Therefore, the values of a and b are:
[tex]a = 2[/tex]
[tex]b = 9[/tex]
[tex]So, the functionf(x)=2x+9.[/tex]
What do you mean by the function?In programming and mathematics, a function is a set of instructions or a block of code that performs a specific task or calculation. A function takes in one or more input values, performs a series of operations on them, and then returns a single output value. Functions are used to modularize code, making it easier to read, understand, and maintain. They can be defined and called within a program to perform repetitive tasks, manipulate data, or solve complex problems. Functions can also be used to create reusable code that can be called from multiple parts of a program or shared between different programs.
To find the values of a and b, we need to use the given information to create a system of two equations.
Let's start by using the first two rows of the table:
[tex]f(0) = a(0) + b = 7[/tex]
[tex]f(1) = a(1) + b = 9[/tex]
Simplifying these equations, we get:
[tex]b = 7\\a + b = 9[/tex]
Substituting b = 7 into the second equation, we get:
[tex]a + 7 = 9[/tex]
Solving for a, we get:
[tex]a = 2[/tex]
Now we can use this value of a to find b. Let's use the third and fourth rows of the table:
[tex]f(2) = a(2) + b = 11\\f(3) = a(3) + b = 13[/tex]
Substituting a = 2 into these equations, we get:
[tex]2 + b = 11\\3 + b = 13[/tex]
Solving for b, we get:
[tex]b = 9[/tex]
Therefore, the values of a and b are:
[tex]a = 2\\b = 9[/tex]
[tex]So, the functionf(x)=2x+9.[/tex]
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DIVIDE 3000 RUPEES AMONG TEENA AND BEENA SO THE THEY GET 40% AND 60% RESPECTIVELY
Answer:
To divide 3000 rupees between Teena and Beena so that they get 40% and 60% respectively, we need to follow these steps:
Step 1: Find the total percentage that Teena and Beena will receive together:
40% + 60% = 100%
This means that Teena and Beena will receive 100% of the total amount, which is 3000 rupees.
Step 2: Calculate the amount that Beena will receive:
60% of 3000 rupees = 0.6 x 3000 = 1800 rupees
Step 3: Calculate the amount that Teena will receive:
40% of 3000 rupees = 0.4 x 3000 = 1200 rupees
Therefore, Beena will receive 1800 rupees, while Teena will receive 1200 rupees
determine the solution for the system of equation -2y=-6x-18 3x-4y=27 ( , )
The solution for the system of equation -2y=-6x-18 3x-4y=27 is (x, y) = (-3, 9).
What is system?A system is an organized set of components that work together to achieve an overall goal. It could be a physical system, such as an automobile, or an abstract system, such as an economic system.
The first step is to isolate one of the variables in one of the equations. To do this, we can multiply both sides of the first equation by -3. This will give us: 6y = 18x + 54.
Next, we need to subtract this equation from the second equation. Doing so gives us: 3x - 6y = -27.
Now we can isolate the variable y. To do this, we can divide both sides of the equation by -6. This will give us: y = -3x - 9.
We have now isolated the variable y in both equations, so we can substitute y = -3x - 9 in the first equation. Doing so gives us: -2(-3x - 9) = -6x - 18.
We can then simplify this equation to get: 6x + 18 = -6x - 18.
Finally, we can solve this equation for x. Doing so gives us x = -3. We can then substitute this value into either equation to find the value of y: y = -3(-3) - 9 = 9.
Therefore, the solution for the system of equation -2y=-6x-18 3x-4y=27 is (x, y) = (-3, 9).
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A used car costs $3450 at present. This is 60% of the cost 4 yr ago. What was the cost of the car 4 yr ago?
Using arithmetic operation it is obtained that the cost of the car 4 years ago was $5750.
What is arithmetic operation?
A subject of mathematics known as arithmetic operations deals with the study and use of numbers in all other branches of mathematics. Basic operations including addition, subtraction, multiplication, and division are included.
Let C be the cost of the car 4 years ago.
According to the problem, the current cost of the car is 60% of the cost 4 years ago, so we can write -
3450 = 0.6C
Use the arithmetic operation of division -
To solve for C, we can divide both sides of the equation by 0.6 -
C = 3450/0.6
C = 5750
Therefore, the cost of the car 4 years ago was $5750.
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QUESTION 5 1 POINT
If cost is represented by C(x) = 3.7x + 9,000 and revenues are represented by R(x) = 4.6x, which equation could be
used to find the break-even point?
Answer:
The function that represents the company's profits is [tex]P(x)=0.9x-9,000[/tex]
Step-by-step explanation:
We are given
The costs of a company are represented by the function
[tex]C(x)=3.7x+9,000[/tex]
Its revenues are represented by the function
[tex]R(x) = 4.6x[/tex]
we know that
[tex]\text{Profit = Revenue - Cost}[/tex]
[tex]P(x)=R(x)-C(x)[/tex]
now, we can plug
[tex]P(x)=4.6x-(3.7x+9,000)[/tex]
now, we can simplify it
[tex]P(x)=0.9x-9,000[/tex]
So,
the function that represents the company's profits is [tex]P(x)=0.9x-9,000[/tex]
The equation used to find the break-even point is 0.9x - 9000.
What is Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
We have,
The costs of a company are represented by the function
C(x) = 3.7x + 9,000
and, revenues function
R(x) = 4.6x
For Break even point
Profit = Revenue - cost
P = 3.7x + 9000 - 4.6x
P = 0.9x - 9000
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A baker makes 8 apple pies. Each apple pie weighs 6 ounces.
How many total pounds of apple pies does the baker make?
Responses?
Answer:
6
Step-by-step explanation:
16 Ounces in a pound
6x8=48
48/8=6
Answer:
3 pounds
Step-by-step explanation:
total pie = 8
weight of 1 pie = 6 ounces
weight of 8 pie = 6 ounces × 8
= 48 ounces
ounce into pound
1 ounce =0.0625 (divide ounces by 16)
48 ounces ÷ 16
=3 pounds
the baker made 3 pounds od apple pie
If this figure was rotated around the x-axis, what would the height be? The radius?
The height and the radius of the figure will remain unchanged as the figure is being just rotated around the axis and not transformed.
What is a transformation?A function transformation "moves," "resizes," or "reflects" the parent function's graph, depending on the case. Function transformations can be broadly divided into three categories:
Translation
Dilation
Reflection
Dilation is the only one of these changes that modifies the original shape's size; the other two just change the shape's placement.
Here in the question,
The figure is being rotated not dilated so the dimensions of the new figure will remain the same.
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How do I solve the satellite question?
What is the perimeter of ABCD?
5x[tex]11ab^{2}(2a^5b^4)[/tex]
Hence,[tex]110a^6b^6[/tex] is the simplified expression as by multiplying 5x11 using the distributive property .
what is expression ?A mathematical expression seems to be a combination of digits, symbols, and operators (like +, -,, and ) that denotes a relation or quantity. A single figure or variable can constitute an expression, as can a collection of several numbers, constants, and operators. It is possible to depict mathematical connections, functions, and processes using expressions. There are various categories into which expressions can be divided, including numerical, algebraic, polynomial, rational, and exponential expressions. These can be assessed by carrying out the relevant operations in the mathematical operation order, i.e., parentheses operations first, multiplication or division second, addition or subtraction third.
given
[tex]5x11ab^2(2a^5b^4)[/tex]
We may multiply 5x11 using the distributive property, and then multiply the variables using exponentiation rules to simplify the formula
[tex]5x11ab^2(2a^5b^4):[/tex]
[tex]55ab^2(2a^5b^4)[/tex] is equal to [tex]5x11ab^2(2a^5b^4)[/tex]
= [tex]110a^(1+5)b^(2+4)[/tex] (using the product rule of exponents)
= [tex]110a^6b^6[/tex]
Hence,[tex]110a^6b^6[/tex] is the simplified expression as by multiplying 5x11 using the distributive property .
