The pattern of 324, 256, 196, 144 is the square of the even numbers in a descending order starting from 18.
What is a sequence?A sequence is a set of things next to each other in a set order. It is also referred to as a series.
According to this question, the following sequence is given: 324, 256, 196, 144. A careful observation of these numbers shows that each is the square of even numbers.
18² = 324
16² = 256
14² = 196
12² = 144
Therefore, the pattern of 324, 256, 196, 144 is the square of the even numbers in a descending order starting from 18.
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Maria has 26 cars available to rent. Let C be the number of cars she would have left after renting R of them. Write an equation relating C to R. Then use this equation to find the number of cars she would have left after renting 23 of them.
Answer:
26 - R = C
3 cars
Step-by-step explanation:
26-R = C
26-23 = 3
Which equation has no solution?
O 1-x-31=5
O 12x-11=0
O15-3x = -8
O|-x+91=0
Since the four choices have solution, there is no choice that have no solutions. (Correct choice: E)
What linear equation has no solution?
Herein we must check each choice to find if a solution exists or not by algebra properties. Now we proceed to check each case:
Choice A
1/(x - 31) = 5
1 = 5 · (x - 31)
1 = 5 · x - 155
5 · x = 156
x = 31.2
Choice B
12 · x - 11 = 0
12 · x = 11
x = 11/12
Choice C
15 - 3 · x = - 8
3 · x = 23
x = 23/3
Choice D
- x + 91 = 0
x = 91
Since the four choices have solution, there is no choice that have no solutions. (Correct choice: E)
RemarkThe statement presents typing mistakes and is incomplete. Correct form is shown below:
Which equation has no solution?
A. 1/(x- 31) = 5
B. 12 · x - 11 = 0
C. 15 - 3 · x = - 8
D. - x + 91 = 0
E. Neither of all
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Simplify the expression.
(8+20)÷4+3
The length of time it takes college students to find a parking spot in the library parking lot follows a normal distribution with a mean of 4.5 minutes and a standard deviation of 1 minute. Find the cut-off time which 75.8% of the college students exceed when trying to find a parking spot in the library parking lot.
Using the normal distribution, it is found that the cut-off time which 75.8% of the college students exceed when trying to find a parking spot in the library parking lot is of 3.7 minutes.
Normal Probability DistributionThe z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score measures how many standard deviations the measure is above or below the mean. Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.The mean and the standard deviation are given as follows:
[tex]\mu = 4.5, \sigma = 1[/tex]
The cut-off time is the 100 - 75.8 = 24.2th percentile, which is X when Z = -0.7, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]-0.7 = \frac{X - 4.5}{1}[/tex]
X - 4.5 = -0.7
X = 3.7.
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For a normal distribution, find the probability of being (a) Between −1 and +1 (b) Between 3 standard deviations below the mean and 2 standard deviations above the mean (c) More than 3.5 standard deviations away from the mean Use the Standard Normal Table in your textbook or Excel to obtain more accuracy.
Using the normal distribution, the probabilities are given as follows:
a) 0.6826 = 68.26%.
b) 0.9759 = 97.59%.
c) 0.0004 = 0.04%.
Normal Probability DistributionThe z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score measures how many standard deviations the measure is above or below the mean. Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.Item a:
The probability is the p-value of Z = 1(0.8413) subtracted by the p-value of Z = -1(0.1587), hence:
0.8413 - 0.1587 = 0.6826
Item b:
The probability is the p-value of Z = 2(0.9772) subtracted by the p-value of Z = -3(0.0013), hence:
0.9772 - 0.0013 = 0.9759.
Item c:
This probability is P(|Z| > 3.5), which is 2 multiplied by the p-value of Z = -3.5, which is of 0.0002.
Hence:
2 x 0.0002 = 0.0004 = 0.04%.
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a. P is equal to the set containing t,v,c and d
b. the set consisting of the elements 2 and 6 is a proper subset of [ 2,6,8,12}
c. the set consisting of the elements 0 and 3 is not a subset of {3,2,4,6}
a.P is equal to the set containing t,v,c and d
p=
The answers to the questions are:
a. p = { t, v, c, q}
b. {2, 6} ⊂ {2,6,8,12}
c. {0, 3} ⊄ {3,2,4,6}
How to write the mathematical expression s using mathematical symbols.To represent sets we use
p = { }
Hence
a. p = { t, v, c, q}
b. If 2 and 6 is a proper subset of [ 2,6,8,12},
This can be represented as
{2, 6} ⊂ {2,6,8,12}
c. the set consisting of the elements 0 and 3 is not a subset of {3,2,4,6} is written as
{0, 3} ⊄ {3,2,4,6}
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At a cost of R55 per box how much would it cost to tile the training room
The total cost needed to tile the training room with an area of 100 m² is R110.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Let assume that the area of the trainig room is 100 m² and one box can complete 50 m², hence:
number of box needed = 100 m² / 50 m² = 2
Total cost = R55 per box * 2 box = R110
The total cost needed to tile the training room with an area of 100 m² is R110.
