Answers
Regarding the exponential function y = 3(2)^x, we have that:
We know that the graph has a y-intercept at (0,3), because the a-value is of 3.We know that the graph models exponential growth, because the b-value is of 2.The numeric value of the function at x = 3 is given as follows: 24.What is the exponential function?An exponential function is defined as follows:
y = ab^(x/n).
In which the parameters are defined as follows:
a is the initial value.b is the rate of change.n is the time needed for the rate of change.The function for this problem is given as follows:
y = 3(2)^x.
Hence the parameters are given as follows:
a = 3 -> y-intercept at (0,3).b = 2 > 1, hence exponential growth.At x = 3, the numeric value of the function is obtained as follows:
y = 3 x 2^3
y = 3 x 8
y = 24.
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Related Questions
If you roll 2 dice, what is the exact binomial probability that the total number rolled will add up to 3 or less
Answers
The exact binomial probability that the total number rolled will add up to 3 or less is 1/12.
What is the exact binomial probability?
The exact binomial probability that the total number rolled will add up to 3 or less is calculated as follows;
The total number that can be rolled with 2 dice is 2 to 12, with 7 being the most likely outcome (the sum of two dice has a maximum of 7).
The probability that the total number is 3 or less is the sum of the probabilities of rolling a 2 and a 1;
The probability P = (1/36) + (2/36)
P = 3/36
P = 1/12
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A group of 4 friends is planning a fun day trip. The
equations in the table represent the number of people n
who can participate in each activity for $29.
Activity
Raft Trip
Amusement Park
Balloon Ride
Cost ($)
6n + 5 = 29
14n = 29
30n 40 29
=
-
Which activity should the friends choose if they want
to spend exactly $29?
Answers
Answer: The friends should choose the Raft Trip if they want to spend exactly $29.
The equation for the Raft Trip is 6n + 5 = 29. Solving for n, we get n = 4. This means that 4 people can participate in the Raft Trip for $29.
The other two activities, the Amusement Park and the Balloon Ride, have equations 14n = 29 and 30n + 40 = 29, respectively. Solving these equations, we find that neither of them allow exactly 4 people to participate for $29.
Step-by-step explanation:
The activity the friends should choose if they want to spend exactly $29 is Raft Trip
Which activity should the friends choose if they want to spend exactly $29?Number of people in the group= 4
Raft Trip:
6n + 5 = 29
6(4) + 5 = 29
24 + 5 = 29
Amusement Park:
14n = 29
14(4) = 29
56 ≠ 29
Balloon Ride:
30n - 40 = 29
30(4) - 40 = 29
120 - 40 = 29
80 ≠ 29
Hence, the friends should choose raft trip it they want to spend exactly $29
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Identify the graph of the system of linear inequalities.
$y\le x-3$y≤x−3
y is greater than or equal to x plus 1$y\ge x+1$y≥x+1
Responses
A system of linear inequalities graphed on a coordinate plane. A solid boundary line is y equals x minus 3. A solid boundary line is y equals x plus 1. The graph is shaded above y equals x plus 1.
Image with alt text: A system of linear inequalities graphed on a coordinate plane. A solid boundary line is y equals x minus 3. A solid boundary line is y equals x plus 1. The graph is shaded above y equals x plus 1.
A system of linear inequalities graphed on a coordinate plane. A solid boundary line is y equals x minus 3. A solid boundary line is y equals x plus 1. The graph is shaded between the boundary lines.
Image with alt text: A system of linear inequalities graphed on a coordinate plane. A solid boundary line is y equals x minus 3. A solid boundary line is y equals x plus 1. The graph is shaded between the boundary lines.
A system of linear inequalities graphed on a coordinate plane. A solid boundary line is y equals x minus 3. A solid boundary line is y equals x plus 1. The graph is shaded below y equals x minus 3.
Image with alt text: A system of linear inequalities graphed on a coordinate plane. A solid boundary line is y equals x minus 3. A solid boundary line is y equals x plus 1. The graph is shaded below y equals x minus 3.
A system of linear inequalities graphed on a coordinate plane. A solid boundary line is y equals x minus 3. A solid boundary line is y equals x plus 1. The graph has no shading.
Image with alt text: A system of linear inequalities graphed on a coordinate plane. A solid boundary line is y equals x minus 3. A solid boundary line is y equals x plus 1. The graph has no shading.
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Answers
The solution for the inequalities, y≥x+1 is (0, 1) and (-1, 0).
and, solution for the inequalities, y≤x−3 is (0, -3) and (3, 0).
