The amount of pollutants that are found in waterways near large cities is normally distributed with mean 9.9 ppm and standard deviation 1.8 ppm. 39 randomly selected large cities are studied. Round all answers to 4 decimal places where possible.
Answers
ANSWER:
a. 9.9, 1.8
b. 9.9, 0.2882
c. 0.5239
d. 0.6368
e. No
f.
Q1 = 9.7069
Q3 = 10.0931
IQR = 0.3862
STEP-BY-STEP EXPLANATION:
a.
X ~ N (9.9, 1.8)
b.
x ~ N (9.9, 1.8/√39)
x ~ N (9.9, 0.2882)
c.
P(X > 9.8)
We calculate the probability as follows:
[tex]\begin{gathered} P\left(X>9.8\right)=1-p\left(\frac{X-9.9}{1.8}<\frac{9.8-9.9}{1.8}\right) \\ \\ P\left(X>9.8\right)=1-p(z<-0.06) \\ \\ P\left(X>9.8\right)=1-0.4761 \\ \\ P\left(X>9.8\right)=0.5239 \end{gathered}[/tex]d.
p (x > 9.8)
We calculate the probability as follows:
[tex]\begin{gathered} P\left(x>9.8\right)=1-p\left(\frac{X-9.9}{\frac{1.8}{\sqrt{39}}}<\frac{9.8-9.9}{\frac{1.8}{\sqrt{39}}}\right) \\ \\ P\left(x>9.8\right)=1-p(z<-0.35) \\ \\ P\left(x>9.8\right)=1-0.3632 \\ \\ P\left(x>9.8\right)=0.6368 \end{gathered}[/tex]e.
No, you don't need to make the assumption
f.
Q1 = 0.25
In this case the value of z = 0.25, so we look for the closest value in the normal table, like this:
Thanks to this, we make the following equation:
[tex]\begin{gathered} -0.67=\frac{x-9.9}{\frac{1.8}{\sqrt{35}}} \\ \\ x-9.9=-0.19311 \\ \\ x=-0.1931+9.9 \\ \\ x=9.7069 \\ \\ Q_1=9.7069 \end{gathered}[/tex]Q3 = 0.75
In this case the value of z = 0.75, so we look for the closest value in the normal table, like this:
Therefore:
[tex]\begin{gathered} -0.67=\frac{x-9.9}{\frac{1.8}{\sqrt{39}}} \\ \\ x-9.9=0.1931 \\ \\ x=0.1931+9.9 \\ \\ x=10.0931 \\ \\ Q_3=10.0931-9.7069 \end{gathered}[/tex]Therefore, the interquartile range would be:
[tex]\begin{gathered} IQR=Q_3-Q_1 \\ \\ IQR=10.0931-9.7069 \\ \\ IQR=0.3862 \end{gathered}[/tex]
Related Questions
Hi I am really confused on this problem and would like help on solving it step by step
Answers
Given:
An exponential function represents the graph of some of the functions given in the option.
Required:
The correct equation represents the given function.
Explanation:
The graph of the function
[tex]y\text{ = 2\lparen}\sqrt{0.3})^x[/tex]is given as
Also, the graph representing the function
[tex]y=2e^{-x}[/tex]is given as
Answer:
Thus the correct answer is option B and option D.
There are 152 students at a small school and 45 of them are freshmen. What fraction of the students are freshmen? Use "/" for the
fraction bar. Do not use spaces in your answer.
Answers
Course ListScore! OU TUUTUTZu anisweredQuestion 11In A XYZ, the sum of the measures of ZX and Y are 55°. What is the measure of ZZ?ZZ=?
Answers
To solve that question we must remember that the sum of all internal angles of a triangle is 180°, we can say that
[tex]\angle X+\angle Y+\angle Z=180[/tex]That's a rule! it's always true.
The problem says that
[tex]\angle X+\angle Y=55[/tex]Then let's use it in our equation!
[tex]\begin{gathered} \operatorname{\angle}X+\operatorname{\angle}Y+\operatorname{\angle}Z=180 \\ \\ 55+\operatorname{\angle}Z=180 \end{gathered}[/tex]Now we can solve it for Z
[tex]\begin{gathered} 55+\angle Z=180 \\ \\ \angle Z=180-55 \\ \\ \angle Z=125° \end{gathered}[/tex]Therefore the measure of Z is 125°
resents "three lessWrite the expression -- 5x(4 + 3x) using words,the sum of negative five times a number andfour minus three times the numberthe product of negative five times a numberand the quantity four plus three times thenumberthe product of three times a number plus thequantity four and five times the numberpresents "thetwo less than theDONE
Answers
Given:
[tex]=-5x(3x+4)[/tex]Sol:.
The product of negative five times a number and the quantity four plus three times the number.
A motor scooter travels 22 mi in the same time that a bicycle covers 8 mi. If the rate of the scooter is 6 mph more than twice the rate of the bicycle, find both rates.The scooter’s rate is ____ mph. (Type an integer or a decimal)
Answers
Let's use the variable x to represent the speed of the scooter and y to represent the speed of the bicycle.
For a same time t, the scooter travels 22 mi and the bicycle travels 8 mi, so we can write the following equation:
[tex]\begin{gathered} distance=speed\cdot time\\ \\ 22=x\cdot t\\ \\ t=\frac{22}{x}\\ \\ 8=y\cdot t\\ \\ t=\frac{8}{y}\\ \\ \frac{22}{x}=\frac{8}{y} \end{gathered}[/tex]Then, if the rate of the scooter is 6 mph more than twice the rate of the bicycle, we have the following equation:
[tex]x=2y+6\\[/tex]Using this value of x in the first equation, let's solve it for y:
[tex]\begin{gathered} \frac{22}{2y+6}=\frac{8}{y}\\ \\ 22y=8(2y+6)\\ \\ 22y=16y+48\\ \\ 6y=48\\ \\ y=8\text{ mph} \end{gathered}[/tex]Now, calculating the value of x, we have:
[tex]\begin{gathered} x=2y+6\\ \\ x=16+6\\ \\ x=22\text{ mph} \end{gathered}[/tex]Therefore the scooter's rate is 22 mph and the bicycle's rate is 8 mph.
Write a formula for the function in the image below.
Answers
The vertex form of a quadratic function is:
[tex]f(x)=a(x-h)^2+k[/tex]Where (h, k) is the vertex. Looking at the graph, the vertex is at (-1, 2), then:
[tex]\begin{gathered} h=-1 \\ k=2 \\ \Rightarrow f(x)=a(x+1)^2+2 \end{gathered}[/tex]Finally, to find "a" we use the fact that 1 is the y-intercept of the graph (where the function is evaluated at x = 0). Then:
[tex]\begin{gathered} f(0)=1\Rightarrow a(0+1)^2+2=1 \\ a=1-2 \\ \Rightarrow a=-1 \end{gathered}[/tex]The final form of the function is:
[tex]f(x)=-(x+1)^2+2[/tex]is the number 6.35 a whole number and a integer
Answers
Natural numbers are all numbers 1, 2, 3, 4… They are the numbers you usually count and they will continue on into infinity. This includes all numbers that can be written as a decimal.
Hence, 6.35 is a natural number. It is natural number, whole number, integer, and rational number.
Problem Solving
20. A city is building 3 parks in a new subdivision. Each park
will be 1.25 acres. How many total acres will the 3 parks
be?
Answers
According to the solving all three parks will cover surface of 37.5 acres in total.
How much area of land is in acres?The imperial and US customary systems both utilize the acre as a unit of land area. An acre is approximately equal to approximately 4,047 [tex]m^{2}[/tex].
How much area will 3 parks cover?Area covered by 3 parks can be calculated by multiplying the area of one park by three.
so, area covered by 3 parks=3×1.25
area covered by 3 parks=3.75
As you know multiplication is the repeated addition so we can obtain the same results by adding 1.25 three times to itself.
These three parks will cover total area of 3.75acres.
To know more about area visit:
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3. For the polynomial: ()=−2(+19)3(−14)(+3)2, do the following:A. Create a table of values that have the x-intercepts of p(x) in the first column and their multiplicities in the second column.B. State the degree and end behavior for p(x). C. Hand sketch a rough graph of p(x). You should have the x-int labeled, but you do not need tick marks for all numbers in between.
