The opposite of Carlo's elevation is 12 feet
Carlos is said to have submerged himself in a 12-foot-deep swimming pool.
Carlos' elevation will be -12 feet with regard to the surface because he submerged himself to the pool's bottom.
The elevation of Carlos as it relates to the ground would be opposite of -12 feet, or -(- 12) feet.
12 feet
Carlos' elevation in relation to the ground is therefore 12 feet higher than it should be.
Thus the opposite of Carlo's elevation is 12 feet .
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please help NEED FAST
a) The quadratic equation behind the parabola is y = (4 / 5) · x² - (8 / 5) · x - 1.
b) There are two x-intercepts: x₁ = - 0.5, x₂ = 2.5.
How to derive a quadratic equation and find its x-intercepts
Mathematically speaking, parabolas are represented by quadratic equations, whose standard form is introduced below:
y = a · x² + b · x + c
Where a, b, c are real coefficients.
The values of the three coefficients are found from the knowledge of three distinct points on Cartesian plane. First, choose the three points:
(x₁, y₁) = (- 0.5, 0), (x₂, y₂) = (2.5, 0), (x₃, y₃) = (0, - 1)
Second, construct the system of linear equations with all the given points and the standard form of the quadratic equation:
0.25 · a - 0.5 · b + c = 0
6.25 · a + 2.5 · b + c = 0
c = - 1
Third, solve the system by numerical methods:
(a, b, c) = (4 / 5, - 8 / 5, - 1)
Fourth, write the quadratic equation:
y = (4 / 5) · x² - (8 / 5) · x - 1
The x-intercepts of the quadratic equation are the points of the curve that pass through the x-axis. Then, the x-intercepts are x₁ = - 0.5 and x₂ = 2.5.
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Express 72 1/2% asa fraction in its lowest term
The percentage of the number is 29/40 when The number is 72 1/2.
Given that,
The number is 72 1/2
We have to find the percentage of the number.
The Latin word "per centum," which means "by the hundred," is where the word "percentage" originally came from. Percentages are fractions when the denominator is 100. To put it another way, it's the relationship between a part and a whole in which the value of the whole is always assumed to be 100.
We have number,
72 1/2
145/2
145/2× 1/100
145/200
29/40
Therefore, The percentage of the number is 29/40 when The number is 72 1/2.
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A circular dartboard has diameter 40cm. Its bull’s eye has diameter of 8 cm. if an amateur throws a dart and it hits the board, what is the probability that the dart hits the bull’s eye.
Answer:
a value of is required in the following exercises, use
A circular dartboard has diameter 40 Its bull's eye has diameter 8
a. If an amateur throws a dart and it hits the board. What is the probability that the dart hits the bull's eye?
b. After many throws, 75 darts have hit the target. Estimate the number hitting the bull's eye.
Step-by-step explanation:
hope it helps! please mark brainlets
which exponential function has an x- intercept?(picture of functions below )
Question: which exponential function has an x-intercept?
Explanation:
Let the function:
[tex]f(x)=100^{x\text{ -5 }}\text{ - 1}[/tex]An x-intercept or zero of the function is when y= f(x)=0. In this case, notice that this occurs when x=5, since:
[tex]f(5)=100^{5\text{ -5 }}\text{ - 1= 100}^0\text{ - 1 = 1-1 =0}[/tex]thus, this function must cross the x-axis at the point x= 5. On the other hand, this function has a horizontal asymptote at y=-1, so the range of this function would be all y > -1. This fact further evidences that this function crosses the x-axis.
Answer: we can conclude that the correct answer is:
[tex]f(x)=100^{x\text{ -5 }}\text{ - 1}[/tex]Sam bought a jacket for $34, which is one-third of the original price. How much did thejacket cost originally?
Let the original cost of the jacket be x.
Now, saying that one-third of the original cost of the jacket is $34, is mathematically equivalent to:
[tex]\frac{1}{3}\times x=34[/tex]Now we have to solve the resulting equation in order to obtain the value of x
This is done as follows:
[tex]\frac{1}{3}\times x=34[/tex][tex]\Rightarrow\frac{x}{3}=34[/tex][tex]\Rightarrow x=3\times34[/tex][tex]x=102[/tex]Therefore, the original cost of the jacket is $102
Which inequality in factored form represents the region less than the quadratic function with zeros-40 and -50 and
includes the point (-55, -75) on the boundary line?
O y<-(x-40)(x-50)
O ys-(x+40)(x+50)
Oys-(x-40)(x - 50)
O y<-(x +40)(x+50)
Please help
The inequality that reflects the given region, according to the Factor Theorem, is:
y< -(x+40)(x+50)
What is the Factor Theorem?When completely factoring polynomials, the factor theorem is employed in mathematics. It is a theorem that relates the factors and zeros of a polynomial. If f(x) is a polynomial of degree n 1 and 'a' is any real number, then (x-a) is a factor of f(x) if f(a)=0.
According to the Factor Theorem, a polynomial function with roots x₁, x₂, ....xₙ is given by
f(x)=a(x-x₁)(x-x₂)...(x-xₙ)
In which a is the leading coefficient.
The roots are given as follows:
x₁=-40, x₂=-50
Hence:
y = a(x + 40)(x +50)
It includes the point (-55,-75), hence:
-75 = a(-55 + 40)(-55 +50)
a = 75/(15 x 5)
a = 1
The equation that is less than the region is:
y< -(x+40)(x+50)
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Answer:
d
Step-by-step explanation:
Isosceles triangle JKL has a perimeter of 36 units and the given vertices.
J (-3, -9)
K (-3, 7)
L (X, -1)
What is the possible x-coordinate for point L?
The possible x-coordinate for point L are x = (-16.85)(10.85)
What is perimeter?For geometry, the perimeter of the shape is defined as the total length of the boundary. The perimeter is determined by adding all the sides and side lengths that enclose the shape. It is measured in units such as centimeters, meters, feet and inches,
For the given question:
JK = [tex]\sqrt{(-3-(-3))^{2}+(-9-7)^{2} }[/tex]
JK = [tex]\sqrt{0^{2} +16^{2} }[/tex]
JK = 16
JL = [tex]\sqrt{(-3-x)^{2} +(-9-(-1))^{2} }[/tex]
JL = [tex]\sqrt{(-3-x)^{2} + 8^{2} }[/tex]
JL = [tex]\sqrt{(-3-x)^{2} + 64}[/tex]
KL = [tex]\sqrt{(-3-x)^{2} + (7-(-1))^{2} }[/tex]
KL = [tex]\sqrt{(-3-x)^{2} + 8^{2} }[/tex]
KL = [tex]\sqrt{(-3-x)^{2} + 64}[/tex]
Since, JK + JL+ KL = 36 [Perimeter of triangle]
As we have already calculated, JK = 16
So, 16 + JL+ KL = 36
JL+ KL = 36 - 16
JL+ KL = 20
Since JKL is an isosceles triangle, JL= KL
So, let's replace KL by JK in the above equation:
JL+ JL = 20
2JL = 20
JL = 10
Now, substitute the value of JL in following equation:
JL = [tex]\sqrt{(-3-x)^{2} + 64}[/tex]
16 = [tex]\sqrt{(-3-x)^{2} + 64}[/tex]
Now square both sides,
256 = (-3-x)² + 64
256-64 = (-3-x)²
192 = (-3-x)²
13.85 = -3-x
x = -3 ± 13.85
x = (-3 - 13.85) (-3 + 13.85)
x = (-16.85)(10.85)
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which of the following is the largest? half of 78a third of 114one-fifth of 190
Let's get the following value for the given statements and check which are the largest.
a) Half of 78.