What is Inequality?Mathematical expressions with inequalities are those in which the two sides are not equal. Contrary to equations, we compare two values in inequality. Less than (or less than or equal to), greater than (or greater than or equal to), or not equal to signs are used in place of the equal sign.
Given:
y≤x−3.........(1)
y≥x+1.............(2)
If we solve the inequality using the graphical method we can see that the inequalities gives the parallel line.
Also, the solution for the inequalities, y≥x+1 is (0, 1) and (-1, 0).
and, the solution for the inequalities, y≤x−3 is (0, -3) and (3, 0).
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A rectangular room is 6 meters longer than it is wide, and its perimeter is 36
meters. Find the dimension of the room.
TH
L
Answers
Step-by-step explanation:
length = width + 6
the perimeter of a rectangle is
2×length + 2×width
by using the first equating as identity in the second we get
36 = 2×(width + 6) + 2×width =
= 2×width + 12 + 2×width = 4×width + 12
24 = 4×width
width = 6 m
length = width + 6 = 6 + 6 = 12 m
he dimensions of the rectangular room are 6 meters by 12 meters of the rectangular room is 6 meters longer than it is wide, and its perimeter is 36 meters by solving equations and geometric measurements.
Given that the room is 6 meters longer than it is wide, we can represent the width as W. Therefore, the length of the room would be W + 6.
The perimeter of a rectangle is calculated by adding all four sides, which in this case is given as 36 meters. We can express this as an equation:
Perimeter = 2 * (Length + Width)
Substituting the values, we get:
36 = 2 * (W + (W + 6))
Simplifying the equation further, we have:
36 = 2 * (2W + 6)
Dividing both sides of the equation by 2, we get:
18 = 2W + 6
Subtracting 6 from both sides, we obtain:
12 = 2W
Dividing both sides by 2, we find:
W = 6
Now that we have the width, we can calculate the length:
Length = Width + 6 = 6 + 6 = 12
Therefore, the dimensions of the rectangular room are 6 meters by 12 meters of the rectangular room is 6 meters longer than it is wide, and its perimeter is 36 meters by solving equations and geometric measurements.
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Can you help me figure out the equation
Answers
The sine function for a specified range of angles is shown graphically in the sine graph. A trigonometric graph's horizontal axis is the angle, which is typically denoted by the symbol, and the y-axis is the sine function of that angle.
How is a sine graph drawn?To graph the sine function, we place the sine of each angle on the vertical y-axis and indicate the angles along the horizontal x axis.
The Sin Formula: What Is It?The ratio of the perpendicular of a right-angled triangle to the hypotenuse is known as the sine of the angle. The following is the sin formula: hypotenuse/perpendicular = sin. sin(n+2) = sin for each n.
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14 units to the right of-2 of a number line
Answers
Answer: 11 (Or I'm wrong)
Step-by-step explanation: -2 -1 0 1 2 3 4 5 6 7 8 9 10 11
what is the solution to 12(x+6)=17
Answers
Answer:
x = -55/12
Step-by-step explanation:
12(x+6) = 17
12x + 72 = 17
12x = -55
x = -55/12
A family wants to rent a car to go on vacation. Company A charges $35.50 and 9¢ per mile. Company B charges $65.50 and 13¢ per mile. How much more does Company B charge for x miles than Company A? PLEASE HELPPPP
Answers
3004¢ more does Company B charge for x miles than Company A.
What is Subtraction?Subtraction is the process of taking away a number from another. It is a primary arithmetic operation that is denoted by a subtraction symbol (-) and is the method of calculating the difference between two numbers.
here, we have,
Company A charges $35.50 and 9¢ per mile.
Company B charges $65.50 and 13¢ per mile.
Also, we could convert dollars to cents by multiply it by 100
Since $1 =100 cents.
so, we get,
Company A charges $35.50 and 9¢ per mile. = 3559
Company B charges $65.50 and 13¢ per mile = 6563
difference = 6563 - 3559
= 3004
Hence, 3004¢ more does Company B charge for x miles than Company A.
