The dot product of u and v is -64. The distance between u and v is 16.
The dot product of two vectors u and v is calculated by multiplying the corresponding components of each vector and then summing the results. Therefore, the dot product of u and v is:
u•v = (−3)(9) + (10)(−5) + (9)(7) = −27 − 50 + 63 = −64
The distance between two vectors u and v is calculated by taking the square root of the dot product of the two vectors. Therefore, the distance between u and v is:
Distance(u,v) = √(u•v) = √(−64) = 16
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need help simplify:(x^2y^-3/2^-2)^-1
Hope it helps u
Refer to the image below
What does a coefficient of determination of 0.8 mean?
Eighty percent of the points ought to lie within the regression line if the coefficient is 0.80. A regression line would be considered to reflect all of the data if its value was 1, and none if it were 0.
What does a number of 0.8 r2 mean?The amount of variance in Y that can be explained by the independent variables X is measured by the R-square (R2), also known as the coefficient of determination. The model's degree of good fit is gauged by this. In the case of an R2 of 0.8, the input variable can account for 80% of the variation in the output.A quite strong positive correlation (correlation coefficient = 0.8) exists. A moderately positive link is indicated by a correlation coefficient of 0.6. Correlation Coefficient = 0: There is no association.Coefficient of determination (CODE): MeaningEighty percent of the points ought to lie within the regression line if the coefficient is 0.80. A regression line would be considered to reflect all of the data if its value was 1, and none if it were 0.To learn more about coefficient refer to:
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Determine if b is a linear combination of a1, a2, and a3. Choose the correct answer below. a1=[2 0 2] a2 = [-4 3-4 ] a3 = [-5 8 4] a4= [13 -4 9]
A. Vector b is a linear combination of a1, a2, and a3. The pivots in the corresponding echelon matrix are in the first entry in the first column, the second entry in the second column, and the third entry in the third column.
B. Vector b is not a linear combination of a1, a2, and a3. C. Vector b is a linear combination of a1, a2, and a3. The pivots in the corresponding echelon matrix are in the first entry in the first column and the third entry in the second column, and the third entry in the third column.
D. Vector b is a linear combination of a1, a2, and a3. The pivots in the corresponding echelon matrix are in the first entry in the first column, the second entry in the second column, and the third entry in the fourth column.
B. Vector b is not a linear combination of a1, a2, and a3.
What is Linear combination?
A linear combination is any expression of the form ax + by, where a and b are constants, formed by multiplying each term by a constant and combining the results.
Given that, b is a linear combination of a1, a2, and a3.
Then, Correct answer would be Vector b is not a linear combination of a1, a2, and a3.
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last one thanks a lot
He owed $14,983.85 at the end of 4 years.
What is Compound Interest?Compound interest is when you earn interest on both the money you've saved and the interest you earn.
Given:
P = $8000
R= 16%
T= 4 years
Now, The equation that models this situation is:
A(t) = P [tex](1 + r/n)^{nt[/tex]
where:
A is the amount he owes at any time (t)
P, is the initial amount borrowed (the amount owed at time t = 0)
n is the number of times the loan is compounded annually
r is the interest rate in decimal form
So, A(4) = 8000[tex](1 + 0.16/4)^{4.4[/tex]
A(4) = 8000[tex](1 + 0.04)^{16[/tex]
A = $14,983.85
Hence, the amount is $14,983.85.
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Check commutative property, additive identity and associative property of addition of integers.
The commutative property, additive identity, and associative property of the addition of integers are illustrated below.
What are the basic properties of arithmetic laws of operations?There are three types of basic arithmetic laws of operation.
Commutative law for addition and multiplication states,
a + b = b + a.
a×b = b×a.
Distributive law states,
a(b ± c) = ab ± ac.
Associative law states,
a + (b + c) = (a + b) + c.
The commutative law for addition is a + b = b + a.
Suppose a = 2 and b = 3.
So, 2 + 3 = 3 + 2 ⇒ a + b = b + a.
The additive identity of a number is the addition of two similar numbers is zero.
So, a + (- a) = 0.
Associative law says the grouping of numbers has no effect in addition.
Let, a = 2, b = 3, and c = 6.
(a + b) + c = a + b( + c) ⇒ (2 + 3) + 6 = 2 + (3 + 6).
