Answer:
(a) The linear formula that models the lean of the renovated tower is:
I = (17 / 300)t + 162
In 2150, the tower will lean 170.44 inches off the perpendicular.
Step-by-step explanation:
Data:
Renovators were able to reduce the tower's 1990 tilt by 17 inches.The resultant tower leans 162 inches off the perpendicular.In 2001, officials forecast that it would take 300 years for the tower to return to its 1990 tilt.(a)
A linear formula has the form:
y = mx + bwhere
y is the dependent variablex is the independent variablem is the slope, andb is the y-axis interceptionIn this case, the dependent variable is the tilt of the tower, measured as the number of inches from the perpendicular. Let´s call "I" this variable. And what does it depend on? It depends on the variable time. The tilt of the tower varies over time.
Therefore, the time (in years) is the independent variable. Let´s call "t" this variable.
The slope (m) is the change in the dependent variable for each unit of the independent variable. So, it is the change in the number of inches from the perpendicular, for each year elapsed.
Officials forecast that it would take 300 years for the tower to return to its 1990 tilt. In other words, 300 years to the tower to lean 17 inches. Or, the tower will lean 17 inches in 300 years. That is the slope (m).
m = (17 / 300) inches per year
The y-axis interception (b) is the value of the dependent variable (I) when the independent variable (t) is equal to zero.
Our t=0 occurs when the tower was reopened, in 2001.
At that time, the tower leaned 162 inches off the perpendicular.
b = 162
Then, the linear formula that models the lean of the renovated tower is:
I = (17 / 300)t + 162
or
I = 162 + (17 / 300)t
To predict the lean of the tower in 2150, let´s substitute the independent variable t in the formula for the time elapsed from 2001 (our t=0) to 2150.
Time elapsed = 2150 - 2001 = 149 years
I = 162 + (17 / 300) * 149
I = 170.44
In 2150, the tower will lean 170.44 inches off the perpendicular.
Final answer:
To predict the lean of the Tower of Pisa in 2150, plug 149 years into the formula l = 162 + (17/300)t, resulting in approximately 170.45 inches lean from the perpendicular.
Explanation:
The question involves constructing a linear model and making a prediction based on that model. Given the information, the linear formula to model the lean of the renovated Tower of Pisa is [tex]\l = 162 + (17/300)t[/tex], where l represents the lean of the tower inches away from the perpendicular, and t represents the number of years since 2001.
To predict the lean of the tower in 2150 using the formula, we need to first calculate the number of years from 2001 until 2150, which is 2150 - 2001 = 149 years. Plugging this value into the formula, we get:
[tex]\[ l = 162 + (17/300) \times 149 \][/tex]
Now, let's calculate the result:
[tex]\[ l = 162 + 0.0567 \times 149 \][/tex]
[tex]\[ l = 162 + 8.4483 \][/tex]
[tex]\[ l = 170.4483 \][/tex]
Therefore, rounding to two decimal places, the predicted lean of the tower in 2150 would be approximately 170.45 inches off the perpendicular.
Suppose that IQ scores have a bell-shaped distribution with a mean of 97 and a standard deviation of 12. Using the empirical rule, what percentage of IQ scores are greater than 133? Please do not round your answer.
Final answer:
Approximately 0.3% of IQ scores are greater than 133 according to the empirical rule, which states that 99.7% of values fall within three standard deviations of the mean in a bell-shaped distribution.
Explanation:
Using the empirical rule (also known as the 68-95-99.7 rule) for a bell-shaped distribution, we can determine the percentage of IQ scores that fall at different distances from the mean.
A score of 133 is three standard deviations above the mean (since the mean is 97 and the standard deviation is 12, 97 + 3(12) = 133). According to the empirical rule, approximately 99.7% of IQ scores fall within three standard deviations of the mean. Therefore, to find the percentage of scores greater than 133, we subtract the bottom 99.7% from 100%, resulting in approximately 0.3%.
Thus, following the empirical rule, 0.3% of IQ scores are greater than 133.
An advertiser wishes to estimate the proportion of adults in Utah who already own a gym membership. He wishes to create a 90% confidence interval with a margin of error of 0.10. How many people must he sample?
Answer:
Step-by-step explanation:
Given that an advertiser wishes to estimate the proportion of adults in Utah who already own a gym membership.
Confidence level wanted = 90%
Critical value Z for 90% = 1.645
p is not known hence for maximum std error we know p =0.5
Let us take p =0.5
Margin of error = [tex]1.645*\sqrt{\frac{pq}{n} } =\\1.645*0.5(\frac{1}{\sqrt{n} } ) 0.10\\n=67.65\\n~68[/tex]
Sample size can be 68
Antonio has $80 in his saving account. He plans to add $32 each month for the next 6 months. How Much Will Antonio have in his account at the end of each month?
Lee needs 15 pieces of string, each one half of a inch long she cut a 6 inch piece of drink into pieces that are each one half of an inch long, how many more pieces of string does she need?
Answer:
3
Step-by-step explanation:
A 6-inch piece of string can be cut into 12 pieces that are 1/2 inch each. If Lee needs 15 pieces, she needs 3 more.
___
Each inch is divided into 2 pieces. That's what 1/2 inch means. 6×2 = 12.
Consider the graph shown. Determine if the graph shows two quantities that vary directly. If possible, determine the constant of proportionality. Explain your reasoning.
Answer:
the quantities do NOT vary directly
Step-by-step explanation:
A graph showing a proportional relationship is a straight line through the origin. This graph goes through (0, 100), so does NOT show a proportional relationship. y does NOT vary directly with x.
what is the estimated product when 620 and 374 are rounded to the nearest hundred and multiplied?
The answer is 240000
Step-by-step explanation:
When you round 620 to the nearest hundred,you will get 600
and when you round 374 to the nearest hundred,you will get 400
multiplying the product after rounding them will give 600×400
=240000
The estimated product when 620 and 374 are rounded to the nearest hundred and multiplied is 240000.
What is a Product?Product is the output obtained when two numbers are multiplied.
The product has to be obtained of numbers 620 and 374
Rounding to nearest hundred
620 can be written as 600
374 can be written as 400
=> 600 * 400
= 240000
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Which company would be best served by the use of inferential statistics?
a company that wanted to know if a new waterproofing treatment worked better than their existing treatment
a company that wanted to know the incomes of their customers
a company that wanted to know the rate of workplace injuries in each of its factories
a company that wanted to know the failure rate of different brands of tires before purchasing tires for its fleet of vehicles
please helpppppppppppppppppppp
I think it 8 I think this is the right answer
Answer:
g(3) = 34
Step-by-step explanation:
To evaluate g(3) substitute x = 3 into g(x), that is
g(3) = 4(3)² - 3(3) + 7 = (4 × 9) - 9 + 7 = 36 - 9 + 7 = 34
Simplify 3√32x^4 z
Assume x and z are nonnegative
Answer:
12x²√2z
Step-by-step explanation:
Given to simplify
3√32x⁴z
This can be written as
3* √32 *√x⁴ *√z--------------------------break down into terms
3*√16*√2*√x⁴*√z------------------------identifying perfect squares
3 * 4* √2 * x² *√z---------------------------collect like terms
12 * x² * √2 * √z-----------------------multiplication
12x² *√2z------------------------puting terms under same root together
12x²√2z
Mrs. Kellen's most recent math test consisted of 50 questions. Some of the questions were worth two points and the rest of the questions were worth 3 points. If there were 115 points available on the test, how many questions were worth 2 points?
Answer:
The answer to your question is: 35 questions worth 2 points and 15 questions worth 3 points.
Step-by-step explanation:
Data
Number of questions = 50
Total points = 115
x = questions worth 2 points
y = questions worth 3 points
Process
write to equations
(1) --------------- x + y = 50
(2) -------------- 2x + 3y = 115
Solve them by substitution
x = 50 - y
2 (50 - y) + 3y = 115
100 - 2y + 3y = 115
3y -2 y = 115 - 100
y = 15
x = 50 - 15
x = 35
Exhibit 2-1 the numbers of hours worked (per week) by 400 statistics students are shown below. Number of hours frequency 0x10 20 10x20 80 20x30 200 30x40 100 refer to exhibit 2-1. The percentage of students working between 10 and 20 hours is _____.
a. 80%
b. 20%
c. 25%
d. 75%
Answer:
b. 20%
Step-by-step explanation:
The distribution of number of hours worked by students is:
0 - 10 = 20
10 - 20 = 80
20 - 30 = 200
30 - 40 = 100
Total number of students = 400
We need to find the percentage of students working between 10 and 20 hours. From the above table we can see that number of students working between 10 and 20 hours is 80. Now we need to convert this into percentage. What we need to evaluate is what percentage of 400 is 80.
The formula for percentage is:
[tex]\frac{\text{Concerned Value}}{\text{Total Value}} \times 100\%[/tex]
Concerned value is 80, total value is 400. So using these in the formula we get:
[tex]\frac{80}{400} \times 100%\\\\ = 20\%[/tex]
Thus, 20% of the students are working between 10 and 20 hours.
The percentage of statistics students working between 10 and 20 hours per week is 20%, which is calculated by dividing the frequency of the group (80 students) by the total number of students (400) and multiplying by 100.
Explanation:The question is asking us to find the percentage of statistics students who work between 10 and 20 hours per week, given the frequency distribution provided in Exhibit 2-1. According to the exhibit, 80 students work between 10 and 20 hours per week. Since the total number of students is 400, we calculate this percentage by taking the number of students in the given category (80 students) and dividing it by the total number of students (400), then multiplying by 100 to get a percentage.
The calculation is:
Percentage = (80 ÷ 400) × 100
Percentage = 0.20 × 100
Percentage = 20%
Therefore, the percentage of students working between 10 and 20 hours is 20%, which corresponds to option b.
Find an equation of the line with the slope m= - 8 that passes through the point (-3,-6). Write the equation in the form Ax +By = C.
Choose the correct answer below.
A. 8x +y = 30
B. 30x +y = - 8
C. 8x+y = - 30
D. 30x +y = 8
Answer:
Step-by-step explanation:
note : an equation is : y - b = m(x - a) ... the point is : A ( a , b) and slope : m
in this exercice : m= - 8 and a= - 3 and b= -6
an equation is : y+6 = -8(x+3)
you can write : y+6 = - 8x -24
8x+y = - 30 .....answer : C
Answer:
C. 8x + y = -30
Step-by-step explanation:
-6 = -8[-3] + b
24
-30 = b
y = -8x - 30
+8x +8x
___________
8x + y = -30 >> Standard Linear Equation
* This is the fastest way to do it.
I am joyous to assist you anytime.
A mammoth bone is found to contain roughly 5% of the isotope C-14. Living elephant bones commonly contain about 40% C-14. Given that C-14 has a half-life of 5,730 years, how long ago did this mammoth die? Please show your work. (hint: no complex math is needed to solve this problem)
Answer:
The mammoth died 17.190 years ago.
Step-by-step explanation:
Given information:
Half-life of C-14 is 5.700 years. Living elephant bones commonly contain about 40% C-14.For every 5700 years, the elephant's bones losses a half-life of C-14. And supposing that the living mammoth bones had the same percentage of C-14.
If the mammoth when living has 40%, then:
After 5.730 years, the mammoth bones will contain 20%. After 11.460 years(2 half-lives), the mammoth bones will contain 10%. After 17.190 years(3 half-lives), the mammoth bones will contain 5%.Answer:
[tex]\large \boxed{\text{17 190 yr ago}}[/tex]
Step-by-step explanation
The amount of C-14 has declined from 40 % to 5 % of the original, that is, to ⅛ of the original amount.
The half-life of C-14 (5730 yr) is the time it takes for half of the isotope to decay.
We can make a table of the amount remaining after each successive half-life.
[tex]\begin{array}{ccc}\textbf{Number of} && \textbf{Fraction} \\\textbf{half-lives} & \textbf{Years} & \textbf{remaining} \\0 &0 & 1 \\1 &5730 &\frac{1}{2 } \\\\2 &11460 &\frac{1}{4 } \\\\3 &17190 &\frac{1}{8} \\\\4 & 22920& \frac{1}{16} \\\end{array}\\\text{We see that the fraction of C-14 is reduced to $\frac{1}{8}$ after three half-lives.}\\\text{The mammoth died $\large \boxed{\textbf{17 190 yr ago}}$}[/tex]
A TV is 16 inches tall and 14 inches wide. Calculate the screen's diagonal length. Round to the nearest whole number.
I came up with 22 in and was wrong.
Answer:
21
Step-by-step explanation:
You were close to de answer but you rounded in a wrong way
If we calculate [tex]\sqrt{16^{2} + 14^{2}}[/tex] we get 21.2602916255
We need to round to the nearest whole number, it means that we have we only have two options: 21 or 22
We need to remember the rounding rules:
If the number you are rounding is followed by 5, 6, 7, 8, or 9, round the number upIf the number you are rounding is followed by 0, 1, 2, 3, or 4, round the number downWe see that 1 is followed by 2, it means that we have to round the number down, so our answer is 21
Which of the following statements best explains why the auditing profession has found it essential to promulgate ethical standards and to establish means for ensuring their observance? A. Ethical standards that emphasise excellence in performance over material rewards establish a reputation for competence and character. B. Vigorous enforcement of an established code of ethics is the best way to prevent unscrupulous acts. C. A distinguishing mark of a profession is its acceptance of responsibility to the public. D. A requirement for a profession is to establish ethical standards that stress primarily a responsibility to clients and colleagues.
Answer:
C. A distinguishing mark of a profession is its acceptance of responsibility to the public.
Step-by-step explanation:
The following statement best explains why the auditing profession has found it essential to promulgate ethical standards and to establish means for ensuring their observance is :
A distinguishing mark of a profession is its acceptance of responsibility to the public.
The best explanation for why ethical standards are crucial in auditing is that professions are expected to be responsible to the public, ensuring trust, honesty, and integrity in their actions which align with their ethical codes.
The statement that best explains why the auditing profession has found it essential to promulgate ethical standards and to establish means for ensuring their observance is: C. A distinguishing mark of a profession is its acceptance of responsibility to the public. This underscores the basic principle that professionals, such as auditors, have a duty to act in the public interest and maintain public confidence in the profession. Professionals act as gatekeepers in various industries, ensuring that a company's actions uphold the law and adhere to established standards, thus serving the public good by promoting honesty and integrity.
