We are given a jar that contains 22 red marble( 1 to 20) and 52 blue marbles (1 to 52). We can proceed to find the solution for each part of the question.
PART 1
Let the probability that the marble is red be P(r).
Therefore,
[tex]P(r)=\frac{Number\text{ of red balls}}{\text{Total number of balls}}[/tex]This gives,
[tex]\begin{gathered} P(r)=\frac{22}{22+52}=\frac{22}{74} \\ \therefore P(r)=\frac{11}{37}=0.297 \end{gathered}[/tex]Therefore, the probability that the marble is red is:
ANSWER= 0.297
PART 2:
Let the probability of picking odd-numbered balls be P(o)
Therefore,
[tex]P\mleft(o\mright)=\frac{Number\text{ of odd balls}}{\text{Total number of balls}}[/tex]We already know that the total number of balls is 72 for the previous question. Therefore, the total number of oddballs will be the sum of odd red balls and odd blue balls. This consists of 11 odd red balls and 26 odd blue balls.
Therefore,
[tex]\begin{gathered} P(o)=\frac{26+11}{74}=\frac{37}{74} \\ \therefore P(o)=0.5 \end{gathered}[/tex]The probability of picking odd-numbered balls is
ANSWER = 0.5
PART 3:
Let the probability of picking a red or odd-numbered ball be P(r U o)
[tex]P(r\cup o)=P(r)+p(o)-p(r\cap o)[/tex]Since we already have the values of P(r) and P(o), therefore we only need to find p(r n o).
p(r n o) is the probability of the ball being red and odd. The number of the red and oddball is 11.
Therefore,
[tex]\begin{gathered} P(r\cap o)=\frac{nu\text{mber of red and odd balls}}{\text{Total number of balls}} \\ =\frac{11}{74} \\ =0.149 \end{gathered}[/tex]This implies that,
[tex]\begin{gathered} P(r\cup o)=P(r)+p(o)-p(r\cap o) \\ P(r\cup o)=0.297+0.5-0.149 \\ \therefore P(r\cup o)=0.648 \end{gathered}[/tex]Hence, the probability of picking a red or odd-numbered ball is
ANSWER = 0.648
PART 4:
Let the probability of picking a blue or even-numbered ball be P(b U e)
Therefore,
[tex]P(b\cup e)=p(b)+p(e)-p(b\cap e)[/tex]From the above formula, we would need to figure out all the parts. p(b) represents the probability of blue marble. This gives,
[tex]\begin{gathered} p(b)=\frac{Number\text{ of blue balls}}{\text{Total number of balls}} \\ \therefore p(b)=\frac{52}{74}=0.703 \end{gathered}[/tex]p(e) represents the probability of even balls. The total number of even balls will be the sum of the even red balls and even blue balls.
[tex]\begin{gathered} p(e)=\frac{26+11}{74}=\frac{37}{74} \\ \therefore p(e)=0.5 \end{gathered}[/tex]p(b n e) represents the probability of blue and even balls. We have 26 blue and even balls
[tex]\begin{gathered} p(b\cap e)=\frac{Number\text{ of blue and even balls}}{\text{Total number of balls}} \\ P(b\cap e)=\frac{26}{74}=0.351 \end{gathered}[/tex]Therefore,
[tex]\begin{gathered} P(b\cup e)=p(b)+p(e)-p(b\cap e) \\ P(b\cup e)=0.703+0.5-0.351 \\ \therefore P(b\cup e)=0.852 \end{gathered}[/tex]Therefore, the probability of picking a blue or an even ball is:
ANSWER = 0.852
Write an equation of a line that goes through (4, 1) and has a slope of 2.
the equation 2x-20/3=2x models temperature change, where x represents the difference in degrees in the last 24 hours. solve for x
a. x = -5
b. x = -2
c. x = 2
d. x= 13
The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions.
The answer is x = -5 for the following equation (2x - 20) /3 = 2x.A formula for the question at hand is 2x minus 20 divided by 3 Equals 2x, or (2x - 20) /3 = 2x.
The difference in degrees over the last 24 hours is represented by x in this equation, which predicts temperature change.
We must find x in the given equation.
