Answer:
a-The mean age and median age are unchanged.
Step-by-step explanation:
By adding the same you are subtracting, the sum of the ages remains the same. Therefore, the mean remains the same since you are dividing the same total of ages by the same number of people.
The middle number continues to be the middle number, so the median also does not change.
Try an example.
The ages are 30, 40, 50, 60, 70
Mean = (30 + 40 + 50 + 60 + 70)/5 = 250/5 = 50
Median: 50
Now add 10 to the greatest value and subtract 10 from the least value.
The ages now are 20, 40, 50, 60, 80
Mean = (20 + 40 + 50 + 60 + 80)/5 = 250/5 = 50
Median: 50
As you can see, both the mean and the median did not change.
Answer: a-The mean age and median age are unchanged.
Answer:
The mean age and median age are unchanged
Step-by-step explanation:
The median will not change when we alter the lowest and highest values so we can eliminate the answers that say the median changes
The mean is found by adding the values together and dividing by the number of values
If we add 10 and subtract 10, we have not changed the total value before dividing, so the mean does not change
What is the solution to the system of equations?
y=-3x – 2
5x + 2y = 15
0 (-40. 19)
(-19.55)
(19-40)
(55.-19)
Answer:
Step-by-step explanation:
y = -3x - 2
5x + 2y = 15
5x + 2(-3x -2) = 15
5x -6x - 4 = 15
-x - 4 = 15
-x = 19
x = -19
y = -3(-19) - 2
y = 57 - 2
y = 55
(-19, 55)
solution is b
What are the steps for constructing a copy of an angle using only a compass and
a straightedge?
Answer:
1. Use a straightedge
2. Draw dots on the line to mark the starting point
3. Place the point of the compass on the point you made or was given
4. Extend the compass so that the pencil is on the 2nd point & make a an arc thru point B
5. Place the compass point on the starting point dot on the line and draw w/ the pencil to create an arc crossing the line.
Answer:
Step 1: Mark the point that will be the vertex of the new angle, and label it P.
Step 2: Draw a ray from P in any direction, with any length. This ray will be one of the sides of the new angle.
Step 3: Place the compass point on the vertex of the original angle, and adjust the compass width to a convenient size.
Step 4: Use the compass to draw an arc intersecting both rays of the original angle at two points, J and K.
Step 5: Move the compass (without changing the width) to point P, and make an arc intersecting the existing ray of the angle. Mark the intersection point, and label it M.
Step 6: Set the compass point on the original angle at point J, and set its width to the length of line segment JK.
Step 7: Move the compass point to M on the new angle, and draw an arc cutting the previous arc. Mark the intersection point and label it L.
Step 8: Draw a ray from point P through point L. The new angle is a copy of the original angle.
Step-by-step explanation:
edmentum
Assume that the probability of the binomial random variable will be approximated using the normal distribution. Describe the area under the normal curve that will be computed. Find the probability that at leastat least 3535 households have a gas stove.
This is not the correct question, the correct question is;
Assume that the probability of the binomial random variable will be approximated using the normal distribution. Describe the area under the normal curve that will be computed. Find the probability that at least 35 households have a gas stove.
Answer: p ( x > 34.5 ) The area to the right of 34.5
Step-by-step explanation:
Given that, x = 35
when using normal approximation
Using continuity correction
so
p ( x ≥ 35 ) = p ( x > 34.5 )
More than means the area is towards the right.
Therefore, the area under the normal curve is,
p ( x > 34.5 ) The area to the right of 34.5
the instantaneous growth rate r of a colony of bacteria t hours after the start of an experiment is given by the function r=0.01t^3-0.07t^2+0.07t+0.15 for 0≤t≤7. find the times for which the instantaneous growth rate is zero.
Answer:
t = 5,-1,3
Step-by-step explanation:
r=0.01t^3-0.07t^2+0.07t+0.15
For simplification let's multiply the equation by 100
100r = t³ - 7t² + 7t + 15
When r= 0
t³ - 7t² + 7t + 15= 0
Let's look for the value of t.
