Answers
By using the table, we see that the correct options are:
a) f(2) = 7
b) f(x) = 3 when x = 8.
c) f⁻¹(7) = 2
d) f⁻¹(x) = 8 when x = 3.
How to use the information in the table?Here we have a table of x and f(x).
First, we want to find f(2). To get that, we need to go to the row where we have x = 2.
In that same row we can see that f(x) = 7.
Then f(2) = 7.
Then it says:
"if f(x) = 3, then x = ?"
This time we do the opposite. We find the row where f(x) = 3, and then we see the value of x in that row.
In the second row (counting from the bottom) we can see that when x = 8, f(x) = 3.
Then:
"if f(x) = 3, x = 8"
Then we want to get the inverse of f(x) evaluated in 7.
Here we use the rule:
[tex]f(x) = y\\f^{-1}(y) = x[/tex]
Then
[tex]f(2) = 7\\f^{-1}(7) = 2[/tex]
The answer here is 2.
Finally:
"if the inverse evaluated in x si 8, then what is the value of x"
Similar to before, we know that when we evaluate f(x) in 8, the outcome is 3.
Then when we evaluate the inverse in 3, the outcome is 8.
So here we must have x = 3.
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Related Questions
The area of each circle is exactly
0.56π square inches.
There are 2 identical circles in the cylinder.
So the total area of all the circles is ??? π square inches.
Answers
Total area of the circle is 1.12π square inches.
What is Area of circle?The Area of circle is π times the square of the radius.
i.e., A = πr²
Given:
Area of one circle = 0.56π
As the second circle is also identical then the area will be same.
So, the total area of circle is
=2* 0.56π
=1.12π square inches.
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The graph of a line has a slope of 3 and passes through the point (–4, –5).
What is the equation of the line in point-slope form?
y – 5 = 3(x – 4)
y – 4 = 3(x – 5)
y + 5 = 3(x + 4)
y + 4 = 3(x + 5)
Answers
Answer
(C) y +5 =3(x+4)
We will use the point-slope formula to solve this problem.
We will use the point-slope formula to solve this problem.(y+5)=3(x+4)
)Explanation:
)Explanation:We can use the point slope formula to solve this problem.
)Explanation:We can use the point slope formula to solve this problem.The point-slope formula states: (y−y1)=m(x−x1)
)Explanation:We can use the point slope formula to solve this problem.The point-slope formula states: (y−y1)=m(x−x1)Where m is the slope and (x1y1) is a point the line passes through.
)Explanation:We can use the point slope formula to solve this problem.The point-slope formula states: (y−y1)=m(x−x1)Where m is the slope and (x1y1) is a point the line passes through.We can substitute the slope and point we were given into this formula to produce the equation we are looking for:
)Explanation:We can use the point slope formula to solve this problem.The point-slope formula states: (y−y1)=m(x−x1)Where m is the slope and (x1y1) is a point the line passes through.We can substitute the slope and point we were given into this formula to produce the equation we are looking for:(y−(−5))=3(x--(4))
=> (y+5)=3(x+4)
What is 11 3/8 divided in half
Answers
Answer:
in fraction form it is : 5 11/16
Decimal form it is : 5.6875
Step-by-step explanation:
convert the mixed number into improper fractions: 11 3/8 = 91/8
= 91/8 / 8/2
Apollyon the fraction rule: a/b / c = a / b * c
= 91/8 * 2
Multiply the numbers: 8 * 2 = 16
= 91/15
convert the improper fractions into mixed numbers: 91/16 = 5 11/16
Final answer of:
= 5 11/16
Why is it important to use the correct units of measurement when working with conversions? Explain by converting 5 feet into inches.
Answers
It is important to use the correct units of measurement when working with conversions because errors may occur. 5 feet = 60 inches.
What is conversion?Conversion means to convert the same thing into different units.
It is important to use the correct units of measurement when working with conversions because errors may occur.