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predict the number of people in a household with 2.5 pounds of waste pounds of waste 0.27,1.41,2.19,2.83,2.19,1.81,0.85,3.05
Answers
The number of people in a household with 2.5 pounds of waste are = 11
and we calculate this on the basis of question below
Predict the number of people in a household with 2.5 pounds of waste pounds of waste 0.27,1.41,2.19,2.83,2.19,1.81,0.85,3.05. In Home 2 3 3 6 4 2 1 5
pound 0.27 ,1.41, 2.19 ,2.83 ,2.19 ,1.81 ,0.85, 3.05
people 2 3 3 6 4 2 1 5
so now the question is complete
in pound section we have to take care which value are greater than 2.5
so 2.83 and 3.05 is greater than 2.5 so here number of people who's home have greater than 2.5 pound of waste are 6+6=11
and rest people who's home has less than 2.5 pound waste are 2+3+3+4+2+1=15
so final ans is 11.
so this question was in complete and this ans is valid for this Question only.
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4. The expression for sum of numbers a and b subtracted from their product is:
(a) a+b-ab
(b) ab-a+b
(c) ab - (a + b)
(d) ab+a-b
Answers
The product of a and b is ab.
The answer is b. ab-a+b
ab is the product, and a+b is the sum, which is SUBTRACTED FROM the product, ab
When converting .000056 into scientific notation, the decimal point will move ___ spaces.
Answers
When converting 0.000056 into scientific notation, the decimal point will move 5 spaces to the right.
The resulting number in scientific notation would be 5.6 x 10^-5.
What is the slope of the line below?
Answers
A winter sports pass at Wood Middle School costs $18. A student without a pass must pay
$1.90 for each event. How many sports events would a student have to attend to make the pass a
better deal?
Answers
18/1.90= 9.473684210526316
Then because you want to see how many events so that the pass is a better deal you need to have more than 9.47… which the closes whole number is 10 since you can’t get entry to a part of an event.
g- given that a part produced in the plant is defective, what is the probability that it went through an electronic inspection?
Answers
The probability that a defective part went through an electronic inspection is 0.2058 or approximately 20.58%.
In order to find the probability that a defective part went through an electronic inspection, Bayes' Theorem will be used. The theorem states that the conditional probability of event A given event B can be calculated as:
P(A | B) = P(B | A) × P(A) / P(B)
where P(A) is the prior probability of event A, P(B | A) is the conditional probability of event B given event A, and P(B) is the overall probability of event B.
In this case, event A is the part that went through an electronic inspection, and event B is the part that is defective. The prior probability of a part going through an electronic inspection is:
P(A) = 0.15, and the overall probability of a part being defective is P(B) = 0.15 × 0.97 + 0.85 × (1 - 0.15) = 0.14695.
The conditional probability of a part being defective given it went through an electronic inspection is P(B | A) = 0.03. The probability of a part that went through an electronic inspection given it's defective is:
P(A | B) = P(B | A) × P(A) / P(B) = 0.03 × 0.15 / 0.14695 = 0.2058
So, the probability that a defective part went through an electronic inspection is 0.2058 or approximately 20.58%.
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Question
At a plant, 30% of all the produced parts are subject to a special electronic inspection. It is known that any produced part which was inspected electronically has no defects with probability 0.15. For a part that was not inspected electronically this probability is only 0.85. What is the probability that it went through an electronic inspection?
Bob has 60 coins consisting of quarters and dimes. The coins combined value is
$13.35. How many quarters and how many dimes does he have?
O q+d= 13.35
0.25g +0.10d = 60
Oq-d=13.35
O
0.25g +0.10d = 60
q+d=60
0.25g +0.10d = 13.35
.25g + d = 60
q+0.10d 13.35
=
Answers
Answer:
Third option
q + d = 60
0.25q + 0.10d = 13.35
Step-by-step explanation:
Given q quarters and d dimes
Total number of coins = q + d and this must equal 60
Therefore q + d = 60
Since each quarter is 25 cents(or $0.25) and each dime is 10 cents($0.10)
Total value = 0.25q + 0.10d = 13.35
Correct set of equations is the third option
A circle has a circumfrence of 75.4, what is the diameter?
Answers
The diameter of the circle is 24 units.
What is a circle:In geometry, the circle is a curved and closed polygon whose boundary line is at equidistance from a point called the center.
A diameter is a line drawn through the circle's center and joining two points on its circumference. The diameter of a circle is twice its radius
The circumference of a circle is known as the circle's perimeter and is the distance a circle travels around its boundary line.
The formula for the circumference of a circle is given by
Circumference of circle = 2πrHere we have
The circumference of a circle is 75.4 units
Let 'r' be the radius of the circle
As we know Circumference of a circle = 2πr
=> 2πr = 75.4
=> 2r(22/7) = 75.4
=> 2r = (75.4 × 7)/22
=> 2r = [527.8]/22
=> 2r = 23.99
=> 2r = 24 (approx)
Therefore,
The diameter of the circle is 24 units.