Let's try a possible division
(t³ - 7t² + 7t + 15)/(t-5) = t² -2t -3
So we've gotten one as t-5
Let's factorize t² -2t -3
= t² +t -3t -3
= t(t+1) -3(t+1)
= (t+1)(t-3)
So we have
(t-5)(t+1)(t-3)
What it means is that the possible values are when
t = 5,-1,3
These are also called the roots of the equation
Answer:I don’t know
Step-by-step explanation: fruit flys are weird
The angles of a
quadrilateral, taken in order
are y, 5y, 4y
and
2y.
Find these angles
Answer:
30, 150, 120, and 60 degrees
Step-by-step explanation:
Since the sum of the interior angles in a quadrilateral is 360 degrees:
y+5y+4y+2y=360
12y=360
y=30
2y=60, 4y=120, 5y=150
Hope this helps!
Step-by-step explanation:
y+5y+ 4y + 2y=360°(sum of a Quadrilateral)
12y=360°
divide both sides by 12
y=30°
5y=(5×30)=150°
4y=(4×30)=120°
2y=(2×30)=60°
Which function is graphed below?
Answer:
Piecewise function;
y = 2x - 2 where x < 2
4 where 2 ≤ x ≤ 5
y = x + 1 where x > 5
Step-by-step explanation:
Function graphed represents the piecewise function.
1). Equation of the line with y-intercept (-2) and slope 'm'.
Since, slope of the line = [tex]\frac{\text{Rise}}{\text{Run}}[/tex]
= [tex]\frac{2}{1}[/tex]
= 2
Therefore, equation of this segment will be in the form of y = mx + b,
⇒ y = 2x - 2 where x < 2
2). Equation of a horizontal line,
y = 4 where 2 ≤ x ≤ 5
3). Equation of the third line in the interval x > 5
Let the equation of the line is,
y = mx + b
Where m = slope of the line
b = y-intercept
Here, slope 'm' = [tex]\frac{\text{Rise}}{\text{Run}}[/tex]
= [tex]\frac{2}{2}[/tex]
= 1
Equation of this line will be,
y = 1(x) + b
y = x + b
Since, this line passes through (5, 6),
6 = 5 + b
b = 6 - 5 = 1
Therefore, equation of this line will be,
y = x + 1 where x > 5
Graphed piecewise function is,
y = 2x - 2 where x < 2
4 where 2 ≤ x ≤ 5
y = x + 1 where x > 5
The solution to -45= n/5 is
Answer:
n=5*-45
n=225
:)
Step-by-step explanation:
Answer:
n = -225
Step-by-step explanation:
-45 = n/5
cross multiply
n = -45 x 5
n= -225
A researcher was interested in comparing the resting pulse rates of people who exercise regularly and people who do not exercise regularly. Independent simple random samples of 16 people ages 30 dash 40 who do not exercise regularly and 12 people ages 30 dash 40 who do exercise regularly were selected, and the resting pulse rate (in beats per minute) of each person was measured. The summary statistics are to the right. Apply the nonpooled t-interval procedure to obtain a 95% confidence interval for the difference, mu 1 minus mu 2, between the mean pulse rate of people who do not exercise and the mean pulse rate of people who do exercise. Assume that the requirements for using the procedure are satisfied and round to two decimal places.
Answer:
We Reject H₀ if t calculated > t tabulated
But in this case,
0.83 is not greater than 2.056
Therefore, we failed to reject H₀
There is no difference between the mean pulse rate of people who do not exercise and the mean pulse rate of people who do exercise.
Step-by-step explanation:
Refer to the attached data.
The Null and Alternate hypothesis is given by
Null hypotheses = H₀: μ₁ = μ₂
Alternate hypotheses = H₁: μ₁ ≠ μ₂
The test statistic is given by
[tex]$ t = \frac{\bar{x}_1 - \bar{x}_2}{\sqrt{\frac{s_1^2}{n_1} + \frac{s_2^2}{n_2} } } $[/tex]
Where [tex]\bar{x}_1[/tex] is the sample mean of people who do not exercise regularly.
Where [tex]\bar{x}_2[/tex] is the sample mean of people who do exercise regularly.
Where [tex]s_1[/tex] is the sample standard deviation of people who do not exercise regularly.
Where [tex]s_2[/tex] is the sample standard deviation of people who do exercise regularly.
Where [tex]n_1[/tex] is the sample size of people who do not exercise regularly.
Where [tex]n_2[/tex] is the sample size of people who do exercise regularly.
[tex]$ t = \frac{72.7 - 69.7}{\sqrt{\frac{10.9^2}{16} + \frac{8.2^2}{12} } } $[/tex]
[tex]t = 0.83[/tex]
The given level of significance is
1 - 0.95 = 0.05
The degree of freedom is
df = 16 + 12 - 2 = 26
From the t-table, df = 26 and significance level 0.05,
t = 2.056 (two-tailed)
Conclusion:
We Reject H₀ if t calculated > t tabulated
But in this case,
0.83 is not greater than 2.056
Therefore, We failed to reject H₀
There is no difference between the mean pulse rate of people who do not exercise and the mean pulse rate of people who do exercise.
Olivia is thinking of a number.She says, "My number is odd. It is a factor of 30 and a multiple of 3"
Answer:
15
Step-by-step explanation:
Factors of 30:
1 , 2, 3, 5, 6, 10, 15, 30
Multiples of 3:
3, 6, 9, 12, 15, etc.
The first number (and only number) shared by both sets is 15, therefore 15 is your answer.
~
Answer:
Your answer would be 15
Step-by-step explanation:
It would be 15 because you can multiply it by 30, it goes into 3 evenly and 15 is an odd number
Find the value of x in the figure
(X+5)* 90*
Answer:
x = 85 deg
Step-by-step explanation:
We can see that there are two straight lines that intersect and that the two angles given are opposite angles.
Because they are opposite angles, the two angles have the same value, i.e
(x + 5) = 90 (subtract 5 from each side)
x = 90 - 5
x = 85 deg
please help. Find the value of x
Answer:
x =24
Step-by-step explanation:
Call the angle in the lower right corner y
The outside angles add to 180 degrees for the large triangle
41+ 94+ y = 180
135 + y = 180
y = 180-136
y =45
The small triangle in the lower right also has angles that add to 180
y+ 111+x = 180
45+111+x = 180
156 + x = 180
x = 180-156
x =24
Answer:
x = 24
Step-by-step explanation:
Angles on a straight line add up to 180 degrees.
a + 111 = 180
180 - 111 = a
a = 69
Angles in a quadrilateral add up to 360 degrees.
69 + 41 + 94 + c = 360
204 + c = 360
c = 360 - 204
c = 156
Angles on a straight line add up to 180 degrees.
x + 156 = 180
x = 180 - 156
x = 24
Immediately after filling my gas tank, I drove 237.1 miles to my favorite campground. I filled my tank again at the campground, and computed that I got 28.7 miles per gallon on the trip. How many gallons of gas did I use on the trip to the campground
Answer:
57,838.4 - 57,491.9 = 346.5 miles
346.5/17.5 = 19.8 miles per gallon.
Hope this helps :-)
Step-by-step explanation:
A 1-inch rise for a 16-inch run makes it easier for the wheelchair rider to ascend a ramp. How long must a ramp be to easily accommodate a 24-inch rise to the door?
Answer: The ramp must be 32 feet long. In inches, 384.
Step-by-step explanation:
For each 16 inches of run, there is one inch of rise. To get 24 inches of rise, multiply 16 by 24 to get 384 inches. To convert to a more useful measurement, convert to feet. 12 inches per foot. 384/12 = 32
Measurement is the process of assigning numbers to physical quantities and phenomena.
If a 1-inch rise for a 16-inch run makes it easier for the wheelchair rider, this can be expressed as:
1inch rise = 16-inch run
In order to determine how long must a ramp be to easily accommodate a 24-inch rise to the door, we can write:
24in rise = x
Divide both expressions:
[tex]\dfrac{1}{24}=\dfrac{16}{x}\\[/tex]
Cross multiply:
[tex]x=16 \times 24\\x=384inches[/tex]
Hence the ramp must be 384inches long in order to easily accommodate a 24-inch rise to the door.
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The triangle ABC formed by AB = 13cm, BC=5cm and
AC = 12cm is
Answer:
Right-angle triangle
Step-by-step explanation:
What is the solution to arccos 0.5 express answer in radians
Answer:
arccos (0.5) is [tex]\frac{\pi}{3}[/tex]
Step-by-step explanation:
With the arccos(0.5) in this problem, you are asked which angle renders its cosine equal to 0.5 (or 1/2).
