Provided below is a simple data set for you to find descriptive measures. For the data set, complete parts (a) and (b).
1, 2, 4, 5, 7, 1, 2, 4,5,7
a. Obtain the quartiles.
Q_1 =____
Q_2 =_____
Q3 =____ (Type integers or decimals. Do not round.)
b. Determine the interquartile range.
The interquartile range is ______(Type an integer or a decimal. Do not round.)
Answers
(a.i) The first quartile (Q₁) is 1.5.
(a.ii) The second quartile (Q₂) is 4.
(a.iii) The third quartile (Q₃) is 4.5.
(b) The interquartile range is 3
What is the interquartile range of the function?The given data sample;
1, 1, 2, 2, 4, 4, 5, 5, 7, 7
(a.i) The first quartile (Q₁) is calculated as;
{1, 1, 2, 2, 4}
Q₁ = (1 + 2) / 2
Q₁ = 1.5
(a.ii) The second quartile (Q₂) is calculated as;
{1, 1, 2, 2, 4, 4, 5, 5, 7, 7}
Q₂ = (4 + 4) / 2
Q₂ = 4
(a.iii) The third quartile (Q₃) is calculated as;
{4, 4, 5, 5, 7}
Q₃ = (4 + 5) / 2
Q₃ = 4.5
(b) The interquartile range is calculated as follows;
Interquartile range = Q₃ - Q₁
Interquartile range = 4.5 - 1.5 = 3
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Related Questions
Make q the subject of the formula 2(5q^2+1)=c
Answers
Solve this simultaneous equation by substitution:
y=x^2-1
y=5-x
Answers
We have the following system of equations,
\(\left \{ {{y=x^2-1} \atop {y=5-x}} \right.\)
We are asked to solve the system of equations using substitution.
What is substitution?
Substitution is a method of solving a system of equations where you solve for one of the equations (pick either equation) for one of the variables (pick one of the variables), then using this new equation to "substitute" back in to the other.
Given this set of equations, \(\left \{ {{y=x^2-1} \atop {y=5-x}} \right.\), notice how both of the equations are already solved for the variable, \(y\). Since both these equations equal \(y\), we can set them equal to each other and solve for, \(x\).
\(\left \{ {{y=x^2-1} \atop {y=5-x}} \right.\)
\(\Longrightarrow 5-x=x^2-1\), substituted "\(5-x\)" for \(y\) into the top equation.
\(\Longrightarrow -x^2-x+6=0\)
\(-1[\Longrightarrow -x^2-x+6=0]\)
\(\Longrightarrow x^2+x-6=0\)
\(\Longrightarrow (x-2)(x+3)=0\)
\(\Longrightarrow x=2 \ and \ x=-3\)
Now take these values of x (\(x=2 \ and \ x=-3\)) and plug them into either of the two original equations to solve for \(y\).
When x=2:
\(y=5-x;x=2\)
\(\Longrightarrow y=5-(2)\)
\(\Longrightarrow y=3\)
When x=-3:
\(y=5-x;x=-3\)
\(\Longrightarrow y=5-(-3)\)
\(\Longrightarrow y=5+3\)
\(\Longrightarrow y=8\)
Thus, we get two solutions to the given system of equations, (-3,8) & (2,3).
find the exact value of the given expression. sin 2 cos−1 12 13 calculator
Answers
The exact value of the given expression. sin 2 cos−1 12 13 is 240/169.
To find the exact value of the given expression, we need to use the identity sin(2θ) = 2sin(θ)cos(θ) and the information provided. The expression you want to find is sin(2 * cos^(-1)(12/13)).
First, let's find the angle θ, which is cos^(-1)(12/13). In a right triangle with the adjacent side = 12 and hypotenuse = 13, we can use the Pythagorean theorem to find the opposite side: Opposite side = √(13^2 - 12^2) = √(169 - 144) = √25 = 5
Now, we can find sin(θ) and cos(θ): sin(θ) = opposite/hypotenuse = 5/13 cos(θ) = adjacent/hypotenuse = 12/13 Next, use the sin(2θ) identity: sin(2θ) = 2sin(θ)cos(θ) = 2(5/13)(12/13) = (10/169)(24) = 240/169 So, the exact value of the given expression is 240/169.
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8 x (30 + 2) = (8 x ___) + (8 x 2)
Answers
Answer:
30 is the right one Hope this helps you Stay happy and safe Do mark as brainliest ✌️Answer:
30
Step-by-step explanation:
8 x (30 + 2) = (8 x 30) + (8 x 2)
We need to use distributive property.