Moreover, professions such as law, medicine, and accounting require professional education and licensing to ensure legal and ethical behavior, with mandated Codes of Ethics that outline the accountability to those served and to the profession itself. Therefore, the maintenance of ethical standards and the enforcement thereof are essential to professional integrity and the protection of public interests.
James wants to be able to make a $30,000 down payment on a new home in three years. If he can invest his savings in an account that earns 6%
interest per year, compounded monthly, about how much will James need to deposit today to achieve his goal?
A.
$25,002
O
B. $25.069
C. $25,189
OD. $35,730
Answer:
B. $25,069
Step-by-step explanation:
An interest of 6% per year, compounded monthly it means that he earns 6/12% = 0.5% of what he has invested every month.
If he invests x money what he will have the first month will be :
Money = x*(1+0.005)
The next month:
Money' = Money*(1+0.005) = x *(1+0.005)(1+0.005) = x* (1+0.005)^2
Therefore in this type of interest the formula is:
Money = x*(1+r)^n
Where:
x is the money invested the first time
r is the interest
n is the number of periods
For this problem:
x = what you have to find
r = 0.005
n = 3 years (1 period is 1 month) then the period is 36 months
Money = 30000
Replacing:
30000 = x * (1+0.005)^36
x = 25,069
Final answer:
To make a $30,000 down payment in three years with an account earning 6% interest compounded monthly, James needs to deposit approximately $25,189.06 today.
Explanation:
Calculating the Present Value for a Future Goal
To achieve a $30,000 down payment in three years with an account that earns 6% interest per year, compounded monthly, we need to calculate the present value of the future goal. Since the interest is compounded monthly, we use the present value formula for compound interest, which is P = A / (1 + r/n)^(nt), where P is the present value, A is the future amount, r is the annual interest rate, n is the number of times the interest is compounded per year, and t is the number of years.
Here, A = $30,000, r = 0.06 (6% converted to decimal), n = 12 (compounded monthly), and t = 3.
So, P = $30,000 / (1 + 0.06/12)^(12*3) = $30,000 / (1 + 0.005)^(36) ≈ $30,000 / 1.191016 = $25,189.06 (rounded to 2 decimal places).
The amount James needs to deposit today is approximately $25,189.06.
For each planet in the solar system it's year is the time it takes a planet to revolve around the center start.The formula E(x)= 0.2x^3/2 Models the number of earth days in a planets year E where X is the average distance of the planet from the center star millions of kilometers there are approximately 88 earth days in the year of the planet mercury what is the average distance of mercury from the center star
The average distance of Mercury from the Sun is found using the formula E(x) = 0.2x^3/2, where E(x) = 88 days, which is the year length for Mercury. Solving for x, the distance comes out to be approximately 57.9 million kilometers.
The question asks us to determine the average distance of Mercury from the center star, which can also be understood as the Sun, given that its year (the period it takes to orbit the Sun) is approximately 88 Earth days. We are provided with the formula E(x) = 0.2x3/2, where E(x) represents the number of Earth days in a planet's year and x is the planet's average distance from the Sun in millions of kilometers.
To solve for x, we set E(x) equal to 88 days and solve for x.
E(x) = 88
0.2x3/2 = 88
x3/2 = 88 / 0.2
x3/2 = 440
Now we take both sides to the power of 2/3 to solve for x.
x = 4402/3
To find the value of x, we calculate 440 raised to the 2/3 power.
x = 4402/3
≈ 57.9
Therefore, the average distance of Mercury from the Sun is approximately 57.9 million kilometers.
Please help!!! step by step
Answer:
x intercept- -2
12x - 8(0)= -24
12x = -24
x = -2
12(0)-8y = -24
-8y = -24
y = 3
y intercept
slope. 2/3
-8y = -12x - 24
y = (2/3)x + 3
Suppose one hundred eleven people who shopped in a special t-shirt store were asked the number of t-shirts they own costing more than $19 each.
Answer:
Option C 41%
Step-by-step explanation:
see the attached figure to better understand the problem
we know that
The number of people who own at most three t-shirts costing more than $19 each is equal to the number of people who own one t-shirt costing more than $19 each, plus the number of people who own two t-shirt costing more than $19 each, plus the number of people who own three t-shirt costing more than $19 each
Observing the graph
The number of people who own one t-shirt costing more than $19 each is 5
The number of people who own two t-shirt costing more than $19 each is 17
The number of people who own tree t-shirt costing more than $19 each is 23
The number of people who own at most three t-shirts costing more than $19 each is
[tex](5+17+23)=45\ people[/tex]
To find out the percentage divided the number of people who own at most three t-shirts costing more than $19 by one hundred eleven people (total people that shopped in a store) and then multiply by 100
[tex](45/111)100= 40.54\%[/tex]
Round to the nearest whole number
[tex]40.54\%=41\%[/tex]
The question involves the application of statistical principles to determine the percentage of people who own at most three expensive t-shirts. Assuming 59% is the correct answer, this means 66 out of the 111 people surveyed own three or fewer such t-shirts. The examples in the question references demonstrate the principles of economics, but aren't directly related to the question.