Recall that there are special angles in the unitary circle that render well know values like 1/2. There are two angle values between 0 and the full circle ([tex]2\pi[/tex] radians), that render cosine function equal 1/2, and they are: [tex]\frac{\pi}{3}[/tex], and [tex]-\frac{\pi}{3}[/tex].
The arccos uses just the first one as answer over the restricted domain between 0 and [tex]\pi[/tex], since otherwise it will not be considered a function.
So the answer is that the arccos (0.5) is [tex]\frac{\pi}{3}[/tex]
Pleaseeee hheeelppp mmmeee
Answer:
A
90 degrees
anticlockwise.
Step-by-step explanation:
It looks much more complicated than it really is. I don't know how to explain this in any other form but to give the answers.
1 A
The center of rotation is where the 90 degree angle has its vertex. So that would be A.
1 B
Follow x. It rotates 90 degrees. So every point must rotate 90 degrees.
1 C
The direction is against the way the clock tells time, so the direction of rotation is anticlockwise.
A politician who is running for the office of mayor of a city with 25,000 registered voters commissions a survey. In the survey, 48% of the 200 registered voters interviewed say they plan to vote for her. a. What is the population of interest?
Answer:
The 25,000 registered voters
Step-by-step explanation:
Population includes the entirety of the set of data, it consists of all the elements of a data set. For example all the students in a school, all the citizens of a country etc.
While the sample is the elements of the population from which observations are drawn from.
Therefore, for the case above, the population is the entirety of the registered voters in the city, that is all the 25,000 registered voters.
A box is filled with 3 yellow cards , 4 green cards. A card is chosen at random from the box. What is the probability that the card is not green?
Answer:
3/7
Step-by-step explanation:
total cards 3+4 = 7
Not green = 7-4 = 3 cards
P ( not green )= not green cards / total = 3/7
Answer:
3/7.
Step-by-step explanation:
There are seven cards in total, four of them being green.
The knowledge of the color of the other cards aren't really nessesary, so you can just subtract four from seven, which is three.
Hope this helped!
Two similar biscuit tins hold the same type of biscuits. The net mass of biscuits in the smaller tin is 1 kg. Find the net mass of biscuits in the larger tin. Net mass of biscuits in larger tin = __?_ kg
Answer:
1.5 kg
Step-by-step explanation:
Assuming it scales linearly: the higher tin holds 9/6 as many biscuits, so:
9/6 · 1 kg = 1.5 kg
Which statements about the circle are correct? Check all that apply Arc PQ is congruent to arc SR. The measure of arc QR is 150 The circumference of circle C is cm. Arc PS measures about 13.1 cm. QS measures about 15.7 cm.
Answer:
1st 2nd 4th 5th
Find the intersection point for the following linear functions. f(x) = 2x + 3 g(x) = -4x − 27
Answer:
(- 5, - 7 )
Step-by-step explanation:
Equate f(x) and g(x), that is
2x + 3 = - 4x - 27 ( add 4x to both sides )
6x + 3 = - 27 ( subtract 3 from both sides )
6x = - 30 ( divide both sides by 6 )
x = - 5
Substitute x = - 5 into either of the 2 functions for y- coordinate
Substituting into f(x)
f(- 5) = 2(- 5) + 3 = - 10 + 3 = - 7
Thus point of intersection = (- 5, - 7 )
solving the equation 2x+3(3x-5)=51 for x gives x = 6 what is the complete solution
Answer:
x = 6
Step-by-step explanation:
2x + 3(3x - 5) = 51
Expand the brackets.
2x + 9x - 15 = 51
Add like terms.
11x - 15 = 51
Add 15 on both sides.
11x = 51 + 15
11x = 66
Divide both sides by 11.
x = 66/11
x = 6
The solution to the equation 2x+3(3x-5)=51 is x = 6
How to determine the complete solution?The equation is given as:
2x+3(3x-5)=51
Expand
2x + 9x - 15 = 51
Evaluate the like terms
11x = 66
Divide both sides by 11
x = 6
Hence, the solution to the equation 2x+3(3x-5)=51 is x = 6
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I NEED HELP PLEASE, THANKS! :)
Answer:
Assume that Sk is valid for n=k and prove that Sn is valid for n= k+ 1
Step-by-step explanation:
This is Principle of Mathematical Induction ---PMI
Step 1: Verify that Sn is valid for n =1
Step 2:Assume that Sk is valid for n=k and prove that Sn is valid for n= k+ 1
LM=9, NR=16, SR=8. Find the perimeter of △SMP.
HURRY FIRST ANSWER I WILL MARK YOU AS BRAINLILIST PROMISE
Answer:
perimeter of △SMP = 25Step-by-step explanation:
The perimeter of the triangle △SMP is the sum of al the sides of the triangle.
Perimeter of △SMP = ||MS|| + ||MP|| + ||SP||
Note that the triangle △LRN, △LSM, △MPN and △SRP are all scalene triangles showing that their sides are different.
Given LM=9, NR=16 and SR=8
NR = NP+PR
Since NP = PR
NR = NP+NP
NR =2NP
NP = NR/2 = 16/2
NP = 8
From △LSM, NP = PR = MS = 8
Also since LM = MN, MN = 9
From △SRP, SR = RP = PS = 9
Also SR = MP = 8
From the equation above, perimeter of △SMP = ||MS|| + ||MP|| + ||SP||
perimeter of △SMP = 8+8+9
perimeter of △SMP = 25
What is the value of n in the numerical sentence?
Answer: n = -2
Step-by-step explanation:
answer:
-2
step by step explanation:
he dot plot shows the number of words students spelled correctly on a pre-test. A number line going from 2 to 11. 0 dots are above 2. 0 dots are above 3. 1 dot is above 4. 2 dots are above 5. 4 dots are above 6. 4 dots are above 7. 3 dots are above 8. 2 dots are above 9. 2 dots are above 10. 0 dots are above 11. Which statement best describes the shape of the graph? The graph is skewed right. The graph is nearly symmetrical. The graph is skewed left. The graph is perfectly symmetrical.
Explanation:
Given information:
A number line going from 2 to 11. 0 dots are above 2. 0 dots are above 3. 1 dot is above 4. 2 dots are above 5. 4 dots are above 6. 4 dots are above 7. 3 dots are above 8. 2 dots are above 9. 2 dots are above 10. 0 dots are above 11.From that we can see the data set is {4,5,5,6,6,6,6,7,7,7,7,8,8,8,9,9,10,10} which produces the dot plot you see in the image attachment below.
It's a bit tricky to see, but the graph is nearly symmetrical. If we were to remove the blue points in the dot plot I provided, then we'll get a perfectly symmetrical distribution. Symmetrical means one half is a mirror copy of the the other half. The center line of a symmetrical distribution is both the mean and median.
Answer:
The Answer On Edge Is A.), Have Fun Dreamers!
Step-by-step explanation:
Complete the following exercises by applying polynomial identities to complex numbers. Show your work. Factor x^2 + 64. Check your work. Factor 16x^2 + 49. Check your work. Find the product of (x + 9i)^2. Find the product of (x − 2i)^2. Find the product of (x + (3+5i))^2.
Answer:
Step-by-step explanation:
Hello,
Factor x^2 + 64.
[tex]\boxed{x^2+64=x^2+8^2=x^2-8^2i^2=(x-8i)(x+8i)}[/tex]
Factor 16x^2 + 49.
[tex]\boxed{16x^2+49=(4x)^2-(7i)^2=(4x-7i)(4x+7i)}[/tex]
Find the product of (x + 9i)^2.
[tex]\boxed{(x+9i)^2=x^2+18xi+(9i)^2=x^2+18xi-81=x^2-81+18xi}[/tex]
Find the product of (x − 2i)^2.
[tex]\boxed{(x-2i)^2=x^2-4xi-4=x^2-4-4xi}[/tex]
Find the product of (x + (3+5i))^2.
[tex]\boxed{(x + (3+5i))^2=x^2+(3+5i)^2+2x(3+5i)=x^2+9-25+30i+6x+10xi}\\\boxed{=x^2+6x-16+(30+10x)i}[/tex]
Hope this helps.
Do not hesitate if you need further explanation.
Thank you
A population consists of 500 elements. We want to draw a simple random sample of 50 elements from this population. On the first selection, the probability of an element being selected is
A. 0.100
B. 0.010
C, 0.001
D. 0.002
Answer:
D. 0.002
Step-by-step explanation:
Given;
total number of sample, N = 500 elements
50 elements are to be drawn from this sample.
The probability of the first selection, out of the 50 elements to be drawn will be = 1 / total number of sample
The probability of the first selection = 1 / 500
The probability of the first selection = 0.002
Therefore, on the first selection, the probability of an element being selected is 0.002
The correct option is "D. 0.002"
On the first selection, the probability of an element being selected is 0.002. Option D is correct.
Given information:
A population consists of 500 elements. so, the total number of samples will be [tex]N = 500[/tex] .
We want to draw a simple random sample of 50 elements.
The probability is defined as the preferred outcomes divided by the total number of samples.
So, the probability of first selection will be calculated as,
[tex]P=\dfrac{1}{500}\\P=0.002[/tex]
Therefore, on the first selection, the probability of an element being selected is 0.002.
For more details, refer to the link:
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Approximate the area under the curve y = x^3 from x = 2 to x = 5 using a Right Endpoint approximation with 6 subdivisions.
Answer:
182.8125
Step-by-step explanation:
Given:
y = x^3
from [2,5] using 6 subdivisions
deltax = (5 - 2)/6 = 3/6 = 0.5
hence the subdivisions are:
[2, 2.5]; [2.5, 3]; [3, 3.5]; [3.5, 4]; [4, 3.5]; [4.5, 5]
hence the right endpoints are:
x1 = 2.5; x2 = 3; x3 = 3.5; x4 =4; x5 = 4.5; x6 = 5
now the area is given by:
A = deltax*[2.5^3 + 3^3 + 3.5^3 + 4^3+ 4.5^3 + 5^3]
A = 0.5*365.625
A = 182.8125
Area using Right Endpoint approximation is 182.8125
The area of the region is an illustration of definite integrals.
The approximation of the area of the region R is 182.8125
The given parameters are:
[tex]\mathbf{f(x) = x^3}[/tex]
[tex]\mathbf{Interval = [2,5]}[/tex]
[tex]\mathbf{n = 6}[/tex] ------ sub intervals
Using 6 sub intervals, we have the partitions to be:
[tex]\mathbf{Partitions = [2,2.5]\ u\ [2.5, 3]\ u\ [3,3.5]\ u\ [3.5,4]\ u\ [4,4.5]\ u\ [4.5,5]}[/tex]
List out the right endpoints
[tex]\mathbf{x= 2.5,\ 3,\ 3.5,\ 4,\ 4.5,\ 5}[/tex]
Calculate f(x) at these partitions
[tex]\mathbf{f(2.5) = 2.5^3 = 15.625}[/tex]
[tex]\mathbf{f(3) = 3^3 = 27}[/tex]
[tex]\mathbf{f(3.5) = 3.5^3 = 42.875}[/tex]
[tex]\mathbf{f(4) = 4^3 = 64}[/tex]
[tex]\mathbf{f(4.5) = 4.5^3 = 91.125}[/tex]
[tex]\mathbf{f(5) = 5^3 = 125}[/tex]
So, the approximated value of the definite integral is:
[tex]\mathbf{\int\limits^5_2 {f(x)} \, dx \approx \frac{1}{2}(\sum f(x))}[/tex]
This becomes
[tex]\mathbf{\int\limits^5_2 {f(x)} \, dx \approx \frac{1}{2}(15.625 + 27 + 42.875 + 64+91.125 + 125)}[/tex]
[tex]\mathbf{\int\limits^5_2 {f(x)} \, dx \approx \frac{1}{2} \times 365.625}[/tex]
[tex]\mathbf{\int\limits^5_2 {f(x)} \, dx \approx 182.8125}[/tex]
Hence, the approximation of the area of the region R is 182.8125
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what is 1/4 x 1/4 x 1/4
Answer:
1/64
Step-by-step explanation:
1/4 × 1/4 × 1/4
Multiply the fractions.
1/4³
= 1/64
Answer:
The answer is 1/64.
Step-by-step explanation:
1/4 x 1/4 x 1/4 = 1/64
In other ways, you can write this as: 1/4³
Hope this helped!