a. The Vοlume = 198 cm³ and height = 7, if it’s a cylinder with a radius οf 3cm.
b. The cοst οf cοffee is $3.96 when $0.02 per cubic centimetre.
What is the fοrmula fοr the vοlume οf the cylinder?The fοrmula fοr the vοlume οf a cylinder is
V = πr²h,
where V is the vοlume, r is the radius, and h is the height.
a) Tο find the height οf the cylinder, we need tο knοw the vοlume οf the cοntainer and the radius. The fοrmula fοr the vοlume οf a cylinder is:
V = πr²h
[tex]$\mathrm{\frac{V }{ h}} = \pi r\² }[/tex]
[tex]$\mathrm{\frac{V }{ h}} = \frac{22}{7} \times 3 \times 3}[/tex]
[tex]$\mathrm{\frac{V }{ h}} = \frac{22}{7} \times 3 \times 3}[/tex]
[tex]$\mathrm{\frac{V }{ h}} = \frac{198}{7}[/tex]
Thus, Vοlume = 198 cm³ and height = 7
b) If the cοntainer frοm is filled with cοffee and cοffee cοsts $0.02 per cubic centimetre, Then the cοst οf cοffee
= $0.02 × 198 cm³
= $3.96
Thus, The Vοlume = 198 cm³ and height = 7, if it’s a cylinder with a radius οf 3cm.
The cοst οf cοffee is $3.96 when $0.02 per cubic centimetre.
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Find the indicated terms of the geometric sequence with the given description.
The fourth term is 18 and the seventh term is (16/3). Find the first and nth terms.
Answer: Let's denote the first term of the geometric sequence as "a", and the common ratio as "r". Then, we can use the given information to set up a system of equations:
a * r^3 = 18 (the fourth term is 18, so ar^3 is the fourth term)
a * r^6 = 16/3 (the seventh term is 16/3, so ar^6 is the seventh term)
To solve for "a" and "r", we can divide the second equation by the first equation:
(a * r^6) / (a * r^3) = (16/3) / 18
Simplifying this expression, we get:
r^3 = (16/3) / 18 = 16/54 = 8/27
Taking the cube root of both sides, we get:
r = 2/3
Substituting this value of "r" into the first equation, we can solve for "a":
a * (2/3)^3 = 18
a = 18 / (2/3)^3
a = 27
Therefore, the first term of the geometric sequence is 27, and the nth term is given by:
a * r^(n-1) = 27 * (2/3)^(n-1)
Step-by-step explanation:
nate went on a trip, and he used a table of values to repeatedly record the time he had been traveling and the distance from his starting point. The function represented by the table of values is linear, and the rate of change is 50 miles per hour. What is one way for Nate to determine the initial value?
After addressing the issue at hand, we can state that We know that when function x = 0, y = b because the function has the form y = mx + b.
what is function?Mathematicians investigate numbers and their varieties, equations and adjacent tissues, shapes but instead their locations, and potential locations for these things. The term "function" refers to the relationship here between set of inputs, each with its own output. A function is a relationship of both inputs and outputs in which each input results in a single, distinct production. Each function has its own domain, codomain, or scope. The letter f is commonly used to denote functions (x). An x represents entry. On functions, each capabilities, so several capabilities, in capabilities, and on operations are the four major types of accessible functions.
We know that the function represented by the table of values has the form y = mx + b because it is linear, where y represents the distance from Nate's starting point and x represents the time he has been travelling.
The rate of change is known to be 50 miles per hour. This means that Nate's distance from his starting point increases by 50 miles for every hour he travels. In other words, m equals 50.
We know that when x = 0, y = b because the function has the form y = mx + b.
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Line h is graphed on a coordinate plane. The equation y=−52x+3 describes line h . Line j contains the point (0,2) and is parallel to line h . Which equation describes line j ? Responses
Step-by-step explanation:
a parallel line has the same slope. they just have different y-intersects (the y- value when x = 0).
the slope is the factor of x : -53
the y-intercept is given with the provided point (0, 2).
so, line j is
y = -53x + 2
Find the (unique) solution to the following systems of equations, if possible, using Cramer's Rule.
(a) x + y = 34 2x - y = 30
(b) 2x - 3y = 5 -4x + 6y = 10
(c) 3x + y = 7 2x - 2y = 7
After answering the presented question, we can conclude that As a equation result, the system of equations solution is [tex]x = 64/3 \\and \\y = 62/3.[/tex]
What is equation?In mathematics, an equation is a statement that states the equality of two expressions. An equation consists of two sides separated by an algebraic equation (=). The argument "2[tex]x + 3 = 9,"[/tex] for example, states that the sentence "2x Plus 3" equals the value "9." The goal of solving equations is to find the value or values of the variable(s) that will allow the equation to be true. Equations can be simple or complex, linear or nonlinear, and contain one or more parts. In the equation [tex]"x^2 + 2x - 3 = 0,"[/tex] the variable x is raised to the second power. Lines are used in many areas of mathematics, including algebra, calculus, and geometry.
[tex](a) x + y = 34[/tex]
[tex]2x - y = 30[/tex]
The matrix of coefficients is | 1 1 | | 2 -1 |
This matrix's determinant is 130 - 342 = -62.
We can obtain the values of x and y using Cramer's Rule as follows:
[tex]x = det(A1)/det(A) = (-64)/(-3), = 64/3.[/tex]
[tex]y = det(A2)/det(A) = (-62)/(-3), = 62/3.[/tex]
As a result, the system of equations solution is [tex]x = 64/3 and y = 62/3.[/tex]
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Note: Enter your answer and show all the steps that you use to solve this problem in the space provided.
Your parents are buying a house for $187,500. They have a good credit rating, are making a 20% down payment, and expect to pay $1,575/month. The interest rate for the mortgage is 4.65%. What must their realized income be before each month?
Be sure to include the following in your response:
The answer to the original question
The mathematical steps for solving the problem demonstrating mathematical reasoning
Their realized income must be $567,000 per year to make the monthly payments on the mortgage.
How much does a mortgage interest rate cost?The average interest rate on a 30-year fixed mortgage as of today, March 9, 2023, is 7.13%, up 7 basis points from one week ago. The average 30-year fixed refinancing interest rate is currently 7.12%, which is a decrease of 2 basis points over the previous week.
We must apply the following calculation to compute the amount of money needed each month to pay the mortgage:
Payment each month is (P * r) / (1 - (1 + r)(-n))
where:
P is the principal sum (the amount of the house minus the down payment)
r is the ongoing interest rate (annual interest rate divided by 12)
n is the overall number of payments (number of years multiplied by 12)
The major sum, as far as we are aware, is:
P = $187,500 - (20% * $187,500) = $150,000
The monthly interest rate is as follows because we also know that the interest rate is 4.65%:
r = 0.0465 / 12 = 0.003875
Finding the total number of payments is our last step. The number of months it will take to pay off the mortgage may be calculated using the knowledge that they will be paying $1,575 per month:
$1,575 = ($150,000 * 0.003875) / (1 - (1 + 0.003875)^(-n))
This equation is simplified, and the result is:
1 - (1 + 0.003875)^(-n) = ($150,000 * 0.003875) / $1,575
(1 + 0.003875)^(-n) = 1 - (($150,000 * 0.003875) / $1,575)
(-n) * log(1 + 0.003875) = log(1 - (($150,000 * 0.003875) / $1,575))
n = log(1 - (($150,000 * 0.003875) / $1,575)) / log(1 + 0.003875)
Calculating n, we discover that it roughly corresponds to 360 months (or 30 years).
Their realised income must therefore be:
Realized income is $1,575 multiplied by 12 months in a year for 30 years, or $567,000 annually.
Their realised income must be $567,000 annually in order to cover the mortgage payments.
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1.) The following two arguments are Invalid arguments, so each breaks at least 1 of the rules. Tell which
of the rules are broken in the following and briefly explain:
ALL P are Q
NO Q are S
Some Pare R
All A are B
All B are C
All Care A
The rule broken in the first argument is of undistributed middle.
The rule broken in the second argument is of exclusive middle.
What is Converse?
In logic and mathematics, converse of statement is formed by switching hypothesis and conclusion of original statement. For example, converse of the statement "If it rains, the streets get wet" is "If the streets get wet, it is raining."