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express using positive exponent
[tex] {3c}^{ - 2} [/tex]
Answer: [tex]\frac{3}{c^2}[/tex]
Step-by-step explanation:
This uses the exponent rule [tex]a^{-b}=\frac{1}{a^b}[/tex].
Verify which of the following are identities.
Answer:
C
Step-by-step explanation:
Equation 1:
[tex]1+\frac{\cos^{2} \theta}{\cot^{2} \theta(1-\sin^{2} \theta)}\\ \\ 1+\frac{\sin^{2} \theta}{\cos^{2} \theta} \\ \\ 1+\tan^{2} \theta \\ \\ \sec^{2} \theta[/tex]
Equation 2:
[tex]15\cos \theta \left(\frac{1}{\cos \theta}-\frac{\cot \theta}{\csc \theta} \right) \\ \\ 15\cos \theta \left(\frac{1}{\cos \theta}-\frac{\cos \theta / \sin \theta}{1/\sin \theta} \right) \\ \\ 15\cos \theta \left(\frac{1}{\cos \theta}-\cos \theta \right) \\ \\ 15\cos \theta \left(\frac{1-\cos^{2} \theta}{\cos \theta} \right) \\ \\ 15(1-\cos^{2} \theta) \\ \\ 15\sin^{2} \theta[/tex]
For A (1, –1), B (–1, 3), and C (4, –1), find a possible location of a fourth point, D, so that a parallelogram is formed using A, B, C, D in any order as vertices.
The possible coordinates for the vertex D of the parallelogram could be (-4, 3)
It is given that A(1, –1), B (–1, 3), and C (4, –1) are the three vertices of the parallelogram.
Let us assume that the vertices are in the order A, C, B, and D where the coordinates of D are (a, b).
In this scenario, if we join AB and CD, they will become the diagonals of the parallelogram ABCD.
According to the properties of a parallelogram, diagonals bisect each other.
Hence, mid-point of AB = mid-point of CD
Now, according to the mid-point theorem, if mid-point of AB is given as (x,y), then,
x = (x₁ + x₂)/2 and y = (y₁ + y₂)/2
Here, for AC,
x₁ = 1, y₁ = -1
x₂ = -1, y₂ = 3
Then, x = ( 1 - 1)/2 and y = (-1 + 3)/2
(x, y) ≡ (0, 1) ............. (1)
Since (x, y) is also the mid-point of CD, we also have,
x₁ = 4, y₁ = -1
x₂ = a, y₂ = b
Then, x = (4 + a)/2 and y = (-1 + b)/2
(x, y) ≡ ((4 + a)/2, (-1 + b)/2) ................... (2)
From (1) and (2),
(4+a)/2 = 0 and (-1+b)/2 = 1
4+a = 0 and (-1+b) = 2
a = -4 and b = 3
Hence, the fourth vertex D of the parallelogram can be possibly located at (-4, 3)
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Which graph shows a negative correlation? A graph with both axes unnumbered. Points show a steady trend. A graph with both axes unnumbered. Points are scattered loosely in the top half of the graph. A graph with both axes unnumbered. Points show a downward trend. A graph with both axes unnumbered. Points are scattered loosely all Over graph.
Answer:
The graph with a downward trend is the negative correlation
Step-by-step explanation:
Answer:
The Downward Slope or 'C' is the answer.
Step-by-step explanation:
Negative Slopes go down
Positive Slopes go up
Random Slopes are random
Scattered Slopes are scattered but together
please help with this question
The value of angle TUS based on the information given about the circle will be 49°.
What is a circle?It should be noted that a circle is a shape consisting of all points in a plane that are at a given distance from a given point, the centre.
Equivalently, a circle is the curve traced out by a point that moves in a plane so that its distance from a given point is constant.
The radius is the line segment extending from the center of a circle or sphere to the circumference or bounding surface.
Here, the value of TUS will be:
= 1/2 × TRS
= 1/2 × 98°
= 49°
In conclusion, the correct option is 49°.
