The age of children in kindergarten on the first day of school is uniformly distributed between 5 and5.76 years old. A first time kindergarten child is selected at random. Round answers to 4 decimalplaces if possible.a. The mean of this distribution isb. The standard deviation isC. The probability that the the child will be older than 5 years old?d. The probability that the child will be between 5.4 and 5.6 years old ise. If such a child is at the 53rd percentile, how old is that child?years old.CalculatorScratchwork Area
Answers
Given the interval of the distribution as
[tex]5-5.76[/tex]a) To find the mean, we will calculate the mid-value of the interval, this is shown below
[tex]\operatorname{mean}=\frac{5+5.76}{2}=\frac{10.76}{2}=5.38[/tex]Hence, the mean is 5.38
b) To find the standard deviation
[tex]\begin{gathered} SD=\sqrt[]{\frac{(b-a)^2}{12}} \\ b=5.76 \\ a=5 \\ SD=\sqrt[]{\frac{(5.76-5)^2}{12}} \\ =\sqrt[]{\frac{0.76^2}{12}}=0.2194 \end{gathered}[/tex]Hence, the standard deviation is 0.2194
c) The probability that the child will be older than 5 years will be
[tex]P(older\text{ than 5 years)=}\frac{5.76-5}{5.76-5}=\frac{0.76}{0.76}=1.0[/tex]Hence, the probability that the child will be older than 5 years is 1.0
d) The probability that the child age is between 5.4 and 5.6 years old will be
[tex]P(\text{ between 5.4 and 5.6 years old)=}\frac{5.6-5.4}{5.76-5}=\frac{0.2}{0.76}=0.2632[/tex]Hence, the probability that the child age is between 5.4 and 5.6 years old is 0.2632
e) If the child is at the 53rd percentile, the age of the child will be
[tex]\begin{gathered} At\text{ 53rd percentile the age}\Rightarrow5+\frac{53}{100}(5.76-5) \\ =5+0.53(0.76) \\ =5.4028 \end{gathered}[/tex]Hence, at the 53rd percentile, the age of the child is 5.4028 years old
Related Questions
Pythagorean Theorem• Create a real-world problem involving threelengths that form a right triangle• Give the measurement of the "legs", then solvefor the missing side
Answers
SOLUTION
Find the perimeter of a rectangle whose length is 150 m and the diagonal is 170 m.
The problem can be modeled using the figure below
Notice that the triangle formed is a right triangle:
Therefore using Pythagorean theorem it follows:
[tex]x^2+150^2=170^2[/tex]Solve for x
[tex]\begin{gathered} x^2=170^2-150^2 \\ x^2=6400 \\ x=80 \end{gathered}[/tex]Therefore the other leg no miss
PLEASE HURRY ASAP
Which of the following could be an algebraic expression for the total cost of dinner, less a $10 coupon, divided by 4 people?
(x − 10) ÷ 4
4x − 10
10 − 4x
4x(10)
Answers
Answer:
(x − 10) ÷ 4
Step-by-step explanation:
So, the equation is trying to figure out how much each person is paying. x = the whole dinner. Then, you take away $10 from the total cost. Then, with that discounted cost, you're dividing by 4 people to figure out how much each person is paying.
Pick a number 1 through 20. Now do it again.Now do it a third time. I am going to writedown my prediction of what numbers youpicked. Assuming no magic was used, what isthe probability I guessed right? Put youranswer in fraction form. (Note: Numbers CANbe used more than once.)
Answers
There are 20 numbers to choose from. Thus, the total sample space is 20.
If you choose one number, the probability of choosing that number is:
[tex]\frac{1}{20}[/tex]Now, if after choosing one number in the first round, you proceed to choose another number in the second round.
The probability of choosing a number for this second round will be:
[tex]\frac{1}{20}[/tex]Note that you are allowed to repeat numbers, so therefore, this is a probability problem with replacement.
For the third round, you choose another number from 1 to 20. The probability is the same as the previous two:
[tex]\frac{1}{20}[/tex]The probability that a person guesses these 3 numbers is the same as the probability of actually choosing the numbers randomly.
Thus the final answer:
[tex]\frac{1}{20}\times\frac{1}{20}\times\frac{1}{20}=\frac{1}{8000}[/tex]Therefore, the final answer is:
[tex]\frac{1}{8000}[/tex]Which graph best represents 16≤x²+y²≤25
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The most appropriate choice for annular region will be given by
This graph represents an annular region shown in the figure
What is annular region?
Annular region represents the space between two concentric circles of different radii.
Equation of annular region centered at (0, 0) is
[tex]a^2 \leq x^2+y^2\leq b^2[/tex]
Here,
[tex]x^2 + y^2\geq 16\\x^2 + y^2 \geq 4^2\\[/tex]
It denotes the outside of a circle of radius 4 centered at (0, 0)
[tex]x^2 + y^2\leq 25\\x^2 + y^2 \leq 5^2\\[/tex]
It denotes the inside of a circle of radius 5 centered at (0, 0)
So the complete graph is being attached here.
This region is known as annular region
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Find the value of f(7) y = f(x) 10 6 4 -10 -8 -6 -4. -2 4 10 -4 -6 GO -10 Answer: Submit Answer
Answers
Answer:
f(7) = -5
Step-by-step explanation:
To find f(7), we would need to first find on the graph 7 on the x-axis.
We would next need to see where 7 on the x-axis meets with the graph. In this case, we would go down.
Now that we see where 7 on the x-axis meets with the graph, we would now look at the number on the y- axis that spot on the graph matches with.
In this case, we would go left from the graph all the way to the y-axis, where the correspo ding number would be -5.
what is 3 +(-4) on a number line
Answers
HELP ASAP I NEED ANSWER NOWW IT'S MISSING PLEASE HELP 50 POINTS
Answers
Answer:
[tex]\textsf{Let $\boxed{x}=\boxed{\textsf{The total dollar amount of all phone sales}}$}\:.[/tex]
[tex]\textsf{Let $\boxed{y}=\boxed{\textsf{The total dollar amount of all computer sales}}$}\:.[/tex]
System of Equations
[tex]\boxed{x + y = 3600}[/tex]
[tex]\boxed{0.04x + 0.06y = 178}[/tex]
Step-by-step explanation:
Given information:
4% commission on the total dollar amount of all phone sales.6% commission on all computer sales.Total sales = $3600Total commission = $178Define the variables:
Let x = The total dollar amount of all phone sales.Let y = The total dollar amount of all computer sales.Convert the percentages into decimal form:
[tex]\implies \sf 4\%=\dfrac{4}{100}=0.04[/tex]
[tex]\implies \sf 6\%=\dfrac{6}{100}=0.06[/tex]
Therefore, the system of equations that could be used to determine the dollar amount of phone sales and computer sales is:
[tex]\begin{cases}x + y = 3600\\0.04x + 0.06y = 178\end{cases}[/tex]
Solving the system of equations
Rewrite the first equation to isolate y:
[tex]\implies x=3600-y[/tex]
Substitute the expression for x into the second equation and solve for y:
[tex]\implies 0.04(3600-y)+0.06y=178[/tex]
[tex]\implies 144-0.04y+0.06y=178[/tex]
[tex]\implies 144+0.02y=178[/tex]
[tex]\implies 0.02y=34[/tex]
[tex]\implies y=1700[/tex]
Therefore, Cameron made $1,700 of computer sales.
Substitute the found value of y into the first equation and solve for x:
[tex]\implies x+1700=3600[/tex]
[tex]\implies x=1900[/tex]
Therefore, Cameron made $1,900 of phone sales.
Find the percent change. Round to the nearest tenth of a percent when necessary. From 50 to 94.
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Percent change of 88%
1) Consider 50 as equivalent to 100% as well as 94 to x.