(2x - 20) /3 = 2x \s (2x - 20) = 3(2x) (2x) ...........(Multiply by 3 on both sides)
2x - 20 + 20 = 6x + 20 ...........(Add 20 to both sides)
2x - 6x = 6x + 20 - 6x ..........(Subtract 6x from both sides) (
-4x = 20 \s x = -5 ..........(Divide by - 4 on both sides)
As a result, x = -5 for the given equation (2x - 20) /3 = 2x.
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Find 3 ratios that are equivalent to 6:15
Answer:12:30,2:5 and 18:45
Step-by-step explanation:
The length of a rectangle is 5 feet more than the width. The perimeter of the rectangle is 58 feet. Find the length & width of the rectangle.
Answer:
Length: 17 ft. Width: 12 ft.
Step-by-step explanation:
x + 5 + x +5 + x + x = 58
4x + 10 = 58
4x = 48
x = 12
12 + 5 = 17
Please solve for y. There should be no actual numbers besides for 9.
Answer:
y= x/(n-9)
Step-by-step explanation:
Move 9 to the right side to get n-9
Take y over to get x=y(n-9)
Then shift n-9 over to other side to get y= x/(n-9)
the area of a right angled triangle is 96cm^2if the two shaded sides of the triangle differ by 2 what is the length of the shorter sides
The triangle have shorter sides of 12.9 and 14.9 cm, respectively
How to determine the lengths of the shorter sides?From the question, the given parameters are:
Triangle type = Right-angled triangleArea of triangle = 96 cm^2Also, from the question, we have:
Two shaded sides of the triangle differ by 2
In this case, the shaded sides of the triangle are
Opposite and Adjacent
This can also be interpreted as
Base and Height
So, we have
Base - Height = 2
The area is calculated as
Area = 0.5 * Base * Height
So, we have
0.5 * Base * Height = 96
This gives
0.5 * (Height + 2) * Height = 96
Divide by 0.5
(h + 2) * h = 192
Using a graphing calculator, we have
h = 12.9
Substitute h = 12.9 in Base - Height = 2
Base - 12.9 = 2
Evaluate
Base = 14.9
Recall that the Opposite and Adjacent are the shorter sides of a right triangle
Hence, the shorter sides are 12.9 and 14.9 cm
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Write the coordinates of the vertices after a reflection over the y-axis
The most appropriate choice for reflection will be given by-
After reflection over y-axis, coordinate of K will become K' (6, -1)
After reflection over y-axis, coordinate of L will become L' (0, -1)
After reflection over y-axis, coordinate of M will become M' (0, -2)
After reflection over y-axis, coordinate of J will become J' (6, -2)
What is reflection?
Reflection of a figure about a line is a transformation in which a mirror image of the figure can be obtained over the line.
The line is called the line of reflection.
Here,
After reflection over the y - axis, sign of x coordinate will be same.
Coordinate of K = (-6, -1)
After reflection over y-axis, coordinate of K will become K' (6, -1)
Coordinate of L = (0, -1)
After reflection over y-axis, coordinate of L will become L' (0, -1)
Coordinate of M = (0, -2)
After reflection over y-axis, coordinate of M will become M' (0, -2)
Coordinate of J = (-6, -2)
After reflection over y-axis, coordinate of J will become J' (6, -2)
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Write a simplified expression for the right half of the equation that can be used to find the nth term in the sequence6,7,8 9,10
Please only answer if you know the answer thank you.
Answer:
x = - 5;
y = 5;
Step-by-step explanation:
Identify the equation.
y = ( 2 / 3 )x + c;
Substitute a point.
5 = ( 2 / 3 )( - 2 ) + c;
5 = ( - 4 / 3 ) + c;
5 - ( - 4 / 3 ) = c;
5 + ( 4 / 3 ) = c;
19 / 3 = c;
y = ( 2 / 3 )x + ( 19 / 3 );
Substitute point A.