Explanation:The question is about determining the percentage of people who own at most three t-shirts costing more than $19 each from a sample of 111 people. Given that the possible percentages provided are 21% and 59%, the process involves the application of statistical principles, particularly dealing with percentages in relation to a specific sample size. This example fits into a branch of mathematics known as statistics, which deals with data analysis, collection, interpretation, presentation, and organization.
Let's assume from the reference that 59% is the correct answer, this conveys that of the 111 people surveyed, approximately 66 people own three or fewer such t-shirts. This is obtained by calculating 59% of 111, which equals about 65.49 and rounds to 66.
In the references provided, there are examples of how the cost of t-shirts affects purchasing decisions. This is related to the principles of economics which involve opportunity cost and budget constraints, but is not directly tied to answering the initial question.
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A hypothesis is ________. a prediction about something that has not yet been observed a statement that explains an observed phenomenon or answers a question an instrument that is used to examine environmental conditions the design of an experiment that can be used in scientific enquiry a proven scientific fact
Answer:
a testable proposition that explains an observed phenomenon or answers a question
Step-by-step explanation:
Basically an hypothesis is a theory given as a solution to a question proposed by a problem in from of you, but that it needs testing before it can be taken as truth or not
A hypothesis is an educated guess or a testable prediction drawn from observations. It is a tentative statement about reality that can be verified through experiments. If a hypothesis explains a large body of experimental data, it may evolve into a theory.
Explanation:A hypothesis is a testable prediction about how the world will behave if our idea is correct. Observations and questioning may lead a scientist to form a hypothesis. In essence, a hypothesis is an educated guess or a tentative statement about reality that can be tested to determine its validity.
An example of a hypothesis is 'if I study all night, I will get a passing grade on the test'. The hypothesis, the educated guess in this scenario, then undergoes a process of testing through experimentation, calculation, and comparison with the experiments of others.
If a hypothesis is capable of explaining a large body of experimental data, it can reach the status of a theory. A theory in scientific terms is a well-substantiated, comprehensive, testable explanation of particular aspects of nature. However, theories can be modified if new data becomes available. This process of questioning, observing, hypothesizing, testing, and eventually forming a theory is known as the scientific method.
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Help me answer these PLEASE ASAP
Answer:
Answered below
Step-by-step explanation:
Sheet 1: Question 3
Vertically opposite angles are equal so you will equate the angles given,
∠LPN = ∠OPM
7 + 13x = -20 + 16x
27 = 3x
x = 9
Sheet 1: Question 4
Vertically opposite angles are equal so you will equate the angles given,
∠ABD = ∠EBC
2x + 20 = 3x + 15
-x = -5
x = 5
Sheet 1: Question 5
Step 1: Find the value of x
Vertically opposite angles are equal so you will equate the angles given,
∠SOP = ∠ROQ
5x = 4x + 10
x = 10
Step 2: Find angles
Angle SOP = 5x = 5(10) = 50°
Angle ROQ = 50° (because it is vertically opposite to angle SOP)
Angle SOR = 180 - 50 (because all angles on a straight line are equal to 180°)
Angle SOR = 130°
Angle POQ = 130° (because it is vertically opposite to angle SOR)
Sheet 1: Question 6
Angle 1 = 72° (because vertically opposite angles)
∠4 + ∠1 + 41 = 180° (because all angles on a straight line are equal to 180°)
∠4 + 72 + 41 = 180
∠4 = 67°
∠3 = 41° (because vertically opposite angles)
∠2 = 67° (because vertically opposite angles)
Sheet 2: Question 3
Step 1: Find the value of x
Sum of complementary angles is equal to 90°
Angle A + Angle B = 90°
7x + 4 + 4x + 9 = 90°
11x = 90 - 13
11x = 77
x = 7
Step 2: Find angle A and angle B using x
Angle A: 7x + 4
7(7) + 4
Angle A = 53°
Angle B: 4x + 9
4(7) + 9
Angle B = 37°
Sheet 3: Question 3
Step 1: Find the value of x
Sum of supplementary angles is equal to 180°.
Angle A + Angle B = 180°
3x - 7 + 2x + 2 = 180°
5x = 185
x = 37
Step 2: Find angle A and angle B using x
Angle A: 3x - 7
3(37)-7
Angle A = 104°
Angle B: 2x + 2
2(37) + 2
Angle B = 76°
Sheet 3: Question 4
Sum of supplementary angles is equal to 180°.
