The values of data that may affect the statistical measures of center and spread are the outliers and extreme values in the female dataset.
Statistical measures of center include the mean, median, and mode, while measures of spread include the range, interquartile range (IQR), variance, and standard deviation.
From the given box plots:
For males:
- The minimum number of hours worked per week is approximately 15.
- The first quartile (Q1) is approximately 20.
- The median (Q2) is approximately 22.
- The third quartile (Q3) is approximately 25.
- The maximum number of hours worked per week is approximately 35.
For females:
- The minimum number of hours worked per week is 0.
- The first quartile (Q1) is approximately 0.
- The median (Q2) is approximately 20.
- The third quartile (Q3) is approximately 25.
- The maximum number of hours worked per week is approximately 50.
In the male dataset, there are no apparent outliers or extreme values since the data is relatively compact with a narrow IQR and no data points far from the quartiles.
However, in the female dataset, there are potential outliers or extreme values:
- The minimum value of 0 hours worked per week is an outlier because it is far below the first quartile.
- The maximum value of approximately 50 hours worked per week is an extreme value because it is far above the third quartile.
These outliers and extreme values in the female dataset can significantly affect the measures of center and spread:
- The mean will be pulled down by the minimum value of 0 and up by the maximum value of 50, potentially making it less representative of the central tendency of the data.
- The range will be much larger due to the extreme maximum value.
- The IQR will not be affected by these outliers since it is based on the middle 50% of the data, but the overall spread of the data will be larger due to the presence of outliers.
- The variance and standard deviation will be increased by the presence of these outliers, indicating a larger spread in the data.
In summary, the outliers and extreme values in the female dataset are the values that may affect the statistical measures of center and spread. These values can skew the mean, increase the variance and standard deviation, and extend the range, making these measures less indicative of the typical work hours for female students.
what is the simplified form of this
y^5 is your answer hope it helps!
If your drop a ball in great salt lake, it will fall 20 inches every second , if the bottom has an elevation of -440.
-Write the expression that you could Use to find how long it will take for the ball to reach the bottom .
-How long did it take for the ball to reach the bottom .
If a die is rolled one time find these probabilities
-of getting less than 7
-Getting a number greater than or equal to 3
In probability, the outcomes of rolling a die are considered. The probability of getting a number less than 7 is 1 or 100% and the probability of rolling a number greater than or equal to 3 is 2/3 or approximately 66.67%
Explanation:This question falls under the topic of probability in Mathematics. In the case of a single die, there are 6 possible outcomes because a die has 6 faces.
For the probability of getting a number less than 7, all outcomes (1,2,3,4,5,6) are less than 7. Thus, the probability is 6 out of 6 or 1.
For the probability of getting a number that's greater than or equal to 3, the favorable outcomes are 3,4,5,6. So, there are 4 such outcomes. The probability, in this case, is 4 out of 6, which simplifies to 2/3.
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what is the value of "m" equal?
First, let's convert the radical terms to exponents. Remember the following:
[tex]\sqrt[n]{x^m} = x^\frac{m}{n}[/tex]
[tex]\sqrt{x^5} = x^{\frac{5}{2}}[/tex]
[tex]\sqrt[4]{x^9} = x^{\frac{9}{4}}[/tex]
[tex]\sqrt[6]{x^5} = x^{\frac{5}{6}}[/tex]
After substituting in the values we just found, our expression looks like:
[tex]\dfrac{(x^{\frac{5}{2}})(x^{\frac{9}{4}})}{x^{\frac{5}{6}}}[/tex]
Now, remember that we can add the exponents of terms that have the same base and are being multiplied by each other. Also, remember that we can subtract the exponents of terms with the same base that are being divided by each other. This is represented as:
[tex]x^a \cdot x^b = x^{(a + b)}[/tex]
[tex]\dfrac{x^c}{x^d} = x^{(c - d)}[/tex]
Thus, we can simplify our expression even more:
[tex]\dfrac{(x^{\frac{5}{2}})(x^{\frac{9}{4}})}{x^{\frac{5}{6}}}[/tex]
[tex]\dfrac{x^{\frac{19}{4}}}{x^{\frac{5}{6}}}[/tex]
[tex]x^{\frac{47}{12}}[/tex]
Our answer is [tex]\boxed{m = \dfrac{47}{12}}[/tex].