Answers
Part A. We are given the following polynomial:
[tex]\mleft(\mright)=-2\mleft(+19\mright)^3\mleft(-14\mright)\mleft(+3\mright)^2[/tex]This is a polynomial of the form:
[tex]p=k(x-a)^b(x-c)^d\ldots(x-e)^f[/tex]The x-intercepts are the numbers that make the polynomial zero, that is:
[tex]\begin{gathered} p=0 \\ (x-a)^b(x-c)^d\ldots(x-e)^f=0 \end{gathered}[/tex]The values of x are then found by setting each factor to zero:
[tex]\begin{gathered} (x-a)=0 \\ (x-c)=0 \\ \text{.} \\ \text{.} \\ (x-e)=0 \end{gathered}[/tex]Therefore, this values are:
[tex]\begin{gathered} x=a \\ x=c \\ \text{.} \\ \text{.} \\ x=e \end{gathered}[/tex]In this case, the x-intercepts are:
[tex]\begin{gathered} x=-19 \\ x=14 \\ x=-3 \end{gathered}[/tex]The multiplicity are the exponents of the factor where we got the x-intercept, therefore, the multiplicities are:
Part B. The degree of a polynomial is the sum of its multiplicities, therefore, the degree in this case is:
[tex]\begin{gathered} n=3+1+2 \\ n=6 \end{gathered}[/tex]To determine the end behavior of the polynomial we need to know the sign of the leading coefficient that is, the sign of the coefficient of the term with the highest power. In this case, the leading coefficient is -2, since the degree of the polynomial is an even number this means that both ends are down. If the leading coefficient were a positive number then both ends would go up. In the case that the leading coefficient was positive and the degree and odd number then the left end would be down and the right end would be up, and if the leading coefficient were a negative number and the degree an odd number then the left end would be up and the right end would be down.
Part C. A sketch of the graph is the following:
If the multiplicity is an odd number the graph will cross the x-axis at that x-intercept and if the multiplicity is an even number it will tangent to the x-axis at that x-intercept.
Which graph represents the equation X =2?
Answers
ANSWER and EXPLANATION
We are given x = 2.
To plot the graph of x = 2, it is important to note that the value of x does not change for this equation.
x is always 2 regardless of the value of y.
This means that we are going to plot a straight line that will straight up (and down as well) at x = 2.
The graph therefore is:
If RT = 36, RS = 2x + 3 and ST = 7x + 6, find RSand ST.
Answers
We know that RT=36 and that RS=2x+3 and ST=7x+6. We notice that
[tex]RT=RS+ST[/tex]Then, plugging the corresponding values and expressions we have
[tex]36=(2x+3)+(7x+6)[/tex]Solving this equation for x,
[tex]\begin{gathered} 36=(2x+3)+(7x+6) \\ 36=2x+3+7x+6 \\ 36=9x+9 \\ 36-9=9x \\ 27=9x \\ x=\frac{27}{9} \\ x=3 \end{gathered}[/tex]Then te value of x is 3.
Once we have the value of x we are able to find the value of RS and ST, we just have to substitute said value in the expressions. Then
[tex]\begin{gathered} RS=2(3)+3=6+3=9 \\ ST=7(3)+6=21+6=27 \end{gathered}[/tex]Therefore RS=9 and ST=27.
what is the effect on the graph of the function f(x) = x² when f(x) is changed to f(x + 8) ?A) shifted up B) shifted left C) shifted right D) shifted down
Answers
Solution
- In order to solve the question, we need to understand the rules guiding the translation of graphs. This rule is given below:
[tex]\begin{gathered} f(x)\to f(x+h) \\ \text{ If h is positive, then, the graph is shifted to the left} \\ \text{ If h is negative, then, the graph is shifted to the right} \end{gathered}[/tex]- The question given to us has h = 8. This means that h is positive, therefore, the graph of f(x) must be shifted to the left by 8 units
Final Answer
The answer is "Shifted Left" (OPTION B)
When point A'(-2,4) is reflected over they-axis, where is the image A"?(2,-4)(2,4)(4,-2)
Answers
Answer:
Explanation
Given a coordinate (x, y), If this coordinate reflected over y axis, the resulting coordinate will be expressed as (-x, y). Note that only the sign of the x coordinate axis was
Two planes fly in opposite directions. One travels 450 mi/h and the other 550 mi/h. How long will it take before they are 4,000 mi apart? The planes must fly Answer hours before they will be 4,000 mi apart.
Answers
Given,
The speed of first plane is 450 miles per hour.
The speed of second plane is 550 miles per hour.
The total distance between plane required is 4000 miles.
As, the planes are moving in opposite direction, then distance cover by both is must be added.
Number of distance both plane becomes apart in one hour is,
[tex]\text{Number of distance = 450+550=1000 miles.}[/tex]The Number of hours required to complete 4000 miles is,
[tex]\text{Time=}\frac{4000}{\text{1}000}=4\text{ hours}[/tex]Hence, it will take 4 hours before they are 4,000 miles apart.