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One can also find the interest rate of the uneven cash flow stream with a financial calculator and solving for the internal rate of return (IRR) using the IRR key. Quantitative Problem: You own a security with the cash flows shown below. 0 1 2 3 4 0 690 365 220 330 If you require an annual return of 12%, what is the present value of this cash flow stream? Do not round intermediate calculations. Round your answer to the nearest cent. $
Answer:
To solve this problem, we need to find the present value of the cash flow stream using a discount rate of 12%. We can use the present value formula:
PV = CF1/(1+r)^1 + CF2/(1+r)^2 + CF3/(1+r)^3 + CF4/(1+r)^4
where PV is the present value, CF1, CF2, CF3, and CF4 are the cash flows at time 1, 2, 3, and 4 respectively, and r is the discount rate.
Substituting the values given in the problem, we get:
PV = 690/(1+0.12)^1 + 365/(1+0.12)^2 + 220/(1+0.12)^3 + 330/(1+0.12)^4
PV = 690/1.12 + 365/1.2544 + 220/1.4049 + 330/1.5735
PV = 616.07 + 290.76 + 156.51 + 209.38
PV = 1272.72
Therefore, the present value of the cash flow stream is $1,272.72.
Step-by-step explanation:
The sum of two numbers is 22. The difference of the two numbers is 0. What are the two numbers?
Answer:
11
Step-by-step explanation:
because 11+11=22 so there are no different with two 11s
PLEASE HELPPPPP
THANKS
Let 0°
Given: tan a =2.4
Find: sin a and cos a
Answer:
sin α = 12/13;cos α = 5/13.-------------------------
Since angle α is between 0° and 90°, it is in the first quadrant and therefore all sin α, cos α and tan α are positive numbers.
Use the following identities:
tan α = sin α / cos α;sin² α + cos² α = 1.Given tan α = 2.4. Using identities, find cosine as follows:
sin α / cos α = 2.4sin α = 2.4 cos αcos² α = 1 - sin² αcos² α = 1 - (2.4 cos² α)²cos² α = 1 - 5.76 cos² αcos² α + 5.76 cos² α = 16.76 cos² α = 12.6 cos α = 1cos α = 1/2.6cos α = 10/26 cos α = 5/13Find sine:
sin² α = 1 - cos² αsin² α = 1 - (5/13)²sin² α = 1 - 25/169sin² α = 144/169sin α = 12/13Write an equation(any form) for the quadratic graphed below:
Answer:
[tex]y = -2(x + 3)^{2} + 3[/tex]
Step-by-step explanation:
The equation for a quadratic graph can be expressed in the Vertex form:
[tex]y = a(x-h)^{2} + k[/tex]
Where:
[tex](h, k)[/tex] = Vertex of the parabola
= Extreme point of the parabola
Step I:
By reading from the graph:
[tex](h, k)[/tex] = [tex](-3, 3)[/tex]
Substitute the values of h and k in the above equation:
[tex]y = a[x- (-3)]^{2} + (3)[/tex]
[tex]y = a(x + 3)^{2} + 3[/tex]
Step II:
Determine a:
Based on the shape of the graph (which is an upside down U), the value of a will be negative:
Count one unit to the right from the vertex and see how far do you go down to touch the graph:
From the graph:
It seems you need to move 2 units down
∴a = [tex]-2[/tex]
Step III:
Substitute this value of a in the above equation:
[tex]y = -2(x + 3)^{2} + 3[/tex]
If you multiply a certain number by 5, and then subtract 3, the answer is 17. Find the number.
Answer:
The number is 4
Step-by-step explanation:
Let us make the unknown number xMake the question an equation{5x-3=17}Solve the equation(5x-3=17)Collect like terms (5x= 17+3)5x=20
Divide both sides by the coefficient of x5x/5=20/5
x=4
Step-by-step explanation:
so let the unknown be x
x+5-3=17
x+2=17
so then you carry +2 over to the left hand side which collecting of like terms
so we have
x=17-2
x=15
so therefore the unknown value x is 15
to check
we substitute 15 for x in the equation
let's go
so we have
15+5-3=17
now using this solve it .