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What is the range of this relation?
(8,9)
(9,8)
(2,10)
(8,8)
(4,8)
(2,7)
Answers
Answer:
(9,7,10,8,7)
Step-by-step explanation:
range is the value of y.
The volume of 10,000 drops of a liquid is 10 fluid ounces. What is the volume of 100 drops?
Answers
Answer:
Step-by-step explanation:
if 10,000/10, find 100drops by moving decimal place
100.00/0.10
so volume is 0.1 flOz
Jack opens a savings account with $470. The account earns 4.4% annual interest compounded quarterly. Part A Enter a function to represent the balance A in the account after t years.
Answers
The function that represents the balance after t years is ,
FV = $470( 1.011)^4t
What is the function that represents the balance after t years?The formula for calculating future value:
FV = P (1 + r)^nm
Where:
FV = Future value
P = Present value
R = interest rate
m = number of compounding
N = number of years
here, we have,
given that,
P = Present value= $470.
R = interest rate = 4.4%/4 =
m = number of compounding =4
N = number of years = t
FV = $470( 1.011)^4t
Hence, The solution is, a function to represent the balance A in the account after t years is, FV = $470( 1.011)^4t
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Mr McClean wants to hire a taxi. He ring three different taxi companies and asks them for their prices. A1 Taxis: A 5 mile journey costs £15 Crazy Cabs: A4 mile journey costs £13 Value Cars: A 10mile journey costs £28 Order the taxi companies from best to least value for money
Answers
Answer:
Value Cars
Step-by-step explanation:
A1 Taxis: A 5-mile journey costs £15
15 divided by 5 = £3 per mile
Crazy Cabs: A 4-mile journey costs £13
13 divided by 4 = £3.25 per mile
Value Cars: A 10-mile journey costs £28
28 divided by 10 = £2.80 per mile
Skyla is trying to order the fractions below. Her first step is to rewrite each fraction with a common denominator. What is the lowest common denominator she could use? 17 20 56 8 1
Answers
Answer:
Below
Step-by-step explanation:
The lowest common denominator is 60
then the fractions become ( L to right) 51/60 50/60 32/60
A pop quiz contains five questions: two
multiple choice questions with four options
each and three true-false questions. If Brad
randomly guesses, what is the probability
that he gets all five answers correct?
Answers
The probability that Brad gets all five answers correct is 1/128.
What is the probability that he gets all five answers correct?From the question, we have the following parameters that can be used in our computation:
true of false = 3
Multichoice = 2
For each multiple choice question, Brad has a 1/4 chance of getting the correct answer by guessing.For each true-false question, Brad has a 1/2 chance of getting the correct answer by guessing.So, the probability that Brad gets all five answers correct is (1/4)^2 * (1/2)^3 = 1/128.
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f(x)=x2 g(x)=– 3x+1 Write your answer as a polynomial or a rational function in simplest form.
Answers
The simplest form of the polynomial is (x²)-3x+1.
A polynomial is a mathematical expression consisting of constants, variables, and exponents. It can be written in the form of a polynomial equation, which is a mathematical equation with one or more variables.
In this example, we have two functions, f(x) and g(x). The polynomial of these two functions can be written in simplest form by combining the functions together.
The polynomial of f(x) and g(x) is written in simplest form as (x²)-3x+1.
This means that for any value of x, the polynomial will evaluate to the value given by the equation.
If x=2, then the polynomial will evaluate to (2(2)²)-3(2)+1=3.
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can someone help me here please! thankyou (complete solution)
Answers
Answer:
1. See below.
[tex]\textsf{2.} \quad \log_x256=\dfrac{1}{2}[/tex]
[tex]\textsf{3.} \quad x^6=1000000[/tex]
[tex]\textsf{4.} \quad \log_2\left(\dfrac{1}{64}\right)=x[/tex]
Step-by-step explanation:
Question 1
Please note that this question is incorrect.
I assume the question is missing an "x" term, since log₉27 ≠ -3.
