Part (A) = Paired, Part (B) = Not Paired, Part (C) = Paired, Part (D) = Paired
Part A:
Compare pre- (beginning of the semester) and post-test (end of the semester) scores of students
Paired, as a subject are the same in both.
Score
A score is a group of 20 (often used in combination with a cardinal number, i.e. fourscore to mean 80), but also often used as an indefinite number.
Part B:
Assess the gender-related salary gap by comparing the salaries of randomly sampled men and women.
Not paired.
Sample
A sample is an outcome of a random experiment. When we sample a random variable, we obtain one specific value out of the set of its possible values. That particular value is called a sample. The possible values and the likelihood of each are determined by the random variable's probability distribution.
Part C:
Compare artery thicknesses at the beginning of a study and after 2 years of taking Vitamin E for the same group of patients.
Paired, as a subject are the same in both.
Vitamin E
Vitamin E is a fat-soluble vitamin with several forms, but alpha-tocopherol is the only one used by the human body.
Part D:
Assess the effectiveness of a diet regimen by comparing the before and after weights of subjects.
Paired, as a subject are the same in both.
Weight
The weight of an object refers to the force of gravity that is acting on the object. Furthermore, its calculation is mass times the acceleration of gravity, w = mg. The SI unit of weight is the newton because weight is a force.
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Compare artery thicknesses at the beginning of a study and after 2 years of taking Vitamin E for the same group of patients.
Paired, as a subject are the same in both.
Vitamin E
Vitamin E is a fat-soluble vitamin with several forms, but alpha-tocopherol is the only one used by the human body.
Please find what the rent per unit needs to be to have a Net Operating Income (NOI) of $100,000.
Assumptions
Please use the following assumptions below:
Rent per unit (per month)
Vacancy Rate (% of Potential Gross Income) 5%
Operating Expenses (% of Effective Gross Income) 30%
Number of Units 18
*Please fill out the blue area Rent per unit (per month)
Vacancy Rate (% of Potential Gross Income)
Operating Expenses (% of Effective Gross Income)
Number of Units
The rent per unit should be $8,354.22 to generate a Net Operating Income (NOI) of $100,000, given the vacancy rate and operating expenses.
What are the operating expenses?The operating expenses are costs that must be deducted from the gross operating income to arrive at the net operating income.
The operating expenses do not include some period expenses, which are indirect costs.
Total
Rent per unit (per month) = $696.19 ($8,354.22/12) $150,376
Vacancy Rate (5% of Potential Gross Income) 7,519
Effective Gross Income $142,857
Operating Expenses (30% of Effective Gross Income) 42,857
Net Operating Income (NOI) $100,000
Number of Units 18
Working Backwards:Gross operating income = net operating income + operating expenses
Operating expenses = 30% of effective gross income
Net operating income = 70% of effective gross income (100 - 30%)
= $100,000
Effective Gross Income (100%) = $142,857 ($100,000 ÷ 70%)
Vacancy rate = 5% of potential gross income
Effective Gross Income = 95% (100 - 5)
Potential gross income = $150,376 ($142,857 ÷ 95%)
Number of units = 18
Rent per unit = $8,354.22 ($150,376/18)
Rent per month = $696.19 ($8,354.22 ÷ 12)
Thus, a rent of $8,354.22 per unit can generate a Net operating income of $100,000.
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Write the complete proof in your paper homework and for online (only) complete the probing statement (if any) that is a part of your proof or related to it.
Given: BD ≅ BF
DE⊥BC
F K ⊥ AB
Prove: ED ≅ F K
The triangle ΔBHK and ΔBDE are congruent with each other. Then the side length ED is equal to the side length HK.
What is the triangle?The polygonal shape of a triangle has a number of sides and three independent variables. Angles in the triangle add up to 180 °.
Replace F with H.
The triangles ΔBHK and ΔBDE are shown.
In triangles ΔBHK and ΔBDE, then we have
BD ≅ BH (Given)
∠HBK = ∠DBE (Common angle)
∠BHK = ∠BDE = 90° (Right angle)
The triangle ΔBHK and ΔBDE are harmonious with one another. Then, at that point, the side length ED is equivalent to the side length HK.