We compute for the half of 78, which we divide 78 by 2. We have
[tex]\frac{78}{2}=39[/tex]b) A third of 114
A third of a number means we divide the number by 3. Dividing 114 by 3, we get
[tex]\frac{114}{3}=38[/tex]c) One-fifth of 190
One-fifth of a number means we divide the number by 3. Dividing 190 by 5, we get
[tex]\frac{190}{5}=38[/tex]As we can see on the results above, the largest is half of 78.
Find the number of different ways that an instructor can choose 4 students from a class of 23 students for a field trip.
We have to find how many ways we can group 23 students in groups of 4.
This can be calculated as a combination of 23 in 4, as order does not matter and there is no repetition.
We can calculate it as:
[tex]\begin{gathered} C(n,r)=\frac{n!}{r!(n-r)!} \\ C(23,4)=\frac{23!}{4!(23-4)!} \\ C(23,4)=\frac{23!}{4!19!} \\ C(23,4)=\frac{23\cdot22\cdot21\cdot20}{4\cdot3\cdot2\cdot1} \\ C(23,4)=\frac{212520}{24} \\ C(23,4)=8855 \end{gathered}[/tex]Answer: there are 8855 ways.
pls help guyssssssssss
Which relation is a function?
I’m confused on this. can anyone help me out?
Answer:
The one the u have marked is a function.
Step-by-step explanation:
If you draw a vertical line through each one, each line only goes through one point
Cole scored 18 points in his team's last game. That was 36% of the team's total points for the
game. How many total points did the team score?
The team's total points for the game was 50.
According to the question,
We have the following information:
Cole scored 18 points in his team's last game. That was 36% of the team's total points for the game.
Now, let's take the score points of the team in the game to be x points.
So, we have the following expression:
36% of x = 18
36x/100 = 18
Multiplying by 100 on both sides of the equation:
36x = 1800
Dividing by 36 on both sides of the equation:
x = 1800/36
x = 50
Hence, the team's total points for the game was 50.
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Biologists notice an alarming trend in the walleye population in Lake Erie. Despite efforts, the population is decreasing by 15% each year. They estimate the walleye population was 26 million at the beginning of the current year. Write a sequence that lists the population for the first 4 years using 26 million as the first term.
Given:
The initial population is p = 26 million.
The decreasing percentage is r = 15% each year = 0.15.
The objective is to write the sequence of population after 4 years.
Explanation:
The general formula of population decrease is,
[tex]A=P(1-r)^t\text{ . . . . .(1)}[/tex]The population in the 1st-year can be calculated by substituting t=1 in equation (1).
[tex]\begin{gathered} A_1=26(1-1.15)^1 \\ =26(0.85) \\ =22.1\text{million} \end{gathered}[/tex]The population in the 2nd year can be calculated by substituting t=2 in equation (1).
[tex]\begin{gathered} A_2=26(1-0.15)^2 \\ =26(0.85)^2 \\ =18.785million \end{gathered}[/tex]The population in the 3rd year can be calculated by substituting t=3 in equation (1).
[tex]\begin{gathered} A_3=26(1-0.15)^3 \\ =26(0.85)^3 \\ =15.967255million \end{gathered}[/tex]Hence, the population for the first 4 years will be,
26million,
22.1million,
18.785million,
15.967255million.
1. Mr. and Mrs. Ryan Miller bought a
refrigerator for $1,416. They agreed to
make 12 equal monthly payments. How
much more than $50 will each payment
be?
2. The $1,416 paid by the Millers (problem 1
to buy the refrigerator included an interest
charge of $188. What was the cash cost of
the refrigerator?
The monthly payment more than $50 is $68 and the original price of the refrigerator is $1228
Mr. and Mrs. Ryan Miller bought a refrigerator for $1,416.
