The original two-digit number is 11 * 10 + 3 = 113.
How to find the original two digit number?Let us correspond to the original two-digit number as "10x + y," with x and y showing the tens and units digits, respectively.
We know from the first piece of information:
x + y = 14
According to the second piece of information:
2(10x + y) + 10y + x = 222
When we simplify this equation, we get:
20x + 22y = 202
We get 10x + 11y = 101 by dividing both sides by 2.
We now have two equations with two variables that can be solved by substitution or elimination. For example, in the first equation, we can solve for x and then substitute into the second equation:
x = 14 - y\s10(14 - y) + 11y = 101
When we simplify this equation, we get: y = 3
Putting y = 3 back into the first equation yields: x = 11.
The original two-digit number is 11 * 10 + 3 = 113.
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In 2004, $6,000 was invested in a mutual fund that earned 9% interest per year.
a) Tell whether the model represents an exponential growth or decay and create a function that models it
b) How much was in the account in 2012?
a) The function would be A(t) = 6000(1 + 0.09)ᵗ
b) The amount in the account in 2012 was approximately $11,737.51.
What is the function model?
In mathematics, a function model is a mathematical equation or expression that represents a relationship between two or more variables. It is a way of describing the behavior or pattern of a particular phenomenon or system.
a) The model represents exponential growth since the amount in the account is increasing with time. The function that models the growth of the investment over time is given by:
A(t) = 6000(1 + 0.09)ᵗ
where A(t) is the amount in the account after t years.
b) To find the amount in the account in 2012, we need to find the value of A(2012 - 2004) = A(8). Substituting t = 8 into the function above, we get:
A(8) = 6000(1 + 0.09)⁸
= 6000(1.09)⁸
≈ $11,737.51
Therefore, the amount in the account in 2012 was approximately $11,737.51.
Hence,
a) The function would be A(t) = 6000(1 + 0.09)ᵗ
b) The amount in the account in 2012 was approximately $11,737.51.
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Help with geometry pls?
The following are the area of the sectors:
6a). π square inches
6b). 24π square centimeters
7a). 9 square centimeters
7b). 16.7 square inches
How to evaluate for the area of the sectors.The area of a sector is calculated by multiplying the fraction of the angle for the sector divided by 360° and πr², where r is the radius.
For question 6:
a). (40/360) × π × 3 in × 3 in = π in²
b). (135/360) × π × 8 cm × 8 cm = 24π cm²
For question 7:
a). (90/360) × π × 6 cm × 6 cm = 9 cm²
b). (60/360) × π × 10 in × 10 in = 16.7π in²
Therefore, the following are the area of the sectors:
6a). π square inches
6b). 24π square centimeters
7a). 9 square centimeters
7b). 16.7 square inches
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There are 3 female teachers and 31 male teachers at Eddie's high school. What is the ratio of the number of female teachers to the number of male teachers?
Answer:
3:31
Step-by-step explanation:
a sample of 250 rdns was randomly selected from a list of all rdns in the state of california for a california policy study. which sampling method was used?
If a sample of 250 RDNS was randomly selected from a list of all RDNS in the state of California for a California policy study, then the sampling method was simple random sample
Here a sample of 250 RDNS was randomly selected from a list of all RDNS.
Sampling is defined as the selecting the individual members or the group that you will actually collect data from in your research. There are five types of sampling method. They are Random, Systematic, Convenience, Cluster, and Stratified.
In the simple random sampling the researchers select the random samples from the population. Here a sample of 250 RDNS was randomly selected from a list of all RDNS.
Therefore, the sampling method that used is simple random sample
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HELP ME PLEASEEEE
Round each fraction to help you estimate the solution for the following equation
nine-tenths minus four-tenths equals.
Options
1. 0
2. 1/2
3. 1
4. 1 1/2
which equation can be used to represent "three minus the difference of a number and one equals one-half of the difference of three times the same numb
The equation can be used to represent "three minus the difference of a number and one equals one-half of the difference of three times the same number" is 3 – (n – 1) = 1/2(3n – 4)
Let the number be n.
Gven: "three minus the difference of a number and one equals one-half of the difference of three times the same number and four"
So,
The expression "three minus the difference of a number and one" represent the equation is;
3 – (n – 1)
Also,
The expression "one-half of the difference of three times the same number and four" represent the equation is;
1/2(3n – 4)
Hence,
Complete expression represents the equation is
3 – (n – 1) = 1/2(3n – 4)
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(1 – n) – 3 = (4 – 3n)
3 – (1 – n) = (4 – 3n)
(n – 1) – 3 = (3n – 4)
3 – (n – 1) = (3n – 4)
Jayden has some dimes and some quarters. He has at most 25 coins worth at least $4.60 combined. If Jayden has 7 dimes, determine all possible values for the number of quarters that he could have. Your answer should be a comma separated list of values.
