Let Vector U= PQ, V=QR, And Vector W=RP, Where P(2, -1), Q(-3, 5) And R(0, 4) Do The Following Tasks. If An Answer Is A Vector, Give It In Component Form. Give Exact Answers In Simplest Form. If An Answer Is Undefined, State So. ______________ A. Find ,S A Unit Vector In The Opposite Direction Of .U ______________ B. Vector 2u - 3/2
Let vector u= PQ, v=QR, and vector w=RP, where P(2, -1), Q(-3, 5) and R(0, 4) Do the following tasks.
If an answer is a vector, give it in component form. Give exact answers in simplest form. If an answer is
undefined, state so.
______________ a. Find ,s a unit vector in the opposite direction of .u
______________ b. vector 2u - 3/2 (w-v)
______________ c. vector (u * (v)) w=
______________ d. vector (w * (v)) =
Answers
a. To find a unit vector in the opposite direction of vector U, we first need to find the opposite direction of U. The opposite direction of U is simply the negative of U, which is -U.
- U = -PQ = -(Q - P) = -( -3 - 2, 5 - (-1) ) = (1, -6)
To get a unit vector in this direction, we need to divide -U by its magnitude:
| -U | = sqrt(1^2 + (-6)^2) = sqrt(37)
So, a unit vector in the opposite direction of U is:
s = (-U) / | -U | = (1/sqrt(37), -6/sqrt(37))
b. We need to first calculate 2U, then (w-v), and then multiply them together and scale by 3/2:
2U = 2(PQ) = 2(Q-P) = 2(-3-2, 5-(-1)) = (-10, 12)
(w-v) = RP - QR = (0, 4) - (-3, 5) = (3, -1)
2U - 3/2(w-v) = 2(-10, 12) - 3/2(3, -1) = (-23, 28.5)
So the vector 2U - 3/2(w-v) is (-23, 28.5).
c. To find the vector (u * (v)) w, we need to first calculate the cross product of u and v, and then multiply the result by w:
u x v = | i j k |
| -3 5 0 |
| 2 -1 0 |
= -5i - 6j - 13k
Now we multiply by w:
(w x (u x v)) = | i j k |
| 0 4 0 |
| -5 -6 -13 |
= (-52, 0, 20)
So the vector (u * (v)) w is (-52, 0, 20).
d. To find the vector (w * (v)), we need to calculate the cross product of w and v:
w x v = | i j k |
| 0 4 0 |
| -3 5 0 |
= (0, 0, 20)
So the vector (w * (v)) is (0, 0, 20).
a. To find a unit vector in the opposite direction of vector u, first find the component form of u:
u = PQ = (Q_x - P_x, Q_y - P_y) = (-3 - 2, 5 - (-1)) = (-5, 6)
Now, find the magnitude of u:
||u|| = √((-5)^2 + (6)^2) = √61
Next, find the unit vector in the opposite direction:
-u/||u|| = (5/√61, -6/√61)
Answer a: (5/√61, -6/√61)
b. First, find the component form of v and w:
v = QR = (R_x - Q_x, R_y - Q_y) = (0 - (-3), 4 - 5) = (3, -1)
w = RP = (P_x - R_x, P_y - R_y) = (2 - 0, -1 - 4) = (2, -5)
Now, find 2u - 3/2 (w - v):
2u - 3/2(w - v) = 2(-5, 6) - 3/2[(2, -5) - (3, -1)] = (-10, 12) - 3/2(-1, -4) = (-10, 12) - (-3/2, -6) = (-7/2, 18)
Answer b: (-7/2, 18)
c. The expression "vector (u * (v)) w" is not well-defined. Vector operations need to be specified, such as addition or dot product.
d. Similarly, the expression "vector (w * (v))" is not well-defined. Please provide the specific vector operation required.
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Related Questions
Jacque needs to buy some pizzas for a party at her office. She's ordering from a restaurant that charges a \$7.50$7.50dollar sign, 7, point, 50 delivery fee and \$14$14dollar sign, 14 per pizza. She wants to buy as many pizzas as she can, and she also needs to keep the delivery fee plus the cost of the pizzas under \$60$60dollar sign, 60. Each pizza is cut into 888 slices, and she wonders how many total slices she can afford. Let PPP represent the number of pizzas that Jacque buys.