They agreed to make 12 equal monthly payments
Monthly payment = 1416 / 12
The monthly payment is $118
more than $50 will each payment be = 118 - 50 = 68
The $1,416 paid by the Miller to buy the refrigerator included an interest charge of $188
The original price is 1416 - 188 = 1228
Therefore, the monthly payment more than $50 is $68 and the original price of the refrigerator is $1228
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Mr. Jones' age is 3 years more than 4 times Mahelet's age. If the sum of their ages is 73, how old is Mahelet?
Mahelet's age is found to be 14 years by solving the simultaneous equations using the given data.
What exactly is a simultaneous equation?A collection of two or more equations, each having two or more variables, whose values can concurrently fulfil one, more, or all of the equations in the collection, with the number of variables being equal to or fewer than the collection's equations.
Given: Mahelet is four times older than Mr. Jones, who is three years older than Mahelet. The total of their ages is 73.
Let, x = Mahelet's age
y = Mr. Jones's age
We know that,
y = 4x +3
x + y = 73
Solving these equations simultaneously we get,
y = 4(73-y) +3
y = 292 - 4y + 3
5y = 295
y = 59
x = 73 - y = 73 - 59 = 14
Therefore, Mahelet's age is found to be 14 years by solving the simultaneous equations.
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if p=3x+4 and v=x+5, find pv-2p+v
Use substitution to simplify the expression.
pv - 2p + v
(3x + 4)(x + 5) - 2(3x + 4) + x + 5
3x² + 15x + 4x + 20 - 6x - 8 + x + 5
3x² + 15x + 4x + x - 6x + 20 + 5 - 8
3x² + 14x + 17
During a snowstorm, Amelia tracked the amount of snow on the ground.When the storm began, there was 1 inch of snow on the ground. For the first 2hours of the storm, snow fell at a constant rate of 3 inches per hour. Thestorm then stopped for 3 hours and then started again at a constant rate of 1inch every 2 hours for the next 6 hours. Make a graph showing the inches ofsnow on the ground over time using the data that Amelia collected.
First, let's write on a table the information about the snow on the ground for the 11 hours it snowed:
period of time in hours amount of snow in inches
0 1
from 0 to 2 1 + t * 3 (initial amount plus 3 in/h * number of hours)
from 2 to 5 1 + 2*3 = 7 (the same amount as when it stopped raining)
from 5 to 11 7 + (t-5)/2 (amount at t = 5 plus 1 in/2h * number of
hours since hour 5)
Now, using this information on a graph, we obtain:
(Lesson 9.8: Other Steady-State Methods.) Consider the following observations: 54 70 75 62 If we choose a batch size of 3, calculate all of the overlapping batch means for me. a. 65.25 b. 62.0, 68.5 c. 66.3, 69.0 d. 65.25 +3 e. None of the above
All of the overlapping batch means for me is (66.3, 69.0).
Given observations:
54 70 75 62
From the given data, if we choose a batch size of 3, then calculating all of the overlapping batch means for me in total
that is :
= 1/3 * (54 + 70 + 75)
= 66.3
and
= 1/3 * (70 + 75 + 62)
= 69.0
So often, the option c is correct from the given
that is 66.3, 69.0
Hence the answer is all of the overlapping batch means for me is (66.3, 69.0).
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2) A taxi service charges a fee of $2.50 and then an additional $2.70 per mile. Determine the relationship.
Data:
• Fixed fee: $2.50
,• Additional: $2.70 per mile
Procedure:
The relationship the problem is describing is a linear one with the form:
[tex]y=mx+b[/tex]In this case, we have a fixed fee that is represented by b in the linear equation, and an additional fee represented by m, which depends on the miles (x) travels.
Thus, the equation would be:
[tex]y=2.7x+2.5[/tex]Based on this equation, you can replace any value of miles (x) given to calculate the total price (y).
