Answer:
x=6
Step-by-step explanation:
Step 1: Simplify both sides of the equation.
5x+4x−68=34−8x
5x+4x+ −68=34+ −8x
(5x+4x)+(−68)=−8x+34(Combine like terms)
9x+−68=−8x+34
9x−68=−8x+34
Step 2: Add 8x to both sides.
9x −68+ 8x= −8x +34 +8x
17x −68 =34
Step 3: Add 68 to both sides.
17x −68 +68= 34 +68
17x=102
Step 4: Divide both sides by 17.
17x /17= 102/17
X=6 > final answer hope i could help :)
Step-by-step explanation:
Let's step through this line by line, looking for a spot where the friend could have made a mistake.
\(5x+4x-68=34-8x\\5x+4x=102-8x\\5x+4x+8x=102\\17x=102\\x=6\)
So, where could the friend have made their mistake? The key here is the transition from step 1 to step 2. What if we had subtracted 68 instead of adding it?
\(5x+4x-68=34-8x\\5x+4x=-34-8x\\5x+4x+8x=-34\\17x=-34\\x=-2\)
There it is. The friend's problem was that they had accidentally subtracted 68 to both sides when they should have added it.
Find the equation of a line that passes through the point (-3,-1) and has a gradient of
1/2.
Leave your answer in the form
y=mx+c
Answer:
Y=2x+2
Step-by-step explanation:
1/5÷3/5=
in simplest form
Answer:
1/5 + 3/5 = 45 = 0.8
Step-by-step explanation:
Spelled result in words is four fifths.
An event is considered to be ________, if all possible outcomes of a random experiment are included in the events.
The set of all possible outcomes is called the sample space. Thus in the context of a random experiment, the sample space is our universal set.
A sample space is a set of potential results from a random experiment. The letter "S" is used to denote the sample space. Events are the subset of possible experiment results. Depending on the experiment, a sample area could contain a variety of results.
The set of all potential outcomes or results of an experiment or random trial is referred to as the sample space in probability theory. The potential ordered outcomes, or sample points, are listed as elements in a set that is used to represent a sample space.
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Which expression is equivalent to x^3 + 2x^2 -3x -6?
A. (x^2 + 3)(x - 2)
B. (x^2 - 3)(x + 2)
C. (x^2 - 2)(x + 3)
D. (x^2 + 2)(x - 3)
Answer: B
Step-by-step explanation:
A --> x^3-2x^2+3x-6
B --> x^3+2x^2-3x-6
C --> x^3+3x^2-2x-6
D --> x^3-3x^2+2x-6
Consider a population consisting of the following five values, which represent the number of video downloads during the academic year for each of five housemates. 9 15 18 11 12 (a) Compute the mean of this population. H = 13 (b) Select a random sample of size 2 by writing the five numbers in this population on slips of paper, mixing them, and then selecting two. Calculate the mean for your sample. (c) Repeatedly select random samples of size 2, and calculate the x value for each sample until you have the values for 25 samples. Describe your results. This answer has not been graded yet. (d) Construct a density histogram using the 25 x values. Are most of the values near the population mean? Do the values differ a lot from sample to sample, or do they tend to be similar?
(a) Mean = (9 + 15 + 18 + 11 + 12) / 5 = 65 / 5 = 13
(b) Mean of the sample = (9 + 15) / 2 = 24 / 2 = 12
(c) The means of the samples vary, but they tend to be close to the population mean of 13.
(d) Since the problem does not provide the values for the 25 x values, we cannot construct a density histogram or determine if most of the values are near the population mean.
(a) The mean of the population is calculated by summing all the values and dividing by the total number of values:
Mean = (9 + 15 + 18 + 11 + 12) / 5 = 65 / 5 = 13
(b) To calculate the mean for a random sample of size 2, we randomly select two values from the population and calculate their mean:
Random sample: 9, 15
Mean of the sample = (9 + 15) / 2 = 24 / 2 = 12
(c) Repeatedly selecting random samples of size 2 and calculating the mean for each sample:
Here are the means for 25 random samples of size 2 (selected without replacement):
Sample 1: 9, 18 -> Mean = (9 + 18) / 2 = 27 / 2 = 13.5
Sample 2: 11, 9 -> Mean = (11 + 9) / 2 = 20 / 2 = 10
Sample 3: 15, 12 -> Mean = (15 + 12) / 2 = 27 / 2 = 13.5
...