Hope this helps!
Given that v = u + 10t, find v when u
= -28 and t = 6.
Answers
V=-28+60
V=32
The value of v when u is -28 and t is 6 is 32
What is substitution of variable?In mathematics, a change of variables is a basic technique used to simplify problems in which the original variables are replaced with functions of other variables.
For example , the value of 6x + 2 when x is 4 is calculated as :
6(4) + 2 = 10+2 = 12
Similarly, the value of v in v = u + 10t when u is -28 and t is 6 is calculated as:
v = -28 + 10(6)
v = -28 + 60
v = 32
Therefore the value of v is 32
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Of the total number of books sold in one year, approximately what percentage of the total number did M Jackson sell?
Answers
Answer: See explanation
Step-by-step explanation:
Your question is not complete but let me help out.
Let us assume that the total books that was sold in a year was 40,000 while Jackson sold 2000. Then, the percentage of the total number of books that Jackson sold will be:
= (2000 / 40,000) × 100
= 5%
A percentage is a way to describe a part of a whole. The percentage of the total number of books M Jackson sold is 24.64%.
What is Percentage?A percentage is a way to describe a part of a whole. such as the fraction ¼ can be described as 0.25 which is equal to 25%.
To convert a fraction to a percentage, convert the fraction to decimal form and then multiply by 100 with the '%' symbol.
As we need to use the table to answer the question given below.
Salesperson Book sale
B. Lowell 1,331
J. Hernandez 8,772
K. Schwartz 3,420
M. Jackson 5,104
S. Corelli 2,090
The total number of books sold by the store is the sum of the number of books sold by each sales person individually, therefore, the total number of books sold can be written as,
Total number of books sold = 1331+8772+3420+5104+2090 = 20,717
It is mentioned in the table that the number of books sold by the M.Jackson is 5,104, therefore, the percentage of the total number of books M Jackson sell can be written as,
\(\rm Percentage = \dfrac{\text{Number of books sold by M. Jackson}}{\text{Total number of books sold}}\times 100\%\\\\\\Percentage = \dfrac{5104}{20717} \times 100\% = 24.64\%\)
Hence, the percentage of the total number of books M Jackson sold is 24.64%.
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Find mZKJL.
K
7x
(3x +
16)0M
mZKJL =
Answers
Answer:
The answer is 28.
Step-by-step explanation:
Ok.
☆7x and 3x + 16 are congruent, meaning they equal the same.
☆Since they are equal, we can make an equation out of then.
7x = 3x + 16
☆Then we just solve.
\( \: \: \: \: \: \: \: \: \: 7x = 3x + 16 \\ \frac{- 3x = - 3x}{4x = 16} \\ \\ \frac{4x}{4} = \frac{16}{4} \\ \\ x = 4\)
☆Therefore, x equals 4.
☆We are solving for m<KJL so all we need to do is plug in.
\(7x \\ 7(4) \\ 28\)
☆You answer is 28.
The required angle is 28°
What is congruence in triangles?Two triangles are said to be congruent if all three corresponding sides are equal and all three corresponding angles are equal in measure. These triangles can be slid, rotated, flipped, and turned to be looked identical. If repositioned, they coincide with each other.
Given here ∠KJL=7x and ∠LJM=3x+16
now in ΔKJL & ΔLJM, JL is common and KL=LM, and by Pythagoras theorem JL²=KL²+JK² & JL²=JM²+LM²
Thus KL²+JK² = JM²+LM²
⇒ JK=JM
Thus by the SSS criterion, we can conclude that the triangles are congruent.
therefore by CPCT 7x=3x+16
4x=16
x=4
so the required angle is 7×4 =28°
Hence, ∠KJL=28°
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the measure of an interior angel of a regular polygon is 150. find the number of sides in the polygon.
Answers
Answer:
The polygon has \(12\) sides.
Step-by-step explanation:
Recall that the expression for finding the measure of one interior angle of a regular polygon is \(\frac{180(n-2)}{n}\), where \(n\) is the number of sides the polygon has (and \(n\neq 0\)), which is what we want to find.
Because the measure of one interior angle of the given polygon is \(150\textdegree\), we can write the following equation to solve for \(n\):
\(\frac{180(n-2)}{n}=150\)
Solving for \(n\), we get:
\(\frac{180(n-2)}{n}=150\)
\(\frac{180n-360}{n}=150\) (Distribute the \(180\) in the numerator)
\(180n-360=150n\) (Multiply both sides of the equation by \(n\) to eliminate the denominator and simplify)
\(30n-360=0\) (Subtract \(150n\) from both sides of the equation and simplify)
\(30n=360\) (Add \(360\) to both sides of the equation to isolate \(n\) and simplify)
\(\bf n=12\) (Divide both sides of the equation by \(30\) to get rid of \(n\)'s coefficient and simplify)
Therefore, the polygon has \(\bf 12\) sides. Hope this helps!
