One technique to write numbers such that you can see the mathematical significance of each individual digit is in expanded form or expanded notation. So the expanded form of (3x-5)³ is 27x³-135x²+225x-125.
How do you write in a more detailed format?One technique to write numbers such that you can see the mathematical significance of each individual digit is in expanded form or expanded notation.
It is also possible to create a mathematical expression using integers that have been divided into distinct place values and decimal places.
5,000 + 300 + 20 + 5 = 5,325 is the expanded notation for the number.
Expanded form of the given expression.
1) We can expand the given term by the direct formula of the algebra
(A-B)³ = A³-B³-3AB(A-B)2)
We have (3x-5)³on comparing with the formula:
A = 3x
B = 5
(3x-5)³
(3x)³-5³-3×3x×5(3x-5)
27x³-125-45x(3x-5) 27x³-125-135x²+225x
So the expanded form of (3x-5)³ is 27x³-135x²+225x-125.
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Simplify and explain 6 + (5 + x) (Hurry!)
Answer:
11+x
Step-by-step explanation:
6 + (5 + x)
because you have a + between 6 and the parentheses then you can just add everything up without warring about them. so:
6+5+x which equals to 11+x
Write each proof. Finish the table.
The ASA and AAS theorems are used in the proof as explained below for each given statements.
How to Write a Proof?A proof is a logical argument that demonstrates the truth of a mathematical statement.
The proof that can be used to prove each given statements are demonstrated below.
14. Proof for ∆UVY ≅ ∆XVW:
Statement Reason
1. V is the midpoint of YW. 1. Given
2. UY || XW 2. Given
3. YV ≅ WV. 3. Def. of midpoint
4. <UYV ≅ <XWV. 4. Alternate <s theorem
5. <UVY ≅ <XVW 5. Vertical<s theorem
6. ∆UVY ≅ ∆XVW 6. ASA
15. Proof for ∆MSP ≅ ∆RQP:
Statement Reason
1. MS ≅ RQ 1. Given
2. MS || RQ 2. Given
3. <MSP ≅ <RQP. 3. Alternate <s theorem
5. <MPS ≅ <QPR 4. Vertical<s theorem
6. ∆MSP ≅ ∆RQP 6. AAS
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The graph of quadratic function f is shown on the grid. Which of these best represents the domain of f?
The domain of the quadratic function is x ≥ -6.
The correct option is C.
What is domain?The collection of all conceivable independent values that a function or relation may take is known as its domain.
Given:
The graph of quadratic function f is shown on the grid.
The domain of f(x) means,
all the values of x where function is defined.
From the graph,
the domain is, x ≥ -6.
Therefore, the domain is x ≥ -6.
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Jenny invests $2,000 at an interest rate of 5%. The amount of money, , in Jenny’s account after t years can be represented using the equation
Answer:
A= 2000*(1+0.05)^t
Explanation: The equation represents the compound interest formula where A is the amount of money in the account, P is the principal amount (initial investment) which is $2,000, r is the interest rate (expressed as a decimal) which is 5% or 0.05, and t is the number of years. The formula shows that the account balance will increase by 5% each year, meaning the interest will be added to the principal and the new interest will be calculated on the new balance.
Step-by-step explanation:
2. MODELING REAL LIFE A dumpster rental fee is $350 for
the first week and $10 for each additional day or any portion
of a day. Write and graph a step function that represents the
cost y (in dollars) to rent the dumpster for x days.
The graph is a step function with a horizontal jump at x=7, where the cost changes from $350 to $10 per day.
What is the Graph?
The graph of the step function that represents the cost of renting a dumpster for x days is a graph that shows how the cost of the rental changes based on the number of days. The x-axis represents the number of days, and the y-axis represents the cost in dollars.
To write the step function that represents the cost of renting a dumpster for x days, we can use the information provided in the problem statement. The cost for the first week is $350, and the cost for each additional day is $10.
We can write the step function as:
y = 350, if x <= 7
y = 350 + 10(x-7), if x > 7
In the first case, if x is less than or equal to 7 (i.e. within the first week), the cost is $350. In the second case, if x is greater than 7 (i.e. more than one week), the cost is $350 for the first week plus $10 for each additional day.
To graph the step function, we can start by plotting the two points on the graph:
(7,350) represents the point at which the cost changes from $350 to $10 per day
(x,y) = (7,350) + (x-7,10x-70)
The graph is a step function with a horizontal jump at x=7, where the cost changes from $350 to $10 per day.
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The science club surveyed 50 students about the number of science courses in which they were enrolled and the time it took them to complete their homework. Classify the random variables from the survey.
Number of science courses, continuous; time to complete homework, continuous
Number of science courses, continuous; time to complete homework, discrete
Number of science courses, discrete; time to complete homework, continuous
Number of science courses, discrete; time to complete homework, discrete
Unable to determine from information given
The correct answer is Number of science courses, discrete; time to complete homework, continuous.
Discrete data is a sort of numerical information that consists of full, concrete numbers with predetermined, set values that can be counted.
The number of science courses enrolled in is likely a whole number, making it a discrete random variable. On the other hand, the time it takes to complete homework could be any value within a continuous range, such as minutes or hours, so it is a continuous random variable.
Hence, the number of science courses is discrete and time to complete homework is continuous.
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Which function has a range limited to only negative numbers?
Answer:
F(x)=-x^2
Step-by-step explanation:
The one example of function with range of only negative number is:
F(x)=-x^2
Why this? We know for every x, x^2 is positive. So -x^2 will be negative.
in how many ways can a committee of 20 members choose a president, a vice-president, and a secretary?
There are 6840 ways to choose a president, a vice-president, and a secretary from a committee of 20 members.
To choose a president, a vice-president, and a secretary from a committee of 20 members,
We will use the formula for combinations,
which is: C(n, k) = n! / (k! (n - k)!)
where n is the total number of members and k is the number of members being chosen.
So, for n = 20 and k = 1, we have:
C(20, 1) = 20! / (1! (20 - 1)!) = 20
This gives us 20 choices for the president.
For the vice president,
We need to choose 1 member from the remaining 19 members.
So, for n = 19 and k = 1,
we have:
C(19, 1) = 19! / (1! (19 - 1)!) = 19
This gives us 19 choices for the vice president.
Finally, for the secretary,
We need to choose 1 member from the remaining 18 members.
So, for n = 18 and k = 1,
we have:
C(18, 1) = 18! / (1! (18 - 1)!) = 18
This gives us 18 choices for the secretary.
Now for finding the total number of ways to choose the three positions, we multiply the number of choices for each position:
So, the required number of ways will be 20 * 19 * 18 = 6840
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what value of x is the solution set 0f 2x-3>11-5x?
The correct option that will make the inequality expression 2x - 3 > 11 - 5x true is when x is equal to 2.
The value of x that makes the inequality expression true.We shall evaluate for the values of x to know that make the inequality expression true as follows;
2x - 3 > 11 - 5x
2x + 5x - 3 > 11 {add the 5x to both sides}
7x > 11 + 3 {add 3 to both sides}
7x > 14
x > 14/7 {divide through by 7}
x > 2
Therefore, the value for x that makes the inequality expression 2x - 3 > 11 - 5x true is 2.
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Answer Choices:
A: y=2x+4
B: y= 0.5x+ 0
C: y+2x+0
D: y=0.5x+4
The slope intercept form for D: y=0.5x+4
What is slope-intercept form?Slope-intercept form is a form of a linear equation, written as y = mx + b, where m is the slope, and b is the y-intercept.
This question is using the slope-intercept form of a linear equation, which is written as y = mx + b, where m is the slope and b is the y-intercept. In this case, the equation y=0.5x+4 is written in the slope-intercept form, with m = 0.5 and b = 4.
To solve this equation, we first need to identify the slope (m). In this case, the slope is 0.5. Then, we need to identify the y-intercept (b). In this case, the y-intercept is 4. Finally, we can use the slope and y-intercept to write the equation in the form of y = mx + b, which is y = 0.5x + 4.
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what is the inequalitys to
7x+9=58
The solution to the inequality 7x + 9 ≤ 58 is given as follows:
x ≤ 7.
How to solve the inequality?The inequality for this problem is defined as follows:
7x + 9 ≤ 58.
Isolating the variable x, we have that:
7x ≤ 58 - 9
7x ≤ 49
x ≤ 49/7
x ≤ 7.
Meaning that the inequality is solved similarly to an equality, with the difference that a range of values is obtained instead of a single value.
Missing InformationThe problem asks for the solution to the inequality 7x + 9 ≤ 58.
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Given the arithmetic series: a +13 + b + 27 + ...
Show that a=6 and b=20
Is alcohol misuse biologically determined or culturally influenced? This debate is most relevant to the issue of:
O observation versus introspection.
O nature versus nurture.
O psychoanalysis versus cognitive psychology.
O structuralism versus functionalism.
O behavior versus mental processes.
The debate over whether alcohol misuse is biologically determined or culturally influenced is most relevant to the issue of nature versus nurture.
What is an nature?Nature refers to the physical world and its natural processes and phenomena, including everything from living organisms and their environments to the physical forces and structures that shape the universe.Diversity of life: The vast array of species and ecosystems that make up the biosphere, each with their own unique characteristics and adaptations.Natural processes: The physical, chemical, and biological processes that shape the Earth and its environment, including weather, erosion, and evolution.Physical structures: The geological and astronomical structures that form the foundation of the Earth, including mountains, oceans, and stars.Balance and harmony: The intricate interdependence of living and nonliving things, where changes in one part of the system can have far-reaching effects on the rest.Nature provides essential resources for human survival and well-being, as well as aesthetic beauty and inspiration. It is important to understand and protect the delicate balance of nature to ensure its continued existence and prosperity for future generations.To learn more about nature refer:
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DESCRIBE A SEQUENCE OF TRANSFORMATIONS THAT WILL MAP ABCD ONTO A’B’C’D’
rotate _____ degrees _____ around E, then ______ over the vertical line k.
Rotate( options )
120.
90
60
180
2 answer options
Counterclockwise
Clockwise
Options answer 3
Translate
Reflect
Rotate
Rotate 90 clockwise around E, then reflected over the vertical line K
what can go into 28 and 49
Answer:The factors of 28 and 49 are 1, 2, 4, 7, 14, 28 and 1, 7, 49 respectively
Step-by-step explanation:Some numbers have 28 and 49 as answers
A bookstore had 70 copies of a magazine. Yesterday, it sold 1/5 of them. Today, it sold 5/7 of what remained. How many copies does the bookstore have left?
Answer: 16
Step-by-step explanation:
1/5 x 70 = 14
70 - 14 = 56
5/7 x 56 = 40
56 - 40 = 16
Answer:
16
Step-by-step explanation:
Yesterday, the bookstore sold 1/5 of the 70 copies, which is 70 * 1/5 = 14 copies.
After selling 14 copies, the bookstore was left with 70 - 14 = 56 copies.
Today, the bookstore sold 5/7 of what remained, which is 5/7 * 56 = 40 copies.
So, the bookstore has 56 - 40 = 16 copies left.
Bianca has two trees in her front yard. One is 71/1/2
meters tall, and the other is 4 meters tall.
The difference in height of the trees in Bianca front yard is 2 3 / 4 metres.
How to find how much taller one tree is to another?Bianca has two trees in her front yard. One is 7 1 / 2 metres tall and the other tree is 4 3 / 4 metres tall.
Therefore, the difference in height of the trees can be calculated as follows:
Let's convert the height of the tree to improper fractions as follows:
7 1 / 2 = 15 / 2 metres
4 3 / 4 = 19 / 4 metres
Therefore,
difference in height of the trees = 15 / 2 - 19 / 4
difference in height of the trees = 30 - 19 / 4
difference in height of the trees = 11 / 4 metres = 2 3 / 4 metres.
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7. What is the maximum level of intensity for passion? After how many years in a relationship does this occur? College algebra
The maximum level of intensity for passion is when there is a feeling of intense desire and excitement.
The years in a relationship that this can occur varies depending on the couple and other factors.
When do people feel passion in a relationship?The maximum level of intensity for passion in a romantic relationship can vary for different individuals and situations. Passion is a feeling of intense desire and excitement, and it can fluctuate over time. Some people may experience intense passion in the early stages of a relationship, while others may find that it grows stronger over time.
It is not possible to set a specific number for the maximum level of intensity for passion as it's subjective and can change over time.
Some people may feel intense passion in the early stages of a relationship, while others may experience it later on. Passion can also come and go in a relationship, and its intensity may fluctuate over time.
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calculate a correlation matrix for the following data. which two variables have a strong positive relationship? fructosamine number of group visits attended infant birthweight in grams 152 6 3175 173 5 3225 174 4 3350 175 4 3400 176 3 3530 183 2 3540 188 3 3525 192 3 3650 202 2 3600 205 2 3550 210 1 3950 215 2 3325 220 2 4500 258 1 4800 group of answer choices number of group visits attended and fructosamine infant birthweight and fructosamine infant birthweight and number of group visits attended
The correlation between two variables is a measure of how strongly they are related to each other.
In order to calculate the correlation between two variables, one must calculate the covariance, which is the average of the product of the deviations of each variable from its mean. The formula for the covariance of two variables, X and Y, is cov(X,Y) = (1/n) Σ (x_i - mean_x)(y_i - mean_y).
The correlation matrix for the given data is as follows:
Number of Group Visits Attended Fructosamine Infant Birthweight (g)
Number of Group Visits Attended 1 -0.20 -0.10
Fructosamine -0.20 1 0.83
Infant Birthweight (g) -0.10 0.83 1
From the above correlation matrix, it can be seen that the two variables with a strong positive relationship are Fructosamine and Infant Birthweight, with a correlation of 0.83. This indicates that as Fructosamine increases, so does the Infant Birthweight.
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hich of the following statements best describes a control group? multiple choice a control group is a comparison group treated in every way like the experimental group, except for the manipulated factor. a control group is a comparison group that does not participate in the experiment but fills out a questionnaire instead. a control group is a group of individuals randomly assigned to a variety of treatments. a control group is a group of individuals who design the procedures of an experiment.
A control group is a group of individuals that is treated in exactly the same way as the experimental group in an experiment, except for the factor that is being manipulated.
This group is used as a comparison to measure the effects of the manipulated factor on the experimental group. The control group is key for determining the validity of the results of an experiment because it helps to ensure that any observed changes are actually due to the manipulated factor. A control group should be chosen at random from the same population as the experimental group and should be given the same conditions as the experimental group, except for the factor that is being manipulated. This helps to ensure that any observed differences in the experimental and control groups are due to the manipulation and not due to any other factor.
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ANSWER ASAP!!!!! PLEASE!!!
(USE THE SCREENSHOT!)
The total weight of the 4 heaviest pumpkins is given as follows:
D. 41 and 3/4 pounds.
How to obtain the total weight of the 4 heaviest pumpkins?The dot plot shows the number of times that each measure appears in the data-set.
Hence the weights of the four-heaviest pumpkins are given as follows:
2 of 10.375 pounds.2 of 10.5 pounds.Then the total weight of all these pumpkins is obtained as follows:
2 x (10.375 + 10.5) = 41.75.
The fraction equivalent to a decimal of 0.75 is given as follows:
3/4.
Which means that the correct option is given by option D.
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One month Jane rented movies 3 and video 5 games for a total of 30$. The next month she rented 6 movies and video 2 games for a total of 18$. Find the rental cost for each movie and each video game.
The rental cost for each movie and each video game are $1.25 and $5.25 respectively
What is an algebraic expression?An algebraic expression can be defined as an expression that is usually composed of terms, variables, constants, factors and coefficients.
These expressions are also made up of some mathematical operations, such as;
DivisionAdditionParenthesesFloor divisionMultiplicationSubtractionFrom the information given;
Let movies be x
Let the video games be y
We have that;
3x + 5y = 30
6x + 2y = 18
Make 'x' the subject from equation 1
x = 30-5y/3
Substitute the value
6(30-5y/3) + 2y = 18
expand the bracket
180 - 30y/3 + 2y = 18
-24y + 180/3 = 18
-24y + 180 = 54
y = $5.25
Then, x = $1.25
Hence, the values are $1.25 and $5.25
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Could someone please help! been struggling on these for a few mins !
The logarithmic form of the exponential expressions are;
1) log2 5 = x
2) log3 10 = y
3) logk 6 = 5
4) log2 32 = 5
5) log3 81 = 4
6) log 3 27 = 3
7) log10 100 = 2
8) logx y = 2
9) log10 x = 20
10) logp q = 10
11) logx y = 1/2
12) log9 3 = 1/2
What is the logarithmic form?We have to note that we can be able to write an exponential equation in the logarithmic form or in the exponential form. In the exponential form we we would have something like;
a^x = P
While in the logarithmic form we can be able to have something like;
logaP =x
These are the two forms that we can be able to write the equations that we have in the question.
