Answers
Step-by-step explanation:
3y-x-5=0
3y=x+5
y=(x+5)/3
y= (1/3)*x + (5/3)
The general equation of y is:
y=mx+b
where:
slope=m
b= y intercept
so, slope is (1/3) and y intercept is (5/3)
and x intercept=0, when you star to graphic you can see that the only option for have y=(5/3) is necessary that the value of x=0. Or:
y intercept= (1/3)*x +(5/3) =(5/3)
(5/3)-(5/3)=(1/3)x
0=(1/3)*x
0/(1/3)=x
x=0.
Related Questions
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)
Answers
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]
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?
Answers
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.
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PLEASE ANSWER:
Which expression is equivalent to the expression below?
4r + 9 + r+ 2p - 3
CHOICES:
5r + 2p + 6
7r + 6
14r - p
5r + 2p - 12
Answers
Answer:
5r + 2p + 6
Step-by-step explanation:
4r+r = 5r
9-3 = 6
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.
Answers
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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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?
Answers
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
If f and t are both even functions, is f 1 t even? If f and t are both odd functions, is f 1 t odd? What if f is even and t is odd? Justify your answers.
Answers
If the [tex]f(x)[/tex] and [tex]t(x)[/tex] are even function then [tex]fo\ t\ (x)[/tex] is an even function, if [tex]f(x)[/tex] and [tex]t(x)[/tex] are odd function then the function [tex]fo\ t\ (x)[/tex] is an odd function and if [tex]f(x)[/tex] is even and [tex]t(x)[/tex] is odd then the function [tex]fo\ t\ (x)[/tex] is an even function.
Further explanation:
An even functrion satisfies the property as shown below:
[tex]\boxed{f(-x)=f(x)}[/tex]
An odd functrion satisfies the property as shown below:
[tex]\boxed{f(-x)=-f(x)}[/tex]
Consider the given composite function as follows:
[tex]\boxed{fo\ t\ (x)=f\left(t(x))\right}[/tex]
If both the function [tex]f(x)[/tex] and [tex]t(x)[/tex] are even function.
[tex]\begin{aligned}fo\ t\ (-x)&=f\left(t(-x))\right\\&=f\left(t(x))\right\\&=fo\ t\ (x)\end{aligned}[/tex]
From the above calculation it is concluded that,
[tex]\boxed{fo\ t\ (-x)=fo\ t\ (x)}[/tex]
This implies that the composite function [tex]fo\ t\ (x)[/tex] is an even function.
If both the function [tex]f(x)[/tex] and [tex]t(x)[/tex] are odd function.
[tex]\begin{aligned}fo\ t\ (-x)&=f\left(t(-x))\right\\&=f\left(-t(x))\right\\&=-fo\ t\ (x)\end{aligned}[/tex]
From the above calculation it is concluded that,
[tex]\boxed{fo\ t\ (-x)=-fo\ t\ (x)}[/tex]
This implies that the composite function [tex]fo\ t\ (x)[/tex] is an odd function.
If the function [tex]f(x)[/tex] is even and [tex]t(x)[/tex] is odd.
[tex]\begin{aligned}fo\ t\ (-x)&=f\left(t(-x))\right\\&=f\left(-t(x))\right\\&=fo\ t\ (x)\end{aligned}[/tex]
From the above calculation it is concluded that,
[tex]\boxed{fo\ t\ (-x)=fo\ t\ (x)}[/tex]
This implies that the composite function [tex]fo\ t\ (x)[/tex] is an even function.
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%
Answers
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.
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.
Answers
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.
The area of a sector in a circle is given by the formula: A=12r2θ , where r is the radius and θ is the central angle measured in radians. Find the rate of change of A with respect to θ if r remains constant. What is the rate when r=2?
Answers
Answer:
Step-by-step explanation:
[tex]A=\frac{1}{2} r^{2} \theta\\\frac{dA}{d\theta} =r \\\\when r=2\\rate of change at r=2 is 2[/tex]
We want to find the rate of change of a given function of two variables when we fix one of the two, and then we want to evaluate it at r = 2.
We will get that the rate of change is:
[tex]\frac{dA(r, \theta)}{d\theta} = 12*r^2[/tex]
And when r = 2, the rate is 48.
-----------------------------------------
We define the rate of change of a function with respect to some variable as the differentiation of the function with respect to that variable.
Here we have the function:
[tex]A(r, \theta) = 12*r^2*\theta[/tex]
We need to differentiate it with respect to θ, we will get:
[tex]\frac{dA(r, \theta)}{d\theta} = 1*12*r^2*\theta^0 = 12*r^2[/tex]
Where I used the general rule to derive functions with exponents:
[tex]f(x) = x^n\\\\\frac{df(x)}{dx} = n*x^{n -1}[/tex]
Now that we know the rate of change, we want to evaluate it in r = 2, we will get:
[tex]\frac{dA(2, \theta)}{d\theta} = 12*2^2 = 48[/tex]
Notice that this does not depend on the value of θ.
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The following data represent weights in kilograms of maize harvest from a random sample of 72 experimental plots on St. Vincent, an island in the Caribbean (Reference: B. G. F. Springer, Proceedings, Caribbean Food Corps. Soc., Vol. 10, pp. 147-152). For convenience, the data are presented in increasing order.
7.8 9.1 9.5 10.0 10.2 10.5 11.1 11.5 11.7 11.8
12.2 12.2 12.5 13.1 13.5 13.7 13.7 14.0 14.4 14.5
14.6 15.2 15.5 16.0 16.0 16.1 16.5 17.2 17.8 18.2
19.0 19.1 19.3 19.8 20.0 20.2 20.3 20.5 20.9 21.1
21.4 21.8 22.0 22.0 22.4 22.5 22.5 22.8 22.8 23.1
23.1 23.2 23.7 23.8 23.8 23.8 23.8 24.0 24.1 24.1
24.5 24.5 24.9 25.1 25.2 25.5 26.1 26.4 26.5 26.7
27.1 29.5
a) Compute the five-number summary.
b) Compute the interquartile range.
c) Make a box-and-whisker plot.
d) Discuss the distribution. Does the lower half of the distribution show more data spread than the upper half?
Answers
Answer:
See explanation
Step-by-step explanation:
7.8 9.1 9.5 10.0 10.2 10.5 11.1 11.5 11.7 11.8
12.2 12.2 12.5 13.1 13.5 13.7 13.7 14.0 14.4 14.5
14.6 15.2 15.5 16.0 16.0 16.1 16.5 17.2 17.8 18.2
19.0 19.1 19.3 19.8 20.0 20.2 20.3 20.5 20.9 21.1
21.4 21.8 22.0 22.0 22.4 22.5 22.5 22.8 22.8 23.1
23.1 23.2 23.7 23.8 23.8 23.8 23.8 24.0 24.1 24.1
24.5 24.5 24.9 25.1 25.2 25.5 26.1 26.4 26.5 26.7
27.1 29.5
A. The five-number summary is
Minimum = 7.8Maximum = 29.5Median [tex]=\dfrac{20.2+20.3}{2}=20.25[/tex][tex]Q_1=\dfrac{14.0+14.4}{2}=14.2[/tex][tex]Q_3=\dfrac{23.8+23.8}{2}=23.8[/tex]B. The interquartile range is
[tex]Q_3-Q_1=23.8-14.2=9.6[/tex]
C. See attached diagram
D. The distribution is not symmetric, the left half shows more data than the right part
Please help!!! step by step
Answers
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
Justify each step in solving the equation 5(y+3)-11=-y-6 by writing a reason for each statement.
Statements Reasons
5(y+3)-11=-y-6 Given
5(y+3)=-y+5
5y+15=y+5
5y=-y-10
6y=-10
y=-5/3 Division Property of Equality/Reduce
Please help!!!
