Answer:
C) median
Step-by-step explanation: test on ed
The most appropriate to describe the center of the data in the histogram is the median
What is an histogram?
Histograms are graphs that are used to represent data, where the length of the bars represent the frequency
The data on the histogram are:
Between 50 and 54 on 2 days; Between 55 and 59 on 3 days; Between 60 and 64 on 3 days; Between 65 and 69 on 18 daysIn the above dataset, the frequency 18 is an outlier because 18 is relatively larger than the remaining frequencies (2 and 3)
The measure of center to represent a dataset with an outlier is the median.
Hence, the most appropriate to describe the center of the data in the histogram is the median
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Consider the statement, "Confidence intervals are underutilized" and explain what the implications might be of using or not using confidence intervals.
Answer:
Step-by-step explanation:
Confidence intervals have been underutilized prior to this time.
The implications of not using confidence intervals include:
- The under-representation or over-representation of research results that amounts from the use of a single figure to represent a statistic.
- In Market Research analysis, neglecting the use of confidence intervals will increase the risk of your portfolio.
Implications/Importance of using confidence intervals include:
- Calculation of confidence interval gives additional information about the likely values of the statistic you are estimating.
- In the presentation and comprehension of results, confidence intervals give more accuracy from the data or metrics captured.
- Given a sample mean, confidence intervals show the likely range of values of the population mean.
A half marathon is 13.1 miles long. Leah is running a half marathon and has completed 7.75 miles. How many miles to
the finish line?
Answer:
5.35 more miles
Answer:
5.35 miles to the finish line
Step-by-step explanation:
Step one
13.1-7.75=
5.35
Find the value of s(t(-3)):
s(x) = - 3x-2
t(x) = 5x - 4
Please helppp!
Step-by-step explanation:
(-3x-2/x) multiply by (-15x+12/x)
A random sample has been taken from a normal distribution. The output from a software package follows:
variable N Men SE Mean StDev Variance Sum
X ? ? 1.58 6.11 ? 751.40
a) Fill in the missing quantities.
b) Find a 95% CI on the popular mean.
Answer:
a) variable = X
N = 15
Mean = 50.0933
SE Mean = 1.58
StDev = 6.11
Variance = 37.3321
Sum = 751.40
b) 95% Confidence interval = (46.997, 53.190) = (47.00, 53.19)
Step-by-step explanation:
variable = X
N = ?
Mean = ?
SE Mean = 1.58
StDev = 6.11
Variance = ?
Sum = 751.40
To fill in the missing quantities, we need to use some of their formulas.
For N, the number of variables
SE = Standard Error of the mean = σₓ = (σ/√N)
σₓ = Standard Error of the mean = 1.58
σ = standard deviation of the sample = 6.11
N = sample size = ?
1.58 = (6.11/√N)
√N = (6.11/1.58) = 3.8671
N = 3.8671² = 14.954374299 = 15 to the nearest whole number.
For the Mean
Mean = (Sum of variables)/(Number of variables)
Mean = ?
Sum of variables = 751.40
Number of variables = N = 15
Mean = (751.40/15) = 50.0933333333 = 50.093
For Variance
Variance = (Standard deviation)² = (6.11)² = 37.3321
b) To compute the confidence interval.
idence Interval for the population mean is basically an interval of range of values where the true population mean can be found with a certain level of confidence.
Mathematically,
Confidence Interval = (Sample mean) ± (Margin of error)
Sample Mean = 50.0933
Margin of Error is the width of the confidence interval about the mean.
It is given mathematically as,
Margin of Error = (Critical value) × (standard Error of the mean)
Critical value will be obtained using the z-distribution. This is because although, there is no information provided for the population standard deviation, the sample size is large enough for the sample properties to approximate the population properties.
To find the critical value from the z-tables,
z at 95% confidence level = 1.960 (from the z-distribution tables)
Standard error of the mean = σₓ = (σ/√N)
Already calculated to be 1.58
95% Confidence Interval = (Sample mean) ± [(Critical value) × (standard Error of the mean)]
CI = 50.0933 ± (1.960 × 1.58)
CI = 50.0933 ± 3.0968
95% CI = (46.9965, 53.1901)
95% Confidence interval = (46.997, 53.190) = (47.00, 53.19)
Hope this Helps!!!