Sample 25: 12, 15 -> Mean = (12 + 15) / 2 = 27 / 2 = 13.5
The means of the samples vary, but they tend to be close to the population mean of 13.
(d) Constructing a density histogram using the 25 x values:
Since the problem does not provide the values for the 25 x values, we cannot construct a density histogram or determine if most of the values are near the population mean.
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which property is
used below?
A. Distributive Property
B. Multiplication Property of Inequality
C. Subtraction Property of Inequality
D. Associative Property of Multiplication
Answer:
B
Step-by-step explanation:
.
Multiplication Property of Inequality because you are multiplying each side by 3. I hope this helps! :)
Select the correct answer.
Simplify the following expression.
A.
B.
C.
D.
I attached the screenshot.
Answer:
B. \( 11^2 \)
Step-by-step explanation:
\( \frac{ {11}^{6} }{ {11}^{4} } = {11}^{6 - 4} = {11}^{2} \\ \)
The simplified form of the given expression is \(\frac{11^{6} }{11^4}\) will be \(11^2\).
What are exponents?The exponents of a number are defined as the representation of a number that shows how many times a number is multiplied by itself.
The given expression is
\(\frac{11^{6} }{11^4}\)
Therefore, the exponent will subtract,
= \(11 ^{6-4}\)
= \(11^2\)
Thus, the simplified form will be \(11^2\).
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What is the percent of change from 4,000 to 1,000?
Answer:
25%
Step-by-step explanation:
1,000x4 would be 4 thousand, so the answer would be 1/4. 1/4 as a percent is 25%.
Use given information to prove that angle DHF = EHG. Write in two-column proof.
After solving the equation the required solution is ∠DHG = ∠EHG
What is angle?
An angle is a figure in Euclidean geometry made up of two rays that share a common terminal and are referred to as the angle's sides and vertices, respectively. Angles created by two rays are in the plane where the rays are located. The meeting of two planes also creates angles. We refer to these as dihedral angles.
Given, ∠1 = ∠3
now,
∠DHF = ∠1 + ∠2
and, ∠EHG = ∠3 + ∠2
∠EHG = ∠1 + ∠2 (As ∠1 = ∠3)
Hence, ∠DHG = ∠EHG
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what is x square plus 8x= 4
A single number that estimates the value of an unknown parameter is called a _______ estimate.
Answer:
A single number that estimates the value of an unknown parameter is called a point estimate.
Step-by-step explanation:
Don't see the point (haha) of elaborating
What is the end behavior of the graph below ? (CHOOSE 2 ANSWERS)
What is the 10th Amendment say?.
According to 10th Amendment it defines the Federal Government only has those powers delegated in the Constitution .
No law establishing a particular religion, forbidding its practice, restricting press or speech freedom, or restricting the right of the people to peacefully assemble and petition the government for redress of grievances may be passed by Congress.
An amendment is a change or improvement that essentially maintains the integrity of the original document. The Bill of Rights is the collective name for the first ten Amendments of the Constitution. It describes Americans' constitutional rights in relation to their government. People are granted civil liberties and rights, such as the freedom of speech, the press, and religion.
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In circle D with m \angle CDE= 60m∠CDE=60 and CD=3CD=3 units, find the length of arc CE. Round to the nearest hundredth
Answer:
Length of arc CE = 3.14 unit (Approx.)
Step-by-step explanation:
Given:
Radius of circle = 3 units
Angle between radius = 60°
Find:
Length of arc CE
Computation:
Length of arc = [θ/360][2πr]
Length of arc CE = [60/360][2(2/7)(3)]
Length of arc CE = [60/360][2(3.14)(3)]
Length of arc CE = [1/6][6(3.14)]
Length of arc CE = 3.14 unit (Approx.)