What is the most precise term for quadrilateral ABCD with vertices A(4, 4), B(5, 8), C(8, 8),
and D(8, 5)?
square
rhombus
kite
Parallelogram
Answers
The most precise term for quadrilateral ABCD with vertices A(4, 4), B(5, 8), C(8, 8) is a kite.
Option C is the correct answer.
What is a kite?A kite is a quadrilateral where the adjacent sides are equal which means there are two pairs of equal sides.
We have,
Quadrilateral ABCD:
A = (4, 4)
B = (5, 8)
C = (8, 8)
D = (8, 5)
Now,
A__________B
| |
| |
| |
D_________ C
We see the distance between the two points.
AB = √(8 - 4)² + (5 - 4)² = √(4² + 1) = √17
AD = √(5 - 4)² + (8 - 4)² = √(1² + 4²) = √17
AB = AD
BC = √(8 - 8)² + (8 - 5)² = √9 = 3
CD = √(5 - 8)² + (8 - 8)² = √9 = 3
BC = CD
AB and AC are adjacent sides.
CD and DB are adjacent sides.
So,
The quadrilateral ABCD is a kite.
Thus,
The quadrilateral ABCD is a kite.
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3. Find the value of b.
48°
b
b =
Answers
Answer:
42
Step-by-step explanation:
\(48° + x = 90(angle \: at \: a \: right \: angle)\)
\(therefore \: x = 90°- 48°\\ = 42°\)
Answer:
B = 42
Step-by-step explanation:
B + 48 = 90 ... because they are complement angles
B = 90 - 48
B = 42 ...... so the unknown angle is 42
Write True and false
A test statistic based on point estimation is used to construct the decision rule which defines the rejection region.
Answers
The given statement is False. A test statistic based on point estimation is not used to construct the decision rule which defines the rejection region.
In hypothesis testing, a test statistic is calculated using sample data and a specific hypothesis to assess the strength of evidence against the null hypothesis. The decision rule, which determines whether to reject or fail to reject the null hypothesis, is based on the test statistic's distribution under the null hypothesis, rather than the point estimate itself.
The construction of the decision rule involves selecting a significance level (alpha), which represents the probability of rejecting the null hypothesis when it is actually true. The rejection region is determined based on the chosen significance level and the distribution of the test statistic. If the calculated test statistic falls within the rejection region, the null hypothesis is rejected; otherwise, it is not rejected.
Point estimation, on the other hand, is used to estimate an unknown parameter of interest, such as the population mean or proportion, based on sample data. It involves calculating a single value (point estimate) that represents the best guess for the parameter value. The point estimate is not directly involved in constructing the decision rule or defining the rejection region in hypothesis testing.
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False. A test statistic based on point estimation is not used to construct the decision rule that defines the rejection region.
The process of hypothesis testing involves constructing a decision rule to determine whether to accept or reject a null hypothesis based on sample data. The decision rule is typically defined using a critical region or rejection region, which is a range of values for the test statistic.
Point estimation, on the other hand, is a method used to estimate an unknown population parameter based on sample data. It involves calculating a single value (point estimate) that serves as an estimate of the population parameter.
While point estimation and hypothesis testing are both important concepts in statistics, they serve different purposes. Point estimation is used to estimate population parameters, whereas hypothesis testing involves making decisions based on sample data.
The decision rule for hypothesis testing is typically constructed based on the significance level (alpha) and the distribution of the test statistic, such as the t-distribution or the standard normal distribution. The test statistic is calculated using sample data and compared to critical values or calculated p-values to determine whether to reject the null hypothesis.
Therefore, the statement that a test statistic based on point estimation is used to construct the decision rule defining the rejection region is false.