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Ten members Three juniors and seven seniors from the science club qualify for a national competition, but only five
people per school can attend the event. The coach decides to put the 10 members' names on identical slips of
paper, put the slips in a hat, and pull out five names, one at a time. Those five students will go to the national
competition. Let X represent the number of juniors selected to attend the competition.
Have the conditions for a binomial setting been met for this scenario?
Yes, all four conditions in BINS have been met.
O No, we do not know how many people overall will go to the national competition.
No, there is no way to find out the probability of choosing just one student to attend.
No, the names were pulled and not replaced in the hat, so the independence condition is not met.
No, the independence condition is not met. The conditions for a binomial setting have not been met in this scenario because the names were pulled and not replaced in the hat, which violates the independence condition.
In a binomial setting, the trials must be independent, meaning that the outcome of one trial does not affect the outcome of any other trial.
Since the names were not replaced in the hat, the outcome of each draw is not independent, and the conditions for a binomial setting have not been met.
Permutation refers to the arrangement of objects in a specific order. For example, if we have three objects A, B, and C, there are six possible permutations: ABC, ACB, BAC, BCA, CAB, and CBA. The number of permutations of n objects is given by n!
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Write a list of steps that are needed to find the measure of LB.
Step-by-step explanation:
They are corresponding angle
adult great basin rattlesnakes have a mean length of 40 inches and a standard deviation of 7.2 inches; the length of adult southern pacific rattlesnakes is also 40 inches on average, but with a standard deviation of 10.8 inches. both species have lengths that follow a normal distribution. you randomly select one great basin rattlesnake and one southern pacific rattlesnake. which is more likely be longer than 43.6 inches?
A Southern Pacific rattlesnake is more likely to be longer than 43.6 inches.
To calculate the probability of a rattlesnake having a length greater than 43.6 inches, we need to find the standard score (z-score) of 43.6 inches for each species and then use a standard normal table to find the corresponding probability.
The formula for the standard score is:
[tex]$z = \frac{x - \mu}{\sigma}$[/tex] where,
x is the value (43.6 inches)[tex]$\mu$[/tex] is the mean length of the species[tex]$\sigma$[/tex] is the standard deviation of the species.For Great Basin rattlesnakes:
[tex]$\mu[/tex] = 40 inches
[tex]$\sigma[/tex] = 7.2 inches
So,
[tex]$z = \frac{43.6 - 40}{7.2} = 0.5$[/tex]
Using a standard normal table, we find that the probability of a Great Basin rattlesnake having a length greater than 43.6 inches is approximately 0.306.
For Southern Pacific rattlesnakes:
[tex]$\mu[/tex] = 40 inches
[tex]$\sigma[/tex] = 10.8 inches
So,
[tex]$z = \frac{43.6 - 40}{10.8} = 0.333$[/tex]
Using a standard normal table, we find that the probability of a Southern Pacific rattlesnake having a length greater than 43.6 inches is approximately 0.379.
So, a Southern Pacific rattlesnake is more likely to be longer than 43.6 inches.
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Make m the subject of the formula d=5m-2
Answer:
m = (d+2)/5
Step-by-step explanation:
d=5m-2
d+2 = 5m
m = (d+2)/5
Given the expression: 10x^2 + 28x − 6
Part A: What is the greatest common factor? Explain how to find it. (3 points)
Part B: Factor the expression completely. Show all necessary steps. (5 points)
Part C: Check your factoring from Part B by multiplying. Show all necessary steps. (2 points)
The solution is, 2 is the greatest common factor.
and, 10x^2 + 28x − 6=0 has solutions, x = -3, 0.2 a simplified version of the equation.
How to find the calculation?In mathematics, multiplication is a method of finding the product of two or more numbers. It is one of the basic arithmetic operations, that we use in everyday life.
here, we have,
Simplifying :
10x^2 + 28x − 6=0
Rearrange the terms so that -6+28x+10x^2 =0
Figuring out the value of the variable "x".
Subtract out the number "2", which is the GCF.
2(-3+14x+5x^2)=0
To factor a trinomial
2(5x^2+15x-x-3)=0
(5x-1)(x+3)= 0
i.e. x= -3
or, x= 1/5
=0.2
Hence, The solution is, 2 is the greatest common factor.
and, 10x^2 + 28x − 6=0 has solutions, x = -3, 0.2 a simplified version of the equation.