Find the arc-length of the sector of a circle with the given radius r and central angle 0. Give the answer in the given unit of measure, rounded to the nearest hundredth.r = 25 m; θ = 12π/7
Given a radius and a central angle in radian, the formula in solving arc length is:
[tex]AB=\theta\times r[/tex]Since the angle and radius are given already in the problem, let's plug it in to the formula above.
[tex]AB=\frac{12\pi}{7}(25m)[/tex]Then, solve.
[tex]AB=\frac{300\pi m}{7}=\frac{942.47779m}{7}\approx134.64m[/tex]Therefore, the length of an arc having a central angle of 12π/7 is approximately 134.64 meters.
You want to order posers to advertise your band. A company charges $109.95 for the first 100 posters and $65 for each additional 100 posters.
Write an equation that represents the cost (in dollars) of the posters of the number (in hundreds) of posters ordered (in slope- intercept form).
The equation that represents the total cost as a function of the number (in hundreds) of posters ordered, x is f(y) = 109.95 + 65x
let
y = total cost
x = numbers in hundreds
cost of first hundred = $109.95
Cost of additional hundred = $65
f(y) = 109.95 + 65x
The total cost of 1000 posters
1000 - first hundred = 900
additional hundreds = 900/100= 9
So,
f(y) = 109.95 + 65x
= 109.95 + 65(9)
= 109.95 + 585
= 694.95
f(y) = $694.95
Therefore, the total cost of 1000 posters is f(y) = $694.95
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Determine the solution to the inequality. |4x − 4| ≥ 8 x ≤ −1 or x ≥ 3 x ≤ −2 or x ≥ 3 x ≤ −3 or x ≥ 4 x ≤ −4 or x ≥ 4
The solution to the inequality will be -
x ≥ 3 or x ≤ -1
What is an Inequality? What is a expression? What is a mathematical equation?An inequality in mathematics compares two values or expressions, showing if one is less than, greater than, or simply not equal to another value.A mathematical expression is made up of terms (constants and variables) separated by mathematical operators.A mathematical equation is used to equate two expressions. Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.We have the given inequality as -
|4x − 4| ≥ 8
We have the inequality as -
|4x − 4| ≥ 8
4x - 4 ≥ 8 or 4x - 4 ≤ - 8
4x ≥ 12 or 4x ≤ - 4
x ≥ 3 or x ≤ -1
Therefore, the solution to the inequality will be -
x ≥ 3 or x ≤ -1
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estimate 15.870 + 6.77 by first rounding each number to the nearest tenth
Given:
15.870 + 6.77
We are required to round each number to the nearest tenth before performing the addition.
The tenth digit is the number first number after the decimal point.
First step:
Round to the nearest tenth
15.870 ==> 15.9
6.77 ==> 6.8
Second step:
Add both numbers after rounding to the nearest tenth
15.9 + 6.8 = 22.7
ANSWER:
22.7
frequency The table and corresponding polygon show information about the waiting times of some patients at a dentist. Frequency What fraction of patients waited for more than 7 minutes? 10- 0- 5 6 7 8 Waiting time (x minutes) 9 10 x Waiting time (x minutes) 5< x≤6 6< x≤7 7< x≤8 8< x≤9 9< x≤ 10
The 31 minutes for the lowest quartile of the waiting times of patients at this surgery.
Given that,
The histogram displays statistics about the average patient wait time in dental offices, expressed in minutes. 3.24 frequency The table and related polygon display data regarding some patients' wait periods at a dentist.
We have to find frequency How many patients waited for longer than seven minute.
The frequency of a given data value is the number of times it happens. We use f to represent a data value's frequency. For instance, if five students received As in science, the grade A was said to have a frequency of five.
In the picture we can see the answer.
Therefore, The 31 minutes for the lowest quartile of the waiting times of patients at this surgery.