Step 1: Find x
1/4(36x-8) + 1/2(6x-20) = 180°
Take LCM
[36x - 8 + 2(6x - 20)]/4 = 180°
36x - 8 +12x - 40 = 180 x 4
48x - 48 = 720
48x = 768
x = 16
Step 2: Find both angles with the help of x
Angle 1: 1/4(36x-8)
1/4[36(16)-8] = 568/4
Angle 1 = 142°
Angle 2: 1/2(6x-20)
1/2[6(16)-20] = 76/2
Angle 2 = 38°
Sheet 4: Question 1
All angles on a straight line are equal to 180°
Angle z + 138° = 180°
Angle z = 180 - 138
Angle z = 42°
Sheet 4: Question 2
Linear pair 1: 5 and 7 (because both angles are on a straight line and are equal to 180°)
Linear pair 2: 6 and 8 (because both angles are on a straight line and are equal to 180°)
Sheet 4: Question 3
Step 1: Find the value of x
All angles on a straight line are equal to 180° or linear pairs are equal to 180°
Angle LMO + Angle OMN = 180°
7x + 20 + 10 + 5x = 180°
12x = 180 - 30
x = 150/12
x = 12.5
Step 2: Find angles using the value of x
Angle LMO: 7x + 20
7(12.5) + 20
Angle LMO = 107.5°
Angle OMN: 10 + 5x
10 + 5(12.5)
Angle OMN = 72.5°
Sheet 4: Question 4
Linear pairs are equal to 180°.
Angle 1 + Angle 2 = 180°
1/3(27x-6) + 1/2(6x-20) = 180°
Take LCM = 6
[2(27x-6) + 3(6x-20)]/6 = 180
54x - 12 + 18x - 60 = 1080
72x - 72 = 1080
72x = 1152
x = 16
!!
Correct answers only please! If you don't know the answer, then please don't guess or say what you think it is.
Mike recently increased the size of his truck tires from the original P215/60R16 to the larger P235/7016. If Mike didn't recalibrate his speedometer, how fast is really going on the new tires when his speedometer shows he is traveling 60 mph?
A. 54.2 mph
B. 63.8 mph
C. 66.4 mph
D. 69.7 mph
Answer:
B. 63.8 mph
Step-by-step explanation:
IN order to solve this problem we just have to keep in mind that the miles per hour is calulcated by the number of revolutions that the tire is doing multiplied by the circumference of the tire, so the circumference of the tire is given by the first set of number in the tire the first one would be:
[tex]first:\frac{215}{60} \\Second: \frac{235}{70}[/tex]
So we just have to multiply it by the first one and then divide it by the second:
[tex]\frac{215}{60}*60=215\\215*\frac{235}{70}=63.8[/tex]
SO when the speedometer is on 60 mph, he will actually be going at 63.8 mph.
Question 25 Janice puts a fence around her rectangular garden. The garden has a length that is 9 feet less than 3 times its width. What is the perimeter of Janice’s fence if the area of her garden is 5,670 square feet?
A) 342 feet
B) 318 feet
C) 300 feet
D) 270 feet
Answer:
Option A - 342 feet
Step-by-step explanation:
Given : Janice puts a fence around her rectangular garden. The garden has a length that is 9 feet less than 3 times its width.
To find : What is the perimeter of Janice fence if the area of her garden is 5,670 square feet?
Solution :
Let the width of the garden be w=x feet.
The garden has a length that is 9 feet less than 3 times its width.
The length of the garden be l=3x-9 feet
The area of the garden is A=5670 square feet.
The formula of area of garden is [tex]A=l\times w[/tex]
[tex]5670=(3x-9)\times x[/tex]
[tex]5670=3x^2-9x[/tex]
[tex]3x^2-9x-5670=0[/tex]
[tex]x^2-3x-1890=0[/tex]
[tex]x^2-45x+42x-1890=0[/tex]
[tex]x(x-45)+42(x-45)=0[/tex]
[tex](x-45)(x+42)=0[/tex]
[tex]x=45,-42[/tex]
Reject x=-42 as measurement cannot be negative.
The width of the garden is w=45 feet.
The length of the garden is l=3(45)-9=135-9=126 feet.
The perimeter of the garden is [tex]P=2(l+w)[/tex]
[tex]P=2(126+45)[/tex]
[tex]P=2(171)[/tex]
[tex]P=342[/tex]
The perimeter of Janice fence is 342 feet.
Therefore, Option A is correct.
The perimeter of Janice's fence is: [tex]\[ {342 \text{ feet}} \][/tex]
To determine the perimeter of Janice's garden, let's follow these steps:
Step 1: Define Variables
Let ( w ) be the width of the garden in feet.
The length ( l ) of the garden is given by: [tex]\[ l = 3w - 9 \][/tex]
Step 2: Set Up the Area Equation
The area of the rectangular garden is given as 5,670 square feet:
[tex]\[ \text{Area} = l \times w \][/tex]
[tex]\[ 5670 = (3w - 9) \times w \][/tex]
Step 3: Solve the Quadratic Equation
Expand and simplify the equation:
[tex]\[ 5670 = 3w^2 - 9w \][/tex]
Rearrange it to standard quadratic form:
[tex]\[ 3w^2 - 9w - 5670 = 0 \][/tex]
Step 4: Factor or Use the Quadratic Formula
Divide through by 3 to simplify:
[tex]\[ w^2 - 3w - 1890 = 0 \][/tex]
Solve using the quadratic formula [tex]\( w = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \)[/tex]:
[tex]\[ a = 1, \, b = -3, \, c = -1890 \][/tex]
[tex]\[ w = \frac{-(-3) \pm \sqrt{(-3)^2 - 4 \cdot 1 \cdot (-1890)}}{2 \cdot 1} \][/tex]
[tex]\[ w = \frac{3 \pm \sqrt{9 + 7560}}{2} \][/tex]
[tex]\[ w = \frac{3 \pm \sqrt{7569}}{2} \][/tex]
[tex]\[ w = \frac{3 \pm 87}{2} \][/tex]
This gives two potential solutions:
[tex]\[ w = \frac{90}{2} = 45 \][/tex]
[tex]\[ w = \frac{-84}{2} = -42 \][/tex]
Since width cannot be negative:
[tex]\[ w = 45 \][/tex]
Step 5: Find the Length
Substitute ( w = 45 ) into the length equation:
[tex]\[ l = 3(45) - 9 \][/tex]
[tex]\[ l = 135 - 9 \][/tex]
[tex]\[ l = 126 \][/tex]
Step 6: Calculate the Perimeter
[tex]\[ P = 2l + 2w \][/tex]
[tex]\[ P = 2(126) + 2(45) \][/tex]
[tex]\[ P = 252 + 90 \][/tex]
[tex]\[ P = 342 \][/tex]
Thus, the perimeter of Janice's fence is: [tex]\[ {342 \text{ feet}} \][/tex]
There are two blue balls and two red balls in a box. At each turn, you will guess the color of the ball you are about to randomly select. If you guess the color correctly, you receive a dollar. You continue to draw balls without replacement, guessing the color at each turn, until there are no balls left. What is the expected value of this game if you play optimally?
Answer: now, the expected value will be x = p1*0$ + p2*1$
where p1 is te probabilty of a fail and p2 the probability of succes.
Ok, we will have 4 steps here.
1) there are 4 balls, and if we chose a spesific colour, there are 50% chance of succes. x = 0.5$
2) there are 3 balls, but yo know that if in the first step you graved a blue ball, then here you have a 66% of getting a red one, so if you play optimaly, you will guess red. x = 0.6$
3a) now there are two posibilities, in the last step yo get the other blue ball, so now are two red balls in the box, and you have guaranted 2 bucks. x = 2$ (but you failed in the last step)
3b) if in 2 you get a red ball, then again you have a 50/50 chance for each colour. x= 0.5$
4) there's only one ball in the box, you get a dollar x = 1 $
so if you go with the 3b path, te expected value will be 2.6$
with 3a) x = 2.5$
The expected value of playing this game, if you play optimally, is $0.83.
Explanation:To calculate the expected value of this game, we need to determine the probability of each outcome and multiply it by the corresponding payout. Let's start with the first draw:
If you guess a blue ball and draw a blue ball, you earn $1. The probability of this happening is 2/4.If you guess a red ball and draw a red ball, you earn $1. The probability of this happening is 2/4.For the second draw, there are two possibilities:
If the first draw was a blue ball, you have one blue ball and two red balls left. The probability of guessing the color correctly and drawing a blue ball is 1/3. So you would earn $1.If the first draw was a red ball, you have two blue balls and one red ball left. The probability of guessing the color correctly and drawing a red ball is 1/3. So you would earn $1.To calculate the expected value, we multiply each outcome by its probability and sum them up:
(2/4) * $1 + (2/4) * $1 + (1/3) * $1 + (1/3) * $1 = $0.83
The expected value of this game, if you play optimally, is $0.83.
Learn more about Expected value of a game here:https://brainly.com/question/33125226
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Line segment CD begins at (−1,1) and ends at (4,1). The segment is translated 2 units down to form line segment C'D'. Line segment C'D' begins at (−1,−1). Enter the coordinates for the end of line segment C'D'. ( , )
Answer:
D' = (4, -1)
Step-by-step explanation:
Translation down by 2 units subtracts 2 from the y-coordinate. The x-coordinate remains unchanged. You can see this in the descriptions of C and C':
C = (-1, 1)C' = (-1, -1) . . . . . 2 is subtracted from y=1 to get y=-1Likewise:
D = (4, 1)D' = (4, -1)__
The translated segment is still a horizontal segment, now at y=-1 instead of at its previous position of y=1.
it was 2nd and 8 and the broncos were on their own 6 yard line and got called for ‘holding’. if the penalty is “...half the distance to the goal line, what is the new line of scrimmage?