3 = ( 2 / 3 )x + ( 19 / 3 );
3 - ( 19 / 3 ) = ( 2 / 3 )x;
( 9 / 3 ) - ( 19 / 3 ) = ( 2 / 3 )x;
- ( 10 / 3 ) = ( 2 / 3 )x;
- ( 10 / 3 )( 3 / 2 ) = x;
( - 30 / 6 ) = x;
- 5 = x;
x = - 5;
Substitute point B. Use common sense and notice that point B is actually the same as the first point.
y = 5;
Answer:
x = -5
y = 5
Step-by-step explanation:
You could write the equation in the point slope form of a line
y - [tex]y_{1}[/tex] = m( x - [tex]x_{1}[/tex])
Use the slope they gave us 2/3. Use the point they gave us for [tex]x_{1}[/tex] ( -2 ) and [tex]y_{1}[/tex] ( 5)
y -5 = 2/3(x - -2)
y - 5 = 2/3(x + 2) Plug in 3 for y to solve for x
3-5 = 2/3(x + 2)
-2 = 2/3x + 4/3 subtract 4/3 from both sides of the equation
-2 - 4/3 = 2/3x
[tex]\frac{-6}{3}[/tex] - [tex]\frac{4}{3}[/tex] = 2/3x
[tex]\frac{-10}{3}[/tex] = 2/3 x Multiply both sides by [tex]\frac{3}{2}[/tex]
([tex]\frac{3}{2}[/tex])[tex]\frac{-10}{3}[/tex] = ([tex]\frac{3}{2}[/tex])([tex]\frac{2}{3}[/tex]) x
-5 = x
substitute in -2 for x to solve for y
y - 5 = 2/3(x + 2)
y - 5 = 2/3(-2+2)
y - 5 = 2/3(0)
y - 5 = 0 Add 5 to both sides
y = 5
The average height of a barometer during one week was 30.84 inches. for six week days of the same week the average height was 30.18 inches. what was the height on sunday?
The height of the barometer on Sunday = 34.8 inches
How is the barometer height on Sunday calculated?
Consider the barometer height for one week,
The average height of a barometer during one week = 30.84 inches
The total height of a barometer during one week = 30.84 * 7
= 215.88
Consider the barometer height for 6 weekdays,
The average height of a barometer for 6 weekdays of the same week= 30.18 inches
The total height of a barometer for 6 weekdays = 30.18 *6
=181.08
The barometer height on Sunday = One week height- 6 days height
=215.88 - 181.08
=34.8 inches
What is a height?
Height is the distance vertically between an object or figure's top and bottom. Height is also referred to as altitude . Average height is the sum of all the heights divided by the number of the given heights.To learn more about height, refer:
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Forty years ago, uncle Luke was 5 times
as old as his
nephew. Today, Uncle Luke is 16 yeas older than his nephew. How
old is uncle Luke now?
Answer: Uncle Luke is at 50 years old
Step-by-step explanation: I went through trial and error first with simple t-charts. In the first one, I simply implemented the piece of info that Luke was 5 times older than the nephew. But then, I realized that Luke would always be 5 years older than his nephew. Here was the info for that t-chart:
[tex]\left \{ {{N=1} \atop {L=5}} \right. \left \{ {{N=2} \atop {L=6}} \right. \left \{ {{N=3} \atop {L=7}} \right.[/tex]
Next, I tried a chart starting with the nephew at 2 years of age, and got an age gap of 8. This helped me realize that I would have to start at 4 years of age in order to have an age gap of 16
[tex]\left \{ {{N=2} \atop {L=10}} \right.[/tex] | [tex]\left \{ {{N=4} \atop {L=20}} \right. \left \{ {{N=5} \atop {L=21}} \right.[/tex] (remember there are 1 increments)
Next, I realized that N=4, L=20 was 40 years ago, so if now the nephew was 44, we can increment 16 to get 50
44+16=50
Use the information given to enter an equation in standard form.Slope is -9, and (3,2) is on the line.
Firts get the equation
Second, write the equation in form of Ax +
Jane wants to save $500 to purchase a new television. She earns $10.50 an hour at her job. The function M(h) = 8h represents the amount of money Jane earns in dollars, M(h), for each hour h that she works. Find M(60).
*Type in your answer.
M(60) =$.
The amount that Jane would earn for working for 60 hours is $630.
What is M(60)?The given function is a linear function. A linear function is a function that changes at a constant rate. When a linear graph is drawn on a coordinate graph, it can slope either upward or downward.
The linear function that represents the total amount she earns is:
Total earnings = cost per hour x total number of hours worked
Total earnings = $10.50 x h
Total earnings = $10.50 x 60 = $630
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Simplify the following expression
Answer:
y
-------------
x²¹ z⁵
Step-by-step explanation:
(x⁻⁹ y³ z⁻²)²
-------------------
x³ y⁵ z
x⁻¹⁸ y⁶ z⁻⁴
-------------------
x³ y⁵ z
y⁶
-------------------
x³ ⁺ ¹⁸ y⁵ z¹ ⁺ ⁴
y
-------------------
x²¹ z⁵
I hope this helps!
After simplification by rule of exponent solution is,
⇒ y / x²¹ z⁵
We have to given that;
The expression is,
⇒ (x⁻⁹ y³ z⁻²)² / x³ y⁵ z
Now, We can simplify by rule of exponent as;
⇒ (x⁻⁹ y³ z⁻²)² / x³ y⁵ z
⇒ x⁻¹⁸ y⁶ z⁻⁴ / x³ y⁵ z
⇒ y⁶ / x³ ⁺ ¹⁸ y⁵ z¹ ⁺ ⁴
⇒ y / x²¹ z⁵
Thus, After simplification by rule of exponent solution is,
⇒ y / x²¹ z⁵
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What is the slope of the line? ASAP.
Answer:
The slope would be 25/1 or 25.
Step-by-step explanation:
Use the formula y2-y1 over x2-x1. Or use rise over run.
if charlene brewster has times of 8.4, 8.6, 8.3, 8.5, 8.7, and 8.5 and a performance rating of 110%, what is the normal time for this operation? is she faster or slower than normal? [px]
Normal time taken for operation = 7.7
Charlene's work performance is faster than normal time.
Need to define Charlene's average time:
8.4 + 8.6 + 8.3 + 8.5 + 8.7 + 8.5)/6
Avg time taken= 8.5.
Performance rating = 110/100 = 1.1
normal time taken: 8.5/1.1
normal time taken= 7.7
hence, 8.5 [tex]\geq[/tex] 7.7
Charlene is faster than normal time.
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-7/8u = -21 solve for u and simplify your answer as much as possible
Answer:
u = 24
Step-by-step explanation:
-7/8u = -21
Solve for u
Multiply each side by -8/7
-8/7 *-7/8u = -21 *-8/7
u =3*8
u = 24
Answer:
u = 1/24
Write the equation:
–7/8u = –21
Get rid of fraction:
–7/2^3 • u = –21
–7 = ( – (8u) ) 21
Solve:
–7 = –8u + 21
–7 + 8u = –8u + 8u + 21
–7 + 8u = 21
–7 + 7 + 8u = 21 + 7
8u = 21 + 7
8u = 28
u = 1/24
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Prove that (X+2)^2+(X-2)^2=2(x^2+4) for all values of x
Answer:
see explanation
Step-by-step explanation:
consider the left side
(x + 2)² + (x - 2)² ← expand factors using FOIL
= x² + 4x + 4 + x² - 4x + 4 ← collect like terms
= 2x² + 8 ← factor out 2 from each term
= 2(x² + 4)
= right side , thus proven
Answer this question for me
Answer:
3.97%
Step-by-step explanation:
You want to know the annual interest rate, compounded daily, that will result in $43,000 growing to $75,000 in 14 years.
FormulaThe formula for the account value is ...
A = P(1 +r/n)^(nt)
where P is the principal invested at annual rate r compounded n times per year for t years.
ApplicationFilling in the given values, we can solve for r.
75000 = 43000(1 +r/365)^(365·14)
75/43 = (1 +r/365)^5110 . . . . . divide by 43000 and reduce the fraction
Taking the 1/5110 power gives ...
(75/43)^(1/5110) = 1 +r/365 ≈ 1.00010886855
r/365 = 0.0010886855 . . . . subtract 1
r = 0.001086855·365 . . . . . multiply by 365
r ≈ 0.039737 = 3.9737%
The required interest rate is about 3.97%.