Answers
Answer:
7.50 +14P < 60
30 slices
Step-by-step explanation:
Delivery fee = $7.50
Cost per pizza = $14
Budget constraints = $60
7.50 + 14P < 60
14p < 60 - 7.50
14p < 52.5
P < 3.75
Each pizza can be cut into 8 slices
how many total slices she can afford?
= 3.75 × 8
= 30 slices
Answer:
7.50 +14P < 60
24 slices
Step-by-step explanation:
Khan Academy Answer
find the volume of the solid obtained by rotating the region bounded by y=sqrt(x-1), y=0, and x=5 about the x-axis
Answers
The volume of the solid obtained by rotating the region bounded by y = √(x - 1), y = 0, and x = 5 about the x-axis is 10π cubic units.
Given, y = √(x - 1), y = 0, and x = 5To find the volume of the solid obtained by rotating the region bounded by y = √(x - 1), y = 0, and x = 5 about the x-axis.Volume of a solid obtained by rotating a region bounded by y = f(x), y = 0, x = a, and x = b about the x-axis is given byV = π∫ab (f(x))^2 dxHere, a = 1, b = 5 and f(x) = √(x - 1)So, the volume of the solid obtained by rotating the region bounded by y = √(x - 1), y = 0, and x = 5 about the x-axis isV = π∫ab (f(x))^2 dxFinding out the limits of integration for the given function y = √(x - 1)When y = 0, √(x - 1) = 0Or, x = 1When x = 5, y = √(5 - 1) = 2So, the limits of integration are a = 1 and b = 5.So, the required volume of the solid can be obtained by solving the integralπ∫ab (f(x))^2 dx = π∫15 (√(x - 1))^2 dx= π∫15 (x - 1) dx= π[(x^2/2 - x)|_1^5]= π[(5^2/2 - 5) - (1^2/2 - 1)]= π(25/2 - 5/2)= 10π
Therefore, the volume of the solid obtained by rotating the region bounded by y = √(x - 1), y = 0, and x = 5 about the x-axis is 10π cubic units.
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What’s the range of 27, 28, 34, 34, 40, 43, 47, 50
Answers
Answer:
23
Step-by-step explanation:
you subtract 50 the max number from 27 the Lowest number
Help on math please
Answers
Answer:
40cm²Step-by-step explanation:
ΔABC ≅ ΔDEF
The length AB = 28 and the length of DE = 7. Since these are corresponding sides, we know that DEF= 1/4 (ΔABC)
So, since ΔABC = 160, we know that ΔDEF will be 1/4 of that, meaning that ΔDEF is 40.
ΔDEF = 40cm²
Answer:
10 cm2
Step-by-step explanation:
The ratio per side is 28/7 = 4
When two similar figures have a ratio of 4:1, the difference between their areas is:
\((4)^{2} :(1)^{2}\)
\(16:1\)
That is, the dimension of the area of the largest figure is 16 times larger than the smallest figure.
So for this case:
the area of the larger figure is
ΔABC = 160 sq.cm
Then the area of the minor figure is:
ΔDEF= 160/16 = 10 sq.cm
Hope this helps
How do organism replace dead or injured cells? Organisms can take cells from other organisms. Organisms are limited to the amount of new cells that they can make through their lifetime. Organisms can make new cells by consuming other organisms. Organisms go through mitosis that allows new identical cells to be made.
Answers
Answer: Organisms go through mitosis that allows new identical cells to be made.
explanation:
mitosis also occures when cells are worn out or are injured and the mitosis will replace the injured cells
Can someone please help me answer these 2 questions with a full explanation of how you got the answer so I can do the rest myself?
Answers
Step-by-step explanation:
hope it will help you answer
You should start with the sin(x) = opposite /hypotenuse
See attachment
Find the 7th term of the geometric progression which begins. 2,-6,18
Answers
Step-by-step explanation:
Find the rule:
2, -6, 18, ...
To get to -6, multiply by -3.
To get to 18, multiply by -3.
The rule is to multiply by -3.
Find the 7th term:
Multiply 18 by -3.
\(-18 \times 3 = -54\)
-54 is the 4th term.
Multiply -54 by-3.
\(-54 \times -3 = 162\)
162 is the 5th term.
Multiply 162 by -3.
\(162 \times -3 =-486\)
-486 is the 6th term.
Multiply -486 by -3.
\(-486 \times -3 = 1458\)
1458 is the 7th term.
The linear function y = g(x) Is graphed in the xy-plane. If g(-3) = 4 and g(2) = 19,
what is the slope of line g?
Answers
The slope of the line g is 3.
What is the slope?In mathematics, a line's slope, also known as its gradient, is a numerical representation of the line's steepness and direction.By calculating the difference between the coordinates of the two points, (x₁,y₁) and (x₂,y₂), it is simple to calculate the slope of a straight line between them. The letter "m" is frequently used to denote slope.So, the slope of line g will be:
y₁ = f(x₁)y₂ = f(x₂)Sope formula: y₂ - y₁/x₂ - x₁
Now, calculate as follows:
y₂ - y₁/x₂ - x₁f(x₂) - f(x₁)/x₂ - x₁y = g(x)x₁ = -3x₂ = 2g(x₁) = g(-3) = 4g(x₂) = g(2) = 19Slope:
g(x₂) - g(x₁)/x₂ - x₁19-4/2-(-3)15/53Therefore, the slope of the line g is 3.
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please answer quickly
Answers
1a. 10. 24
1b. 125/243
2a. 0. 0048
2b. 32/3125
3a. 0. 64
3b. 0. 0031
4a. 2/5
4b. 48. 735
5a. 2. 36
5b. 1. 39
How to determine the values
1a. Given the values
(2/5)^2/(1/2)^6
Multiply both the numerator and denominator by the powers
⇒ \(\frac{\frac{4}{25} }{\frac{1}{64} }\)
To find the common ration, multiply thus;
⇒ \(\frac{4}{25}\) × \(\frac{64}{1}\)
⇒ \(\frac{256}{25}\)
= 10. 24
1b. (5/7)^2 × (5/7)^1
= \(\frac{25}{49}\) × \(\frac{5}{7}\)
= \(\frac{125}{343}\)
= 125/243
2a. 0. 6^1 × 0. 2^3
= 0. 6 × 0. 008
= 0. 0048
2b. (2/5)^3 × (2/5)^2
= \(\frac{8}{125}\) × \(\frac{4}{25}\)
= \(\frac{32}{3125}\)
= 32/ 3125
3a. 1^99 - 0. 6^2
= 1 - 0. 36
= 0. 64
3b. (0. 2 ) ^1 × (1/8)^2
= 0. 2 × 1/64
= 0. 2 × 0. 016
= 0. 0031
4a. (1/2)^2/ (5/8)^1
= \(\frac{\frac{1}{4} }{\frac{5}{8} }\)
Take the inverse of the denominator
= \(\frac{1}{4}\) × \(\frac{8}{5}\)
= 2/5
4b. 7^2 - 0. 5^3
= 49 - 0. 125
= 48. 875
5a. 3^1 - 0. 8 ^2
= 3 - 0. 64
= 2. 36
5b. 0. 7^2 + 0. 9^1
= 0. 49 + 0. 9
= 1. 39
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Which is the first step in solving
X-2 = 2?
Answers
Answer:
The first step is to find a number that when subtracted from 2 gives you 2.
Step-by-step explanation:
The algebraic part of this problem would be to add the -2 (adding 2 to both sides) to both sides, so
first x-2=2, then x-2(+2)=2(+2) which would give us,
x=4
*note: the parenthesis are just to show that we are adding the 2, to make it more understandable.
Suppose that csc θ = 20 and that 0 ≤θ ≤π/2, find the value of
the other 5 trigonometric functions to 4 digits. In this case,
there will only be one possible value for each other trig
function.
Answers
It is given that csc θ = 20 and 0 ≤θ ≤π/2.
Now, sin θ = 1/csc θ = 1/20cos θ = cos(π/2 - θ) = sin θ = 1/20tan θ = sin θ/cos θ = 1cot θ = 1/tan θ = cos θ = 1/20sec θ = 1/cos θ = 20
Therefore, the value of other 5 trigonometric functions to 4 digits is:
sin θ = 0.0500
cos θ = 0.9988
tan θ = 0.0502
cot θ = 19.9400
sec θ = 1.0012
Hence, the other 5 trigonometric functions to 4 digits for
csc θ = 20 and 0 ≤θ ≤π/2 are sin θ = 0.0500,
cos θ = 0.9988,
tan θ = 0.0502,
cot θ = 19.9400 and sec θ = 1.0012.
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please help asap!!
-
-
-
-
Answers
Answer:
a. y = 2x + 1
b. 20
Step-by-step explanation:
a. With each increasing figure, two more blocks are added on. Through this, we can determine the rule:
y = 2x + 1
y being the total number of blocks in a figure
x being the number of the figure.
_________
b. To figure out which figure number has 41 squares, we can set the equation we found equal to 41.
41 = 2x + 1
40 = 2x
20 = x
So figure 20 will have 41 squares.
Identify the boundary line for each system of inequalities
Answers
The boundary lines are y > -3x + 4: dotted line and y <= 8x + 1: solid line
How to determine the boundary linesFrom the question, we have the following parameters that can be used in our computation:
y > -3x + 4
y <= 8x + 1
The boundary line for the inequality "<" is a dotted line, which means that the endpoint is not included in the solution set.
The boundary line for the inequality ">=" is a solid line, which means that the endpoint is included in the solution set.
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Helppppppppppppppppppppppppppppppppp
Answers
Answer 4:00pm= 15
Step-by-step explanation:
45 plus 15 is 4:00
what is the best big-o function for the worst case scenario analysis of a linar search of a list of size n (counting the number of comparisons)?
Answers
Big O notation focuses on the worst-case scenario analysis, which is 0(n) for a simple search. It’s a reassurance that a simple search will never be slower than O(n) time.
Imagine that you're a teacher with a student named Ram. You want to find his records, so you use a simple search algorithm to go through your school district's database.
You know that a simple search takes O(n) times to run. This means in the worst case, you'll have to search through every single record to find Ram
After a simple search, you find that Ram records are the very first entry in the database. You don't have to look at every entry.
Did this algorithm take O(n) time Or did it take O(1) time because you found Ram records on the first try?
In this case, 0(1) is the best-case scenario – you were lucky that Ram records were at the top. But Big O notation focuses on the worst-case scenario, which is 0(n) for a simple search. It’s a reassurance that a simple search will never be slower than O(n) time.
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what do the symbols p with hat on top, x with bar on top, and s represent? variables of interest sample statistics defined variables population parameters
Answers
The symbols p,x, and s represent sample statistics.
- p (pronounced "p-hat") is the sample proportion. It is used to estimate the population proportion. It is computed as the number of successes in the sample divided by the sample size.
-x (pronounced "x-bar") is the sample mean. It is used to estimate the population mean. It is computed as the sum of all the values in the sample divided by the sample size.
- s is the sample standard deviation. It is used to estimate the population standard deviation. It measures how spread out the data is in the sample. It is computed as the square root of the sum of the squared deviations from the sample mean divided by the sample size minus one.
These sample statistics are used to make inferences about the corresponding population parameters, which are denoted by Greek letters such as μ (mu) for the population mean and σ (sigma) for the population standard deviation.
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ace company provided the following data on december 31, 2021: cash 1,500,000 inventories 280,000 prepaid supplies 120,000 land 360,000 furniture & fixtures 60,000 accounts payable 385,000 salaries & wages payable 12,000 net sales and other revenue 770,000 cost and expenses 340,000 retained earnings, jan. 01, 2021 1,100,000 on december 31, 2021, what amount should be reported as current assets
Answers
Amount reported as Current Assets = 1,912,000
Current assets are items that a corporation utilizes, replaces, or turns into cash during a typical operating cycle. They are also known as short-term assets (typically less than 12 months). It sets them apart from long-term assets or those that a company utilizes for more than a year. Current assets are referred to as liquid assets since they may be converted into cash more readily than long-term assets.
The balance sheet shows both current and long-term assets, which combined comprise all of the company's assets.
Amounts reported as Current Assets are :
Cash = 1,500,000
Inventories = 280,000
Prepaid Supplies = 120,000
Salaries and Wages Payable = 12,000
Total Amount = 1,500,000 + 280,000 + 120,000 + 12,000 = 1,912,000
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The city of London, England, has an
elevation of 11 meters.
Which of these describes the elevation
of London?
below sea level
at sea level
above sea level
Answers
Answer:
above sea level
Step-by-step explanation:
Find the type and number of roots of the following equations using the discriminat
Answers
Recall that the discriminant of a quadratic equation:
\(ax^2+bx+c=0\)is:
\(\Delta=b^2-4ac\text{.}\)Also, if:
\(\begin{cases}\Delta>0\text{ the quadratic equation has 2 different real roots,} \\ \Delta=0\text{ the quadratic equation has 1 root of }multiplicity\text{ 2,} \\ \Delta<0\text{ the quadratic equation has 2 different imaginary roots.}\end{cases}\)Now, notice that the discriminant of the given equation is:
\(\Delta=4^2-4\cdot1\cdot(-2)\text{.}\)Simplifying the above result we get:
\(\Delta=16+8=24.\)Since 24>0, we get that the given equation has 2 different real roots.
Answer: The given equation has 2 different real roots.
the daily supply of oxygen for a particularmulticellular organism is provided by 625sq ft of lawn. A total of 4,375 sq ft of lawn would provide the daily supplies of oxygen for how many organisms?
Answers
7 organisms
Explanation:Area of lawn that supplies oxygen for a particular multicellular organism = 625 sq ft
Total area of the lawn = 4,375 sq ft
Number of organisms = 4375/625
Number of organisms = 7
A total of 4,375 sq ft of lawn would provide the daily supplies of oxygen for 7 organisms
Solve the following inequality: 38 < 4x+3+7 – 3x.
a. x < 28
b. x > 28
c. x < 4
d. x > 4
Answers
To solve the given inequality, first we have to simplify the given inequality.38 < x + 10 After simplification we get, 38 - 10 < x or 28 < x.
The correct option is B.
The given inequality is 38 < 4x + 3 + 7 - 3x. Simplify the inequality38 < x + 10 - 4x + 3 + 7 - 3x38 < -x + 20 Combine the like terms on the right side and simplify 38 + x - 20 < 0 or x + 18 < 0x < -18 + 0 or x < -18. The given inequality is 38 < 4x + 3 + 7 - 3x. To solve the given inequality, we will simplify the given inequality.
Simplify the inequality38 < x + 10 - 4x + 3 + 7 - 3x38 < -x + 20 Combine the like terms on the right side and simplify 38 + x - 20 < 0 or x + 18 < 0x < -18 + 0 or x < -18. Combine the like terms on the right side and simplify38 + x - 20 < 0 or x + 18 < 0x < -18 + 0 or x < -18.So, the answer is x > 28. In other words, 28 is less than x and x is greater than 28. Hence, the answer is x > 28.
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true or false: the general fertility rate refers to the number of live births reported in an area during a given time interval divided by the number of women age 15 to 44 years in the area. group of answer choices true false
Answers
The general fertility rate refers to the number of live births reported in an area during a given time interval divided by the number of women age 15 to 44 years in the area is false
The general fertility rate refers to the number of live births reported in an area during a given time interval per 1,000 women of reproductive age (usually defined as 15 to 44 years old) in the same area.
Therefore, it is a rate or a ratio that expresses the number of births in relation to the number of women of reproductive age in a population.
Hence, the statement is False that the general fertility rate refers to the number of live births reported in an area during a given time interval divided by the number of women age 15 to 44 years in the area is false
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Please help me and the answer is not 6.4
Answers
Answer:
4.9
Step-by-step explanation:
10 total points) Suppose that Susan enjoys sugar in her coffee. She has very particular preferences. and she must have exactly four spoonfiuls of sugar for each cup of coffee. Let C be the number of cups of coffee, and S be the number of spoonfuls of sugar. Also, let Pc be the price of a cup of coffee and PS be the price of a spoonful of sugar. Suppose Susan has $12 to spend on Coffec and Sugar (M=$12). Also, the price of a spoonful of Sugar is P5=$.25. Graph Susan's Price Consumption Curve for prices, Pc=$1,Pc=$2, and PC=$3. Please put the number of cups of coffee (C) on the horizontal axis, and the number of spoonfiuls of Sugar (S) on the vertical axis. Be sure to graph each budget constraint associated with each price of Coffee, identify Susan's optimal bundle on each budget constraint, and make sure your graph is labeled carefully and accurately.
Answers
When Pc = $1, the budget constraint is C + 0.25S = 12. The graph will have a horizontal intercept at C = 12 and a vertical intercept at S = 48.
When Pc = $2, the budget constraint is 2C + 0.25S = 12. The graph will have a horizontal intercept at C = 6 and a vertical intercept at S = 48.
When Pc = $3, the budget constraint is 3C + 0.25S = 12. The graph will have a horizontal intercept at C = 4 and a vertical intercept at S = 48.
Let's start with Pc = $1:
Since Susan has $12 to spend, we can express her budget constraint as follows:
Pc * C + PS * S = M
$1 * C + $0.25 * S = $12
To find the maximum number of cups of coffee, C, we'll set S = 0 and solve for C:
$1 * C + $0.25 * 0 = $12
C = 12
Similarly, to find the maximum number of spoonfuls of sugar, S, we'll set C = 0 and solve for S:
$1 * 0 + $0.25 * S = $12
S = 48
Next, let's consider Pc = $2:
Using the same process, we can find the maximum values of C and S:
$2 * C + $0.25 * S = $12
Setting S = 0, we find:
$2 * C + $0.25 * 0 = $12
C = 6
Setting C = 0, we find:
$2 * 0 + $0.25 * S = $12
S = 48
Finally, let's consider Pc = $3:
$3 * C + $0.25 * S = $12
Setting S = 0, we find:
$3 * C + $0.25 * 0 = $12
C = 4
Setting C = 0, we find:
$3 * 0 + $0.25 * S = $12
S = 48
Now, let's plot these budget constraints on a graph with C (number of cups of coffee) on the horizontal axis and S (number of spoonfuls of sugar) on the vertical axis.
css
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48 | A
|
|
24 |
|
|
12 | B
|
|
0 |__|__|__|__|__|__|__|__|__|__|
0 4 6 12 16 20 24 28 32 36 40
Here, point A represents the budget constraint for Pc = $1 (C + 0.25S = 12), and point B represents the budget constraint for Pc = $2 (2C + 0.25S = 12). The curve starts at (12, 0) and slopes downwards.
Since the third budget constraint for Pc = $3 (3C + 0.25S = 12) intersects the previous two budget constraints, we'll draw a dotted line to represent it:
css
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48 | A
| |
| /
24 | /
| /
|/
12 | B
|
|
0 |__|__|__|__|__|__|__|__|__|__|
0 4 6 12 16 20 24 28 32 36 40
To find Susan's optimal bundle on each budget constraint, we'll look for the point of tangency (highest indifference curve) between the budget constraint and the indifference curves. Unfortunately, without additional information about Susan's preferences, we can't determine her exact preferences and optimal bundle.
Note: The graph above is a basic representation of Susan's price consumption curve, but it may not be perfectly accurate due to limitations in text-based formatting.
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Let X = the score out of 3 points on a randomly selected quiz in a Prob
& Stat course. The table gives the probability distribution of X.
Value
0
1
2
3
Probability
0. 05
0. 15
0. 60
A) Find the missing value for P(X = 1) in the probability distribution.
B) P(X 2 2) =
C) P(X > 2) =
D) The probability of "At least 2" is equivalent to
Answers
A. The missing value for P(X = 1) is 0.20.
B. The value of P(X ≤ 2) is 0.85.
C. The value of P(X > 2) is 0.15.
D. The probability of "At least 2" is equivalent to P(X >= 2), which is 0.75.
In probability theory, a probability distribution is a function that assigns probabilities to each possible value of a random variable.
In this Problem, we have a probability distribution for the score on a quiz, with X being the random variable and the table providing the probability of each possible score. In this answer, we will use the given probability distribution to answer the questions posed.
A) Find the missing value for P(X = 1) in the probability distribution.
To find the missing value for P(X = 1), we need to use the fact that the sum of the probabilities for all possible values of X must be equal to 1. Therefore, we can set up an equation:
P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) = 1
Substituting in the given probabilities, we get:
0.05 + P(X = 1) + 0.60 + 0.15 = 1
Simplifying, we get:
P(X = 1) = 0.20
Therefore, the missing value for P(X = 1) is 0.20.
B) P(X ≤ 2) =
To find P(X ≤ 2), we need to add up the probabilities of X being less than or equal to 2. This is equivalent to:
P(X ≤ 2) = P(X = 0) + P(X = 1) + P(X = 2)
Substituting in the given probabilities, we get:
P(X ≤ 2) = 0.05 + 0.20 + 0.60 = 0.85
Therefore, P(X ≤ 2) is 0.85.
C) P(X > 2) =
To find P(X > 2), we need to add up the probabilities of X being greater than 2. This is equivalent to:
P(X > 2) = P(X = 3)
Substituting in the given probabilities, we get:
P(X > 2) = 0.15
Therefore, P(X > 2) is 0.15.
D) The probability of "At least 2" is equivalent to P(X >= 2)
To find the probability of "At least 2," we need to add up the probabilities of X being greater than or equal to 2. This is equivalent to:
P(X ≥ 2) = P(X = 2) + P(X = 3)
Substituting in the given probabilities, we get:
P(X ≥ 2) = 0.60 + 0.15 = 0.75
Therefore, the probability of "At least 2" is equivalent to P(X ≥ 2), which is 0.75.
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find the distance between each pair of points in the coordinate plane.(3,1) and (3,-5)
Answers
We have the following:
\(d(P_1,P_2)=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2}\)Now,
\(\begin{gathered} P_1=(3,1)=(x_1,y_1) \\ P_2=(3,-5)=(x_2,y_2) \end{gathered}\)replacing:
\(\begin{gathered} d=\sqrt[]{x_2-x_1)^2+(y_2-y_1)^2} \\ d=\sqrt[]{(3-3)^2+(-5-1_{})^2} \\ d=\sqrt[]{0^2+(-6)^2} \\ d=\sqrt[]{36} \\ d=6 \end{gathered}\)Therefore, the answer is 6 units
Name BOTH pairs of alternate interior angles. HELPPPPP PLEASE!!!!!!
Answers
Answer:
Angles 6 and 2
Step-by-step explanation:
They are in the "interior" of the figure, plus, ik how to do this
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Tyler, Jackie, Pam, and Marc all live on the same street. Tyler lives 1/2 mile from the neighborhood's public school. Jackie lives 5/9 mile from the school. Pam lives 4/7 mile from the school, and Marc lives 2/5 mile from the school. Who lives farthest from the school?
Answers
Answer:
pam
Step-by-step explanation:
you can make all fractions equivalent using a common denominator of 620 or change each to a decimal, then compare:
1/2 = .50
5/9 = .55
4/7 = .57
2/5 = .40
George's dog ran out of its crate. It ran 22 meters, turned and ran 11 meters, and then turned 120° to face its crate. How far away from its crate is George's dog? Round to the nearest hundredth.
Answers
George's dog is approximately 32.41 meters away from its crate, if it ran 22 meters, turned and ran 11 meters, and then turned 120° to face its crate.
To determine the distance from George's dog to its crate after the described movements, we can use the concept of a triangle and trigonometry.
The dog initially runs 22 meters, then turns and runs 11 meters, forming the two sides of a triangle. The third side of the triangle represents the distance from the dog's final position to the crate.
To find this distance, we can use the Law of Cosines, which states that in a triangle with sides a, b, and c and angle C opposite side c, the equation is c² = a² + b² - 2abcos(C).
In this case, a = 22 meters, b = 11 meters, and C = 120°. Plugging these values into the equation, we have
c² = 22² + 11² - 2(22)(11)cos(120°).
Evaluating the expression, we get
c ≈ 32.41 meters.
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Please answer this problem I can't seem to figure it out.
