The mean absolute deviation (MAD) is a statistical measure of how much the different data points "move away" from the mean of the data set. In this case the weights of the bears have been given, the mean has been calculated and the MAD is derived by deducting each data point from the mean. The MAD has been given already by the way. Some data points fall below the mean while some are above it. but whatever the difference is, you'll have to take the "absolute value" that is positive value only. For example, the mean weight of the black bears is 299, and the weight of the first black bear is 102, that gives you adifference of 197. note that the result should be negative 197 (-197) but we are interested in the absolute values only.
Same way you find the absolute deviation for the other data points and you have, 197, 148, 51, 43, 154, and 199. Sum up these numbers and divide by the number of observed data (number of black bears) and you have 792 divided by 6 which gives you 132. This means the mean absolute deviation of the observed data is 132 as compared to the mean which is 299.
If you compare the MAD of the black bears with that of the grizzly bears, you would see that the MAD of the grizzly bears is more varied, because 104 2/3 moves further away from 419 than the MAD of the black bears which is 132 moving away from 299.
solve by factoring, by square roots, by completing the square, or using the quadratic formulaSolve for x in the equation belowX^2 −15x+54=0
STEP 1: Identify and Set up.
We have a quadratic equation and are asked to solve, i.e, solve for x. We approach this problem via the factoring method.
We look for two factors of the third term, c that add up to the coefficient of x, favtorise and solve.
STEP 2: Execute
[tex]\begin{gathered} x^2-15x+54=0 \\ \text{the factors are -6 and -9} \\ x^2-9x-6x+54=0 \\ Factorizing\text{ gives us:} \\ x(x-9)-6(x-9)=0 \\ (x-9)(x-6)=0 \\ x\text{ is either 9 or 6} \end{gathered}[/tex]x = 9 and x = 6
QuestionLet x be a constant. The 5th term of an arithmetic sequence is a5=4x−3. The 9th term of the sequence is a9=12x+9. Find the first term of the sequence. Write your answer in simplest form.
The nth term of an arithmetic sequence is :
[tex]a_n=a_1+d(n-1)[/tex]From the problem, we have :
[tex]\begin{gathered} a_5=4x-3 \\ a_9=12x+9 \end{gathered}[/tex]Substitute a5 and n = 5 :
[tex]\begin{gathered} a_n=a_1+d(n-1) \\ a_5=a_1+d(5-1) \\ 4x-3=a_1+4d \end{gathered}[/tex]Rewrite the equation as d in terms of x and a1 :
[tex]\begin{gathered} 4x-3=a_1+4d \\ 4x-3-a_1=4d \\ d=\frac{4x-3-a_1}{4} \end{gathered}[/tex]Subsitute a9 and n = 9
[tex]\begin{gathered} a_n=a_1+d(n-1) \\ a_9=a_1+d(9-1) \\ 12x+9=a_1+8d \end{gathered}[/tex]Rewrite the equation as d in terms of x and a1 :
[tex]\begin{gathered} 12x+9=a_1+8d \\ 12x+9-a_1=8d \\ d=\frac{12x+9-a_1}{8} \end{gathered}[/tex]Now, equate two equations of d :
[tex]\begin{gathered} \frac{4x-3-a_1}{4}=\frac{12x+9-a_1}{8} \\ 8(4x-3-a_1)=4(12x+9-a_1) \\ 32x-24-8a_1=48x+36-4a_1 \\ 4a_1-8a_1=48x+36-32x+24 \\ -4a_1=16x+60 \\ a_1=-4x-15 \end{gathered}[/tex]The answer is a1 = -4x-15
If the 5th term of an arithmetic sequence is a5=4x−3. The 9th term of the sequence is a9=12x+9. The first term of the sequence is -4x-15
What is Sequence?a sequence is an enumerated collection of objects in which repetitions are allowed and order matters.
The nth term of AP
aₙ=a+(n-1)d..(1)
From give we have,
a₅=4x−3
a₉=12x+9.
