Answer:
The correct option is;
(Choice B) Both the mean and median will increase, but the mean will increase by more than the median.
Step-by-step explanation:
Here, we are expected to show the differences (advantages/properties) of the mean and median
Note that the definition of the mean is the sum of the value of all data points divided by the number of data points
Assuming the four accountants each earn $ 55,000.00
Therefore, initial mean before getting rd of the part-time accountant is
(55+ 55+ 55 + 55 + 10)/5 = 46
Final mean after the part-time accountant is gone =(55+ 55+ 55 + 55 )/4 = 55
Therefore the mean increases
However, the median is given by the middle value when the list of values are arranged in increasing order as
55, 55, 55, 55, 10
Therefore the initial median is 55
Final median after the part-time accountant is gone is
55, 55, 55, 55
Therefore, final = (55 + 55)/2 = 55
That is the median remains the same that is little or increase.
Therefore, since the range of values for the full time accountants salaries weigh less than the difference between the average full time salary and a single part time, both the mean and the median will increase but the mean will increase more than the median
Answer:
b
Step-by-step explanation:
The height of a trapezoid is 8 in. And its area is 64 in2. One base of the trapezoid is 6 inches longer than the other base. What are the lengths of the bases?
Answer:
5 and 11
Step-by-step explanation:
The area of a trapezoid is
A = 1/2 (b1+b2)*h
We know the height is 8 and the area is 64.
Let one of the bases is b and the other is b+6
64 = 1/2 (b+ b+6) *8
Combine like terms
64 = 4 (2b+6)
Divide each side by 4
64/4 = 4/4 *(2b+6)
16 = 2b+6
Subtract 6 from each side
16-6 = 2b+6-6
10 =2b
Divide each side by2
10/2 =2b/2
5=b
The second base is
5+6 =11
Grace had 4 3/8 yards of elastic. She used 1 2/3 yards of the elastic to make bracelets for her friends. How many yards of elastic does she have now?
A. 6 1/24
B. 3 7/24
C. 2 17/24
D. 3 17/24
Answer: D. 3 17/24
Step-by-step explanation:
4 3/8 - 1 2/3
Chef Selena is making her special dish that requires pasta, sauce, and onions. She has 5 1/8 pounds of pasta, 6 pounds of sauce, and 4 7/8 pounds of onions. How many servings of her dish can she make if each serving is 1/2 pound? Which two equations are needed to solve the problem?
Answer:
[tex]\text{Total Weight of Food Made}, x=5\frac{1}{8}+6+4\frac{7}{8}\\\text{Number of Servings}, y=x \div \frac{1}{2}[/tex]
Step-by-step explanation:
The Weight of Ingredients to be used by Chef Selena are:
[tex]5\frac{1}{8}[/tex] pounds of pasta, 6 pounds of sauce; and [tex]4\frac{7}{8}[/tex] pounds of onions.Total Weight of Food Made, x
[tex]=5\frac{1}{8}+6+4\frac{7}{8}\\=5+6+4+\frac{1}{8}+\frac{7}{8}\\=16 \: Pounds[/tex]
Since each serving is [tex]\frac{1}{2} Pounds[/tex]
Number of Servings of her dish, y
[tex]16 \div \frac{1}{2}\\ =32 \: Servings[/tex]
The two equations needed to solve the problem are therefore:
[tex]\text{Total Weight of Food Made}, x=5\frac{1}{8}+6+4\frac{7}{8}\\\text{Number of Servings}, y=x \div \frac{1}{2}[/tex]
Jose Has scored 28,24,26,27,and 21 Points in his five basketball game so far. How many points does he need to score in his next game so that his average mean is 25 points per game
Answer:
The correct answer is 24.
Step-by-step explanation:
Jose wants to have an average mean of 25 points per game in his 6 basket ball matches.
Total points Jose plans to achieve in 6 games is 25 × 6 = 150.
Points score by him in the first five matches are 28, 24, 26, 27 and 21.
Total points in 5 matches is 126.
Thus the points he need to score in his next game to have an average mean of 25 is given by 150 - 126 = 24.