Find the exact solution to the equation 42 equals 3 x squared, leaving your answer in square root form. Show your work.
State if your solution is rational or irrational. Explain.
Find the closest integer approximation to your solution and explain how you found it.
The solution is x = √ 14, it is irrational
The closest integer approximation to the solution is 4
How to determine the valueFrom the information given, we have that;
42 equals 3 x squared
This is represented as;
3x² = 42
Let's take the following steps to determine the value of x
Divide both sides by the coefficient of x²
x² = 42/3
x² = 14
Take the square root of both sides, we have;
x = √ 14
The solution is an irrational number
What is an irrational number?An irrational number is described as a number that cannot be expressed in a fractional form.
They are real numbers that expressed as quotients
Examples of irrational numbers are;
√5, √7, √11, √13
Now, let's find the square root, we have
= 3. 74
Take '7' as 1 and add to the whole number 3, we get;
= 4 ; to the closest integer
Hence, the value is 4
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Does anyone know the answer to this question ?? PLS HELP.
Only answer if you know the answer !!!!
Polynomial function of least degree having real coefficient with given leading coefficient 1 and having zeros 3, 4 +i is equal to x³ -11x² +41x -51.
As given,
Standard form of the polynomial function:
f(x) = r(x-a)(x-b)(x -c)
r : leading coefficient
a, b, c are zeros
Polynomial function of least degree having real coefficient with given leading coefficient 1 and having zeros 3, 4 +i is given by
f(x) = 1(x -3) (x -(4+i))(x - (4-i))
⇒ f(x) = (x -3) (x-4 -i)(x -4 +i)
⇒ f(x) = (x-3) [(x-4)² -i²]
⇒f(x) = (x-3)(x² -8x +16+1)
⇒f(x) =(x-3)(x² -8x+17)
⇒f(x) = x³-11x² +41x-51
Therefore, polynomial function of least degree having real coefficient with given leading coefficient 1 and having zeros 3, 4 +i is equal to
x³ -11x² +41x -51.
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HELP ME PLSS OMLLL IMA CRY
Answer:
Remember, ratios are just fractions, and fractions are just division problems.
Step-by-step explanation:
Step-by-step explanation:
25%of 20 is 5
subtract from the total of the whole candy.
ross is camping 4 miles west and 11 miles north (-4,11)
Using the equation for the distance between two points, the distance between Ross and Rachel is given by the following option:
D. 19 miles.
What is the distance between two points?Suppose that we have two points with coordinates [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex]. The shortest distance between them is given by the equation presented as follows:
[tex]D = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
This formula is derived from the Pythagorean Theorem, as the points form a right triangle in the xy-plane, and the hypotenuse represents the distance between them.
Their coordinates in this problem are as follows:
Ross: (-4, 11).Rachel: (8, -4).Each unit on the plane represents a mile, hence their distance is given as follows:
[tex]D = \sqrt{(8 - (-4))^2+(-4 - 11)^2}[/tex]
D = 19.2 miles.
Rounded to 19 miles, hence option D is correct.
Missing informationThe complete problem is given by the image at the end of the answer.
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Renna pushes the elevator button, but the elevator does not move. The mass limit for the elevator is 450450450 kilograms (\text{kg}kgstart text, k, g, end text), but Renna and her load of identical packages mass a total of 620\,\text{kg}620kg620, start text, k, g, end text. Each package has a mass of 37.4\,\text{kg}37.4kg37, point, 4, start text, k, g, end text.
Write an inequality to determine the number of packages, ppp, Renna could remove from the elevator to meet the mass requirement.
pls help
The inequality to determine the number of packages Renna could remove from the elevator to meet the mass requirement is 620 - 37.4g = 450.
What is an inequality?An inequality is simply used to show the relationship between the expressions that are not equal.
The mass limit is given as 450 grams. Renna has a package that has a weight of 620g.
Each package has 37.4g.
Let the number of packages to remove be p.
The expression will be:
= 620 - (37.4 × p) = 450
620 - 37.4g = 450.
This illustrates the concept of inequality.