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If x>0, then x^(3/4)/x^(-¼)
HELPP PLEASEEE
Answer:
x
Step-by-step explanation:
using the rule of exponents
[tex]\frac{a^{m} }{a^{n} }[/tex] = [tex]a^{(m-n)}[/tex]
given
[tex]\frac{x^{\frac{3}{4} } }{x^{-\frac{1}{4} } }[/tex]
= [tex]x^{\frac{3}{4}-(-\frac{1}{4}) }[/tex]
= [tex]x^{(\frac{3}{4}+\frac{1}{4}) }[/tex]
= [tex]x^{1}[/tex]
= x
Answer:
[tex]\large\text{$\dfrac{x^{\left(\frac{3}{4}\right)}}{x^{\left(-\frac{1}{4}\right)}}=x$}[/tex]
Step-by-step explanation:
Given expression:
[tex]\large\text{$\dfrac{x^{\left(\frac{3}{4}\right)}}{x^{\left(-\frac{1}{4}\right)}}$}[/tex]
[tex]\textsf{Apply exponent rule} \quad \dfrac{a^b}{a^c}=a^{b-c}:[/tex]
[tex]\implies \large\text{$x^{\left(\frac{3}{4}-\left(-\frac{1}{4}\right)\right)}$}[/tex]
Simplify:
[tex]\implies \large\text{$x^{\left(\frac{3}{4}+\frac{1}{4}\right)}$}[/tex]
[tex]\implies \large\text{$x^{\left(\frac{4}{4}\right)}$}[/tex]
[tex]\implies \large\text{$x^{1}$}[/tex]
[tex]\textsf{Apply exponent rule} \quad a^1=a:[/tex]
[tex]\implies \large\text{$x$}[/tex]
PLEASE HELP IT'S DUE NOW.. :(
Slope intercept form of equation of line f and line g is
Equation of line f
y = 1.75x + 3.5
Equation of line g
y = -4x - 8
First option is correct
What is equation of line in slope intercept form?
The most general form of equation of line in slope intercept form is given by y = mx + c
Where m is the slope of the line and c is the y intercept of the line.
Slope of a line is the tangent of the angle that the line makes with the positive direction of x axis.
If [tex]\theta[/tex] is the angle that the line makes with the positive direction of x axis, then slope (m) is given by
m = [tex]tan\theta[/tex]
The distance from the origin to the point where the line cuts the x axis is the x intercept of the line.
The distance from the origin to the point where the line cuts the y axis is the y intercept of the line.
Here,
For line f
The line passes through (2, 7) and (4, 10.5)
Slope =
[tex]\frac{10.5 - 7}{4 - 2}\\\frac{3.5}{2}\\\frac{7}{4}[/tex]
Equation of line =
[tex]y - 7 = \frac{7}{4}(x - 2)[/tex]
y = 1.75x - 3.5+7
y = 1.75x + 3.5
For line g
The line passes through (-3, 4) and (-2, 0)
Slope =
[tex]\frac{0-4}{-2-(-3))}\\-4[/tex]
Equation of line =
y - 4 = -4(x - (-3))
y - 4 = -4x-12\\
y =-4x-12+4\\
y = -4x-8
The first option is correct
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use the unit circle to find sec(7/6)
Step 1
Draw the unit circle required
Step 2
Find the value sec(7π/6) in cosine
[tex]\begin{gathered} \sec (\frac{7\pi}{6})=\frac{1}{cos(\frac{7\pi}{6})} \\ \sec (x)=\frac{1}{cos(x)} \end{gathered}[/tex]Step 3
Find cos(7π/6)
The trigonometric unit circle and a trigonometric table gives;
[tex]\begin{gathered} \cos (\frac{7\pi}{6})=\cos (\frac{\pi}{6}+\pi) \\ \cos (\frac{7\pi}{6})=\text{cos}(\frac{\pi}{6})\cos (\pi)-\sin (\frac{\pi}{6})sin\pi=-\cos (\frac{\pi}{6}) \\ \cos (\frac{7\pi}{6})=\frac{\sqrt[]{3}}{2}(-1)-(\frac{1}{2})(0)=-\frac{\sqrt[]{3}}{2} \\ \cos (\frac{7\pi}{6})=-\frac{\sqrt[]{3}}{2} \end{gathered}[/tex]Step 4