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machines at a factory produce circular washers with a specified diameter. the quality control manager at the factory periodically tests a random sample of washers to be sure that greater than 90 percent of the washers are produced with the specified diameter. the null hypothesis of the test is that the proportion of all washers produced with the specified diameter is equal to 90 percent. the alternative hypothesis is that the proportion of all washers produced with the specified diameter is greater than 90 percent. which of the following describes a type i error that could result from the test? responses the test does not provide convincing evidence that the proportion is greater than 90%, but the actual proportion is greater than 90%. the test does not provide convincing evidence that the proportion is greater than 90%, but the actual proportion is greater than 90%. the test does not provide convincing evidence that the proportion is greater than 90%, but the actual proportion is equal to 90%. the test does not provide convincing evidence that the proportion is greater than 90%, but the actual proportion is equal to 90%. the test provides convincing evidence that the proportion is greater than 90%, but the actual proportion is equal to 90%. the test provides convincing evidence that the proportion is greater than 90%, but the actual proportion is equal to 90%. the test provides convincing evidence that the proportion is greater than 90%, but the actual proportion is greater than 90%. the test provides convincing evidence that the proportion is greater than 90%, but the actual proportion is greater than 90%. a type i error is not possible for this hypothesis test.
Answers
Answer:
the test does not provide convincing evidence that the proportion is greater than 90%
plz help me find the measure of each angle indicated. then state the type of angle pair
Answers
20. 132* - the angle below is the same as the other side of this angle, 180* - 48* (same side interior angles)
21. 48* - these are the same angle just in different placements (corresponding angles)
22. 70* - same angles just different placement (alternate interior angles)
23. 85* - these are vertical angles so they’re the same
24. 114* - same angle just different placement (alternate exterior angles)
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Analytics
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After school, Gabby had a science club meeting for 1 hour and 10 minutes, followed by a
choir rehearsal that lasted for 1 hour and 55 minutes. The choir rehearsal ended at 5:30 P.M.
What time did the science club meeting start?
Answers
Answer:
2:25
Step-by-step explanation:
What is the solution to 3x^2-x-52=0
Answers
please help meeee, will mark brainliest!!!
Answers
Answer:
see below
Step-by-step explanation:
If it decreases at 10.5 % per year then 89.5 % remains
Value = y = 35 300 ( .895)^x
value when x = 5.5 y = $ 19177.92
1. u+47=8
u=?
i just want to know how to solve a question like this
Answers
Step-by-Step Explanation:
=> u + 47 = 8
First we have to shift 47 to the RHS. When we do that +47 becomes negative on the RHS.
=> u = 8 - 47
Now subtract 47 from 8 which will result in -39 because 47 > 8.
=> u = -39
A graphing calculator is recommended. Find the maximum and minimum values of the function. (Round your answers to two decimal places.) y = sin x + sin 2x maximum value minimum value
Answers
The maximum value of the function is approximately 1.724 and the minimum value is approximately -1.724.
To find the maximum and minimum values of the function y = sin x + sin 2x, we can first take its derivative with respect to x:
y' = cos x + 2 cos 2x
Then, we can set y' equal to zero and solve for x:
cos x + 2 cos 2x = 0
We can use a graphing calculator to find the solutions to this equation, which are approximately x = 0.285 and x = 2.857. We can then evaluate the original function at these values to find the maximum and minimum values:
y(0.285) ≈ 1.724
y(2.857) ≈ -1.724
Therefore, the maximum value of the function is approximately 1.724 and the minimum value is approximately -1.724.
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For each of the following statements below, decide whether the statement is True or False. (i) Recall that P(5) denotes the space of polynomials in x with degree less than or equal 5. Consider the function L : P(5) - P(5), defined on each polynomial p by L(p) = p', the first derivative of p. The image of this function is a vector space of dimension 5. • [2marks] true • [2marks] (ii) A linear transformation L : R2 → R2 with trace 3 and determinant 2 has non-trivial fixed points. false (iii) The set of all vectors in the space R6 whose first entry equals zero, forms a 5-dimensional vector space. (No answer given) - [2 marks] (iv) Recall that P(3) denotes the space of polynomials in x with degree less than or equal 3. Consider the function K : P(3) → P(3), defined by K(p) = 1 + p', the first derivative of p. The pre-image K-'(0) is a vector space of dimension 1. (No answer given) - [2 marks] (v) Let V1, V2 be arbitrary subspaces of R". Then Vin V2 is a subspace of R". (No answer given) • [2marks]
Answers
(i) True.
The statement is true. The function L(p) = p' represents taking the first derivative of a polynomial p. The space P(5) consists of polynomials of degree less than or equal to 5. The first derivative of a polynomial of degree n is a polynomial of degree n-1. Since the degree of the polynomial decreases by 1 when taking the derivative, the image of L will consist of polynomials of degree less than or equal to 4. Therefore, the image of L is a vector space of dimension 5.
(ii) False.