What is the GCF of 42 and 70
Answers
To find the GCF of 42 and 70,
List the prime factors of each numbers,
The prime factors of 42 and 70 is
[tex]\begin{gathered} 42\Rightarrow2\times3\times7 \\ 70\Rightarrow2\times5\times7 \end{gathered}[/tex]42 and 70 share the common factors below
[tex]2\text{ and 7}[/tex]Multiply the common factors to find the GCF
The GCF of 42 and 70 will be
[tex]\text{GCF}=2\times7=14[/tex]Hence, the GCF of 42 and 70 is 14
Kui Software tinite Algebra 2 Compound Inequalities Solve each compound inequality and graph its solution. Name Samanthace ballos Date valgan 1) n+15-3 or-in- Perut k 2) ohs- n2-3-1
Answers
n<4 or n>8
10) Let's solve that compound inequality:
12 + 4n> 44 or 10 -12n> -38
2) Solving each one separately
12 + 4n > 44 Subtracting 12 from both sides
4n > 44 -12
4n > 32 Divide both sides by 4
n> 8
10 -12n> -38 Subtracting 10 from both sides
-12n > -38 -10
-12n > -48 Divide both sides by -1 and flipping the sign
n < 4
3) Graphing the solution, we have:
Notice that for that, we'll use open dots since 4 and 8 are not included.
write a quadratic fuction f whose zeros are -3 and -13
Answers
The zeros of a quadratic function are the points where the graph cuts the x axis.
If one zero is - 3, it means that
x = - 3
x + 3 = 0
Thus, one of the factors is (x + 3)
If another zero is - 13, it means that
x = - 13
x + 13 = 0
Thus, one of the factors is (x + 13)
Thus, the quadratic function would be
(x + 3)(x + 13)
We would open the brackets by multiplyingeach term inside one bracket by each term inside the other. Thus, we have
x * x + x * 13 + 3 * x + 3 * 13
x^2 + 13x + 3x + 39
x^2 + 16x + 39
Thus, the quadratic function is
f(x) = x^2 + 16x + 39
Write the expression as a sum and/or difference of logarithms. Express powers as factors.log7(343x)
Answers
Recall the product rule of logarithms
[tex]\log _b(xy)=\log _b(x)+\log _b(y)[/tex]Apply the product rule to the given and we get
[tex]\log _7(343x)=\log _7(343)+\log _7(x)[/tex]use the quadratic formula to solve the equation2x^2-1=11xthe solution(s) are/is x=?
Answers
Answer:
[tex]\begin{gathered} x=\frac{1}{4}(11-\sqrt[]{129}) \\ \\ x=\frac{1}{4}(11+\sqrt[]{129}) \end{gathered}[/tex]Explanation:
To solve the equation we first subtract 11x from both sides to write
[tex]2x^2-11x-1=0[/tex]Now we use the quadratic formula in which a = 2, b = -11, and c = -1
[tex]x=\frac{11\pm\sqrt[]{11^2-4(2)(-1)}}{2\cdot2}[/tex][tex]x=\frac{11\pm\sqrt[]{11^2-4(2)(-1)}}{2\cdot2}[/tex]which gives
[tex]\begin{gathered} x=\frac{1}{4}(11-\sqrt[]{129}) \\ x=\frac{1}{4}(11+\sqrt[]{129}) \end{gathered}[/tex]which are our solutions!
10 in.What is the volume of atriangular pyramid that is10 in. tall and has a basearea of 9 square in.?9cubic inchesVolume of a pyramid: V = {Bh (Where "B" is the area of the pyramid's base.)=
Answers
You have to calculate the volume of a pyramid with a height of 10in and a base area of 9 in²
The volume of a pyramid is equal to one third the product of the area of the base (B) and the height (h), following the formula:
[tex]V=\frac{1}{3}Bh[/tex]Replace the values on the formula and calculate the volume:
[tex]\begin{gathered} V=\frac{1}{3}\cdot9\cdot10 \\ V=30in^3 \end{gathered}[/tex]The volume is equal to 30 cubic inches.
A manufacturer knows that their items have a normally distributed length, with a mean of 8.4 inches, and standard deviation of 1.4 inches.If one item is chosen at random, what is the probability that it is less than 11.8 inches long?
Answers
We will make use of the z-score to calculate the probability. The z-score is calculated using the formula:
[tex]z=\frac{x-\mu}{\sigma}[/tex]where x is the score, μ is the mean, and σ is the standard deviation.
