Answer:
1/6 = 2/12 = 3/18 = 4/24 = 5/30 = 6/36 = 7/42 = 8/48 = 9/54 = 10/60........
The value of x in the equation 14(12x−36)=5x+18 is?
Answer:
x=522/163
Step-by-step explanation:
14(12x−36)=5x+18
168x-504=5x+18
168x-504+504=5x+18+504
163x=522
163x/163=522/163
x=522/163
x=3.20
Answer:
I got 3.2 in decimal form or 522/163 in a fraction
You have four fun things in a bag (scorpion, tarantula, centipede, and wasp). You reach into the bag and randomly grab two fun things, one after the other, keeping both. Create a tree diagram, table, or list that models the sample space for this event.
Answer: Here is a table that models the sample space for this event:
Scorpion Tarantula Centipede Wasp
First S1 T1 C1 W1
Second S2 T2 C2 W2
Each combination of two fun things is represented by a two-letter code. For example, "S1T2" represents grabbing the scorpion first and the tarantula second.
Here is the list of all possible outcomes:
S1S2
S1T2
S1C2
S1W2
T1S2
T1T2
T1C2
T1W2
C1S2
C1T2
C1C2
C1W2
W1S2
W1T2
W1C2
W1W2
And here is a tree diagram that shows the same information:
|----S2
|----T2
First --|----C2
|----W2
|
|----S2
|----T2
Second--|----C2
|----W2
The branches on the left represent the first fun thing that is grabbed, and the branches on the right represent the second fun thing that is grabbed.
Step-by-step explanation:
A customer purchased 10 items at a rummage sale. The prices paid are given in the table. What amount of change should the customer have received given that the customer paid with a $20 bill?
The amount of change that the customer will be given when payment is made with a $20 bill would be = $7.15. That is option G.
How to calculate the cost balance of the customer?The total number of items purchased by the customer = 10
The cost for 5 items = $1.60× 5 = $8
The cost of 3 items = $1.25×3 = $3.75
The cost of 2 items = $0.55×2 = $1.1
The total cost = 8+3.75+1.1 = $12.85
Therefore, the change of the customer when $20 bill is used = 20-12.85
= $7.15.
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A rancher has 600
feet of fencing to put around a rectangular field and then subdivide the field into 3
identical smaller rectangular plots by placing two fences parallel to one of the field's shorter sides. Find the dimensions that maximize the enclosed area. Write your answers as fractions reduced to lowest terms.
The dimensions of the rectangular field that maximize the enclosed area are 150 feet by 75 feet.
What is area?
An object's area is how much space it takes up in two dimensions. It is the measurement of the quantity of unit squares that completely cover the surface of a closed figure.
Let's call the length of the rectangle "l" and the width "w".
We can write two equations based on the given information -
Perimeter equation: 2l + 4w = 600 (since there are two sets of parallel sides, we have to add an extra "w" to the perimeter equation)
Area equation: A = 3lw (since the field is divided into 3 equal parts)
We want to maximize the enclosed area, which means we want to find the values of "l" and "w" that make the area as large as possible.
We can use the perimeter equation to solve for one of the variables in terms of the other -
2l + 4w = 600
2l = 600 - 4w
l = 300 - 2w
Now we can substitute this expression for "l" into the area equation -
A = 3lw
A = 3(300 - 2w)w
A = 900w - 6w²
To find the maximum area, we can take the derivative of this equation with respect to "w" and set it equal to zero -
dA/dw = 900 - 12w = 0
12w = 900
w = 75
So the width of each of the smaller rectangular plots is 75 feet.
We can use the perimeter equation to find the length -
2l + 4w = 600
2l + 4(75) = 600
2l = 300
l = 150
Therefore, the dimensions value are obtained as 150 feet by 75 feet.
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What is the area of the trapezoid? ___ units 2
The area of the trapezoid is 176 square units.
What is a trapezoid?
A trapezoid, which is also referred to as a trapezium, is a flat, closed shape with four straight sides and one set of parallel sides.
A trapezium's parallel bases and non-parallel legs are referred to as its bases and legs, respectively. The legs of a trapezium can also be parallel. The parallel sides may be vertical, horizontal, or angled.
The altitude is the length of the parallel sides measured perpendicularly.
The height of the trapezoid is 4 units.
The parallel sides of the trapezoids are 17 units and (5+17+5) = 27 units.
The area of a trapezoid is half of the product of the height and the sum of parallel sides.
The area of the trapezoid is
1/2 × 4 ×(17+27)
= 176 square units
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HELLLPPPPP me please
The length and the width of the model are Length = 2 and Width = 3x² + 5x + 6
Why 6x cant be the lengthThe expression 6x cant be the length because 12 cannot divide 6x without becoming a radical expression
Calculating the length and the widthWe have
Area = 6x² + 10x + 12
Factor out 2
Area = 2(3x² + 5x + 6)
This means that
Length = 2 and Width = 3x² + 5x + 6
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Simplify: 5/6-17/12-5/3 A. -19/12 B.-17/12 C.1/4 D.23/12
HELP ASAP pls!!!
Answer:
The simplified expression is -13/12. (are you sure you don't have a typo somewhere), double checked.
Step-by-step explanation:
First, let's simplify the expression inside the absolute value bars:
5/6 - 17/12 = 10/12 - 17/12 = -7/12
Next, we can simplify the expression outside the absolute value bars:
| -7/12 | - | 5/3 |
= 7/12 - 5/3 (since the absolute value of -7/12 is 7/12)
= 7/12 - 20/12
= -13/12
The simplified expression is -13/12.
_______________________
Simplify the following:
abs(5/6 - 17/12) - abs(5/3)
Put 5/6 - 17/12 over the common denominator 12. 5/6 - 17/12 = (2×5)/12 - 17/12:
abs(((2×5)/12 - 17/12)) - abs(5/3)
2×5 = 10:
abs(10/12 - 17/12) - abs(5/3)
10/12 - 17/12 = (10 - 17)/12:
abs(((10 - 17)/12)) - abs(5/3)
10 - 17 = -7:
abs((-7)/12) - abs(5/3)
Since 5/3 is a non-negative constant, abs(5/3) = 5/3:
abs(-7/12) - 5/3
Since -7/12 is a negative constant, abs(-7/12) = 7/12:
7/12 - 5/3
Put 7/12 - 5/3 over the common denominator 12. 7/12 - 5/3 = 7/12 + (4 (-5))/12:
7/12 - (5×4)/12
4 (-5) = -20:
7/12 + (-20)/12
7/12 - 20/12 = (7 - 20)/12:
(7 - 20)/12
7 - 20 = -13:
Answer: (-13)/12
How long would it take for a ball dropped from the top of a 81ft building to hit the ground round your answer to two decimal places
Answer:
Set the height equal to (1/2)gt^2 and solve for t.
h = (1/2)gt^2
t = (2h/g)^1/2
Plug in the numbers and get your answer in seconds:
h = 81 ft
g = 32 ft/s^2
Step-by-step explanation:
Indicate whether the two functions are equal. If the two functions are not equal, then give an element of the domain on which the two functions have different values.
(a). f: Z → Z, where f(x) = x^2.
g: Z → Z, where g(x) = |x|^2.
(b). f: Z × Z → Z, where f(x,y) = |x + y|.
g: Z × Z → Z, where g(x,y) = |x| +| y|.
(c). B = {0, 1}
f: B × B → B × B, where f(x,y) = (1-y, 1-x)
g: B × B → B × B, where g(x,y) = (x,y)
The functions are equal in option A, and aren't equal in B (try input x =1 and y = -1) and in C (try input x = 0 and y = 0).
Are the functions equal in the domains?The first one is:
(a). f: Z → Z, where f(x) = x^2.
g: Z → Z, where g(x) = |x|^2.
Yes, these functions are equal, this happens because both outcomes will always be positive, indifeterent of the absolute value part.
b) f: Z × Z → Z, where f(x,y) = |x + y|.
g: Z × Z → Z, where g(x,y) = |x| +| y|.
These are different, if x = 1 and y = -1
f(1, - 1) = |1 - 1| = 0
g(1, -1) = |1| + |-1| = 2
c) B = {0, 1}
f: B × B → B × B, where f(x,y) = (1-y, 1-x)
g: B × B → B × B, where g(x,y) = (x,y)
This is clearly false, when x and y are 0 and 0 we have:
f(0, 0) = (1 - 0, 1 - 0) = (1, 1)
While g gives:
g(0, 0) = (0, 0)
These functions are different.
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The equivalent expression
The equivalent expression is (x -2)/(x+4)(x + 6)
How to determine the equivalent expressionIt is important to note that algebraic expressions are defined as expressions composed of coefficients, terms, variables, constants and factors.
They are also made up of arithmetic operations.
Also, equivalent expressions are defined as expressions that have the same solution but differs in the arrangement of the terms.
From the information given, we have the expression;
(x - 2)/x² + 10x + 24
Now, let's factorize the denominator, we have;
x² + 10x + 24. Find the pair factors of 24 that add up to 10, we get;
x² + 4x + 6x + 24
Factorize in pairs
x(x + 4) + 6(x + 4)
Then, substitute the expressions;
(x -2)/(x+4)(x + 6)
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The mean for the math component of the New Century Achievement Test is reported as 100, with a standard deviation (σ) of 15. A sample of 400 students throughout a particular school district reveals a mean (Symbol) score of 110. Estimate the mean score for all the students in the district, using a 99% confidence interval.
Answer: To estimate the mean score for all the students in the district, we can use a confidence interval. We are given that the sample size is 400, the sample mean is 110, the population means is 100, and the population standard deviation is 15. We are asked to find a 99% confidence interval for the population mean.
The formula for a confidence interval for the population mean with known population standard deviation is:
Confidence interval = sample mean ± z*(σ/√n)
where:
sample mean = 110 (given)
σ = 15 (given)
n = 400 (given)
z = the critical value from the standard normal distribution for a 99% confidence level, which is 2.576.
Substituting the values, we get:
Confidence interval = 110 ± 2.576*(15/√400)
Confidence interval = 110 ± 1.92
Therefore, the 99% confidence interval for the population mean score is (110 - 1.92, 110 + 1.92), or (108.08, 111.92). We can be 99% confident that the true population mean score for all the students in the district falls between 108.08 and 111.92.
Step-by-step explanation:
Find f(x) + g (x). f(x) = 8-4x-x``3 g(x) = x`2 + 7x - 9
After answering the presented question, we can conclude that equation Therefore, f(x) + g(x) = [tex]-x^3 + x^2 + 3x - 1.[/tex]
What is equation?An equation is a mathematical statement that validates the equivalent of two expressions joined by the equal symbol '='. For instance, 2x - 5 = 13. 2x-5 and 13 are two examples of expressions. The character '=' connects the two expressions. An equation is a mathematical formula that has two algebras on each side of an assignment operator (=). It demonstrates the equivalency link between the left and middle formulas. L.H.S. = R.H.S. (left side = right side) in any formula.
To find f(x) + g(x),
[tex]f(x) = 8 - 4x - x^3\\g(x) = x^2 + 7x - 9\\f(x) + g(x) = (8 - 4x - x^3) + (x^2 + 7x - 9)\\f(x) + g(x) = -x^3 + x^2 + 3x - 1\\[/tex]
Therefore, f(x) + g(x) = [tex]-x^3 + x^2 + 3x - 1.[/tex][tex]-x^3 + x^2 + 3x - 1.[/tex]
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Triangle RST was dilated by a scale factor of 5 to create triangle LMN. (Show your work)
If tan R = 5/2.5 find the measure of segments LM and MN.
Therefore , the solution of the given problem of triangle comes out to be segments LM and MN have equal 10x measures.
What exactly is a triangle?A triangle is a polygon because it has two or more additional parts. It has the simple form of a rectangle. A triangle can only be distinguished from a conventional triangle by its three sides, A, B, but not C. So when borders are still not exactly collinear, Euclidean geometry results in a single area as opposed to a cube. Three edges and three angles are the characteristics of triangles.
Here,
Given that RS and LM are the respective sides of the two triangles, if we set x as the length of RS, then LM's length is 5x and ST's length is 2x. The duration of MN is five times that of ST, which is ten times longer.
We can now calculate the length of RS using the tangent of angle R:
=> tan R=RS/ST
=> 5/2.5=2
We thus have:
=> RS = 2
=> ST = 2x
We can determine the length of RT using the Pythagorean theorem:
=> RT/ST = sin R
=> RT = ST sin R
=> 2.5 (2/29) = 4.337 sin R = 2.5
We can now determine the lengths of LM and MN using the similarity of the triangles:
=> RM = 5 (2x) LM = 5 = 10
=> MN = 5 ST = 5 (two times) = 10
As a result, segments LM and MN have equal 10x measures.
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The values of LM = 12.5 and MN = 25
Define the term triangle?A triangle is a closed geometric figure consisting of three line segments or sides, connected to each other at three endpoints or vertices. Each side of a triangle intersects with exactly two other sides, and the vertices are the points where the sides meet.
From the given figures, both the triangles are right angle triangle.
[tex]tan R=\frac{5}{2.5} = \frac{ST}{RS}[/tex]
So, ST = 5 and RS = 2.5
Since, ΔRST is 5th to create ΔLMN,
its corresponding sides are 5 times the length LM corresponding sides of RS. So, its length
LM = 5×2.5 = 12.5
LM = 12.5
MN corresponding sides of ST. So, its length
MN = 5×5 = 25
MN = 25
Therefore, The values of LM = 12.5 and MN = 25.
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I will mark you brainiest!
Please do it in steps
What is the base of a parallelogram with an area of 36 units2 and a height of 9 units?
The base length of the parallelogram found using the area formula is 4 units.
What is a parallelogram?
A basic quadrilateral with two sets of parallel sides is known as a parallelogram. A parallelogram's facing or opposing sides are of equal length, and its opposing angles are of similar size. A parallelogram has adjacent angles that add up to 180 degrees. 360 degrees is the sum of all interior angles.
A parallelogram's area is the area that it takes up in a two-dimensional plane. The parallelogram's area is calculated by multiplying the base length by the height.
Each shape's perimeter can be defined as either the entire length or total distance encircling the object. The entire distance between a parallelogram's boundaries is also known as the parallelogram's perimeter.
Given,
The area of the parallelogram A =36 sq. units
The height of the parallelogram h = 9 units
We are asked to find the base length b.
Now the formula for the area of the parallelogram is:
A = b * h
36 = b * 9
b = 36/9 = 4 units.
Therefore the base length of the parallelogram, found using the area formula is 4 units.
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If the length and breadth of a rectangle are 12 cm and 5 cm respectively, what will be the length of its diagonal?
NEED HELP WILL GIVE BRAINLIEST IF I GET FULL HELP ON BOTH QUESTIONS
The inverse of the function is y = (-3x + 50)/4.
The domain of the inverse function are {4, 5, 6, 10}.
The range of the inverse function are {5, 8, 9, 13}.
What is the point-slope form?Mathematically, the point-slope form of a straight line can be calculated by using this mathematical expression:
y - y₁ = m(x - x₁) or y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)
Where:
m represents the slope.x and y are the points.At point (5, 10), an equation of the line f(x) can be calculated by using the point-slope form:
y - 10 = (6 - 10)/(8 - 5)(x - 5)
y - 10 = -4/3(x - 5)
y = -4x/3 + 20/3 + 10
y = -4x/3 + 50/3
y = (-4x + 50)/3
In order to determine the inverse of any function, you should swap both the input value (x-value) and output value (y-value) as follows;
x = (-4y + 50)/3
3x = -4y + 50
4y = -3x + 50
y = (-3x + 50)/4
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An alloy is made up of 93.5 parts aluminum, 5 parts zinc, and 1.5 parts copper. A foundry
has 164 pounds of aluminum available. Find the weight of the zinc and copper that will be
needed to make the alloy.
Answer: Since the alloy is made up of 93.5 parts aluminum, 5 parts zinc, and 1.5 parts copper, we can express the weight of zinc and copper needed to make the alloy as a ratio to the weight of aluminum needed. Let x be the weight of aluminum needed in pounds, then we have:
Weight of aluminum: Weight of zinc: Weight of copper = 93.5: 5 : 1.5
We know that the foundry has 164 pounds of aluminum available, so we can substitute x = 164 into the above ratio and solve for the weights of zinc and copper:
164: Weight of zinc: Weight of copper = 93.5: 5 : 1.5
Cross-multiplying, we get:
164 × 5 = 93.5 × Weight of zinc
Weight of zinc = (164 × 5) / 93.5
Weight of zinc = 8.76 pounds (rounded to two decimal places)
Similarly, cross-multiplying the above ratio gives us:
164: Weight of zinc: Weight of copper = 93.5: 5 : 1.5
164 × 1.5 = 93.5 × Weight of copper
Weight of copper = (164 × 1.5) / 93.5
Weight of copper = 2.63 pounds (rounded to two decimal places)
Therefore, the weight of zinc needed to make the alloy is 8.76 pounds and the weight of copper needed is 2.63 pounds.
Step-by-step explanation:
85 POINTS!!! With brainiest 5th grade please complete this page below you can print it or do it online please just do it
Answer:
1. 8
2. 24
3. 15
4. 135
b. 135 x 1/9
5. the answer is 24
Four components of 55
Answer: 1, 5, 11, 55
Step-by-step explanation:
A recipe for bread calls for 4 cups of flour for every 1/2 cup of water. Using the same recipe, how much
water will you need for 5 cups of flour?
Answer:
According to the recipe, the ratio of flour to water is 4:0.5 or 8:1 (since 1/2 can be simplified to 0.5).
To determine how much water is needed for 5 cups of flour, we can use this ratio:
8:1 = 5:x
where x represents the amount of water needed.
To solve for x, we can cross-multiply:
8x = 5 * 1
8x = 5
x = 5/8
Therefore, you will need 5/8 cup of water for 5 cups of flour, using the given recipe.
Step-by-step explanation:
Please help . A burglar alarm system has six fail-safe components. The probability of each failing is 0.05. Find the probability that fewer than three will fail. Round to the nearest thousandth.
Answer:
Answer:
0.050
Rounded to the nearest 0.001 or
the Thousandths Place.
Step-by-step explanation:
Explanation
0.05__
You rounded to the nearest thousandths place. The _ in the thousandths place rounds down to 0 because the digit to the right in the ten thousandths place is _.
0.050
When the digit to the right is less than 5 we round toward 0.
0.05 was rounded down toward zero to 0.050
Give me some help please
Answer: 56 cm
Step-by-step explanation:
The total cost of producing a type of boat is given by C(x)=21000−40x+0.1x^2
, where x is the number of boats produced. How many boats should be produced to incur minimum cost?
Using differentiation, 200 boats should be produced to incur minimum cost
What is meant by differntiation?A function's sensitivity to change with respect to a change in its argument is measured by the derivative of a function of a real variable in mathematics. A crucial calculus technique is the derivative.
Differentiation is a technique for determining a function's derivative. In mathematics, the technique of differentiation is used to determine the instantaneous rate of change in a function dependent on one of its variables. The most typical illustration is the velocity, or rate of change of displacement with respect to time.
Minimum boats can be found by differentiating the given function,
[tex]C(x)=21000 - 40x+0.1x^2[/tex]
Differentiating with respect to x,
0 = 0.2x - 40
0.2x = 40
x = 200
∴ 200 boats should be produced to incur minimum cost.
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Use appropriate method to solve the following. 1. If twice the age of a son is added to age of a father, then the sum is 56. If twice the age of the father is added to the age of son, then the sum is 82. Find the ages of father and son. 2. In a two-digit number, the sum of the digits is 13. Twice the tens digit exceeds the units digit by one. Find the numbers. 3. I am thinking of a two-digit number. If I write 3 to the left of my number, and double this three digit number, the result is 27 times my original number What is my original number?
Answer:
Step-by-step explanation:
Let the age of the son be $s$ and the age of the father be $f$. From the first equation, we have $2s + f = 56$, and from the second equation, we have $f + 2s = 82$. Solving this system of equations, we get $s = 12$ and $f = 32$, so the son is 12 years old and the father is 32 years old.
Let the two-digit number be $10t+u$, where $t$ is the tens digit and $u$ is the units digit. We are given that $t+u=13$ and $2t-u=1$. Solving this system of equations, we get $t=7$ and $u=6$, so the two-digit number is $76$.
Let the two-digit number be $10x+y$, where $x$ is the tens digit and $y$ is the units digit. We are given that $2(10+x+y) = 27(10x+y)$, or $20+2x+2y = 270x+27y$. Simplifying this equation, we get $268x-25y = 10$. Since $y$ is a digit, we know that $0 \leq y \leq 9$. We can check that $x=1$ is too small, so we try $x=2$. Plugging in $x=2$, we get $536-25y=10$, which gives $y=21/5$, which is not a digit. Thus, there is no solution for a two-digit number.
what is the measure of MN
Answer:
45 degrees I think
Step-by-step explanation:
sorry if wrong
the distance between (-7, 3) and (5, 3)
Answer:
12
Step-by-step explanation:
7+5
Answer:
.
Step-by-step explanation:
The distance between two points (x1, y1) and (x2, y2) is given by the formula:
d = sqrt((x2 - x1)^2 + (y2 - y1)^2)
Here, (x1, y1) = (-7, 3) and (x2, y2) = (5, 3).
Substituting these values, we get:
d = sqrt((5 - (-7))^2 + (3 - 3)^2)
= sqrt((12)^2 + (0)^2)
= sqrt(144)
= 12
Therefore, the distance between (-7, 3) and (5, 3) is 12 units.
Suppose I am rolling a standard 6-sided dice. Let A be the event I roll a prime number, Let B be the event I roll a number less than or equal to 4. I ran a trial 10 times and got the results 2, 4, 3, 1, 5, 6, 1, 3, 2, 1
What is the experimental P(B)
The experimental probability of rolling a number less than or equal to 4 is 0.7.
How is conditional probability calculated? What does it mean?The likelihood that an event (A) will occur given the occurrence of another event (B) is known as conditional probability. P(A|B), which stands for "the probability of A given B," is used to express it. You must first determine P(A and B) by multiplying the odds of A and B happening together. Next, you may compute P(A|B). The conditional probability of A given B is then obtained by dividing the result by P(B).
Several situations in everyday life, including medical diagnosis, industrial quality control, and risk assessment in insurance, call for the usage of conditional probability.
Given that, the trial was run 10 times.
Thus,
P(B) = (number of times B occurred) / (total number of trials)
= 7 / 10
= 0.7
Therefore, the experimental probability of rolling a number less than or equal to 4 is 0.7.
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Marty has a piece of rope with exactly 7 knots tied at equal intervals as shown. using the rope, he wants to make triangles so that each vertex of the triangle occurs at a knot. how many triangles can Marty make?
(a) 4
(b) 1
(c) 2
(d) 3
Using algebra, Marty can make 4 triangles from a rope with 7 knots.
What do you mean by algebra?Algebra, a branch of mathematics, facilitates the representation of situations or issues as mathematical expressions. Mathematical operations like addition, subtraction, multiplication, and division are combined with variables like x, y, and z to produce a meaningful mathematical expression.
All branches of mathematics, such as trigonometry, calculus, and coordinate geometry, employ algebra. Algebraically, 2x + 4 = 8 is a simple expression.
Now here in the question,
3 knots form the vertices of a triangle.
Remaining 4 knots out of the 7 can be distributed as:
4+0+0 .......(on 3 sides)
3+1+0
2+2+0
2+1+1
Therefore, Marty can make 4 triangles from the rope with 7 knots.
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construct a quadratic equation of -2 +3
[tex]\begin{cases} x = -2 &\implies x +2=0\\ x = 3 &\implies x -3=0\\ \end{cases} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{original~polynomial}{a ( x +2 )( x -3 ) = \stackrel{0}{y}}\hspace{4em}\stackrel{\textit{now, assuming that}}{a=1}\hspace{5em}1( x +2 )( x -3 ) =y \\\\\\ ~\hfill {\Large \begin{array}{llll} x^2-x-6=y \end{array}}~\hfill[/tex]
On a menu, there are 5 beef options, 3 pork options, 6 chicken options, and 4 vegetarian options. One of the options is selected at random. Determine the theoretical probability of selecting a meat option. Express your answer as a fraction in simplest form. HELP!
Answer: The theoretical probability of selecting a meat option is 7/9.
Step-by-step explanation:
5 beef + 3 pork + 6 chicken + 4 veggie = 18 options total
meat options = 18 (total) - 4 veggie = 14 meat options
14/18 = 7/9