Answer:
the 3 yard line
Step-by-step explanation:
A man with a mass of 65 kg skis down a frictionless hill that is 4.7 m high. At the bottom of the hill the terrain levels out. As the man reaches the horizontal section, he grabs a 23 kg backpack and skis off a 1.7 m high ledge. At what horizontal distance from the edge of the ledge does the man land?
Answer: 4,85 meters
Step-by-step explanation:
Using energy we get the velocity when the man gets to the bottom of the hill
mgh=1/2 m v^2
Then the velocity is the squareroot of two times the mass times the gravity constant =9,598 m/s2
Using energy again, we can get the velocity on the edge of the ledge (using the second mass, the one of the man plus the backpack)
1/2 M1 V1^2=1/2 M2 V2^2
We get V2=8,24 m/s2
Then we have to analyze the jump, horizontally, with constant velocity, and vertically, with constant acceleration equals to the gravity constant.
To get the time we analyze the vertical move
Y=1/2 g t^2
t=59 seconds
To get the horizontal distance we use
X= v t
X=4,85 meters.
In 1955 an antique car that originally cost $3,668 is valued today at $62,125 if in excellent condition, which is 1 3/4 times as much as a car in very nice condition, if you can find an owner willing to part with one for any price.What would be the value of the car in very nice condition?
Answer:
The value of the car in very nice condition will be $35500.
Step-by-step explanation:
Let the value of car in a very nice condition be = x
The value $62125 is [tex]1\frac{3}{4}[/tex] or [tex]\frac{7}{4}[/tex] or 1.75 times of x.
Now, we can calculate for x:
[tex]1.75x=62125[/tex]
[tex]x=\frac{62125}{1.75}[/tex]
x = 35500
Hence, the value of the car in very nice condition will be $35500.
The value of the car in very nice condition is $35,500. This is determined by dividing the value of the car in excellent condition by 1.75.
To determine the value of the car in very nice condition, you need to use the information that a car in excellent condition is worth 1 3/4 times (or 1.75 times) as much as a car in very nice condition.
Given the value of the car in excellent condition is $62,125, you can set up the equation:
Value in Excellent Condition = 1.75 * Value in Very Nice ConditionSubstitute the known value:
$62,125 = 1.75 * Value in Very Nice ConditionTo find the Value in Very Nice Condition, divide both sides by 1.75:
Value in Very Nice Condition = [tex]\frac{\$62,125}{1.75}[/tex]Value in Very Nice Condition = $35,500Hence, the value of the car in very nice condition is $35,500.
Calculate the net death rate for the year based on the following statistics: 15,567 discharges with 245 deaths (75 deaths occurring under 48 hours). Eight of the 245 deaths were medical examiner's cases.
Answer:
13665.6 deaths per year
Step-by-step explanation:
We can determine certain statistics based on the information. If 15567 patients where discharge and 245 deaths were recorded, the total number of patients were:
[tex]=15567+245=15812[/tex]
If 75 deaths occured in the first 48 hours we have a death rate of:
[tex]=75/48=1.56[/tex]
1.56 deaths per hour.
We want the death rate per year. If we have the death rate per hour we can determine the death rate per year:
[tex]1.56\cdot{24}\cdot{365}=13665.6[tex]
13665.6 deaths per year
The correct net death rate for the year is [tex]\(\frac{172}{15567}\).[/tex]
To calculate the net death rate for the year, we need to consider the total number of deaths that occurred and the total number of discharges. The net death rate is calculated by dividing the number of deaths by the number of discharges.
From the given statistics, we have:
- Total discharges: 15,567
- Total deaths: 245
However, we need to adjust the total deaths to account for the deaths that occurred under 48 hours and the medical examiner's cases, as these might not be included in the net death rate calculation.
- Deaths under 48 hours: 75
- Medical examiner's cases: 8
The deaths under 48 hours and the medical examiner's cases are typically excluded from the net death rate calculation because they may not reflect the quality of care provided by the hospital. Therefore, we subtract these from the total deaths:
Adjusted deaths = Total deaths - Deaths under 48 hours - Medical examiner's cases
Adjusted deaths = 245 - 75 - 8
Adjusted deaths = 162
Now, we can calculate the net death rate:
Net death rate =[tex]\(\frac{\text{Adjusted deaths}}{\text{Total discharges}}\)[/tex]
Net death rate = [tex]\(\frac{162}{15567}\)[/tex]
This gives us the net death rate for the year based on the adjusted number of deaths."
What is the quadratic formula?
Answer:
I guess u want to know the quadratic function and its formula is, AX*2 + BX + C. Otherwhise you want to know how to get 0 and get the Xm if you want to know how to solve a quadratic. That formula is, (-B +/- [tex]\sqrt{x}[/tex] (B*2 - 4AC) ) . 1/2 (where A, B and C are the number at the original function).
Step-by-step explanation: