===========================================================
Explanation:
Since we have an odd number of values, this tells us that the median is part of the data set. It's the middle most item after we sort the values.
Recall that the mode is the most frequent item. Since the mode and median are the same, this must mean x can only be equal to one of the following
4, 9, 7 or 8
We can only pick one of those values.
----------------------
If x = 4, then the set {4,9,7,8,x} updates to {4,9,7,8,4} which sorts to {4,4,7,8,9}
The middle most item is in slot 3, which would be 7. So the median is 7.
The median 7 does not match with the mode 4.
So we cross x = 4 off the list.
-----------------------
If x = 7, then we have {4,7,7,8,9}
The mode is 7 and the median is 7. So far, so good.
Now let's compute the mean. Add up the values and divide by 5 because there are 5 items.
(4+7+7+8+9)/5 = 35/5 = 7
We've shown that the set {4,7,7,8,9} has mean 7.
Overall, that set has the same mean, median and mode. So the answer is confirmed.
I'll let you check the cases when x = 8 and x = 9.
1. Which expression is equivalent to 9k + 16? Explain why.
A 4 + 5k + 10 +6
B 4 + 3k + 2k + 10 +6
C2k +7 + 10 + 6
D 3k + 4k + 2k + 10 +6
Answer:
D
Step-by-step explanation:
3k +4k+2k+10+6
Collect like terms
9k +16
Answred Gauthmath
Answer:
D 3k + 4k + 2k + 10 +6
Step-by-step explanation:
A 4 + 5k + 10 +6 Combine like terms
5k+ 20 not equal
B 4 + 3k + 2k + 10 +6 Combine like terms
5k +20
C 2k +7 + 10 + 6 Combine like terms
2k + 23
D 3k + 4k + 2k + 10 +6 Combine like terms
9k+ 16
which of the following tables represents an inverse variation between x and y
Answer:
I think that d is the answer
Simplify to the extent possible:
(logx16)(log2 x)
Answer:
Step-by-step explanation:
Use the change-of-base rule.
William's assembly unit has decided to use a p-Chart with 2-sigma control limits to monitor the proportion of defective castings produced by their production process. The quality control manager randomly samples 150 castings at 10 successively selected time periods and counts the number of defective castings in the sample.
Sample Defects
1 9
2 14
3 9
4 9
5 13
6 8
7 12
8 10
9 12
10 11
Required:
a. What is the Center Line of the control chart?
b. What value of z should be used to construct the control chart?
c. What is the Upper Control Limit?
d. What is the Lower Control Limit?
Answer: attached below is the missing p chart
a) 0.07133
b) 2
c) 0.098
d) 0.045
Step-by-step explanation:
sample size = 150 castings
number of periods = 10
a) Determine the center Line of the control chart
( 0.06 + 0.0933 + 0.06 + 0.06 + 0.0867 + 0.0533 + 0.08 + 0.067 + 0.08 + 0.073) / 10
mean = 0.07133
standard deviation = 0.01335
b) Determine the value of Z to be used
Given that we are using 2sigma limits .
the value of Z to be used = 2
c) Upper limit control
= mean value + z-value * std
= 0.0713 + 2*0.01335 = 0.098
d) Lower Control Limit
= mean value - z-value * std
= 0.0713 - 2*0.01335 = 0.045
In another case, p and 2p are the first and second term respectively of an arithmetic progression. The nth term is 336 and the of the first n terms is 7224. Write down two equations in n and p and hence find the values of n and p
Consecutive terms in this sequence differ by p.
First term: p
Second term: p + p = 2p
Third term: 2p + p = 3p
and so on. It follows that the n-th term satisfies
np = 336
Presumably you meant to say the "sum of the first n terms" is 7224, which is to say
p + 2p + 3p + … + np = 7224
which can be rewritten as
p (1 + 2 + 3 + … + n) = 7224
p (n (n + 1)/2) = 7224
n (n + 1) p = 14,448
Substitute the first equation in the second one and solve for n :
336 (n + 1) = 14,448
n + 1 = 43
n = 42
Now solve for p :
42p = 336
p = 8
About 9% of the population has a particular genetic mutation. 400 people are randomly selected. Find the mean for the number of people with the genetic mutation in such groups of 400
Answer:
36 people
Step-by-step explanation:
The expected value E(X) = mean of sample = np
Where, p = population proportion, p = 9% = 0.09
n = sample size, = 400
The mean of the number of people with genetic mutation, E(X) = np = (400 * 0.09) = 36
36 people
Please help me solve log3(2x+5)=3
Answer:
x = -2
Step-by-step explanation:
Divide both sides by 3
3 (2x + 5)/3 = 3/3
Simplify
2x + 5 = 1
Subtract 5 from both sides
2x + 5 - 5 = 1 - 5
Simplify
2x = -4
Divide both sides by 2
2x/2 = -4/2
Simplify: 2x/2
Divide the numbers: 2/2 = 1
= x
Simplify: -4/2
Apply the fraction rule: -1/b = -a/b
= - 4/2
Divide the numbers: 4/2 = 2
= -2
x = -2
Which equation is true?
f of negative 10 = 1
f of 2 = negative 10
f of 0 = 6
f of 1 = negative 10
Answer:
f(0) = 6
Step-by-step explanation:
Complete question:
The function f (x) is given by the set of ordered pairs 1,0 (-10,2), (0,6) (3,17) (-2,-1) which equation is true
f(-10)=1
f(2)=-10
f(0)=6
f(1)=-10
Given the coordinate (x, y). This shows that the input function is x and the output function is y, i.e. f(x) = y
From the pair of coordinates given, hence;
f(1) = 0
f(-10) = 2
f(0) = 6
f(3) = 17
f(-2) = -1
From the following options, this shows that f(0) = 6 is correct
Answer:
f(0) = 6
Step-by-step explanation:
EDGE
The mean examination mark of a random sample of 1390 students is 67% with a standard deviation of 8.1%.
How many students scored above 80%? (Round to the nearest student)
Answer:
76 students scored above 80%.
Step-by-step explanation:
Normal Probability Distribution
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
The mean examination mark of a random sample of 1390 students is 67% with a standard deviation of 8.1%.
This means that [tex]\mu = 67, \sigma = 8.1[/tex]
Proportion above 80:
1 subtracted by the p-value of Z when X = 80, so:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{80 - 67}{8.1}[/tex]
[tex]Z = 1.6[/tex]
[tex]Z = 1.6[/tex] has a p-value of 0.9452.
1 - 0.9452 = 0.0548.
Out of 1390 students:
0.0548*1390 = 76
76 students scored above 80%.
What is the value of cot ø= 2/3 what is the value of csc ø
Answer:
Step-by-step explanation:
cotθ = cosθ/sinθ = 2/3
sinθ = 3/√(2²+3²) = 3/√13
cscθ = 1/sinθ = √13/3
Question 7(Multiple Choice Worth 1 points)
(07.02 MC)
Jason has two bags with 6 tiles each. The files in each bag are shown below
1
2
3
4
5
6
Without looking, Jason draws a file from the first bag and then a file from the second bag What is the probability of Jason drawing the file numbered 5 from the first bag and an odd file from the second bag?
0
영
o
Answer:a.3/6
Step-by-step explanation:
Because there’s a total of 12 files in each bag which is 6 in each
find the area of a semicircle whose radius is 2.4 cm
Answer:
15.072
Step-by-step explanation:
Pls Mark Brainiest okay
Answer:
2.88 pi or approximately 9.0432 cm^2
Step-by-step explanation:
The area of a semicircle is 1/2 the area of a circle
A = 1/2 pi r^2
A = 1/2 pi ( 2.4)^2
A = 2.88 pi cm^2
If we use 3.14 as an approximation for pi
A = 2.88 * 3.14
A =9.0432 cm^2
In another state, all license plates consist of 6 symbols chosen from the 26 letters of the alphabet and the digits 0-9. How many license plates are possible if no repetitions are allowed and there must be exactly 3 letters followed by 3 numbers
Answer:
11,232,000 license plates are possible.
Step-by-step explanation:
The order in which the symbols are chosen is important(ABC is a different plate than BAC), which means that the permutations formula is used to solve this question.
Permutations formula:
The number of possible permutations of x elements from a set of n elements is given by the following formula:
[tex]P_{(n,x)} = \frac{n!}{(n-x)!}[/tex]
In this question:
3 letters from a set of 26.
3 digits from a set of 10. So
[tex]T = P_{26,3}P_{10,3} = \frac{26!}{23!} \times \frac{10!}{7!} = 11232000[/tex]
11,232,000 license plates are possible.
please help
Find the missing side of this right
triangle.
X
7
12
X
= [?]
Answer:
13.9 (if x is the Hypotenuse)
Step-by-step explanation:
which one is the Hypotenuse (the side opposite of the 90 degree angle) ?
because that determines the calculation.
if x is the Hypotenuse then Pythagoras looks like this
x² = 7² + 12² = 49 + 144 = 193
x = sqrt(193) = 13.9
if 12 is the Hypotenuse, then it looks like this
12² = 7² + x²
144 = 49 + x²
95 = x²
x = sqrt(95) = 9.75
This is a list of the heights ( each nearest cm ) of 12 children
150 134 136 139 131 141
132 134 136 137 150 146
Select the type of the data.