The first argument violates the rule of the undistributed middle. The argument appears to be the fallacy of the converse of the inverse. This is a form of invalid reasoning where the contrapositive of a true statement is used as evidence for the original statement. The argument could be stated in syllogistic form as:
Premise 1: All P are Q.
Premise 2: No Q are S.
Conclusion: Some P are not S.
This argument is invalid because it violates the rule of the undistributed middle. The middle term Q is not distributed in either premise, which means that we cannot logically conclude anything about the relationship between P and S.
The second argument violates the rule of the exclusive middle. The argument appears to be the fallacy of the illicit conversion. This is a form of invalid reasoning where the subject and predicate terms of a statement are switched without changing the truth value of the statement. The argument could be stated in syllogistic form as:
Premise 1: All A are B.
Premise 2: All B are C.
Conclusion: All C are A.
This argument is invalid because it violates the rule of the exclusive middle. The argument assumes that there are only three categories of things: A, B, and C. However, this assumption is not justified, and there may be other categories that are not included in the argument.
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Find all the remaining zeros if 1-2i is a zero. f(x)=4x^(4)+17x^(2)+14x+65
Answer:
Step-by-step explanation:
If 1-2i is a zero of the polynomial, then its conjugate 1+2i is also a zero. This is because complex zeros of a polynomial with real coefficients always occur in conjugate pairs.
Let's use synthetic division to factor out the polynomial with the given zeros:
1-2i | 4 0 17 14 65
| 4 -8i -9+2i -12
-------------------
4 4 -8i -9+2i 53
So we have factored the polynomial as:
f(x) = (x - 1 + 2i)(x - 1 - 2i)(4x^2 + 4x - 53)
Now we need to find the zeros of the quadratic factor:
4x^2 + 4x - 53 = 0
Using the quadratic formula, we get:
x = (-4 ± sqrt(16 + 4453)) / 8
x = (-4 ± sqrt(848)) / 8
x = (-4 ± 4sqrt(53)) / 8
x = (-1 ± sqrt(53)) / 2
So the remaining zeros are (-1 + sqrt(53))/2 and (-1 - sqrt(53))/2.
What is the rate of change in miles ran from September 18th to September 21st?
sion Problems
How you solve each problem.
Yuki and Jake made 52 snowballs if they wanted to
share them evenly with 2 other friends, how many
snowbalis would each of the 4 of them get?
The answer is each of the 4 friends would get 13 snowballs.
52 divided by 4 = 13
Answer: 52 divided by 4 is 13 each of them would get 13 snowballlllsssssss!!!!
Step-by-step explanation:
just now
Mathematics
College
Look at the relative-frequency table below of the probability distribution of the discrete random variable X, with X = "the number of pets in a household."
x P(X = x)
0 .09
1 .29
2 .42
3 .15
4 .05
What is the expected value of pets in a randomly selected household?
Answer: To find the expected value of X, we need to multiply each possible value of X by its probability and then add up the results:
E(X) = Σ(x * P(X = x))
where Σ denotes the sum over all possible values of X.
Using the table given, we have:
E(X) = 0 * 0.09 + 1 * 0.29 + 2 * 0.42 + 3 * 0.15 + 4 * 0.05
E(X) = 0 + 0.29 + 0.84 + 0.45 + 0.2
E(X) = 1.78
Therefore, the expected value of pets in a randomly selected household is 1.78.
Step-by-step explanation:
what is the answer to this ?
Answer:
-f(x+3) and -2f(x)+4
Step-by-step explanation:
it is all the ones with a negative in front of the function, so that is -f(x+3) and -2f(x)+4.
Please help! For each function, state whether it is linear, quadratic, or exponential.
The types of functions are as follows:
1) Quadratic function
2) None of the above
3) Exponential function.
What is a function?
A relation between a set of inputs and a set of allowable outputs is called a function. It has the property that every input is associated with exactly one output. A function from one set X to another allocates precisely one element of the other set Y to each element of X. Both the set X and the set Y are referred to as the function's domain and codomain, respectively. The basic conception of functions was the relationship between fluctuating quantities and other variables.
The ways to determine the different functions are as follows:
a) If for a constant change in x-values, the y-values also change constantly, the function is linear.
b) If as the x values change constantly, the y- values also change, but the difference in differences of y-values remains constant, then the function is quadratic.
c) If the ratio between two consecutive y- values is the same, when x-values change constantly, then the function is exponential.
Let us look into each function.
1) x-values are increasing constantly by one.
The difference in y-values are:
13-7 = 6
21-13 = 8
31-21 = 10
43-31 = 12
Now the difference of difference in y-values.
8-6 = 2
10-8 = 2
12-10 = 2
This is constant. So the function is a quadratic function.
2) The difference in y-values are:
-6+21 = 15
-21+30 = 9
-33+30= -3
-30 + 33 = 3
This function can be categorised as none of the above.
3) The ratio of the consecutive y-values are:
-12/-3 = 4
-48/-12 = 4
-192/-48 = 4
-768/-192 = 4
Since the ratio is constant, the function is an exponential function.
Therefore the types of functions are as follows:
1) Quadratic function
2) None of the above
3) Exponential function.
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Choose ALL answers that describe the polygon.
Answer:
ParallelogramQuadrilateralRectangleStep-by-step explanation:
You want to know the names of a 4-sided figure with opposite sides congruent and adjacent sides perpendicular.
Congruent sidesA 4-sided figure is a quadrilateral.
When opposite sides are the same length, the quadrilateral is a parallelogram.
When corners of a parallelogram are right angles, it is a rectangle.
__
Additional comment
A rhombus also has congruent adjacent sides, as does a square. We are not told that is the case here. A trapezoid is not a parallelogram.
Find the Value of X using trigonometry. Round your answer to the nearest tenth.
Answer:
x ≈ 46.1
Step-by-step explanation:
using the sine ratio in the right triangle
sin19° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{15}{x}[/tex] ( multiply both sides by x )
x × sin19° = 15 ( divide both sides by sin19° )
x = [tex]\frac{15}{sin19}[/tex] ≈ 46.1 ( to the nearest tenth )
Write the inverse of the function p(x)=4x - 8. Show all work for full credit.
Answer:
To find the inverse of the function p(x) = 4x - 8, we need to switch the x and y variables and solve for y.
Step 1: Replace p(x) with y.
y = 4x - 8
Step 2: Switch x and y variables.
x = 4y - 8
Step 3: Solve for y.
Add 8 to both sides:
x + 8 = 4y
Divide both sides by 4:
y = (x + 8)/4
Therefore, the inverse of the function p(x) = 4x - 8 is q(x) = (x + 8)/4.
Step-by-step explanation:
Samuel has 7 cups of raisins. He uses 1/8 cup of raisins to make one muffin. How many muffins can be made with 7 cups of raisins?
Answer:
56 muffins
Step-by-step explanation:
Since it takes 1/8 cup to make one muffin, 1 cup can make 8 times as many muffins or 8 muffins with 1 cup of raisins
With 7 cups he can make 7 x 8 = 56 muffins
Elsa has completed 56 deliveries so far this week. She needs to make 70 deliveries for the week. What percentage of her deliveries has Elsa completed?
Answer:
80 percent
Step-by-step explanation:
12 people sit down for dinner at gullo's. 1/6 order a shrimp poboy. 1/2 order a cheese burger . The rest order a salad
What expression would you use to determine how many people ordered the salad
What expression would you use to determine how many people did not order the
How many people order a salad
We may take the number of people who ordered a salad out of the total to find the number of individuals who did not order one:
12 - 4 = 8 people did not order a salad.
The expression to use to estimate the number of persons that ordered the salad would be
(1/3) x 12 = 4 people ordered a salad
what is an expression?Every mathematical statement that includes numbers, variables, and an arithmetic operation between them is known as an expression or algebraic expression. In the phrase 4m + 5, for instance, the terms 4m and 5 are separated from the variable m by the arithmetic sign +.
Everything with a variable value is anything whose value changes over time. Typically, alphabetical letters like a, b, c, m, n, p, x, y, and z are used to denote expression variables. A combination of several variables and integers can be used to create a variety of expressions.
from the question:
We can utilize the information that 1/6 of customers ordered a shrimp po'boy and 1/2 ordered a cheeseburger to estimate how many individuals ordered the salad. Hence, the proportion of customers that choose a salad is:
1 - (1/6 + 1/2) = 1 - 2/3 = 1/3
Hence, to count how many people ordered the salad, the statement would be:
4 individuals (1/3) x 12 ordered salads.
We may take the number of people who ordered a salad out of the total to find the number of individuals who did not order one:
Those who did not order a salad were 12 - 4 = 8.
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Help ASAP PLEASE Determine the scale factor used to create the image
A 1/2
B 2
C1/4
D 4
Answer:
The answer is B)2
Step-by-step explanation:
As you can see, the length and height of the bigger rectangle is twice the length and height of the smaller rectangle.
Graph the linear equation by finding and plotting its intercepts.
x-y=1
Answer: To graph the linear equation x - y = 1, we can find its intercepts by setting one of the variables to zero and solving for the other.
Step-by-step explanation:
Setting x = 0, we get:
0 - y = 1
Solving for y, we get:
y = -1
So the y-intercept is (0, -1).
Setting y = 0, we get:
x - 0 = 1
Solving for x, we get:
x = 1
So the x-intercept is (1, 0).
Now we can plot the intercepts on a coordinate plane and draw a straight line passing through them:
|
| .
| .
| .
| .
| .
| .
------------------------------------------
| | | | |
-2 -1 0 1 2
Therefore, the graph of the linear equation x - y = 1 is a straight line passing through the points (0, -1) and (1, 0).
The combination of your locker contains 3 non-repeating digits from the numbers 0-9.
What would the answer be to the question above if you absolutely choose 9 as your first digit?
There are total 56 combination of your locker contains 3 non-repeating digits from the numbers 0-9.
Combinations are mathematical operations that count all possible arrangements of a set of components when the order in which they are selected is irrelevant. Components for combos can be selected in any hierarchy.
Moreover, there are two other kinds of combinations (the specific sequence is not relevant at this time): It's acceptable to repeat phrases like "coins in your pocket" (5,5,5,10,10) In the same way, lottery numbers (2,14,15,27,30,33)
Combinations are mathematical operations that count all possible arrangements of a set of components when the order in which they are selected is irrelevant. Components for combos can be selected in any hierarchy.
Permutations and combinations are compatible.
As the first digit is fixed i.e. 9,
So, there are 2 non-repeating digits left,
Using permutations,
we are left with 8 × 7 = 56 ways.
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The high temperatures for several days are shown in the table. Which answer describes the average rate of change from day 3 to day 5?
Responses
The high temperature changed by an average of −6 degrees per day from day 3 to day 5.
The high temperature changed by an average of −2 degrees per day from day 3 to day 5.
The high temperature changed by an average of −4 degrees per day from day 3 to day 5.
The high temperature changed by an average of −3 degrees per day from day 3 to day 5.
"From days 3 to 5, the high temperature changed by an average of almost 4 degrees per day," is the appropriate answer.
How to determine the average rate of change?We can determine the average rate of change from day 3 to day 5 by splitting the difference in high temperature between those two days by the distance between them (which is 2), or 2.
The highest temps on Day 3 was 85°F.
The highest temperature on Day 5 was 77°F.
Extreme temperature variation: 77°F to 85°F equals -8°F
Between day three and day five, there are two days.
(Change in maximum temperature) / (number of days) yields an average rate of change of -8°F / 2°F per day.
This leads to the conclusion that the right response is "The high temperature changed by an average of 4 degrees per day from day 3 to day 5".
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In the figure below, there are three right trangles. Complete the following.
(a) Write a similiarity statement relating the three right triangles.
(b)Complete each proportion.
a. ΔEGF~ΔGHF~ΔEHG are the similarities between the three right triangles.
b. HF/HG = GH/EH; EF/EG = EG/EH
Information about Similar Triangles?According to the similar right triangle theorem, if a right triangle's altitude is drawn from its right angle, two similar right triangles are created, and both similar right triangles are identical to the original right triangle. All three right triangles are essentially the same.
Similar triangles contain three pairs of comparable side lengths that are proportionate to one another, or whose ratios are identical.