Let's assume 27 should be "x":
[tex]\implies \log_9x=-3[/tex]
[tex]\textsf{Apply the log law}: \quad \log_ab=c \iff b=a^c[/tex]
[tex]\implies x=9^{-3}[/tex]
If, however, the 9 is supposed to be "x":
[tex]\implies \log_x27=-3[/tex]
[tex]\implies x^{-3}=27[/tex]
Question 2Given exponential equation:
[tex]\sqrt{x}=256[/tex]
[tex]\textsf{Apply exponent rule} \quad \sqrt{a}=a^{\frac{1}{2}}:[/tex]
[tex]\implies x^{\frac{1}{2}}=256[/tex]
[tex]\textsf{Apply the log law}: \quad \log_ab=c \iff a^c=b[/tex]
[tex]\implies \log_x256=\dfrac{1}{2}[/tex]
Question 3Given logarithmic equation:
[tex]\log_x1000000=6[/tex]
[tex]\textsf{Apply the log law}: \quad \log_ab=c \iff a^c=b[/tex]
[tex]\implies x^6=1000000[/tex]
Question 4Given exponential equation:
[tex]2^x=\dfrac{1}{64}[/tex]
[tex]\textsf{Apply the log law}: \quad \log_ab=c \iff a^c=b[/tex]
[tex]\implies \log_2\left(\dfrac{1}{64}\right)=x[/tex]
Find the length of the third side. If necessary, write in simplest radical form.
Answers
Answer:
8
Step-by-step explanation:
If my calculations are correct the third side is 8
In the number 455,025, which place value is 1000 times the value of the 2?
A. Hundreds
B. Thousands
C. Ten thousands
D. Hundred thousands
Answers
Answer:
Ten thousands
Step-by-step explanation:
20 x 1000 = 20,000 therefore, ten thousands
there are 4 teachers for every 100 students at Brians school. if there are 950 students, write and solve a proportion showing how many teachers are at the school
Answers
Step-by-step explanation:
We can set up the proportion with students on the bottom and teachers on the to
[tex] \frac{4}{100} = \frac{x}{950} [/tex]
Now we cross multiply
[tex]100x = (950)(4)[/tex]
[tex]100x = 3800[/tex]
Lastly, we will divide both sides by 100
[tex]x = 38[/tex]
Claire says that the AA Criterion should be called the AAA Criterion. Explain why Claire might say this. Do you agree? Explain.
Answers
No, AA Criterion should not be called the AAA Criterion, because we need only two angles to be equal to prove the similarity.
What is AA criterion?According to the AA triangle similarity criterion, two triangles are considered similar if their three angles are identical to one another. Equi-angular triangles are comparable in a nutshell.
Since just two pairs of angles must be equal in order for the third pair to be automatically equal thanks to the angle sum property of triangles, the proper term for this criterion would then be the AAA(Angle-Angle-Angle) criterion. However, we refer to it as the AA criterion instead.
Hence, no, because we need only two angles to be equal to prove the similarity.
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Which statement is true about the number 403, 043?
A. The 3 on the left is 100 times greater than the 3 on the right.
B. The 3 on the left is 1,000 times greater than the 3 on the right.
C. The O on the left is 100 times greater than the 0 on the right.
D. The 0 on the left is 1,000 times greater than the 3 on the right.
Answers
Option A If the adage regarding the number 403, 043 is accurate, the three on the left is 100 times bigger than the three on the right.
The enlarged number 100 is what?As a result, 100 is enlarged to 100+0+0.The numerals that are used to represent numbers when they have digits or symbols can be categorized into two groups. These groups could be referred to as the arithmetic numerals (0, 1, 2, 3, 4, 5, 6, 7, 8, 9) and the geometric numerals (1, 10, 100, 1000, 10000,...), respectively.Numbers are arithmetic values that are used to represent quantities. So a number is a mathematical idea used for counting, measuring, and labeling. Mathematics is based on numbers, so to speak.Option A If the adage regarding the number 403, 043 is accurate, the three on the left is 100 times bigger than the three on the right.To learn more about number refer to:
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For summer Nicole charges a flat fee of $5, plus $20 per hour.
1. Write an equation for babysitting.
2. What is the slope
3.what does the slope represent
4.what is the y-intercept
5.what does the y-intercept represent
Answers
Answer:
The equation for babysitting can be written as y = 20x + 5, where y is the total cost and x is the number of hours.
The slope of the equation is 20, which represents the rate of change in the total cost (y) with respect to the number of hours (x).
The slope represents the rate at which the total cost changes for each unit change in the number of hours. In this case, for each hour of babysitting, the total cost increases by $20.
The y-intercept of the equation is 5, which represents the cost when x = 0, i.e. when there is no babysitting time.
The y-intercept represents the starting value of the total cost, in this case, the amount charged for babysitting even when there is no babysitting time.
Step-by-step explanation: