The amount that the bank loaned out at 7.9% is $1,574.00
How do represent the amounts lent at different rates?
On the assumption that x amount was loaned at 7.9% and that the remaining amount, (8,200-x) was loan out at 7.4%, we can determine the interest charged on each loan as the loan multiplied by the interest rate
interest on 7.9% loan=7.9%*x=0.079x
interest on 7.4% loan=7.4%*(8200-x)
interest on 7.4% loan=606.80-0.074x
total interest=0.079x+606.80-0.074x
total interest=0.005x+606.80
total interest on loans=614.67
614.67=0.005x+606.80
614.67-606.80=0.005x
7.87=0.005x
x=7.87/0.005
x=amount loaned at 7.9%=$1,574.00
y=$8200-$1574
y=$6,626.00
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Evaluate the given expression for x = 10.
8x+7
What’s this I don’t understand
Answer:
16/725
Step-by-step explanation:
Can someone explain this please.
Using proportions, the solution for the golden section is given as follows:
|AC|/|AB| = 1.6181.
What is a proportion?A proportion is a fraction of a total amount, and the measures can be related using a rule of three, which derives from proportional relationships.
Due to this, relations between variables, either direct(when both increase or both decrease) or inverse proportional(when one increases and the other decreases, or vice versa), can be built to find the desired measures in the problem, or equations to find these measures, involving operations such as division and multiplication, as they involve unit rates.
For this problem, the segment lengths are given as follows:
|AC| = 1.|AB| = x.|BC| = 1 - x.The following proportion is true for the segment:
|AC|/|AB| = |AB|/|BC|
Hence:
1/x = x/1 - x.
x² = 1 - x
x² + x - 1 = 0.
Which is a quadratic equation with solution x = 0.618.
Then the solution for the golden section is given as follows:
|AC|/|AB| = 1/x = 1/0.618 = 1.6181.
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Answer:
(1 +√5)/2 ≈ 1.618034
Step-by-step explanation:
Given point B on segment AC, you want the "golden proportion" ratio AC/AB, such that AC/AB = AB/BC. A diagram is shown with A=0, B=x, C=1.
RedefineWe can solve for the golden proportion directly by redefining points on the line segment as ...
A = 0B = 1C = rThen we have AB = 1, AC = r, BC = r-1 and the proportion of interest is ...
AC/AB = AB/BC
r/1 = 1/(r -1)
SolutionCross-multiplying gives ...
r² -r = 1
Completing the square, we have ...
r² -r + 1/4 = 5/4
(r -1/2)² = 5/4
Taking the square root gives ...
r - 1/2 = 1/2√5
r = 1/2 + 1/2√5 = (1 +√5)/2 ≈ 1.618034
The golden ratio is (1+√5)/2 ≈ 1.618034.
__
Additional comment
This ratio appears many places in math, science, and nature. It is commonly given the name Φ or φ (phi). For example, it is the limiting value of the ratio of successive terms of the Fibonacci sequence, and is deeply embedded in the quantum description of the universe.
Use a related equation that has the variable on one side. Then simplify the other
side.
12n = 48
n = 60
n=36
n=4
n=1/4
Answer:
n=4
Step-by-step explanation:
12n/12 = 48/12 the n=4
n = 60
n=36
n=4
n=1/4
Determine whether the statement is true or false if x=8, y=2 , and z=3 .
x+y>z+y
Given that x = 8, y = 2, and z = 3, the inequality x + y > z + y is true.
Inequality refers to the relationship between two non-equal expressions. It can be denoted by > for greater than, < for less than, >/= for greater than and equal to, and </= for less than and equal to.
To check if the inequality x + y > z + y is true when x = 8, y = 2, and z = 3, plug in or substitute the value of each variable to the inequality and evaluate.
x + y > z + y
8 + 2 > 3 + 2
10 > 5
Since 10 is greater than 5, the given values satisfies the inequality, then the statement is true.
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Just the answer please
Answer:
One can use either the slope formula m = (y2 – y1)/(x2 – x1) or the standard line equation, y = mx + b to solve for the slope, m.
Step-by-step explanation:
Pick two points on the line and determine their coordinates. Determine the difference in y-coordinates of these two points (rise). Determine the difference in x-coordinates for these two points (run). Divide the difference in y-coordinates by the difference in x-coordinates (rise/run or slope).
Can someone explain how to do proofs?
Answer:
Draw the figure that illustrates what is to be proved. ...
List the given statements, and then list the conclusion to be proved. ...
Mark the figure according to what you can deduce about it from the information given. ...
Write the steps down carefully, without skipping even the simplest one.
Step-by-step explanation:
a starting lineup in a basketball consists of two guards, two forwards, and a center. a. a certain college team has on its roster 4 centers, 5 guards, 5 forwards, and one individual (x) who can play either guard or forward. how many different starting lineups can be created? (hint: consider lineups without x, then lineups with x as guard, then lineups with x as foward.)
Different starting lineups can be created - 120+60+120=300. A certain college team has on its roster 4 centers, 5 guards, 5 forwards, and one individual (x) who can play either guard or forward.
1. A lineup without x is an example. You must decide.
5 quards, 2 guards;two of the three forwards;from 4 centers, 1 center.It can be made as -
2C5 × 2C3× 1C4 = 10× 3×4 = 120 ways
2. Consider starting lineups with guard x. You must decide.
2 guards chosen from 6 quards (at least one of them must be x);two of the three forwards;from 4 centers, 1 center.1C5×2C3×1C4 = 5×3×4 = 60 ways
3. Think about lineups where x is the forward. You must decide.
5 quards, 2 guards;2 forwards from 4 forwards (x must be one of them);from 4 centers, 1 center.2C5×1C3×1C4 = 10×3×4 = 120 ways.
Therefore, total number different lineups is - 120+60+120=300.
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__________ is the principle that the statistical analysis of plaintext and ciphertext results in a form of dispersion rendering one structurally independent of the other.
Diffusion is the principle that the statistical analysis of plaintext and ciphertext results in a form of dispersion rendering one structurally independent of the other.
In a simple language, whenever there is a change in one character of the plaintext there is a multiple changes in the ciphertext. The changes do not reveal the information as the structure of plaintext.
What is ciphertext?
Whenever the encrypted text changes from plaintext to encrypted algorithm then it is known as the ciphertext. It cannot be read until it is decrypted with the help of the key. And the decryption cipher algorithm changes ciphertext to plaintext text to make it readable.
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How can you use surveys, experiments and observational studies to make inferences about a population?
Surveys, Experiments, and Observational studies are some common methods of data collection in statistical studies that involve people.
A survey is a means to gather information about a group of individuals by asking some of them to respond to questions. A survey may require participants to fill out forms, respond to online questionnaires, take part in in-person interviews, or respond to questions over the phone.
In an experiment, as opposed to an observational study, different treatments are purposefully applied to several groups, and the groups are then compared to see whether there are any differences in a certain variable of interest termed a response. Researchers can determine whether various treatments have distinct effects by using a well-designed experiment.
In an observational study, a researcher utilizes data from observations to learn about a group of people. Aside from assessing their replies, the people being watched are particularly not hampered.
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please help me i need to get this
Hello,
[tex]6x + 2 = x + 17[/tex]
[tex]6x - x = 17 - 2[/tex]
[tex]5x = 15[/tex]
[tex]x = \frac{15}{5} = 3[/tex]
Aisha buys a new car.
Cash price: $4500
Credit terms:
Deposit 25% of cash price + 12 monthly payments of $320
She buys the car using the credit terms. How much more than the cash price will she pay overall for the car?
465 is the cost of the cash price will she pay overall for the car.
What is cost ?
The entire cost of all fixed and variable expenses for a particular stage in the value chain is the total cost of a business function. In other words, it is the overall cost incurred during the various stages a product goes through to reach the consumer.Your cost function might resemble this, for example, if your variable costs for labor are fixed regardless of quantity while your variable costs for supplies vary depending on the amount of each item. Total costs are calculated as fixed costs plus labor costs plus (unit count * material variable costs).25 % of cash price 4500 × 25% = 1125
12 monthly 320 × 12 = 3840
All 1125 + 3840 = 4965
more than 4965 - 4500 = 465
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If -x + 5y = 7 is a true equation, what would be the value of -2(-x + 5y)?
Answer:
-14
Step-by-step explanation:
If u put x+5y into -2(-x+5y)
Add all that up
-2(x+5y) =(-2) (7) = -14
Please help me ASAP due today please
A fraction that is equals to 5 is given by: 10/2.
What is a fraction?A fraction is modeled as follows:
a/b.
In which:
a is the numerator.b is the denominator.The equivalent of a fraction is a division operation, that is, the example fraction is equivalent to the division of a by b.
Hence, a fraction that is equivalent to 5 is a division of two numbers that result in 5, for example 10 and 2, hence:
A fraction that is equals to 5 is given by: 10/2.
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Convert 99 grams into pounds. Round your answer to the nearest hundredth.
Convert 99 grams into pounds is 0.22.
In the US, the pound is the unit of mass that is utilized. It is symbolized by the letter lbs. Therefore, we must calculate the estimated number of grams in a pound. Both pounds and grams can be converted into one another as units of mass.
Since both systems of units may carry the same mass, the fundamental conversion rate between pounds and grams is crucial for international trade. Because just writing the numbers makes no sense, units should always be written after the final solution has been evaluated. The method of transposition may be used to discover the conversion of a given number of values from one unit to another by multiplying or dividing both sides of the equation by the same number.
Covert the unit = 99 gram
99 gram = 0.218258 pound
Rounding the converted number is 0.22.
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gragh the linear equation. find three points to solve the equation ,then plot on the gragh . -3x+2y=2
The attached below is the graph and the three points to solve the equation is (0,1) , (1,5/2) and (-1,-1/2)
According to the question the equation that we have been given is
-3x + 2y = 2
We need to graph the linear equation. For this we will first put different values of x in the above equation and then find the values of y which will be the coordinates of the graph.
First put x = 0
-3(0) + 2y = 2
2y = 2
y = 1
hence the first coordinate is (0,1)
Similarly put, x = 1
-3(1) + 2y = 2
2y = 5
y = 5/2
when x= -1 then y = -1/2
Thus the three point or coordinates are (0,1) , (1,5/2) and (-1,-1/2) and below is the graph.
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matt is five years older than twice his cousin andy’s age. the sum of their ages is less than 35. let x represent andy's age. which inequality represents andy’s possible age? 0
The inequality: y < 10 represents Andy's age.
What is an inequality?Inequality refers to a relation which makes a non-equal comparison between two numbers or other mathematical expressions.
Given:
Matt is five years order than twice Andy's agesum of their ages < 35x = Andy's ageTo find: Inequality that represents Andy's possible age.
Finding:
Let y = Andy's age
According to the question,
x = 2y + 5
x + y < 35
=> 2y + 5 + y < 35
=> 3y < 30
=> y < 10
Hence, the inequality: y < 10 represents Andy's age.
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A toy car was kicked toward the target. the horizontal component of velocity was 8 m/s and the vertical component was 6m/s. calculate the magnitude of the resultant velocity of the soccer ball.
The magnitude of the resultant velocity of the soccer ball is 10 m/s .
Let the horizontal component of velocity be [tex]V_{x}[/tex] and the vertical component of velocity be [tex]V_{y}[/tex].
The magnitude of the resultant velocity will be represented by V.
So, we can write
The horizontal component of velocity = [tex]V_{x}[/tex] = 8 m/s
The vertical component of velocity = [tex]V_{y}[/tex] = 6 m/s
The relation between horizontal component, vertical component and resultant velocity is,
[tex]V^{2} = V_{x} ^{2} + V_{y} ^{2}[/tex]
On substituting value of horizontal component and vertical component, we get
[tex]V^{2}[/tex] = [tex](8)^{2} + (6)^{2}[/tex]
[tex]V^{2}[/tex] = 64 + 36
[tex]V^{2}[/tex] = 100
V = [tex]\sqrt{100}[/tex]
V = 10 m/s
The magnitude of the resultant velocity of the soccer ball is 10 m/s .
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200,40,8 arithmetric or geometric or neither
Answer:
this is geometric, you are multiplying by 1/5.
Step-by-step explanation:
Your friend has $100 when he goes to the fair. he spends $10 to enter the fair and $20 on food. rides at the fair cost $2 per ride. which function can be used to determine how much money he has left over after x rides? f(x) = −2x 70 f(x) = 2x 70 f(x) = −2x − 70 f(x) = −30x $100
The function which can be used to determine the amount of money he has left over after x rides is f(x)=-2x+70.
This function is linear. A linear variable function can be written in the form of y=f(x)=a+bx, where a and b are integers and x, is the variable. This function has one independent variable and one dependent variable. In the above given function y=f(x)=a+bx; y is the dependent variable and x is the independent variable.
Here since x number of rides are taken and the cost per ride is x so the total cost of x rides is given as 2x.
Since there is a total of $100 and an amount of ($10+$20=$30) is spent on entry and food respectively.
Therefore, total amount left after all the expenses can be expressed as:
f(x)=100-(30+2x)
f(x)=70-2x
f(x)=-2x+70
Therefore, function which can be used to determine the amount of money he has left over after x rides is f(x)=-2x+70.
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Identify the graph of f(x)=7-8x-x². Then identify the vertex and axis of symmetry.
WILL GIVE BRAINLIEST IF YOU EXPLAIN JOS TO SOLVE
Answer:
(see attached file)
vertex: (-4, 23)
axis of symmetry: x = -4
Step-by-step explanation:
The axis of symmetry always passes through the vertex of the parabola. The x -coordinate of the vertex is the equation of the axis of symmetry of the parabola.
(i'm not the best at explaining things, but khan academy has some amazing math resources if you want to check it out)
Choose the inequality whose solution set is represented by this graph.
The correct option is option A , such that inequality is x - 3y < 5.
What are the inequalities ?
Inequalities are the expressions in which both sides are not equal and the equal sign in between is replaced by less than , greater than, etc.
We know that the slope intercept form of equation is given by y = mx + c , where m is the slope and c is the y - intercept.
In the graph , the upward sloping line has x and y intercepts of 5 and -3.
So its equation in slope intercept form is given by ,
- 3y = - x + 5
And the inequality with that boundary line is given by ,
- 3y < - x + 5
or
x - 3y < 5
Therefore , the inequality represented by graph is x - 3y < 5 or option A is correct.
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what's the differences between indirect and direct object? and can i get an example plss
Answer:
Step-by-step explanation:
A direct object is the object in which the verb is acting on. For example, in the sentence “He sold his car,” “car” is a direct object. An indirect object is the recipient of the direct object, as in “The man gave his wife a necklace.” “Necklace” is the direct object, and “wife” is the indirect object
Mariam read 4 books in 5 months. What was her rate of reading, in books per month? Give your answer as a whole number or a FRACTION in simplest form.
Answer:
¼ per month or 2 books in 2½ months
Mariam read 4 books in 5 months, resulting in a rate of reading of 4/5 books per month.
Use the concept of fraction defined as:
A fraction is a part of the whole number and a way to split up a number into equal parts. Or, A number which is expressed as a quotient is called a fraction. It can be written in the form of p: q, which is equivalent to p / q.
Given that,
Mariam read 4 books
She read the books in 5 months
We need to find her rate of reading, in books per month
To find the rate of reading,
Divide the number of books read by the number of months it took to read them.
In this case, Mariam read 4 books in 5 months.
So, the rate of reading would be 4 books divided by 5 months.
Simplifying this fraction, we have 4/5,
Hence, Mariam's rate of reading is 4/5 books per month.
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I need help with this question.
The distance between the two points in the simplest radical form is √61
Distance between two pointsFrom the question, we are to determine the distance between the two marked points
The marked points are (-8, 6) and (-3, 0)
The distance, d, between two points can be calculated by using the formula,
d = √((x₂ - x₁)² + (y₂ - y₁)²)
x₁ = -8
x₂ = -3
y₁ = 6
y₂ = 0
Thus,
The distance, d, between the points is
d = √((-3 - -8)² + (0 - 6)²)
d = √((-3 + 8)² + ( -6)²)
d = √((5)² + 36)
d = √(25 + 36)
d = √61
Hence, the distance between the two points in the simplest radical form is √61
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(Please help)-5 - (-5/3)
Answer:
25/3
Step-by-step explanation:
company A rents copiers for a monthly charge of $90 plus 6 cents per copy. Company B rents copiers for a monthly charge of $180 plus 3 cents per copy. What’s the number of copies above which company As charges are the higher of the two ?
By using athematic operations, we get the cost of the company A's 3000 copies is greater than that of the other two.
What are arithmetic operations?
The arithmetic operator is used to carry out mathematical operations on the specified operands, including addition, subtraction, multiplication, division, and modulus. A few examples of arithmetic operators are as follows: 5 + 3 = 8, 5 - 3 = 2, 2 * 4 = 8, etc.
Given that:
Copier rentals from company A cost $90 per month + 6 cents every copy and
Copier rentals from company A cost $180 per month + 3 cents every copy
Let the number of copies be x
Total rents for a month of Company A [tex]= 90+0.06x[/tex]
Total copiers rents for a month of Company B [tex]= 180+0.03x[/tex]
Total rents for a month of Company A = Total copiers rents for a month of Company B
⇒[tex]90+0.06x= 180+0.03x[/tex]
Taking unknown value left side
[tex]0.06x-0.03x=180-90\\0.03x=90\\x=\frac{90}{0.03} \\x=3000[/tex]
Therefore, by using athematic operations , we get the cost of the company A's 3000 copies is greater than that of the other two.
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I NEED HELP ASAP PLSS
Step-by-step explanation:
2)4(5x+6)
3)a)its 4x not 16x because 2x+ 6x is 8x and 8x-4x=4x
b)2x+6x-4x=15+12-3
4x=24
x=24/4=6
that's all I can answer
r. gao and a. j. kleywegt. distributionally robust stochastic optimization with wasserstein distance. arxiv preprint arxiv:1604.02199, 2016.
Distributionally robust stochastic optimization (DRSO) is a framework for decision-making problems under certainty, which finds solutions that perform well for a chosen set of probability distributions.
Review on r. gao and a. j. kleywegt. distributionally robust stochastic optimization with wasserstein distance -
A paradigm for decision-making under certainty called distributionally resistant stochastic optimization (DRSO) seeks solutions that function well for a specified set of probability distributions. There have been many different methods offered for describing a set of distributions. The decision is significant since it has an impact on the outcomes, and the relative effectiveness of various options depends on the traits of the issues. In this study, we take into account issues where various random variables show some degree of reliance, but the precise values of the parameters describing the dependence are unknown.We also get the DRSO problem in a dual reformulation. The formulation also has the advantage of avoiding a problem related to the one-sided moment constraints in moment-based DRSO issues, which is a desirable result.Learn more about DRSO
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a politician is interested in the proportion of voters in his district who think he is doing a good job. define the following in terms of the study. give examples where appropriate.
The percentages of voters for politicians districts are determined by parameters including district work, leadership, teamwork, etc.
Who are politicians, exactly?A politician is a person who participates in party politics by voting or holding elective office in the government. Legislation is proposed, supported, rejected, and created by politicians to rule the nation and, by implication, its citizens. Politics is the process by which those who live in groups decide on things. Politics is the process of establishing agreements between individuals so that they may coexist in social units like tribes, cities, or nations. Some individuals may invest a significant amount of effort in reaching such agreements in huge groupings, such as nations. A formal set of fundamental objectives that are backed by a political party or individual candidate in order to appeal to the general public is known as a political party platform (US English), party program, or party manifesto (preferential term in British and frequently Commonwealth English). The ultimate goal of these documents is to win the support and votes of the general public on complex issues or topics.
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