The possible values of the number of quarters are at least 14 and more.
What is inequality?It shows a relationship between two numbers or two expressions.
There are commonly used four inequalities:
Less than = <
Greater than = >
Less than and equal = ≤
Greater than and equal = ≥
We have,
1 dime = $0.10
1 quarter = $0.25
Number of dimes = x
Number of quarters = y
Now,
He has at most 25 coins worth at least $4.60 combined.
This means
we can write two inequalities.
x + y ≤ 25 ____(1)
0.10x + 0.25y ≥ 4.60 _____(2)
Now,
From (1) and (2).
x ≤ 25 - y
Substituting in (2).
0.10x + 0.25y = 4.60
0.10 (25 - y) + 0.25y ≥ 4.60
2.5 - 0.10y + 0.25y ≥ 4.60
2.5 + 0.15y ≥ 4.60
0.15y ≥ 4.60 - 2.5
0.15y ≥ 2.1
y ≥ 2.1/0.15
y ≥ 14
This means,
y is at least 14.
Thus,
The possible values of the number of quarters are at least 14 and more.
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Algebra tiles??
Please help!!
Answer:
(-x+2)(2x+1) — first option
Step-by-step explanation:
The rectangles represent an x, red means negative and yellow is positive.
The squares represent a unit (the number 1).
The diagram attached below demonstrates how this works.
Basically the top row of this tile equation is (-x + 2)And the column is (2x+1).
Expanding this makes -2x²+3x+2
sufficient and necessary? 1 point possible (graded) suppose that we have some loss function that may or may not have multiple critical points. we have found a critical point such that f''(w)>0 , so that we know that it is a minimum. what can we say about it being a global minimum?
In order to determine whether a critical point of a loss function is a global minimum, it is necessary to consider the second derivative of the function.
If the second derivative is positive at the critical point, then we can say with certainty that the critical point is a local minimum. However, this does not necessarily mean that it is a function function. This is because there may be other local minima at points which the second derivative is negative, and in this case, the critical point must be compared to these points to determine if it is indeed the global minimum.
In order to assess whether a local minimum is a global minimum, we must first identify any other local minima. This can be done by locating the points at which the first derivative of the function is equal to zero and then evaluating the second derivative of the function at these points. If the second derivative is negative at any of the points, then we have identified a local minimum. Then, we can compare the value of the loss function at the points function as local minima to the value of the loss function at the critical point. If the value of the loss function at the critical point is lower than the value of the loss function at the other local minima, then the critical point is the global minimum. If the values are equal, then the critical point is a global minimum if and only if it is the only local minimum.Overall, identifying whether a critical point of a loss function is a global minimum requires both sufficiency and necessity. It is necessary to evaluate the second derivative of the function at the critical point in order to determine whether it is a local minimum, and it is also necessary to identify any other local minima and compare the value of the loss function at the critical point to the value of the function at the other local minima in order to determine whether the critical point is the global minimum.
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please help meeeeeeeeeee
The number of pet-owners that are in the union of cat owners and other pet owners is given as follows:
20 pet-owners.
How to obtain the union of two sets?The set representing the union of two sets is composed by all the elements that belong to at least one of the sets.
Hence the union of pet-owners that are in the union of cat owners and other owners is composed as follows:
1 + 1 + 3 + 6 = 11 cat owners.7 + 2 = 9 other owners who are not cat owners.Hence the total number is given as follows:
11 + 9 = 20.
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the coordinates of the endpoints of no are n(5,16) and o(19,9). point p is on no and divides it such that np:op is 4:3. what are the coordinates of p?
The coordinates of point P are (12, 12.5).
to put different elements or individuals in a coordinated effort.
To find the coordinates of point P, we can use the fact that P divides NO into two segments in the ratio of 4:3.
First, we can find the distance between points N and O using the distance formula:
d(NO) = sqrt((19-5)^2 + (9-16)^2) = sqrt(196 + 49) = sqrt(245)
Next, we can use the ratio of 4:3 to determine the distance between P and O:
d(OP) = (3/7) * d(NO) = (3/7) * sqrt(245)
Similarly, we can find the distance between P and N:
d(NP) = (4/7) * d(NO) = (4/7) * sqrt(245)
Now, we can use the midpoint formula to find the coordinates of P:
x-coordinate of P = (x-coordinate of N + x-coordinate of O) / 2 = (5 + 19) / 2 = 12
y-coordinate of P = (y-coordinate of N + y-coordinate of O) / 2 = (16 + 9) / 2 = 12.5
So the coordinates of point P are (12, 12.5).
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the density of zinc is 7.13 g/cm3. calculate the probability that a density measurement of the post-1982 pennies made using the caliper method is within 5% of the density of zinc. use the caliper data for the entire lab session to perform your calculation, and assume that the data fits a normal distribution.
As per the density the probability that a density measurement of the post-1982 pennies is 0.3565 g/cm3.
Density is an important physical property that can help identify materials. In this case, we are interested in the density of zinc and how it relates to the post-1982 pennies.
To calculate the probability of a density measurement within 5% of the density of zinc, we need to first determine the range of densities that fall within 5% of the zinc density.
The 5% range of the zinc density is calculated by multiplying the zinc density (7.13 g/cm3) by 5% (0.05), which gives us 0.3565 g/cm3.
The upper and lower limits of this range are then calculated by adding and subtracting this value from the zinc density, respectively.
The upper limit is 7.4865 g/cm3 (7.13 + 0.3565),
while the lower limit is 6.7735 g/cm3 (7.13 - 0.3565).
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how to find the average value of a function on an interval?
To find the average value of a function on an interval dividing the definite integral [tex]\int\limits^a_b f{(x)} \, dx[/tex] by the length of the interval.
The definition of average value of a function is -"The average value of a function is the height of the rectangle that has an area that is equivalent to the area under the curve of the function."
When there's a need to find the average value of a function, rather than adding up numbers we can just integrate, and instead of dividing by the number of values we can just divide by the length of the interval.
Adding values → Integration
Number of values → Length of the interval
When we use the length of the interval it makes more sense as we all know intervals have an infinite number of values, so it is more appropriate to use the length of the interval instead.
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Factor 80+60. Write your answer in the form a(b+c) where a is the GCF of 80 and 60.
Answer:
20(4+3)
Step-by-step explanation:
GCF of 80 and 60 = 20
20*4=80
20*3=60
20(4+3)
hope this helps! :)
Solve the inequality for x and identify the graph of its solution.
2|x+3|< 4
Choose the answer that gives both the correct solution and the correct graph.
only 0.02% of credit card holders of a company report the loss or theft of their credit cards each month. the company has 15,000 credit cards in the city of memphis. what is the probability that during the next month in the city of memphis a. no one reports the loss or theft of his or her credit cards? b. every credit card is lost or stolen? c. six people report the loss or theft of their cards? d. at least nine people report the loss or theft of their cards?
a) The probability that no one reports the loss or theft of their credit cards is 0.0498.
b) The probability that every credit card is lost or stolen is practically zero.
c) The probability that exactly six people report the loss or theft of their cards is 0.1042
d) The probability that at least nine people report the loss or theft of their cards is 0.2142
a. To calculate the probability that no one reports the loss or theft of their credit cards, we can use the Poisson distribution with an average of λ = 0.02% * 15,000 = 3.
The probability that no one reports the loss or theft of their credit cards is:
P(X = 0) = e^(-λ) * (λ^0 / 0!) = e^(-3) * (1 / 1) = 0.0498 or approximately 5%.
b. The probability that every credit card is lost or stolen is:
P(X = 15000) = e^(-λ) * (λ^15000 / 15000!)
Since λ is very small, the probability of all 15000 credit cards being lost or stolen in a month is practically zero.
c. To calculate the probability that six people report the loss or theft of their cards, we again use the Poisson distribution with an average of λ = 3.
The probability that exactly six people report the loss or theft of their cards is:
P(X = 6) = e^(-λ) * (λ^6 / 6!) = e^(-3) * (3^6 / 720) = 0.1042 or approximately 10.4%.
d. To calculate the probability that at least nine people report the loss or theft of their cards, we need to sum the probabilities for X = 9, 10, 11, ..., 15, since there are only 15,000 credit cards in total.
The probability that at least nine people report the loss or theft of their cards is:
P(X >= 9) = Σ(i=9 to 15) P(X = i) = Σ(i=9 to 15) e^(-λ) * (λ^i / i!)
This is a tedious calculation to do by hand, but we can use a calculator or software to find that P(X >= 9) is approximately 0.2142 or 21.42%.
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Julissa wants to join her local gym. A gym membership is $27 a month with a one–time initiation fee of $117. Which equation represents the amount of money, y, she will spend on her gym membership for x months?
y=117x+27
y=27x+117
x=117y+27
x=27y+117
The equation to represent the amount of money, y, Julissa will spend on her gym membership for x months is y=117x+27, which means that for each month Julissa has a membership, she will pay $117 for the initiation fee plus $27 for the monthly fee.
If Julissa has a gym membership for 3 months:
y = 117x + 27
y = 117(3) + 27
y = 360 + 27
y = 387
The equation y=117x+27 is used to represent the amount of money, y, that Julissa will spend on her gym membership for x months. This equation states that for each month of membership, Julissa will pay $117 for the initiation fee plus $27 for the monthly fee. This can be calculated for any number of months by substituting the value of x into the equation. For example, if Julissa has a gym membership for 3 months, y = 117x + 27 can be rearranged as y = 117(3) + 27, which equals y = 360 + 27. This is a total of 387 dollars, which is the amount Julissa will spend for 3 months of gym membership.
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A cable company charges an installation fee to install cable at a residence. There is also a monthly fee for the cable service. The total cost for months 2, 4, 6 and 8 are $145, $255, $365, and $475, respectively. How much is the installation fee? Assume that the relationship between the two quantities is linear
$13,000 and $15,000.
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Find 6x3/5. Use model at the right to find the product
The multiplication of the given fraction 6 × 3/5 is 15 or 3 3/5
How to multiply fraction?Fraction refers to numbers which comprises of a numerator and a denominator. A numerator is the upper or top value of a fraction while a denominator is the lower or bottom value of a fraction.
6 × 3/5
multiply the numerator and denominator separately
= (6 × 3) / (1 × 5)
= 18/5
= 3 3/5
Therefore, 3 3/5 is the solution to the multiplication of the fraction.
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Joe and Martha shared 56 books joe had 2 more books than Martha how many did Martha have
Answer:
26
Step-by-step explanation:
56/2 -2
What is the light collecting area (aperture), in [m2], of a telescope with the primary mirror diameter: 50 [cm]?
The area of the aperture storing light is 0.196 [tex]m^{2}[/tex].
What are shapes?Mathematical figures which have a set of pre defined properties are known as shapes. For example, Square shape is a mathematical figure who has four sides and all of them are equal in length and all the four corner of square have an angle of 90 degree. Similarly if there a figure who has been formed by the help of four lines of equal length but the corners are not 90 degrees then it will be Rhombus and not Square.
Now for the given question:
Diameter of the mirror=50 cm
we convert dia. unit in meter as area is asked in meter.
Dia.= [tex]\frac{50}{100}[/tex]
= [tex]\frac{1}{2}[/tex]
Area of a circle=π× [tex](\frac{dia}{2} )^{2}[/tex]
=π×[tex](\frac{1}{4} )^{2}[/tex]
Area= π/16
π=3.14
Area=[tex]\frac{3.14}{16}[/tex]
= 0.196 [tex]m^{2}[/tex]
Hence area of the aperture is 0.196 [tex]m^{2}[/tex].
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3(x+2) x 10 x 7/70-2(x+2)
The solution of the given expression results as 105(x+2)/33-x
What is an expression?Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
We are Given the expression;
[3(x+2)*10*7]÷70 - 2(x+2)
Solving further
= 3(x+2)*70÷70 - 2(x+2)
= 210(x+2)/70-2x-4
= 210(x+2)/66-2x
= 210(x+2)/2(33-x)
= 105(x+2)/33-x
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. a school has 100 business majors, 60 math majors, and 40 psych majors. every student at the school belongs to one and only one of these majors. three different students are chosen to be interviewed for a focus group. how many ways are there to choose this focus group where all three students do not all come from the same major?
Number of ways are there to choose this focus group where all three students do not all come from the same major is 240,000
It is given that a school have three majors i.ie, business, math and psych
Number of students in business majors is 100
Number of students in math majors is 60
Number of students in psych majors is 40
Total number of students (100+60+40) = 200 students
Three different students are chosen to be interviewed for a focus group.
Therefore, number of student in focus group = 3
Now, number of ways are there to choose this focus group where all three students do not all come from the same major
= [tex]^{100}C_{1} \times ^{60}C_{1}\times^{40}C_{1}[/tex]
= 100×60×40
= 240,000 ways
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Jack Tupp, an auto parts dealer, earns 15% commission on his first $2,000 in
auto part sales, and 5% on the balance. Jack sold earned $5,975 worth of
auto parts last week. How much commission did Jack make?
Answer: Jack made $898.25 in commission
Step-by-step explanation:
Jack made $898.25 in commission. ($2,000 x 15%) + ($3,975 x 5%) = $898.25
[tex]5975-2000=3975[/tex] this is the amount jack earns 5% commission on
I need help
I'm confused
According to the information, the number sequences would go as follows: arithmetic: 1, 9, 17, 25, 33...; 83, 84, 85, 86, 87... Geometric: 6, 24, 96, 384, 1536...; 1, 6, 36, 216, 1296...; 7, 14, 28, 56, 112...; neither: 4, 9, 16, 25, 36...; 1, 1, 2, 3, 5, 8, 13,...
How to identify the sequences that belong to each category?To identify the sequences that belong to each category, we must take into account the difference between a geometric sequence and an arithmetic sequence. In the case of geometric sequences, they are those sequences made up of numbers that are the result of multiplying the first number by a common factor.
On the other hand, arithmetic sequences are those that are made up of numbers that differ from the previous and the following number by a fixed amount. According to the above, the values would be classified as follows:
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Pls show your work thank you will mark the Brainliest
Answer:
12.3
Step-by-step explanation:
take x=0 because intercept means cutting the y axis when x=o
Answer:
Step-by-step explanation:
7
The second smallest number that has 1,2,3,4 and 5 in them
12354 is the second smallest number that contains the digits 1, 2, 3, 4 and 5 in that order. It can be used in a variety of ways, such as counting, addition, subtraction, multiplication and division, as well as to represent dates and times.
The second smallest number that has 1,2,3,4 and 5 in them is 12354. This number is made up of the digits 1, 2, 3, 4, and 5 in that order. It is the second smallest number because the smallest number that contains these digits is 12345.
To form this number, we start by arranging the digits in descending order, from the largest to the smallest, 5, 4, 3, 2 and 1. We then combine the digits together to form 12354.
12354 is the second smallest number because it contains all the digits 1, 2, 3, 4 and 5 in that order. This number can be used in different ways, such as counting, addition, subtraction, multiplication and division. For example, 12354 divided by 4 equals 3088.75.
The number 12354 can also be used in other ways, such as to represent a date or time. For example, the number 12354 can represent the date 12/3/54, which is December 3, 1954.
In conclusion, 12354 is the second smallest number that contains the digits 1, 2, 3, 4 and 5 in that order. It can be used in a variety of ways, such as counting, addition, subtraction, multiplication and division, as well as to represent dates and times.
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I need help, Find the volume of this object. Use 3 for Pi.
The volume of the given 3 - D figure is 156.36 cubic inches.
What is volume?A volume is a collection of a three dimensional coordinate points enclosed by a two dimensional coordinate points.
Given is the 3 - D figure as shown in the image.
We can write the volume as -
V = πr²h/3 + lbh
V = (3.14 x 3 x 3 x 8)/3 + (9 x 9 x 1)
V = 156.36 cubic inches
Therefore, the volume of the given 3 - D figure is 156.36 cubic inches.
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Scatter plot, 8 grades help please!!!
The equation of the trend line in the graph can be found to be y = 5 x + 15
How to find the equation of the trend line ?The equation of the trend line takes the form :
y = Slope ( x ) + y intercept
From the diagram, we know the y - intercept is 15 as this is where the line intercepts the y - axis.
The slope can be found by picking a point and using the formula. We will pick ( 1, 20 ).
The slope is:
20 = Slope ( 1 ) + 15
Slope = 20 - 15
Slope = 5
The equation is:
y = 5 x + 15
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Plot the z intercepts y-intercept, vertex and axis of symmetry of the function h(x)=(x+1)^2-4
The axis of symmetry of the function is x=-1.
What is the function?Functions are the fundamental part of the calculus in mathematics. The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x.
The given function is h(x)=(x+1)²-4.
Graph the parabola using the direction, vertex, focus, and axis of symmetry.
Direction: Opens Up
Vertex: (-1,-4)
Focus: (-1,-15/4)
Axis of Symmetry: x=-1
Directrix: y= -17/4
Plot the points (-3, 0), (-2, -3), (-1, -4), (0, -3) and (1, 0)
To find the x-intercept, substitute in 0 for y and solve for x. To find the y-intercept, substitute in 0 for x and solve for y.
x-intercept(s): (1,0),(-3,0)
y-intercept(s): (0,-3)
Therefore, the axis of symmetry of the function is x=-1.
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