This statement in the article is wrong because $2.69 is not the mean price ($2.81)
How to determine what is wrong with the data?The prices from 5 gas stations surveyed are given as:
$2.79, $2.99, $2.69, $2.89, and $2.69.
There are no outliers in the dataset
So, the dataset can be summarized by the mean
The mean is
Mean = Sum/Count
So, we have
Mean = ($2.79+ $2.99+ $2.69+ $2.89+$2.69)/5
Evaluate
Mean = 2.81
The article quoted $2.69 as the typical price
This statement in the article is wrong because $2.69 is not the mean price ($2.81)
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Please solve for meeee
Answer: 58 degrees
Step-by-step explanation:
a+b=90 ==> angles a and b are on a right angle which measures 90 degrees.
32+b=90
b=58 degrees
5. Tad needs to measure where the free-
throw line should be in front of his
basketball goal. He knows his feet are
1 1/8 feet long and the free-throw line
should be 15 feet from the backboard.
How many toe-to-toe steps does Tad
need to take to mark off 15 feet?
10.i
A basketball court has symmetry; one half of the court is a mirror image of the other. The entire basketball court ( is 94 feet by 50 feet. On each half-court, painted lines show the free throw lane and circle, as well as the three-point arc, whose distance from the basket varies based on the level of hoops being played.
The borders of the court have their own commonsense names:
Along the length of the court, the borders are the sidelines.
Along the ends, the borders are the endlines, or baselines.
Separating both halves of the court is a midcourt line.
In the very center of the midcourt line is the center circle (12 feet in diameter), where the center toss takes place to begin the game.
The free throw lane is the hub of the action in each half-court. This rectangle is 12 feet wide — 16 feet at the men's pro level. Its length, as measured from the basket to the free throw line, is 15 feet at all levels. An offensive player may not stand inside the lane for more than three seconds unless he or one of his teammates is shooting the ball. After a shot is taken, the count starts over again. A defensive player may remain inside the lane for as long as he desires.
A player fouled by another player sometimes receives free throws, also known as foul shots. She takes these shots (they aren't really "throws") from the free throw line at the end of the lane — 15 feet from the basket. The shots are "free" because a defender does not guard the shooter .The remaining players line up alongside the free throw lane (or behind the shooter) and cannot interfere with the shot. They line up in order, on either side of the lane, of defense-offense-defense-offense. (Up to four players may stand on one side of the lane.) If a player opts not to take a spot (say, for example, the second defensive spot), then a player from the opposing team is permitted to step into that spot. The fans behind the basket usually scream, jump up and down, and wave their hands to try to distract an opposing team's shooter during free throws.
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What is the image of image of the point (-7,-3) after a rotation of 180 degrees counterclockwise
PLEASE
The image of image of the point [tex](-7,-3)[/tex] after a rotation of [tex]180[/tex] degrees counterclockwise is [tex](7,3)[/tex]
According to the question statement, point [tex](-7,-3)[/tex] is rotated by [tex]180[/tex] degrees counterclockwise, we are supposed to find out the image of the point after the rotation.
Point [tex](-7,-3)[/tex] lies in the Third quadrant of the Cartesian Plane.
When it will be rotated by [tex]180[/tex] degrees counterclockwise, it will shift to the first quadrant of the Cartesian Plane.
Therefore the coordinates will become as [tex](7,3)[/tex].
Cartesian Plane: The cartesian plane is defined as a two-dimensional coordinate plane that is made or formed by the intersection of the x-axis and y-axis or horizontal and vertical axes.To learn more about coordinates and plane, click on the link given below:
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Challenge The temperatures at sunrise and sunset
are shown in the table. What was the temperature
change on each day? On which day did the
temperature change the most?
Day 1
Day 2
Daily Temperatures
Temperature at Temperature at
Sunrise (°C) Sunset (°C)
- 13.94
- 9.12
18.37
28.17
What was the temperature change on Day 1?
°C
(Simplify your answer. Type an integer or decimal rounded to the nearest hundredth as needed.)