50 ----------- 100%
94 ------------ x
2) Now we can set the ratios and cross multiply then:
[tex]\begin{gathered} \frac{50}{94}=\frac{100}{x} \\ 50x=94\cdot100 \\ 50x=9400 \\ \frac{50x}{50}=\frac{9400}{50} \\ x=188 \\ \end{gathered}[/tex]So 94 corresponds to 188%. Then we can see that there was an increase. Since 94 >50.
But we need to subtract from 100% to find out the percent change from 50 to 94.
188%-100%= 88%
3) Hence, the answer is an increase of 88%
Zan took her dog, Simba, to the dog park on Saturday afternoon. There were more than 20 dogs running around the park when they arrived. Determine which inequality describes the dogs at the park. d < 20 d > 20 d ≥ 20 d ≤ 20
Answers
Answer:
Number 2 is the answer to this question.
The inequality to represent the given scenario is d>20. Therefore, option B is the correct answer.
What are inequalities?Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.
Given that, there were more than 20 dogs running around the park when they arrived.
Let the number of dogs be d.
So, the inequality is d>20
Therefore, option B is the correct answer.
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Hello! Question is in photo please help me out.
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The value of x for the given similar triangle will be 5 units.
What is the similarity?If two objects are having the same shape then they will be termed as similar. So in mathematics, if two figures have the same shapes, lines or angles then they are called similar.
If two figures have three sides similar then they will be similar by side-by-side property which is written as SSS.
From the similarity concept, the value of x will be calculated as:-
( 10 / x ) = ( 6 / 3 )
10 = 2x
x = 10 / 2
x = 5
Therefore, the value of x for the given similar triangle will be 5 units.
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A sequence is defined by the recursive formula f(n + 1) = 1.56(0). Which sequence could be generated using the formula? 0 -12 -18, -27 ! EE 0 -20, 30, -45, -18, -16.5, -15, ... 0-16, -17.5, -19, ...
Answers
f(n+1) is
[tex]f(n+1)=\frac{3}{2}^nf(n-(n-1)[/tex]Therefore, substitutig, we get, option c.
| Log Out Which function has a y-intercept that is equivalent to the y intercept of 3x - 4y = 16? A y = 4x + 1 B y = - 4x + 16 © y = 3x + 4 D y = 2x - 4
Answers
The slope-intercept form of a line is given by:
y = mx + b
where:
m = slope
b = y-intercept
From:
[tex]\begin{gathered} 3x-4y=16 \\ 4y=3x-16 \\ y=\frac{3}{4}x-4 \end{gathered}[/tex]Therefore, the y-intercept of this line is -4.
Hence, the correct option is:
[tex]y=2x-4[/tex]. BUILD PERSEVERANCE Factor the algebraic
expression 7.2x²y-0.9xy².
Answers
Please help ASAP
Question is attached below
Answers
Answer:
√30/4
I Hope that This Helped!
A doll’s house has an original price of $x. It is sold for $350 after its original price has been decreased by 5% and then by 10%. Find x.