PLEASE HELP I GIVE BRAINLIEST AND 25 POINTS JUST ANSWER GOOD!!! ATTACHED IS SEQUENCES QUESTION. ONLY ONE QUESTION PLEASEEE I NEED IT IN 5 MINUTES PLEASEEE
Answer:
First box: 6
Second box: 10
Third box: 14
Step-by-step explanation:
The rule is to add the same number to each box. I tried adding different numbers, and I stopped at 4. 2 + 4 is 6, 6+4 is 10, 10+4 is 14, and 14+4 is 18. Therefore, you fill in the numbers accordingly.
Hope this helps!
~gloriouspurpose~
which of the following equations is equal to 2x^2+8 A. (2x-4i)(x-2i) B. (2x+4i)(x+2i) C. (2x-2i)(x+6i) D. (2x-4i)(x+2i)
Answer:
(2x-4i) (x+2i)
Step-by-step explanation:
2x^2+8
Factor out 2
2 ( x^2+4)
Writing as the difference of squares a^2 -b^2 = (a-b) (a+b)
2 ( x^2 -(2i)^2)
2 ( x-2i) (x+2i)
Multiplying the 2 into the first term
(2x-4i) (x+2i)
What is the sign of f
Answer:
The sign of f is used to symbolize many things. In physics it is commonly used to mean frequency and in music it is used to symbolize forte, which means loud.
A tank contains 3,000 L of brine with 16 kg of dissolved salt. Pure water enters the tank at a rate of 30 L/min. The solution is kept thoroughly mixed and drains from the tank at the same rate. (a) How much salt is in the tank after t minutes
Answer:
The amount of salt in the tank after t minutes is
y= 16e^(t/100)kg
Step- by-step Explanation
The tank contain 3000L of the brine
The rate is 30L/ min
The solution is mixed thoroughly, therefore, the rate in= rate out
dy/dt= rate in to the tank= rate out of the tank
CHECK THE ATTACHMENT FOR DETAILED EXPLANATION
Suppose you were given the function F(x)=x^4-2x^3+3x^2-10x+3 and the factor (x-2). What is the value of a?
Answer:
Hope it helps..........The given the function F(x)=x^4-2x^3+3x^2-10x+3 and the factor (x-2). Hence, the value of x is 7.5.
What is a function?Function is a type of relation, or rule, that maps one input to specific single output.
The given the function F(x)=x^4-2x^3+3x^2-10x+3 and the factor (x-2).
here x = 2
Substitute in the function;
F(x)=x^4-2x^3+3x^2 - ax+3
F(2) = 2^4-2(2)^3+3(2)^2 - a(2) +3
F(2) = 16 - 16 + 12 - 2a +3
F(2) = 15 - 2a
15 - 2a = 0
15 = 2a
a = 7.5
Hence, the value of x is 7.5
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A triangular plot of land has one side along a straight road measuring 147147 feet. A second side makes a 2323degrees° angle with the road, and the third side makes a 2222degrees° angle with the road. How long are the other two sides?
Answer:
81.23 ft and 77.88 ft long
Step-by-step explanation:
The sum of the internal angles of a triangle is 180 degrees, the missing angle is:
[tex]a+b+c=180\\a+23+22=180\\a=135^o[/tex]
According to the Law of Sines:
[tex]\frac{A}{sin(a)}= \frac{B}{sin(b)}= \frac{C}{sin(c)}[/tex]
Let A be the side that is 147 feet long, the length of the other two sides are:
[tex]\frac{A}{sin(a)}= \frac{B}{sin(b)}\\B=\frac{sin(23)*147}{sin(135)}\\B=81.23\ ft\\\\\frac{A}{sin(a)}= \frac{C}{sin(c)}\\C=\frac{sin(22)*147}{sin(135)}\\C=77.88\ ft[/tex]
The other two sides are 81.23 ft and 77.88 ft long
the construction of creating the perpendicular bisector of PQ is started below. How would the construction be different if you changed the compass setting in the next step of the perpendicular bisector construction?
Answer: It will not create a perpendicular bisector.
Explanation:
If the compass is the same setting as the first arc and drawn from point B, the points of intersection of the arcs will pass through the midpoint of AB (thus creating a perpendicular bisector).
