x \notin B \vee x \in C)$[/tex].
Then we have that [tex]$(x \in A \wedge x \notin B) \vee(x \in A \wedge x \in C)$[/tex].
So by definition of [tex]$\cup$[/tex] and [tex]$\cap$[/tex], we have [tex]$x \in(A-B) \cup(x \in(A \cap C))[/tex].
I can see a contradiction here in that LHS says x ∈ C but the RHS says x ∉ C.
For example, as longer as [tex]$C \neq 0$[/tex]. Let A = 4, B = 2, C = 1.
Then A - (B - C) = 4 - (2 - 1) = 4 - 1 = 3
On the other side (A - B) - C = (4 - 2) - 1 = 2 - 1 = 1.
The results exists different, so we contain disproven the hypothesis by counterexample.
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A bank deposit slip shows a total of $441 in $1 loonies and $2 coins. If the number of $2 coins was 3 times the number of $1 loonies, how many of each are there?
Answers
The number of $1 loonies are 63 and the number of $2 coins are 189
Let x be the number of $1 loonies and y be the number of $2 coins.
A bank deposit slip shows a total of $441 in $1 loonies and $2 coins.
so, we get an equation,
x + 2y = 441 .................(1)
The number of $2 coins was 3 times the number of $1 loonies.
so, we get an equation,
y = 3x .............(2)
Substitute the above value of in equation (1),
x + 2(3x) = 441
x + 6x = 441
7x = 441
x = 63
Substitute above value of x in equation (2),
y = 3 * 63
y = 189
Therefore, the number of $1 loonies are 63 and the number of $2 coins are 189
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