Answer:
15.08
Step-by-step explanation:
360/48 (2π18)
how to solve equations with the substitution method
Answer:
In a system, the substitution method is one of the 3 main ways to solve a system and can be very efficient at times.
Skills needed: Systems, Algebra
Step-by-step explanation:
1) Let's say we are given two equations below:
\(y=4x \\ 4x-5y=-32\)
We can use substitution here by substituting in for \(y\) in the second equation. This means we put in \(4x\) for \(y\) in the 2nd equation so we only have \(x\) variables in the equation, allowing us to solve for \(x\).
2) Solving it out:
\(1) 4x-5(4x)=-32 \\ 2) 4x-20x=-32 \\3) -16x=-32 \\4)x=2\\5)y=4x = 4(2) = 8 \\ 6)y=8\)
We essentially substitute in that value as seen in step 1. Steps 2 and 3 are just simplifying the left side and allowing for us to solve. Step 4 is where we divide by -16 on both sides to solve for x. Step 5 and 6 show us solving for y using the value for x. We get \(x=2,y=8\)
Explanation:
The substitution property of equality says ...
if A = B and A = C then B = C.
The value B can be put in place of A, because they are equal to each other.
This idea is used to solve equations by making a substitution that reduces the number of variables involved. This is done by writing an expression for one of the variables in terms of the other variable(s).
Example 1
In a 2-variable system of equations, for example, we might have ...
y = 3x +2
y = x -4
Each equation gives an expression for y in terms of x. That expression can be used where y is in the other equation.
3x +2 = x -4 . . . . . using the expression for y of the first equation to substitute for y in the second equation.
This gives a 3-step equation in one variable, so is easily solved for the value of x. Then either of the original equations can be used to find the value of y. Here, x=-3, so y=-3-4 = -7 (using the second equation to find y).
Example 2
The idea of substitution can be used to solve equations of all kinds. Sometimes, the substitution is a bit messy. Nevertheless, it can reduce the problem to one that is more manageable.
A recent Brainly question involved the equations ...
2y = 3x -1
4x^2 -15xy +9y^2 = 0
This system reduces to a single quadratic in one variable by substituting for x or y in the second equation. We used y = (3x -1)/2, so the second equation became ...
4x^2 -15x(3x -1)/2 +9((3x -1)/2)^2 = 0 . . . . the bold expression subs for y
This requires some simplification to get it to the usual quadratic form, but the problem can now be solved in a straightforward way.
_____
Additional comments
You can choose the substitution you want to make so that it simplifies your work. You might want to choose to substitute for a variable that has an easy expression to find. In a system of linear equations, you will usually look first for a variable with a coefficient of (plus or minus) 1. It will generally be easy to write the expression that can be substituted for that variable.
Sometimes, you don't need to find an expression for the "bare" variable. You may be able to substitute easily for some multiple of the variable.
Example 3
2x +3y = 4
3x +6y = 7
The value 6y is twice the value 3y, so we can write these equations as ...
3y = 4 -2x . . . . . first equation solved for 3y
2x +2(3y) = 7 . . . second equation written in terms of 3y
Now, we have an expression for 3y and a place to substitute it.
2x +2(4 -2x) = 7 . . . . . 4 -2x substituted for 3y
Can you help me solve this?
Answer:
y=1/3x+6
Step-by-step explanation:
Answer:
y=1/3x+6
Step-by-step explanation:
what value of x will make x^(2)=64 true
Answer:
x=8
Step-by-step explanation:
x^(2)=64
Square root both sides of your equation to isolate your x.
x=\(\sqrt{64}\)
x=8
Hey there!
x^2 = 64
TAKE the SQUARE ROOT OF 64
√64 = 8 or -√64 = 8
Thus, your answer should be: x = 8 or x = -8
Good luck on your assignment & enjoy day!
~Amphitrite1040:)
A clinic has several doctors. Every patient, on average, requires about 27 minutes with a doctor Each doctor works 8 hours per day and 7 days per week. The clinic also operates 8 hours per day and 7 days per week. Based on past observations, the clinic must serve 122 patients per day. How many doctors should the clinic hires in order to serve 122 patients per day? Use at least 4 decimals in your calculation and answer.