Substitute n=5 in (1)
a₅=a+4d
4x-3=a+4d
4d=4x-3-a
d=4x-3-a/4...(2)
Substitute n=9 in (1)
a₉=a+8d
12x+9=a+8d
12x+9-a/8=d..(3)
Equate 2 and 3
4x-3-a/4=12x+9-a/8
8(4x-3-a)=4(12x+9-a)
32x-24-8a=48x+36-4a
32x-24-8a-48x-36+4a=0
-16x-4a-60
-16x-60=4a
a=-4x-15
Hence the first term of the AP sequence is -4x-15
To learn more on Sequence click:
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need HELPPPPPPP with
let x be the number that we pick. So the final answer and the pattern is:
[tex]\frac{2(x+4)-6}{2}=(x+4)-3=x+1[/tex]so the pattern is that we get the x+1 if we choose x. so the pattern is to add 1 to the initial number
Would lines 4x+3y=52 and 3x-4y=44 be perpendicular parallel or neither? I just need a brief explanation with the answer
Would lines 4x+3y=52 and 3x-4y=44 be perpendicular parallel or neither?
step 1
Find out the slopes of the given lines
4x+3y=52
isolate the variable y
3y=-4x+52
y=-(4/3)x+52/3 ------> m=-4/3
3x-4y=44
4y=3x-44
y=(3/4)x-44/4 ------> m=3/4
step 2
Compare their slopes
m=-4/3 and m=3/4
the slopes are opposite reciprocal
that means
the lines are perpendicular1.question The preimage was(-3, 4) and after the rotation the image was (3, -4). What many degrees counterclockwise did the point rotate?a) 90b) 270c) none aboved) 1802. question
Answer:
Question 1
d) 180
Question 2:
b T <8, 14>
Explanation:
Here is a graph of the two points.
As can be seen, the two points are on the opposite sides of teacher other, meaning the point (-3,4) has to rotate 180 degrees to get to (3, -4) and vice versa.
Question 2
The coordinates of A and B are
A = (5, 6)
B = (-3, -8 )
If we want to go from B to A, we need to add 8 to the x-coordinate and 14 to the y-coordinate.
Therefore, the translation
[tex]B\rightarrow A\text{ is T<8,14>}[/tex]
upper menu options: 1 3 7 8left menu options: 10 11 12 15
In order to find the amount of blue paint needed, we can write the following rule of three:
[tex]\begin{gathered} \text{green}\to\text{blue} \\ 1\text{ batch}\to2\frac{3}{8}\text{ oz} \\ 5\text{ batches}\to x\text{ oz} \end{gathered}[/tex]First, let's convert the mixed number into an improper fraction:
[tex]2\frac{3}{8}=2+\frac{3}{8}=\frac{16}{8}+\frac{3}{8}=\frac{19}{8}[/tex]From this rule of three, we can write the following equation and solve it for x:
[tex]\begin{gathered} \frac{1}{5}=\frac{\frac{19}{8}}{x} \\ x\cdot1=5\cdot\frac{19}{8} \\ x=\frac{95}{8} \\ x=\frac{88}{8}+\frac{7}{8} \\ x=11+\frac{7}{8} \\ x=11\frac{7}{8} \end{gathered}[/tex]Therefore the upper menu is 7 and the left menu is 11.
Bradley rolls two fair 6-sided dice with faces numbered 1 through 6. What is the probability that the sum of her two rolls has an odd number of factors?
Answer:
The probability that the sum of her two rolls has an odd number of factors will be;
[tex]P=\frac{7}{36}[/tex]Explanation:
We want to find the probability that the sum of her two rolls has an odd number of factors.
For the two rolls the total number of possible outcomes is;
[tex]6\times6=36[/tex]Let us list out the possible outcomes of the two rolls;
[tex]\begin{gathered} (\text{outcome)= sum= number of factors of the sum} \\ \mleft(1,1\mright)=2=2\text{ factors} \\ (1,2)=3=2\text{ factors} \\ (1,3)=4=3\text{ factors} \\ (1,4)=5=2\text{ factors} \\ (1,5)=6=4\text{ factors} \\ (1,6)=7=2\text{ factors} \\ \end{gathered}[/tex][tex]\begin{gathered} (2,1)=3=2\text{ factors} \\ (2,2)=4=3\text{ factors} \\ (2,3)=5=2\text{ factors} \\ (2,4)=6=4\text{ factors} \\ (2,5)=7=2\text{ factors} \\ (2,6)=8=4\text{ factors} \end{gathered}[/tex][tex]\begin{gathered} (3,1)=4=3\text{ factors} \\ (3,2)=5=2\text{ factors} \\ (3,3)=6=4\text{ factors} \\ (3,4)=7=2\text{ factors} \\ (3,5)=8=4\text{ factors} \\ (3,6)=9=3\text{ factors} \end{gathered}[/tex][tex]\begin{gathered} (4,1)=5=2\text{ factors} \\ (4,2)=6=4\text{ factors} \\ (4,3)=7=2\text{ factors} \\ (4,4)=8=4\text{ factors} \\ (4,5)=9=3\text{ factors} \\ (4,6)=10=4\text{ factors} \\ \end{gathered}[/tex][tex]\begin{gathered} (5,1)=6=4\text{ factors} \\ (5,2)=7=2\text{ factors} \\ (5,3)=8=4\text{ factors} \\ (5,4)=9=3\text{ factors} \\ (5,5)=10=4\text{ factors} \\ (5,6)=11=2\text{ factors} \end{gathered}[/tex][tex]\begin{gathered} (6,1)=7=2\text{ factors} \\ (6,2)=8=4\text{ factors} \\ (6,3)=9=3\text{ factors} \\ (6,4)=10=4\text{ factors} \\ (6,5)=11=2\text{ factors} \\ (6,6)=12=6\text{ factors} \end{gathered}[/tex]From the listed possible outcomes, the number of oucomes with odd number of factors of the sum is;
[tex]n_A=7[/tex]Total number of possibles outcomes is;
[tex]n_T=36[/tex]The probability that the sum of her two rolls has an odd number of factors will be;
[tex]\begin{gathered} P=\frac{n_A}{n_T}=\frac{7}{36} \\ P=\frac{7}{36} \end{gathered}[/tex]True or False Then need explanation in one paragraph or word
1) True
2) False
3) True
4) False
5) False
Explanations:Domains are indepedent variables for which a function exists while the range are dependent variables for which a function exist.
Foa a given coordinates (x, y), all the sets of first coordinates are the domain while all the sets of second coordinates are the range;
All functions are also known as relations but not all given relations are function.
Based on the explanations above, then;
1) A relation is a set of ordered pairs is TRUE
2) The set of all the first coordinates is called is range is FALSE
3) All functions are relations is TRUE
4) The set of all the second coordinates is called is domain is FALSE
5) All relations are function is FALSE
Express (5/6x + 4) 2 as trinomial in simplest form (2 is an exponent)
We are given the expression (5/6x + 4)^2 and we are asked to express it as a trinomial in the simplest form.
To do this, we will be using the FOIL method. FOIL stands for First-Outer-Inner-Last.
The product will then be:
[tex]\begin{gathered} (\frac{5}{6}x+4)^2=(\frac{5}{6}x+4)(\frac{5}{6}x+4) \\ \\ (\frac{5}{6}x+4)^2=(\frac{5}{6}x)^2+(\frac{5}{6}x)(4)+(4)(\frac{5}{6}x)+4(4) \\ \\ (\frac{5}{6}x+4)^2=\frac{25}{36}x^2+\frac{10}{3}x+\frac{10}{3}x+16 \\ \\ (\frac{5}{6}x+4)^2=\frac{25}{36}x^2+\frac{20}{3}x+16 \end{gathered}[/tex]So, the final answer is 25/36 x^2 + 20/3 x + 16.
mason used a 30% coupon to buy a new computer. after the discount, the cost of the computer was $728. determine the original price of the computer . show your work . calculate how much money Mason saved by using the coupon . show your work .
Let's call x to the original price.
Given that Mason used a 30% coupon, then he paid 0.3x dollars less.
After the discount, the cost of the computer was $728, then
x - 0.3x = 728
0.7x = 728
x = 728/0.7
x = 1040
The original price of the computer was $1040
Mason saves 30% of $1040, which is computed as follows:
[tex]1040\cdot\frac{30}{100}=312[/tex]Mason saves $312
What is the Center and radius of x2+67+y2=8y+20x
Let's rewrite the expression as:
[tex]\begin{gathered} x^2+67+y^2-8y-20x=0 \\ so\colon \\ (x-10)^2+(y-4)^2-49=0 \\ (x-10)^2+(y-4)^2=49 \end{gathered}[/tex]Which is the standard equation of a circle:
[tex](x-h)^2+(y-k)^2=r^2[/tex]Where (h,k) is the coordinates of center of the circle and r is the radius
Therefore, the center is:
[tex]\begin{gathered} (h,k)=(10,4) \\ \end{gathered}[/tex]And the radius is:
[tex]r=\sqrt[]{49}=7[/tex]find two expressions that are equivalent by the distributive property 42g+2142g+3. 7(6g+3) 7g+7select all that apply42g+217(6g+3)7g+742g+3
the expressions are
42g+21 and 7(6g+3)
because
[tex]\begin{gathered} 7(6g+3) \\ 7\times6g+7\times3 \\ 42g+21 \end{gathered}[/tex]the expressions are equivalents
Jack has $205 and he is spending $2 each day. Which algebraic expression describes this situation, where d represents the number of days?
M= 205 - 2d
1) We can write a mathematical sentence for that situation, considering Jack's initial amount of money: $205 and the fact that we don't know the number of days (d). But we do know that each day costs Jack $2, i.e. minus 2 dollars per day.
2) Therefore, we can write out the following:
[tex]M_{}=205-2d[/tex]Where M stands for Jack's money and "d" stands for the number of days.
3) Hence the answer is
M= 205 - 2d
I need help solving this problem any help is appreciated
If we want to solve this problem we first need to list a few properties of trigonometric functions:
[tex]\begin{gathered} \text{cot }\theta=\frac{\cos\theta}{\sin\theta} \\ \sin^2\theta+\cos^2\theta=1 \end{gathered}[/tex]We are told that cot(θ)=1/2. Using the first equation and this data we obtain the following:
[tex]\frac{1}{2}=\frac{\cos\theta}{\sin\theta}[/tex]We multiply both sides and we get an expression for the cosine of θ:
[tex]\begin{gathered} \frac{1}{2}\sin\theta=\frac{\cos\theta}{\sin\theta}\cdot\sin\theta \\ \cos\theta=\frac{1}{2}\sin\theta \end{gathered}[/tex]Now we are going to take the second property I wrote in the begining and replace the cosine of θ with this new expression that we found:
[tex]\begin{gathered} \sin^2\theta+\cos^2\theta=\sin^2\theta+(\frac{1}{2}\sin\theta)^2=1 \\ \sin^2\theta+\frac{1}{4}\sin^2\theta=1 \\ \frac{5}{4}\sin^2\theta=1 \end{gathered}[/tex]We must solve this equation for the sine of θ. We can multiply both sides by 4/5:
[tex]\begin{gathered} \frac{4}{5}\cdot\frac{5}{4}\sin^2\theta=1\cdot\frac{4}{5} \\ \sin^2\theta=\frac{4}{5} \end{gathered}[/tex]And we apply a square root to both sides:
[tex]\begin{gathered} \sqrt{\sin^2\theta}=\sqrt{\frac{4}{5}} \\ |\sin\theta|=\frac{2}{\sqrt{5}} \end{gathered}[/tex]We are told that θ is located in quadrant I which means that its sine is positive. Therefore we get:
[tex]\sin\theta=\frac{2}{\sqrt{5}}[/tex]AnswerThen the answer is 2/√5
find f such that the given conditions are satisfiedf’(x)=x-4, f(2)=-1
Given:
[tex]f^{\prime}\left(x\right)=x-4,\text{ and}f\left(2\right)=-1[/tex]To find:
The correct function.
Explanation:
Let us consider the function given in option D.
[tex]f(x)=\frac{x^2}{2}-4x+5[/tex]Differentiating with respect to x we get,
[tex]\begin{gathered} f^{\prime}(x)=\frac{2x}{2}-4 \\ f^{\prime}(x)=x-4 \end{gathered}[/tex]Substituting x = 2 in the function f(x), we get
[tex]\begin{gathered} f(2)=\frac{2^2}{2}-4(2)+5 \\ =2-8+5 \\ =-6+5 \\ f(2)=-1 \end{gathered}[/tex]Therefore, the given conditions are satisfied.
So, the function is,
[tex]f(x)=\frac{x^{2}}{2}-4x+5[/tex]Final answer: Option D
Rewrite the following equation y - 7 = -4(x + 1)
Express the difference in medians as a multiple of the IQR of EACH dataset.Class A.Class B440506070Height (inches)
From the given box plot, let's express the difference in the medians of the IQR of each data.
Given:
Median of class A = 56
Q1 of class A = 50
Q3 of class A = 58
Median of class B = 52
Q1 of class B = 48
Q3 of class B = 54
Thus, we have:
IQR for class A = Q3 - Q1 = 58 - 50 = 8
IQR for class B = Q3 - Q1 = 54 - 48 = 6
Diffrence in median = 56 - 52 = 4
Thus, to find the expression of the difference in medians as a multiple of IQR of each data, we have:
[tex]\begin{gathered} \text{Difference class A: 4 = 8}\ast n \\ \\ \text{Difference class B: 4 = 6 }\ast n \end{gathered}[/tex]Let's solve for each difference.
Difference class A:
[tex]n=\frac{4}{8}=\frac{1}{2}[/tex]Difference class B:
[tex]n=\frac{4}{6}=\frac{2}{3}[/tex]ANSWER:
[tex]\begin{gathered} \text{CLass A = }\frac{1}{2} \\ \\ \text{Class B = }\frac{2}{3} \end{gathered}[/tex]The original price of a pair ofjeans was $40. The price wasmarked down to $35. What is thepercent of decrease in the price?
SOLUTION
From the question, the original price of the jeans was $40, then the price was reduced to $35. Decrease in price becomes
[tex]40-35=5\text{ dollars }[/tex]Percent decrease becomes
[tex]\begin{gathered} =\frac{decrease\text{ in price}}{original\text{ price}}\times100 \\ =\frac{5}{40}\times100 \\ =\frac{1}{8}\times100 \\ =12.5 \end{gathered}[/tex]hence the answer is 12.5%
Spongebob was trying to fill up Gary's bath with water. He noticed the tub filled up 1 gallon per minute.AContinuousBDiscrete
given data:
Spongebob was trying to fill up Gary's bath with water. He noticed the tub filled up 1 gallon per minute.
to find what kind of data this is.
it is discrete because it is measurable. that is countiuse while countable.
Thus the answer is discrete.
Solve the system: y = 12 + 4x y = -33 - 5x
The equation system is:
[tex]\begin{gathered} y=12+4x \\ y=-33-5x \end{gathered}[/tex]So we can made the equation equal so:
[tex]\begin{gathered} 12+4x=-33-5x \\ 4x+5x=-33-12 \\ 9x=-45 \\ x=-\frac{45}{9} \\ x=-5 \end{gathered}[/tex]Now we can replace the value of x to find y in the first equation so:
[tex]\begin{gathered} y=12+4(-5) \\ y=12-20 \\ y=-8 \end{gathered}[/tex]so the solution is:
[tex](-5,-8)[/tex]Flora has an annual income of $18,500. She has $6,500 withheld asdeductions. What is the amount of each paycheck if she gets paidsemimonthly?a. $500b. $461.54c. $711.54d. $1,000
To calculate the amount of each semimonthly paycheck, we need to find the actual amount of money Flora actually receives annually.
Her income is $18500, but $6500 are deducted. Then:
[tex]18500-6500=12000[/tex]The actual money she receives in one year, after deductions, is $12000.
If she receives semimonthly paychecks, we need to bear in mind that in total she receives 24 paychecks in one year. This considering that semimonthly means that she receives two paychecks in a month.
Then, we just need to divide $12000 by 24 to obtain the amount of each paycheck:
[tex]\frac{12000}{24}=500[/tex]The amount of each paycheck is $500.
The correct answer is option a.
(3x-3)
[6(x - 10)] What is the value of x?
at work one day, erica recieved 18 packages. speed delivery delivered three times as many as ralphs express, while ralphs express delivered two more than send quick service. how many packages did each service deliver to erica
Answer:
Let the number of packages delivered by Ralph's Express be x.
The number of packages delivered by Speedee Delivery would then be 4x.
The number of packages delivered by Send Quick Package Service would be x-5.
Adding all of these together,
x + 4x + (x - 5) = 6x -5
6x - 5 = 55
6x = 60
x = 10
Hence,
Ralph's Express delivered 10 packages.
Speedee Delivery delivered 40 packages.
Send Quick Package Service delivered 5 packages. Hope this help's you
Step-by-step explanation:
What is the inverse operation for addition?additionsubtractiondivisionmultiplication
The inverse operation for addition is subtraction.
Hence, the answer is Subtraction.
8 and 7 are like terms true or false
8 and 7 are like terms, because they share the same power of x:
[tex]\begin{gathered} 8x^0\rightarrow8 \\ 7x^0\rightarrow7 \end{gathered}[/tex]which expression is equivalent to 7y + 7y?
Evaluate the value of expression.
[tex]7y+7y=14y[/tex]So answer is 14y.
the number of employees Forrester company of vindication each year by 4% of the company currently k670 employees and this rate continues from the number of employees in 16 years
The expression for number of employee after n year if population, P decreases at rate of r % is,
[tex]p=P(1-\frac{r}{100})^n[/tex]Substitute the values in the formula to determine the population after 16 years.
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The bag contains,
Red (R) marbles is 9, Green (G) marbles is 7 and Blue (B) marbles is 4,
Total marbles (possible outcome) is,
[tex]\text{Total marbles = (R) + (G) +(B) = 9 + 7 + 4 = 20 marbles}[/tex]Let P(R) represent the probablity of picking a red marble,
P(G) represent the probability of picking a green marble and,
P(B) represent the probability of picking a blue marble.
Probability , P, is,
[tex]\text{Prob, P =}\frac{required\text{ outcome}}{possible\text{ outcome}}[/tex][tex]\begin{gathered} P(R)=\frac{9}{20} \\ P(G)=\frac{7}{20} \\ P(B)=\frac{4}{20} \end{gathered}[/tex]Probablity of drawing a Red marble (R) and then a blue marble (B) without being replaced,
That means once a marble is drawn, the total marbles (possible outcome) reduces as well,
[tex]\begin{gathered} \text{Prob of a red marble P(R) =}\frac{9}{20} \\ \text{Prob of }a\text{ blue marble =}\frac{4}{19} \\ \text{After a marble is selected without replacement, marbles left is 19} \\ \text{Prob of red marble + prob of blue marble = P(R) + P(B) = }\frac{9}{20}+\frac{4}{19}=\frac{251}{380} \\ \text{Hence, the probability is }\frac{251}{380} \end{gathered}[/tex]Hence, the best option is G.
i gave away 10% of my summer job earnings. If i give away $256, how much did i earn over the summer?
ok
$256 --------------------------- 10%
x --------------------------100%
x = (100 x 256) / 10
x = 25600 / 10
x = $2560
I earned $2560 over the summer
11 Jamal has a sudden medical emergency, and although his doctors do not agree, he is sure that it was caused by an antibiotic he took to prepare for a tooth extraction. Jamal posts a picture of himself in the hospital on his social media with the hashtag #antibioticskill. Although hashtags can raise awareness of important issues, what might happen if Jamal’s post were to go viral? A. People could be influenced into groupthink and reject antibiotics without knowing the facts. B. People would be encouraged to research the side effects that antibiotics cause before accepting them. C. Jamal would be investigated for making unfounded claims about a product online. D. Jamal could cause people to be more willing to listen to their doctor’s advice.
Answer:
A.
Step-by-step explanation:
A. People could be influenced into groupthink and reject antibiotics without knowing the facts.