Answer:
The students would be expected to choose rock be 80 or students choose hip hop be 160 or choose to country be 120.
Step-by-step explanation:
Given:
In a survey of 90 students 20 choose rock, 40 choose hip hop and 30 choose country.
Now, to find the students expected to choose hip hop or rock or country in a school of 360 students.
Let the number of students expected to choose rock be [tex]x.[/tex]
Let the number of students expected to choose hip hop be [tex]y.[/tex]
Let the number of students expected to choose country be [tex]z.[/tex]
Total number of students = 360.
Now, to get the number of students choosing hip hop or rock or country by using cross multiplication method:
In a survey of 90 students 20 choose rock.
So, 90 is equivalent to 20.
Thus, 360 is equivalent to [tex]x[/tex].
[tex]\frac{90}{20} =\frac{360}{x} \\\\By\ cross\ multiplying\ we\ get:\\\\90x=7200\\\\Dividing\ both\ sides\ by\ 90\ we\ get:\\\\x=80.[/tex]
Thus, the number of students expected to choose rock is 80.
Now,
In a survey of 90 students 40 choose hip hop.
So, 90 is equivalent to 40.
Thus, 360 is equivalent to [tex]y.[/tex]
[tex]\frac{90}{40} =\frac{360}{y} \\\\By\ cross\ multiplying\ we\ get:\\\\90y=14400\\\\Dividing\ both\ sides\ by\ 90\ we\ get:\\\\y=160.[/tex]
Therefore, 160 students expected to choose hip hop.
And,
In a survey of 90 students 30 choose country.
So, 90 is equivalent to 30.
Thus, 360 is equivalent to [tex]y.[/tex]
[tex]\frac{90}{30} =\frac{360}{z} \\\\By\ cross\ multiplying\ we\ get:\\\\90x=10800\\\\Dividing\ both\ sides\ by\ 90\ we\ get:\\\\x=120.[/tex]
Hence, 120 students expected to choose country.
Therefore, the students would be expected to choose rock be 80 or students choose hip hop be 160 or choose to country be 120.
4+35=23+43-23+46-34-34+6
Answer:
4+35=39, 23+43-23+46-34-34+6=27. So it is a no solution question.
Step-by-step explanation:
Both of the equations do not equal
Answer:
69
Step-by-step explanation:
I love the number 69, and tbh it's the answer to everything
antiderivative of Find the most general antiderivative of the function. (Check your answer by differentiation. Use C for the constant of the Find the most general antiderivative of the function. (Check your answer by differentiation. Use C for the constant of the antiderivative.) f(x) = 6 x 5 − 8x4 − 9x2.) f(x) = 6x5 − 8x4 − 9x2 the function.
Answer:
x^6 - (8/5)x^5 - 3x^3 + C.
Step-by-step explanation:
f(x) = 6x^5 - 8x^4 - 9x^2.
Using the general form antiderivative of Ax^m = Ax(m+1) / (m+1)+ C:
Antiderivative = 6 * x^(5+1) / 6 - 8 * x^(4+1) / 5 - 9 * x^(2+1) / 3 + C
= 6x^6/6 - 8x^5/5 - 9x^3/3 + C
= x^6 - (8/5)x^5 - 3x^3 + C.
Differentiating:
f'(x) = 6x^(6-1) - 8 x^(5-4) - 9x^(3-1) + 0
f'(x) = 6x^5 - 8x^4 - 9x^2.
The most general antiderivative of the given function f(x) = 6x5 − 8x4 − 9x2 is F(x) = x^6 - 8/5 * x^5 - 3x^3 + C, where C is the constant of the antiderivative.
Explanation:To find the most general antiderivative of the given function f(x) = 6x5 − 8x4 − 9x2, we need to perform the process of integration, which is the reverse of differentiation. The antiderivative F(x) will be found by integrating each term of the function separately.