1 foot = 12 inches
Then we have
5 feet = 60 inches
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Una empresa embotelladora de gaseosas lanzará su propia bebida "Delicia" de un litro a un costo variable de S/ 2.50 por unidad, los costos fijos son S/ 18,500. Cada unidad tiene un precio de venta de S/ 4.50. Entonces, determine el número de botellas de un litro que deben venderse para que la empresa obtenga utilidades de S/ 30 000.
Answers
Por la ecuación de utilidad, necesitamos una producción de 7,667 botellas de un litro de capacidad para obtener un total de utilidades de S/ 30.000.
¿Cómo determinar las utilidades por la venta de bebidas gaseosas?
Las utilidades (U') se obtienen de sustraer los costes de producción (Cp) a las utilidades netas (U). Los costes de producción (Cp) son la suma de costes variables (C') y costes fijos (C). y la utilidades netas proceden de la venta de botellas. En consecuencia, tenemos la siguiente expresión:
U' = U - Cp
U' = U - C' - C
A continuación, desarrollamos y resolvemos la ecuación resultante:
30000 = 4.50 · x - 2.50 · x - 18500
1.50 · x = 11500
x = 7667
Por la ecuación de utilidad, necesitamos una producción de 7,667 botellas de un litro de capacidad para obtener un total de utilidades de S/ 30.000.
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Somebody help please
Answers
Answer:
Emily raised $37.50
Justin raised $57.50
Step-by-step explanation:
(Step 1)
Say "x" equals the amount of money Emily made and "y" equals the amount of money Justin made. You can set up an equation with both of these variables because we know that they made a combined $95.
x = Emily's earnings
y = Justin's earnings
Emily + Justin = 95
x + y = 95
(Step 2)
The fact that there are two variables makes it difficult to find how much each person made individually. However, we can eliminate the "y" variable when we remember that Justin made $20 more than Emily. Now, we can substitute "x + 20" in for "y".
x + 20 = y
x + y = 95
x + (x + 20) = 95
(Step 3)
Finally, we can solve for the "x" variable.
x + (x + 20) = 95
2x + 20 = 95 <------ Combine like terms
2x = 75 <------ Subtract 20 from both sides
x = 37.5 <------- Divide both sides by 2
(Step 4)
Since we know the value of "x", we can plug it into one of the equations to find the value of "y".
x + 20 = y
37.5 + 20 = y
y = 57.5
Answer:
Emily raised $37.5 and justin raised $57.5
60°
X
x
60°
x = [ ? ]
Ingresar
Answers
Answer: 30
Step-by-step explanation:
Since there are two angles that measure [tex]60^{\circ}[/tex], the triangle is equilateral. This means that the angle bisector of the third angle is an altitude, and thus we have two right triangles with acute angles [tex]60^{\circ}[/tex] and [tex]x[/tex]. It follows that x=30.
A triangle has squares on its three sides as shown below. What is the value of x? 3 cm U x cm 4 cm 3 centimeters 4 centimeters 5 centimeters 07 centimeters A triangle has squares on its three sides as shown below . What is the value of x ? 3 cm U x cm 4 cm 3 centimeters 4 centimeters 5 centimeters 07 centimeters
Answers
The value of x is 10 centimeters
How to solve for x?The complete question is in the image
The value of x is calculated using the following Pythagoras theorem
x^2 = 6^2 + 8^2
Evaluate the sum of exponents
x^2 = 100
Take the square roots
x = 10
Hence, the value of x is 10 centimeters
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Need the answer for number 3 please!!!
Answers
Answer:
Step-by-step explanation:
THe square root of 10 x 15 x 24 is
Answers
[tex]\large\blue\implies \tt \large \: \sqrt{10 \: \times \: 15 \: \times \: 24} [/tex]
[tex]\large\blue\implies \tt \large \: \sqrt{150 \: \times \: 24} [/tex]
[tex]\large\blue\implies \tt \large \: \sqrt{3600} [/tex]
[tex]\large\blue\implies \tt \large \: \sqrt{3600} \: = \: 60[/tex]
[tex]\large\blue\implies \tt \large \:60[/tex]
What is the point-slope form of a line with slope 3/2 that contains the point
(-1, 2)?