I believe u can do it
or I just do it
so we hv the unknown to be x
x*5-3=17
5x-3=17
5x=17+3
5x=20
x=20/5
x=4
A sum of money is shared such that Mark gets twice as much as Sofia and Tina gets ½ of Sofia's share. Express these amounts in the form of a proportion. If Tina receives $1 200, how much do Mark and Sofia each receive?
Answer:
Step-by-step explanation:
Answer:
Mark gets $4800
Sofia gets $2400
Step-by-step explanation:
Let M, S and T represent the amounts that Mark, Sofia and Tina get respectively
We have the following
M = 2S
S = M/2
T = S/2 = M/2 ÷ 2 = M/4
Therefore the ratio of M : S; T can be expressed in terms of M as
M : M/2 : M/4
Multiplying throughout by 4 gives
4M : 2M : M
Removing the common M the proportion is
4 : 2 : 1
If T = 1200 then from T = S/2, s = 2T = 2 x 1200 = 2400
Since M = 2S, M = 2 x 2400 = 4800
So
Mark gets $4800
Sofia gets $2400
The ratio of the amounts obtained
4800: 2400: 1200
Dividing by 1200 gives us
4800/1200: 2400/1200: 1200/1200
= 4 : 2 : 1
This question: 1 point(s) possible
The access code for a car's security system consists of four digits. The first digit cannot be 4 and the last digit must be odd. How many different codes are available?
The number of different codes available is
Answer: 4500
Step-by-step explanation:
1st 0, 1, 2, 3 ,5 ,6 ,7 ,8 ,9
2nd 0, 1, 2 ,3 ,4 ,5 ,6 ,7 ,8 , 9
3rd 0, 1, 2 ,3 ,4 ,5 ,6 ,7 ,8 , 9
4th 1, 3, 5, 7, 9
9 x 10x 10 x 5= 4500
Please help!! Correct answer gets brainliest!!
Answer:
c
Step-by-step explanation:
Answer:
B
Step-by-step explanation:
First, the shape is wrong
2(8×3)+2(8×4)+2(3×4)=
2(24)+2(32)+2(12)=
48+64+24=136
Given: trap. SPQR with SP || QR ; MN is the median of the trap. m
Answer: Without additional information about the trap, it is not possible to determine the value of m or any other measurements of the shape. Could you please provide more information or context for the problem?
NEED HELP 35 POINTS!
Find x.
5 in.
8 in.
x
15 in.
Answer:
The answer is 24 in
Step-by-step explanation:
This solution is for "SIMILAR TRIANGLES";
Let us letter the shape starting from left to right A-B-C-D-E
Angle A is similar to Angle E, so is Angle B similar to Angle D, that is, "Alternate interior angles" while Angle ACB is similar to Angle DCE, that is, "Vertical Angles";
Line AB = 5 in is parallel to line DE = 15 in
So, K = DE / AB = 15 / 5 = 3
Line CD = K * CB = 3 * 8 = 24 in
Mark bike 4⁄10 mile in 1⁄5 of an hour find mark's average speed in mph
The average speed in mph is 2 mph
What is Average Speed?Average Speed is the total distance that something has traveled by the total amount of time it took it to travel that distance. It is also the total distance traveled by the moving object and the amount of total time the object spent moving.
Average speed = Distance traveled/Time taken
Where Distance traveled = 4/10 mile
Time taken = 1/5 of an hour
To get the average speed in mph,
Average speed = (4/10)/(1`/5)
Average speed = 4/10 * 5/1
Average speed = 20/10
Average speed = 2 mph
Therefore, the average speed is 2mph
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Cindy is evaluating the expression -5m - 31 for
-2p + r
m = 1, n.= -4, p = -3, and r = -2. Her work is
shown below.