The antiderivative of f(x) will then be:
F(x) = ∫6x5 dx - ∫8x4 dx - ∫9x2 dx,
Transitioning to the next step by applying the power rule for integration, we add 1 to the exponent and divide by the new exponent, we obtain
F(x) = 6/6 * x^(5+1) - 8/5 * x^(4+1) - 9/3 * x^(2+1) + C
Simplified, the antiderivative F(x) becomes:
F(x) = x^6 - 8/5 * x^5 - 3x^3 + C,
where C is the constant of the antiderivative.
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79. Revenue. The revenue (in dollars) from the sale of x infant car seats is given by R1x2 = 60x - 0.025x2 0 ... X ... 2,400 (A) Find the average change in revenue if production is changed from 1,000 car seats to 1,050 car seats. (B) Use the four-step process to find R′1x2. (C) Find the revenue and the instantaneous rate of change of revenue at a production level of 1,000 car seats, and write a brief verbal interpretation of these results.
Question:
59 Revenue. The revenue (in dollars) from the sale of x infant car seats for infants is given by
R(x) =60·x - 0.025·x² 0 ≤ x ≤ 2400
(A) Find the average change in revenue if production is changed from 1,000 car seats to 1,050 car seats.
(B) Use the four-step process to find
(C) Find the revenue and the instantaneous rate of change of revenue at a production level of 1,000 car seats, and write a brief verbal interpretation of these results
Answer:
(A) $437.5
(B) R'(x) = 60 - 0.05·x
(C) $10
Step-by-step explanation:
(A) Here we have the change in revenue when production is increased from 1,000 car seats to 1,050 car seats is given as follows;
R(1050) - R(1000) = 60×1050 - 0.025×1050² - (60×1000 - 0.025×1000²)
R(1050) - R(1000) = 63000 - 27562.5 - 35000 = $437.5
(B) R'(x) is given by
Step 1. R(x + h) = 60·(x+h) - 0.025·(x+h)²
Step 2 R(x + h) - R(x) = 60·(x+h) - 0.025·(x+h)² - 60·x - 0.025·x² = [tex]-\frac{h^2+(2x-2400)h}{40}[/tex]
Step 3
[tex]\frac{R(x+h)- R(x)}{h} = -\frac{h^2+(2x-2400)h}{40 \times h} = -\frac{h +2x - 2400}{40}[/tex]
Step 4
[tex]\lim_{h \to 0} \frac{R(x+h)- R(x)}{h} = \lim_{h \to 0} -\frac{ h +2x - 2400}{40}[/tex]
∴ R'(x) = 60 - 0.05·x
(c) The revenue at a production level of 1000 car seats is
R(1000) = (60×1000 - 0.025×1000²) = $35,000
The instantaneous rate of change of revenue is given as follows
R'(x) = 60 - 0.05·x = 60 - 0.05×1000 = $10.
A) The average change in revenue when production is changed from 1,000 car seats to 1,050 car seats is $8.75. B) The derivative of the revenue function R1(x) with respect to x is R′1(x) = 60 - 0.05x. C) At a production level of 1,000 car seats, the revenue is $35,000 and the instantaneous rate of change of revenue is $10.
Explanation:(A) To find the average change in revenue, we need to calculate the change in revenue and divide it by the change in the number of car seats produced. Let's calculate:
For 1,000 car seats, the revenue is R1(1000) = 60(1000) - 0.025(10002) = $60,000 - $25,000 = $35,000.For 1,050 car seats, the revenue is R1(1050) = 60(1050) - 0.025(1050x2) = $63,000 - $27,562.50 = $35,437.50.The change in revenue is $35,437.50 - $35,000 = $437.50.The change in the number of car seats produced is 1,050 - 1,000 = 50.The average change in revenue is $437.50/50 = $8.75.(B) To find R′1(x), we need to calculate the derivative of the revenue function R1(x) with respect to x. Let's differentiate:
R′1(x) = d/dx(60x - 0.025x2) = 60 - 0.05x
(C) At a production level of 1,000 car seats, the revenue is $35,000. The instantaneous rate of change of revenue (also known as the marginal revenue) at this production level can be found by substituting x = 1,000 into R′1(x):
R′1(1000) = 60 - 0.05(1000) = 60 - 50 = $10. The revenue at this production level is $35,000 and the instantaneous rate of change of revenue is $10, which represents the additional revenue obtained from producing one additional car seat.