Answers
Answer:
Step-by-step explanation:
0.95x*0.9=0.855
350/0.855=409.35
x=409.35
Nicholas earned $2,000.00 working over the summer and wants to put the money into a savings account. A savings account at bank A earns 5% simple interest and a savings account at bank B earns 4% interest compounded quarterly. If Nicholas plans to deposit the $2,000.00 and leave it in the account for 4 years, at which bank would he earn more interest? A. The interest earned cannot be calculated from the given information. B. The interest earned at both banks will be the same. C. bank A D. bank B
Answers
Answer:
Choice C
==> Bank A
Step-by-step explanation:
Principal P = $2000
Bank A calculation
Simple Interest at 5% for 4 years = Prt = 2000 x 5/100 x 4 = $400
Bank B Calculation
At 4% interest compounded quarterly, the accrued value(Principal + Interest) is given by the formula:
[tex]A = P(1 + r/n)^{nt}[/tex]
where
P = principal
r = annual interest rate as percentage
n = number of compounding per year
t = number of years
We have r = 4/ 100 = 0.04
n = 4 since interest is computed quarterly or 4 times a year
t = 4 years
[tex]A = 2000 ( 1 + 0.04/4)^{(4) \cdot (4)}\\\\A = 2000 (1.01)^{16} = \$2,345.16\\\\\text{Interest } = 2345.16 - 2000 = $345.16[/tex]
Since interest earned at bank A (400) > interest earned at bank B(345.16), the answer would be C. ==> Bank A
sixty and four hundredths in decimal form
Answers
60 + 0.04 = 60.04
The answer is 60.04
In the the diagram to the right, sphere O with radius 5 cm is intersected by a plane 4 cm from center O. Find the radiusof the cross section O A
Answers
Since a right triangle is formed, the radius of the cross-section is the missing side of the triangle.
Apply the Pythagorean theorem:
C^2 = a^2 + b^2
Where:
c = hypotenuse = 5
a & b = the other 2 legs of the triangle = 4 and x
Replacing:
5^2 = 4^2 + x^2
solve for x ( radius of the cross-section)
25 = 16 + x^2
25-16 = x^2
9 = x^2
√9 = x
x = 3 cm
i need help with this please check work when you finish answering
Answers
ANSWER :
The answer is A. 2π
EXPLANATION :
Period can be determine by getting the measurement of one complete cycle.
From the graph.
One complete cycle is the blue mark.
Therefore, the period is 2π
Research one of the methods listed above or another method of your choice for factoring trinomials of the form ax² + bx + c.State the method you are using and explain the process of factoring a trinomial in words, modeling the process by using examples that contain all the steps to factor the trinomial
Answers
The grouping (a · c) method is another method for factoring trinomials of the form ax² + bx + c.
The process of factoring a trinomial using the grouping method is,
First, find a GCF and then factor it out.The coefficient of the leading phrase an is then multiplied by the constant term c. List the elements of this product (a · c) to discover the pair of factors, f1, and f2, that add to b, the middle-term coefficient. When c is positive, the sign of the components of (a · c) is the same - Find the pair of factors that adds to b if the middle-term bx is positive. If the middle-term bx is negative, both factors are negative. When c is negative, the elements of (a · c) have the inverse sign - Find the pair of factors that subtracts to b. The largest of these factors has the same sign as the middle term.Rewrite the middle term bx with the components f1 and f2 from Step 2. The phrase currently has four terms: ax² + bx + c = ax² + f1x + f2x + cThen, as illustrated, group the expression's terms into binomial pairs: (ax² + f1x) + (f2x + c) Then, for each pair, factor out a GCF The terms will have a common binomial factor if the equation can be factored by grouping. To write the factorization, subtract the common binomial factor.Finally, double the result to confirm.Learn more about factoring trinomials at
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anne took a test in chemistry she scored 20 markes out of 50 work out her percentge mark
Answers
Answer:
40%
Step-by-step explanation:
to change a fraction to a percentage multiply by 100% , that is
[tex]\frac{20}{50}[/tex] × 100% = 0.4 × 100% = 40%
Answer:
40%
Step-by-step explanation:
Total Mark = 50Mark obtained = 20Percentage = (Mark obtained/Total mark) x 100(20/50) x 100(2/5) x 1002 x 2040%yes I am having problems learning about equations
Answers
If we have a function [Equation] it would look something like this:
3x+y=4
In order to solve for both values and graph it [If that's what you are trying to do], you solve for y and then replace values [Of your own choosing, or they are given to be studyed] in x, after we replace the values in x, we are going to have the respective value of y.