=5m - 31 =
-5(1) - 3(-4)
-2p + r
=2(-3) + (-2)
= 끌=-끔=-4
a. What error did Cindy make in her computation?
b. What is the correct answer?
The correct answer for the expression is -5(1) - 3(-4) = 7 and -2p + r = 4.
What is substitution method?The algebraic approach to solving simultaneous linear equations is known as substitution technique. The value of one variable from one equation is substituted in the second equation in this procedure, as the name implies. By doing this, a pair of linear equations are combined into a single equation with a single variable, making it simpler to solve.
The given expression is: -5m - 3n for m = 1, n.= -4 and -2p + r for p = -3, and r = -2.
The correct steps are:
For, -5m - 3n substitute the value of m = 1 and n = -4:
-5(1) - 3(-4)
-5 + 12 = 7
For -2p + r:
-2(-3) + (-2)
6 - 2 = 4
Hence, the correct answer for the expression is -5(1) - 3(-4) = 7 and -2p + r = 4.
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Two spinners-One 5 and one 6. What is the probability that you get the same numbers as a previous spin?
Answer: Since the spinners have 5 and 6 numbers respectively, the total number of outcomes is 5 x 6 = 30.
If we get the same number as a previous spin, it means that the first spin is irrelevant, and we only care about the second spin. Therefore, the probability of getting the same number as a previous spin is the same as the probability of getting any specific number on the second spin, which is 1 out of 6.
Therefore, the probability of getting the same number as a previous spin is 1/6, or approximately 0.17 to two decimal places.
Step-by-step explanation:
Find the x and y intercept
Find the vertical and horizontal asymptotes
s(x)=6/ x^2 - 5x - 6
Answer:
To find the x and y intercepts, we set x and y to zero respectively:
x-intercept: setting y = 0 gives us 6/(x^2 - 5x - 6) = 0, which has no real solutions.
y-intercept: setting x = 0 gives us s(0) = 6/(-6) = -1.
To find the vertical asymptotes, we set the denominator equal to zero and solve for x:
x^2 - 5x - 6 = 0
(x - 6)(x + 1) = 0
This gives us two vertical asymptotes at x = 6 and x = -1.
To find the horizontal asymptote, we need to look at the behavior of the function as x approaches infinity and negative infinity. As x becomes very large in magnitude, the terms involving x^2 become much larger than the terms involving x or the constant term, and so we can ignore those terms. This gives us:
s(x) ≈ 6/x^2 as x → ±∞
Therefore, the horizontal asymptote is y = 0.
In summary:
x-intercept: none
y-intercept: (0, -1)
vertical asymptotes: x = 6 and x = -1
horizontal asymptote: y = 0
If you have anymore questions, feel free to comment and I will answer them 8-5 I am on.
Step-by-step explanation:
←
A group of winning ticket holders share equally in a $90,000,000 lottery. Before
the money is divided, three more winning ticket holders are declared. As a
result, each person's share is reduced by $1,000,000. How many people were
in the original group of winners?
We take the positive root:
n = (-3 + 27) / 2 = 12. Therefore, there were 12 people in the original group of winners.
How to solve the equation?Let's assume that there were n people in the original group of winners, and each person's share was x dollars. Then we know that:
n * x = $90,000,000
After three more winners are declared, the total number of winners becomes n + 3. Each person's share is then reduced by $1,000,000, so the new share per person is (x - $1,000,000). We can then write:
(n + 3) * (x - $1,000,000) = $90,000,000
Expanding the equation, we get:
nx - $1,000,000n + 3x - $3,000,000 = $90,000,000
Simplifying, we get:
nx + 3x = $1,000,000n + $93,000,000
Factoring out x and n, we get:
x(n + 3) = $1,000,000(n + 3) + $90,000,000
Dividing both sides by (n + 3), we get:
x = $1,000,000 + ($90,000,000 / (n + 3))
We can substitute this expression for x in the first equation:
n * ($1,000,000 + ($90,000,000 / (n + 3))) = $90,000,000
Expanding and simplifying, we get:
[tex]$n^2$[/tex]+ 3n - 270 = 0
Using the quadratic formula, we get:
n = [tex](-3\± \sqrt{(729)) / 2[/tex]
n = (-3 ± 27) / 2
Since n has to be positive, we take the positive root:
n = (-3 + 27) / 2 = 12
Therefore, there were 12 people in the original group of winners.