Evaluate using distributive property
16 x ( -3/8)+16 x 1/4
Final answer:
The expression 16 x (-3/8) + 16 x 1/4 is evaluated using the distributive property to get -6 + 4, which equals -2.
Explanation:
To evaluate the expression 16 x ( -3/8) + 16 x 1/4 using the distributive property, we will distribute the 16 into the terms inside the parentheses.
Here is the step-by-step process:
Multiply 16 by (-3/8): 16 × (-3/8) = -6.
Multiply 16 by 1/4: 16 × 1/4 = 4.
Add these two results together: -6 + 4 = -2.
Therefore, the evaluation of the expression 16 x ( -3/8) + 16 x 1/4 is -2.
Two numbers have an absolute value of 37. Which of the two number is farther from 1 on the number line
If I understand what you're saying. It would be the absolute value of -37, which is 37. Also, the absolute value of 37 is 37.
The absolue valor of 37 is 37
What are the x- and y-intercepts of 2x+4y=8
x-intercept: (4,0)
y-intercept: (0,2)
mario earned three times as much monry last year as his wife elena.the total amount that the two earned was 11,000.how much money did elena earn
a.)Which two points should you use to find the equation of the model? Explain.
B.) Use the two points you chose in part a to find the slope of the linear model, rounded to three decimal places. Show your work.
c.) What is the equation of the linear model in point-slope form?
d.) Rearrange the equation you wrote in part c into slope-intercept form. Show your work.
Part a)
we know that
to find the equation of the line, I will use the two points that are closest to the line
Let
A(1,14)
B(7,7)
Part b)
Find the slope
we know that
the formula to find the slope between two points is equal to
[tex]m=(y2-y1)/(x2-x1)[/tex]
substitute
[tex]m=(7-14)/(7-1)[/tex]
[tex]m=(-7)/(6)[/tex]
[tex]m=-7/6=-1.167[/tex]
the answer part b) is
the slope is [tex]m=-7/6=-1.167[/tex]
Part c)
we know that
the equation of the line in point slope form is equal to
[tex]y-y1=m(x-x1)[/tex]
use the point B (7,7)
[tex]y-7=(-7/6)*(x-7)[/tex]
therefore
the answer part c) is
[tex]y-7=(-7/6)*(x-7)[/tex]
Part d)
we know that
the equation of the line in slope-intercept for is equal to
[tex]y=mx+b[/tex]
we have
[tex]y-7=(-7/6)*(x-7)[/tex]
[tex]y=(-7/6)x+(49/6)+7[/tex]
[tex]y=(-7/6)x+(91/6)[/tex]
therefore
the answer Part d) is
[tex]y=(-7/6)x+(91/6)[/tex] or [tex]y=-1.167x+15.167[/tex]
75,575 how do the values of the digit differ in the number?
Answer:
75,575 - ten-thousands place; this 7 is worth 70,000
75,575 - thousands place; this 5 is worth 5,000
75,575 - hundreds place; this 5 is worth 500
75,575 - tens place; this 7 is worth 70
75,575 - ones place; this 5 is worth 5
find the missing part to make the sentence true 5+4= +3
The Yu family and the Sainz family went on vacation together and each family leased a car. The leasing company charged a flat rental fee for the week, plus a charge for each mile driven. The Yu's drove 222 miles; their car cost $110.30 for the week. The Sainz's drove 147 miles; their car cost $99.05. What is the linear equation that represents the cost of a rental car? Round to the nearest hundredth
Answer:
y = 0.15x+77 is the equation linear connecting total cost y and miles driven x
Step-by-step explanation:
Given that the leasing company charged a flat rental fee for the week, plus a charge for each mile driven.
Let flat rental fee be c and cost per mile driven = m and miles driven = x
Total cost =y
Then y = mx+C is the linear equation.
to find m and c, we use the fact that y =110.30 when x = 222
i.e. 110.30 = c+222x
and similarly 99.05 = c+147x
Subtract to eliminate c
11.25 = 75 x
0.15 =x
Substitute in I equation
110.30 = c+222(0.15)
c = 77
Hence y = 0.15x+77 is the equation linear connecting total cost y and miles driven x
Answer:
y = 0.15x+77
Step-by-step explanation:
i did it
how many times does 100 go into 750
100 can go into 750 7.5 times :)
750 divided by 100 is 7.5 so 100 goes into 750 7.5 times
Polygon F has an area of 36 square units. Aimar drew a scaled version of Polygon F and labeled it Polygon G. Polygon G has an area of 4 square units
Area is a squared number. We know that from the label we use when we solve problems involving area. Perimeter is a single unit label. This single unit label can also be used to find scale factor, since single unit labels are one-to-one. If the area of polygon F is 36, that means that the single unit measure was a number that was squared to get to the area. Same goes for polygon G. That means that in order to find the single unit measure of each of those we have to take the square root of the area. The square root of 36 is 6, and the square root of 4 is 2. 6:2 is the scale factor, but that can be reduced to 3:1, larger to smaller.
Answer:
1/3
Step-by-step explanation:
khan academy answer
The function "g" is defined as g(x)=5x+a, where "a" is a constant. If g(4)=31, what is the value of "a"?
To find the constant 'a' in the function g(x) = 5x + a, you can substitute the known values into the function. Here, it leads us to the equation 5*4 + a = 31. Solving this equation gives 'a' = 11.
Explanation:The question gives us the value of g(4) and asks us to find the constant 'a' in the function g(x) = 5x + a.
To solve for 'a', we can substitute the known values into the equation. We know that g(4) = 31, and the function g(x) is defined as 5x + a. Therefore, we replace 'x' with 4 in the function. This gives us 5*4 + a = 31.
Solving this equation, we find that 20 + a = 31. By subtracting 20 from both sides of the equation, we can solve for 'a', giving us 'a' = 31 - 20 = 11.
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In △XYZ, XY=XZ.
Find the length of XY of △XYZ if XY=2a, YZ=3a+1, and XZ=5a−12.
4
6.5
8
29
*Q2:
In △ABC, m∠A=(4x+7)° and m∠B=(5x−3)°.
What is m∠B?
Question 2 options:
47°
10°
45°
93°
Answer:
XY=8
Step-by-step explanation:
In △XYZ, XY=XZ
It is isosceles triangle whose equal sides are XY=XZ
We are given,
XY=2a
YZ=3a+1
XZ=5a-12
XY=XZ
So, 2a=5a-12
Solve for a,
2a-5a=-12
-3a=-12
a=4
Now we put a=4 into XY=2a
So, XY=2(4)=8
Answer:
1.In △XYZ, XY=XZ.
We have to Find the length of XY of △XYZ if XY=2a, YZ=3a+1, and XZ=5a−12.
Now, X Y=X Z [given]
→2 a= 5 a-12
Bringing like terms on same side
→2 a-5 a=-12
→-3 a=-12
→a=(-12)÷(-3)
a=4 is correct answer among all the options.
2.In △ABC, m∠A=(4x+7)° and m∠B=(5x−3)°.
What is m∠B?
Ans: as ∠ C not given we can't find ∠B.
A total of 676 tickets were sold for the school play. They were either adult tickets or student tickets. There were 74 fewer student tickets sold than adult tickets. How many adult tickets were sold?
There were 375 adult tickets sold.
Explanation:This question involves a concept in basic algebra. Let's denote the number of adult tickets as A and the number student tickets as S. From the problem, we know that the total number of tickets sold is 676, so A+S=676. The problem also tells us that there were 74 fewer student tickets sold than adult tickets, so we know that S=A-74.
We can substitute the value of S from the second equation into the first equation which gives us A+(A-74)=676. By solving this equation we find that A=375, so there were 375 adult tickets sold.
Let's denote the number of adult tickets sold as x. Since there were 74 fewer student tickets sold, the number of student tickets sold is x - 74. The total number of tickets sold is the sum of the adult and student tickets, which is 676.
Therefore, we can write the equation:
x + (x - 74) = 676
Simplifying the equation:
2x - 74 = 676
Adding 74 to both sides:
2x = 750
Dividing by 2:
x = 375
So, 375 adult tickets were sold.
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Create a ratio table for making lemonade with a lemon juice to water of ratio of 1:3 show how much lemon juice would be needed if u use 36 cups of water to make lemonade
There is 1 serving of lemon juice to 3 cups water. Hence why it's 1:3 ratio.
Since it's 1:3, then 2 servings to 6 cups of water, so on and so forth.
Multiply your lemon juice servings by 3 to find out how many cups of water for the table.
To find how much lemon juice for 36 cups of water, just divide 36 by 3 to get 12. 12 servings of lemon juice is just right for your 36 cups of water.
Answer: There is 12 servings of lemon juice needed for 36 cups of water.
Step-by-step explanation:
Since we have given that
Number of cups of water to make lemonade = 36
Ratio of lemon juice to water = 1 : 3
So, number of lemon juice cups be x
number of cups of water be 3x.
According to question, it becomes,
[tex]3x=36\\\\x=\dfrac{36}{3}\\\\x=12[/tex]
Hence, there is 12 servings of lemon juice needed for 36 cups of water.
PLEASE HELP ASAP
15 POINTS
1/2(4x-5) + 5/2 = 10
Use the distributive property:
2x - 5/2 + 5/2 = 10
Use addition property:
2x = 10
Divide both sides by 2:
x = 10/2
x = 5
Question number 3 lol I need help please
the answer is b. to calculate 5% interest you multiply whatever by 0.05, this immediately eliminates any other answer
Please solve this problem with full sentences and explain it please.
Question 2
(02.05 MC)
Triangle PQR is transformed to triangle P'Q'R'. Triangle PQR has vertices P(8, 0), Q(6, 2), and R(−2, −4). Triangle P'Q'R' has vertices P'(4, 0), Q'(3, 1), and R'(−1, −2).
Plot triangles PQR and P'Q'R' on your own coordinate grid.
Part A: What is the scale factor of the dilation that transforms triangle PQR to triangle P'Q'R'? Explain your answer. (4 points)
Part B: Write the coordinates of triangle P"Q"R" obtained after P'Q'R' is reflected about the y-axis. (4 points)
Part C: Are the two triangles PQR and P''Q''R'' congruent? Explain your answer. (2 points)
ANSWER TO QUESTION 1.
We plot the points:
[tex]P(8,0)[/tex]
[tex]Q(6,2)[/tex]
and
[tex]R(-2,-4)[/tex]
We plot the image triangle also with the points,
[tex]P'(4,0)[/tex]
[tex]Q'(3,1)[/tex]
and
[tex]R(-1,-2)[/tex]
See graph in attachment.
ANSWER TO QUESTION 2.
The scale factor is the ratio of the image length to the object length.
[tex]Scale\: factor=\frac{|P'Q'|}{|PQ|}[/tex].
We need to use the distance formula to determine the two lengths.
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
[tex]|P'Q'|=\sqrt{(3-4)^2+(1-0)^2}[/tex]
[tex]|P'Q'|=\sqrt{(-1)^2+(1)^2}[/tex]
[tex]|P'Q'|=\sqrt{1+1}[/tex]
[tex]|P'Q'|=\sqrt{2}[/tex]
[tex]|PQ|=\sqrt{(6-8)^2+(2-0)^2}[/tex]
[tex]|PQ|=\sqrt{(-2)^2+(2)^2}[/tex]
[tex]|PQ|=\sqrt{4+4}[/tex]
[tex]|PQ|=\sqrt{8}[/tex]
[tex]|PQ|=2\sqrt{2}[/tex]
Therefore the scale factor of the dilation is
[tex]Scale\: factor=\frac{\sqrt{2}}{2\sqrt{2}}[/tex].
[tex]Scale\: factor=\frac{1}{2}[/tex].
ANSWER TO QUESTION 3
For a reflection in the y-axis we negate the x-coordinates. That means we are using the y-axis as our mirror line. The mapping is given as follows:
[tex]P'(4,0)\rightarrow P''(-4,0)[/tex]
[tex]Q'(3,1)\rightarrow Q''(-3,1)[/tex]
and
[tex]R(-1,-2)\rightarrow R''(1,-2)[/tex]
ANSWER TO QUESTION 4
We can see from the diagram that, PQR is bigger than P"Q"R".
The reason is that PQR was reduced by scale factor of half and then reflected in the y-axis to obtain P"Q"R".
Since dilation is not a rigid motion, the two triangles PQR and P''Q''R" are not equal in all respect, therefore they are not congruent.
A rectangle has a width of 2cm and a perimeter of 25cm. Find the length and the area .
2w + 2l = 25
2 * 2 + 2l = 25
Simplfiy.
4 + 2l = 25
Subtract 4 from both sides.
2l = 21
Divide both sides by 2.
l = 10.5
Now that we have the value of l, we can find the area.
A = lw
A = 10.5 * 2
A = 21.
The length is 10.5cm.
The area of the rectangle is 21cm^2
Using the discriminant, determine the number of real solutions.
2x^2+7x-15=0
- no real solutions
-one real solution
-two real solutions
Answer:
Since discriminant is positive, therefore, the given quadratic equation has two real solutions. Correct answer is the last option.
Step-by-step explanation:
We have been given a quadratic equation and we need to figure out the number of real solutions of the equation.
[tex]2x^{2}+7x-15=0[/tex]
We know that discriminant of a general quadratic equation [tex]ax^{2}+bx+c=0[/tex] is given by [tex]D=b^{2}-4ac[/tex]
For the given quadratic equation [tex]2x^{2}+7x-15=0[/tex], we have [tex]a=2,b=7,c=-15[/tex]. Upon substituting these values in the formula for discriminant, we get:
[tex]D=7^{2}-4(2)(-15)[/tex]
[tex]D=49+120[/tex]
[tex]D=169[/tex]
Since discriminant is a positive number, therefore, the given quadratic equation has two real solutions. Hence, the last option is the correct answer.
Answer:
two real solutions
Step-by-step explanation:
what is the value of x?
A) x=2.25
B) x=11.25
C) x=13
D) x=22
What is 16x9+67x9 can someone help me?
Answer: 747
Step-by-step explanation:
16x9+67x9
First multiply 16 and 9 which is equal to 144
144+67x9
now multiply 67 and 9 which is equal to 603
144+603
Now add 144 and 603 which is equal to 747
So the answer to 16x9+67x9 is 747
use PEMDAS
16 * 9 + 67 * 9 =
144 + 603 =
747
A container holds 80,000 ounces of water. There is a small leak in the the container. Every 96 minutes, 1.9 ounces of water leak out. What is the total change in water after 8 hours?
It is known that 60 minutes equals 1 hour.
Therefore, the first thing we do to solve the problem is to calculate how many hours are equivalent to 96 minutes.
For that we calculate:
[tex]96 minutes * \frac{1 hour}{60minutes}=\frac{96}{60}=1.6hours\\[/tex]
Thus:
96 minutes = 1.6 hours.
1.9 ounces of water are lost every 1.6 hours.
Therefore, in 8 hours the amount of water lost is:
[tex]\frac{8hours}{1.6hours}*1.9 = 9.5\\[/tex] ounces of water
After 8 hours, 9.5 ounces of water are lost
Therefore, the amount of water left in the tank after 8 hours is:
[tex]80 000-9.5=79990.5[/tex] ounces
Choose the answer. 3. (1 pt) Which is an example of the distributive property? A. 9 • (t + 5) = 9t + 45 B. 9 • (t + 5) = (t + 5) • 9 C. 9 • (t + 5) = (9 • t) + 5 D. 9 • (t + 5) = 9t + 5
For this case, we have:
The generic definition of the distributive property is:
[tex]a (b + c) = ab + ac\\[/tex]
Therefore, the option that fits the definition is given by:
[tex]9 (t + 5) = 9t + 45[/tex]
where the property is verified.
Thus, the correct option is A.
Answer:
Option A
michelle bought 70 pounds of cocoa powder for her bakery
plzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz
which number is prime? 4. 13. 26. 15.
2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, etc.
so 13
13. A prime number is a number which cannot be factored anymore. 4 can be factored as 2 x 2, 26 can be factored as 13 x 2, and 15 can be factored as 3 x 5.