Discrete
Continuous
Categorical
Qualitative
choose one
NO FAKE ANSWERS
FIRST MARKED BRAINLIST
qualitative
Step-by-step explanation:
b cos the question is in quality format
Answer:
cutee!
SUP???
Hiii friend :]
cuteee~!
prettyyy
The function above models hhh, the height of a flower pot in meters, ttt seconds after it falls from a fourth floor balcony. What is the height of the flower pot, in meters, 333 seconds after it falls
Answer:
See explanation
Step-by-step explanation:
The question is incomplete, as the function is not given.
However, I will give a general rule.
From the question, we understand that the question requires the value of h(3)
Assume:
[tex]h(t) = 20 - 4t[/tex]
Then:
[tex]h(3) = 20 - 4*3[/tex]
[tex]h(3) = 20 - 12[/tex]
[tex]h(3) = 8[/tex]
A G.P is such that the 3rd term minus a first term is 48. The 4th term minus 2nd term 144. Find: (i) Common ratio ii) The first term (ii) 6th term of the sequence
Answer:
Step-by-step explanation:
r is the common ratio.
Third term minus first term is 48.
a₃ - a₁ = 48
a₃ = a₁r²
a₁r² - a₁ = 48
a₁(r²-1) = 48
r²-1 = 48/a₁
Fourth term minus second term is 144.
a₄ - a₂ = 144
a₂ = a₁r
a₄ = a₁r³
a₁r³ - a₁r = 144
a₁r(r²-1) = 144
r²-1 = 144/(a₁r)
48/a₁ = 144/(a₁r)
r = 3
:::::
r²-1 = 48/a₁
a₁ = 6
:::::
a₆ = a₁r⁵ = 1458
(i) The common ratio for the given condition is 3.
ii) The first term of the sequence is 6.
iii) The 6th term of the sequence is 1458.
What is a sequence?It is defined as the systematic way of representing the data that follows a certain rule of arithmetic.
Divergent sequences are those in which the terms never stabilize; instead, they constantly increase or decrease as n approaches infinity,
It is given that a is a geometric progression such that the 3rd term minus a first term is 48. The 4th term minus the 2nd term 144.
Each number following the first in a geometric sequence is multiplied by a particular number, known as the common ratio.
As the third term minus the first term is 48.
a₃ - a₁ = 48
a₃ = a₁r²
a₁r² - a₁ = 48
a₁(r²-1) = 48
r²-1 = 48/a₁
The fourth term minus the second term is 144.
a₄ - a₂ = 144
a₂ = a₁r
a₄ = a₁r³
a₁r³ - a₁r = 144
a₁r(r²-1) = 144
r²-1 = 144/(a₁r)
48/a₁ = 144/(a₁r)
r = 3
r²-1 = 48/a₁
a₁ = 6
a₆ = a₁r⁵ = 1458
Thus the common ratio for the given condition is 3, the first term of the sequence is 6 and the 6th term of the sequence is 1458.
Learn more about the sequence here:
brainly.com/question/21961097
#SPJ2
Which equation could represent a linear combination of the systems?
9514 1404 393
Answer:
(b) 0 = -78
Step-by-step explanation:
Subtracting 6 times the first equation from the second will give ...
(4x +15y) -6(2/3x +5/2y) = (12) -6(15)
0 = -78
Answer:
the answer is b
Step-by-step explanation:
a pit is 7m long, 5m wide,and 8m deep how many cubic meter of sand will fill the pit?
Answer:
280
Step-by-step explanation:
7 x 5 x 8
after adjusting the number of servings in a recipe Charlotte determine that she will need 53 tbsp of flour one cup is equivalent to 16T . how much cups of flour will be required
Answer:
3.31 cups
Step-by-step explanation:
1/× =16/53
16x = 53
x = 53/16
x = 3.3125
I tried everything from adding to dividing, subtracting, multiplying but still no correct answer. Can someone help me out here please? Thank you!
Answer:
a)125/291
b) 48/73
Step-by-step explanation:
a) total of yes/total asked
b) total above average yes/ total above average (yes and no)
Answer:
See explanation. You didn't specify on whether the problem asks for a fraction or decimal, so I put both decimal and fraction.
Step-by-step explanation:
First we answer a:
Total amount of people polled is 291. Number of people who wear glasses is: [tex]48 + 51 + 26 = 125[/tex]
Divide to get the proportion: [tex]\frac{125}{291}[/tex] which is also equal to: 0.4295532646
Then we answer b:
b asks for the proportion of all above average readers who wear glasses, so the total number would be: [tex]48 + 25 = 73[/tex]. The number of above average readers who wear glasses is then 48.
We then get the proportion: [tex]\frac{48}{73}[/tex], which is also equal to 0.6575342466.
Which of the following describes an angle with a vertex at Z?
What is the area of the triangle formed from (0,-3), (0,4), and (4,-3)?
A. 24 square units
B. 48 square units
C. 14 square units
O D. 6 square units
Rectangle QRST with vertices Q(-3,2), R(-1,4), S(2,1), and T(0,-1)) in the x-axis
Answer:
D
Step-by-step explanation:
The coordinate of the new rectangle after the reflection across will be Q'(-3, -2), R'(-1, -4), S'(2, -1), and T'(0, 1). Then the correct option is D.
What is a transformation of a point?A spatial transformation is each mapping of feature space to itself and it maintains some spatial correlation between figures.
The reflection does not change the shape and size of the geometry. But flipped the image.
Rectangle QRST with vertices Q(-3, 2), R(-1, 4), S(2, 1), and T(0, -1).
The coordinate of the new rectangle after the reflection across is given as,
Q' = (-3, -2)
R' = (-1, -4)
S' = (2, -1)
T' = (0, 1)
The coordinate of the new rectangle after the reflection across will be Q'(-3, -2), R'(-1, -4), S'(2, -1), and T'(0, 1). Then the correct option is D.
More about the transformation of a point link is given below.
https://brainly.com/question/27224339
#SPJ2
I need help with this
Answer:
D. Rotation reflection is the right answer
Answer:
Rotation, reflection
Step-by-step explanation:
R and I are equal so if you rotate clockwise you'll see I is in the top left and R would be in the bottom left. By reflecting, it's like flipping a pancake. R will now be in the in the top left on top of I.
(It's kind of weird to explain) Sorry if that was confusing.
Assume that the wavelengths of photosynthetically active radiations (PAR) are uniformly distributed at integer nanometers in the red spectrum from 640 to 680 nm. What is the mean and variance of the wavelength distribution for this radiation?
A survey of 77 teenagers finds that 30 have 5 or more servings of soft drinks a week. a. Give a 90% confidence interval for the proportion of teenagers who have 5 or more servings of soft drinks a week. b. In the general population, 30% have 5 or more servings of soft drinks a week. Is there evidence that a higher proportion of teenagers have 5 or more servings of soft drinks a week than the general population
Answer:
a) The 90% confidence interval for the proportion of teenagers who have 5 or more servings of soft drinks a week is (0.2982, 0.481).
b) 30% = 0.3 is part of the confidence interval, which means that there is no evidence that a higher proportion of teenagers have 5 or more servings of soft drinks a week than the general population.
Step-by-step explanation:
Question a:
In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which
z is the z-score that has a p-value of [tex]1 - \frac{\alpha}{2}[/tex].
A survey of 77 teenagers finds that 30 have 5 or more servings of soft drinks a week.
This means that [tex]n = 77, \pi = \frac{30}{77} = 0.3896[/tex]
90% confidence level
So [tex]\alpha = 0.1[/tex], z is the value of Z that has a p-value of [tex]1 - \frac{0.1}{2} = 0.95[/tex], so [tex]Z = 1.645[/tex].
The lower limit of this interval is:
[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.3896 - 1.645\sqrt{\frac{0.3896*0.6104}{77}} = 0.2982[/tex]
The upper limit of this interval is:
[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.3896 + 1.645\sqrt{\frac{0.3896*0.6104}{77}} = 0.481[/tex]
The 90% confidence interval for the proportion of teenagers who have 5 or more servings of soft drinks a week is (0.2982, 0.481).
Question b:
30% = 0.3 is part of the confidence interval, which means that there is no evidence that a higher proportion of teenagers have 5 or more servings of soft drinks a week than the general population.
round 8 5/6 to the nearest whole number
Answer:
9
Step-by-step explanation:
8 5/6
5/6 is close to 1 so it will round up
8+1 = 9
8 5/6 rounds to 9
Answer:
[tex]9[/tex]
Step-by-step explanation:
Step 1: Round [tex]8\frac{5}{6}[/tex] to the nearest whole number
In order to round up, the fraction needs to be either 1/2 or greater than 1/2. In our case, it is greater than half therefore we will round up to 9.
Answer: [tex]9[/tex]
Solve the system of equations below using the inverse of matrix
Answer:
(x, y) = (4,-3)
Step-by-step explanation:
...............
.
.
.
.
The temperature at 5 a.m. was −7.4°C. By 9 a.m., the temperature was −4.7°C. How much warmer was the temperature at 9 a.m.?
Answer:
2.7°C.
Step-by-step explanation:
If it was -7.4°C. at 5 am, then -4.7°C. at 9am, then the temperature rose by 2.7°C.
Proof:
-7.4
-4.7
--------
2.7
