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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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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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
The sum of three consecutive integers is -15.
If 1 is added to each integer, what is the product.
of the three resulting integers?
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
2x-3/x divided 7/x^2
Answer:
2x-3/7x
Step-by-step explanation:
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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36-u=261 solve for u
Answer:
u = -225
Step-by-step explanation:
36 - u = 261
-u = 261 - 36
-u = 225
u = -225
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.
Simplify the expression.
(8+20)÷4+3
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!
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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Write the equation of the line of best fit using the slope-intercept formula y=mx+b. Show all your work, including the points used to determine the slope and how the equation was determined.
The equation of the line of best fit using the slope-intercept formula y=mx+b is y = x - 5
Equation of the line of best fitA line is the shortest distance between two points. The equation in point-slope form is expressed as:
y =. mx + b
m is the slope
b is the y intercept
Using the coordinate points (25, 20) and (60, 55)
Slope = 55-20/60-25
Slope = 35/35
Slope = 1
For the intercept
20 = 1(25) + b
b = 20 - 25
b = -5
Substitute
y = x + (-5)
y = x - 5
Hence the equation of the line of best fit using the slope-intercept formula y=mx+b is y = x - 5
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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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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
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].
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.
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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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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1.The time taken to complete a motorcycle race is normally distributed, with an average time (µ) of 2.5 hours and a standard deviation (sigma) of 0.5 hours.
What is the probability that a randomly selected cyclist will take between 2.35 and 2.45 hours to complete the race?
Using the normal distribution, there is a 0.0781 = 7.81% probability that a randomly selected cyclist will take between 2.35 and 2.45 hours to complete the race.
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, respectively, by:
[tex]\mu = 2.5, \sigma = 0.5[/tex].
The probability that a randomly selected cyclist will take between 2.35 and 2.45 hours is the p-value of Z when X = 2.45 subtracted by the p-value of Z when X = 2.35, hence:
X = 2.45:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{2.45 - 2.5}{0.5}[/tex]
Z = -0.1
Z = -0.1 has a p-value of 0.4602.
X = 2.35:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{2.35 - 2.5}{0.5}[/tex]
Z = -0.3
Z = -0.3 has a p-value of 0.3821.
0.4602 - 0.3821 = 0.0781.
0.0781 = 7.81% probability that a randomly selected cyclist will take between 2.35 and 2.45 hours to complete the race.
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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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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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find the unknown side of the right triangle using the information given leg=12m, leg=6 m
Answer:
Step-by-step explanation:
Given
Leg = 10
Leg = 6
hypotenuse = ?
equation
c^2 = a^2 + b^2
a = 10
b = 6
Solution
c^2 = 10^2 + 6^2 Expand
c^2 = 100 + 36 Combine
c^2 = 136 Take the square root of both sides
√c^2 = √136
c = 11.66
answer
hypotenuse = 11.66
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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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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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°.
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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There are two bags containing only orange and red marbles. Bag A has 2 orange marbles and 6 red marbles. Bag B has 4 orange marbles and 16 red marbles. A marble is randomly chosen from each bag. List these events from least likely to most likely. Event 1: choosing an orange or red marble from Bag B. Event 2: choosing an orange marble from Bag B. Event 3: choosing an orange marble from Bag A. Event 4: choosing a purple marble from Bag A. Least likely Event Event, Event, X Most likely Event Ś ?
Answer:
From least to most likely:
Event 4, Event 2, Event 3, Event 1
Step-by-step explanation:
Event 1 has a 100% chance because there are only red and orange marbles in the bag.
In event 2, there are 4 orange marbles in the bag, giving us a (4/20) chance. This is 20%
In event 3, there are 2 orange marbles of 8 total, giving us an (2/8) chance. This is 25%
Lastly, there are no purple marbles in either bag, giving us a 0% chance of this occurring.
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]