If you change the setting of the compass and draw an arc from point B, the points of intersection of the arcs will still create a perpendicular line but will not pass through the midpoint of AB (creating a perpendicular line but not a perpendicular bisector).
A perpendicular bisector divides a line segment into two equal segments.
If the compass setting is changed, the line will not be bisected.
To bisect a line, the positioning of the compass must be done as follows:
Place the compass at the endpoint of the line segment, then draw an arcRepeat the above process for the other endpoint of the line segment.Trace the point of intersection of the two arcs, to the line that is being bisected.The above points are what is being done in the given construction.
Any step or setting other than that, would not create a perpendicular bisector.
Hence, if the compass setting is changed, the perpendicular bisector of the line would not be drawn.
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A contractor is setting up new accounts for the local cable company. She earns $75 for each customer account she sets up. Which expression models this situation, and how much will she profit if she sets up 8 customers? (The variable c represents the number of customers.) Question 4 options: A) c – 75; $9.78 B) 75c; $600 C) c + 75; $600 D) 75/c; $9.78
Answer:
B
Step-by-step explanation:
The contractor gets $75 for every single customer she sets up. Okay, so if she sets up 1 customer, she gets $75, if she sets up 2, she gets $150 and so on.
This is a multiplication expression since multiplication is just repeated addition, which is what is happening in this case, where the contractor gets $75 added to her account every time she sets another person up.
At this point you can just eliminate the other answer options except for B, so it is B.
But to double check... if you multiply 75 by 8, you would get $600, which is B.
Answer:
d
Step-by-step explanation:
75/c; $9.78
Suppose a random variable x is best described by a uniform probability distribution with range 22 to 55. Find the value of a that makes the following probability statements true.
a. P(X <= a) =0.95
b. P(X < a)= 0.49
c. P(X >= a)= 0.85
d. P(X >a )= 0.89
e. P(1.83 <= x <=a)= 0.31
Answer:
(a) The value of a is 53.35.
(b) The value of a is 38.17.
(c) The value of a is 26.95.
(d) The value of a is 25.63.
(e) The value of a is 12.06.
Step-by-step explanation:
The probability density function of X is:
[tex]f_{X}(x)=\frac{1}{55-22}=\frac{1}{33}[/tex]
Here, 22 < X < 55.
(a)
Compute the value of a as follows:
[tex]P(X\leq a)=\int\limits^{a}_{22} {\frac{1}{33}} \, dx \\\\0.95=\frac{1}{33}\cdot \int\limits^{a}_{22} {1} \, dx \\\\0.95\times 33=[x]^{a}_{22}\\\\31.35=a-22\\\\a=31.35+22\\\\a=53.35[/tex]
Thus, the value of a is 53.35.
(b)
Compute the value of a as follows:
[tex]P(X< a)=\int\limits^{a}_{22} {\frac{1}{33}} \, dx \\\\0.95=\frac{1}{33}\cdot \int\limits^{a}_{22} {1} \, dx \\\\0.49\times 33=[x]^{a}_{22}\\\\16.17=a-22\\\\a=16.17+22\\\\a=38.17[/tex]
Thus, the value of a is 38.17.
(c)
Compute the value of a as follows:
[tex]P(X\geq a)=\int\limits^{55}_{a} {\frac{1}{33}} \, dx \\\\0.85=\frac{1}{33}\cdot \int\limits^{55}_{a} {1} \, dx \\\\0.85\times 33=[x]^{55}_{a}\\\\28.05=55-a\\\\a=55-28.05\\\\a=26.95[/tex]
Thus, the value of a is 26.95.
(d)
Compute the value of a as follows:
[tex]P(X\geq a)=\int\limits^{55}_{a} {\frac{1}{33}} \, dx \\\\0.89=\frac{1}{33}\cdot \int\limits^{55}_{a} {1} \, dx \\\\0.89\times 33=[x]^{55}_{a}\\\\29.37=55-a\\\\a=55-29.37\\\\a=25.63[/tex]
Thus, the value of a is 25.63.
(e)
Compute the value of a as follows:
[tex]P(1.83\leq X\leq a)=\int\limits^{a}_{1.83} {\frac{1}{33}} \, dx \\\\0.31=\frac{1}{33}\cdot \int\limits^{a}_{1.83} {1} \, dx \\\\0.31\times 33=[x]^{a}_{1.83}\\\\10.23=a-1.83\\\\a=10.23+1.83\\\\a=12.06[/tex]
Thus, the value of a is 12.06.
The total number of hamburgers sold by a national fast-food chain is growing exponentially. If 3 billion had been sold by 2003 and 9 billion had been sold by 2010, how many will have been sold by 2013
Answer:
F(10) = 14.41 Billion
The total number of hamburgers that will have been sold by 2013 is 14.41 billion.
Step-by-step explanation:
The exponential function representing the total number of hamburgers sold by a national fast-food chain which grows exponentially can be expressed as;
f(t) = p(a)^t
In 2003, t = 0 and f(0) = 3 Billion
f(0) = p = 3 billion
The initial value p = 3 billion
In 2010, t = (2010-2003) = 7
f(7) = p(a)^7 = 9 billion
3(a)^7 = 9
a^7 = 9/3 = 3
a = 3^(1/7)
Therefore, the function f(t) is;
f(t) = 3(3)^(t/7) .......2
In 2013, t = (2013 - 2003) = 10
Substituting t = 10 into equation 2;
f(10) = 3(3)^(10/7)
F(10) = 14.41195997001 Billion
F(10) = 14.41 Billion
The total number of hamburgers that will have been sold by 2013 is 14.41 billion.
CAN SOMEONEHELP PLS ASAP
Answer:
a ≈ 2.2
Step-by-step explanation:
Using the Cosine rule in Δ ABC
a² = b² + c² - 2bc cos A
Here b = 3, c = 4 and A = 32° , thus
a² = 3² + 4² - (2 × 3 × 4 × cos32° )
= 9 + 16 - 24cos32°
= 25 - 24cos32° ( take the square root of both sides )
a = [tex]\sqrt{25-24cos32}[/tex] ≈ 2.2
Write a two column proof Given: AB || DC; BC || AE Prove: BC/EA = BD/EB
Answer:
AB || DC Given
∠ABE ≅ ∠CDB Alternate interior angles are congruent
BC || AE Given
∠CBD ≅ ∠BEA Alternate interior angles are congruent
ΔAEB is similar to ΔCBD AA Similarity Postulate
BC / EA = BD / EB Similar sides are proportional
Can Someone help me!!! I need this ASAP! What number? Increased by 130% is 69? FYI: the answer is less than 69
Answer:
Hey there!
There are a few ways you could solve this problem, but the easiest would to be writing an equation.
You could say-
2.3x=69
Divide by 2.3
x=30
Hope this helps :)
Answer:
30
Step-by-step explanation:
the answer is 30 bc increasing something by 130% is multiplying it by 2.3 so technically you have to divide 69 by 2.3 which equals to 30
Which of the following relations is a function?
A{(3,-1), (2, 3), (3, 4), (1,7)}
B{(1, 2), (2, 3), (3, 4), (4, 5)}.
C{(3, 0), (4, -3), (6, 7), (4,4)}
D{(1, 2), (1, 3), (2, 8), (3, 9)}
Answer:
B
Step-by-step explanation:
A is not a function because the same x value is repeated twice with different y values. The same goes for C and D so the answer is C.
Answer:
B.
Step-by-step explanation:
Well a relation is a set of points and a function is a relation where every x value corresponds to only 1 y value.
So lets see which x values in these relations have only 1 y value.
A. Well a isn’t a function because the number 3 which is a x value had two y values which are -1 and 4.
B. This relation is a function because there are no similar x values.
C. This is not a function because the x value 4 has two y values which are 4 and -3.
D. This is not a function because the number 1 has 2 and 3 as y values.
If a linear function passes through two points (x1, y1) and (x2, y2), what is the average value of the function on the interval from x1 to x2
Answer:
(y1+y2)/2
Step-by-step explanation:
adding and dividing by the total is the way to calculate the average
Which proportion would convert 18 ounces into pounds?
Answer:
16 ounces = 1 pound
Step-by-step explanation:
You would just do 18/16 = 1.125 pounds. There are always 16 ounces in a pound, so it always works like this
solve the proportion for y 11/8=y/13
Answer:
We can use the cross products property.
11/8 = y / 13
8y = 11 * 13
y = 11 * 13 / 8 = 17.875
Answer:
y=17.875
Step-by-step explanation:
[tex]\frac{11}{8} = \frac{y}{13}[/tex]
11(13)=8y
143=8y
y=17.875
The sets L and B are given below.
L= (-2, 2, 8)
B= (-2, 1, 2, 4, 8)
Find the intersection of L and B.
Find the union of L and B.
Write your answers using set notation (in roster form).
[tex]L= (-2, 2, 8) \\
B= (-2, 1, 2, 4, 8) \\ L \: n \: B \: = \: ( - 2, 2, 8) \\ L \: u \: B = ( - 2, 2, 1, 4, 8)[/tex]
A 37 bag sample had a mean of 421 grams. Assume the population standard deviation is known to be 29. A level of significance of 0.05 will be used. State the null and alternative hypothesis.
Answer: [tex]H_0:\mu=421[/tex]
[tex]H_a : \mu\neq421[/tex]
Step-by-step explanation:
A null hypothesis is a type of hypothesis that is used in statistics that assumes there is no difference between particular characteristics of a population wheres the alternative hypothesis shows that there is a difference.Given: A 37 bag sample had a mean of 421 grams.
Let [tex]\mu[/tex] be the population mean.
Then, the null hypothesis would be:
[tex]H_0:\mu=421[/tex]
whereas the alternative hypothesis would be:
[tex]H_a : \mu\neq421[/tex]
At a DBE lecture of 100 students, there are 29 women and 23 men. Out of these students, 4 are teachers and 24 are either men nor teachers. Find the number of women teachers attending the lecture
Answer:
20 teachers
Step-by-step explanation:
Because if you take 100 and minus it by 29, 23, 4 and 24 you get 20.
2. A ski lodge offers two weekend packages. Package A provides 2 nights and 3 meals for $280. Package B provides 2 nights and 5 meals for $320. Write and solve a system of equations to find the costs per night and per meal. (Assume the cost per night and cost per meal are the same for both packages.) Use n to represent the cost per night and m to represent the cost of each meal. (8 points) Step 1: The equation representing package A is given. Complete the system of equations by writing an equation to represent package B. (1 point) Package A: 2n + 3m = 280 Package B: ___________________ Step 2: Select a method for solving the system. Which method did you choose? Why? (2 points) Step 3: Solve the system of equations to find the costs per night and per meal. Show your work.(3 points) Step 4: Explain the meaning of the solutions for m and n. (2 points: 1 point each)
Answer:
see below
Step-by-step explanation:
Package A
2n + 3m = 280
Package B
2n + 5m = 320
Using elimination to eliminate n since the coefficient is the same
Subtracting the A equation from the B equation
2n + 5m = 320
-2n - 3m = -280
------------------------
2m = 40
Divide by 2
2m/2 = 40/2
m = 20
Now finding n
2n+3m = 280
2n +3(20) = 280
2n+60 = 280
Subtract 60 from each side
2n +60-60= 280-60
2n = 220
Divide by 2
2n/2 = 220/2
n = 110
The cost per night is 110 and the cost per meal is 20
The first steps in writing f(x) = 4x2 + 48x + 10 in vertex form are shown. f(x) = 4(x2 + 12x) + 10 (twelve-halves) squared = 36 What is the function written in vertex form?
Answer:
[tex]f(x)=4(x+6)^2-134[/tex]
Step-by-step explanation:
We are required to write the function[tex]f(x) = 4x^2 + 48x + 10[/tex] in vertex form.
First, bring the constant to the left-hand side.
[tex]f(x) -10= 4x^2 + 48x[/tex]
Factorize the right hand side.
[tex]f(x) -10= 4(x^2 + 12x)[/tex]
Take note of the factored term(4) and write it in the form below.
[tex]f(x) -10+4\Box= 4(x^2 + 12x+\Box)[/tex]
[tex]\Box = (\frac{\text{Coefficient of x}}{2} )^2\\\\\text{Coefficient of x}=12\\\\\Box = (\frac{12}{2} )^2 =6^2=36[/tex]
Substitute 36 for the boxes.
[tex]f(x) -10+4\boxed{36}= 4(x^2 + 12x+\boxed{36})[/tex]
[tex]f(x) -10+144= 4(x^2 + 12x+6^2)[/tex]
[tex]f(x) +134= 4(x+6)^2\\f(x)=4(x+6)^2-134[/tex]
The function written in vertex form is [tex]f(x)=4(x+6)^2-134[/tex]
Answer:
C
Step-by-step explanation:
I just finished the unit test on Edge. and got a 100% and I selected "c" as my answer.
A rectangular playground is to be fenced off and divided in two by another fence parallel to one side of the playground. Three hundred feet of fencing is used
dimensions of the playground that maximize the total enclosed area. What is the maximum area?
The smaller dimension is
feet
Answer:
50 ft by 75 ft3750 square feetStep-by-step explanation:
Let x represent the length of the side not parallel to the partition. Then the length of the side parallel to the partition is ...
y = (300 -2x)/3
And the enclosed area is ...
A = xy = x(300 -2x)/3 = (2/3)(x)(150 -x)
This is the equation of a parabola with x-intercepts at x=0 and x=150. The line of symmetry, hence the vertex, is located halfway between these values, at x=75.
The maximum area is enclosed when the dimensions are ...
50 ft by 75 ft
That maximum area is 3750 square feet.
_____
Comment on the solution
The generic solution to problems of this sort is that half the fence (cost) is used in each of the orthogonal directions. Here, half the fence is 150 ft, so the long side measures 150'/2 = 75', and the short side measures 150'/3 = 50'. This remains true regardless of the number of partitions, and regardless if part or all of one side is missing (e.g. bounded by a barn or river).
A data set includes 104body temperatures of healthy adult humans having a mean of 98.7degreesFand a standard deviation of 0.66degreesF.Construct a 99%confidence interval estimate of the mean body temperature of all healthy humans. What does the sample suggest about the use of 98.6degreesFas the mean body temperature?
Answer:
The 99% confidence interval estimate of the mean body temperature of all healthy humans is between 98.53ºF and 98.87 ºF. 98.6ºF is part of the interval, so the sample suggests that the use of 98.6ºF as the mean body temperature is correct.
Step-by-step explanation:
We have the standard deviation for the sample, so we use the t-distribution to solve this question.
The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So
df = 104 - 1 = 103
99% confidence interval
Now, we have to find a value of T, which is found looking at the t table, with 103 degrees of freedom(y-axis) and a confidence level of [tex]1 - \frac{1 - 0.99}{2} = 0.995[/tex]. So we have T = 2.624
The margin of error is:
[tex]M = T\frac{s}{\sqrt{n}} = 2.624\frac{0.66}{\sqrt{104}} = 0.17[/tex]
In which s is the standard deviation of the sample and n is the size of the sample.
The lower end of the interval is the sample mean subtracted by M. So it is 98.7 - 0.17 = 98.53ºF.
The upper end of the interval is the sample mean added to M. So it is 98.7 + 0.17 = 98.87 ºF.
The 99% confidence interval estimate of the mean body temperature of all healthy humans is between 98.53ºF and 98.87 ºF. 98.6ºF is part of the interval, so the sample suggests that the use of 98.6ºF as the mean body temperature is correct.
What is the standard form for 80000 + 200+ 2
Answer:
80202
Step-by-step explanation:
Simply add according to number value:
200 - 2 goes into hundreds place
2 - 2 goes into ones place
80000 - 8 goes into ten-thousands place
17. Which of the following trigonometric functions can be described as a reciprocal trig function?
O A. sin(e)
O B. sin-1(0)
O C. arctan(e)
O D. sec(0)
Answer:
Step-by-step explanation:
Reciprocal trig functions are opposite or mirror of the normal trig functions. The normal trig functions are as follows:
Sine = opposite side/hypotenuse
Cosine = adjacent side/hypotenuse
Tangent = opposite side/adjacent side
The reciprocals of the above trig ratios would be
Cosecant = hypotenuse/opposite side
Secant = hypotenuse/adjacent side
Cotangent = adjacent side/opposite side
Therefore, looking at the given options, the trigonometric function that can be described as a reciprocal trig function is
D. sec(0)