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For the truncated cuboid of height 3 m, top 5 m, base 8 m and side length of 1.5 m. Find the volume
Therefore, the volume of the truncated cuboid is approximately 68 + 4*√(30) cubic meters.
What is volume?Volume is a measure of the amount of space occupied by a three-dimensional object. It is the amount of three-dimensional space enclosed by the boundaries of an object. Volume is typically measured in cubic units, such as cubic meters (m³) or cubic centimeters (cm³).
Here,
The truncated cuboid is a solid figure that is obtained by cutting off the top of a rectangular prism (cuboid) with a plane that is parallel to the base. The formula for the volume of a truncated cuboid is:
V = h/3 * (A + √(A*B) + B)
where V is the volume, h is the height of the truncated portion, A is the area of the top face, and B is the area of the base face.
In this case, the height of the truncated portion is 3 m, the top face has an area of 5 m x 8 m = 40 m², and the base face has an area of 8 m x 1.5 m = 12 m². Therefore:
A + B = 40 + 12 = 52 m²
√(AB) = √(4012) = √(480) = 4*√(30)
Substituting these values into the formula, we get:
V = 3/3 * (52 + 4√(30) + 12)
V = 68 + 4√(30)
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What is the surface area?
9 in
9 in
9 in
square inches
Answer:
The surface area of an object is the total area of all its faces. For a cube with sides of length 9 inches, the surface area can be calculated as follows:
The cube has six faces, all of which are identical squares.
The area of one square face is 9 inches x 9 inches = 81 square inches.
Therefore, the total surface area of the cube is 6 x 81 square inches = 486 square inches.
So the surface area of a cube with sides of 9 inches is 486 square inches.
Simplify (3x3y2 − 5xy4 − 2xy) + (2x3y2 + 5xy4 + 3xy). 5x3y2 − 2xy4 + xy 5x3y2 − 2xy4 − 5xy 5x3y2 + xy 5x3y2 − xy
After Simplifying, we get: [tex]5x^3y^2 + xy - 2xy^4[/tex]
What is pοlynοmials ?Pοlynοmials are algebraic expressiοns made up οf cοefficients and variables. Occasiοnally, variables are referred tο as indeterminates.
Fοr pοlynοmial expressiοns, additiοn, subtractiοn, multiplicatiοn, and pοsitive integer expοnents are all pοssible; hοwever, divisiοn by variable is nοt. x²+x-12 is an illustratiοn οf a single-variable pοlynοmial. Three terms are invοlved in this example: x², x, and -12.
The Greek wοrds "pοlynοmial" and "nοminal," which tοgether mean "many terms," are the sοurce οf the English wοrd pοlynοmial. There is nο limit tο the number οf terms that a pοlynοmial can have.
When we add the twο pοlynοmials term by term, we get:
[tex](3x^3y^2 - 5xy^4 - 2xy) + (2x^3y^2 + 5xy^4 + 3xy) = 3x^3y^2 + 2x^3y^2 - 5xy^4 + 5xy^4 - 2xy + 3xy[/tex]
Simplifying, we get: [tex]5x^3y^2 + xy - 2xy^4[/tex]
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Answer:
5x^3y^2+xy (C)
Step by Step:
(3x^3y^2 − 5xy^4 − 2xy) + (2x^3y^2 + 5xy^4 + 3xy) =
3x^3y^2 − 5xy^4 − 2xy + 2x^3y^2 + 5xy^4 + 3xy =
(3 + 2)x^3y^2 + (-5 + 5)xy^4 + (-2 + 3)xy =
5x^3y^2 + xy
hope this helps (btw it's C)
Beverly has a bag of marbles that weighs 30 grams. She knows that each marble weighs 1.5 grams and the bag weighs 1.5 grams. Which equation could she use to determine how many marbles are in the bag? Select all that apply. (1.5)x + 1.5 = 30 30 – x = 2(1.5) (1.5)(30) = 1.5x 1.5 + x = 30 1.5x = 30 – 1.5
(1.5)x + 1.5 = 30 and 1.5x = 28.5 are the correct equations that Beverly could use to determine how many marbles are in the bag.