From our previous example, it would be:
y = -3x+4
So, when we start replacing the values of X, we will get the respective values for Y, let's try doing it from -3 to 3.
x = -3 => y = -3(-3)+4 => y = 13
x = -2 => y = -3(-2)+4 => y = 10
x = -1 => y = -3(-1)+4 ) => y = 7
x = 0 => y = -3(0)+4 => y = 4
x = 1 => y = -3(1)+4 => y = 1
x = 2 => y = -3(2)+4 => y = -2
x = 2 => y = -3(3)+4 => y = -5
From this, we would end up with the following points:
(-3, 13)
(-2, 10)
(-1, 7)
(0, 4)
(1, 1)
(2,
A) list roots and multiplicity.B) domain and range C) degree : 4 D) equation (show work by solving for a)
Answers
ANSWER :
A. (-3, 0) multiplicity 1, (-1, 0) multiplicity 1, (1, 0) multiplicity 1 and (3, 0) multiplicity 1.
B. Domain : (-∞, ∞)
C. Range : (-16, ∞)
D. Degree : 4
E. f(x) = (x + 3)(x + 1)(x - 1)(x - 3)
EXPLANATION :
From the problem, we have a graph in the illustration.
A. Roots are the points in which the graph intersects the x-axis.
Multiplicity means how many times the graph intersects at the specific point.
Roots :
The graph intersects at (-3, 0) multiplicity 1, (-1, 0) multiplicity 1, (1, 0) multiplicity 1 and (3, 0) multiplicity 1.
B. Domain and Range.
Domain is the set of x-values in the graph.
Range is the set of y-values in the graph.
From the graph,
Domain :
x values are all real numbers. (-∞, ∞)
Range :
y values are from y = -16 to the positive infinity. That will be (-16, ∞)
C. Degree : 4
D. The equation of a function with a degree of 4 is given by :
[tex]f(x)=a(x-b)(x-c)(x-d)(x-e)[/tex]where a = coefficient
b, c, d and e are the roots of the function.
Since we already solved for the roots, that will be :
b = -3, c = -1, d = 1 and e = 3
The equation will be :
[tex]f(x)=a(x+3)(x+1)(x-1)(x-3)[/tex]Plug in the given point (0, 9) then solve for the value of "a"
[tex]\begin{gathered} 9=a(0+3)(0+1)(0-1)(0-3) \\ 9=a(3)(1)(-1)(-3) \\ 9=9a \\ a=\frac{9}{9} \\ a=1 \end{gathered}[/tex]The equation will be :
[tex]f(x)=(x+3)(x+1)(x-1)(x-3)[/tex]I need over y-axis, y = x, and y = -x
Answers
Given:
(3,2)
Reflection on x axis: (3,-2)
Reflection on y-axis: (-3,2)
Reflection of y=x : (2,3)
Reflection on y=-x : (-2,-3)
A = {2, 3, 4, 5, 6, 7}
B = {2, 4, 7, 8)
C = {2,4}.
Which of the following mathematical statements is true?
Answers
The mathematical statement is as follows:
(a) B ⊄ A
(b) C ⊂ A
(c) B ⊄ C
(d) ∅ ⊂ B
(e) C ⊂ C
(f) C ⊂ B
What is meant by sets?A set contains elements or members that can be mathematical objects of any kind, including numbers, symbols, points in space, lines, other geometric shapes, variables, or even other sets. A set is a mathematical model for a collection of various things.
The way that sets are represented by a person is always the same: as a group of clearly defined objects or elements. A capital letter designates a set. The cardinal number of a set is the number of elements in the finite set.
Let A = {2, 3, 4, 5, 6, 7} B = {2, 4, 7, 8) and C = {2, 4}.
The mathematical statement is as follows:
(a) B ⊄ A
(b) C ⊂ A
(c) B ⊄ C
(d) ∅ ⊂ B
(e) C ⊂ C
(f) C ⊂ B
belongs to ⊂ sign is used if an element belongs to the given set and vice versa.
The complete question is:
Let A = {2, 3, 4, 5, 6, 7} B = {2, 4, 7, 8) C = {2, 4}. Fill in the blanks by ⊂ or ⊄ to make the resulting statements true.
(a) B __ A
(b) C __ A
(c) B __ C
(d) ∅ __ B
(e) C __ C
(f) C __ B
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3. Jamie's grade has increased 42 points over the last 6 weeks because he
has turned in homework and done a few retakes. If his grade increased the
same amount each week, what integer represents his change in grade?
Answers
Answer:
7
Step-by-step explanation:
(x = increase each week)
(6=weeks)
(42= total Grade Change)
Linear equation:
42=6x
Solved:
x=7
please helppppppppppppppppppppppppppppppp!
Answers
Answer:
(9 x 27) x 5
Step-by-step explanation:
First we have to figure out the powers. 3 To the power of 2 is 9 and 3 to the power of 3 is 27 so we first multiply that and later multiply 5
And so it’s 3^8 • 3^10
And the you add the exponents together so it’s 3^8+10
So then it would be 3^18
But simplified would be 387420489
The five number summary of a dataset is given as
0, 4, 8, 12, 17
An observation is considered an outlier if it is below:
An observation is considered an outlier if it is above:
Answers
An observation is considered an outlier if it is below -16.75
An observation is considered an outlier if it is above 33.25
Extremely low or high values in a data set are considered outliers. Outliers are a product of statistical observational errors and variability. They frequently produce significant statistical issues, hence they are frequently left out of the study.
We must think about if it meets the following criteria in order to identify an outlier:
Q₁ - 1.5 (IQQ) ⇒ for lower value
Q₃ + 1.5 (IQR) ⇒ for higher value
Q₁ stands for the lower quantile, Q₃ for the higher quantile, and IQR for the inter-quantile range. Using the previous data,
Q₁ and Q₃ come from:
Q₁ = (0 + 4) / 2 = 4 / 2 = 2
Q₃ = (12 + 17) / 2 = 29 / 2 = 14.5
IQR = Q₃ - Q₁ = 14.5 - 2 = 12.5
(a) An observation is considered an outlier if it is below:
Q₁ - 1.5 (IQR) = 2 - 1.5 (12.5) = 2 - 18.75 = -16.75
An outlier is a number that is less than -16.75
(b) An observation is considered an outlier if it is above:
Q₃ + 1.5 (IQR) = 14.5 + 1.5 (12.5) = 14.5 + 18.75 = 33.25
An outlier is a number that is greater than 33.25
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Solve for x:
3(x+1)-22+13=12
Answers
Answer:
x=6
Step-by-step explanation:
3 (x+1) -22 +13=12
3x+3 -22+13=12
3x+3-9=12
3x-6= 12
3x= 12+6
3x= 18
x= 18/3
x= 6
For each relation, decide whether or not it is a function.
Answers
Relation 1 and Relation 3 are functions while Relation 2 and Relation 4 are not functions.
Function is a relation which maps a set to another set with some criteria.
It includes a property that one element of the domain set should only be related to exactly one element in the range set. That is, same element from the domain cannot be related to different elements in the range. Also all elements in the domain should have images in the range also.
Now we will check all the relations given one-by-one.
In relation 1, the relations are:
Chair ---------> 0
Pencil --------> 0
Paper ---------> 4
Star ------------> 1
Here All the domain elements are mapped only once to one element from the range. So it is a function.
In relation 2, the relations are:
4 ----------------> 5
4 ----------------> 9
0 ----------------> -9
1 -----------------> 4
8 -----------------> -4
Here 4 is mapped to both 5 and 9. So it does not satisfy the definition of a function and hence is not an function.
In relation 3, the relations are:
z -----------------> c
k -----------------> a
a -----------------> k
c ------------------> c
Here also all elements in the domain are mapped only once to an element from the range. So it is a function.
In relation 4, the relations are:
-4 -----------------> m
-4 -----------------> d
-4 -----------------> c
9 -----------------> s
Here, -4 is mapped to m, d and s. So it cannot be a function as it has more than one images.
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