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yesterday, you typed 8 pages in 48 minutes. Today, you typed 20 pages in 2 hours. plot the two points where x is the time in minutes and y is the number of pages
A plot of the two points, where x is the time in minutes and y is the number of pages is shown in the graph attached below.
How to plot the points?First of all, we would convert the value of time in hours to minutes as follows;
Conversion:
60 minutes = 1 hour.
x minutes = 2 hours.
Cross-multiplying, we have:
x minutes = 60 minutes × 2 hours
x minutes = 120 minutes.
In this scenario, the time in minutes would be plotted on the x-axis (x-coordinate) of the graph while the number of pages would be plotted on the y-axis (y-coordinate) of the graph.
Next, we would use an online graphing calculator to plot the points representing the time in minutes and the number of pages on a coordinate axes as shown in the image attached below.
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PLSSS HELP TURLY KNOW THISSSS
Answer: 100
Step-by-step explanation:
x/2 = 50
Multiply both sides by 2:
x = 100
Answer:
Easy Peasy, MULTIPLY 2 by 50
ANSWER IS 100Just type 100
PLEASE HELP SOLVE FOR X AND Y
The variables are x = 1/2 and y = 5/3
How to solve for the variable x and y?From the figure, we have been told 21x = 5x + 8. So let's solve for x.
21x = 5x + 8
21x - 5x = 8
16x = 8
x = 8/16
x = 1/2 = 0.5
Using the Basic Proportionality Theorem or Thales’s Theorem, which states that "If three or more parallel lines intersect two transversals, then they cut off the transversals proportionally". We can say:
(20y-2)/(17y + 3) = (5x+8)/(21x)
Substitute x = 0.5 and solve for y:
(20y-2)/(17y + 3) = (5(0.5) + 8)/(21(0.5))
(20y-2)/(17y + 3) = (10.5)/(10.5)
(20y-2)/(17y + 3) = 1
20y-2 = 17y + 3
20y - 17y = 3 + 2
3y = 5
y = 5/3
Thus, the variables are x = 1/2 and y = 5/3
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Michelle bought a car that costs $25,800 and put a down of $8,000 on it. The car loan is for 60 months and has an interest rate of 3.99%. How much will she actually pay for the car? What will her monthly payment be?
Topic: Exponential Growth & Decay Word Problem
Formula: A=P(1+r)^t
Please help this is due at 10:00!!!
Answer:
$327.73
Step-by-step explanation:
$25,800 - $8,000 = $17,800
The car loan is a total of 60 months (so at 60 her payment will be $0) and the interest rate is 3.99%
Growth formula: A = P(1+r)^t
We're asking for what value at x = 60 would make P(1+r)^60 = 0?
As such, $327.73
Graph the equation shown below by
transforming the given graph of the parent
function.
y=3•2 - 3
The graph of the exponential function y = 3(2)^x - 3 is given by the image presented at the end of the answer.
How to graph the exponential function?The parent function is given as follows:
y = 2^x.
Which has:
An initial value of 1.An horizontal asymptote of y = 0.Then the transformations are given as follows:
Multiplication by 3 -> vertical stretch by a factor of 3 -> initial value of 3.Subtraction by 3 -> shift down by 3 units -> horizontal asymptote of y = -3.More can be learned about exponential functions at https://brainly.com/question/25537936
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What’s the slope and y intercept for y-5=2(x-5)
The slope and y intercept for y-5=2(x-5) is 2 and -5 respectively.
What is Linear equation ?
Linear equation can be defined as the equation in which the highest degree is one.
Given
expression
y- 5 = 2(x-5)
y - 5 = 2x - 10
y = 2x+5-10
y = 2x-5
Its in the form of y = mx+c
where m is slope
and c is y intercept.
So,
From the equation ,
we can say that m = 2 that is slope = 2 and y intercept is -5.
Therefore, The slope and y intercept for y-5=2(x-5) is 2 and -5 respectively.
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A function is a rule that assigns each _____ exactly one ____.
Answer:
input, output
Step-by-step explanation:
A function is a rule that assigns each input exactly one output.
Some questions that have you check a list of points, a table of values, a graph or an equation, to figure out if its a function... you check to see if every x only has one y to go with it. This is what the vertical line test does also.