The smallest possible value for a term in the five-term arithmetic sequence is 1.The sum of a five-term arithmetic sequence is given as 100 and all terms are positive integers. Let's call the first term "a" and the common difference "d".
The five terms can be represented as a, a + d, a + 2d, a + 3d, and a + 4d. The sum of these five terms is 100, which can be represented as:
a + (a + d) + (a + 2d) + (a + 3d) + (a + 4d) = 100
Simplifying the expression, we get:
5a + 10d = 100
Dividing both sides by 5, we get:
a + 2d = 20
Since all terms are positive integers, it follows that "a" and "d" must also be positive integers. The smallest possible value for "a" is 1, and the smallest possible value for "d" is 1. Substituting these values into the expression for "a + 2d" yields:
1 + 2 * 1 = 3
Thus, the smallest possible value for a term in the five-term arithmetic sequence is 1.
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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
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
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.
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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Find the length of the third side. If necessary, write in simplest radical form.
Answer:
8
Step-by-step explanation:
If my calculations are correct the third side is 8
referring to exercise 9, what is the probability that a person diagnosed as having cancer actually has the disease?
The probability that a patient who has been diagnosed with cancer truly has the illness 0.406
It is known from prior experience that there is a 0.05 chance of choosing a cancer-positive adult over 40 in a certain area of the nation. What is the likelihood that an adult over the age of 40 will be given a cancer diagnosis if the probability of a doctor correctly diagnosing a person with cancer as having the disease is 0.78 and the probability of a doctor incorrectly diagnosing a person without cancer as having the disease is 0.06.
We wish to compute P(C | D) this time. Bayes rule is used in this process.
[tex]& P(C \mid D)=\frac{P(C n D)}{P(D)} \\\\& =\frac{P(C) P(D \mid C)}{P(C) P(D \mid C)+P\left(C^{\circ}\right) P\left(D \mid C^*\right)} \\\\& =\frac{0.05 * 0.78}{(0.05 * 0.78)+(0.95 * 0.06)} \\\\& =\frac{0.039}{0.039+0.057} \\\\& =\frac{0.039}{0.096} \\\\& =0.406[/tex]
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If you roll 2 dice, what is the exact binomial probability that the total number rolled will add up to 3 or less
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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can someone help me here please! thankyou (complete solution)
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]
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
Answer:
Ten thousands
Step-by-step explanation:
20 x 1000 = 20,000 therefore, ten thousands
When converting .000056 into scientific notation, the decimal point will move ___ spaces.
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.
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
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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what’s the value of x
Check the picture below.
[tex]\cfrac{24+x}{24}~~ = ~~\cfrac{36+12}{36}\implies \cfrac{24+x}{24}=\cfrac{48}{36}\implies \cfrac{24+x}{24}=\cfrac{4}{3} \\\\\\ 72+3x=96\implies 3x=24\implies x=\cfrac{24}{3}\implies x=8[/tex]
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
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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The volume of 10,000 drops of a liquid is 10 fluid ounces. What is the volume of 100 drops?
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
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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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 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?
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?
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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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.
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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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
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]
f(x)=x2 g(x)=– 3x+1 Write your answer as a polynomial or a rational function in simplest form.
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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Use the table to find the average rate of change over the interval [1,9]
Type your answer in the blank, with no spaces.
Answer:
1.6
Step-by-step explanation:
[tex]\displaystyle \frac{f(b)-f(a)}{b-a}\\\\=\frac{f(9)-f(1)}{9-1}\\ \\=\frac{15.8-3}{8}\\ \\=\frac{12.8}{8}\\ \\=1.6[/tex]
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?
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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What is the range of this relation?
(8,9)
(9,8)
(2,10)
(8,8)
(4,8)
(2,7)
Answer:
(9,7,10,8,7)
Step-by-step explanation:
range is the value of y.
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
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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Claire says that the AA Criterion should be called the AAA Criterion. Explain why Claire might say this. Do you agree? Explain.
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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A circle has a circumfrence of 75.4, what is the diameter?
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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Can you help me figure out the equation
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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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
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
=
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
14 units to the right of-2 of a number line
Answer: 11 (Or I'm wrong)
Step-by-step explanation: -2 -1 0 1 2 3 4 5 6 7 8 9 10 11
A ranger in a 120 m high tower on a plain first noted that the angle of depression to a fire was 4°. Twenty minutes later the angle of depression was 6°.
If a ranger in a 120 m high tower on a plain first noted that the angle of depression to a fire was 4°. The fire travelled 31,968 meters.
How to find the metre the fire travelled?Distance = d = v * t
Let v represent speed of the fire .
Where :
t = time elapsed in seconds = 20 * 60 = 1200 seconds
Using the tangent function:
d / v = tan(6°) - tan(4°)
Simplify this expression using the identity:
tan(A + B) = (tan(A) + tan(B)) / (1 - tan(A)tan(B))
Applying this to the above equation, we get:
d / v = (tan(6°) - tan(4°)) / (1 + tan(6°)tan(4°))
Using a calculator to evaluate the tangent values
d / v = 26.64 / v
d = 26.64 * v
Substituting the value of t, we get:
d = 26.64 * v
= 26.64 * 1200
= 31,968 meters (rounded to the nearest meter)
Therefore the fire travelled 31,968 meters.
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The complete question is:
A ranger in a 120 m high tower on a plain first noted that the angle of depression to a fire was 4°. Twenty minutes later the angle of depression was 6°. The fire travelled m (to nearest metre)
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
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: