The value of c such that the function f is a probability density function is 2
How to determine the value of c?The density function is given as:
f(x) = cxe^(−x^2) if x ≥ 0
f(x) = 0 if x < 0.
We start by integrating the function f(x)
∫f(x) = 1
This gives
∫ cxe^(−x^2) = 1
Next, we integrate the function using a graphing calculator.
From the graphing calculator, we have:
c/2 * (0 + 1) = 1
Evaluate the sum
c/2 * 1 = 1
Evaluate the product
c/2 = 1
Multiply both sides of the equation by 2
c = 2
Hence, the value of c such that the function f is a probability density function is 2
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Amy and Richard each solved an equation using the quadratic formula.
Amy's Equation and Method
Latex: 4x^2+7x-20=0
4
x
2
+
7
x
−
20
=
0
Step 1: Latex: x=\frac{-7\pm \sqrt{7^2-4(1)(20)}}{2(4)}
x
=
−
7
±
√
7
2
−
4
(
1
)
(
20
)
2
(
4
)
Step 2: Latex: x=\frac{-7\pm \sqrt{49-80}}{8}
x
=
−
7
±
√
49
−
80
8
Step 3: Latex: x=\frac{-7\pm \sqrt{-31}}{8}
x
=
−
7
±
√
−
31
8
Step 4: Latex: x=\frac{-7\pm i\sqrt{31}}{8}
x
=
−
7
±
i
√
31
8
Richard's Equation and Method
Latex: x^2-6x+8=0
x
2
−
6
x
+
8
=
0
Step 1: Latex: x=\frac{6\pm \sqrt{(-6)^2-4(1)(8)}}{2(1)}
x
=
6
±
√
(
−
6
)
2
−
4
(
1
)
(
8
)
2
(
1
)
Step 2: Latex: x=\frac{6\pm \sqrt{36-32}}{2}
x
=
6
±
√
36
−
32
2
Step 3: Latex: x=\frac{6\pm \sqrt{4}}{2}
x
=
6
±
√
4
2
Step 4: Latex: x=\frac{6+\sqrt{4}}{2}
x
=
6
+
√
4
2
and Latex: x=\frac{6-\sqrt{4}}{2}
x
=
6
−
√
4
2
Step 5: Latex: x=\frac{6+2}{2}
x
=
6
+
2
2
and Latex: x=\frac{6-2i}{2}
x
=
6
−
2
i
2
Step 6: Latex: x=4
x
=
4
and Latex: x=3-i
x
=
3
−
i
Both students made a mistake.
Describe the mistake each student made.
Explain what each student needs to do to fix their mistake.
Create your own quadratic equation, and explain how to use the quadratic formula to solve it. Be specific, using Latex: a\textsf{, }b\textsf{,} and Latex: c
c
of your equation and giving the solutions to the equation you chose.
Number your responses from 1 to 3 so your instructor can tell which question you're responding to. You may not receive full credit if your teacher cannot determine that you've answered each question.
Search entries or author
The mistake each student made and what each student needs to do to fix their mistake is;
Amy didn't include the negative sign for the 20, so she should include itRichard added a negative sign underneath the radicalQuadratic equationx² - 6x + 8 = 0
x = - b ± √b² - 4ac / 2a
where,
a = 1b = -6c = 8x = - b ± √b² - 4ac / 2a
= -(-6) ± √(-6)² - 4(1)(8) / 2(1)
= 6 ± √36 - 32 / 2
= 6 ± √4 / 2
= 6 ± 2 / 2
x = 6/2 + 2/2 or 6/2 - 2/2
= 3 + 1 or 3 - 1
x = 4 or 2
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NO LINKS!! Please help me with this problem
Answer:
y²/324 -x²/36 = 1
Step-by-step explanation:
Where (0, ±b) are the ends of the transverse axis and y = ±(b/a)x describes the asymptotes, the equation of the hyperbola can be written as ...
y²/b² -x²/a² = 1
ApplicationHere, we have transverse axis endpoints of (0, ±18) and asymptotes of y = ±3x, so we can conclude ...
b = 18
b/a = 3 ⇒ a = 18/3 = 6
The equation of the hyperbola in standard form is ...
y²/324 -x²/36 = 1
What is the length of the line segment PQ on the coordinate grid?
A fourquadrant coordinate grid from negative 50 to positive 50 in increments of 10 is drawn. Point P is plotted on the ordered pair negative 20, 10. Point Q is plotted on the ordered pair 10, 10. The points are connected by a line.
20 units
30 units
40 units
50 units
Using the formula for the distance between two points, the length of the line segment PQ is of 30 units.
What is the distance between two points?Suppose that we have two points, [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex]. The distance between them is given by:
[tex]D = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
The coordinates of the endpoints for this problem are given by:
P(-20,10).Q(10,10).Hence the distance is given by:
D = sqrt[(-20 -10)² + (10 - 10)] = 30 units.
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Answer: 30 units
Step-by-step explanation:
One number is 6 more than another. The difference between their squares is 204. What are the numbers?
Answer: 20 and 14
Step-by-step explanation:
Using a little guess and check, we can figure out that the numbers are 6 apart and the difference between their squares is 204.
[tex]20^2 = 400\\14^2=196[/tex]
[tex]20^2-14^2 = 204[/tex]
A trick to doing this is to start with a number that is easily squared like 10 or 20 and see if the difference between their numbers is larger or smaller and change your numbers based on them.
Hope this helped :)
Answer:
14 and 20
Step-by-step explanation:
Let x and y be two numbers where x < y.
We are given :
y - x = 6
y² - x² = 204
Then
y - x = 6
(y - x)(y + x) = 204
Then
y - x = 6
6 × (y + x) = 204
then
y - x = 6 (Equation 1)
y + x = 34 (Equation 2)
Then
(Equation 1) + (Equation 2) ⇒ 2y = 40 ⇒ y = 20
Now ,we substitute y by 20 in equation 1 :
y - x = 6
⇔ 20 - x = 6
⇔ 20 - 6 = x
⇔ x = 14
ASAP help me with this ty!
Answer:
96 degrees
Step-by-step explanation:
The angle bisectors splits the two angles mentioned down the middle so the 2 angles are equal to each other.
4x + 4 = 2(x + 13) Distribute the 2
4x + 4 = 2x + 26 Subtract 2x from both sides
2x + 4 = 26 Subtract 4 from both sides
2x = 22 Divide both sides by 2
x = 11 Plug that back into either the right side or the left side of the original equation
4x + 4
4(11) + 4
44 + 4
48. Each angle is 48 degrees. 48 + 48 is 96
Find the value of x
[tex] \qquad \qquad \bf \huge\star \: \: \large{ \underline{Answer} } \huge \: \: \star[/tex]
x = 35°[tex]\textsf{ \underline{\underline{Steps to solve the problem} }:}[/tex]
[tex]\qquad❖ \: \sf \:4x + 1 + x + 4 = 180[/tex]
[ by linear pair ]
[tex]\qquad❖ \: \sf \:5x + 5 = 180[/tex]
[tex]\qquad❖ \: \sf \:5(x + 1) = 180[/tex]
[tex]\qquad❖ \: \sf \:x + 1 = 180 \div 5[/tex]
[tex]\qquad❖ \: \sf \:x + 1 = 36[/tex]
[tex]\qquad❖ \: \sf \:x = 36 - 1[/tex]
[tex]\qquad❖ \: \sf \:x = 35[/tex]
[tex] \qquad \large \sf {Conclusion} : [/tex]
x = 35°Two regular 6-sided dice are tossed. Compute the probability that the sum of the pops on the upward faces of the 2 dice is the following. 1
Answer: 0
Step-by-step explanation:
I need help with question
Answer
square root of 128 Lies between two square numbe
121 = 11 ^ 2
(11.1) ^ 2 = 133.1
So, √128 lies between 11.0 and 11.1.
Option A: 11.0 and 11.15x-3>17 or -2x+2>8 inequality
The solution of the inequality is as follows;
x > 4 or x < -3
How to solve inequality?The inequality can be solve as follows:
5x - 3 > 17 or -2x + 2 > 8
Let's solve the first inequality,
5x - 3 > 17
add 3 to both sides of the inequality
5x - 3 + 3 > 17 + 3
5x > 20
divide both sides by 5
5x / 5 > 20 / 5
x > 4
-2x + 2 > 8
subtract 2 from both sides
-2x + 2 - 2 > 8 - 2
-2x > 6
divide both sides by -2
-2x / -2 > 6 / -2
x < -3
Therefore, x > 4 or x < -3
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A community college employs 88 full-time faculty members. To gain the faculty's opinions about an upcoming building project, the college president wishes to obtain a simple random sample that will consist of 9 faculty members. He numbers the faculty from 1 to 88. Complete parts (a)
-Using the provided random number table, the president closes his eyes and drops his ink pen on the table. It points to the digit in row 3, column 6. Using this position as the starting point and proceeding downward, determine the numbers for the 9 faculty members who will be included in the sample.
The numbers that would be included in the sample are 4, 1, 1, 4, 7, 9, 2, 6, 4, 7, 4, 4, 1, 0, 3, 0, 5, 0, 7, 1, 1, 6, 5, 4, 9
How to determine the number that will be included in the sample?The complete question is added as an attachment
The given parameters are:
Row = 3
Column = 6
From the attached figure, the entries in row 3 are:
4, 1, 1, 4, 7, 9, 2, 6, 4, 7, 4, 4, 1, 0, 3, 0, 5, 0, 7 1
From the attached figure, the entries in column 6 are:
1, 6, 9, 5, 4, 9
Hence, the numbers that would be included in the sample are 4, 1, 1, 4, 7, 9, 2, 6, 4, 7, 4, 4, 1, 0, 3, 0, 5, 0, 7, 1, 1, 6, 5, 4, 9
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Of the stamps in a book, 5/12 came from Brian's collection and 24 came from Amy's. Of the rest, 15 were Jo's, 3/10 were Carl's and 27 were purchased. How many stamps are there in the book? HELPPP
Algebraic expressions are mathematical statements that consist of both number(s) and alphabet(x). Thus the number of stamps in the book is 66[tex]\frac{43}{60}[/tex] (67).
Algebraic expressions are mathematical statements that consist of both number(s) and alphabet(x). Majorly, the alphabet in the expression is referred to as the unknown value which has to be determined.
When the power of any of the alphabets contained in an algebraic expression is more than one, then it can be referred to as a polynomial.
In the given question, let the number of stamps in the book be represented by N.
So that;
N - 5/12 + 24 + 15 + 3/10 + 27 = 0
N - (5/12 + 24 + 15 + 3/10 + 27) = 0
N - [tex]\frac{8006}{120}[/tex] = 0
N - 66[tex]\frac{43}{60}[/tex] = 0
N = 66[tex]\frac{43}{60}[/tex]
= 66.72
N ≅ 67
Therefore the number of stamps in the book is approximately 67.
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Find equations of the following. y = x^2 − z^2, (6, 32, 2) (a) the tangent plane (b) the normal line
The equation for the tangent plane is 12x - y + 4z - 56 = 0 and the equation for normal line is (x - 6)/12 = (32 - y) = (z - 2)/4
Finding the Equations for Tangent Plane and Normal Line:
The given function is,
f(x, y, z) = x² - y - z² = 0
∂f/ ∂x = 2x
∂f/ ∂y = -1
∂f/ ∂z = 2z
At given point (6, 32, 2),
∂f/ ∂x = 12
∂f/ ∂y = -1
∂f/ ∂z = 4
(a) The equation of tangent plane is given as follows,
(∂f/ ∂x)(x-x₁) + (∂f/ ∂y)(y-y₁) + (∂f/ ∂z)(z-z₁) = 0
12(x - 6) - 1(y - 32) + 4(z - 4) = 0
12x - 72 - y + 32 + 4z - 16 = 0
The required tangent plane is,
12x - y + 4z - 56 = 0
(b) The equation for normal line is given as,
(x-x₁) / (∂f/ ∂x) = (y-y₁) / (y-y₁) = (z-z₁) / (∂f/ ∂z)
(x - 6)/12 = (y - 32)/(-1) = (z - 2)/4
Thus, the required equation of normal line is,
(x - 6)/12 = (32 - y) = (z - 2)/4
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Find the arc length, x, when
r = 1 and 0 = 5 radians.
п
9
5л
9
1
X
X =
?TT
The arc length of the circle is 5π/9 units
How to determine the arc length?From the question, we have the following parameters
Angle, ∅ = 5π/9
Radius, r = 1 unit
The arc length (x) is calculated as
x = r∅
Substitute the known values in the above equation
x = 5π/9 * 1
Evaluate the product
x = 5π/9
Hence, the arc length of the circle is 5π/9 units
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Number lineWhich of these numbers represents the difference between -3 and -2
The number which represents the difference between the numbers given -3 and -2 as in the task content is; 1.
Which number represents the difference between -3 and -2 in the task content?It follows from the task content that the difference between the given numbers -3 and -2 is to be determined by means of the number line.
On this note, since, it follows that the difference between two numbers in the number line is given by the absolute value of their arithmetic difference.
It follows that the number which is required in this scenario is; |-3-(-2)| = |-1| = 1.
This follows from the fact that the absolute value big any number is that number with a positive polarity.
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need this answered asap Which function has a minimum and is transformed to the right and down from the parent function, f(x) = x2? g(x) = –9(x + 1)2 – 7 g(x) = 4(x – 3)2 + 1 g(x) = –3(x – 4)2 – 6 g(x) = 8(x – 3)2 – 5
The function that has a minimum and is transformed to the right and down from the parent function is; g(x) = 8(x² - 3²) - 5
How to Interpret Functions?By inspection, only Functions B) and D) have a minimum.
For the first function in option B, we have:
g(x) = 4(x²- 6x + 9) + 1
This can be simplified to;
g(x) = 4( x - 3 )² + 1
Thus, we can say that this first function is transformed to the right and up from the parent function.
For the second function in option D, we have;
g(x) = 8(x² - 6x + 9 ) - 5
The function can be simplified to get;
g(x) = 8( x - 3 )² - 5
Thus, we can say that it is transformed to the right and down.
The function that has a minimum and is transformed to the right and down from the parent function is D
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Answer: option D
Step-by-step explanation:
PLEASE HELP ME WITH THIS QUESTION ASAPP
Answer:
Trapezoid
Step-by-step explanation:
One pair of parallel sides.
sin theta =-(1)/(\sqrt(17))and (3\pi )/(2)<=\theta <=2\pi then tan\theta =
Using a trigonometric identity, and considering that the angle is in the fourth quadrant, the tangent of the angle is given as follows:
tan(theta) = -1/4
Which trigonometric identity relates the sine and the cosine of an angle?The following identity is used to relate the measures, considering an angle [tex]\theta[/tex]:
[tex]\sin^2{\theta} + \cos^2{\theta} = 1[/tex]
For this problem, the sine is given as follows:
[tex]\sin{\theta} = -\frac{1}{\sqrt{17}}[/tex]
Then the cosine, which we need to find the tangent, is found as follows:
[tex]\sin^2{\theta} + \cos^2{\theta} = 1[/tex]
[tex]\left(-\frac{1}{\sqrt{17}}\right)^2 + \cos^2{\theta} = 1[/tex]
[tex]\frac{1}{17} + \cos^2{\theta} = 1[/tex]
[tex]\cos^2{\theta} = \frac{16}{17}[/tex]
[tex]\cos{\theta} = \pm \sqrt{\frac{16}{17}}[/tex]
Since the angle is in the fourth quadrant, the cosine is positive, hence:
[tex]\cos{\theta} = \frac{4}{\sqrt{17}}[/tex]
What is the tangent of an angle?It is the sine of the angle divided by the cosine of the angle, hence:
[tex]\tan{\theta} = \frac{\sin{\theta}}{\cos{\theta}} = \frac{-\frac{1}{\sqrt{17}}}{\frac{4}{\sqrt{17}}} = -\frac{1}{4}[/tex]
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PLEASE HELP ALOT OF POINYSAshlee is working with a local construction firm to improve Interstate 35.
The construction firm has created steel supports that will be arranged
into triangular shapes with side lengths of 6 feet, 9 feet, and where the
third side of each triangle has various lengths. They have asked Ashlee to
design a package that she could guarantee would fit all the materials. She
decided to use constructions to determine the maximum value for the
unknown side, x, and then ship all her materials in a box of length x feet.
Which is the best conclusion for Ashlee to make?
The best conclusion for Ashlee to make is (c) Ashlee determined that the box must be less than 15 feet by verifying the triangle inequality theorem.
How to determine the maximum lengths?
The side lengths of the triangle are given as:
6 feet and 9 feet
Let the third side be x.
By triangle inequality theorem, we have:
a + b > c
So, we have
6 + 9 > x
6 + x > 9
9 + x > 6
Evaluate the inequalities
15 > x
x > 3
x > -3
Remove the negative inequality
15 > x
x > 3
Combine the inequalities
3 < x < 15
So, the maximum side is less than 15
Hence, the best conclusion for Ashlee to make is (c) Ashlee determined that the box must be less than 15 feet by verifying the triangle inequality theorem.
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How tall is a pole if a 40 ft guy wire reaches from the top of that pole
to a point on the ground 19 ft from the bottom of the pole?
Sarah, Tony, and Megan are helping their parents plan the layout of the backyard. The patio is as wide as the fire pit, and 5 feet long. The pool is enlarged to yield the following layout:
If the patio is as wide as the fire pit, and 5 feet long then area of backyard can be expressed as [tex]2x^{2}+16x+30[/tex].
Given that the patio is as wide as the fire pit, and 5 feet long.
We are required to form an equation which can describe the area of the backyard.
Equation is relationship between two or more variables that are expressed in equal to form. Equations of two variables look like ax+by=c. It may be linear equation, quadratic equation, cubic equation or many more depending on the powers of the variable.
If we see the figure carefully then we can find that the length of the backyard is 2x+6 and the breadth of the backyard is 5+x and backyard is in shape of rectangle.
Area of rectangle =Length *breadth
=(2x+6)*(5+x)
=30+10x+6x+2[tex]x^{2}[/tex].
Hence if the patio is as wide as the fire pit, and 5 feet long then area of backyard can be expressed as [tex]2x^{2}+16x+30[/tex].
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sin^4x rewrite the power as a product of two squared terms
sin^4x as a product of two squared terms is sin^2(x) * sin^2(x)
How to rewrite the expression?The sine expression is given as
sin^4x
The above means
sin x raised to the power of 4
This in other words, the expression is represented as
(sin(x))^4
Express 4 as 2 + 2
(sin(x))^(2 + 2)
Apply the law of indices
(sin(x))^2 * (sin(x))^2
This gives
sin^2(x) * sin^2(x)
Hence, sin^4x as a product of two squared terms is sin^2(x) * sin^2(x)
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Which of the following is the solution to 8√3 + 7√3?
15√9
15√6
15√3
56√3
Which of the following is the solution to √15 * √45 simplified?
√675
8√3
15√15
15√3
Which of the following is the solution to 15√10 - 3√10?
12√10
5√10
12√100
45√10
Answer:
Q1: Third Choice. 15√3
Q2: Fourth Choice. 15√3
Q3: First Choice. 12√10
Step-by-step explanation:
Question 1: Which of the following is the solution to 8√3 + 7√3?Given expression
8√3 + 7√3
Simplify by addition
Remember that terms with the same radical part can add together directly
= (8 + 7) √3
[tex]\Large\boxed{=15\sqrt{3} }[/tex]
Question 2: Which of the following is the solution to √15 * √45 simplified?Given expression
√15 × √45
Factorize each radical
= √(3 × 5) × √(9 × 5)
= √3 × √5 × √9 × √5
Simplify necessary radicals
= √3 × √5 × 3 × √5
= 3 × √3 × √5 × √5
Simplify by multiplication
When radicals multiply, combine them under one radical sign
= 3√3 × √(5 × 5)
= 3√3 × 5
[tex]\Large\boxed{=15\sqrt{3} }[/tex]
Questions 3: Which of the following is the solution to 15√10 - 3√10?Given expression
15√10 - 3√10
Simplify by subtraction
Remember that terms with the same radical part can subtract each other directly
= (15 - 3) √10
[tex]\Large\boxed{=12\sqrt{10} }[/tex]
Hope this helps!! :)
Please let me know if you have any questions
PLease see attached. This is an algebra question
The solution for the given expression is 16.
Power RulesThere are different power rules, see some them:
1. Multiplication with the same base: you should repeat the base and add the exponents.
2. Division with the same base: you should repeat the base and subctract the exponents.
3.Power. For this rule, you should repeat the base and multiply the exponents.
4. Zero Exponent. When you have an exponent equals to zero, the result must be 1.
First, you apply the Power Rules - Power for [tex](\frac{2^2x^2y}{xy^3} )^2}[/tex]. For this rule, you should repeat the base and multiply the exponents. Thus, the result will be:[tex]\frac{16x^4y^2}{x^2y^6}[/tex].
After that, you should apply the Power Rules - Division . For this rule, you should repeat the base and subctract the exponents. Thus, the result will be:[tex]\frac{16x^2}{y^4}[/tex].
Now, you should replace the variable x by 4 and the variable y by 2. Thus, the result will be:[tex]\frac{16*4^2}{2^4}=\frac{16*16}{16} =16*1=16[/tex]
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QUESTION 3 The probability that it will rain on a given day is 63%. A child has a 12% chance of falling in dry weather and is three times as likely to fall in wet weather. Draw a tree diagram to represent all outcomes of the above information. What is the probability that a child will not fall on any given day? What is the probability that a child will fall in dry weather? 3.1 draw a tree diagram to represent all outcomes of the above information
Answer + Step-by-step explanation:
the probability that a child will not fall on any given day :
= (63 × 64 + 27 × 88) ÷ 100
= 64.08 %
the probability that a child will fall in dry weather :
= (27 × 12) ÷ 100
= 3.24 %
Write a quadratic function fwhose zeros are 2 and 8.
f(x) = 0
Use the grouping method to factor the polynomial below completely.
x³ + 2x² + 4x+8
The polynomial equation x³ + 2x² + 4x+8 can be expressed as the method of factor polynomial exists (x² + 4)(x + 2).
What is a factoring method?The factoring process concerns removing factors from an experiment and then using them in the analytical method of factor analysis.
Polynomials exist as expressions with one or more terms with a non-zero coefficient. A polynomial can contain more than one term.
A mathematical expression of one or more additional algebraic terms each of which consists of a constant multiplied by one or more variables presented to a nonnegative integral power.
Given: x³ + 2x² + 4x+8
x³ + 2x² + 4x+8 = 0
simplifying the equation, we get
(x³+2x²)+(4x+8 )= 0
x²(x+2)+4(x+2)= 0
factorizing the above equation, we get
(x+2)(x²+4) = 0
Therefore, the polynomial equation x³ + 2x² + 4x+8 can be expressed as the method of factor polynomial exists (x² + 4)(x + 2).
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20 is 50% of what number? If necessary, round to the nearest tenth.
Answer:
20 is 50% of 40.
Step-by-step explanation:
1% = 1/100
50% = 50/100 or 1/2
1/2 = 20/n
1*20/2*20 = 20/n
20/40 = 20/n
n = 40
$2,870 per month. He pays $574 a month for rent. What percent of his monthly pay goes to rent?
we know that 2870 is the 100%, what is 574 off of it in percentage?
[tex]\begin{array}{ccll} amount&\%\\ \cline{1-2} 2870 & 100\\ 574& x \end{array} \implies \cfrac{2870}{574}~~=~~\cfrac{100}{x} \\\\\\ 5=\cfrac{100}{x}\implies 5x=100\implies x=\cfrac{100}{5}\implies x=20[/tex]
The percent of his monthly pay which goes to rent if he earns a total of $2,870 per month is 20%.
What percent of his monthly pay goes to rent?Amount earned per month = $2,870
Amount paid for rent = $574
Let
The unknown percent = x
x% of $2,870 = $574
x/100 × 2,870 = 574
2,870x/100 = 574
cross product
2,870x = 57,400
divide both sides by 2,870
x = 57,400/2,870
x = 20%
Ultimately, 20% of the monthly pay goes to rent.
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the first term of a geometric sequence is 400 and the common ratio is 0.5. what is the 5th term of the sequence.
Answer:
25
Step-by-step explanation:
Geometric sequence
General form of a geometric sequence:
[tex]a_n=ar^{n-1}[/tex]
where:
a = first termr = common ratio[tex]a_n[/tex] = nth termGiven values:
a = 400r = 0.5n = 5Substitute the given values into the formula and solve:
[tex]\implies a_5=400(0.5)^{5-1}[/tex]
[tex]\implies a_5=400(0.5)^{4}[/tex]
[tex]\implies a_5=400(0.0625)[/tex]
[tex]\implies a_5=25[/tex]
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What is the largest prime number p such that 8 times p is less than 1000?
Answer:
113
Step-by-step explanation:
first we need to divide 1000 by 8 to get 125.
Our prime number has to be less than 125.
The largest prime number less than 125 is 113.