Answers
Explanation:
5(y+3)-11=-y-6 Given
5(y+3)=-y+5 . . . . addition property of equality (11 is added)
5y+15=y+5 . . . . . distributive property (5 is distributed)
5y=-y-10 . . . . . . . addition property of equality (-15 is added)
6y=-10 . . . . . . . . . addition property of equality (y is added)
y=-5/3 Division Property of Equality/Reduce
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?
Answers
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.
Help me answer these PLEASE ASAP
Answers
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
!!
This is due tomorrow and I haven't done it at ALL. Please and thank you.
Answers
Answer:
C
Step-by-step explanation:
First, when fractions get raised to an exponent, both the numerator and the denominator get raised to the power.
When exponents get raised to a power, the powers multiply.
E.g. [tex](x^2)^3=(x^2)(x^2)(x^2)=(x*x)(x*x)(x*x)=x^6[/tex]
In this case,
[tex](\frac{4^3}{5^-^2})^5=\frac{4^(^3^*^5^)}{5^(^-^2^*^5^)}=\frac{4^1^5}{5^-^1^0}\\[/tex]
Note that [tex]x^-^n=\frac{1}{x^n}[/tex]
So, 1/5^(-10) = 5^10
So, our answer is C
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.
Answers
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.
What is the length of x in the diagram below ?
Answers
Firstly we calculate the height(h)...,
by using trigonometry ratios
;tan 45° = h/5
;where.. h = 5 tan 45°
;h = 5
Then we calculate the side x...using the height h and the angle of 30°
by also using trigonometry ratios
; sin 30° = 5/x
;where.. x = 5/(sin 30°)
Hence...., x = 10
Answer: x = 10
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?
Answers
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.
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
Answers
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.
The times (in minutes) that several underwriters took to review applications for similar insurance coverage are 50, 230, 52, and 57. What is the median length of time required to review an application?
109.0
141.0
97.25
54.5
Answers
Answer:
The answer is 54.5
Step-by-step explanation:
The median of a set of observations is the value in the middle in case there is an uneven number of observations or the average between the two values in the middle.
First we arrange the times from less time to longer times.
50 - 52 - 57 - 230 .
The values in the middle are 52 - 57
And the average between this two values is 54.5. Thus that is the median legth of time.
Answer:
The median length of time required to review an application is 54.5 minutes.
Step-by-step explanation:
The times (in minutes) that several underwriters took to review applications for similar insurance coverage are 50, 230, 52, and 57.
Arranging in ascending order we get
50,52,57,230
Median length of time = [tex]\frac{52+57}{2}=54.5[/tex]
Hence, the median length of time required to review an application is 54.5 minutes.
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
Answers
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.
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
Answers
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.
Given A = {(1, 3)(-1, 5)(6, 4)}, B = {(2, 0)(4, 6)(-4, 5)(0, 0)} and C = {(1, 1)(0, 2)(0, 3)(0, 4)(-3, 5)}, answer the following multiple choice question: From the list of sets A, B, and C, state the domain of set B. Domain of set B: {0, 6, 5} Domain of set B: {2, 4, -4, 0} Set B does not have a domain
Answers
Answer:
Domain of set B: {2, 4, -4, 0}
Step-by-step explanation:
The domain of the function whose ordered pairs are listed in set B is the set of first numbers of those pairs: {2, 4, -4, 0}.
_____
Comment on the question
A "set" does not have a domain. A "function" has a domain. To make any sense of this question, we have to interpret the question to mean the function described by the ordered pairs in the set.
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?
Answers
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.
Answers
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 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
Answers
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?
Answers
Answer:
the 3 yard line
Step-by-step explanation:
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
Answers
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.
What is the quadratic formula?
Answers
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:
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
Answers
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.
Learn more about hypothesis here:https://brainly.com/question/35154833
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