1. The temperature change on each day is as follows:
Day 1 = 32.31°CDay 2 = 37.29°C2. The temperature change on Day 1 was 32.31°C.
3. The temperature changed the most on Day 2.
What is a temperature change?A temperature change is a process whereby the degree of hotness or coldness varies from one time to another.
In this instance, the temperature changes can be computed by subtracting the temperature at Sunrise from the temperature at Sunset in degrees Centigrade or degrees Fahrenheit, as the case may be.
Data and Calculations:Daily Temperatures
Temperature at Temperature at Temperature
Sunrise (°C) Sunset (°C) Change
Day 1 - 13.94 18.37 32.31°C
Day 2 - 9.12 28.17 37.29°C
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Identify the lower class limits, upper class limits,
class width, class midpoints, and class boundaries for
the given frequency distribution. Also identify the
number of individuals included in the summary.
Age (yr) when
award was won
20-29
30-39
40-49
50-59
60-69
70-79
80-89
Frequency
27
32
15
3
5
1
1
The upper class limits are- 29, 39, 49, 59, 69, 79, 89
The lower class limits are- 20, 30, 40, 50, 60, 70, 80
The class midpoints are- 24.5, 24.5, 44.5, 54.5, 64.5, 74.5, 84.5
The class boundaries are- 29.5, 39.5, 49.5, 59.5, 69.5, 79.5
And the number of individuals included in the summary is 84.
Here, we are given the following dataset-
Age (yr) when Frequency
award was won
20-29 27
30-39 32
40-49 15
50-59 3
60-69 5
70-79 1
80-89 1
Upper class limit is the largest data value that can go in a class.
Thus, the upper class limits are- 29, 39, 49, 59, 69, 79, 89
Lower class limit is the smallest data value that can go in a class.
Thus, the lower class limits are- 20, 30, 40, 50, 60, 70, 80
The class midpoint is the average of the upper and lower limits of a class. Class midpoint = (upper limit + lower limit)/ 2
Thus, the class midpoints are- 24.5, 24.5, 44.5, 54.5, 64.5, 74.5, 84.5
Class boundary is the midpoint of the upper class limit of a class and the lower class limit of the previous class.
Thus, the class boundaries are- 29.5, 39.5, 49.5, 59.5, 69.5, 79.5
Frequency gives us the number of individuals/ objects belonging to a particular class.
Thus, the number of individuals included in the summary = 27 + 32 + 15 + 3 + 5 + 1 + 1 = 84
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At Elmo's, an old-fashioned barber shop in Melbourne, Florida, 66% of all customers get a haircut, 49% get a shave, and 40% get both.
a) What is the probability that a randomly selected person doesn't get a shave and doesn't get a haircut? Your answer should have at least 3 decimal places.
b) What is the probability that a randomly selected person gets a shave, given that they get a haircut? Your answer should have at least 3 decimal places.
The probability that a randomly selected person doesn't get a shave and doesn't get a haircut is 0.250.
The probability that a randomly selected person gets a shave, given that they get a haircut is 0.606.
What is the probability?The probability that a person selected at random would not get a shave or a haircut can be found as:
= 1 - (Prob. of haircut + Prob. of shave - Prob. of both)
= 1 - (0.66 + 0.49 - .40)
= 0.250
The probability that a random person would get a shave given they have gotten a haircut is:
= Probability of both / Probability of getting a haircut
= 0.40 / 0.66
= 0.606
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*Please help*
Xavier bought a new boat for $24,000 in the year 2009. He knows that the value of the boat has depreciated linearly. If the value of the boat in 2010 was $18,500, what was the annual rate of change of the boat's value? Round your answer to the nearest hundredth if necessary.
Answer:
5500 is correct Answer.
Please mark me as brainlist answer.
Simplify negative 2 and 3 over 5 minus 6 and 2 over 7.
The value of the expression is -311/35
How to simplify the expression?The expression is given as
negative 2 and 3 over 5 minus 6 and 2 over 7.
Rewrite properly as
- 2 3/5 - 6 2/7
Express as improper fraction
-13/5 - 44/7
Take the LCM
(-13 * 7 - 44 * 5)/35
Evaluate
-311/35
Hence, the value of the expression is -311/35
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Is this a function or not. Then state domain and range. WILL GIVE BRAINLEIST
Answer:
Yes
Step-by-step explanation:
It is a function look at the numbers
Laura is completing a 15-week exercise program where she increases the amount of time she works out by the same amount. She exercised 20 minutes per day the third week, 50 minutes per day the ninth week, and 60 minutes per day the eleventh week.
What is the function that represents the sequence?
The logical function that represents the amount of workout Laura does in each week along with her simultaneous increase in workout can be given by Arithmetic Progression.
It is represented as An = A + (n-1)d. Here, A represents the first term, or the amount of workout done in first week, d represents common difference or the difference in workout done in next week to its previous week, n represents the number of terms or the number of weeks for which data is to be calculated and An represents the workout done in nth week.
Arithmetic progression refers to the sequence of numbers such that each succeeding number increases with respect to previous number by fixed/ constant value. Thus, there exists constant amount of difference between each consecutive pair of number.
Since, Laura's workout pattern varies such that the amount of workout she does in one week increases by same amount in next week, so we get an arithmetic progression of her workout pattern.
Hence, her workout pattern can be traced as A, A+d, A+2d, A+3A, ..., An.
Thus, An = A + [(n-1)*d]
A3 = A +[(3-1)*d] = A + [2d] = 20 ...(1)
A9 = A +[(9-1)*d] = A + [8d] = 50 ...(2)
A11 = A +[(11-1)*d] = A + [10d] = 60 ...(3)
Solving equation (1) and (2), we get d = 5 and A = 10.
Thus, we conclude by saying that the function of her exercise routine is given by arithmetic progression and the amount of workout that she increases each week is given by 'd' that is 5 minutes.
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write 336 mi in 11.2 h as a rate in simplest form
Answer:
30 mL/h
Step-by-step explanation:
You want the rate 336 ml in 11.2 h as a rate in simplest form.
Unit rateThe rate can be expressed in simplest form in a number of ways. We usually want rates involving time to be expressed with time units in the denominator:
(336 mL) / (11.2 h) = 30 mL/h
__
Additional comment
Medicine is often prescribed on a "per day" basis. In 24 hours, this rate would be ...
(30 mL/h)×(24 h/day) = 720 mL/day
The machine setup to dispense this medicine might use time units of minutes:
(30 mL/h) / (60 min/h) = (1/2) mL/min
The percent of 12th graders in a certain state who have ever used cigarettes for each of the years 2000 through 2014 can be modeled by p= -1.773t+60.442, where p is equal to the percent
and t is equal to number of years after 2000. When will the percent be less than 30 %?
The percent will be less than 30% after the year
(Round to the nearest year as needed.)
example Get more help -
The percent will be less than 30% after the year 2017
Let 'p' be the percent of 12th graders in a certain state who have ever used cigarettes for each of the years 2000 through 2014.
Let 't' be the number of years after 2000.
We have to find when the percent is less than 30%.
The function modelling the percent and the number of years through 2000 and 2014 is p= -1.773t+60.442
So first we need to find the number of years corresponding to 30%.
Substitute p = 30 in the above linear equation.
i.e., 30 = -1.773t+60.442
-1.773t = 30 - 60.442 = -30.442
Therefore, t = 30.442/1.773 = 17.17 ≈ 17 years
Since t denotes the number of years after 2000, when t = 17, the year is 2000+17 = 2017
So the percent will be less than 30% after the year 2017
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THIS IS IMPORTANT
Where can you find the pulse that is closest to your head?
elbow
wrist
neck
foot
Answer:
Neck
Step-by-step explanation:
Which one is closest to your head?
T-T
Real number root for V-49
Step-by-step explanation:
there is no real number solution for the square root of a negative number.
a sqare root multiplied by itself had to deliver exactly the number inside the square root.
so for sqrt(-49), what can be the answer ?
which number multiplied by itself gives -49 ?
it any negative number at that.
because
a × a = a²
and
-a × -a = a² but definitely not -a².
we get a negative number only, when we multiply a positive number with a negative number or vice versa.
the only solution is complex or imaginary (based on the imaginary number i):
i² = -1
i = sqrt(-1)
so, sqrt(-49) = sqrt(49 × -1) = 7×sqrt(-1) = 7i
but again, no real solution.
List a and b for each of them
1) The intersection of sets A and B is; A ∩ B = {1, 3}
2) The complement of set A is; A' = {4, 5, 6, 9, 10}
How to interpret Mathematical Sets?
We are given the sets;
U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
A = {1, 2, 3, 7, 8}
B = {1, 3, 9, 10}
1) The intersection of sets A and B simply means the numbers that are common to both sets. Thus;
A ∩ B = {1, 3}
2) The complement of set A is defined as the set that contains the elements present in the universal set but not in set A. Thus;
A' = {4, 5, 6, 9, 10}
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A rectangle is twice as long as it is wide and has the same perimeter as a square whose area is 36 square feet larger than that of the rectangle. what are the dimensions of both the rectangle and the square?
Answer:
rectangle: 12 ft × 24 ftsquare: 18 ft squareStep-by-step explanation:
You want the dimensions of a rectangle and square such that they have the same perimeter, but the square has an area of 36 more square feet. The rectangle is twice as long as wide.
SetupLet x represent the side length of the square. Then its area is x², and the area of the rectangle is (x² -36).
This area is the product of length and width. The expression factors as ...
rectangle area = x² -36 = (x +6)(x -6)
SolutionIf we assume these factors are the dimensions of the rectangle, then the longer dimension is twice the shorter one:
(x +6) = 2(x -6)
18 = x . . . . . . . . . add 12-x to both sides
This is the side length of the square. The rectangle dimensions are ...
x+6 = 18+6 = 24 . . . . feet long
x -6 = 18 -6 = 12 . . . . feet wide
The rectangle is 12 feet wide and 24 feet long. The square is 18 feet on a side.
__
Additional comment
The perimeter in each case is 4x = 2((x+6) +(x -6)) = 72 ft.
The area of the rectangle is (12 ft)(24 ft) = 288 ft². The area of the square is (18 ft)² = 324 ft², a value that is 36 ft² more than the rectangle area.
Alternate solution
Using x for the width of the rectangle, the length is 2x and its area is x(2x) = 2x². The perimeter is 2(x +2x) = 6x, so the side length of the square is (6x)/4 = 3/2x and its area is (3/2x)² = 9/4x².
The difference is 36 square feet, so we have ...
9/4x² -2x² = 36 = x²/4 ⇒ x = √(36·4) = 6·2 = 12 . . . . width of rectangle
What is the value of this expression if h 8, j = -1, and k = -12?
Value of the given expression j³k/h0 is 12
h = 8
j=-1
h = 8
In order to do this, we need to change the values of h, j, and k in the given statement = (-1)^3 (-12) / 8^0 ....(1)
Find the denominator by using (1)
(-1)³ (-12) / 1
Analyze each exponent.
= 12/1
Hence, j³k/h0 = 12
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Complete Question -
What is the value of this expression if h=8 ,j= -1 , and k= -12? j³k/h0
if this is solved you will be awarded a high mark prove the following formula 1 + sec²=cot²
This relationship is not true.
[tex]1 + \sec^2(x) = 1 + (1 - \tan^2(x)) = 2 - \tan^2(x)[/tex]
and
[tex]\cot^2(x) = \dfrac1{\tan^2(x)}[/tex]
Rewrite the equation in terms of only tangent.
[tex]2 - \tan^2(x) = \dfrac1{\tan^2(x)} \iff \tan^4(x) - 2\tan^2(x) + 1 = 0[/tex]
Factorize the left side.
[tex]\left(\tan^2(x) - 1\right)^2 = 0[/tex]
Solve for [tex]\tan(x)[/tex].