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suppose that you were trying to predict house price based on square footage, distance from the beach, and lot size for miami, florida. run a multiple regression predicting price based on square footage, and lot size. assume you are trying to determine if the slope of lot size is different than 0, and you find a p value 0.5677. what conclusion can you make?
The slope for lot size is not different from 0.
We will let the slope of the size be β
So the hypothesis can be: β = 0 (Null Hypothesis) , β≠ 0 (Alternate Hypothesis)
If we consider a confidence level (the probability for which we can be confident that the null hypothesis is true) to be 95% (Probability = 0.95) then the level for which we are not confident that the null hypothesis is true will be (100 - 95)% = 5% (Probability = 0.05)
Thus, for this coefficient the P value is 0.5782.
As the p-value is more than the Probability for which we are not confident (0.05), so in this regard we can state then there is no such significance difference seen in this regard. Thus, we accept the null hypothesis here. This means that we can take the coefficient to be 0.
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What does do the congruence criterion mean.
Please explain what AAS, SSS, ASA, and HL mean.
AAS = Angle , angle and one side of 2 congruent triangles
SSS = All 3 sides are measure same of the 2 triangles.
ASA = 2 angles and the side between them are same
HL = A right triangle is congruent if its hypotenuse and one of its legs are congruent with the hypotenuse and one of its other legs.
What is meant by congruency?The dimensions of the triangles' sides and angles determine whether two or more triangles are congruent. A triangle's size is determined by its three sides, and its shape by its three angles. Pairs of corresponding sides and corresponding angles in two triangles are said to be equal if they are congruent. They share a similar size and shape. In triangles, there are numerous congruence conditions. For the two triangles to be congruent, they must be the same size and shape. It should be possible to superimpose the two triangles under examination. A triangle's position or appearance appears to change when we rotate, reflect, and/or translate it. In that situation, we must recognize the six components of a triangle.
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Simplify the following radical
√175x^5
Simplified version of the given radical expression would be...
[tex]5x^2\sqrt{7x}[/tex]
Hope this helps!
triangle ABC has coordinates A(1,4) B(3.-2) and C(4,2) . Find the coordinates of the image ABC after a reflection over the x axis.
The given vertices are A(1,4), B(3,-2), and C(4,2).
The reflection over the x-axis is expressed as
[tex](x,y)\rightarrow(x,-y)[/tex]This means we have to multiple each y-coordinate with -1. Let's do it!
[tex]\begin{gathered} A(1,4)\rightarrow A^{\prime}(1,-4) \\ B(3,-2)\rightarrow B^{\prime}(3,2) \\ C(4,2)\rightarrow C^{\prime}(4,-2) \end{gathered}[/tex]Therefore, the vertices of the new triangle are A'(1,-4), B'(3,2), and C'(4,-2)Eli dug a trench
18
20
of a meter long. The next day he dug another 17
20
B
of a meter. What is a reasonable estimate of the total length of the trench?
The summation is the adding two quantities thus the reasonable estimate of the total length of the trench is 1 1/2 meters so option (C) is correct.
What is summation?A summation, also abbreviated as a sum, is the outcome of adding two or more numbers or quantities.
There could be only two terms, but there could be one hundred, a thousand, or a million.
Here are always an integer number of terms in a summation.
As per the given,
Length of the trench on the first day = 18/20 meters
Length of the trench on the second day = 9/20
Total length of the trench = 18/20 + 9/20
Take LCM as 20
⇒ (18 + 9)/20 = 27/20
⇒ 1.35 which is closest among the given option by 1 1/2 meters.
Hence "The summation is the adding two quantities thus the reasonable estimate of the total length of the trench is 1 1/2 meters".
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Does anyone have an answer or explanation? I kind of need it before 12pm (CDT)
A museum charges $10 for general admission and $2 for each special exhibit you attend.
What does f(0) = 10 represent in the context of this problem?
Answer:
i d k 20???????????
Step-by-step explanation:
Answer:
The visitor attended no special exhibits and so paid a total of $10 just to get in.
An equation to represent the cost of admission could look like this:
f(x) is the total cost.
x is the number of special exhibits attended.
f(x) = 2x + 10
If I see no special exhibits on my visit,
x = 0, then
f(0) = 2•0 + 10
f(0) = 10
I only pay $10.