The point of intersection of the two lines is (-3.4, -1.2).
How to find the slope of each line?Step 1: The slope of a line passing through two points (x1,y1) and (x2,y2) can be found using the formula:
m = (y2-y1)/(x2-x1)
Using this formula, we can find the slope of the first line:
m1 = (−2−3)/(-5 -5) = −5/(-10) = 1/2
And the slope of the second line:
m2 = (−4−4)/(2 -(-6)) = -8/4 = -2
Step 2: Find the y-intercept of each line
The y-intercept of a line in slope-intercept form (y = mx + b) is the value of y when x=0. We can use one of the two given points on each line to find the y-intercept:
For the first line passing through points (5,3) and (−5,−2):
y = mx + b
3 = (1/2)(5) + b
b = 3 - 5/2
b = 1/2
So the first line can be written as y = 1/2x + 1/2
For the second line passing through points (−6,4) and (2,−4):
y = mx + b
4 = (-2)(−6) + b
b = 4 - 12
b = -8
So the second line can be written as y = -2x - 8
Step 3: Each line in slope-intercept form (y = mx + b):
First line: y = 1/2x + 1/2
Second line: y = -2x - 8
Step 4: To find the point of intersection of the two lines, we need to solve the system of equations. We can solve for x by setting the two right-hand sides equal to each other:
1/2x + 1/2 = -2x - 8
(x + 1)/2 = -2x - 8
x + 1 = -4x - 16
5x = -16 - 1
5x = -17
x = -17/5
x = -3.4
Now that we know x, we can find y by substituting x=10 into one of the two equations:
y = -2x - 8
y = -2(-3.4) - 8
y = - 1.2
Thus, the point of intersection of the two lines is (-3.4, -1.2).
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According to Money magazine, Maryland had the highest median annual household income of any state in 2018 at $75,847.† Assume that annual household income in Maryland follows a normal distribution with a median of $75,847 and standard deviation of $33,800.
(a) What is the probability that a household in Maryland has an annual income of $90,000 or more? (Round your answer to four decimal places.)
(b) What is the probability that a household in Maryland has an annual income of $50,000 or less? (Round your answer to four decimal places.)
The required probability that a household in Maryland with annual income of ,
$90,000 or more is equal to 0.3377.
$50,000 or less is equal to 0.2218.
Annual household income in Maryland follows a normal distribution ,
Median = $75,847
Standard deviation = $33,800
Probability of household in Maryland has an annual income of $90,000 or more.
Let X be the random variable representing the annual household income in Maryland.
Then,
find P(X ≥ $90,000).
Standardize the variable X using the formula,
Z = (X - μ) / σ
where μ is the mean (or median, in this case)
And σ is the standard deviation.
Substituting the given values, we get,
Z = (90,000 - 75,847) / 33,800
⇒ Z = 0.4187
Using a standard normal distribution table
greater than 0.4187 as 0.3377.
P(X ≥ $90,000)
= P(Z ≥ 0.4187)
= 0.3377
Probability that a household in Maryland has an annual income of $90,000 or more is 0.3377(rounded to four decimal places).
Probability that a household in Maryland has an annual income of $50,000 or less.
P(X ≤ $50,000).
Standardizing X, we get,
Z = (50,000 - 75,847) / 33,800
⇒ Z = -0.7674
Using a standard normal distribution table
Probability that a standard normal variable is less than -0.7674 as 0.2218. This implies,
P(X ≤ $50,000)
= P(Z ≤ -0.7674)
= 0.2218
Probability that a household in Maryland has an annual income of $50,000 or less is 0.2218.
Therefore, the probability with annual income of $90,000 or more and $50,000 or less is equal to 0.3377 and 0.2218 respectively.
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which formula describes the following vector field? here the x-axis is horizontal and the y-axis is vertical.
The formula that describes the vector field in which, x-axis is horizontal and the y-axis is vertical, is option B: F(x,y) = (y,1).
A vector field is a function that assigns a vector to each point in space. It can be represented as a group of arrows, each connected to a location in space and having a specific magnitude and direction.
The vector field that describes the given conditions is F(x,y) = (y,1). This means that at any point (x,y), the vector field will have a magnitude of 1 and will be pointing in the positive y direction.
The horizontal component of a vector is found by multiplying its magnitude by the cosine of the angle it makes with the positive x-axis. The vertical component of a vector is found by multiplying its magnitude by the sine of the angle it makes with the positive x-axis.
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Complete question is:
Which formula describes the following vector field? here the x-axis is horizontal and the y-axis is vertical. (Refer the image)
O F(x,y) = (1,7)
O F(x,y) = (y,1)
O F(x,y) = (1,x)
O F(x,y) = (x,1)
Find the 6th term of the geometric sequence described below.
m₁ = -3(-5)-1
Show your work here
Hint: To add an exponent (z"), type "exponent" or press "A"
Answer:
m₆ = 9375
Step-by-step explanation:
Given sequence is
[tex]m,_i = -3(-5)^{i - 1}[/tex]
To find the 6th term, all you have to do is substitute i = 6 and compute
For i = 6 we get
[tex]m_6 = -3(-5)^{6 - 1}\\= -3(-5)^5\\\\= -3(-3125) \\\\= 9375[/tex]
A negative number raised to an odd number is negative that is why (-5)⁵ is negative
NEED ANSWERS FAST WILL MARK BRAINLIEST
Find the missing length indicated
Answer: i think its 10
Step-by-step explanation:
Step-by-step explanation:
because of 2 lines being parallel, this creates 2 similar triangles.
and that means the ratio between 2 corresponding sides must be the same for all pairs of corresponding sides.
so,
4/(4+5) = 8/(8 + ?)
4/9 = 8/(8 + ?)
4(8 + ?) = 8×9
8 + ? = 8×9/4 = 2×9 = 18
? = 10
which of the following numeric measures would be most likely to produce invalid statistical analysis?
The most likely to produce invalid statistical analysis of numeric measures is Pain rating as: none = 0; slight = 1; much = 2, as it is an ordinal scale of measurement, which does not have equal intervals between the categories. So, the correct answer is B).
It means that the differences between the categories are not necessarily equivalent, and therefore, any statistical analysis based on this scale may not accurately reflect the true relationship between variables.
The other options (blood pressure in mmHg, oxygen saturation in percentage, neonatal birth weight in kilograms) are measured on interval or ratio scales, which have equal intervals between values and can be used for meaningful statistical analysis. so, the correct option is B).
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____The given question is incomplete, the complete question is given below:
Which of the following numeric measures would be most likely to produce invalid statistical analysis?A)Analysis of patients' blood pressures in mmHgB)Pain rating as: none = 0; slight = 1; much = 2C)Assessment of oxygen saturation in percentageD)Analysis of neonatal birthweight in kilogr
4.5. Using Linear Scale
Solve the following scenarios.
8. You have a map that is missing a scale. The distance from Point A to Point B is
five inches on the map, and after driving it, you know it is 250 miles in reality.
The scale of the map is 1 inch to 50 miles, or 1:50.
What is distance?
Distance is defined as the space between two points in space.
To find the scale of the map in inches per mile, we can use the ratio of the distance on the map to the actual distance:
5 inches on the map / 250 miles in reality
Simplifying this ratio gives:
1 inch on the map / 50 miles in reality
Therefore, the scale of the map is 1 inch to 50 miles, or 1:50.
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Weekly CPU time used by an accounting firm has probability density
function (measured in hours) given by
f(x) = { 3/64 * x^2
(4 − x) 0 ≤ x ≤ 4
0 Otherwise }
(a) Find the F(x) for weekly CPU time.
(b) Find the probability that the of weekly CPU time will exceed two hours
for a selected week.
(c) Find the expected value and variance of weekly CPU time.
(d) Find the probability that the of weekly CPU time will be within half an
hour of the expected weekly CPU time.
(e) The CPU time costs the firm $200 per hour. Find the expected value
and variance of the weekly cost for CPU time.
Using probability, we can find that:
E(Y)= 2.4, Var (Y) = 0.64
E(Y) = 480, Var(Y) = 25,600
Define probability?The probability of an event is the proportion of favourable outcomes to all other potential outcomes. To determine how likely an event is, use the following formula:
Probability (Event) = Positive Results/Total Results = x/n
Given,
The weekly CPU time is as follows:
f(y) where, 0≤y≤4
Here, probability density function is 4-y is correct, or else we get negative expected values.
We have to find E(Y) and var(Y)
E(Y) = 2.4
var (Y) = E(Y²)-(E(Y)) ²
= 6.4 - (2.4) ²
= 0.64
The CPU time is costing the firm $200 per hour.
Now, we find E(Y) and var(Y) of the weekly cost for the CPU time.
Y = 200E
E(Y) = 200 × 2.4
= 480
var(Y) = 200V(Y)
= 200 × 0.64
= 25600
We can observe that the weekly cost is not exceeding $600 as weekly cost for CPU time = 480.
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Walmart was having a sale on video games. They offered a 15% discount on a game that was originally priced at $30. After the sale, the discounted price of the game was increased by 10%. What is the new price of the game after this increase?
Answer:
28.05$
Step-by-step explanation:
The game got a discount of 15%.
New price is (30$) ( 0.85 ) = 25.5$ (since the discount is 15% you only pay for the 85% of the original price)
Then an increase of 10%. this is:
New price: 25.5$ (1.10) = 28.05
New price is 28$ with 5 cents
Find the derivative of f(x) = -2x^3 by the limit process…
Answer:
f'(x) = -6x^2
f'(-5) = -150
f'(0) = 0
f'(√17) = -102
Sarah is a psychologist at an practise. she earns a basic salary of R3000 per month as well as 20% commission on income up to R 5000. She receives an additional 10% bonus on top of the normal commission rate on earning above R 5000. If Sarah did work to the value of R 12000 ,how much did she earn in total???
Answer:
Sarah earns R6 100 in total for her work to the value of R12 000.
Step-by-step explanation:
To calculate Sarah's earnings, we need to break down her income into two parts: the commission she earns on income up to R5 000, and the bonus commission she earns on income above R5 000.
Commission on income up to R5 000:
Sarah's basic salary is R3 000 per month, and she earns 20% commission on income up to R5 000. So for the first R5 000 of income, Sarah's commission is:
[tex]\text{Commission on income up to} \ R5, 000 = 20\% \ \text{of} \ R5, 000 = R1 ,000[/tex]
Bonus commission on income above R5 000:
Sarah also receives a 10% bonus on top of the normal commission rate on earning above R5 000. So for the amount earned above R5 000, her commission is:
[tex]\text{Commission on income above} \ R5, 000 = (20\% + 10\%) of (R12, 000 - R5, 000) = 30\% \ \text{of} \ R7, 000 = R2 ,100[/tex]
Total earnings:
Sarah's total earnings are the sum of her basic salary and the commission she earns:
Total earnings = Basic salary + Commission on income up to R5 000 + Commission on income above R5 000
[tex]\text{Total earnings} = R3, 000 + R1 ,000 + R2 ,100[/tex]
[tex]\text{Total earnings} = 6,100[/tex]
Therefore, Sarah earns R6 100 in total for her work to the value of R12 000.
How many strings of length 5 of the letters A, B, C, D, and E contain exactly one A and exactly one D if repetition of letters is allowed?
320 such sequences exist. We must determine how many strings of length five have precisely one A and one D. Any of the final four options may be used for the remaining three characters. (B, C, D, E).
Using the multiplication concept, we can count this. After selecting the A's location from among five options, the D's position can be found among four options. For the final three positions, there are a total of four options. The total amount of strings is thus:
5 × 4 × 4 × 4 × 1 = 320
Thus, 320 such sequences exist.
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ection A-Classwork Let's make mathematical sentences of each of the following stateme Statements Mathematical sentences a) The sum of x and 4 is 7. b) The difference of y and 5 is 4. c) Two times x is 10. d) Two times y added to 3 is 9. e) f) x is more than 2 by 1. 3 is less than y by 2.
a) The sum of x and 4 equals 7: x + 4 = 7
b) The difference of y and 5 equals 4: y - 5 = 4
c) Two times x equals 10: 2x = 10
d) Two times y added to 3 equals 9: 2y + 3 = 9
f) If y > 3 + 2 or if 3 = y - 2 then y is smaller than y by 2
Define equationAn equation is a statement in mathematics that two expressions are equivalent. It has two sides that are divided by the equals sign (=). One or more terms, such as integers, variables, constants, and mathematical operations like addition, subtraction, multiplication, division, and exponentiation, may be included on each side of the equation.
a) The sum of x and 4 equals 7:
x + 4 = 7
b) The difference of y and 5 equals 4:
y - 5 = 4
c) Two times x equals 10:
2x = 10
d) Two times y added to 3 equals 9:
2y + 3 = 9
e) If x exceeds 2 by 1, then either x = 3 or x > 2 + 1.
f) If 3 is smaller than y by 2 then either y > 3 + 2 or 3 = y - 2
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solve using systems answer in a ordered pair
y = –x + 3
y = 4x – 2
Answer:
(1,2)
Step-by-step explanation:
Pre-SolvingWe are given the following system of equations:
y = -x + 3
y = 4x - 2
And we want to solve it, with the answer in an ordered pair.
SolvingBecause both systems are equal to y, we can set both of the equations equal to each other, and solve for x in that way.
This is possible due to transitivity, which states that if a=b, and b=c, then a=c.
Hence,
-x + 3 = 4x - 2 (same as y=y)
We can add x to both sides.
3 = 5x - 2
Add 2 to both sides.
5 = 5x
Divide both sides by 5.
1 = x
Now, we can use this value to find y.
Substitute 1 as x in either y = -x + 3 or y = 4x - 2
Taking y = -x + 3 for instance:
y = -1 + 3 = 2
So, we now that x=1, y=2.
As an ordered pair, that is (1,2).
Can someone actually see if I got this correct for this answer please
Your total grade point average (GPA) for the semester is 2.67.
What is GPA ?GPA stands for Grade Point Average. It is a numerical calculation used to measure the academic success of a student. It is calculated by taking the average of all grades received by a student across all courses taken in a given semester or academic year. Each course is assigned a specific number of credit hours, and each grade is assigned a numerical value based on the school’s grading scale. The numerical value of each grade is then multiplied by the number of credit hours for the course, and the total of all courses is added together to determine a student’s GPA.
A higher GPA is generally indicative of higher academic performance while a lower GPA is generally indicative of lower academic performance. A student’s GPA is used by schools, employers, and other organizations to evaluate a student’s academic record.
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This would give you a total of 29.0. Divide this by 10 credit hours and you get a GPA of 2.85 for the semester.
What is GPA?GPA stands for Grade Point Average. It is an academic measure of a student's performance in a course or program of study. It is calculated by dividing the total number of grade points earned by the total number of credit hours taken. A grade point average is typically expressed as a number on a 4.0 scale. A 4.0 GPA is considered to be the highest possible grade point average, while anything below a 2.0 GPA is usually considered to be failing.
This is calculated by adding up the total number of credit hours (10 credit hours) and then multiplying each grade by the respective number of credit hours. A=4.0, B=3.0, C=2.0.
So, you would multiply 4.0 by 3 for FYE 105, 3.0 by 3 for ENG 101, 2.0 by 3 for MAT 150, 2.0 by 3 for BIO 112, and 4.0 by 1 for BIO 113.
This would give you a total of 29.0.
Divide this by 10 credit hours and you get a GPA of 2.85 for the semester.
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which statemnt is ture when the dimensions of a two-dimensional figures are dilated by a scale factor of 2
When a shape is dilated, the size of the shape changes. The true statement is (d) The scale factor is 2.5.
Dilation:
Dilation is the process of changing the size of an object or shape by reducing or increasing its size by a specific scale factor. For example, a circle with a radius of 10 units shrinks to a circle with a radius of 5 units. Applications of this method are in photography, arts and crafts, sign making and more.
According to the Question:
How to determine the scale factor
In figure A, we have:
Length = 0.6
In figure B, we have:
Length =1.5
The scale factor is then calculated as:
K = 1.5/0.6
Dividing the equation:
k = 2.5
Hence, the true statement is (d) The scale factor is 2.5.
Complete Question:
The first figure is dilated to form the second figure. Which statement is true?
The scale factor is 0.4.
The scale factor is 0.9.
The scale factor is 2.1.
The scale factor is 2.5.
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Test the conjecture. 1) A rectangle has an area of 54 square units. A scale factor of is applied to the rectangle to create a scaled figure. What is the area of the scaled figure?
9 units 6 units
Answer:
Step-by-step explanation:
yr face add more points NOW
There are two types of trees to plant in the yard type A trees are 36 inches tall and grows 8 inches per year type B are 18 inches tall but grow 10 inches per year when will the trees be the same height
As a result, both varieties of trees will be the same height after 9 years. We can change both equations to a = 9 to verify this: Height of the type A tree is 36 + 8(9) or 36 + 72 inches, whereas the height of the type B tree is 18 + 10(9) or 18 + 90 inches.
What function do height and distance serve in everyday life?Trigonometry includes heights and distances, and it has numerous uses in practical daily life. It utilised to compute height of towers, structures, mountains, etc., and distance between any two objects such celestial bodies others. ,sys,s tos.as to .... and.
Let's use "a" to denote the number of years after planting the trees.
A type A tree will reach the following height after "a" years:
Height of type A tree = 36 + 8a
After "a" years, the height of a type B tree will be:
Height of type B tree = 18 + 10a
We must set the two types of trees' heights equal to one another and solve for "a" to determine when they will reach the same height:
36 + 8a = 18 + 10a
Subtracting 8a from both sides, we get:
36 = 18 + 2a
Subtracting 18 from both sides, we get:
18 = 2a
Dividing both sides by 2, we get:
a = 9
Therefore, after 9 years, both types of trees will be the same height.
To check this, we can substitute a = 9 into both equations:
Height of type A tree = 36 + 8(9) = 36 + 72 = 108 inches
Height of type B tree = 18 + 10(9) = 18 + 90 = 108 inches
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Question:
You have two types of trees to plant in your yard: type A trees are 36 inches tall and grow 8 inches per year, while type B trees are 18 inches tall and grow 10 inches per year. At what point in time will the trees be the same height? How tall will the trees be at that time?
On the day a video was posted online, 5 people watched the video. The next day the number of viewers had doubled. Assume the
number of viewers continues to double each day.
1. On which day will 640 people see the video? Explain or show your reasoning.
2. What strategy would you use to find the first day when more than 20,000 people will see the video (if the trend continues)?
On the 7th day after the videο was pοsted, 640 peοple will see the videο.
What is Statistics?Statistics is the discipline that cοncerns the cοllectiοn, οrganizatiοn, analysis, interpretatiοn, and presentatiοn οf data.
1 Let's start by finding the pattern in the number οf viewers. We knοw that οn the first day, 5 peοple watched the videο. On the next day, the number οf viewers dοubled tο 5 x 2 = 10. On the third day, the number οf viewers dοubled again tο 10 x 2 = 20. We can see that the number οf viewers is dοubling each day, which means we can write the number οf viewers as:
[tex]V = 5 x 2^n[/tex]
where n is the number οf days after the videο was pοsted.
Nοw we want tο find οn which day the number οf viewers will be 640. Sο we can set V equal tο 640 and sοlve fοr n:
[tex]640 = 5 x 2^n[/tex]
[tex]2^n = 128[/tex]
n = lοg2(128) = 7
2. Tο find the first day when mοre than 20,000 peοple will see the videο, we can set V equal tο 20,000 and sοlve fοr n:
[tex]20,000 = 5 x 2^n[/tex]
2^n = 4,000
n = lοg2(4,000) ≈ 11.29
Since n represents the number οf days after the videο was pοsted, we can rοund up tο the next whοle number tο find the first day when mοre than 20,000 peοple will see the videο. Therefοre, οn the 12th day after the videο was pοsted, mοre than 20,000 peοple will see the videο if the trend cοntinues
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Evaluate the double integral.$ iint_{D}({color{red}7} x + {color{red}6} y),dA $, $ D $ is bounded by $ y=sqrt{x} $ and $ y=x^2 $
The final value of the integral as [tex]$\frac{191}{60}$[/tex] which represents the total "volume" of [tex]$f(x,y)=7x+6y$[/tex] over the region[tex]$D$.[/tex]
The given double integral can be rewritten as:
[tex]\iint_D 7x \, dA + \iint_D 6y \, dA[/tex]
where [tex]D$ is the region bounded by $y=\sqrt{x}$ and $y=x^2$.[/tex]
To evaluate this integral, we first check the intersection points of the two curves:
[tex]\sqrt{x} = x^2 \quad \Right arrow \quad x = 0 \text{ or } x =1[/tex]
Therefore, the region D is shown in the figure below:
region D
Next, we can choose to integrate with respect to [tex]x$ or $y$[/tex]. Since the lower boundary of D is given by [tex]$y=\sqrt{x}$[/tex]which is a function of [tex]x$,[/tex] we choose to integrate with respect to x first:
[tex]\begin{aligned} \iint_D 7x \, dA &= \int_0^1\int_{\sqrt{x}}^{x^2} 7x \, dydx \\ &= \int_0^1 7x(x^2-\sqrt{x}) \, dx \\ &= \frac{56}{15} \end{aligned}[/tex]
Similarly, we can evaluate the other integral:
[tex]\begin{aligned} \iint_D 6y \, dA &= \int_0^1\int_{\sqrt{x}}^{x^2} 6y \, dydx \\ &= \int_0^1 6\left(\frac{x^4-\sqrt{x}}{2}\right) \, dx \\ &= \frac{49}{20} \end{aligned}[/tex]
Therefore, the value of the given double integral is:
[tex]\iint_D (7x+6y) \, dA = \frac{56}{15}+\frac{49}{20} = \frac{191}{60}[/tex]
In summary, we evaluated the given double integral by splitting it into two integrals, integrating with respect to x first and then with respect to y , over the region bounded by [tex]y=\sqrt{x}$ and $y=x^2$[/tex]. By doing so, we obtained the final value of the integral as [tex]\frac{191}{60}$,[/tex] which represents the total "volume" of [tex]$f(x,y)=7x+6y$[/tex] over the region D.
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what is the proof that complex numbers with absolute value 1 constitute a group under multiplication?
To prove that complex numbers with absolute value 1 constitute a group under multiplication, they must satisfy the four axioms of a group which includes
ClosureAssociativityIdentity elementInverseWhat are complex numbers?
In mathematics, a complex number is described as an element of a number system that extends the real numbers with a specific element denoted i, called the imaginary unit and can be expressed in the form a + bi, where a and b are real numbers.
The four axioms of a group includes:
Closure: The product of any two complex numbers with absolute value 1 is another complex number with absolute value 1.
Associativity: The product of any three complex numbers with absolute value 1 is the same irrespective of the order in which the multiplication is performed.
Identity: There exists an element in the group, denoted by 1, such that 1 times any element in the group is equal to that element.
Inverse: there exists another element in the group, denoted by the reciprocal or inverse, such that their product is equal to the identity element for each element in the group.
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Decide if the events A and B are mutually exclusive or not mutually exclusive. A card is drawn from a standard deck of 52 playing cards.
Event A: The Result is a club
Event B: The result is a king
Are they mutually exclusive or not mutually exclusive?
What is 0.1 in exponent form
Answer:
pretty-pretty sure its 1/10
Step-by-step explanation:
Convert to a mixed number by placing the numbers to the right of the decimal over
10
. Reduce the fraction.
1
10
How many functions are there from the set {1, 2, . . . , n}, where n is a positive integer, to the set {0, 1} a) that are one-to-one? b) that assign 0 to both 1 and n? c) that assign 1 to exactly one of the positive integers less than n?
The number of functions ,
(a) that are one-to-one are 0.
(b) that assign 0 to both 1 and n are 2ⁿ⁻²,
(c) that assign "1" to exactly one of positive-integers less than n are 2.(n-1).
Part(a) : We have to find total number of "one-to-one" functions from the set {1,2,......,n} to {0,1}.
⇒ If n=1 then there are 2 possible functions depending whether 1 is mapped to "0" or "1" ,So there are 2 such functions.
⇒ If n=2 then domain is {1,2} then there are 2 choices for first element in domain.
Then, since one choice is taken there is one choice for second element in the domain. So, if n=2 we have 2×1 = 2 functions.
⇒ If value of n is greater than 2 then domain will be {1,2,....n} then only two value of this domain will be mapped to codomain {0,1} to provide a one-to-one function and
So, domain will not be used fully so there does not exist any one-to-one function.
Part(b) : Every element in the domain {1, 2, . . . , n} has two options in codomain {0, 1},
So, there are total of "2n" functions from domain to co-domain.
Since, the function assigns 0 to both 1 and n.
There are "n-2" elements left in domain which can be assigned 0 or 1.
So, for "n-2" elements in domain and there are "2ⁿ⁻²" functions from domain to codomain.
Part(c) : The domain set has "n" elements and codomain set has "2" elements.
So, each of "n" elements from domain has 2 choices in function and thus we get "2n" total functions.
There are "n-1" elements less than "n" in domain.
Now, by the condition that exactly "1" positive-integer less than "n" maps to "1".
So, all other remaining less than n (i.e. n-2) must be map to 0.
We find this number in ⁿ⁻²C₁ ways = n-2;
So, total number of ways in which elements less than "n" can be mapped is = n-2(mapped to 0) +1(mapped to 1) = n-1
Also, "n" can be mapped to either "0" or "1" which means., nth element have two-choices.
So, there are 2.(n-1) possible functions.
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Which equation calculates the total amount of milk needed to make 7 milkshakes if each milkshake requires 3 4 cup of milk? A. 7 × 3 4 = 21 28 cups B. 7 + 3 4 = 7 3 4 cups C. 7 × 1 4 = 7 4 , or 1 3 4 cups D. 7 × 3 4 = 21 4 , or 5 1 4 cups
Answer:
D
Step-by-step explanation:
7/1 times 3/4 equals 21/4 cups of milk
7. Convert 37/6 to a mixed number.
A. 6¹6
B. 623
C. 65
D.556
[tex] \boxed{ \red{ \mathfrak{A.\: 6 \frac{1}{6} }}}[/tex]
To the nearest hundredth, what is the volume of the sphere? (Use 3.14 for pie.)
Therefore, the volume of the sphere to the nearest hundredth is 724,775.70 cubic millimeters.
What is volume?Volume is a measurement of the amount of space occupied by a three-dimensional object. It is often expressed in units such as cubic meters (m³), cubic centimeters (cm³), cubic feet (ft³), or gallons (gal), depending on the context. The volume of a solid object can be calculated by multiplying its length, width, and height or using a specific formula depending on the shape of the object. For example, the volume of a rectangular box can be calculated as length x width x height, while the volume of a cylinder can be calculated as π x radius² x height. In general, volume is an important concept in many fields, including physics, chemistry, engineering, and architecture. It is often used to describe the capacity of containers, the displacement of fluids, and the amount of material used in construction or manufacturing.
Here,
The formula for the volume of a sphere is given as V = (4/3)πr³, where r is the radius of the sphere and π is approximately 3.14.
Substituting the given value of the radius, we get:
V = (4/3) x 3.14 x 48³
V ≈ 724,775.68 cubic millimeters
Rounding this value to the nearest hundredth, we get:
V ≈ 724,775.68 ≈ 724,775.70 cubic millimeters (rounded to two decimal places)
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PLEASEE HELP!
Draw an angle that is 90 degrees. Make sure to draw the symbol on the angle.
Step-by-step explanation:
This is just the corner of a rectangle or a square :
Oliver's normal rate of pay is $10.40 an hour.
How much is he paid for working 5 hours overtime one Saturday at time-and-a-half?
Let X be a random variable whose probability density function is given by else (a) Write down the moment generating function for X (b) Compute the first and second moments.
a) The moment generating function of X is
M(t) =
{ (1/(2-t)) e^(-2t) + (1/(2-t)) (1/(1+t)) if t<1
{ infinity if t>=1
b) The first moment (mean) of X is 3/4.
The second moment (expected value of X^2) of X is 7/8
(a) The moment generating function (MGF) of a random variable X with probability density function f(x) is defined as M(t) = E(e^(tX)), where E(.) denotes the expected value operator. Therefore, the MGF of X is
M(t) = E(e^(tX)) = ∫[0,∞) e^(tx) f(x) dx
Substituting the given probability density function f(x), we get
M(t) = ∫[0,∞) e^(tx) (e^(-2x) + (e^-x)/2) dx
Simplifying and integrating by parts, we get
M(t) = [(1/(2-t)) e^(-2t) + (1/(2-t)) (1/(1+t))] for t<1, and
M(t) = infinity for t>=1
Therefore, the MGF of X is
M(t) =
{ (1/(2-t)) e^(-2t) + (1/(2-t)) (1/(1+t)) if t<1
{ infinity if t>=1
(b) To compute the first moment (i.e., the mean or expected value) of X, we take the first derivative of the MGF at t=0
E(X) = M'(0) = d(M(t))/dt | t=0
Differentiating the MGF and simplifying, we get
E(X) = 3/4
To compute the second moment (i.e., the expected value of X^2), we take the second derivative of the MGF at t=0
E(X^2) = M''(0) = d^2(M(t))/dt^2 | t=0
Differentiating the MGF again and simplifying, we get
E(X^2) = 7/8
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The given question is incomplete, the complete question is:
Let x be a random variable whose probability density function is given by f(x) = e^(-2x) + (e^-x)/2 when x>0 f(x) = 0 when else, a) write down the moment generating function X (b) Compute the first and second moments
Hence, determine the circumstances of the base base of a coffee tin
Answer:
We can write the diameter and circumferance of base as -
D = 2√(750ρ/πh)
C = 2π√(750ρ/πh)
Step-by-step explanation:
What is function?
A function is a relation between a dependent and independent variable.
Mathematically, we can write → y = f(x) = ax + b.
Given is to find the diameter and height of the tin can.
Assume the density of coffee as {ρ}. We can write the volume of the tin can as -
Volume = mass x density
Volume = 750ρ
We can write -
πr²h = 750ρ
r = √(750ρ/πh)
D = 2r
D = 2√(750ρ/πh)
Now, we can write the circumferance as -
C = 2πr
C = 2π√(750ρ/πh)
Therefore, we can write the diameter and circumferance of base as -
D = 2√(750ρ/πh)
C = 2π√(750ρ/πh)
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