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Complete question:
Circle R has a radius of 6 inches. Points S, T, and U lie on circle R, clockwise in alphabetical order. If m∠TRS = 98°, what is m∠TUS?
What is the discount and sale price of a $300 item that has been discounted at 10%?
Answer:
Discount: $30 off
New Sale Price: $270
Step-by-step explanation:
$300*10% =
30
$300-30=
$270
or
$300*.1=
30
$300-30=
$270
How does doubling the lengths of the sides of a rectangle to form a similar rectangle affect the area
Doubling the lengths of the sides of a rectangle quadruple the area
How to determine the effect?Let the dimension of the rectangle be L and W.
So, the area is
A = LW
When the lengths are doubled, we have:
A2 = 2L * 2W
This gives
A2 = 4LW
This means that the initial area is multiplied by 4
Hence, doubling the lengths of the sides of a rectangle quadruple the area
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36-u=261 solve for u
Answer:
u = -225
Step-by-step explanation:
36 - u = 261
-u = 261 - 36
-u = 225
u = -225
The company stock you are monitoring for your Economics class increases five-eighths point the first week and then it increases one- half point the second week and one-quarter point the third week. What is the total increase during the three weeks?
Based on the change in the company stock over the three weeks, the total increase in those three weeks is 1.38%.
how much did the stock increase by?assuming the stock has a value of $1, the value in the third week would be:
= 1 x (1 + 5/8%) x (1 + 1/2%) x (1 + 1/4%)
= $1.013809453125
the total increase is:
= (1.013809453125 - 1) / 1
= 1.38%
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A closed box has a square base with side length ll feet and height hh feet. Given that the volume of the box is 29 cubic feet, express the surface area of the box in terms of ll only.
The surface area of the closed box in terms of l only, which has the square base is,[tex]2l^2 + \frac{116}{l}[/tex]
How to determine the surface areaThe volume of cuboid or box can be given as,
Volume = l × b × h
Here, (l) is the length, (b) is the width of the box and (h) is the height of the box.
A closed box has a square base with side length l feet and height h feet. Therefore, the length and width will be the same.
Then the volume of the box is 29 cubic feet. Thus,
29 = l × l × h
29 = [tex]l^2 h[/tex]
[tex]h = \frac{l^2}{29}[/tex]
The surface area of the square base box is,
Area = [tex]2l^2 + 4lh[/tex]
Substitute the value of h
Area = [tex]2l^2 + 4l\frac{29}{l^2}[/tex]
Area = ,[tex]2l^2 + \frac{116}{l}[/tex]
Therefore, the surface area of the closed box in terms of l only, which has the square base is,[tex]2l^2 + \frac{116}{l}[/tex]
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mimi read 1/4 of a book on wednesday. she read 82 more pages on thursday, and she finished the book on friday by reading the last 98 pages. how many pages were in mimi's book.
Answer:
240 pages
Step-by-step explanation:
Let x = the TOTAL number of pages in the book. So we'll add up all her reading for the week and it should equal x, the total number of pages.
see image.
Solve the right triangle ABC, with C = 90°.
A = 38.5°, b = 43.5 cm. Find B, a, and c. Round to the nearest tenth.
Your last five customer interactions lasted 2, 3, 6, 8, and 4 minutes."
Employee: "That means I've averaged __________ minutes across those 5 interactions."
Answer:
4.6 minutes
Step-by-step explanation:
Average = the sum of the numbers/ the number of numbers
Plug in the numbers: 2+3+6+8+4/5 = 23/5 = 4.6 minutes
Sam has purchased collision insurance with a $100-deductible clause, and automobile medical payments insurance in the amount of $500. In an accident in which Sam is at fault, Sam incurs injuries for a total expense of $650. Also, $1,400 worth of damage is done to Sam's car. How much does the insurance company pay Sam? Benefit payment?
The amount that the insurance company will pay is $1800.
How to illustrate the information?It should be noted that the insurance company will pay John for the expenses of his injuries and repair of the car.
For the injury, he will get:
= $500 + ($1400 - $100)
= $500 + $2300
= $1800
Therefore, the amount is $1800.
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Suppose we want to choose letters, without replacement, from distinct letters.
(a) If the order of the choices is relevant, how many ways can this be done?
(b) If the order of the choices is not relevant, how many ways can this be done?
The number of ways when the choice is not relevant is 1716
How to determine the number of ways?The number of letters are:
Letter, n = 13
The letter to choose are:
r = 6
Relevant choice
When the choice is relevant, we have:
[tex]Ways = ^nP_r[/tex]
This gives
[tex]Ways = ^{13}P_6[/tex]
Evaluate
Ways = 241235520
Hence, the number of ways when the choice is relevant is 1235520
Not relevant choice
When the choice is not relevant, we have:
[tex]Ways = ^nC_r[/tex]
This gives
[tex]Ways = ^{13}C_6[/tex]
Evaluate
Ways = 1716
Hence, the number of ways when the choice is not relevant is 1716
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The graph below shows the price of different numbers of mats below at a store:
Which equation can be used to determine p, the cost of b mats?
P= 10.50+b
B= 10.50+p
B= 10.50p
P=10.50b
Answer:
The answer to your question is p = 10.50b
Step-by-step explanation:
Since you want to find p, you're looking for an equation that has
p = <something>
The last selection has this form
p = 10.50b
I hope this helps and have a good day!
In the year 2000, The U.S. Budgeted $25,003 million for Natural Resources and Environment. In 2014, they budgeted $40,156 million. What was the absolute and relative change in environmental spending from 2000 to 2014?
Using it's concepts, we have that:
The absolute change was of $15,153 million.The relative change was of 60.60%.What is the absolute change of two values?The absolute change between two values is given by the absolute value of the difference between two values.
In this problem, the values are of $40,156 million, which is the final value, and $25,003 million, which is the initial value, hence the absolute change is:
A = 40,156 - 25,003 = $15,153 million.
What is the relative change?The relative change is the absolute change multiplied by 100% and divided by the initial value, hence:
(15,153/25,003) x 100% = 60.60%.
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Explain how to determine if Carlos’s allowance is directly proportional to the number of chores he completes.
A 2-column table with 3 rows. Column 1 is labeled number of chores with entries 10, 13, 15. Column 2 is labeled Allowance with entries 75 dollars, 97 dollars and 50 cents, 112 dollars and 50 cents.
Using a proportional relationship, it is found that Carlos earns an allowance of $7.5 for each chore that he completes.
What is a proportional relationship?A proportional relationship is a function in which the output variable is given by the input variable multiplied by a constant of proportionality, that is:
y = kx
In which k is the constant of proportionality.
In this problem, the constant is:
k = 75/10 = 97.5/13 = 112.5/15 = 7.5.
Hence Carlos earns an allowance of $7.5 for each chore that he completes.
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A=(-3,-2) B=x,3 C=(4,5) if AB = BC what is the value of X
Answer:
x=1
Step-by-step explanation:
[tex] \sqrt{( - 3 - x) ^{2} + {( - 2 - 3)}^{2} } = \\ \sqrt{ {(4 - x)}^{2} + {(5 - 3)}^{2} } \\ \\ 9 + 6x + {x}^{2} + 25 = \\ 16 - 8x + {x}^{2} + 4 = = = > \\ 34 + 6x = 20 - 8x = > \\ 14 = 14x = = = > x = 1[/tex]
Done
The value of x that makes up the coordinate of B is -1
How to find the value of xTo find the value of x, we need to determine the coordinates of point B.
Since A to (B) = B to (C), the distance from point A to point B is equal to the distance from point B to point C. The distance between two points in a coordinate plane can be calculated using the distance formula:
Distance = √((x₂ - x₁)² + (y₂ - y₁)²)
Let's calculate the distances:
Distance A to (B):
x₁ = -3 (x-coordinate of point A)
y₁ = -2 (y-coordinate of point A)
x₂ = x (x-coordinate of point B)
y₂ = 3 (y-coordinate of point B)
Distance A to (B) = √((x - (-3))² + (3 - (-2))²)
Distance A to (B) =√((x + 3)² + 5²)
Distance A to (B) = √(x² + 6x + 9 + 25)
Distance A to (B) = √(x² + 6x + 34)
Distance B to (C):
x₁ = x (x-coordinate of point B)
y₁ = 3 (y-coordinate of point B)
x₂ = 4 (x-coordinate of point C)
y₂ = 5 (y-coordinate of point C)
Distance B to (C) = √((4 - x)² + (5 - 3)²)
Distance B to (C) = √((4 - x)² + 2²)
Distance B to (C) = √((4 - x)² + 4)
Distance B to (C) = √(x² - 8x + 20)
Since A to (B) = B to (C):
√(x² + 6x + 34) = √(x² - 8x + 20)
Now, we can square both sides to get rid of the square root:
x² + 6x + 34 = x² - 8x + 20
Next, move all the x terms to one side of the equation:
x² - x² + 6x + 8x = 20 - 34
Combine like terms:
14x = -14
Finally, solve for x:
x = -14 / 14
x = -1
So the value of x is -1. Point B is located at (-1, 3).
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Complete the table by finding the missing equivalent form for each row. a = b = c =
Answer:
a=10%, b=25/100, c=1/2
Step-by-step explanation:
a: If the denominator is exactly 100, then the numerator represents a percentage.
b: when you change a fraction to have a greater denominator, an easy way to figure out how to change the numerator to match it and make the value of the rewritten fraction equal to the old version, is to divide the new value of the denominator by the old value (in this case being 100/4=25), and put the answer where the numerator goes.
c: When simplifying a fraction with a lesser numerator than denominator, find the greatest common factor (a factor is a whole number a number can be divided by without resulting in a negative or a decimal number) and divide both the numerator and denominator by it.
PLEASE NEED HELP
The lifespans of crocodiles have an approximately Normal distribution, with a mean of 18 years and a standard deviation of 2.6 years. What proportion of crocodiles live between 17.5 and 20.5 years?
Find the z-table here.
0.3147
0.4068
0.5932
0.6853
Using the normal distribution, it is found that 0.4068 of crocodiles live between 17.5 and 20.5 years.
Normal Probability DistributionThe z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score measures how many standard deviations the measure is above or below the mean. Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.The mean and the standard deviation are given as follows:
[tex]\mu = 18, \sigma = 2.6[/tex]
The proportion of crocodiles live between 17.5 and 20.5 years is the p-value of Z when X = 20.5 subtracted by the p-value of Z when X = 17.5, hence:
X = 20.5:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{20.5 - 18}{2.6}[/tex]
Z = 0.96
Z = 0.96 has a p-value of 0.8315.
X = 17.5:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{17.5 - 18}{2.6}[/tex]
Z = -0.19
Z = -0.19 has a p-value of 0.4247.
0.8315 - 0.4247 = 0.4068
0.4068 of crocodiles live between 17.5 and 20.5 years.
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AB = 6cm, AC = 12cm
Calculate the length of CD.
Give your answer to 3 significant figures.
In the given diagram, the length of CD is 12.7 cm
TrigonometryFrom the question, we are to determine the length of CD
First, we will calculate the length of CB
From the Pythagorean theorem,
|CA|² = |CB|² + |BA|²
12² = |CB|² + 6²
144 = |CB|² + 36
|CB|² = 144 - 36
|CB|² = 108
|CB| = √108
|CB| = 6√3 cm
Now, to find CD
Using SOH CAH TOA
sin55° = |CB| / |CD|
sin55° = 6√3 / |CD|
|CD| = 6√3 / sin55°
|CD| = 12.7 cm
Hence, the length of CD is 12.7 cm
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IM IN A HURRY PLEASE HELP ME QUESTION IS DOWN BELOW WORTH 15 POINTS each
Answer:
a) ∠VUW
b) VY
c) XYV
d) 180°
e) 65°
Step-by-step explanation:
Part A:A central angle is an angle that creates an arc in a circle, while also having its vertex as the center of the circle.
Here the center is U. So, the vertex of the angle must include U.
This means that there are multiple answers to part a.
The answers can be:
∠VUW
∠WUX
∠XUV
Part B:A minor arc is any arc that doesn't exceed 180°.
The possible answers for part b, using this definition are:
WV
VY
XY
Part C:The answer you inputted here is incorrect.
The order of the letters matter.
A tip for you to never mess these up is to trace the letters you've chosen with your finger and see if that image you make with your finger matches up with the shape you wanted to make.
An arc that makes a semicircle is an arc that connects the endpoints of the diameter. The diameter in this case is VX.
This means that your answer must start with V and end with X, or the other way around. (Meaning you could start with x and end with v, but always make sure you keep the endpoints of the diameter as the endpoints of the arc.)
The possible answers for this part are either:
VYX or VWX
Part D:This arc intercepts the diameter, which is a straight line and a central angle.
The angle of a diameter is 180°.
The arc of an intercepted central angle has the same measure of the central angle itself.
So, the measure of VWX is 180°.
Part E:If an arc intercepts a central angle, then the arc has the same measure as the central angle.
This rule works the other way around, too.
So, the central angle has the same measure as the minor arc that it intercepts.
Measure of arc VUW is 65°, so m∠VUW is also 65°.