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answers to bad dog breakout
Without specific context or questions from 'Bad Dog Breakout', it's challenging to provide a specific answer. It's recommended to read the text carefully, breakdown the text, and note down important points such as characters, plot, and themes.
Explanation:I apologize but without the detailed context or exact questions from 'Bad Dog Breakout', it's challenging to provide a specific answer. 'Bad Dog Breakout' might be a literary work or a segment from an English curriculum, and the questions can vary greatly. However, I encourage you to read and comprehend the text carefully. Breaking it down paragraph by paragraph, identifying characters, noting down the plot, any significant themes and important details might help.
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Connor went to a carnival with 22.50$. He bought a hot dog and a drink for $3.75 and he wanted to spend the rest of his money on ride tickets which cost $1.25 each. What is the maximum number of ride tickets that he can buy
Answer:
15
Step-by-step explanation:
22.50-3.75=18.75
18.75/1.25=15
BRAINLIEST WOULD BE APPERCIATED
The maximum number of ride tickets that he can buy is; 15
Division:Connor has 22.50$, bought a hot dog and a drink for $3.75.
In essence, the amount Connor has left is;
$22.50 - $3.75= $18.75
Therefore, if he wanted to spend the rest of his money on ride tickets which cost $1.25 each, the maximum number of ride tickets that he can buy can be evaluated as follows;
No. of ride tickets = $18.75/$1.25
No. of ride tickets = 15
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What is the domain of the function y=sqrt x+4
Answer:
domain of y = sqrt (x+4) is [-4, +inf)
Step-by-step explanation:
[-4, +inf), -4 is included because sqrt(-4 + 4) is defined but is undefined at the points from (-inf, -5].
If six people decide to come to a basketball game, but three of them are only 2/5 sure that they will stay for the entire time (the other three are sure they'll stay the whole time), what is the probability that at the end, at least 5 people stayed the entire time
Answer:
the probability that at the end, at least 5 people stayed the entire time = 0.352
Step-by-step explanation:
From the question, 3 of the people are sure to stay the whole time. So, we'll deduct 3 from 6.which leaves us with 3 that are only 2/5 or 0.4 sure that they will stay the whole time.
Thus, what we need to compute to fulfill the probability that at the end, at least 5 people stayed the entire time of which we know 3 will stay, so for the remaining 3,we'll compute;
P[≥2] which is x~bin(3,0.4)
Thus;
P(≥2) = (C(3,2) x 0.4² x 0.6) + (C(3,3) x 0.4³)
P(≥2) = 0.288 + 0.064
P(≥2) = 0.352
find the value of sin(θ) for an angle θ in standard position with a terminal ray that passes through the point (-5, -12)
Answer:
c. -12/13
Step-by-step explanation:
it will be the y-coordinate divided by the distance from the origin, or (-12) / [tex]\sqrt{5^2+12^2}[/tex] = -12/13
Answer:
C. -12/13
Step-by-step explanation:
(-5,-12) is in the third quadrant
So sin would be negative
Hypotenuse = sqrt(5² + 12²)
sqrt(169)
13
sin(theta) = -12/13
Halla la media aritmética para las siguientes situaciones: i. Para poder clasificar a las finales de Jokie, el equipo debe tener un promedio de goles mayor a 20 puntos. Los siguientes son los puntajes obtenidos: 25, 12, 15, 23, 24, 39, 13, 31, 19, 16. ¿Clasificaron a finales? AYUDENME
Answer:
The team qualified for the finals.
Step-by-step explanation:
The question is:
Find the arithmetic mean for the following situations: i. In order to qualify for the Jokie Finals, the team must have a goal average greater than 20 points. The following are the scores obtained: 25, 12, 15, 23, 24, 39, 13, 31, 19, 16. Did they qualify for the finals? HELP ME
The average goal the team must have to win the Jokie finals is more than 20 points.