Given that the measure of ∠x is 123°, and the measure of ∠y is 51°, find the measure of ∠z. °
Answer:
The measure of angle z is 59°.
Step-by-step explanation:
Final answer:
To find the measure of ∠z when ∠x = 123° and ∠y = 51°, add the angles and subtract the sum from 180°.
Explanation:
Given:
∠x = 123°
∠y = 51°
To find ∠z:
Add ∠x and ∠y: 123° + 51° = 174°
Since the sum of angles in a triangle is 180°, subtract the sum of ∠x and ∠y from 180° to find ∠z: 180° - 174° = 6°
Hence, ∠z = 6°.
What is the value of the rational expression x-2x2-3/4x2-12 when x = 3?
-1/4
0
1/4
undefined
Answer:
(-135)/4
Step-by-step explanation:
Evaluate -(3 x^2)/4 - 2 x^2 + x - 12 where x = 3:
-(3 x^2)/4 - 2 x^2 + x - 12 = 3 - 2×3^2 - 3/4×3^2 - 12
3^2 = 9:
3 - 29 - 3/4×3^2 - 12
3^2 = 9:
3 - 2×9 - 3/4×9 - 12
-2×9 = -18:
3 + -18 - 3/4×9 - 12
-3×9 = -27:
3 - 18 + (-27)/4 - 12
Put 3 - 18 - 27/4 - 12 over the common denominator 4. 3 - 18 - 27/4 - 12 = (4×3)/4 + (4 (-18))/4 - 27/4 + (4 (-12))/4:
(4×3)/4 - (18×4)/4 - 27/4 - (12×4)/4
4×3 = 12:
12/4 - (18×4)/4 - 27/4 - (12×4)/4
4 (-18) = -72:
12/4 + (-72)/4 - 27/4 - (12×4)/4
4 (-12) = -48:
12/4 - 72/4 - 27/4 + (-48)/4
12/4 - 72/4 - 27/4 - 48/4 = (12 - 72 - 27 - 48)/4:
(12 - 72 - 27 - 48)/4
12 - 72 - 27 - 48 = 12 - (72 + 27 + 48):
(12 - (72 + 27 + 48))/4
| 1 |
| 7 | 2
| 4 | 8
+ | 2 | 7
1 | 4 | 7:
(12 - 147)/4
12 - 147 = -(147 - 12):
(-(147 - 12))/4
| 1 | 4 | 7
- | | 1 | 2
| 1 | 3 | 5:
Answer: (-135)/4
Michael is packing his bags for his vacation. He has 6 unique toy animals, but only 5 fit in his bag. How many different groups of 5 toy animals can he take?
Answer:
6 different groups of toy animals
Step-by-step explanation:
In this question, we are to calculate the number of different groups of toy animals Michael can take.
Since we are selecting, this is clearly a COMBINATION question. Now from the question, we are trying to select 5 toy animals from a group of 6 different animals to fit in the bag
The number of ways we can do this is 6C5 ways
Mathematically, if we have to select a number of r items from a group of n items, the number of ways this can be done is;
nCr = n!/(n-r)!r!
Using the case in the question, we have; 6!/5!(6-5)! = 6!/5!1! = 720/120 = 6 groups
Answer:
6 different groups of toy animals
Step-by-step explanation:
The question above can be solved by applying the Combination technique
Combination technique uses the formula:
nCk = n! /k!(n-k)!
Where in the question above:
n = 6
k = 5
Therefore we have , 6C5
= 6! / 5! (6-5)!
= 6!/ 5!(1!)
6! = 6×5×4×3×2×1
5! = 5×4×3×2×1
Hence,
= (6×5×4×3×2×1) / (5×4×3×2×1)(1)
= 6
Hence, Michael can take 6 different groups of toy animals with him on his vacation.
The mean intelligence quotient (IQ) score is 100, with a standard deviation of 15, and the scores are normally distributed. Given this information, the approximate percentage of the population with an IQ greater than 130 is closest to _________.
Answer:
2.28% is the approximate percentage of the population with an IQ greater than 130.
Step-by-step explanation:
We are given the following information in the question:
Mean, μ = 100
Standard Deviation, σ = 15
We are given that the distribution of score is a bell shaped distribution that is a normal distribution.
Formula:
[tex]z_{score} = \displaystyle\frac{x-\mu}{\sigma}[/tex]
P(IQ greater than 130)
[tex]P( x > 130) = P( z > \displaystyle\frac{130 - 100}{15}) = P(z > 2)[/tex]
[tex]= 1 - P(z \leq 2)[/tex]
Calculation the value from standard normal z table, we have,
[tex]P(x > 130) = 1 - 0.9772 = 0.0228 = 2.28\%[/tex]
2.28% is the approximate percentage of the population with an IQ greater than 130.
The approximate percentage of the population with an IQ greater than 130 will be 2.28%.
What is a normal distribution?The Gaussian Distribution is another name for it. The most significant continuous probability distribution is this one. Because the curve resembles a bell, it is also known as a bell curve.
The z-score is a statistical evaluation of a value's correlation to the mean of a collection of values, expressed in terms of standard deviation.
The mean intelligence quotient (IQ) score is 100, with a standard deviation of 15, and the scores are normally distributed.
Then the approximate percentage of the population with an IQ greater than 130 will be
The value of z-score
z = (130 - 100) / 15
z = 30 / 15
z = 2
Then the probability will be
P(x > 130) = P(z > 2)
P(x > 130) = 1 - P(z < 2)
P(x > 130) = 1 - 0.97725
P(x > 130) = 0.02275
Then the percentage will be
P = 0.02275 x 100
P = 2.275%
P ≅ 2.28%
More about the normal distribution link is given below.
https://brainly.com/question/12421652
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Imagine we found a strong positive correlation between worry and sleep disturbances and we hypothesized that drinking caffeine before going to bed would exacerbate this relationship. What type of analysis could we conduct to test this hypothesis?a. Moderationb. Mediationc. ANCOVAd. Two-way ANOVA
Answer:
The correct option is;
a. Moderation
Step-by-step explanation:
Here we have that the analysis is to check the hypothesis that drinking caffeine would exacerbate the effect of sleep disturbance caused worry is a form of moderator analysis.
A moderator analysis is one in which we attempt to determine if the relationship between two investigated variables is dependent on the magnitude or presence of a third variable. We refer to the third variable as the moderator or moderator variable.
Jose is working two summer jobs, making $10 per hour washing cars and $9 per hour walking dogs. Last week Jose worked a total of 13 hours and earned a total of $122. Write a system of equations that could be used to determine the number of hours Jose worked washing cars last week and the number of hours he worked walking dogs last week. Define the variables that you use to write the system.
Answer:
x+y =13
10x + 9y =122
Step-by-step explanation:
Hi, to answer this question we have to write a system of equations:
The sum of the hours he worked washing cars (x) and the hours he worked walking dogs(y) will be equal to the total hours worked (13)
x+y =13For the second equation the product of the number of hours he worked washing cars(x) and the price per hour ($10) plus the product of the number of hours he worked walking dogs (y) and the price per hour ($9) will be equal to the total amount earned (122)-
10x + 9y =122So, the system of equations is:
x+y =13 10x + 9y =122Where:
x: number of hours Jose worked washing cars
y: number of hours Jose worked walking dogs
Based on the information given, the equation will be:
x + y = 1310x + 9y = 122Based on the information given, the sum of the hours he worked washing cars and the hours he worked walking dogs will be equal to the total hours worked. Thia can be represented by:
x + y = 13
On the other hand, the product of the number of hours he worked washing cars and the price per hour plus the product of the number of hours he worked walking dogs and the price per hour can be represented with the equation:
10x + 9y = 122
In conclusion, the equation will be x + y = 13 and 10x + 9y = 122.
Learn more about equations on:
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Evaluate each expression
Answer:
a. 32
b. 27
c. 64
d. 36
e. 1/16
f. 1/9
Answer:
a.32
b.27
c.64
d.36
e.1/16
f.1/9
Step-by-step explanation:
Hope it helps.!
If the volume of an object is 100cm3 and the density is 4g/cm3. What is the mass of the object in g?
Answer:
400g
Step-by-step explanation:
mass= density × volume
Substitute the given value of density and volume.
Mass of the object
= 4(100)
= 400g
On Friday, 112 grocery shoppers bought a candy bar from the checkout line and 588 grocery shoppers did not. What percentage of shoppers did NOT buy a candy bar?
Answer: 84%
Step-by-step explanation:
112 grocery shoppers bought a candy bar and 588 grocery shoppers did not.
Number of grocery shoppers that bought candy bar = 112
Number of grocery shoppers that did not buy candy bar= 588
Total number of grocery shoppers= 112+588 = 700
Percentage of shoppers did not buy a candy bar= 588/700 × 100
= 0.84 × 100
= 84%
Answer:
0.84 = 84%
Step-by-step explanation:
First we need to find the total number of grocery shoppers.
If 112 bought a candy bar and 588 did not, the total number of grocery shoppers is:
588 + 112 = 700
Now, to calculate the percentage of grocery shoppers that didn't buy a candy bar, we make a division between the number of grocery shoppers that didn't buy a candy bar and the total number of grocery shoppers:
588 / 700 = 0.84 = 84%
Order these to Least to greatest -3/4, -2, -1/4, 2
-2. -3/4, -1/4, 2
-2 = -2
-3/4 = -0.75
-1/4 = -0.25
2 = 2
A box contains 5 red marbles and 7 green marbles. Find the probability of drawing 2 red marbles.
1. a) with replacement
2. b) without replacement
Answer:
1) 25/144 or 0.1736
2) 5/33 or 0.1515
Step-by-step explanation:
Total marbles: 5 + 7 = 12
1) 5/12 × 5/12
25/144
0.173611111
2) 5/12 × 4/11
5/33
0.151515151515
Answer:
1. 25/144
2. 5/33
Step-by-step explanation:
1. There are a total of 12 marbles. The probability of drawing the first marble red is: 5/12. Since we replace the marble, when we draw the second marble, the probability will also be 5/12. So we multiply them together and get: 25/144.
2. Again the probability of drawing the first marble red is 5/12. However, this time we're not replacing. This means that there are 12 - 1 = 11 remaining marbles and 5 - 1 = 4 remaining red marbles. Then the probability of choosing a second red marble is: 4/11. Multiply these two together: (5/12) * (4/11) = 20/132 = 5/33
Hope this helps!
In a certain Algebra 2 class of 28 students, 8 of them play basketball and 14 of them play baseball. There are 12 students who play neither sport. What is the probability that a student chosen randomly from the class plays basketball or baseball
Answer:
[tex]P(B \cup b) =\frac{4}{7}[/tex]
Step-by-step explanation:
Total Number of students, the Universal Set [tex]n(\mathcal{E})[/tex]=28
Let the number of those who play basketball =B
Let the number of those who play baseball =n
Number who play neither sport, [tex]n(B\cup b)'[/tex]=12
From Set Theory,
Since we want to determine the probability that a student chosen randomly from the class plays basketball or baseball, we only simply exclude those who play neither sports.
Mathematically,From Set Theory,
[tex]\mathcal{E}=n(B \cup b)+n(B \cup b)'\\28=n(B \cup b)+12\\n(B \cup b)=28-12\\n(B \cup b)=16[/tex]
The Probability that a student chosen randomly from the class plays basketball or baseball
[tex]P(B \cup b)=\frac{n(B \cup b)}{n(\mathcal{E})}\\=\dfrac{16}{28}\\ =\dfrac{4}{7}[/tex]
Answer:
4/7
Step-by-step explanation:
4/7
Each of forty-one pet owners was asked, "Does your pet eat more dry food or wet food?" Here are the results. Among the cat owners,6 chose "Dry food" and 8 chose "Wet food". Among the dog owners, 14 chose "Dry food" and 13 chose "Wet food".
No, pet does not eat more dry food than wet food.
Here's the detailed explanation of the table:
Dog Owners: Among the owners of dogs, 6 prefer to feed their pets wet food, while 11 prefer to feed them dry food.Cat Owners: Among the owners of cats, 12 prefer to feed their pets wet food, which is typically more common for cats due to their need for higher moisture content in their diet, and 15 prefer to feed them dry food.The numbers in the table are called "frequencies," and they show how many responses fell into each category. The table allows us to quickly see and compare the food preferences of dog and cat owners. For instance, we can observe that:
More cat owners prefer wet food for their pets compared to dog owners (12 versus 6).More dog owners prefer dry food compared to wet food (11 versus 6).Similarly, more cat owners prefer dry food compared to wet food, but the preference is less pronounced (15 versus 12).This table does not provide the total number of respondents in each category, but since we know that there are 44 pet owners in total, we could infer additional information if needed.
For example, we can calculate the total number of dog owners (6 + 11 = 17) and the total number of cat owners (12 + 15 = 27) from the table.
The completed table is given below.
The complete question is given below:
Let B1W2 denote the outcome that the first ball drawn is B1 and the second ball drawn is W2. Because the first ball is replaced before the second ball is drawn, the outcomes of the experiment are equally likely. List all 25 possible outcomes of the experiment on a sheet of paper.Consider the event that the first ball that is drawn is blue.
Answer:
[tex]\{B_1B_1, B_1B_2, B_1W_1, B_1W_2, B_1W_3, \\B_2B_1, B_2B_2, B_2W_1, B_2W_2, B_2W_3, \\[/tex]
[tex]W_1B_1,W_1B_2, W_1W_1, W_1W_2, W_1W_3, \\W_2B_1, W_2B_2, W_2W_1,W_2W_2, W_2W_3, \\W_3B_1, W_3B_2, W_3W_1, W_3W_2, W_3W_3\}[/tex]
Step-by-step explanation:
[tex]\text{If an urn contains two blue balls} (denoted \:B_1 \:and \:B_2) \text{and three white balls}[/tex],[tex](denoted \:W_1, W_2, \:and\: W_3)[/tex]
If One ball is drawn, its color is recorded, and it is replaced in the urn. Then another ball is drawn and its color is recorded.
The 25 Possible outcomes of this experiment are listed below:
[tex]\{B_1B_1, B_1B_2, B_1W_1, B_1W_2, B_1W_3, \\B_2B_1, B_2B_2, B_2W_1, B_2W_2, B_2W_3, \\[/tex]
[tex]W_1B_1,W_1B_2, W_1W_1, W_1W_2, W_1W_3, \\W_2B_1, W_2B_2, W_2W_1,W_2W_2, W_2W_3, \\W_3B_1, W_3B_2, W_3W_1, W_3W_2, W_3W_3\}[/tex]
The tree diagram of this event is also attached.
Solve for x in the equation x^2 - 4x-9= 29
I'm guessing 4+-√42 if u can understand it's the last one....
3. What is x?
E
4x+ 5
H
5/7 = p + 4/7
p =
Solve the equation.
Step-by-step explanation:
p=5/7-4/7
7p=1
p=1/7
hope it helps
Answer:
Step-by-step explanation:
Question 1 (1 point)
Evaluate if t=-2, x=3 and z=5
4z + 3x -t
Answer:
27
Step-by-step explanation:
4(5) + 3(3) - 2
20 + 9 - 2
27
If you reflect point A (3, 4) over
the y-axis, what is the reflected
point?
The rule for reflecting a point over the y-axis is this:
(x, y) ---> (-x, y)
The x term becomes the opposite and the y term stays the same
(3, 4) ---> (-3, 4)
Hope this helped! Let me know if you have any further questions!
~Just a girl in love with Shawn Mendes
Ken can walk
40
4040 dogs in
8
88 hours.
How many dogs can Ken walk in
12
1212 hours?
Answer:
Hey. I'm not sure if you have typos, but if you're saying ''Ken can walk 40 dogs in 8 hours, how many dogs can Ken walk in 12 hours", the answer is 60.
Step-by-step explanation:
So, we get our answer by dividing the amount of dogs Ken can walk by the amount of hours. 40/8 = 5. He walks 5 dogs an hour. Now that we know he walks 5 dogs an hour, we can multiply by 5 for each hour. 5 (Dogs/Hour) x 12 (Hours the dogs were walked) = 60, and that is our final answer.
Multiply and simplify the following complex numbers: (1 + 2i) x (1 - 4i)
Answer:
9-2i
Step-by-step explanation:
(1 + 2i) * (1 - 4i)
(1*1)-(1*4i)+(2i*1)-(2i)*(4i)
(1)-(4i)+(2i)-(8i^2)
i^2 = -1
1-4i+2i+8
1-2i+8
9-2i
The multiplication and simplification of the complex numbers (1 + 2i) x (1 - 4i) results in 9 - 2i.
Explanation:To multiply and simplify the complex numbers (1 + 2i) and (1 - 4i), we must use the distributive property, just like in normal algebra. We get (1*1) + (1*-4i) + (2i*1) + (2i*-4i), which is 1 - 4i + 2i - 8i². But remember, in complex numbers, i² equals -1, so it simplifies further to 1 - 2i -8(-1), or 1 - 2i + 8, and finally, 9 - 2i which is our final, simplified result.
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Find the length of the missing side. (Use the Pythagorean theorem)
Answer:
20
Step-by-step explanation:
12square + 16 square=400
Square root it = 20
Answer:
Step-by-step explanation:
a^2+b^2=c^2
144+256=?
144+256=400
the square root of 400 is 20
so the missing side is 20
If I am going 70 miles per hour and I am talking to someone for 66 seconds and 513 milliseconds how long would it take for my car to travel with the extra time
Answer:
Car would have traveled [tex]1.283[/tex] miles more with the extra time
Step-by-step explanation:
Given
Speed of the car - [tex]70[/tex] miles per hour
Speed of car in miles per second
[tex]\frac{70}{60* 60}[/tex]
[tex]= 0.0194[/tex] miles per second
Time wasted in talking instead of travelling
[tex]66[/tex] seconds and [tex]513[/tex] milliseconds
Total time wasted in seconds
[tex]66 + \frac{513}{1000} \\66 + 0.513[/tex]
[tex]66.153[/tex] seconds
Distance that would have been traveled in this time instead of talking
[tex]0.0194[/tex] miles per second [tex]* 66.153[/tex] seconds
[tex]= 0.0194 * 66.153[/tex] miles
[tex]= 1.283[/tex] miles
You are building a sandbox for your little sister. You want to make sure that she has 200 cubic ft. Of space to play. Give a possible length, width, and height of the sandbox.
Answer:
10x10x2
Step-by-step explanation:
10 * 10 * 2 = 200
Which expression is NOT equivalent to −3/8·(−4+1/2)?
Drag this expression to the box.
Answer:
The answer to your question is the first option
Step-by-step explanation:
Original expression
-3/8 (-4 + 1/2)
First option -3/8 (-4) + (3/8)(1/2) This option is not equivalent because
they forgot the negative sign of the
second term.
Second option (-3/8)(-4) + (-3/8)(1/2) This option is equivalent to the
original. Distributive property
Third option (-3/2)(-3 1/2) This option is equivalent to the original
Fourth option (-3/8)(-3) + (-3/8)(-1/2) This option is equivalent to the original
I need help with #11 and #12 how do I do this?
Answer:
11. x = 6; y = 6.5
12. x = 2; y = 4
Step-by-step explanation:
In each figure, the hash marks on the lines indicate the parallel lines (marked with red arrows) are equally-spaced. That means the two expressions involving x are equal to each other, and the two expressions involving y are equal to each other.
__
11. 2x +1 = x +7
x = 6 . . . . . . . subtract (x+1) from both sides
and
3y -8 = y +5
2y = 13 . . . . add (8-y) to both sides
y = 6.5 . . . . divide by the coefficient of y
__
12. x +3 = 3/2x +2
1 = 1/2x . . . . . subtract (x+2)
2 = x . . . . . . . multiply by 2
and
2y -1 = 3y -5
4 = y . . . . . . add (5 -2y)
Answer:
11. x=6;y=6.5 12. x=2;y=4
Step-by-step explanation:
hope that helped