A.y+2=(x + 1)
B. y-2-(x-1)
C. y+2=(x-1)
D. y-2-(x+1)
Answers
Answer:
[tex]\boldsymbol{\rm{y-2=\dfrac{3}{2}(x+1)}}[/tex], or DStep-by-step explanation:
Hello
If a line's equation has the form [tex]\boldsymbol{\rm{y-y1=m(x-x1)}}[/tex], then it's considered to be in point-slope form.
In that formula,
[tex]\boldsymbol{\rm{y1}}[/tex] is the y co-ordinate (2nd co-ordinate) of the point (here it's given as 2)[tex]\boldsymbol{\rm{m}}[/tex] is the slope, here it's 3/2[tex]\boldsymbol{\rm {x1}}[/tex] is the x co-ordinate (the first co-ordinate) of the point.Now you know why this equation is called point-slope form!
Now that we're familiar with the equation, let's plug in the information that's given to us...
[tex]\boldsymbol{\rm{y-2=\displaystyle\frac{3}{2}(x-(-1)}}[/tex] | simplify
[tex]\boldsymbol{\rm{y-2=\displaystyle\frac{3}{2}(x+1)}}[/tex]
[tex]\pmb{\tt{done~!!}}[/tex]
[tex]\orange\hspace{300pt}\above3[/tex]
y - 2=(x+1) , or D because its rlly simple u just need to ask someone else for help.
Need help now due in 5 minutes pls help quick now pls pls pls pls pls
Answers
Answer: A and D
Step-by-step explanation:
- Career A's spread is more concentrated while Career B's spread is more dispersed or spread out
- Career A's median is 25 and Career B's median is 30
- Therefore A and D are the correct answers
hope this helps :)
What is the slope of the line shown below?
Answers
Answer:
(1/2)
Step-by-step explanation:
From one point, if you go up one and over 2 you will get exactly one block up than from your initial point. And since the graph is pointing down on left side, that means it's positive.
Determine the amount of interest the principal in each account had earned. (From Example 2)
3. On March 3, Raul Avila deposited $10,000 in a savings account that pays 5.5% interest compounded daily until June 21.
4. On March 26, Samuel Griffin deposited $20,000 in a savings account that pays 5.5% interest compounded daily until July 24.
Answers
The amount of interest that the principal in each account had earned is as follows:
Raul Avila = $167.12
Samuel Griffin = $364.91
How is compound interest computed?The compound interests can be calculated using the compound interest formula:
A = P(1 + \frac{r}{n})^{nt}
Where:
A = final amount
P = initial principal balance
r = interest rate
n = number of times interest applied per time period
t = number of time periods elapsed
It can also be computed using an online finance calculator as follows:
Data and Calculations:Raul Avila:N (# of periods) = 110 days
I/Y (Interest per year) = 5.5%
PV (Present Value) = $10,000
PMT (Periodic Payment) = $0
Results:
FV = $10,167.12
Total Interest = $167.12
Samuel Griffin:N (# of periods) = 120 days
I/Y (Interest per year) = 5.5%
PV (Present Value) = $20,000
PMT (Periodic Payment) = $0
Results:
FV = $20,364.91
Total Interest = $364.91
Thus, using the online finance calculator, the compound interest for each principal has been computed as $167.12 and $364.91, respectively.
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when a relation is drawn on an xy-plane what is another name for the set of all x values from its graph?
Answers
Another name for the set of all x-values for a relation is: domain.
What is the Domain of a Relation?
The domain of a relation can be defined as all the x-values that corresponds to the y-values that are plotted on a graph.