The goals obtained by the team are:
X = {25, 12, 15, 23, 24, 39, 13, 31, 19, 16}
The arithmetic mean is the average value of a data set. The formula to compute the arithmetic mean is:
[tex]\bar X=\frac{1}{n}\sum X_{i}[/tex]
Compute the arithmetic mean of the goals scored by the players as follows:
[tex]\bar X=\frac{1}{n}\sum X_{i}[/tex]
[tex]=\frac{1}{10}\times (25+12+15+23+24+39+13+31+19+16)[/tex]
[tex]=\frac{1}{10}\times 217\\[/tex]
[tex]=21.7[/tex]
The arithmetic mean of the goals scored by the players is 21.7 points.
The average score is greater than 20 points.
Thus, the team qualified for the finals.
Which expression is equivalent to 5(c + d) + 2(c + d)?
Question 5 options:
7(c + d)
7 + (c + d)
7c + d
7 + 7d
Please I will give brainliest
Answer:
A) 7(c + d)
Step-by-step explanation:
5(c + d) + 2(c + d)
5c + 5d + 2c + 2d
7c + 7d
7(c + d)
Answer:
A
Step-by-step explanation:
Distribute the 5
5(c + d) + 2(c + d)
5*c+5*d +2(c + d)
5c+5d +2(c + d)
Distribute the 2
5c+5d+ 2*c+2*d
5c+5d+2c+2d
Combine like terms (combine the ds and the cs)
5c+2c +5d+2d
7c+7d
A is equivalent to this answer
7(c + d)
Distribute the 7
7*c+7*d
7c+7d
So, A is the answer
plz help ill give brailest
Answer:
[tex]\frac{4^{15} }{b^{21} }[/tex]
Step-by-step explanation:
First, multiply the exponent 7 and the -3 together, giving you:
[tex]b^{-21}[/tex]
Then, multiply the exponent 5 and the -3 together, giving you:
[tex]4^{-15}[/tex]
But since you can't have a negative exponent, you need to switch the numbers in their places. This is because, when you have a negative exponent, you either switch it to under 1 or over 1, depending on where it currently is:
[tex]\frac{4^{15} }{b^{21} }[/tex]
Determine if each equation is a linear equation.
[Linear equation / Not a linear equation]
1) [tex]5x_1 + x_2 - 7x_3 = 4[/tex]
2) [tex]5x_1 + 4.6x_2 + 12x_3 = -5[/tex]
3) [tex]3x_1 - x_3 = -5x_2 + 7[/tex]
4) [tex]3x_1x_2 + x_3 = 5[/tex]
5) [tex]4x_1^3 + x_2 = 5[/tex]
6) [tex]6x_1 - 4x_2 + x_3 = 0[/tex]
Answer:
Linear-1,2,3,6
Nin-Linear-4,5
Step-by-step explanation:
A linear equation is an equation in which the highest power of the variable is 1.
Out of the given equations, the following are linear.
1) [tex]5x_1 + x_2 - 7x_3 = 4[/tex]
2) [tex]5x_1 + 4.6x_2 + 12x_3 = -5[/tex]
3) [tex]3x_1 - x_3 = -5x_2 + 7[/tex]
6) [tex]6x_1 - 4x_2 + x_3 = 0[/tex]
These equations on the other hand are nonlinear.
4) [tex]3x_1x_2 + x_3 = 5[/tex]
5) [tex]4x_1^3 + x_2 = 5[/tex]
No 4 contains a term which is the product of two variables therefore it is not linear.
No 5 contains a term whose highest power is 3. Such an equation is a Cubic Equation.
Which ordered pair is a solution of the equation y-4=7(x-6)
Answer:
y=7x-38
Step-by-step explanation:
Which equation can be used to find the surface area of the cylinder?
A cylinder with a diameter of 6 centimeters and height of 14 centimeters.
S = 2 pi (14) squared + 2 pi (14) (6)
S = 2 (3) squared + 2 (3) (14)
S = 2 pi (6) squared + 2 pi (6) (14)
S = 2 pi (3) squared + 2 pi (3) (14)
Answer:
S = 2 pi (3) squared + 2 pi (3) (14)
Step-by-step explanation:
The formula for the area of a circle is ...