How to determine the equations of the marblesLet x be the number of marbles in the bag.
Each marble weighs 1.5 grams and the bag weighs 1.5 grams.
Therefore, the total weight of the marbles and the bag is 1.5x + 1.5 grams.
But we know that the total weight is 30 grams.
So, we can write the equation:
1.5x + 1.5 = 30
Simplifying this equation, we get:
1.5x = 28.5
Therefore, the number of marbles in the bag is x = 19.
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Find the probability that a 42 person shift will put together between 193.2 and 201.6 computers per hour.
The probability that a 42 person shift will put together between 193.2 and 201.6 computers per hour is given as follows:
0.0006 = 0.06%.
How to obtain probabilities using the normal distribution?The z-score of a measure X of a normally distributed variable that has mean represented by [tex]\mu[/tex] and standard deviation represented by [tex]\sigma[/tex] is obtained by the equation presented as follows:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score represents how many standard deviations the measure X is above or below the mean of the distribution of the data-set, depending if the obtained z-score is positive(above the mean) or negative(below the mean).The z-score table is used to obtain the p-value of the z-score, and it represents the percentile of the measure X in the distribution.By the Central Limit Theorem, the sampling distribution of sample means of size n has standard deviation given by the equation presented as follows: [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].The parameters for this problem are given as follows:
[tex]\mu = 4.2, \sigma = 0.8, n = 42, s = \frac{0.8}{\sqrt{42}} = 0.1234[/tex]
The probability that a 42 person shift will put together between 193.2 and 201.6 computers per hour is equivalent to the probability of a sample mean between 193.2/42 = 4.6 and 201.6/42 = 4.8.
The probability is the p-value of Z when X = 4.8 subtracted by the p-value of Z when X = 4.6, hence:
Z = (4.8 - 4.2)/0.1234
Z = 4.86
Z = 4.86 has a p-value of 1.
Z = (4.6 - 4.2)/0.1234
Z = 3.24
Z = 3.24 has a p-value of 0.9994.
Hence:
1 - 0.9994 = 0.0006 = 0.06%.
Missing InformationThe missing section is given by the image presented at the end of the answer.
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If f left parenthesis x right parenthesis equals x minus 2 and g left parenthesis x right parenthesis equals 2 x minus 6, then g left parenthesis 4 right parenthesis divided by f left parenthesis 3 right parenthesis = __________.
a.)
2
b.)
1
c.)
3
d.)
0
The value g left parenthesis 4 right parenthesis divided by f left parenthesis 3 right parenthesis is 2.
What is parenthesis?
Parenthesis, also known as round brackets, are a type of punctuation used in writing to enclose additional information within a sentence that is not essential to the meaning of the sentence, but can provide clarification, emphasis, or further explanation. They are usually shown as two curved lines facing each other, like this: ().
For example, consider the sentence: "The concert, which was held at the arena last night, was sold out (as expected)." The words "as expected" are enclosed in parentheses, indicating that they are not necessary to the main meaning of the sentence, but provide additional information that may be of interest to the reader.
Parentheses can also be used to enclose mathematical equations, citations, or references in writing.
In this problem, we first need to substitute the given values of x in the functions f(x) and g(x).
f(x) = x - 2
f(3) = 3 - 2 = 1
g(x) = 2x - 6
g(4) = 2(4) - 6 = 2
So, [tex] \frac{g(4)}{f(3)} = \frac{2}{1} = 2[/tex]
Therefore,the value of g(4)/f(3) is 2.
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