[tex]\tan^2(x) - 1 = 0[/tex]
[tex]\tan^2(x) = 1[/tex]
[tex]\tan(x) = \pm 1[/tex]
[tex]x = \pm\tan^{-1}(1) + n\pi = \pm\dfrac\pi4 + n\pi[/tex]
where [tex]n[/tex] is an integer. That is, the equation only holds for certain values of [tex]x[/tex], as opposed to all [tex]x[/tex], so it's not an identity.
Andrew can paint the neighbor's house 5 times as fast as Bailey. The year Andrew and Bailey worked together, it took them 2 days. How long would it take each to paint the house?
Answer:
12 days for Bailey
2.4 days for Andrew
Step-by-step explanation:
If Andrew is 5 times as fast, then Andrew + Bailey are 6 times as fast as Bailey alone.
That means Bailey would take 2*6 = 12 days to paint alone.
Since Andrew is 5 times faster, he'd only take 12/5 = 2.4 days.
Write the first trigonometric function in terms of the second for in the given quadrant. (No theta symbol so used word)
sec(theta), tan(theta); theta in Quadrant IV
sec(theta) =
The expression of [tex] \mathbf{sec( \theta)}[/tex] in terms of [tex]tan( \theta)[/tex] in Quadrant IV is presented as follows;
[tex] sec( \theta) = \sqrt{{tan( \theta)}^{2} + 1} [/tex]
Which trigonometric identity can be used to express the required function?The given trigonometric functions are;
[tex]sec( \theta)[/tex]
[tex]tan( \theta)[/tex]
[tex] {sec( \theta)}^{2} = {tan( \theta)}^{2} + 1[/tex]
In Quadrant IV, the tangent of an angle is -ve, while the secant is +ve
However, the square of -ve is positive;
(-ve)² = +veTherefore;
[tex] \left({tan( \theta)}^{2} + 1 \right) \: is \: positive[/tex]
Which gives;
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A college football team will play 14 games next fall each game can result in 2 possible outcomes find the total possible number of outcomes for the season
There will be an outcome of 16380 times.
What is an outcome?
An outcome is a potential consequence of an event or trial in probability theory. A specific experiment can have any number of outcomes, and they are all distinct and unrelated to one another.The football team will play 14 games
and each game can result in one of 2
Hence, the total possible number of outcomes for the season is [tex]2^{14}[/tex].
Now, let us explain
Let the result can be represented by an 'ordered set" i.e. 14- box.
|1|2|3|4|5|6|7|8|9|10|11|12|13|14|
Hence, the first box can be filled in 2 ways.
Similarly, all boxes.
Hence, the total number of cases will be,
2*2*2*2.... 14 times
= [tex]2^{14}\\[/tex]
=16380 times.
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You buy a new computer for $1500. The value of the computer decreases by 6% every year. How much is the computer worth after 4 years?
Answer: Your computer will be worth $1,171.12
Step-by-step explanation:
[tex]a_n = 1500(0.94)^4\\a_n=\boxed{1171.12}[/tex]
The sale price of a new refrigerator is $705 and sales tax is figured at 0.05 times the price. What is the total amount paid for the refrigerator?
The amount paid for the refrigerator is $740.25.
How to calculate the price?From the information, the sale price of a new refrigerator is $705 and sales tax is figured at 0.05 times the price.
The price of the refrigerator will be:
= $705 + (0.05 × $705)
= $705 + $35.25
= $740.25
Therefore, the amount paid for the refrigerator is $740.25
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Makayla and Nathan both leave the library at the Same time, but in opposite directions. If Nathan travels 8 mph faster than makayla and after 6 hours they are 192 miles apart, how fast is each traveling?
The speed of Makayla and Nathan are 12 mph and 20 mph respectively.
What is relation between speed and time?A moving body's speed is the distance it travels in one unit of time. If the distance is in kilometers and the time is in hours, the speed is in kilometers per hour. If the distance is expressed in meters and the time is measured in seconds, the speed is measured in meters per second.Let the speed of Makayla is 'x' mph.
and the speed of Nathan is 'y' mph.
The total distance travelled by both is 129 miles.
The time taken by each is 6 hours, same for both.
Speed = distance / time
Distance = speed × time
Makayla's covered distance = xt
Nathan's covered distance = yt
Total distance = xt + yt
xt + yt = 192
As, Nathan travels 8 mph faster than makayla.
The,
y = x + 8, t = 6 hours substitute;
xt + (x+ 8)t = 192
2x + 8 = 192/6
On simplification;
x = 12 mph (Makayla's speed)
Y = x + 8
y = 12 + 8
y = 20 mph (Nathan's speed)
Therefore, the speed of Makayla and Nathan are x = 12 mph and y = 20 mph respective;y.
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Find the domain and range of the relation. Also determine whether the relation is a function.
{(6,3), (8,5), (-4,-4), (5,5)}
The domain is:
D: {-4, 5, 6, 8}
The range is:
R: {-4, 3, 5}
And yes, the relation is a function.
How to determine the domain and range?
For a relation that maps elements x into elements y (in the form (x, y)), we define the domain as the set of the inputs (values of x) and the range as the set of the outputs (values of y).
Here our relation is defined by: {(6,3), (8,5), (-4,-4), (5,5)}
The domain is the set of the first values of each pair, so we have:
D: {-4, 5, 6, 8}
The range is the set of the second values of each pair:
R: {-4, 3, 5}
Now, is this a function?
Yes, it is a function, because each input is mapped into only one output.
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Find the distance between X(-2,4) and Y(6,1)
Answer:
Exact Distance = [tex]\boldsymbol{\sqrt{73}}[/tex] units
Approximate Distance = 8.544 units
====================================================
Explanation:
I'll relabel the points as A and B, and I'll be using the distance formula.
[tex]A = (x_1,y_1) = (-2,4) \text{ and } B = (x_2, y_2) = (6,1)\\\\d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}\\\\d = \sqrt{(-2-6)^2 + (4-1)^2}\\\\d = \sqrt{(-8)^2 + (3)^2}\\\\d = \sqrt{64 + 9}\\\\d = \sqrt{73}\\\\d \approx 8.544\\\\[/tex]
The exact distance is [tex]\sqrt{73}[/tex] units.
The approximate distance is roughly 8.544 units.
Round the approximate value however your teacher instructs.
pls answer if wrong i ban you
The coordinates of L are: (8,-4)
Here, triangle is rotated 270° counterclockwise. So the rule that we have to apply here is
(x, y) → (y, -x)
Based on the rule given in step 1, we have to find the vertices of the rotated figure.
(x, y) → (y, -x)
L(4,8) → L'(8.-4)
M(4,3) → M'(3,-4)
N(8,8) → N'(8,-8)
Vertices of the rotated figure are:
L'(8.-4) M'(3,-4) N'(8,-8)
Hence we get the desired result.
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Expand and simplify (5x - 2)^2
Answer:
The value of x = 2/5
Step-by-step explanation:
=>(5x - 2)²
=> (5x)² + 2² - 2(5x)(2)
=> 25x² -20x +4
=> 25x² -10x -10x +4
=> (5x-2) (5x-2)
=> x = 2/5 or 2/5
Suppose you make monthly mortgage payments of $1,345 and have 10 years left on the mortgage (next payment due next month). Assuming a 3.6% stated annual interest rate for the mortgage, how much would you need today to pay off the mortgage?
I will need $1,61,884.2 to pay off the mortgage.
This problem is related to simple interest and we have to calculate the amount after 10 years which is payable in the form of mortgage.
The monthly mortgage payment is $1,345.
Rate of interest is 3.6% per annum.
Time is given to be 10 years.
Simple interest for 10 years = 1345×3.6×10/100
= $ 484.2
So, the total money required to clear the mortgage
= $(1345×12×10) + $ 484.2
= $161400 + $484.2
= $ 1,61,884.2
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Simplify: 2.4 × 10-4
The four is a exponent
Answer: 20
Step-by-step explanation:
Multiply 2.4*10-4
Calculate 24-4
the answer is (12x^10000)/5