A = πr²
The cylinder has two circular bases with radius 3 cm, so their combined area in square centimeters is ...
A = 2π(3²) . . . . . . matches a term in the last choice
__
The lateral area of the cylinder is the product of the height and the circumference of the base. That is ...
A = 2πrh
For the given radius and height, the lateral area in square centimeters is ...
A = 2π(3)(14) . . . . . . matches a term in the last choice
__
The total surface area is the sum of the areas of the bases and the lateral area, so is ...
S = 2π(3²) +2π(3)(14) . . . . . matches the last choice
_____
Comment on answer choices
We could choose the correct answer based solely on the area of the bases of the cylinder.
Answer:
S = 2 pi (3) squared + 2 pi (3) (14)
Step-by-step explanation:
Bryan is asked to write an inequality to represent the graph.
A number line going from negative 16 to negative 10. An open circle is at negative 14. Everything to the right of the circle is shaded.
He writes Negative 14 less-than-or-equal-to x.
Which error did Bryan make?
Answer:
c
Step-by-step explanation:
The error was to include the number -14 in the inequality.
What is an Inequality?An inequality is a statement that is formed when two expressions are joined using an inequality operator.
The inequality that represents the statement is
x > -14
Bryan wrote the inequality as x ≥ -14 , which is wrong as there is an open circle at -14 on the number line.
An open circle depicts that the number is not included.
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hey guys:) how can one solve this?
x⁴ - 2x + 2
please with an explanation
Answer:
81x+2
Step-by-step explanation:
2x+x=3x
3×3×3×3=81x
Your friend has two standard decks of 52 playing cards and asks you to randomly draw one card from each deck. What is the probability that you will draw two spades? Express your first answer as a fraction in simplest form
Answer:
Hence the probability of getting 2 spades will be 1/16
Step-by-step explanation:
Given:
Two deck if playing cards
To Find:
Probability that will get two spades
Solution:
As we know that ,there 52 playing cards in a deck
and 13 of that are spades
So probability of getting spade from a deck is ,
P(spades)=total number of spades /Total number of cards.
P=13/52
P=1/4
Similar for the second deck of card,
Required probability is that , getting spades from each deck
It is given by,
Required probability =Probability of spades in 1st AND Probability of spade in 2nd deck
As there is use of AND operator there should multiplication of two events,
Required probability =1/4*1/4
=1/16
can you guys please help me with number 13 and with shown work
Answer:
Step-by-step explanation:
Let's solve for c.
6c−9d=111
Step 1: Add 9d to both sides.
6c−9d+9d=111+9d
6c=9d+111
Step 2: Divide both sides by 6.
6c
6
=
9d+111
6c=3/2 d+37/2
Answer:
c= 3/2 d+37/2
Second one
Let's solve for c.
5c−9d=103
Step 1: Add 9d to both sides.
5c−9d+9d=103+9d
5c=9d+103
Step 2: Divide both sides by 5.
5c
5
=
9d+103
5c =9/5 d+103/5
Answer:
c=8, d = -7
Step-by-step explanation:
6c - 9d = 111
5c - 9d = 103
Multiply the second equation by -1
-5c + 9d = -103
Add this to the first equation to eliminate d
6c - 9d = 111
-5c + 9d = -103
------------------------
c = 8
Now we need to find 9
6c - 9d = 111
Substitute in c=8
6(8) -9d = 111
48 - 9d = 111
Subtract 48 from each side
49-48 -9d = 111-48
-9d =63
Divide each side by -9
-9d/-9 = 63/-9
d = -7
A yearbook company was investigating whether there is a significant difference between two states in the percents of high school students who order yearbooks. From a random sample of 150 students selected from one state, 70 had ordered a yearbook. From a random sample of 100 students selected from the other state, 65 had ordered a yearbook. Which of the following is the most appropriate method for analyzing the results?A. A one-sample zz-test for a sample proportionB. A one-sample zz-test for a population proportionC. A two-sample zz-test for a difference in sample proportionsD. A two-sample zz-test for a difference in population proportionsE. A two-sample zz-test for a population proportion
Answer:
D. A two-sample z-test for a difference in population proportions
Step-by-step explanation:
There are two samples, and we want to test for the difference between the proportions of two different populations.