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There are 99 males and 121 females participating in a marathon. What percent of the participants are female?
Enter your answer in the box.
_____%
determine whether the improper integral diverges or converges. evaluate the integral if it converges. 14/(x-8^2
Therefore ,the answer of this integration problem comes out to be 4/9.
Integrity, what is it?To describe notions like displacement, area, volume, and other results of the combination of incredibly small inputs, an integral in mathematics imparts numerical values to functions. Integration is a method used in the process of integral discovery.
Here,
Given :
=> [tex]\int\limits^9_7 {\frac{14}{(x-8)^{2} } } \, dx[/tex]
=> substitute x- 8 =u
=>du/dt =d(x-8)/dx = 1
=>du/dt =1
=> [tex]\int\limits^9_7 14{\frac{1}{(x-8)^{2} } } \, dx[/tex]
Substituting x- 8 =u
=> [tex]\int\limits^9_7 14{\frac{1}{(u)^{2} } } \, dx[/tex]
=> 14 [ [tex]\left \{ {{9} \atop {7}} \right. (\frac{-1}{u} )[/tex] ]
=> 14( -1/9) + 1/7)
=> 14 ( ( 9 -7 ) / 63 )
=> 14 (2/63)
=> 28/63
=>4/9
Therefore ,the answer of this integration problem comes out to be 4/9.
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What is the lateral of the drawing
Answer:
Step-by-step explanation:
the lateral area of the drawing the lateral area of the drawing is 40 mi2. Area rectangle = w * l 5 * 2 = 10 mi² (area 1 rectangle) then you multiply by 4 10 * 4 = 40 mi² or 5 * 2 * 4 = 40 mi²
Answer:
294 m²
Step-by-step explanation:
You want the lateral area of a regular hexagonal prism with side lengths 7 m and height 7 m.
Lateral areaThe lateral area is the sum of the areas of the 6 square faces.
Each of the 6 faces is a square 7 m on the edge. Its area is ...
(7 m)² = 49 m²
There are 6 of these square faces, so their total area is ...
6 × 49 m² = 294 m²
The lateral area of the prism is 294 m².
To prepare for his mountain biking trip, Rhyan bought four tire patches. Rhyan paid using a gift card that had $22.20 on it. After the sale, Rhyan’s gift card had $1.90 remaining.
Which equations could you use to find the price of one tire patch? Select all that apply.
4x – 1.9 = 22.2
4x – 22.2 = 1.9
4x + 1.9 = 22.2
4x + 22.2 = –1.9
22.2 – 4x = 1.9
Answer:
4x + 1.9 = 22.2
22.2 - 4x = 1.9
Step-by-step explanation:
Define the variable:
Let x be the cost of one tire patch (in dollars).Given information:
Number of tire patches purchased = 4Total amount available to spend = $22.20Amount remaining after sale = $1.90First equation
The cost of 4 tire patches and the amount remaining on the gift card equals the total amount on the gift card:
⇒ 4x + $1.90 = $22.20
⇒ 4x + 1.9 = 22.2
Second equation
The total amount on the gift card less the cost of 4 tire patches equals the amount remaining:
⇒ $22.20 - 4x = $1.90
⇒ 22.2 - 4x = 1.9
Answer:
4x + 1.9 = 22.2
22.2 - 4x = 1.9
Step-by-step explanation:
Find the average rate of change of g (x)=-2x³ +5x² from x=2 to x = 3.
Simplify your answer as much as possible.
The average rate of change of g (x)=-2x³ +5x² from x=2 to x = 3 is
a(x)= -13
What is meant by average rate of change?It represents the average change in the function's per-unit value during that time period. On the function's graph, it is generated from the slope of the line connecting the interval's ends. Following is the formula for the average rate of change:
a(x) = [f(b) - f(a)]/(b - a)
where,
a(x) = Average Rate of Change
f(a) = Function Value at a
f(b) = Function Value at b
Given,
g (x)=-2x³ +5x² from x=2 to x = 3
Average rate of change is a(x)
g (x)=-2x³ +5x²
Put x=2 in the above equation
g(2)= -2(2)³+5(2)²
= -16+20
=4
g(2)=4
Now, put x=3 in the above equation
g(3)= -2(3)³+5(3)²
= -57+45
= -9
We know that,
Average rate of change a(x)= (g(b)-g(a))/(b-a)
a(x)= g(3)-g(2)/(3-2)
a(x)= (-9-4)/1
a(x)= -13
Therefore, the average rate of change a(x)= -13
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Drag the tiles to the boxes to form correct pairs. Not all tiles will be used.
Determine which statements are the converse, inverse, and contrapositive of the following statement.
If a figure is a square, it is a polygon.
Answer:
Step-by-step explanation:
For g(x) = 12x - 2, evaluate g (1).
A. -1
B. 1
C. 2
D. -2
Answer:
B
Step-by-step explanation:
g(x) = 12x - 2
g(1/4) = 12(1/4) - 2 ==> plug in 1/4 for x
g(1/4) = 12 * 1/4 - 2
g(1/4) = 12/4 - 2
g(1/4) = 3 - 2
g(1/4) = 1 ==> B
Answer:
Step-by-step explanation:
To evaluate g(1) for the function g(x) = 12x - 2, you can substitute the value 1 for x in the function:
g(1) = 12(1) - 2
g(1) = 12 - 2
g(1) = 10
Therefore, g(1) = 10. B
Let S represent the number of randomly selected adults in a community surveyed to find someone with a certain genetic trait.The random variable S follows a geometric distribution with mean 4.66. Which of the following is a correct interpretation of the mean?answer choicesA value randomly selected from the distribution of S is expected to be 4.66.In repeated sampling from the distribution of S, the average of the values will approach 4.66.For a sample of values randomly selected from the distribution of S, the average of the sample will be 4.66.The probability is 0.66 that a value randomly selected from the distribution of S will be close to the mean.For a sample of values randomly selected from the distribution of S, the average of the sample will vary from the population mean by no more than 4.66.
Step-by-step explanation:
correct interpretation of the mean?answer choicesA value randomly selected from the distribution of S is expected to be 4.66.In repeated sampling from the distribution of S, the average of the values will approach 4.66.For
In gym class, the yellow team and the blue team played soccer. Ali doesn't remember the final score of the game, but she does remember the following.
*There were six goals scored in total
*Neither team scored more than two goals in a row at any point in the game
*The blue team won the game
Determine all the possible final scores and the different ways each score could have been obtained.
The final score is of:
4-2 for the Blue team.
The number of ways that each score could have been obtained is of:
8.
How to obtain the score?These three bullet points are given:
There were six goals scored in total.Neither team scored more than two goals in a row at any point in the game.The blue team won the game.The possible scores with six goals and the blue team winning are of:
6 - 0.5 - 1.4 - 2.If the team didn't score more than two goals in a row at any point of the game, the difference is of two, hence the score was 4 - 2.
The goals can be arranged as follows:
Blue - Blue - Yellow - 3!. (for the last 3 goals there are no restrictions).Blue - Yellow - Blue - Yellow - Blue - Blue.Yellow - Blue - Blue - Yellow - Blue - Blue.Then the total number is of ways that the goals could be obtained is of:
3! + 1 + 1 = 8.
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Aaliyah invests $7,000.00 at 4% simple interest for 1103 days.
How much interest is earned over the 1103 day period?
The interest earned over the 1103 day period is _______
How much is in the account at the end of the 1103 day period?
Aaliyah will have __________
in the account at the end of the 1103 day period.
The interest earned over the 1103 day period is $840
Aaliyah will have $7840 in the account at the end of the 1103 day period.
What is simple interest?Simple interest is defined as the amount of money that is paid to an individual following an investment that is made to an account.
The amount of money invested = $7,000.00
The rate of interest= 4%
The time of investment = 1103 = 3 years
Simple interest = P×T×R/100
= 7000×4×3/100
= 84000/100
= $840
The amount of money that is in the account at the end of the 1103 day period = 7000 + 840 = $7,840
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Harry and Tim both made New Year’s Resolution. Harry made 5 more resolutions than Tim. Together they made 13 resolutions. How many resolutions did Harry make?
The specified number of New Year's resolutions Harry makes which is 5 more than the resolutions Tim makes, and the total number of resolutions of 13 indicates a word problem with a solution that Harry makes 9 New Year's resolutions.
What is a word problem?A word problem is a mathematics or science question, presented using complete sentences, rather that mathematical expressions or science symbols.
A word problem consists of presenting a problem in terms of a real situation such, with the solution being obtained easiest through the use of mathematical or science procedures.
Let x represent the number of resolutions Tim makes
The number of resolutions Harry makes = x + 5
The number of resolutions Harry and Tim made together = 13
Therefore, we get; x + x + 5 = 13
2·x + 5 = 13
2·x = 13 - 5 = 8
x = 8 ÷ 2 = 4
The number of resolutions Tim makes, x = 4
The number of resolutions Harry makes = x + 5
Therefore, the number of resolutions Harry makes = 4 + 5 = 9
Harry made 9 New Year's resolutions
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help me out on this please
The results were as follows: a) x = +6, -6; b) x = +-2.6591; c) x = +- 3.1622; and d) x =+-5.
What are square root of a number?Get a number that, when multiplied twice by itself, equals the original number in order to find the square root of any integer. Similar to this, we must discover a number that, when multiplied three times by itself, equals the original number in order to get the cube root of any integer. equivalently for 4throots and so on.
We have
a)
[tex]x^{2}[/tex] = 36
so x= [tex]\sqrt{36}[/tex]
x = +6, -6
b)
[tex]x^{2}[/tex] = [tex]\sqrt{50}[/tex]
x = [tex]\sqrt[4]{50}[/tex]
x = +-2.6591
c)
[tex]x^{2}[/tex] = [tex]\sqrt{100}[/tex]
x = [tex]\sqrt[4]{100}[/tex]
x = +- 3.1622
d)
2[tex]x^{2}[/tex] = 50
[tex]x^{2}[/tex] = 50/2
[tex]x^{2}[/tex] = 25
x =+-5
Thus a) x = +6, -6; b) x = +-2.6591; c) x = +- 3.1622; and d) x =+-5.
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A bus company took a tour bus on the ferry when there were 30 people aboard. The ferry charged the bus company $180. The following week, the bus had 50 people on board and the ferry charged them $220. How much is the "base rate" for the empty bus? hint: look at the difference between number of people and cost to get cost per person and then cost without people
How much does each person cost?
Write an equation to show cost, c, of a bus with x number of people on it
Answer:
Base rate: $120
Rate: $2 per person
Equation: f(x)=2x+120
Step-by-step explanation:
If 30 people cost $180 and 50 people cost $220, the charge for 20 extra people is $40. This means, [tex]\frac{220-180dollars}{50-30people}=\frac{40dollars}{20people}=2\frac{dollars}{person}[/tex].
These values correspond to a base rate for the bus of $120.
The function for the cost per bus with x number of people on it would be:
[tex]f(x)=2x+100[/tex]
This can be checked by using the values given in the problem:
[tex]f(30)=2(30)+120=180\\f(50)=2(50)+120=220[/tex]
The base rate of $120 and $2 per person satisfies the given equation and established values.
O For a period of time, an island's
population grows exponentially. If the
continuous growth rate is 3% per year and
the current population is 1,767, what will
the population be 10 years from now?
0.03 - 10
≈2,385
5,867
A) 1767e
3) 1767e0.12.
C) 442e0.03-10
D) 1767e0.09
10
≈
≈597
0.09 - 10
≈4,346
valuate each expression
The population of the island after 10 years will be approximately 2385.
What is the formula for exponential growth and exponential decaying function?The formula for exponential growth is [tex]y = y_0e^{(kt)}.[/tex]
The formula for exponential decay is [tex]y = y_0e^{(-kt)}[/tex].
Increases in a population's or a dispersed group's membership are referred to as population growth. The actual annual increase in the human population is about 83 million, or 1.1%.
Given, an island's population grows exponentially and the continuous growth rate is 3% per year and the current population is 1,767.
∴ The population be 10 years from now will be,
[tex]y_{10} = y_0e^{(0.03)\times10}[/tex].
We have written 3% as a decimal and it is the correct way of putting it into the formula for exponential growth or decaying equations.
[tex]y_{10} = 1767e^{0.3}[/tex].
[tex]y_{10} = 1767\times1.35[/tex].
[tex]y_{10} = 2385[/tex].
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solve: 2cos(x)+sqrt2=0 less than x less than 2pi
Check all that apply.
a.pi/4
b.3pi/4
c.5pi/4
d.7pi/4
The option that applies to 2cos(x)+sqrt2=0 less than x less than 2pi is options C and D:
c.5pi/4
d.7pi/4
What is the solution about?To solve this equation, we can start by isolating the cosine term on one side of the equation:
[tex]2cos(x) = -\sqrt{2[/tex]
[tex]cos(x) = \sqrt{\frac{2}{2} } }[/tex]
The cosine function has a range of [-1, 1], so the only possible value for cos(x) is -sqrt(2)/2. This means that the only solution to the equation is x = acos(-sqrt(2)/2).
The inverse cosine function, denoted as "arccos," gives us the angle whose cosine is a given value. In this case, we want to find the angle whose cosine is -sqrt(2)/2. The domain of the arccos function is [-1, 1], so the range of the function is [0, pi]. This means that the solution x must be an angle in the range [0, pi].
Since the problem specifies that the solution must be in the range [0, 2pi], we need to consider all possible angles in that range that satisfy the equation. This means that the possible solutions are:
[tex]x = acos(-\sqrt (2)/2) + 2\pi *k[/tex]
where k is an integer.
Substituting the values from the given choices into this equation, we find that the possible solutions are:
[tex]a. x = acos(-\sqrt{\frac{2}{2} } + 2\pi 0 = \pi /4 + 0 = \pi /4\\b. x = acos(-\sqrt{\frac{2}{2} } + 2\pi 1 = \pi /4 + 2\pi = 3\pi /4\\c. x = acos(-\sqrt{\frac{2}{2} } + 2\pi 2 = \pi /4 + 4\pi = 5\pi /4\\d. x = acos(-\sqrt{\frac{2}{2} } + 2\pi 3 = \pi /4 + 6\pi = 7\pi /4[/tex]
Therefore, the correct answer is c. and d.
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Answer:
b.3pi/4
c.5pi/4
Step-by-step explanation:
Draw the dilation of ABCD using center D and scale factor 1/3. Label the dilation IJKL
According to question.
Given data,
The dilation of ABCD using centre D
And scale factor 1/3
Lebel the dilation IJKL.
With the help of figure,
The dilation of ABCD shown in the figure,
The centre of D shown in the figure,
when EFGH, IJKL are obtained from scaling factor ½,1/3 respectively,
then,
ABCD≈EFGH
and
ABCD≈IJKL
Therefore,
EFGH≈IJKL
(Quadrilaterals similar to the same quadrilateral)
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Four times a number is equal to the number increased by 12. Find the number
Answer:
number is 4
Step-by-step explanation:
let n be the number then 4 times the number is 4n and
4n = n + 12 ( subtract n from both sides )
3n = 12 ( divide both sides by 3 )
n = 4
that is the number is 4
Twenty percent of U.S. adults have some type of mental illness. You randomly select 6 U.S. adults. Find the probability that the number of adults having some type of mental illness is:
a)exactly two
b)at least one
c)less than three
d)find the mean, variance, and standard deviation for this distribution
The mean is 1.2 ,variance is 0.96 and standard deviation of the given data is 96 square root.we can find all these data by using formula of probability.
what is probability?Probability means possibility.It is a branch that deals with occurrence of random event.The value is given in the probability from 0 to 1.Probability is how likely something is to happen.It is used in real life for analysis data.we can find probability to favorable outcomes divided by total outcomes.
What is difference between standard deviation and variation?Standard deviation measures how far apart numbers are in a data set.Variance gives us the actual value to how much the numbers in a data set vary from the mean.The variance is equal to the square standard deviation and standard deviation is the square root of the variance.
NOW we have data
Person(ill)=20% =0.20 n=6
For Exactly two p(x) =2
now we get 24.58% by using binomial theorem and putting value in the formula.
NOW for at least one p(x)>1 By putting value we get 0.7379.
Now for less than three p(x<30) we get 0.9011
Now to find mean
Mean=person (ill) multiply n
Mean = 0.20 * 6
Mean= 1.2
Variance= 1.2*0.80
=0.96
IN the last we find standard deviation.it will be 96 square root.
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on Monday Therease went to the doctor and got an antibiotic for strep throat. The doctor told her take a dose of 4.8 ml every 12 hours for 7 days. If Thereas took her first dose at 9:00 AM on Monday, what day and time should she take her 7th dose?
The day and time that Thereas should take her 7th dose, given that she should take the dose every 12 hours is 9 am on Thursday.
How to find the day to take the dose ?From the first day that Therease took the dose which was 9 am on Monday, the table to show the days and times she takes the other doses, based on her taking them every 12 hours is:
Day Time
First dose Monday 9 am
Second dose Monday 9 pm
Third dose Tuesday 9 am
Fourth dose Tuesday 9 pm
Fifth dose Wednesday 9 am
Sixth dose Wednesday 9 pm
Seventh dose Thursday 9 am
Therese will therefore take the seventh dose at 9 am on Thursday.
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Please help me with this problem, I've been trying for more than twenty minutes. pls help.
Answer:
The inequality has two prime solutions. To determine the number of prime solutions that the inequality has, we need to first solve the inequality to find its solutions. Since the inequality involves a polynomial, we can use the techniques of algebraic manipulation and factoring to solve it.
We begin by multiplying out the left-hand side of the inequality to obtain:
(n²-17)(n²-100)≤0
This expression can be further simplified by multiplying out the terms in the brackets, which gives us:
n⁴ - 117n² + 1700 ≤ 0
To solve this inequality, we need to find the values of n that make the left-hand side equal to zero. We can do this by setting the expression equal to zero and then factoring it to obtain:
n⁴ - 117n² + 1700 = 0
n² (n² - 117) + 1700 = 0
(n² - 19)(n² - 90) + 1700 = 0
(n² - 19)(n² - 90) = -1700
To find the solutions of this equation, we need to find the values of n that make the left-hand side equal to zero. We can do this by setting each factor equal to zero and solving for n:
n² - 19 = 0 or n² - 90 = 0
n² = 19 or n² = 90
n = ±√19 or n = ±√90
Since the problem states that n is a prime number, we need to consider only the solutions where n is a prime number. Of the solutions above, only n = ±√19 and n = ±√90 are prime numbers, so these are the only solutions that we need to consider. Since there are two such solutions, the inequality has two prime
Y is the midpoint of XZ and W is the midpoint of VX. If VZ = s + 14 and WY = s, what is the value of s?
Y is the midpoint of XZ and W is the midpoint of VX. If VZ = s + 14 and WY = s, the value of s is 14.
Define midpoint.The point that divides a line segment into two equal halves is known as the midway in geometry. A point that divides a line segment into two equal halves is the midpoint of the segment. In other words, the line segment's midpoint is precisely in the middle. The midpoint of a line segment is known as the midpoint in geometry. It is the centroid of the segment and of the ends, and it is equally distant from both of them. It cuts the section in half.
Given,
VZ = s + 14
WY = s
VZ bisects WY
VZ = 2WY
s + 14 = 2(s)
s + 14 = 2s
2s - s = 14
s = 14
Y is the midpoint of XZ and W is the midpoint of VX. If VZ = s + 14 and WY = s, the value of s is 14.
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1536 divide by 48. State your answer and describe
whether your answer is reasonable or
not.
Answer:
32
Step-by-step explanation:
1536 divided by 48 is 32.
I'd say the answer is reasonable because the number is a positive number and also because each item/thing is equal to they are the same thing and nothing is too big or too small.
Given the function g(x) = |x - 4|, find the value of g(1).
The length of a shirt is 80 cm. Fatima needs to buy a fabric twice this length. What length of the fabric must she buy?
Answer:
160 cm
Step-by-step explanation:
the question says twice this length
the length is 80 cm, therefore
[tex]80 \times 2 = 160[/tex]
This is because the question is dimply asking you to double the length of the shirt
5. A person's weight varies directly with gravity. If a person weighs 180 pounds on Earth, they will weigh
only 30 pounds on the moon. If Haresh weighs 54 pounds on Earth, how much would he weigh on the
moon?
When Haresh weighs 54 pounds on Earth, his weigh on the moon will be 9 pounds.
How to calculate the value of the weight?From the information, person's weight varies directly with gravity. If a person weighs 180 pounds on Earth, they will weigh only 30 pounds on the moon.
The constant of proportionality will be:
= 180 / 30.
= 6..
Therefore, Haresh weighs 54 pounds on Earth, his weigh on the moon will be:
= 54 / 6
= 9 pounds.
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so I am still very confused because when I do it the same it tells me I am wrong did I do something wrong my assignment is DUE TODAY!!!!!!!!! :(
PLEASE HELP ME NOW :(
Answer:
7.5 minutes
4/3 km
Step-by-step explanation:
Use a proportion.
2 km is to 3 min as 5 km is to x min
2/3 = 5/x
2x = 3 × 5
2x = 15
x = 7.5
Answer: 7.5 minutes
2 km is to 3 min as x km is to 2 min
2/3 = x/2
3x = 2 × 2
3x = 4
x = 4/3
Answer: 4/3 km
Let M be the amount of money left on the card, t weeks after the beginning of the fall semester. enter a linear equation to model the data. use week 0 and week 14 to calculate the slope. round your slope to 2 decimal places.
The amount of money on the card decreases by $1.43 per week. The slope is a measure of the steepness of a line
The slope can be positive, negative, or zero. A positive slope means that the line slopes upward from left to right, which means that the value of the dependent variable (in this case, M) increases as the value of the independent variable (t) increases. A negative slope means that the line slopes downward from left to right, which means that the value of the dependent variable decreases as the value of the independent variable increases.
To find the linear equation that models the data, we need to find the slope of the line. The slope is calculated by using the formula:
slope =[tex](y_2 - y_1) / (x_2 - x_1)[/tex]
Where [tex](x_1, y_1)[/tex] and [tex](x_2, y_2)[/tex] are two points on the line. In this case, we can use week 0 and week 14 as our two points. Let's say that at week 0, M = $100 and at week 14, M = $80. Then the slope would be:
slope = ($80 - $100) / (14 - 0) = -$20 / 14 = -$1.43
So the linear equation that models the data is:
M = -$1.43 * t + $100
The missing part in the question is shown in the attachment.
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What are the values of t and u?
t = ?°
u= ?
By using properties of triangle, it can be calculated that-
t = 60°
u = 8
What is a triangle?
A triangle is a three sided two dimensional figure. A triangle has three sides and three interior angles.
Based on the sides of a triangle, triangle may be classified as equilateral, isosceles and scalene
Triangle whose all three sides are equal is called equilateral
Triangle whose two sides are equal is called isosceles
Triangle whose all sides are unequal is called scalene
Here,
[tex]\angle[/tex]FGE = 90°
[tex]\angle[/tex]GFE = 30°
[tex]\angle FEG[/tex] = 180 - (90 + 30)
= 180 - 120
= 60°
t = 60°
Since FE = HE and [tex]\Delta[/tex]FGE and [tex]\Delta[/tex]FGE are right angle triangles,
So FG = FH
u = 8
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