Answer:
The value of a mathematical expression is the result of the computation described by this expression when the variables and constants in it are assigned values. The value of a function, given the value(s) assigned to its argument(s), is the quantity assumed by the function for these argument values.
hope it helps
Work out the perimeter of this semicircle.
Take a to be 3.142
10 cm
Answer:
perimeter=1/2*2πr
Step-by-step explanation:
1/2*2*3.142*10
=31.42
What is the law of large numbers?
If you were using the relative frequency of an event to estimate the probability of the event, would it be better to use 100 trials or 500 trials? Explain.
The Law of Large Numbers is a fundamental concept in probability theory and statistics stating the number of trials of a random event increases, the average of the outcomes approaches the expected value of the event. It's better to use 500 trials.
In other words, as we repeat an experiment a large number of times, the proportion of times that a certain outcome occurs will converge to its probability of occurrence. This is an important concept in statistical inference, as it helps to ensure that the results of a sample are representative of the population from which it was drawn.
Now, if you were using the relative frequency of an event to estimate the probability of the event, it would be better to use 500 trials rather than 100 trials. The reason is that the larger the number of trials, the more accurate the estimate of the probability is likely to be.
Using a larger sample size reduces the impact of random variation and provides a more precise estimate of the true probability. The Law of Large Numbers tells us that as the sample size increases, the relative frequency of the event should converge to the true probability, so a larger sample size will generally give a more reliable estimate
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If angle 1 and angle 2 form a linear pair and angle 1 is 18 degrees less than five times the measure of angle 2, then the angle 1 is _____ degrees
Answer:
Angle 1 is 147 degrees
Step-by-step explanation:
When two angles form a linear pair, then we have the intersection of two lines
So what this mean is that both angles lie on a straight line and the sum of both angles is 180.
Let the angle 2 be x
We are told that angle 1 is 18 degrees less than 5 times the measure of angle 2;
What we are saying here is that; angle 1 = 5x - 18
So let’s add both together to give 180
angle 1 + angle 2 = 180
x + 5x -18 = 180
6x = 180+ 18
6x = 198
x = 198/6
x = 33 degrees
But angle 1 is 5x -18 = 5(33) -18 = 165 -18 = 147 degrees
Sandy’s 8th grade math class receives $13.50 for every 5 boxes of chocolates that they sell. Which graph shows this relationship with the same unit rate?
Answer:
See Explanation
Step-by-step explanation:
The graphs are not given; however, I'll answer with the graph equation and also attach the graph...
Represent the boxes with x and the cash received with y.
When x = 5
y = 13.50
When x = 10
y = 27
First, we need to get the slope of the graph.
m = (y2 - y1)/(x2 - x1).
m = (27 - 13.5)/(10 - 5)
m = 13.5/5
m = 2.7
Next, is to determine the graph equation using
y - y1 = m(x - x1)
y - 13.5 = 2.7(x - 5)
y - 13.5 = 2.7x - 13.5
y = 2.7x - 13.5 + 13.5
y = 2.7x..
See Attachment for graph
PLEASE HELP! it’s would be really appreciated
Answer:
46 degrees
Step-by-step explanation:
180 - 102 - 32 equals to 46
Which rational number is one tick mark to the left of Negative three-fourths on the number line below? A number line going from negative 2 to positive 2 in increments of 1. There are 4 equal spaces between each number. Negative 1 and one-fourth –1 Negative StartFraction 2 Over 4 EndFraction 0
Answer:
(B) -1
Step-by-step explanation:
We want to determine the rational number which is one tick mark to the left of \(-\dfrac{3}{4}\) .
If the number is to the left, it must be less than \(-\dfrac{3}{4}\) .
Since there are 4 equal spaces between each number, the numbers between -1 and 0 are:
\(-1,-\dfrac{3}{4},-\dfrac{2}{4},-\dfrac{1}{4},0\)
We can then see that the number one tick to the left of \(-\dfrac{3}{4}\) is -1.
The correct option is B.
Answer:
B?????
Step-by-step explanation:
Sketch the region enclosed by the given curves. decide whether to integrate with respect to x or y. theb find the region of the area. y-1/x, y=1/x^2, x=6
Area = ∫[0, 1] (upper curve - lower curve) dy
The upper curve is y - 1/x, and the lower curve is y = 1/x^2.
Area = ∫[0, 1] (y - 1/x - 1/x^2) dy
Evaluate this integral within the given limits of integration to find the area of the region.
The curves provided are:
y - 1/x
y = 1/x^2
x = 6
Let's find the points of intersection between the curves:
Setting the two equations equal to each other, we have:
1/x^2 = 1/x
To simplify the equation, we can multiply both sides by x^2:
1 = x
So the point of intersection between the curves y - 1/x and y = 1/x^2 occurs at (1, 1).
Now, let's sketch the region enclosed by the curves:
Curve y - 1/x:
The curve y - 1/x represents a hyperbola that approaches the x-axis as x approaches positive or negative infinity. It intersects the x-axis at x = 1. The curve extends towards positive and negative y-values.
Curve y = 1/x^2:
The curve y = 1/x^2 is a downward-opening hyperbola. It approaches the x-axis as x approaches positive or negative infinity. The curve has asymptotes at x = 0 and does not intersect the x-axis.
Line x = 6:
The line x = 6 is a vertical line passing through x = 6.
To determine whether to integrate with respect to x or y, we need to consider the orientation of the region. Looking at the given curves, it is clear that the region is vertically bounded. Therefore, we'll integrate with respect to y.
To find the area of the region, we need to determine the limits of integration. The region is bounded by the curves y - 1/x and y = 1/x^2, and it extends from the y-axis to the point of intersection at (1, 1). Therefore, the limits of integration for y are from 0 to 1.
Now, let's calculate the area using the definite integral:
Area = ∫[0, 1] (upper curve - lower curve) dy
The upper curve is y - 1/x, and the lower curve is y = 1/x^2.
Area = ∫[0, 1] (y - 1/x - 1/x^2) dy
Evaluate this integral within the given limits of integration to find the area of the region.
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The region enclosed by the curves y = 1/x, y = 1/\(x^2\), and x = 6 can be found by integrating with respect to x. The region lies in the first quadrant and is bounded by the curves and the line x = 6.
To sketch the region enclosed by the curves, we can start by plotting the graphs of y = 1/x and y = 1/\(x^2\). The curve y = 1/x represents a hyperbola that passes through the points (1, 1), (2, 0.5), (3, 0.33), and so on. The curve y = 1/\(x^2\) is a hyperbola that approaches the x-axis as x increases. The line x = 6 is a vertical line passing through x = 6.
To find the region of the area enclosed by these curves, we need to determine the limits of integration. The region lies to the right of the y-axis (x > 0) and is bounded by the curves y = 1/x and y = 1/\(x^2\). The left boundary of the region is the curve y = 1/x, and the right boundary is the curve y = 1/\(x^2\). The lower boundary is the x-axis, and the upper boundary is the curve y = 1/x.
To calculate the area of this region, we can integrate with respect to x. The limits of integration are x = 1 (the intersection point of the curves y = 1/x and y = 1/\(x^2\)) and x = 6 (the given line). The integral that represents the area is ∫[1, 6] (1/x - 1/\(x^2\)) dx. By evaluating this integral, we can find the area of the region enclosed by the given curves.
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PLS HELPPPPPPP I WILL GIVE 40 PTSSSSS AND BRAINLYEST IF YOU HELP GOOD AND FOOL ANSWERS WILL BE REPORTED
The surface area of the prism is 78 square units, which corresponds to option A.
How to solve for the surface areaYou provided three dimensions: 5 units, 3 units, and 3 units. I assume these are the dimensions of a rectangular prism.
Let's label the dimensions: length (l) = 5 units, width (w) = 3 units, and height (h) = 3 units.
There are two bases, and their areas are equal:
Base Area = l * w = 5 * 3 = 15 square units
There are also three pairs of lateral faces. The areas of the lateral faces are:
Two faces with dimensions l and h: 2 * (l * h) = 2 * (5 * 3) = 30 square units
Two faces with dimensions w and h: 2 * (w * h) = 2 * (3 * 3) = 18 square units
Now, add the areas of all the faces together:
Surface Area = Base Area * 2 + Lateral Area = 15 * 2 + 30 + 18 = 30 + 30 + 18 = 78 square units
So, the surface area of the prism is 78 square units, which corresponds to option A.
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Find the partial fraction decomposition of
2 + 36 3 + 2
by creating a system of equations for the values you are seeking. Solve that matrix using 3 different techniques. We studied substitution, elimination, Gaussian elimination, matrix inverses, and Cramer’s rule.
a) The system of equations is:
b) Detailed solution of system using method 1:
c) Detailed solution of system using method 2:
d) Detailed solution of system using method 3:
e) Solution of the original question: the partial fraction decomposition.
Answer:
a b c d are the answers
Step-by-step explanation:
What is the value of x that satisfies the equation -3x - 6 = 30? I NEED HELP ASAP PLS!!!!! YOU GET 15 POINTS!!
Answer:
x = -12
Step-by-step explanation:
First, move the constant to the right and change its sign.
-3x = 30 + 6
Next, add the numbers
-3x = 36
Lastly, divide both sides by -3
x = -12
a 50 foot ladder is set against the side of a house so that it reaches up 48 feet. of mila grabs the ladder at its base and pulls it 6 feet farther from the house, how far up the side of the house will the ladder reach now?
The ladder on pulling 6 feet father from the house now reaches 45.83 feet, which is lower than previous height.
The distance between ladder and house, the distance till ladder reaches and length of ladder given by Pythagoras theorem. The distance till ladder reaches is perpendicular, ladder is hypotenuse and the base is horizontal distance between the two. So, finding the base first.
Base² = 50² - 48²
Base² = 2500 - 2304
Base² = 196
Base = ✓196
Base or horizontal distance = 14 feet.
Now, on moving 6 feet, the horizontal distance will be 14 + 6 = 20 feet. Finding the new height or perpendicular now.
50² = 20² + Perpendicular²
Perpendicular² = 2500 - 400
Perpendicular² = 2100
Perpendicular = 45.83 feet
Hence, the ladder now reached to 45.83 feet height of the house.
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Can someone explain to me what to do and what is the correct answer please? I would really like to know what to do, thank u in advance if u help me!<3
The total bill is 86.50 he leaves 15% tip what is the total cost of the meal
Answer:
99.47
Step-by-step explanation:
86.50/15 =
+86.50 =
99.47
Historically, the industries with the most complaints to the Better Business Bureau have been banks, cable and satellite television companies, collection agencies, cellular phone providers, and new car dealerships. The results for a sample of complaints are contained in the file BBB. Click on the datafile logo to reference the data. a. Construct a frequency distribution for the number of complaints by industry. CategoryObserved Frequency Bank 26 Cable 44 Car 42 Cell 60 Collection 28 Total 200 b. Using , conduct a hypothesis test to determine whether the probability of a complaint is the same for the five industries. The test-statistic is (to 3 decimals). -value (to 4 decimals) What is your conclusion
Chi-squared goodness of fit test to determine equality of complaint probability in 5 industries.
This question seems to be asking for a chi-squared goodness of fit test to determine if there is evidence to suggest that the probability of a complaint is the same for all five industries.
Here's how you could perform the hypothesis test:
H0: For each of the five industries, the likelihood of a complaint is the same.
Ha: For at least one industry, there are variable odds of receiving a complaint.
Test-statistic:
Calculate the expected frequency for each industry by multiplying the total number of complaints by the proportion of complaints in each industry.Subtract the expected frequency from the observed frequency for each industry, square the result, and divide by the expected frequency.Sum up the results for all five industries.-value:
Find the critical value of a chi-squared distribution with 4 degrees of freedom (5 industries - 1) at a given level of significance (e.g. 0.05).Conclusion:
Reject the null hypothesis if the test statistic exceeds the crucial value. There is evidence to suggest that the probability of a complaint is different for at least one industry.If the test-statistic is less than or equal to the critical value, fail to reject the null hypothesis. There is not enough evidence to suggest that the probability of a complaint is different for any of the industries.I hope that helps! If you have the data and would like to perform the test and find the test-statistic and -value, I'd be happy to assist you further.
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Darrell estimates that it will take him 9 days to complete every world on a new video game. It actually takes him 12 days. What is the percent error of Darrell's estimate? Round the percent to the nearest tenth if necessary.
Answer:
25%
Step-by-step explanation:
A circular spinner has a radius of 6 inches. The spinner is divided into three sections of unequal area. The sector labeled green has a central angle of 90°. A point on the spinner is randomly selected.
What is the probability that the randomly selected point falls in the green sector?
The probability of selecting a point in the green sector is 1/4 or 0.25.
The area of a circle with radius 6 inches is given by the formula A = πr², where r is the radius of the circle.
Substituting r = 6, we have A = π(6)² = 36π square inches.
The area of a sector of a circle with central angle θ and radius r is given by the formula A = (θ/360)πr².
Substituting θ = 90 and r = 6, we have A = (90/360)π(6)² = 9π square inches.
Therefore, the probability of selecting a point in the green sector is given by the ratio of the area of the green sector to the total area of the circle:
P(green) = (area of green sector) / (total area of circle)
= (9π square inches) / (36π square inches)
= 1/4
Thus, the required probability is 1/4 or 0.25.
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Find the product of (x + (3+5i))^2
Answer:
x^2 +6x +10xi -16 +30i
Step-by-step explanation:
(x + (3+5i))^2
Rewriting as
(x + (3+5i)) (x + (3+5i))
Let 3+5i = m
(x + m) (x + m)
FOILing
x^2 + xm+xm+m^2
x^2 +2xm + m^2
Replacing m with 3+5i
x^2 +2x (3+5i) +(3+5i)^2
Distribute
x^2 +6x +10xi +(3+5i)^2
Now FOIL (3+5i)^2
( 3+5i) ( 3+5i)
3*3+ 3*5i + 3*5i+ 25i^2
= 9 +15i+15i +25(-1)
9+30i -25
-16 +30 i
Replacing that in the equation
x^2 +6x +10xi -16 +30i
Answer:
x² + 6x + 10xi -16 + 30i
Step-by-step explanation:
(x + (3 + 5i) )²
use the binomial theorem:
(a + b)² = a² + 2ab + b² to expand (x + (3 + 5i) )²
substitute the values,
x² + (6 + 10i)x + (-16 + 30i)
therefore
x² + 6x + 10xi -16 + 30i
as a town gets smaller, the population of its high school decreases by 6% each year. the senior class has 250 students right now. in how many years will it have about 150 students solve without graphing using pert
An equation of the question is 250 × 0.94^n = 150 and in approx 8 years it will have about 150 students.
The population of its high school decreases by 6% each year.
The senior class has 250 students now.
Each year decrease in population = 6% = 0.06
So it can be = 1 - 0.06 = 0.94
Total student now = 250
Let n be the number of years before the class will have students.
So the equation should be = 250 × 0.94^n
After years left students = 150.
Now the equation should be
250 × 0.94^n = 150
Now solving the equation.
Divide by 250 on both side, we get
0.94^n = 150/250
0.94^n = 3/5
Taking log on both side, we get
log(0.94^n) = log(3/5)
Using the formula log(m^n) = n logm and log(m/n) = log m - log n
n log(0.94) = log3 - log5
Now finding the value of log using calculator
n (-0.062) = 1.099 - 1.61
(-0.062)n = -0.511
Divide by (-0.062) on both side, we get
n = 8.242
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The complete question is:
As a town gets smaller, the population of its high school decreases by 6% each year. The senior class has 250 students now. In how many years will it have about 150 students? Write an equation. Then solve the equation without graphing. Write an equation to represent this situation. Let n be the number of years before the class will have students.
The number of hours, H, of daylight in Madrid as a function of date is approximated by the formula
H=12+2. 4sin(0. 0172(t−80)),
where t is the number of days since the start of the year. (We can think of t=0 as the stroke of midnight on Dec. 31/Jan 1; thus, January falls between t=0 and t=31, February falls between t=31 and t=59, etc. ).
Find the average number of hours of daylight in Madrid (assuming in each case that it is not a leap year):
The average number of hours of daylight in Madrid is approximately 12.01 hours.
To find the average number of hours of daylight in Madrid, we need to integrate the formula for H over the range of days in a year and divide the result by the number of days in a year.
The formula for H is H=12+2.4sin(0.0172(t−80)).
We can integrate this formula over the range of days in a year as follows:
\($\int_{0}^{364} H dt = \int_{0}^{364} (12+2.4\sin(0.0172(t-80))) dt$\)
We can simplify this integral by using the fact that the integral of sin(x) over one period is zero, and the period of sin(0.0172(t−80)) is 2π/0.0172, which is approximately 365. Therefore, we have:
\($\int_{0}^{364} H dt = \int_{0}^{364} 12 dt = 12(365) = 4380$\)
Dividing this result by the number of days in a year, we get:
Average hours of daylight = 4380/365 ≈ 12.01 hours.
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The price of a laptop decreased from RS50 000 to Rs45 000. Calculate the percentage decrease in the price.
Answer:
Step-by-step explanation:
loss amount=Rs 50000-Rs 45000
=Rs 5000
loss%=loss amount/original amount100%
=5000/50000*100
=500000/50000
=10%
a straight line passes through the point P(-1,5). Another line which passes through Q(-4,4) intersects the first line at point R( µ,5) where µ is a constant . If <PRQ = 90° find the value of R
Answer:
\(\mu=-4\)
Step-by-step explanation:
We know that \(\overline{PR} \perp \overline{QR}\).
Since \(\overline{PR}\) is horizontal, \(\overline{QR}\) is vertical. Therefore, \(\mu=-4\).
What is the Roman number of 500 and 1000?
Answer:
500=D 100=M
Step-by-step explanation:
I hope that helps :D
Find the slope of the line through each pair of points
Answer:
Answer of 3 is 5/4. and of no 4 is -11/-26. I think the image will help you.
Formula for slope is y2-y1/x2-x1
NEED HELP FAST PLEASE
Pete must buy 1200 shirts for his
department stores to sell. Two of Pete's suppliers are offering deals on bulk purchases of shirts. Ana is offering the shirts at $10 each, with a "Buy 5, Get 1
Free" discount. Jun is offering the shirts at
$8 each.
Complete the statements below to compare the offers.
What would Pete pay Ana for the shirts?
The ratio of shirts Pete pays for to all the shirts Pete gets is 5:
__/__ of 1200 is ___
___× $10 = $
What would Pete pay Jun for the shirt
1200 x $8 = $___
1. The ratio of shirts Pete pays for to all shirts is 1000.
2. Pete would pay Ana $8.33 for each shirt.
3. Pete would pay Jun $9600 for the shirt.
What would Pete pay Ana for the shirts?To determine what Pete would pay Ana for the shirts, we can use the "Buy 5, Get 1 Free" discount. The ratio of shirts Pete pays for to all the shirts Pete gets is 5:6 (5 shirts paid, and 1 shirt received for free).
To fill in the statements:
1. The ratio of shirts Pete pays for to all the shirts Pete gets is 5:6 of 1200 is ____.
To find the missing value, we can set up the following equation:
5/6 * 1200 = x
Solving for x, we have:
x = (5/6) * 1200 = 1000
So, the ratio of shirts Pete pays for to all the shirts Pete gets is 5:6 of 1200 is 1000.
2. ___ × $10 = $
Pete pays $10 for each shirt. Since the ratio is 5:6, the missing value can be calculated as follows:
5/6 * $10 = $8.33 (rounded to two decimal places)
Therefore, Pete would pay Ana $8.33 for each shirt.
3. What would Pete pay Jun for the shirt?
Pete would pay Jun $8 for each shirt. Since Pete needs 1200 shirts, we can calculate the total amount he would pay Jun as follows:
1200 x $8 = $9600
Therefore, Pete would pay Jun $9600 for the shirts.
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TRUE OR FALSE if a line passes through the points (20,5) and (10,10), then the slope of the line is -2.
False. The slope of the line is actually -0.5.
Let's determine the slope of the line that passes through the points (20, 5) and (10, 10). To find the slope, we can use the formula:
Slope (m) = (y2 - y1) / (x2 - x1)
Plugging in the coordinates of the two points, we get:
m = (10 - 5) / (10 - 20) = (5) / (-10) = -1/2
The slope of the line is -1/2. Therefore, the statement "If a line passes through the points (20, 5) and (10, 10), then the slope of the line is -2" is FALSE.
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12. Ms. Lacy wants to work out. Drop It Like It's Hot gym charges a monthly rate of $25 and
a $5.00 fee for each class. Kickin' It gym charges $20.00 monthly and $7.50 per class.
How many classes would Ms. Lacy need to attend for Kickin' It gym to be less expensive
than Drop It Like It's Hot gym?
a. More than 2 classes
b. Less than 2 classes
c. Less than 12 classes
d. More than 12 classes
Tt5
Answer:
more than 12 classes
Step-by-step explanation:
pls help its due on monday...
It's easy math but I am not very good at it, I need some help. can someone help me????? solve all 3of them please!
Answer:
1. 458 - 247 = 211
2. 58.92 - 43.87 = 15.05
3. 51/8 - 15/8 = 4.5
Here you go ! Hope this helps !
Answer:
1. 458 - 247 = c
2. 58.92 - 43.87 = c
3.\(\frac{51}{8}\) - \(\frac{15}{8}\) = c
Step-by-step explanation:
Hope this helps! <3
To make his special energy drink, Jerome uses 8 cups of water and 3 cups of drink mix.
A)What is the ratio of water to drink mix? (2 points)
B)What is the ratio of drink mix to water? (2 points)
C)What is the ratio of drink mix to mixed energy drink? (2 points)
D) What is the ratio of water to mixed energy drink? (2 points)
Answer:
8 : 3
3 : 8
8 : 11
Step-by-step explanation:
Answer:
A) 8 : 3
B) 3 : 8
C) 3 : 11 [water + drink mix = 3 + 8 = 11]
D) 8 : 11
help - i'll give brainliest
Answer:
W=91.2
Step-by-step explanation:
7.6=1212⋅7.6=12⋅12
=91.2
have a good day