The clinic should hire at least 7 doctors in order to serve 122 patients per day.
To determine how many doctors the clinic should hire in order to serve 122 patients per day, we need to calculate the number of patients each doctor can see within their working hours.
Let's start by calculating the total number of minutes each doctor works per day. Since each doctor works 8 hours per day and there are 60 minutes in an hour, the total minutes worked by a doctor per day would be 8 hours × 60 minutes = 480 minutes.
Next, we need to find out how many patients a doctor can see within their working hours. Given that each patient requires an average of 27 minutes with a doctor, the number of patients a doctor can see per day would be 480 minutes ÷ 27 minutes per patient = 17.7778 patients.
Since we can't have a fractional number of patients, we need to round this number up to the nearest whole number to ensure that each patient gets the required attention. Therefore, each doctor can see approximately 18 patients per day.
To serve 122 patients per day, we divide the total number of patients by the number of patients each doctor can see per day: 122 patients ÷ 18 patients per doctor = 6.7778 doctors.
Again, we can't have a fractional number of doctors, so we need to round this number up to the nearest whole number. Therefore, the clinic should hire at least 7 doctors to serve 122 patients per day.
In summary, the clinic should hire at least 7 doctors in order to serve 122 patients per day.
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Answer question pls
Down below
Answer:
1 is after 0 and 4 before 6 then -3 3rd from -5
Step-by-step explanation:
Answer:
1 = ➡️
4 =➡️
-3 = ⬅️
HOPE YOU LIKE IT
6-7(x+1)= -3(2-x)
How do you solve this?
\(6 - 7(x + 1) = - 3(2 - x)\)
Distribute/Simplify\(6 - 7x - 7 = - 6 + 3x \\ - 1 - 7x = - 6 + 3x\)
Solve the equation for x-term by making x as the subject.\( - 1 + 6 = 7x + 3x \\ 5 = 10x \\ \frac{5}{10} = x \\ \frac{1}{2} = x\)
Answer Check by substituting the value of x in the equation.\(6 - 7( \frac{1}{2} ) - 7 = - 6 + 3( \frac{1}{2} ) \\ 6 - \frac{7}{2} - 7 = - 6 + \frac{3}{2} \Longrightarrow \sf{You \: \: can \: \: change \: \: sides \: \: to \: \: make \: \: it \: \: easier} \\ 6 - 7 + 6 = \frac{7}{2} + \frac{3}{2} \\ 5 = \frac{10}{2} \\ 5 = 5 \: \green{ \checkmark}\)
The equation is true for x = 1/2.
Answer\( \large \boxed{x = \frac{1}{2} } \: \: \: \: \green{ \checkmark}\)
find the value of x please
Answer:
A. 40°Step-by-step explanation:
AO = CO = radius
AO = CO ⇒ AB = BC and m∠AOB = m∠BOC = ¹/₂m∠AOC
From BDOE:
m∠EOB + m∠OBC + m∠CDE + m∠DEO = 360°
(65° + 75°) + 90° + x + 90° = 360°
140° + 180° + x = 360°
x = 40°
what is the value of x in the equation 1/5 x- 2/3 y = 30, when y = 15? 4, 8 ,80 ,200 Select one .
The value of x in the equation when y = 15 is 200.
To find the value of x in the equation, we substitute y = 15 into the equation and solve for x:
1/5 x - 2/3 y = 30
Replacing y with 15:
1/5 x - 2/3 * 15 = 30
1/5 x - 10 = 30
1/5 x = 30 + 10
1/5 x = 40
Multiplying both sides by 5 to isolate x:
x = 40 * 5
x = 200
Therefore, the value of x in the equation when y = 15 is 200.
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What is \(\sqrt{1} ?\\\)
list and describe two specialized alternatives not often used as a continuity strategy. quizlet
1. P-adic Numbers:
P-adic numbers are a specialized alternative not commonly used as a continuity strategy in mathematics. They are an extension of the real numbers that provide a different way of measuring and analyzing numbers. P-adic numbers are based on a different concept of distance, known as the p-adic metric. This metric assigns a measure of closeness or distance between numbers based on their divisibility by a prime number, p. P-adic numbers have unique properties and can be useful in number theory, algebraic geometry, and other branches of mathematics. However, they are not typically employed as a continuity strategy in practical applications.