The corresponding side lengths are taken into account when constructing similarity statements.
A similarity assertion linking the three right triangles is thus: ΔEGF~ΔGHF~ΔEHG.
b. They will have the following side ratios: EF/EG = EG/EH HF/HG = GH/EH
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Consider the given function.
ƒ(1): =
5,
I < -2
3, -2 <=<0
0,
0 <=<2
> 2
-3,
Which graph represents the given function?
A graph that represent the given function include the following: graph C.
What is a piecewise-defined function?In Mathematics, a piecewise-defined function can be defined as a type of function that is defined by two (2) or more mathematical expressions over a specific domain.
By critically observing the graph of the piecewise-defined function g shown in the image attached below, we can logically deduce the following functions;
When the domain is x < -2, we have:
f(x) = 5 (< should be used because the endpoint is an open circle).
When the domain is -2 ≤ x < 0, we have:
f(x) = 3 (< should be used because the endpoint is an open circle and ≤ for the closed circle).
When the domain is 0 ≤ x < 2, we have:
f(x) = 0 (< should be used because the endpoint is an open circle and ≤ for the closed circle).
When the domain is x ≥ 2, we have:
f(x) = -3 (≥ should be used because the endpoint is a closed circle).
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PLEASE HURRY WILL GIVE 100 POINTS!!!!!!!
Using the Distributive Property as a good first step to solving the equation, you could simplify to get which of these choices?
5(4x + 3) = -4(5 - 2x)
Answer:
e
Step-by-step explanation:
5(4x +3)=-4(5-2x)
5×4x +5×3=-4 ×5 -4 × -2x
20x +15=-20+8x
The mean weight of all Goliath grouper caught on the Treasure coast is 418 pounds, with a standard deviation of 74 pounds. Suppose a random sample of 39 Goliath Grouper from the Treasure Coast are caught and weighed.
Determine the probability that the average weight of the sample of 39 Goliath Grouper is within 14 pounds of the average weight of all Goliath Grouper caught on the Treasure Coast. Round the solution to four decimal places, if necessary.
Therefore, the probability that the average weight of the sample of 39 Goliath Grouper is within 14 pounds of the average weight of all Goliath Grouper caught on the Treasure Coast is approximately 0.2342 or 23.42%.
What is mean?In mathematics and statistics, the mean is a measure of central tendency of a set of numerical data. It is also known as the arithmetic mean or average, and is calculated by summing up all the values in the dataset and then dividing by the number of values. The mean provides a useful summary of the data as it gives an idea of the typical or average value in the dataset. It is commonly used in various fields, including finance, science, and social sciences, to analyze and interpret data. However, the mean can be sensitive to extreme values or outliers in the dataset, so it is important to consider other measures of central tendency, such as the median and mode, in addition to the mean.
Here,
We can approach this problem using the central limit theorem, which states that the distribution of sample means will be approximately normal, with a mean equal to the population mean and a standard deviation equal to the population standard deviation divided by the square root of the sample size.
Let's first calculate the standard error of the mean:
standard error of the mean = standard deviation / sqrt(sample size)
= 74 / √(39)
≈ 11.83
Next, we need to find the z-score corresponding to a sample mean within 14 pounds of the population mean:
z = (sample mean - population mean) / standard error of the mean
= (418 - 14 - 418) / 11.83
= -1.19
Using a standard normal distribution table or calculator, we can find that the probability of a z-score less than -1.19 is about 0.1171. Since we're interested in the probability that the sample mean is within 14 pounds of the population mean, we can multiply this probability by 2 to account for the area under the curve in both tails:
P(sample mean within 14 pounds of population mean) ≈ 2 * 0.1171 ≈ 0.2342
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Write an explicit formula for a_na n , the n^{\text{th}}n th term of the sequence 14, 16, 18, ...14,16,18,....
The n-th term οf the sequence is given by the fοrmula a_n = 2n + 12.
What is Arithmetic Prοgressiοn?An arithmetic prοgressiοn is a sequence οf numbers where each term is οbtained by adding a fixed value (called the cοmmοn difference) tο the previοus term. It is a type οf sequence that fοllοws a specific pattern, where the difference between cοnsecutive terms is cοnstant. Arithmetic prοgressiοns are cοmmοnly used in mathematics and variοus fields such as finance, physics, and cοmputer science.
The given sequence has a cοmmοn difference οf 2 between cοnsecutive terms. Therefοre, we can find the n-th term by adding (n-1) times the cοmmοn difference tο the first term οf the sequence.
The first term οf the sequence is 14, and the cοmmοn difference is 2.
Sο, the explicit fοrmula fοr the n-th term οf the sequence is:
a_n = 14 + 2(n-1)
Simplifying, we get:
a_n = 2n + 12
Therefοre, the n-th term οf the sequence is given by the fοrmula a_n = 2n + 12.
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the area is 32cm2 pls solve find the total shaded area
The triangular system has, by means of fractions, a total shaded area of 27 / 2 square centimeters.
How to determine the total shaded area of a triangleIn this problem we have the area of an entire triangle, from which we need to determine the total shaded area, this can be done by subtracting triangles from the entire triangle, by means of fractions, whose complete operation is shown below:
A = 32 - (1 / 4) · 32 - (3 / 4) · (1 / 4) · 32 - (3 / 4)² · (1 / 4) · 32
A = [1 - 1 / 4 - (3 / 4) · (1 / 4) - (3 / 4)² · (1 / 4)] · 32
A = 27 / 2 cm²
Please notice that shaded areas are positive and blank areas are negative.
By means of fractions, the total shaded area of the triangular system is equal to 27 / 2 square centimeters.
RemarkThe statement is incomplete. After a quick investigation we conclude that the complete statement is the following:
The area of a complete triangle (without blank spaces) is 32 square centimeters, please compute the total shaded area, that is, the area of the composite figure seen in the figure.
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At the end of the spring semester, the dean of students sent a survey to the entire freshman class. One question asked the students how much weight they had gained or lost since the beginning of the school year.
The average was a gain of µ = 15 pounds with a standard deviation of
= 6. The distribution of scores was approximately normal.
A sample of n = 4 students is selected, and the average weight change is computed for the sample.
What is the probability that the sample mean will be greater than M = 10 pounds? In symbols, what is p (M > 10) (four decimals)
The probability that the sample mean weight change is greater than 10 pounds is p(M > 10) = 0.9088.
What is the probability?To find the probability that the sample mean will be greater than M = 10 pounds, we need to standardize the sample mean using the formula for z-score:
z = (M - µ) / (σ / √n)
Substituting the given values, we get:
z = (10 - 15) / (6 / √4)
z = -1.33
Using a standard normal distribution table or calculator, we can find the probability that z is greater than -1.33, which is approximately 0.9088.
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Johnathan is using a hose to fill his pool with water. The pool already had 2,000 gallons of water in it before he started, and the hose puts water into the pool at a rate of 360 gallons per hour. Let g represent the number of gallons that the hose has put into the pool after a given number of hours. Let h represent the number of hours that the hose has put water into the pool. Let w represent the total number of gallons of water in the pool. Complete the equations so that: Equation 1 shows the relationship between g and h. Equation 2 shows the relationship between g and w.
Therefore, Equations 1 and 2 are: Equation 1: g = 360h
Equation 2: w = 2,000 + 360h.
What is equation?An equation is a mathematical statement that shows that two expressions are equal. It consists of two sides separated by an equal sign (=). The expressions on both sides of the equation can contain variables, constants, and mathematical operations such as addition, subtraction, multiplication, and division. The goal in solving an equation is to find the value of the variable that makes the equation true. Equations are used extensively in mathematics and science to model real-world phenomena and solve problems.
by the question.
We know that the hose puts water into the pool at a rate of 360 gallons per hour. Therefore, after h hours, the hose has put g gallons of water into the pool. We can express this relationship using the following equation:
Equation 1: g = 360h
We also know that the pool already had 2,000 gallons of water in it before Johnathan started filling it with the hose. Therefore, the total number of gallons of water in the pool after h hours is given by:
w = 2,000 + g
We can substitute the expression for g from Equation 1 into this equation to obtain an equation that relates g and w:
Equation 2: w = 2,000 + 360h
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