What expression represents the profit, and what is the profit
if 240 cell phones are sold?
O 40x – 30; $2,400
40x - 30; $9,570
O 70x + 50; $16, 850
O 70x + 50; $28,800
Answer:
C: 70x+50; $16,850
Step-by-step explanation:
I just took the test don’t fail :)
Which is the equation of a line that has a slope of 4 and passes through point (1, 6)?
Answer:
The answer to your question is y = 4x + 2
Step-by-step explanation:
Data
slope = m = 4
Point = (1, 6)
Process
1.- Write the equation of the line in the point slope form.
y - y1 = m(x - x1)
2.- Identify the values of x1 and y1
x1 = 1 y1 = 6
3.- Substitution
y - 6 = 4(x - 1)
4.- Simplification
y - 6 = 4x - 4
5.- Solve for y
y = 4x - 4 + 6
6.- Result
y = 4x + 2
Find the area of a circle with a circumference of \blueD{50.24}50.24start color #11accd, 50, point, 24, end color #11accd units.
Answer:
[tex]201 cm^2[/tex]
Step-by-step explanation:
The circumference of a circle is given by:
[tex]c=2\pi r[/tex]
where
r is the radius of the circle
For the circle in this problem,
c = 50.24 cm
Therefore the radius is:
[tex]r=\frac{c}{2\pi}=\frac{50.24}{2\pi}=8 cm[/tex]
The area of a circle is given by the formula
[tex]A=\pi r^2[/tex]
where r is the radius.
For the circle in this problem,
r = 8 cm
So the area is
[tex]A=\pi \cdot 8^2 = 201 cm^2[/tex]
The area of the circle is 201 cm square.
Calculation of the area of the circle:Since we know that
Circumference of the circle = [tex]2\pi r[/tex]
So here radius should be
[tex]= c\div 2\pi \\\\= 50.24\div 2\pi[/tex]
= 8 cm
Now the area of the circle is
[tex]= \pi r^2\\\\= 3.14\times 8^2[/tex]
= 201
Hence, we can conclude that The area of the circle is 201 cm square.
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Just Logarithms! 80 points!
1. Evaluate: log216
Select the appropriate response
A) 0
B) -1
C) 7
2. Express as a simple logarithm 2loge2+3logen.
Select the appropriate response:
A) Ln 2n2
B) ln 4n3
C) 4Ln 2n2
3. Solve log3 (27)
Select the appropriate response
A) 1
B) 2
C) 3
D) 8
4. Solve log2 (64)
Select the appropriate response:
A) 6
B) 5
C) 4
D) 13
5. Solve: log5 (625)
Select the appropriate response
A) 4
B) 6
C) 9
D) 2
6. Evaluate: log216
Select the appropriate response
A) 5
B) 8
C) 4
7. Solve log3 (81)
Select the appropriate response
A) 8
B) 6
C) 4
D) 72
8. Solve log4 (1)
Select the appropriate response
A) 0
B) 3
C) 1
D) 5
Also I don’t know why there is one two times with different answers
1. A) 0 (I’m not totally sure since there are two of the same thing, but with different answers.)
2. (Not sure)
3. C) 3
4. A) 6
5. A) 4
6. C) 4 (I’m pretty sure it’s 4 if it’s in the way I think it should be in to get 4.)
7. C) 4
8. A) 0
(I tried my best, I’m probably wrong, because I don’t exactly know how to do logarithms yet. Sorry if I got some wrong.)
Answer:
1) B
2) B
3) C
4) A
5) A
6) C
7) C
8) A
4m=4(m−1)
I'm not sure if this is right but i got 0= -4
Answer:
Don't worry, there is no solution.
Step-by-step explanation:
If you end up with 0 equaling something that isntn0 when you're simply solving a variable, there is no solution. But if you get 0=0, it's all real numbers.
what’s the 2nd term in the sequence?
