Answer:
-1
Step-by-step explanation:
The product of the slopes of perpendicular lines is always -1 .
the chef at a school cafeteria asked students whether they like peas. for the students surveyed, are liking peas and being male independent or dependent events? justify your answer
A.) Dependent;
P(likes peas) =39%
P(male/likes peas) =54%
since these probabilities are not equal, the events are dependent.
B.) Dependent;
P(likes peas) =39%
P(likes peas/male) = 42%
since these probabilities are not equal, the events are dependent.
C.) Independent;
P(likes peas) =39%
P(likes peas/male) =42%
since these probabilities are not equal, the events are independent.
D.) Independent;
P(likes peas) =39%
P(male/likes peas) =54%
since these probabilities are not equal, these events are independent.
Answer:
Option B
Step-by-step explanation:
Given:
total No. of students liking peas= 78
total no. of male students= 100
total number of students= 200
no. of male students liking peas= 42
Now we need to find are liking peas and being male independent or dependent events
P(likes peas)= 78/00
=0.39
=39%
P(likes peas/male) = 42/100
= 42%
as the two probabilities are not equal the two events are dependent.
Hence option B is correct: Dependent;
since these probabilities are not equal, the events are dependent!
Answer:
B
Step-by-step explanation:
In the Dependent case the following relation must be satisfied:
p(a|b) = p(a∩b)/p(b)
Or, in terms of this problem:
p(like peas|male) = p(like peas∩male)/p(male)
The probabilities of this events are:
p(like peas|male) = 42/100 = 42%
p(like peas∩male) = 42/200 = 21%
p(male) = 100/200 = 50%
Therefore, the events are dependent
In the Independent case the following relation must be satisfied:
p(a|b) = p(a)
or
p(like peas|male) = p(like peas)
p(like peas) = 78/200 = 39%
The equation is not satisfied.
When two equal forces are inclined at an angle 2a their resultant is twice as great as
when they are inclined at an angle 2B. Show that cosa = 2 cosß.
Step-by-step answer:
Referring to the attached diagram, the resultant of two forces each with magnitude F and inclined to each other at 2a equals
Ra = 2Fcos(a) ..............................(1)
Similarly, the resultant of two forces each with magnitude F and inclined to each other at 2b equals
Rb = 2Fcos(b)..............................(2)
We are given that
Ra = 2Rb ....................................(3)
Substitute (1) & (2) in (3) gives
2Fcos(a) = 2(2Fcos(b))
Expand
2Fcos(a) = 4Fcos(b)
Simplify
cos(a) = 2 cos(b) QED
Note: Please note that you might have a faster response if you posted this question in the physics or the (new) Engineering section.
Have a nice day!
The first two terms in a geometric series are 20, 22. To two decimal places, the sum of the first k terms of the series is 271.59. Find k.
Answer:
k=9
Step-by-step explanation:
First find r=22/20=1.1
The sum of the first k terms formula is a1•(1-r^k)/(1-r)
a1=20 and the sum is 271.59
Now plug in these values in the formula and find k.
271.59=20(1-1.1^k)/(1-1.1)
When you simplify this equation, you will get k=ln(2.358)/ln(1.1)
k=9
#2 and please provide explaination !
Answer:
Total overripe fruit = 48
Step-by-step explanation:
Step 1: Assume the value of oranges
Let oranges be x
Oranges = x
Apples = 32 + x
Overripe oranges = 3/5 of oranges
= 3x/5
Overripe apples = 1/3 of apples
= 1/3 (32 + x)
Step 2: Find x (oranges)
Number of overripe apples and number or overripe oranges are equal.
3x/5 = 1/3 (32 + x)
3 (3x) = 5(32 + x)
9x = 160 + 5x
4x = 160
x = 40
Step 3: Find the total number of overripe fruit.
Total overripe fruit = Overripe apples + Overripe oranges
Total overripe fruit = 1/3 (32 + x) + 3x/5
Total overripe fruit = 1/3 (32 + 40) + 3(40)/5
Total overripe fruit = 24 + 24
Total overripe fruit = 48
!!
Find the volume of the composite solid
Answer:
[tex]\large\boxed{V=(157.5+27.648\pi)\ yd^3}[/tex]
Step-by-step explanation:
We have the rectangular prism and the cone.
The formula of a volume of
1) a rectangular prism
[tex]V=lwh[/tex]
l - length
w - width
h - height
2) a cone
[tex]V=\dfrac{1}{3}\pi r^2H[/tex]
r - radius
H - height
We have:
1)
l = 7yd, w = 5yd, h = 4.5yd
Substitute:
[tex]V_R=(7)(5)(4.5)=157.5\ yd^3[/tex]
2)
r = 4.8yd, l = 6yd
l - slant height
Use the Pythagorean theorem to calculate H :
[tex]H^2+r^2=l^2[/tex]
Substitute:
[tex]H^2+4.8^2=6^2[/tex]
[tex]H^2+23.04=36[/tex] subtract 23.04 from both sides
[tex]H^2=12.96\to H=\sqrt{12.96}\\\\H=3.6\ yd[/tex]
Calculate the volume:
[tex]V_C=\dfrac{1}{3}\pi(4.8)^2(3.6)=\dfrac{82.944}{3}\pi=27.648\pi\ yd^3[/tex]
The volume of the composite solid:
[tex]V=V_R+V_C[/tex]
Substitute:
[tex]V=(157.5+27.648\pi)\ yd^3[/tex]
What is the simplified form of the expression?
Answer:
7c^2d-7c+4d-10
Step-by-step explanation:
Start off with the term that has c^2 in it. 5c^2d + 2C = 7c^2d, then since you have multiple choice, the d value differs between the two answer choices that have 7c^2d so you can do +3d +d to get +4d to get the fourth answer choice.
To check your work, you can add/subtract each term to see if you get 7c^2d-7c+4d-10
17:44
What is the common ratio of the sequence?
-2, 6, -18,54
OOOO
Mark this and retum
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Answer:
The common ratio is -3
Step-by-step explanation:
we know that
In a Geometric Sequence each term is found by multiplying the previous term by a constant called the common ratio
In this problem we have
-2,6,-18,54...
Let
a1=-2, a2=6,a3=-18,a4=54
a2/a1=6/-2=-3
a3/a2=-18/6=-3
a4/a3=54/-18=-3
Each term (except the first term) is found by multiplying the previous term by -3
therefore
we have a geometric sequence and the common ratio is -3
The height of a particular triangle equals its base length. A new triangle is formed by dividing the hype by 2 and its area is 36 in^2 less than the area of the triangle. what are the height and base lengths of original triangle?
Answer:
Height and base are both 12 in
Step-by-step explanation:
Formula area triangle: area = (height * base) /2
Since for the first triangle height and base are the same we will call is x.
The area for the first triangle is
area = (x^2) /2 = 0.5x^2
The new triangle area is
first triangle - 36 = ((x/2) * x)/2
0,5x^2 - 36 = (0,5x * x)/2
0,5x^2 - 36 = (0,5x^2)/2
0,5x^2 - 36 = 0,25x^2
0,25x^2 = 36
x^2 = 144
X = square root (144) = 12 in
Find m DEF
A. 30
B. 60
C. 90
D.120
The little red lines on each side of the triangle mean that the sides are all equal.
A triangle that has all 3 sides the same is an equilateral triangle.
Because all the sides are identical all 3 inside angles are also identical.
180 / 3 = 60 degrees
The outside angle which is DEF would equal 180 - the inside angle.
DEF = 180 - 60 = 120.
The answer is D.
Answer:
120°
Step-by-step explanation:
It is an equilateral triangle, so all its sides and internal angles measure the same.
The sum of the internal angles of a triangle must be 180°, so each internal angle measures 60°.
The DEF angle is an external angle of that triangle, we can use the next property:
An external angle of a triangle is the sum of the internal angles opposed to it.
The two opposite angles to DEF are DCE and CDE:
DEF = DCE + CDE = 60 ° + 60 ° = 120°
Another way to find this same result is to notice that DEF + DEC total 180° since they form a straight line, and we know that DEC measures 60°
So:
DEF + DEC = 180 °
DEF = 180 ° - DEC
DEF = 180 ° -60 °
DEF = 120 °
What is the solution set of this system of equations?
y=x2-3x-4
x=y+8
A {(-1.0), (4.0)}
B. {(8.0). (0.8)}
c. {(0.0)}
D. {(2. -6)
E
There is no real solution.
Reset
Next
Answer:
No real solutions.
Step-by-step explanation:
[tex]y=x^2-3x-4[/tex]
[tex]x=y+8[/tex]
I'm going to subtract the second expression for y and plug it into the first equation.
So solving x=y+8 for y by subtracting 8 on both sides gives us y=x-8.
I'm going to insert this for the first y like so:
[tex]x-8=x^2-3x-4[/tex]
Now I'm going to move everything to one side.
I'm going to subtract x on both sides and add 8 on both sides.
[tex]0=x^2-3x-x-4+8[/tex]
Simplifying:
[tex]0=x^2-3x+4[/tex]
Now our job since the coefficient of x^2 is 1 is to find two numbers that multiply to be 4 and at the same time add up to be -3. I can't think of any such numbers.
Let's check the discriminant.
Compare [tex]x^2-3x+4[/tex] to [tex]ax^2+bx+c[/tex].
So [tex]a=1,b=-3,c=4[/tex].
The discriminant is [tex]b^2-4ac[/tex].
So plugging in our numbers we get [tex](-3)^2-4(1)(4)[/tex].
Time to simplify:
[tex](-3)^2-4(1)(4)[/tex]
[tex]9-16[/tex]
[tex]-7[/tex]
So since the discriminant is negative, then the solutions will not be real.
In △ABC,a=14, b=17, and c=22. Find m∠A
Answer:
m∠A = 39.5°
Step-by-step explanation:
* Lets revise how to find the measure of an angle by using the cosine rule
- In any triangle ABC
# ∠A is opposite to side a
# ∠B is opposite to side b
# ∠C is opposite to side c
- The cosine rule is:
# a² = b² + c² - 2bc × cos(A)
# b² = a² + c² - 2ac × cos(B)
# c² = a² + b² - 2ab × cos(C)
- To find the angles use this rule
# m∠A = [tex]cos^{-1}\frac{b^{2}+c^{2}-a^{2}}{2bc}[/tex]
# m∠B = [tex]cos^{-1}\frac{a^{2}+c^{2}-b^{2}}{2ac}[/tex]
# m∠C = [tex]cos^{-1}\frac{a^{2}+b^{2}-c^{2}}{2ab}[/tex]
* Lets solve the problem
∵ a = 14 , b = 17 , c = 22
∵ m∠A = [tex]cos^{-1}\frac{b^{2}+c^{2}-a^{2}}{2bc}[/tex]
∴ m∠A = [tex]cos^{-1}\frac{17^{2}+22^{2}-14^{2}}{2(17)(22)}[/tex]
∴ m∠A = [tex]cos^{-1}\frac{289+484-196}{748}[/tex]
∴ m∠A = [tex]cos^{-1}\frac{577}{748}[/tex]
∴ m∠A = 39.5°
Answer:
∠A = 39.52°
Step-by-step explanation:
In Δ ABC,
a = 14, b = 17 and c = 22 then we have to find the measure of ∠A.
Since a² = b² + c² - 2.b.c.cosA [ From cosine law]
(14)² = (17)²+ (22)² - 2(17)(22)cosA
196 = 289 + 484 - (748)cosA
196 = 773 - (748)cosA
748(cosA) = 773 - 196 = 577
cosA = [tex]\frac{577}{748}=0.7714[/tex]
A = [tex]cos^{-1}(0.7714)[/tex]
A = 39.52°
to the nearest hundreth, what is the area of a circle with a radius of 5 units?
it's d, since the area of a circle is radius squared times pi
3.14×5^2= 78.4
What is the equation of the following line? Be sure to scroll down to see all the answers
Answer:
y = 6x
Step-by-step explanation:
Find slope
Formula
y2 - y1/x2 - x10 - (-3) = 3
0 - (-1/2) = 1/2
Simplify
3/(1/2) = 6
y = 6x
y-intercept
The line crosses the origin, so the y-intercept is 0.
Answer
y = 6x
What was Weston’s error?
In Step 2, the second fraction should have been out of a multiple of 40.
In Step 2, the multiplication relationship shown should have been division.
In Step 4, the decimal should not have been moved.
In Step 4, the decimal should have been moved two places instead of one.
Check the picture below.
Answer:
[tex]\frac{2.5}{100}=0.025\:or\:2.5\%[/tex]
Step-by-step explanation:
In step 4.
Weston made a mistake when he divided 2.5 by 100. He wrote it as he had multiplied 2.5 by 10 instead of moving the point back two decimals places to the left.
In the Step 4:
[tex]\frac{2.5}{100}= 0.025\:or\:2.5\:\%[/tex]
This can be verified by dividing 1 over 40, that'll give us 0.025
Jay and Hanna are selling programs at a Mariners game. Hanna sells 5 times more programs
than Jay does. The difference in sales between them is 204. How many programs did each
sell?
Answer:
51 and 255
Step-by-step explanation:
Let the number of programs sold by Jay be x.
Then programs sold by Hanna is 5x.
Also, the difference between them is 204.
5x - x =204
4x = 204
x = 204/4
x = 51
Therefore, Jay sold 51 programs and Hanna sold 5 x 51 = 255 programs.
Please mark Brainliest if this helps!
Jay sold 51 programs and Hanna sold 255 programs.
To determine how many programs Jay and Hanna sold, let's start by defining some variables.
Let [tex]J[/tex] be the number of programs Jay sold.
Since Hanna sells 5 times more programs than Jay, we can express her sales as [tex]5J[/tex].
We know the difference in their sales is 204 programs.
Therefore, we can write the equation:
[tex]5J - J = 204[/tex]
Simplify the equation:
[tex]4J = 204[/tex]
Next, solve for [tex]J[/tex] by dividing both sides by 4:
[tex]J = \frac{204}{4}[/tex]
[tex]J = 51[/tex]
So, Jay sold 51 programs.
Since Hanna sells 5 times more programs than Jay, we can calculate Hanna's sales as:
[tex]5 \times 51 = 255[/tex]
Find the lateral area of each prism. Round to the nearest tenth if necessary.
The dimension labeled 11 is the height of the prism.
Question 4 options:
334 units2
264 units2
299 units2
312 units2
Answer:
264 unit^2.
Step-by-step explanation:
The lateral area is the sum of the 2 sides of area 5*11 and the 2 sides of area 7^11.
That would be 2 * 5 * 11 + 2*7*11
= 264 unit^2.
For this case we have that by definition, the lateral area of a prism is given by:
[tex]LA = 2ac + 2bc[/tex]
Where:
a: It is the height
b: It is the width
c: It's the long
According to the figure we have:
[tex]a = 5 \ units\\b = 7 \ units\\c = 11 \ units[/tex]
Substituting:
[tex]LA = 2 * 5 * 11 + 2 * 7 * 11\\LA = 110 + 154\\LA = 264[/tex]
Finally, the lateral area of the prism is [tex]264 \ units ^ 2[/tex]
ANswer:
Option B
what’s the equation of the line with the given properties passes through (-4,-2) and (-4,5)
Answer:
x = -4
Step-by-step explanation:
Notice that the two points given, share the same x-value even when the y-value changes. This is because the equation is going to be a vertical line at -4 on the x-axis. Being a vertical line, you cannot take its slope using the slope formula of: m = (y2 - y1) / (x2 - x1) because the denominator will result in a 0 and you cannot divide by 0 in mathematics.
HelP MeEe
A virus that initially infected four people is spreading at a rate of 15% each week. The following function represents the weekly spread of the virus: f(x) = 4(1.15)x. Rewrite the function to show how quickly the virus spreads each day and calculate this rate as a percentage.
f(x) = 4(1.15)7x; spreads at a rate of approximately 1.5% daily
f(x) = 4(1.02)7x; spreads at a rate of approximately 2% daily
f(x) = 4(1.157)x; spreads at a rate of approximately 2.66% daily
f(x) = 4(1.02)x; spreads at a rate of approximately 0.2% daily
Answer:
f(x) = 4(1.02)^(7x); spreads at a rate of approximately 2% daily
Step-by-step explanation:
The weekly number of people infected is:
f(x) = 4(1.15)^x
So the daily number of people infected is:
f(x) = 4(1+r)^(7x)
To find the value of the daily rate r, we set this equal to the first equation.
4(1.15)^x = 4(1+r)^(7x)
(1.15)^x = (1+r)^(7x)
(1.15)^x = ((1+r)^7)^x
1.15 = (1+r)^7
1.02 = 1+r
r = 0.02
So the equation is f(x) = 4(1.02)^(7x), and the daily rate is approximately 2%.
Using exponential functions, it is found the daily function for the spread is:
[tex]f(x) = 4\left(\frac{1.15}{7}\rigth)^{x}[/tex], and it spreads at a rate of approximately 2% daily.
An exponential function has the following format:
[tex]y = ab^x[/tex]
In which:
a is the initial value.b is the rate of change.In this problem, the function for the weekly spread is:
[tex]f(x) = 4(1.15)^x[/tex]
A week has 7 days, thus, to find the daily spread, we divide the rate of change by 7, that is:
[tex]f(x) = 4\left(\frac{1.15}{7}\right)^x[/tex]
[tex]\frac{15}{7} \approx 2.1[/tex], thus, it spreads at a rate of approximately 2% daily.
A similar problem is given at https://brainly.com/question/23416643
given the function f(x) = 2^x, find the value of f−1(32). (1 point) f−1(32) = 0 f−1(32) = 1 f−1(32) = 5 f−1(32) = 16
Answer:
5
Step-by-step explanation:
The inverse of [tex]f(x)=2^x[/tex] is [tex]g(x)=\log_2(x)[/tex].
[tex]g(32)=\log_2(32)[/tex]
[tex]\log_2(32)=5[/tex] since [tex]2^5=32[/tex].
[tex]g(32)=\log_2(32)=5[/tex]
Note: In general, the inverse of [tex]f(x)=a^x[/tex] is [tex]g(x)=\log_a(x)[/tex].
Examine the equation: 4x = 2 − y Which equation represents the equivalent equation in slope-intercept form?
y = –4x + 2
y = –4x - 2
x = 2 - 4y
x = 8 - 4y
Answer:
[tex]y=-4x+2[/tex]
Step-by-step explanation:
Since, the slope intercept form of a line is,
[tex]y=mx+c[/tex]
Here, the given equation is,
[tex]4x=2-y[/tex]
[tex]4x+y=2[/tex] ( Additive property of equality )
[tex]y=-4x+2[/tex] ( Subtraction property of equality )
Hence, the equation that represents the equivalent equation of the given equation in slope-intercept form is,
[tex]y=-4x+2[/tex]
First option is correct.
Answer:
Step-by-step explanation:
WILL GIVE BRAINLEIST PLEASE HURRY SUPER EASY. A fall candle gift set has 4 vanilla candles and 6 pumpkin spice candles. Use v to represent the cost of each vanilla candle and p to represent the cost of each pumpkin candle. Write and simplify and expression that represents the total cost of 4 sets.
Answer:
total cost= 16v+24p
Step-by-step explanation:
One set 4v+6p
Multiply the. expression by 4 because we are buying 4 sets
4v+6p
*4. *4
16v+24p
Answer:
(4v + 6p)4 = n
Step-by-step explanation:
If 1 set is
4v + 6p,
Then multiply it by 4 to get the total cost of 4 sets. Since there is so price for 1 set, we could use n for the missing total cost.
Please answer this correctly
Answer:
1) 0.0008306
2) 0.00008306
3) 0.000008306
4) 0.0000008306
Step-by-step explanation:
Please mark me the brainliest... . I am sure the answers are correct.
Answer:
0.0008306
0.00008306
0.000008306
0.0000008306
Step-by-step explanation:
0.008306 ÷ 10 = 0.0008306
0.008306 ÷ 100 = 0.00008306
0.008306 ÷ 1000 = 0.000008306
0.008306 ÷ 10000 = 0.0000008306
The quadratic equation x2 + 2x -- 8 = 0 can be rewritten as (x + 4)(x - 2) = 0.
What is the multiplicity of the root x = --4?
Answer:
multiplicity of 1
Step-by-step explanation:
Given the roots of an equation are
x = - 4 ← multiplicity 1
(x + 4)² = 0
x + 4 = 0 or x + 4 = 0 , hence
x = - 4 or x = - 4 , that is
x = - 4 ← with multiplicity 2
(x + 4)³ = 0
has roots x = - 4 with multiplicity 3
The multiplicity is determined by the exponent the factor is raised to
Rosalie takes the bus everyday to school. The ride is 8 minutes long. If she goes to school for 176 days, how many minutes does she spend on the school bus?
Answer:
1408 min.
Step-by-step explanation:
8 × 176 = 1408.
Answer:
1408
Step-by-step explanation:
Human body temperatures are normally distributed with a mean of 98.20°F and a standard deviation of 0.62°F. If 19 people are randomly selected, find the probability that their mean body temperature will be less than 98.50°F.
0.0833
0.4826
0.3343
0.9826
Final Answer:
The probability that the mean body temperature of a sample of 19 people will be less than 98.50°F is approximately 0.9826.
Explanation:
To find the probability that the mean body temperature of a sample of 19 people will be less than 98.50°F, we can use the Central Limit Theorem, which states that the sampling distribution of the sample mean will be normally distributed if the sample size is sufficiently large. In this case, we can assume a sample size of 19 is large enough.
Given:
- Population mean (μ) = 98.20°F
- Population standard deviation (σ) = 0.62°F
- Sample size (n) = 19
- Target sample mean (X) = 98.50°F
We need to do the following steps:
1. Calculate the standard error of the mean (SEM), which is the standard deviation of the sampling distribution of the sample mean.
SEM = σ / √n
2. Calculate the Z-score for the sample mean of 98.50°F. The Z-score represents how many standard errors the value is away from the population mean.
Z = (X - μ) / SEM
3. Use the Z-score to find the area to the left of it on the standard normal distribution, which represents the probability that the sample mean is less than 98.50°F.
Let's calculate each step:
1. Calculate SEM:
SEM = σ / √n
= 0.62 / √19
≈ 0.62 / 4.3589
≈ 0.1422
2. Calculate Z-score:
Z = (X - μ) / SEM
= (98.50 - 98.20) / 0.1422
≈ 0.30 / 0.1422
≈ 2.1095
3. Lastly, to find the probability that the sample mean is less than 98.50°F, we look up the Z-score in the standard normal distribution table (Z-table), use statistical software, or a calculator that provides the cumulative distribution function (CDF) for the normal distribution.
A Z-score of 2.1095 corresponds to a probability of about 0.9826 (using Z-table or a calculator).
Therefore, the probability that the mean body temperature of a sample of 19 people will be less than 98.50°F is approximately 0.9826.
Among the options given, the closest to 0.9826 is 0.9826 itself. Hence, that is the correct answer.
Find the value of the expression. m(m + p) for m = 3 and p = 4
HELP PLEASE!
[tex]21[/tex]
Explanation:Substitute in the values. [tex]3(3+4)[/tex]Distribute. [tex]3*3\ +\ 3*4[/tex]Simplify with multiplication. [tex]9+12[/tex]Simplify with addition. [tex]21[/tex]The graph of which equation has a slope of 4?
(1) y = 4x -3 (3) y = -4x + 3
(2) y = 3x - 4 (4) y=-3x + 4
Please help :( I don’t get it
Answer:
(1)
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
We are looking for an equation of the form
y = 4x ± c ( since slope m = 4)
The only equation which fits the description is
y = 4x - 3 → (1)
The data set below has 7 values. Find the mean absolute deviation for the data set. If necessary, round your answer to the nearest hundredth. 12, 17, 16, 9, 18, 10, 9
Final answer:
To find the mean absolute deviation (MAD) for the data set, calculate the mean, subtract it from each data value to find deviations, take the absolute values, and then find their mean. The MAD for the data set 12, 17, 16, 9, 18, 10, 9 is approximately 3.43.
Explanation:
To find the mean absolute deviation (MAD) for a given data set, we follow these steps:
Calculate the mean (average) of the data set.
Subtract the mean from each data value to find the deviations.
Take the absolute value of each deviation.
Find the average of these absolute values to determine the MAD.
The data set provided is: 12, 17, 16, 9, 18, 10, 9. First, let's calculate the mean:
(12 + 17 + 16 + 9 + 18 + 10 + 9) / 7 = 91 / 7 = 13
Next, we'll find the absolute deviations from the mean:
|12 - 13| = 1
|17 - 13| = 4
|16 - 13| = 3
|9 - 13| = 4
|18 - 13| = 5
|10 - 13| = 3
|9 - 13| = 4
Lastly, we calculate the mean of these absolute values:
(1 + 4 + 3 + 4 + 5 + 3 + 4) / 7 = 24 / 7 ≈ 3.43
The mean absolute deviation of the data set is approximately 3.43.
Final answer:
The mean absolute deviation of the data set is calculated by finding the mean, determining the absolute deviation of each value from the mean, and then taking the mean of those deviations. For this set, the mean absolute deviation is 3.43.
Explanation:
To find the mean absolute deviation, we follow these steps:
First, we calculate the mean of the data set: (12 + 17 + 16 + 9 + 18 + 10 + 9) ÷ 7 = 91 ÷ 7 = 13.
Next, we find the absolute deviation of each data point from the mean:
Add these absolute deviations: 1 + 4 + 3 + 4 + 5 + 3 + 4 = 24.
Finally, we find the mean of these absolute deviations: 24 ÷ 7 = 3.43 (rounded to the nearest hundredth).
The mean absolute deviation for the data set is 3.43.
Let A = {1, 2, 3, 4, 5} and B = {2, 4}. What is A ∩ B?
[tex]A\cap B=\{x:x\in A \wedge x\in B\}[/tex]
[tex]A\cap B=\{2,4\}[/tex]
For this case we have the following sets:
A = {1,2,3,4,5}
B = {2,4}
We must find the intersection of both sets, the symbol ∩ denotes intersection. That is, the numbers in common of both.
We have to:
A∩B = {2,4}
Answer:
The insterseccion of both sets is:
A∩B = {2,4}
Suppose BCA is congruent to EDA. Using only the information provided in this problem, can you use the
SSS Postulate or the SAS Postulate to prove triangle ABC is congruent to triangle AED?
Answer:
A. By SAS only
Step-by-step explanation:
Side Side Side postulate (SSS) states that if three sides of one triangle are congruent to three sides of another triangle, then these two triangles are congruent.
Side Angle Side postulate (SAS) states that if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then these two triangles are congruent.
In triangles ABC and AED:
sides ACand AD are congruent (from the diagram);angles BCA and EDA are congruent (given);sides BC and ED are congruent (from the diagram).So, SAS postulate can be applied.
SSS postulate cannot be applied, because it is not given that sides AB and AE are conruent.
Answer:
ΔABC and ΔAED are congruent to each other by SAS rule.
Step-by-step explanation:
We are given a figure in the question.
The figure shows that:
AC = AD, BC = ED, ∠BAC = ∠EAD
We are also given that triangle BCA is congruent to triangle EDA.
Now, we need to prove that triangle ABC is congruent to triangle AED.
We will use SAS criterion of congruence.
In ΔABC and ΔAED,
AC = AD, ∠BAC = ∠EAD, , BC = ED( all given in the figure)
Hence, the two triangles are congruent to each other by SAS rule.