2. Nonstandard Analysis:
Nonstandard analysis is a mathematical framework that provides an alternative approach to calculus and analysis. It introduces new types of numbers called "infinitesimals" and "infinite numbers" that lie between the standard real numbers but are infinitely smaller or larger than any real number. Nonstandard analysis allows for more rigorous treatment of infinitesimal quantities and provides a different perspective on limits, continuity, and differentiation. While nonstandard analysis has theoretical implications and can provide valuable insights in mathematical research, it is not commonly used as a continuity strategy in practical applications where standard analysis and calculus are more prevalent.
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1. Find the slant height of a square pyramid with a surface area of 57 square feet and a base perimeter of 12 feet
Answer:
Slant height = 8 feet.
Step-by-step explanation:
If the perimeter of the square base = 12 then each side of the base = 12/4
= 3 feet and its area = 3*3 = 9 ft^2
The area of one of the triangular sides = 1/2 * 3 * h where h is slant height.
So total surface area = 57 = 9 + 4 * 1.5h
9 + 6h = 57
6h = 48
h = 8 feet.
Blair & Rosen, Inc. (B&R), is a brokerage firm that specializes in investment portfolios designed to meet the specific risk tolerances of its clients. A client who contacted B&R this past week has a maximum of $85,000 to invest. B&R's investment advisor decides to recommend a portfolio consisting of two investment funds: an Internet fund and a Blue Chip fund. The Internet fund has a projected annual return of 9%, whereas the Blue Chip fund has a projected annual return of 8%. The investment advisor requires that at most $55,000 of the client's funds should be invested in the Internet fund. B&R services include a risk rating for each investment alternative. The Internet fund, which is the more risky of the two investment alternatives, has a risk rating of 6 per thousand dollars invested. The Blue Chip fund has a risk rating of 4 per thousand dollars invested. For example, if $10,000 is invested in each of the two investment funds, B&R's risk rating for the portfolio would be
6(10) + 4(10) = 100.
Finally, B&R developed a questionnaire to measure each client's risk tolerance. Based on the responses, each client is classified as a conservative, moderate, or aggressive investor. Suppose that the questionnaire results classified the current client as a moderate investor. B&R recommends that a client who is a moderate investor limit his or her portfolio to a maximum risk rating of 410.
(a)
Formulate a linear programming model to find the best investment strategy for this client. (Assume N is the amount invested in the internet fund project and B is the amount invested in the Blue Chip fund. Express the amounts invested in thousands of dollars.)
Max _______________ s.t.
Available investment funds
Maximum investment in the internet fund
Maximum risk for a moderate investor
N, B ≥ 0
(b)
Build a spreadsheet model and solve the problem using Excel Solver. What is the recommended investment portfolio (in dollars) for this client?
internet fund$
blue chip fund$
What is the annual return (in dollars) for the portfolio?
$
(b)
Suppose that a second client with $85,000 to invest has been classified as an aggressive investor. B&R recommends that the maximum portfolio risk rating for an aggressive investor is 450. What is the recommended investment portfolio (in dollars) for this aggressive investor?
internet fund$
blue chip fund$
(d)
Suppose that a third client with $85,000 to invest has been classified as a conservative investor. B&R recommends that the maximum portfolio risk rating for a conservative investor is 320. Develop the recommended investment portfolio (in dollars) for the conservative investor.
internet fund$
blue chip fund$
A. N, B ≥ 0 (non-negativity constraint)
B. The recommended investment portfolio (in dollars) for this client can be found by reading the values in cells A1 and B1.
C. You can solve for the recommended investment portfolio (in dollars) by reading the values in cells A1 and B1.
D. You can solve for the recommended investment portfolio (in dollars) by reading the values in cells A1 and B1.
(a)
The linear programming model to find the best investment strategy for this client can be formulated as follows:
Maximize: 0.09N + 0.08B
Subject to:
N + B ≤ 85 (maximum investment of $85,000)
N ≤ 55 (maximum investment of $55,000 in the internet fund)
6N + 4B ≤ 410 (maximum risk rating of 410 for a moderate investor)
N, B ≥ 0 (non-negativity constraint)
(b)
To solve the problem using Excel Solver, you can set up the following spreadsheet model:
Cell A1: N (amount invested in the internet fund)
Cell B1: B (amount invested in the Blue Chip fund)
Cell C1: =0.09A1 + 0.08B1 (annual return for the portfolio)
Constraints:
Cell A2: ≤ 85
Cell B2: ≤ 85
Cell C2: ≤ 55
Cell D2: ≤ 410
The objective is to maximize the value in cell C1 by changing the values in cells A1 and B1, subject to the constraints.
Using Excel Solver, set the objective to maximize the value in cell C1 by changing the values in cells A1 and B1, subject to the constraints in cells A2, B2, C2, and D2.
The recommended investment portfolio (in dollars) for this client can be found by reading the values in cells A1 and B1.
(b)
For the aggressive investor with a maximum portfolio risk rating of 450, the linear programming model remains the same, except for the constraint on the maximum risk rating.
The new constraint would be: 6N + 4B ≤ 450
Using the same spreadsheet model as before, with the updated constraint, you can solve for the recommended investment portfolio (in dollars) by reading the values in cells A1 and B1.
(d)
For the conservative investor with a maximum portfolio risk rating of 320, the linear programming model remains the same, except for the constraint on the maximum risk rating.
The new constraint would be: 6N + 4B ≤ 320
Using the same spreadsheet model as before, with the updated constraint, you can solve for the recommended investment portfolio (in dollars) by reading the values in cells A1 and B1.
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I Need Help With This Question
Answer:
Step-by-step explanation:
Dont do it. Just take the detention
A certain health insurance plan costs $3000 per year for a family of six. If each member of the family has $750 in medical expenses in a year, and the plan pays 100 percent of those expenses, how much will the family save by purchasing the plan?
Answer:$1,500
Step-by-step explanation:
6 * 750 = 4,500
4,500- 3,000= 1,500
someone pls help asap i’m very desperate! thanks!!
Answer:
A: $250B: $600, earns more interestStep-by-step explanation:
The simple interest formula is ...
I = Prt . . . . . r is the interest rate, t is the number of years
Solving for P, we have ...
P = I/(rt)
Account A6 months is 1/2 year, so the principal is ...
P = $4.38/(0.035×1/2) = $250.2857...
Rounded to the nearest dollar, the principal invested is $250.
__
Account BUsing the same approach, for 18 months, t = 18/12 = 3/2 = 1.5.
P = $20.70/(0.023×1.5) = $600
The principal in Account B is $600.
__
First Month's Interest
Using the interest formula, the first month's interest in each account is ...
A: I = 250×0.035×1/12 = $0.73
B: I = 600×0.023×1/12 = $1.15
Account B earns more interest in the first month.
Comparing a census of a large population to a sample drawn from it, we expect that theA. sample is usually a more practical method of obtaining the desired information.B. accuracy of the observations in the census is surely higher than in the sample.C. sample must be a large fraction of the population to be accurate.
Comparing a census of a large population to a sample drawn from it, we expect that the sample is usually a more practical method of obtaining the desired information.
This is because a census involves collecting data from every individual in the population, which can be time-consuming, expensive, and logistically challenging, especially for large populations. In contrast, a sample is a smaller, more manageable subset of the population, making it easier to gather and analyze data.
However, it's essential to note that the accuracy of the observations in the census is generally higher than in the sample, as the census covers the entire population, eliminating any sampling error. In comparison, a sample may be subject to various biases or inaccuracies, depending on the sampling technique used and the sample size.
To ensure that the sample accurately represents the population, it is crucial to select a sample that is both random and of an appropriate size. While the sample doesn't need to be a large fraction of the population, it should be sufficiently large to provide reliable estimates and minimize sampling error. Overall, sampling is a practical and efficient approach to obtaining information about a population when properly conducted, balancing the need for accuracy with resource constraints.
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