Find sec(7π/6)
[tex]\begin{gathered} \sec (x)=\frac{1}{cos(x)} \\ \text{sec}(\frac{7\pi}{6})=\frac{1}{\cos (\frac{7\pi}{6})} \\ \text{sec}(\frac{7\pi}{6})=\frac{1}{-\frac{\sqrt[]{3}}{2}} \\ \text{sec}(\frac{7\pi}{6})=-\frac{2}{\sqrt[]{3}} \end{gathered}[/tex]Step 5
Rationalize the denominator
[tex]\begin{gathered} \sec (\frac{7\pi}{6})=-\frac{2}{\sqrt[]{3}}\times\frac{\sqrt[]{3}}{\sqrt[]{3}} \\ \sec (\frac{7\pi}{6})=-\frac{2\sqrt[]{3}}{\sqrt[]{9}} \\ \sec (\frac{7\pi}{6})=-\frac{2\sqrt[]{3}}{3} \end{gathered}[/tex]Hence,
[tex]\sec (\frac{7\pi}{6})=-\frac{2\sqrt[]{3}}{3}[/tex]Identify the sampling technique used (or to be used) in the following scenarios. Possible answers could be simple random, systematic random or stratified random sampling.
a)
This sampling technique is simple random sampling, since the students are selected at random by drawing their names from a piece of paper.
b)
Since there is a condition to select a resident (being the sixth resident of the list), this technique is classified as systematic random sampling.
c)
The 20 students were selected by using a table of random numbers without any criteria. Therefores, this is a simple random sampling technique.
d)
Since, among the 100 selected random people, there was a pre determined subgroup of 5 barangays, this is a stratified random sampling technique.
e)
Since everyone in the sample was selected at random by dwaring lots, this is a simple random sampling technique.
a store has 24 saltwater fish. the store has 4 tanks for the fish. each tank has an equal number of fish. how many fish are in each tank
Answer:
Step-by-step explanation:
Answer: 6
there are 24 fish and 4 tanks so divide 24 by 4 and you'll have 6
Answer:
the number of fish in each tank is 6
Step-by-step explanation:
becuause 24 divided be 4 is 6
1 months amren 5 movies and 3 video games for a total of $36. the next month he went 7 movies and 9 video games for a total of $78. find the rental cost for each movie in each video game.rental cost for each movie:rental cost for each video games:
Each movie cost $3.75 while each video game cost $5.75
Here, we want to get rental costs
We start by using variables to represent the costs of the movie and the video game
Let the cost of a movie be m and the cost of a video game be g
Thus, we have it that;
[tex]5m\text{ + 3g = 36}[/tex]and;
[tex]7m\text{ + 9g = 78}[/tex]So, we have two equations to solve simlutaneously
That would yield;
[tex]\begin{gathered} \text{From i;} \\ 5m\text{ + 3g = 36} \\ 3g\text{ = 36-5m} \\ we\text{ can have equation }ii\text{ as;} \\ 7m\text{ + 3(3g) = 78} \\ 7m\text{ + 3(36-5m) = 78} \\ 7m\text{ + 108-15m = 78} \\ 108-78\text{ = 15m-7m} \\ 8m\text{ = 30} \\ m\text{ = }\frac{30}{8} \\ m\text{ = \$3.75} \end{gathered}[/tex]Now, to get the value of g, we make a substitution into any of the equations;
[tex]\begin{gathered} 3g\text{ = 36-5m} \\ 3g\text{ = 36-5(3.75)} \\ 3g\text{ = 36-18.75} \\ 3g\text{ = 17.25} \\ g\text{ = }\frac{17.25}{3} \\ g\text{ = 5.75} \end{gathered}[/tex]