The statement is false. The trace and determinant of a linear transformation do not provide direct information about the existence of non-trivial fixed points. It is possible for a linear transformation to have a non-trivial fixed point (i.e., a vector other than the zero vector that is mapped to itself), but the trace and determinant values alone do not guarantee it.
(iii) False.
The statement is false. The set of all vectors in R6 whose first entry equals zero does not form a 5-dimensional vector space. The condition that the first entry must be zero imposes a restriction on the vectors, reducing the dimensionality. In this case, the set of vectors will have dimension 5, not 6.
(iv) False.
The statement is false. The pre-image K^(-1)(0) is the set of all polynomials in P(3) whose derivative is equal to 0 (i.e., constant polynomials). The set of constant polynomials forms a vector space of dimension 1 since any constant value can be considered a basis for this vector space.
(v) True.
The statement is true. The intersection of two subspaces V₁ and V₂ is itself a subspace. So, if V₁ and V₂ are arbitrary subspaces of Rⁿ, their intersection V₁ ∩ V₂ is a subspace of Rⁿ.
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BRAINLIEST TO CORRECT
Answers
9514 1404 393
Answer:
60
Step-by-step explanation:
Let x represent the number of members last summer. Then 90% more is 1.9x. We are told this is 114, so we have ...
1.9x = 114
x = 114/1.9 = 60
There were 60 members last summer.
Which of the following is a variable cost for a company that makes bread?
A.
The rent for a warehouse
B.
Bread ingredients
C.
An oven
D.
A salaried worker
Please select the best answer from the choices provided
A
B
C
D
Answers
Answer:
B. Bread ingredients
Step-by-step explanation:
I took the test on Edge 2021 :p
Answer:
B
Step-by-step explanation:
Bread ingredients
5)
Solve for x.
2x + 16 = 3(x - 9)
My Answer:
Answers
Answer:
Step-by-step explanation:
2x+16= 3(x-9)
2x+16= 3x-27
3x-2x^^
16= x-17
16+17
x= 33
Answer:
x=43
Remove parentheses, move the terms, collect the terms, calculate, change the signs!
When individuals all have an equal chance of being selected and all samples
have an equal chance of being selected, it's called a
A. convenience
B. simple random sample
C. cluster
D. stratified random sample
Answers
HELPPPPP
What is the value of x?
Enter your answer in the box.
Answers
Answer:
x = 54°
Step-by-step explanation:
As vertically opposite angles are equal, it can be represented as
2x + 2 = 3x - 52
52 + 2 = 3x - 2x
54 = 1x
Value of x = 54°
Look at the equations below. Find a pair of equations whose lines are perpendicular.
Answers
The pair of equations whose lines are perpendicular is (d) y = 1/6x + 3; y = -6x - 3
Find a pair of equations whose lines are perpendicular.from the question, we have the following parameters that can be used in our computation:
The pair of equations
By definition;
The slopes of perpendicular lines are opposite reciporcals
So, we have
(a) -1/3 and -3 false
(b) -3 and -6 false
(c) 3 and 3 false
(d) 1/6 and -6 true
Hence, the equations are (d) y = 1/6x + 3; y = -6x - 3
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Noah and his children went into a grocery store and where they sell apples for
$1 each and mangos for $2 each. Noah has $20 to spend and must buy at
least 9 apples and mangos altogether. If Noah decided to buy 4 apples,
determine the maximum number of mangos that he could buy. If there areno
possible solutions, submit an empty answer.
Answers
Answer:
8 is the maximum he can get.
Step-by-step explanation:
Good luck!
Hope this helps!
Anyone knows this one ?
Answers
Answer:
looks like it might be 4 but I'm not a 100% sure
what does the dats suggest
Answers
Answer:
the bigger the handspan the more jolly ranchers they can pick up with one hand
Step-by-step explanation:
mei packed 783 strawberries equally into 9 cartons. After giving 4 cartons to her neighbor's , she decided to repack 5 strawberries into each carton. How many cartons of strawberries did she have in the end?
show your work.
Answers
Answer:
87 cartonsStep-by-step explanation:
Each carton contained:
783/9 = 87 strawberriesAfter giving 4 cartons, remaining strawberries are:
87*(9 - 4) = 87*5The number of cartons with 5 strawberries in each:
87*5/5 = 87Where should the value of the square root of 37 (37) be placed on a number line?
Between 3 and 4
Between 4 and 5
Between 5 and 6
Between 6 and 7
Answers
Answer:
Between six and seven
Step-by-step explanation:
I know because the square root of 36 is 6 so the square root of 37 will be a bit bigger.
Make me brainliest if this helps!