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McKenzie has a credit card with a balance of $936. The APR on this credit card is 13.96% and is compounded monthly.
Part A: If McKenzie makes payments of $250 per month, how long will it take her to pay off the credit card? Round the APR to the nearest thousandth
Part B: In the problem above, how much interest will McKenzie have paid when she pays off the credit card?
Part C: How much more interest will McKenzie pay if she only pays $150 per month?
If McKenzie pays $150 per month, she will have paid a total of $92.832 in interest when she pays off her credit card. This is $36.224 more than she would have paid if she had paid $250 per month.
What is APR?APR stands for Annual Percentage Rate, which is the interest rate associated with a loan, credit card, or other type of borrowing. It is expressed as a percentage and is typically higher than the interest rate because it includes additional costs associated with the loan such as origination fees, processing fees, and other costs.
Part A:
To calculate how long it will take McKenzie to pay off her credit card, we need to use the formula:
T = (B x i) / P
Where T is the total number of payments, B is the initial balance, i is the interest rate (in decimal form) and P is the amount of the payments.
In this case, B = 936, i = 0.01396 (13.96% expressed as a decimal) and P = 250. So, substituting these values into the formula, we get:
T = (936 x 0.01396) / 250
T = 3.784
Since payments are made monthly, we can round this to 4 payments. Therefore, it will take McKenzie 4 months to pay off her credit card if she makes payments of $250 per month.
Part B:
To calculate the amount of interest McKenzie will have paid when she pays off her credit card, we can use the formula:
I = B x i x T
Where I is the total amount of interest paid, B is the initial balance, i is the interest rate (in decimal form) and T is the total number of payments.
In this case, B = 936, i = 0.01396 and T = 4 (since we calculated this in Part A). So, substituting these values into the formula, we get:
I = 936 x 0.01396 x 4
I = 56.608
Therefore, McKenzie will have paid a total of $56.608 in interest when she pays off her credit card.
Part C:
To calculate how much more interest McKenzie will pay if she only pays $150 per month, we first need to calculate how long it will take her to pay off the credit card using this lower payment amount.
Using the same formula from Part A, we get:
T = (936 x 0.01396) / 150
T = 6.576
Since payments are made monthly, we can round this to 7 payments. Therefore, it will take McKenzie 7 months to pay off her credit card if she makes payments of $150 per month.
Now, to calculate the amount of interest McKenzie will have paid if she pays $150 per month, we can use the same formula from Part B:
I = B x i x T
Where I is the total amount of interest paid, B is the initial balance, i is the interest rate (in decimal form) and T is the total number of payments.
In this case, B = 936, i = 0.01396 and T = 7. So, substituting these values into the formula, we get:
I = 936 x 0.01396 x 7
I = 92.832
Therefore, if McKenzie pays $150 per month, she will have paid a total of $92.832 in interest when she pays off her credit card. This is $36.224 more than she would have paid if she had paid $250 per month.
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pls someone help me on this
Answer:
110° and 215°
Step-by-step explanation:
the bearing of D from C is the angle from the north line at C measured in a clockwise direction from C to D
(a)
bearing of D from C is the purple angle, that is 110°
(b)
bearing of D from C is the blue angle , that is 215°
which of the following is correct? 'a' = 'a'. 0 = '0' 'b' < 'd' 'x' >' y'
'a' = 'a' and 'b' < 'd' are correct an rest are incorrect.
'a' = 'a' is correct. In programming and computer science, single quotes are used to denote a string literal, and equality between strings is determined by their lexicographical order. In this case, 'a' and 'a' are the same string, so they are equal.
0 = '0' is incorrect. In programming, 0 is a numerical value, while '0' is a string literal. They cannot be directly compared as equal, unless you cast the string to a numerical type, like this:
python
0 == int('0')
'b' < 'd' is correct. In the lexicographical order of strings, 'b' comes before 'd', so 'b' is considered to be less than 'd'.
'x' > 'y' is incorrect. In the lexicographical order of strings, 'x' comes after 'y', so 'x' is considered to be greater than 'y'.
Therefore, 'a' = 'a' and 'b' < 'd' are correct an rest are incorrect.
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3. ) Lucille bought 15 mangoes for P225. 00, how much will she pay for 25 mangoes
at the same rate?
At the same price rate, Lucille has to pay P375.00 for 25 mangoes she bought.
From the case, we know that:
Q₁ = 15 mangoes
P₁ = P225.00
Q₂ = 25 mangoes
P₂?
To solve this problem, we need to find the price rate of each unit of mangoes. We can make a mathematical equation as:
P = Q x P(q)
where:
P(q) = price rate per unit
Then:
P₁ = Q₁ x P(q)
P225.00 = 15 x P(q)
P(q) = P225.00 : 15
P(q) = P15.00 per mangoe
We can use the value of price rate per unit to answer our question:
P₂ = Q₂ x P(q)
P₂ = 25 x P15.00
P₂ = P375.00
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What image below shows a line?
Answer:
The last graph shows a line.
Step-by-step explanation:
In order, from top to bottom, you have an Angle, a Point, a Ray, and a Line.
The Ray (the one you have marked as the answer) is NOT correct because is has an endpoint and continues in only one direction.
The last image IS correct, it is a Line as it goes on forever in both directions. Honestly, they should have put arrows at each end.
Hope this helps!
suppose x=ae−t be5t. verify that x=ae−t be5t is a solution to x′′−4x′−5x=0 by substituting it into the differential equation. (enter the terms in the order given.)
The given equation, x = ae−t be5t, is a solution to x′′−4x′−5x=0.
x′′ - 4x′ - 5x = (ae−t be5t)′′ - 4(ae−t be5t)′ - 5(ae−t be5t) = -e−2t be5t - 4(-e−t be5t) - 5(ae−t be5t) = 0
1. x = ae−t be5t
2. x′ = -e−t be5t
3. x′′ = -e−2t be5t
x′′−4x′−5x=ae−t be5t(−e−t be5t−4e−t be5t−5ae−t be5t)
Simplify:
x′′−4x′−5x=ae−t be5t(−e−t (5b+4)−5a)
Set to 0:
ae−t be5t(−e−t (5b+4)−5a) = 0
Divide by ae−t be5t:
−e−t (5b+4)−5a = 0
Solve for b:
b = −4/5a
4. substitute x, x′ and x′′ into the differential equation
5. (ae−t be5t)′′ - 4(ae−t be5t)′ - 5(ae−t be5t) = -e−2t be5t - 4(-e−t be5t) - 5(ae−t be5t) = 0
The given equation, x = ae−t be5t, is a solution to x′′−4x′−5x=0.
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The scatter plot shows a hiker's elevation above sea level during a hike from the base to the top of a mountain. The equation of a trend line for the hiker's elevation is y=9.27x+622, where x represents the number of minutes and y represents the hiker's elevation in feet. Use the equation of the trend line to estimate the hiker's elevation after 140 minutes.
By using the equation of the trend line, it can be estimated that the hiker's elevation after 140 minutes will be, 1919.8 feet
What is an Equation ?An equation is a mathematical term, which indicates that the value of two algebraic expressions are equal. There are various parts of an equation which are, coefficients, variables, constants, terms, operators, expressions, and equal to sign.
For example, 3x+2y=0.
Types of equation
1. Linear Equation
2. Quadratic Equation
3. Cubic Equation
Given that,
The equation of a trend line for the hiker's elevation is,
y = 9.27x + 622
x represents the number of minutes
y represents the hiker's elevation in feet
Elevation after 140 minutes = ?
Now, putting value of x as 140 in the given equation,
y = (9.27 x 140) + 622
= 1297.8 + 622
= 1919.8
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factorise
factorise 3x¹²+24
Estimate the minimum rate of gasoline consumption and the specific time which it occurs Tne minimum rate of consumption (Type integers or decimals ) gallons per day, this occurs after__ days
The minimum rate of gasoline consumption is typically 0.5 gallons per day, which occurs after five days of vehicle inactivity. This is because the fuel system needs time to dissipate the fuel in the lines and the evaporative system.
The minimum rate of gasoline consumption is the amount used when a vehicle is not in use. This is typically 0.5 gallons per day and occurs after five days of a vehicle being inactive. This is because the fuel system needs time to dissipate the fuel in the lines and the evaporative system. When the vehicle is not used, the fuel system is not under pressure and the fuel in the lines and evaporative system is able to dissipate. This occurs gradually over a period of five days and once this has happened, the minimum rate of gasoline consumption is reached. The fuel system needs to dissipate the fuel in order to prevent it from becoming stale or evaporating, and this is the reason why the minimum rate of gasoline consumption is reached after five days of inactivity.
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A local store is keeping track of service times. the table below shows the number of customers served and the time it took.
It does not always take the same time to serve every customer. Option A is correct.
What is proportionality?proportionality is defined as between two or more sets of values, and how these values are related to each other in the sense are they directly proportional or inversely proportional to each other.
Here,
From the table,
For every order, the pair compare the unit rate of serving the customer.
1
unit rate = 2 / 8
unit rate = 1 / 4
unit rate = it took 4 minutes to serve a customer.
2.
unit rate = 4 / 16
unit rate = 1 / 4
unit rate = it took 4 minutes to serve a customer.
3
unit rate = 7 / 21
unit rate = 1 / 3
unit rate = it took 3 minutes to serve a customer.
Thus, It does not always take the same time to serve every customer. Option A is correct.
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given that y
[tex]y = x2 + 3x - 2[/tex]
[tex]y = x{2} + 3x - 2[/tex]
a carton of eggs costs 4.30 how many for one egg
Answer:
Step-by-step explanation:
if a carton of eggs is 4.30 then 1 egg is then 1 egg is 75 cents
PLEASE HELP!!!!!!!!!!!!!!!!!!!
Greta needs to get 15 packs of business cards. • Greta's budget for business cards is $200. • The number of cards she can have printed, c, can be represented by the inequality 15c < 200. • Plug the numbers 12, 16, 18, and 8 into the inequality to check which paper Greta can use for her business cards and stay within her budget. In this case, ____ and ____ satisfy the inequality. Greta can use ____________ or ______________paper for her business cards without exceeding her $200 budget. Number Inequality < True or False? 12 15(12) < 200 ______ < 200 True False 16 15(16) < 200 ______ < 200 True False 18 15(18) < 200 ______ < 200 True False 8 15(8) < 200 ______ < 200 True False
The cost of printing the paper at the values are:-
15C < 200
180< 200 at c = 12
120< 200 at C = 8
What is inequality?When two expressions are connected by a sign like "not equal to," "greater than," or "less than," it is said to be inequitable. The inequality shows the greater than and less than relationship between variables and the numbers.
Given that Greta needs to get 15 packs of business cards. • Greta's budget for business cards is $200. • The number of cards she can have printed, c, can be represented by the inequality 15c < 200.
The cost of printing the cards at different numbers of the cards will be calculated as:-
15C < 200
At C = 12
15x 12 < 200
180 < 200 True
At C = 16,
15 x 16 < 200
240 > 200 False
At C = 18,
15 x 18 < 200
270 > 200 False
At C = 8
15 x 8 < 200
120 < 200 True
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Geometry: Unit 5: Relationships in Triangles. Homework 1: Triangle Midsegments
HELP!!!
For each triangles, the answers are:
FH = 24; JL = 74; KJ = 60; FJ = 30AE = 26; AN = 58; CT = 21,5; Perimeter of AEN = 127x = 15x = 6JL = 78GH = 94x = 8°x = 12.7°∠WYZ = 20°∠ACB = 117°Perimeter of MNP = 130Let's discuss each triangle we have:
1. We know that:
∠KJL = ∠KFG = ∠GHL --> face the same direction
∠KFG = ∠FGH
∠GKF = ∠GHF = ∠HGL = ∠HFJ
∠KLJ = ∠GFH = ∠KGF = ∠FHJ
Hence:
KL = 2KG = 2FH
48 = 2FH
FH = 24
JL = 3FG
JL = 2 (37)
JL = 74
KJ = 2GH
KJ = 2(30)
KJ = 60
FJ = 1/2 KJ
FJ = 1/2 (60)
FJ = 30
2. ∠AEN = ∠PTC = ∠NPT = ∠ACT
∠EAN = ∠PTN = ∠CPT = ∠ECP
∠ENA = ∠CTA = ∠PCT
Hence:
AE = 2PT
AE = 2(13) = 26
AN = 2CP
AN = 2(29) = 58
CT = 1/2 EN
CT = 1/2 (43) = 21.5
Perimeter of AEN = AE + EN + AN
Perimeter of AEN = 26 + 43 + 58
Perimeter of AEN = 127
3. Both lines are parallel with each other and both triangles have ratio of 1 : 2, then:
10x + 44 = 2(8x - 23)
10x + 44 = 16x - 46
6x = 90
x = 15
4. Both lines are parallel with each other and both triangles have ratio of 1 : 2, then:
19x - 28 = 2(6x + 7)
19x - 28 = 12x + 14
7x = 42
x = 6
5. Both lines are parallel with each other and both triangles have ratio of 1 : 2, then:
4x + 34 = 2(5x - 16)
4x + 34 = 10x - 32
6x = 66
x = 11
JL = 4x + 34
JL = 4(11) + 34
JL = 78
6. Both lines are parallel with each other and both triangle have ratio 1 : 2, then:
(9x - 59) = 2(3x - 4)
9x - 59 = 6x - 8
3x = 51
x = 17
GH = 9x - 59
GH = 9(17) - 59
GH = 94
7. (6x + 1)° = (9x - 23)°
3x = 24
x = 8
8. (5x - 24)° + (8x + 9)° = 180°
13x - 15 = 180
13x = 165
x = 12.7°
9. (16x - 3)° + (3x - 7)° = 180°
19x - 10 = 180°
19x = 190
x = 10°
∠WYZ = ∠WVX
∠WYZ = 3x - 7
∠WYZ = 3(10) - 7 = 23°
10. (11x - 2)° = (6x + 13)°
5x = 15
x = 3°
∠ACB + ∠CAB + ∠ABC = 180°
∠ACB + 62 + (6x + 13) = 180°
∠ACB + 62 + (6(3) + 13) = 180°
∠ACB + 62 + 31 = 180°
∠ACB = 117°
11. ∠MNP = ∠MQS = ∠SRP = ∠QSR
∠MNP = ∠RSP = ∠NQR = ∠QRS
∠NPM = ∠QSM = ∠NRQ = ∠RQS
Then:
MN = 2RS
5x - 34 = 2(x + 4)
5x - 34 = 2x + 8
3x = 42
x = 14 --> RS = x + 4 = 18
MN = 2RS = 2(18) = 36
MP = 2QR = 2(25) = 50
NP = 2SQ = 2(22) = 44
Perimeter of MNP = MN + NP + MP
Perimeter of MNP = 36 + 50 + 44
Perimeter of MNP = 130
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Find x. PLEASE PLEASE HELP
Check the picture below.
[tex]\cfrac{16}{x+2}=\cfrac{40}{3x}\implies 48x=40x+80\implies 8x=80\implies x=\cfrac{80}{8}\implies \boxed{x=10}[/tex]
Answer:
x = 10
Step-by-step explanation:
UT is an angle bisector and divides the opposite side into segments that are proportional to the other two sides, that is
[tex]\frac{US}{RU}[/tex] = [tex]\frac{ST}{RT}[/tex] ( substitute values )
[tex]\frac{x+2}{3x}[/tex] = [tex]\frac{16}{40}[/tex] = [tex]\frac{2}{5}[/tex] ( cross- multiply )
2 × 3x = 5(x + 2)
6x = 5x + 10 ( subtract 5x from both sides )
x = 10
Computer Alpha’s password must be exactly 10 characters long; a character can be a letter (not case sensitive), number (0 through 9), or one of 13 special characters.
a) How many possible passwords can there be?
b) If there must be at least one special character and at least two numbers, how many possible passwords can there be?
c) Howmanydifferentpasswordscanbemadebyrearrangingthecharacters"AA!!!56555"?
d) Computer Omega’s password requirement must be exactly four 4-letter "words" (any four letters make a "word"; there are no spaces between the words) typed in a row.
How many possible passwords can there be?
e) Which computer is easier to hack (i.e., guess a correct password at random)?
The number of possible combinations for a password is an important aspect of computer security.
A password is a crucial aspect of computer security. It is used to protect personal information and keep unauthorized users from accessing important data.
a) For Computer Alpha's password, there are 26 letters (not case-sensitive), 10 numbers (0-9), and 13 special characters.
The formula for combination is nCr, where n is the total number of items, and r is the number of items to choose from.
In this case, n is 10 and r is 49, so the number of possible combinations is
=> 49C10 = 3,738,383,600.
b) If there must be at least one special character and at least two numbers, the number of possible combinations decreases.
The total number of possible combinations is
=> 10C2 x 13C1 x 36C7.
c) The password "AA!!!56555" has 8 characters. The number of different passwords that can be made by rearranging these characters is 8!.
d) For Computer Omega's password, there are 26 letters and four "words" of four letters each.
The number of possible combinations is
=> 26⁴ x 26⁴ x 26⁴ x 26⁴ = 208,827,064,576,000.
e) Based on the number of possible combinations, Computer Omega is easier to hack compared to Computer Alpha. This is because there are fewer possible combinations for Computer Omega's password.
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Algebraic Expressions (100 pts )
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Answer:
4
Step-by-step explanation:
You have a table of values, x is the input and y is the output. One trick to figure out the answer is to look at the x input "0". We notice that when we input 0, we get an output of 4, therefore meaning that every other function value is simply an addition of 4.
-2 + 4 = 2
-1 + 4 = 3
0 + 4 = 4
1 + 4 = 5
2 + 4 = 6
3 + 4 = 7
Therefore, the equation is [y = x + 4]
each edge length of a rectangular solid is a prime number. if the volume of the rectangular solid is 385 cubic units, what is the total surface area, in square units, of the rectangular solid?
The total surface area, in square units, of the rectangular solid is 334.
What is a rectangular solid?A rectangular prism is a polyhedron in geometry that has two parallel and congruent bases. It also goes by the name cuboid. Six faces, each with a rectangle shape and twelve edges, make up a rectangular prism.The base is square and is 4 inches in both length and breadth. V = lbh provides the volume of a rectangular solid.A three-dimensional solid form with six faces, including rectangular bases, is called a rectangular prism. A rectangular prism also refers to a cuboid.Any two of these dimensions can be the same (making it a "square prism") or all three can be different in rectangular prisms that aren't cubes.Given data :
The volume of the rectangular solid = 385 = 5 x 7 x 11
So, two sides will be 5 x 7 = 35 x 2 = 70
another two sides will be 5 x 11 = 55 x 2 = 110
and the last two sides will be 7 x 11 = 77 x 2 = 154
the total surface area, in square units, of the rectangular solid =
70 + 110 + 154 = 334
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when using the general multiplication rule, p(a and b) is equal to
The General Multiplication Rule in probability states that the probability of the intersection (occurrence) of two events, A and B, is equal to the product of their individual probabilities. The formula can be written as follows:
p(A and B) = p(A) * p(B | A)
where p(A) represents the probability of event A occurring, and p(B | A) represents the probability of event B occurring given that event A has already occurred.
The formula reflects the idea that the probability of both events occurring is equal to the probability of one event occurring, multiplied by the probability of the other event occurring given that the first event has already happened.
For example, let's say we have two events: "rolling a 6 on a dice" (A) and "choosing a spade from a deck of cards" (B). The probability of rolling a 6 on a dice is 1/6, and the probability of choosing a spade given that a 6 was rolled is 13/52. Using the general multiplication rule, the probability of both events occurring would be (1/6) * (13/52) = 13/312.
In summary, the general multiplication rule is a fundamental concept in probability that helps us calculate the probability of the intersection of two events.
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A basket holds n apples. You pick (2n - 3) apples, and your friend picks
(n + 4) apples
a. Write an expression that represents how many apples you and your friend
pick together.
b. How many baskets would you need if you collected 10 apples with your
friend?
(a). The number of apples you and your friend picked is 3n+1.
(b). The number of baskets would you need if you collected 10 apples with your friend is [tex]\frac{10}n}[/tex].
As per given data a basket holds n apples.
The number of apples your friend picked =n+4
The number of apples you picked =2n-3
The number of apples you and your friend picked can be obtained by just adding the apples picked by both
=(2n-3)+(n+4)
=2n+n+4-3 ( By using commutative property)
=3n+1 ( Combining like terms)
The commutative property states that the numbers on which we operate can be moved or swapped from their position without making any difference to the answer. The property holds for Addition and Multiplication, but not for subtraction and division.Therefore, the number of apples you and your friend picked is 3n+1.
(b).
For carry n apples basket required is = 1
To find the number of baskets needed to collect 10 apples, we can use the expression:
number of baskets = 10 / (number of apples in one basket) = [tex]\frac{10}n}[/tex]
Therefore, the number of baskets would you need if you collected 10 apples with your friend is [tex]\frac{10}n}[/tex].
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