They are referred to as the input or the domain of the relation. Therefore, another name for the set of all x-values plotted for a relation on a graph is: domain.
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Factorize x^2+√4x+2x+2
Answers
Answer:
x^2+4x+2
Step-by-step explanation:
Which statements are always true regarding the diagram? Select three options. m∠5 + m∠3 = m∠4 m∠3 + m∠4 + m∠5 = 180° m∠5 + m∠6 =180° m∠2 + m∠3 = m∠6 m∠2 + m∠3 + m∠5 = 180°
Answers
Based on the triangle sum theorem, exterior angle theorem, the true statements are:
m∠5 + m∠6 = 180°
m∠2 + m∠3 = m∠6
m∠2 + m∠3 + m∠5 = 180°
What is the Triangle Sum Theorem and the Exterior Angle Theorem?According to the triangle sum theorem, m∠2 + m∠3 + m∠5 = 180°.
Also, based on the exterior angle theorem, m∠2 + m∠3 = m∠6.
∠5 and ∠6 are a pair of linear angles, therefore: m∠5 + m∠6 = 180°.
In summary, the true statements about the diagram given are:
m∠5 + m∠6 = 180°m∠2 + m∠3 = m∠6 m∠2 + m∠3 + m∠5 = 180°Learn more about the triangle sum theorem on:
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5. In a high school, 60% of the students live east of the school and 40% live west of the school. Among the students who live east of the school, 30% are in the math club, and among the students who live west of the school, 20% are in the math club. a. Find the probability that a randomly selected student is from east of the school and in the math club. b. Given that a student is from west of the school, what is the probability that he or she is in the math club? c. Is participation in the math club independent from whether a student lives east or west of the school? Justify your answer.
Answers
The probability for part (a) is 0.18, for part (b) is 0.08, and for part (c) is 0.26.
What is probability?It is defined as the ratio of the number of favorable outcomes to the total number of outcomes, in other words, the probability is the number that shows the happening of the event.
a. Find the probability that a randomly selected student is from east of the school and in the math club:
P(east ∩ math club) = 0.6×0.3 = 0.18
b. Given that a student is from west of the school, what is the probability that he or she is in the math club?
P(west ∩ math club) = 0.4×0.2 = 0.08
c. Is participation in the math club independent of whether a student lives east or west of the school?
P(math club) = P(east ∩ math club) + P(west ∩ math club)
= 0.18 + 0.08
= 0.26
Thus, the probability for part (a) is 0.18, for part (b) is 0.08, and for part (c) is 0.26.
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100 POINTS!!! In one area, the lowest angle of elevation of the sun in winter is 21° Find the distance x that a plant needing full sun can be placed from a fence that is 10.5 feet high. Round your answer to the tenths place when necessary.
Answers
To find the length of the missing side x, use Tan trigonometric formula
Tan: [tex]\frac{opposite}{Adjacent}[/tex]
Tan 21 = [tex]\frac{10.5}{x}[/tex]
Tan 21 × [tex]\frac{1}{10.5}[/tex] = [tex]\frac{10.5}{x}[/tex]×[tex]\frac{1}{10.5}[/tex]
[tex]\frac{10.5}{Tan 21}=x[/tex]
x=27.4
X= 27.4 ft
Hope it helps!
Answer:
x = 27.4 ft
Step-by-step explanation:
Here given:
opposite side: 10.5 ftadjacent side: x ftto that angle: 21°So, use tan rule:
[tex]\sf tan(\theta) = \dfrac{opposite}{adjacent}[/tex]
insert values
[tex]\sf tan(21) = \dfrac{10.5}{x}[/tex]
make 'x' subject
[tex]\sf x= \dfrac{10.5}{tan(21) }[/tex]
calculate value
[tex]\sf x = 27.35343...[/tex]
rounded to nearest tenth
[tex]\sf x = 27.4 \ ft[/tex]
what is the strategy when figuring out the IQR and the 5-number summary for the data
Answers
The strategy when figuring out the IQR and the 5-number summary for the data include arrangement from lowest to highest.
What is 5-number summary?This is used to summarize distribution of data obtained or given in a sample and they include:
First quartile(Q1) valueMedianThird quartile(Q3) valueMinimumMaximum.Proper arrangement of the data ensures accuracy in the results/values thereby making the most appropriate choice.
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Find the amount and compound interest on 1 (a) Rs. 16000 for 2+1/3 years at 15% per annum. 3
Answers
The amount and compound interest are Rs22169.11 and Rs6169.11 respectively
Compound interestThe formula for calculating the compound interest is expressed as:
P(t) = P0(1+r)^t
Substitute the given parameters
P(7/3) = 16000(1+0.15)^7/3
P(7/3) = 16000(1.15)^7/3
P(7/3) = 22169.11
For the interest
Interest = 22169.11 - 16000
Interest = 6169.11
Hence the amount and compound interest are Rs22169.11 and Rs6169.11 respectively
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Graph the function on the interval [-5, 2).
g(x) = [[x+4]]
4
Answers
Answer:
x=2 , y=6
Given: the interval (-5, 2) The graph are given that;
•°• g(x) = [ [ x +4 ] ]
g(-5) = [[ -5+4]]
= -1 (imposible)
g(2) = [[2+4]] = 6
x = 2
Let g(x) = y
= [[ x+4]]
y = 6
g(x) = 6 ✔
•°• x + 4 = 6
x = 2
g(y) = [[ y+4]] = 10
y + 4 = 10
y = 6
x = 2 , y = 6 ✔✔✔✔
Need the answer for number 3 please!!
Answers
Answer: No
Step-by-step explanation:
The graph is increasing, yet as p increases, the value of 100/p decreases, meaning that the graph should be decreasing.
A committee of 4
is being formed randomly from the employees at a school: 4
administrators, 30
teachers, and 4
staff. What is the probability that all 4
members are teachers? Express your answer as a fraction in lowest terms or a decimal rounded to the nearest millionth.
Answers
The probability that all 4 are teachers is 0.0000135.
How to solve for the probabilityThe total number is =
4 + 30 + 4
= 38
The committee of 4 from 38 =
38C4 = 73815
The committee of 4 from 4 teachers =
4C4 = 1 way
The total favorable cases = 1 way
Probability = favorability/ total cases
= 1/73815
= 0.0000135
Hence the probability that all 4 are teachers is 0.0000135.
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PLEASE HELP !!! URGENT!!!
What is the range of f(x)?
O {f(x)
O {f(x)|-∞
O {f(x)|4
O {f(x)|0sf(x)<∞}
Answers
Answer:
best ans is { f(x)| –∞ < f(x) ≤ 4}
Step-by-step explanation:
usually to find the range of a fn, u need to see what the value can be. the graph show only a small range of x values. but u can see f(x) is definitely < 4. so the ans is { f(x)| –∞ < f(x) ≤ 4}
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Participants in a darts tournament get 4 points
if they hit the red circle, 1 point if they hit the
blue circle, and no points if they miss both
circles. Each participant has 4 darts. How
many different scores are possible if everyone
gets at least one point?
Answers
Using the Fundamental Counting Theorem, it is found that 80 different scores are possible if everyone gets at least one point.
What is the Fundamental Counting Theorem?It is a theorem that states that if there are n things, each with [tex]n_1, n_2, \cdots, n_n[/tex] ways to be done, each thing independent of the other, the number of ways they can be done is:
[tex]N = n_1 \times n_2 \times \cdots \times n_n[/tex]
There are 4 darts, and for each dart 3 possible scores, hence:
[tex]n_1 = n_2 = n_3 = n_4 = 3[/tex]
Hence the number of possible scores, removing the one score with zero points on all four rounds, is:
N = 3 x 3 x 3 x 3 - 1 = 80.
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From a group of 6 men and 4 women, how many committees of 2 men and 3 women can be formed?
Answers
The number of ways committees of 2 men and 3 women can be formed is 60.
What is Permutation and Combination ?The method of arranging objects in order is called Permutation and the method of selecting things from a group of objects such that the order doesn't matter is called Combination.
Total Men = 6
Total Women = 4
Committee should consists of 2 men and 3 women
2 men from 6 men can be selected in [tex]\rm ^6 C _2[/tex] ways
3 women from 4 women can be selected in [tex]\rm ^4C_3[/tex] ways
The number of ways committees of 2 men and 3 women can be formed can be determined by Multiplication Principle
[tex]\rm ^6 C _2[/tex] * [tex]\rm ^4C_3[/tex]
15 * 4
= 60 ways
Therefore the number of ways committees of 2 men and 3 women can be formed is 60.
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5. In 2011, Manitoba progressive income tax rates were 10.8% on the first $31,000, 12.75% on the next $36,000, anc
17.4% on any additional income. If your gross taxable earnings for the year were $85,000, what percentage of your
earnings did you pay in taxes?
Answers
Step-by-step explanation:
0 <= income <= 31000 : 10.8%
31000 < income <= 31000+36000 = 67000 : 12.75%
67000 < income < anything above 67000 : 17.4%
the total income is
$85,000
the taxes paid are
10.8% of 31000 = $3348
12.75% of 67000 - 31000 = 12.75% of 36000 = $4590
17.4% of 85000 - 67000 = 17.4% of 18000 = $3132
so, out of $85000 you paid
3348
4590
3132
----------
$11,070
taxes
100% = 85000
1% = 100%/100 = 85000/100 = 850
how many % are 11070 ?
well, as many as how often 1% fits into that amount :
11070 / 850 = 13.02352941...% ≈ 13.02%
What number is 15% of 43
?
43 % of 300 is what
number?
12% of what number is 43?
43 is what percent of 106?
What percent of 43 is 6?
Answers
Step-by-step explanation:
So when a question asks what is x% of the y number. It's asking you to convert the x into decimal form by dividing by 100 and then multiply it by y. This gives you the equation: [tex]y * \frac{x}{100}[/tex] which gives you x% of y. so 15% of 43 is [tex]43 * \frac{15}{100} = 6.45[/tex]. 43% of 300 is [tex]300 * \frac{43}{100} = 129[/tex].
the 12% of what number is 43 is a bit more tricky. It's asking you to instead find a number in which 12% of it is equal to 43. So instead of plugging solving for the percentage (which is already given) you solve for y. This gives you the following equation: [tex]y * \frac{12}{100} = 43[/tex]. Now all you do is calculate 12/100 which gives you [tex]y * 0.12 = 43[/tex]. now divide both sides by 0.12 to solve for y. This gives you [tex]y = 358.\overline{33}[/tex]
43 is what percent of 106? This question is also a bit tricky, but instead of solving for y, you're solving for x. So plug in the known values, which gives you the equation: [tex]106 * \frac{x}{100} = 43[/tex]. Divide both sides by 106 to get [tex]\frac{x}{100} \approx 0.406[/tex] and now multiply both sides by 100. this gives you [tex]x \approx 40.57[/tex] which is the answer 40.57%
What percent of 43 is 6. This is asking the same thing just in a different way. So percentage = unknown, entire number = 43, entire number * percentage = 6. With these values we get the equation: [tex]43 * \frac{x}{100} = 6[/tex]. Divide both sides by 43 to get [tex]\frac{x}{100} \approx 0.140[/tex] now multiply by 100 to get [tex]x \approx 13.95[/tex] which is the answer 13.95%
can somebody please explain question (i) and (ii) to me
Answers
hey buddy, if u attach your question to this we can help you to find an answer for your question.
☆...hope this helps...☆
_♡_mashi_♡_