Given that a = 1, b = 2, and C = -3, evaluate
ab²- ac²/ 2bc
Answers
Answer:
5/12
pls Mark as brainliest
Related Questions
the area of square of length of side 6cm is
Answers
Answer:
36
Step-by-step explanation:
its a square so all sides are equal so do 6 times 6
Answer: 36 cm squared
Step-by-step explanation:
first, we know squares have all equal sides, which means the square has 6cm for each side
we then multiply the base x height which equals 36
finally, since we are finding area, we put a “squared” symbol, or the word “squared”
An account earns simple annual interest.
$1500 at 4% for 5 years
Answers
Answer:
a) Interest earned = $300
b) balance = $1800
Step-by-step explanation:
a) I = Prt
P = $1500
r = 0.04
t = 5yrs
Substitute
I = ($1500)(0.04)(5)
Multiply
I = $300
b) balance = previous + interest earned
balance = $1500 + $300 = $1800
The account amounts to $1800 at 4% simple interest for 5 years.
What is simple interest?We know simple interest (SI) is given by SI = (p×r×t)/100, where
p = principle, r = rate in percentage, and t = time in years.
Given, An account earns simple annual interest $1500 at 4% for 5 years.
∴ P = $1500, r = 4%, t = 5 years.
So, SI = (1500×4×5)/100.
SI = 15×20.
SI = $300.
So, The total amount after 5 years at 4% simple interest is $(1500+300).
= $1800.
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How many diagonals does a
rectangle have?
Answers
A rectangle has two pairs of opposite sides that are equal in length and four right angles.
To determine the number of diagonals a rectangle has, we need to consider that a diagonal connects any two non-adjacent vertices of a shape.
In a rectangle, there are four vertices. For each vertex, we can draw a diagonal to any of the other three vertices that are not adjacent. Since there are four vertices in total, we can draw a diagonal from each of the four vertices to three other vertices, resulting in a total of 4 * 3 = 12 diagonals.
However, we must keep in mind that each diagonal is counted twice since it connects two different vertices. Therefore, we need to divide the total count of diagonals by 2, giving us the final answer.
Hence, a rectangle has 12/2 = 6 diagonals.
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Drag each expression to show if it is equivalent to 25, 52, 2 × 5, or none
Answers
Answer:
rag each expression to show whether it is equivalent to 36x + 9, ... 3.2/5. 20. AthenaSinclair. Ambitious. 467 answers. 151.9K people helped ... Lastly,, we will look at the final expression given which is 4(9x + 2). ... (25 votes).
Step-by-step explanation:
A help desk has two employees with one working during the day and one working at night. The number of hours the first employee works (X1) is normally distributed with mean 8.6 and standard deviation 0.1 and the number of hours the second employee works (X2) is normally distributed with mean 8.4 and standard deviation 0.9. Suppose that the amount of time that the employees overlap (X3) is normally distributed with mean 0.2 and standard deviation 0.2. Finally, assume that X1, X2, and X3 are independent. We are interested in the total time that the help desk has an employee present, i.e., Z = X1 + X2 - X3. A) What is the expected value of Z, the total time that the help desk has an employee present? B) What is the variance of Z? C) What is the probability that Z is between 15.9 and 16.1? D) What is the probability that Z is greater than 16?
Answers
Answer:
a) 16.8 hours.
b) 0.86 hours squared.
c) 0.0606 = 6.06% probability that Z is between 15.9 and 16.1.
d) 0.8051 = 80.51% probability that Z is greater than 16
Step-by-step explanation:
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Sum of normal variables:
When we add normal variables, the mean is the sum of each mean, while the variance is the sum of each variance. The standard deviation is the squared root of the variance.
In this question:
X1: Mean 8.6, standard deviation 0.1
X2: Mean 8.4, standard deviation 0.9
X3: Mean 0.2, standard deviation 0.2
Z = X1 + X2 - X3.
Mean:
[tex]\mu = 8.6 + 8.4 - 0.2 = 16.8[/tex]
Variance:
[tex]\sigma^{2} = 0.1^2 + 0.9^2 + 0.2^2 = 0.86[/tex]
Standard deviation:
[tex]\sigma = \sqrt{\sigma^{2}} = \sqrt{0.86} = 0.9274[/tex]
A) What is the expected value of Z, the total time that the help desk has an employee present?
[tex]\mu = 16.8[/tex]
So 16.8 hours.
B) What is the variance of Z?
[tex]\sigma = 0.86[/tex]
So 0.86 hours squared.
C) What is the probability that Z is between 15.9 and 16.1?
This is the pvalue of Z when X = 16.1 subtracted by the pvalue of Z when X = 15.9. So
X = 16.1
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{16.1 - 16.8}{0.9274}[/tex]
[tex]Z = -0.75[/tex]
[tex]Z = -0.75[/tex] has a pvalue of 0.2266
X = 15.9
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{15.9 - 16.8}{0.9274}[/tex]
[tex]Z = -0.97[/tex]
[tex]Z = -0.97[/tex] has a pvalue of 0.1660
0.2266 - 0.1660 = 0.0606
0.0606 = 6.06% probability that Z is between 15.9 and 16.1.
D) What is the probability that Z is greater than 16?
This is 1 subtracted by the pvalue of Z when X = 16. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{16 - 16.8}{0.9274}[/tex]
[tex]Z = -0.86[/tex]
[tex]Z = -0.86[/tex] has a pvalue of 0.1949
1 - 0.1949 = 0.8051
0.8051 = 80.51% probability that Z is greater than 16
Please help on this question
Answers
Answer: C
Step-by-step explanation:
Since she can speak more than 7, you can mentally get rid of A and B because the circles on the number line show less than or equal to and more than or equal to, and we already know she can speak more than 7 languages.
So between the less than or greater than symbol you need to pick the line that has the arrow pointing in the direction of the greater than symbol because she can speak more than 7 languages
The answer would be C because greater than symbols point in the same direction of the line >
Which set of directions correctly describes how to plot the point (8, 4) on the coordinate plane?
A. Start at the origin. Move 8 units to the right, then move 4 units up.
B. Start at the origin. Move 8 units up, then move 4 units to the right.
C. Start at the origin. Move 8 units to the left, then move 4 units up.
D. Start at the origin. Move 8 units up, then move 4 units to the left.
Answers
Answer:
A
Step-by-step explanation:
Answer:
A
Step-by-step explanation:
(x, y)
Left and right affects the x, up and down affects the y.
Since it's a positive 4, it goes up. We can eliminate B and D.
Since it's a positive 8, it goes right. A.
Which equation represents a linear function that has a slope of 4/5 and a y-intercept of -6?
Answers
Answer:
WOW THAT IS A LOT OF POINTS BRO
Step-by-step explanation:
Answer:
B
Step-by-step explanation:
A pair of jeans normally costs £40.
In the sales, there is 25% off.
Work out how much the jeans are in the sales.
Answers
Answer:
£30
Step-by-step explanation:
100% - 25% =75%
75% of £40
=£30
If you want to dilate a triangle, does the center of dilation have to be on the triangle? Can it be inside the triangle? Outside the triangle?
Answers
Answer:
No, it can be anywhere on the graph.
Step-by-step explanation:
Answer:
Attached
Step-by-step explanation:
Just a supplement of the above answer
I would really appreciate it if someone could answer this I will give a brainlist:)
Answers
Steps:
72^2 + 65^2= c^2
5184 + 4225= c^2
9409= c^2
C= 97
[tex]97.[/tex]
Step-by-step explanation:
By using Pythagoras theorem
AC² = AB² + BC².
Let AB = 72 and BC = 65.
AC² = 72² + 65²
AC² = 5184 + 4225
AC² = 9409.
AC = √9409
AC = 97.
What is the GCF of 22 and 32?
Answers
Answer:
The GFC of 22 and 32 is 2
Step-by-step explanation:
8+8+8=24 as multiplecation sentence
Answers
Answer
Hola la respuesta que buscas es bastante simple pero no lo sé
Step-by-step explanation:
Five plumbers charge different hourly
rates: $35, $42, $52, $38, and $42.
Find the mean, median, mode, MAD,
and IQR of these values. Which
measure of center and which measure
of variability best describe the data?
Answers
Explanation: for mean you add all the numbers up and divide it based upon how much numbers there are in total, so for this problem it would be:
$35 + $42 + $52 + $38 + 42 ÷ 5 = 41.8
**The median is: $42**
Explanation: to find the median we arrange the numbers from least to greatest or greatest to least you’ll get the same answer for median.
Original: $*35, $*42, $52, $*38, $*42
Least to greatest: ($35, $38, $42, $42, $52)
Greatest to least: $52, $42, $42, $38, $35)
Then we find the number in the center which is: $42 for the median.
**The mode is: $42**
Explanation: To find the mode we just see what number was repeated the most which in this case is $42
**MAD (Mean Absolute Deviation) is: $4.24**
Explanation to find the MAD we need to first add all the numbers up and divide them by the number of elements there are in the data set in total.
So we do,
$35 + $42 + $52 + $38 + 42 ÷ 5 = 41.8
Just as we did for finding the mean the difference for this though is after we’ve found this number we subtract each number by 41.8
and when we subtract the rule is there is no negative numbers so if any you subtract turn out to be negative you change it to positive so it would be:
$35 - $41.8 = (-6.8) change to + = 6.8
$42 - $41.8 = 0.2
$52 - $41.8 = 10.2
$38 - $41.8 = (-3.8) change to + = 3.8
$42 - $41.8 = 0.2
Then we add all the numbers up we just got and divide it by the number of elements in the date set so we do, $6.8 + $0.2 + $10.2 + $3.8 + $0.2 = 21.2 ÷ 5 = $4.24
**IQR (Interquartile Range) is: $10.5**
Explanation to find the IQR we order the numbers least to greatest or greatest to least it doesn’t matter which order you do it.
Greatest to least: $52, $42, $42, $38, $35
Least to greatest: $35, $38, $42, $42, $52
Q1 is: $36.5
Explanation: we get this by adding:
$35 + $38 ÷ 2 = 36.5
Q2 is: $42
Explanation: it’s right in the center
Q3 is: $47
Explanation: we get this by adding:
$42 + $52 ÷ 2 = $47
In order to find IQR we need to do Q3 - Q1
So, $47 - $36.5 = $10.5
**Measure of the center: (Mean = $41.8, Median = $42, Mode = $42, Range = $17**
Explanation: for range we simply subtract the biggest number from the smallest one which would be $52 - $35 = $17
**Measure of variability: (range = $42, Standard deviation = $2.91, Variance = $8.48)**
Explanation for standard of deviation we first find the mean which is $41.8, then we subtract each number be $41.8 which will give us these numbers which we’ll multiple by 2:
$6.8 x 2 = $13.6
$0.2 x 2 = $0.4
$10.2 x2 = $20.4
$3.8 x 2 = $7.6
$0.2 x 2 = $0.4
Then the numbers you get you add up and divide it by the number of elements in the data, which would be $13.6 + $0.4 + $20.4 + $7.6 + $0.4 = 42.4 ÷ 5 = 8.48
So the variance is: $8.48
Then to find the standard deviation we square root $8.48 which gives us: $2.91
The population of a town in North Carolina is modeled by the function f(x) = 10,520(1.041)'. If the initial population (that is, the population when x = O) was
measured January 1, 2012, what was the initial population?
Answers
Answer:
Step-by-step explanation:
This is an exponential growth function of the form
y=ar^x
Where y=final value, a=initial value, r=common ratio, x=term number.
Since a=10,520, that was the initial population in 2012.
How to multiply decimals 627.30 x .58
Answers
Answer:
363.834
Step-by-step explanation:
multiply 627.30 with .58 and move the decimal points.
The height of a building is 60 m long to the nearest degree what is the angle of elevation of the sun on a building cast a shadow that is 80 m long
Answers
Answer:
80m
Step-by-step explanation:
A standard fair dice is rolled twice.
What is the probability of getting an odd number on the first roll and any number except 1 on the other?
Answers
Answer:
5/12Step-by-step explanation:
Probability = favorable outcomes / total outcomes
P(odd) = 3/6 = 1/2 (there are 3 odd numbers out of 6 on a dice)P(no 1) = 5/6P(odd and no 1) = 1/2*5/6 = 5/12Answer:
5/12
Step-by-step explanation:
Hope this helps
The sum of a number y and 3 is 4.5. Pls help!!!
Answers
Answer:
60
Step-by-step explanation:
Answer: 1.5
Step-by-step explanation:
I did 4.5 subtract 3 and got 1.5= y
Write an equation for a line perpendicular to y=4x+1 and passing through the point (12,-7).
y =
Answers
Answer:
Step-by-step explanation:
y = 4x + 1
Slope of line = 4
Slope of perpendicular to line = -¼
Point-slope equation for line of slope -¼ that passes through (12, -7):
y+7= -¼(x-12)
Unit test
The table below shows the worth of each of Warren's three companies.
Company
Worth (in millions of dollars)
Margie's Travel
- 12.28
Fifth Coffee
-6.91
Northwind Traders
1.72
Help Warren sort his companies from least to greatest absolute value of worth.
Fifth Coffee
Northwind Traders
Margie's Travel
Og
Report a problem
Answers
Answer:
north wind traders,fifth cofffe, margies coffe
Step-by-step explanation:
anwsers from khan.
PLEASE HELP 5 POINTS
Answers
Answer:
V = 9 x 3 x 3 = 81 ft³
81 ft³ is the volume.
y=|x-3|+|x+2|-|x-5|, if -2 Please do not put links.
Answers
What is the probability that both ties he chooses are solid white
Answers
Answer:
[tex]\frac{1}{25}[/tex]
Step-by-step explanation:
Total outcome is 10
Favorable outcome is 2
The probability to choose solid white tie is [tex]\frac{1}{5}[/tex]
The probability that both ties he chooses are solid white is
[tex]\frac{1}{5}[/tex] × [tex]\frac{1}{5}[/tex] = [tex]\frac{1}{25}[/tex]
A cylinder has a base radius of 8ft and a height of 17ft. What is its volume in cubic ft, to the nearest tenths place?
Answers
Answer:
Step-by-step explanation:
Volume = πr²h = π·8²·17 = 1088π ≅ 3,418.1 ft³
Since this cylinder has a radius of 8 feet, its volume is equal to 3,418.5 cubic feet.
Given the following data:
Radius of cylinder = 8 feet.
Height of cylinder = 17 feet.
How to calculate the volume?Mathematically, the volume of a cylinder is given by this formula:
V = πr²h
Where:
h is the height.r is the radius.Substituting the given parameters into the formula, we have;
V = 3.142 × 8² × 17
V = 3.142 × 64 × 17
V = 3,418.5 cubic ft.
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Help ASAP !!!! I’m almost done
Answers
Answer:
1. 30.48cm
2. 5.77yds
3. 540min
4. 1200cm
5. 8.45qt
6. 168hr
7. 4535.92grams
8. 15yd
9. 32.808ft
Step-by-step explanation:
hope this helps :)
MATH 20 POINTS HELP PLZ :)
Answers
Answer:
the answer is C.
Step-by-step explanation:
HELP ASAP
The radius of a quarter circle is 1.4 millimeters. What is the quarter circle's area?
Answers
Answer:
A = 1.5386
Step-by-step explanation:
Quarter circle area formula:
A = (πr²)/4
A= (π1.4²)/4
A = (3.14*1.96)/4
A = (6.1544)/4
A = 1.5386
Kyle soles 18 of 24 puzzles in a puzzle book. he says that he can use an equivalent fraction to find the percent of puzzles in the book that he solved. how can he do that? what ia the percent?
PLEASE
Answers
Answer:
He solved 75% of the puzzles!
Step-by-step explanation:
Okay, let's look at our fraction 18 out of 24. We can see that they are both even numbers, so at worst, we can divide the entire fraction by two. However, they have a GCF of six, so we will use that.
18 3
---- divided by 6 = ----
24 4
Now that we have the fraction 3/4, we can turn that into a percentage!
3/4 is 0.75. To get the percentage, we multiply that by 100--now we have 75%.
Consider random samples of size 80 drawn from population A with proportion 0.48 and random samples of size 66 drawn from population B with proportion 0.13 . (a) Find the standard error of the distribution of differences in sample proportions, . Round your answer for the standard error to three decimal places. standard error
Answers
Answer:
Standard error = 0.070
Step-by-step explanation:
Formula for the standard error of the distribution of differences in sample proportions is;
σ_(A - B) = √((p_a^(1 - p_a^)/n_a) + (p_b^(1 - p_b^)/n_b))
We are given;
p_a^ = 0.48
n_a = 80
p_b^ = 0.13
n_b = 66
Thus;
σ_(A - B) = √((0.48(1 - 0.48)/80) + (0.14(1 - 0.13)/66))
σ_(A - B) = √0.00496545455
σ_(A - B) = 0.070