Answer:a fgbvffjnfv
Step-by-step explanation:
I need to go 1,373 miles but the plane travels at 575 miles per hour. how long would it take me to get to my destination?
Answer:2.38782608695652173913043478260869565217
Step-by-step explanation:
you divide 1373 by 575
what are 3 equivalent ratios to 3/4?
Answer:
6/8, 9/12, 12/16
Step-by-step explanation:
Multiply the numerator and denominator by the same amount to maintain the same ration.
[tex]\frac{3}{4} =\frac{6}{8} = \frac{9}{12} =\frac{12}{16}[/tex]
What is the diagonal length of the suitcase
Answer: The diagonal length of the suitcase is 30 inches. Assuming that the length and height of the suitcase form a right angle (90 degree angle), you can use the Pythagorean Theorem ( a2+b2 = c2) to solve this problem. The diagonal length is equal to the square root of the sum of the length squared and the height squared.
Step-by-step explanation:
Answer:
30
Step-by-step explanation:
if you think about a rectangle cut by its diagonal then yoou can see that its just 2 right triangles and youre looking for the long end
Using pythagorean theorem you put in the numbers
[tex]24^{2} + 18^2 = c^2[/tex]
solving gives you
[tex]900 = c^2[/tex]
[tex]\sqrt{900} = c[/tex]
30 = c
find the length of the third side to the nearest tenth
Answer:
7.1
Step-by-step explanation:
You can use the Pythagorean Theorem to solve this:
[tex]a^{2} + b^{2} = c^{2}[/tex]
All you need to do is plug in the numbers (in this case, they've already given you the hypotenuse, which is c in the formula, are you're solving for the leg).
[tex]7^{2} + b^{2} = 10^{2}[/tex]
49 + [tex]b^{2}[/tex] = 100
Subtract 49 from both sides:
49 + [tex]b^{2}[/tex] = 100
-49 -49
___________
[tex]b^{2}[/tex] = 51
Square root both sides:
[tex]\sqrt{b^2} = \sqrt{51}[/tex]
b = 7.14
b = 7.1
Weekend Curfews
Determine the values of the letters to complete the
conditional relative frequency table by column.
16 Years
Old
17 Years
Old
Total
0.9
b
0.88
Before
10 p.m.
After
10 p.m.
0.15
0.12
1
Total |
1.0
1.0
Answer: therefore A= 0.1 and B=0.85
Step-by-step explanation:
The values of 'a' and 'b' in the frequency table are 0.1 and 0.1
We have,
To complete the conditional relative frequency table, we need to find the values of the letters 'a' and 'b'.
We know that the total for each row and column should add up to 1.
So, we can use this information to set up two equations and solve for the values of 'a' and 'b'.
Equation 1:
0.9 + b = 0.88
This equation represents the total percentage of students aged 16 years who finish homework before 10 pm.
We subtract 0.9 and 0.88 from both sides to get:
b = 0.88 - 0.9
b = -0.02
This means that the value of 'b' is negative, which doesn't make sense.
So, we made an error in setting up the equation.
We can check the table to find the correct value of 'b'.
We know that the total for the column "Before 10 pm" should be 1.
This means that the sum of the percentages 0.9 and 'b' should be equal to 1.
So,
Equation 2:
0.9 + b = 1
Solving for 'b', we get:
b = 1 - 0.9
b = 0.1
Now, we can use Equation 2 to solve for 'a':
0.15 + a = 0.12
Subtracting 0.15 from both sides, we get:
a = 0.12 - 0.15
a = -0.03
Again, we get a negative value for 'a', which doesn't make sense.
So, we need to check our work again.
We know that the total for the row "16 years" should be 1.
This means that the sum of the percentages 0.9 and 'a' should be equal to 1.
So,
0.9 + a = 1
Solving for 'a', we get:
a = 1 - 0.9
a = 0.1
Therefore,
The values of 'a' and 'b' in the frequency table are 0.1 and 0.1
Learn more about the frequency table here:
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