From the question, we have the following parameters:
[tex]\begin{gathered} x=11.8 \\ \mu=8.4 \\ \sigma=1.4 \end{gathered}[/tex]Therefore, we have the z-score to be:
[tex]\begin{gathered} z=\frac{11.8-8.4}{1.4} \\ z=2.43 \end{gathered}[/tex]Using a calculator, we can get the probability value to be:
[tex]P=0.9925[/tex]The probability is 0.9925 or 99.25%.
Hi I am the mom can you help me on this question so I can show my daughter too because I am confused
Answers
Using the area method in finding the quotient.
The values of A and B are as follows,
A = C/6
B = D/6
A is the quotient of C and 6,
B is the quotient of D and 6.
From the problem, we only have choices of number to input in the boxes.
48, 9, 90, 8, 540, 36 and 0
We will select one to number to be the value of C and the value A must be in the given numbers to be used.
Let's say C = 48
A = 48/6 = 8
Since 8 is included in the list of numbers. This is applicable.
Now for D and B,
Note that the sum of C and D must be equal to the given dividend, the dividend from the problem is 588
Since we already have the value of C = 48, the value of D must be :
588 - C = D
588 - 48 = 540
And 540 is also included in the list of numbers, so D = 540
The value of B will be :
B = D/6
B = 540/6
B = 90
90 is also included in the list of numbers.
The final diagram will be :
For part B, the quotient is the sum of A and B
A = 8, B = 90
Quotient = A + B
= 8 + 90
Quotient = 98
Plot the Trapezoid ABCD with vertices A(-8,-4),B(-5, -1), C(0, -2), and D(-4,-8) in the x-axis.
Answers
Let's begin by listing out the information given to us:
ABCD is a trapezoid
A (-8, -4); B (-5, -1); C (0, -2); D (-4, -8)
We will proceed to plotting this points on a Cartesian plane, we have:
What is 120 plus 5% sales tax
Answers
Answer:
126
Step-by-step explanation:
Hello!
Since you are adding 5% of 120 to 120, we can simply find 105% of 120.
To do that, we can multiply 120 by the number value of the percentage.
Find the Total Price105% of 1201.05 * 120126The total price after the sales tax is 126.
The product of two integers is -24. The difference between the two integers is 14. The sum of two integers is 10. What are the two integers?
Answers
Answer:
12 & -2
Step-by-step explanation:
m^3n^-6p^0 i dont understand how to solve this problem it has exponents
Answers
ANSWER:
[tex]\frac{m^3}{n^6}[/tex]STEP-BY-STEP EXPLANATION:
We have the following expression:
[tex]m^3n^{-6}p^0\:\:[/tex]We simplify as follows:
[tex]\begin{gathered} a^{-b}=\frac{1}{a^b}\rightarrow n^{-6}=\frac{1}{n^6} \\ \\ p^{0}=1 \\ \\ \text{ We replacing:} \\ \\ m^3n^{-6}p^0\:\:=m^3\cdot\frac{1}{n^6}\cdot\:1=\frac{m^3}{n^6} \end{gathered}[/tex]-1514,2 – 30r2y3 + 45ryjent of517is 3(x^3)y + 6x(y^2) - 3.1. Whe3(x^3)y - 6x(y^2) +9Res-3(x^3)y + 6x(y^2) - 33(x^2)y + 5x(y^2) - 93(x^3)y + 5x(y^2) + 3
Answers
To find the quotient of the first part, we can start by noticing that all the factors on the denominator are present in all terms of the numerator, so we can factor those out and cancel with the denominator ones:
[tex]\frac{15x^4y^2-30x^2y^3+45xy}{5xy}=\frac{5xy\cdot3x^3y+5xy\cdot(-6xy^2)+5xy\cdot9}{5xy}=\frac{5xy\cdot(3x^3y-6xy^2+9)}{5xy}=3x^3y-6xy^2+9[/tex]So, the first dropdown option is
[tex]3x^3y-6xy^2+9[/tex]Also, this is the quotient, so we will use it for the second part.
The second part says that if we divide by one of the options (let's call it a), we will get:
[tex]\frac{3x^3y-6xy+9}{a}=x^3y-2xy^2+3[/tex]As we can see, no terms on the final result has fractional coefficient, so the number a has to be a common factor of all the terms coefficients. the coefficients are 3, -6 and 9, so the only common factors are 1 and 3, so the answer should be 3:
[tex]\frac{3x^3y-6xy+9}{3}=\frac{3(x^3y-2xy+3)}{3}=x^3y-2xy^2+3[/tex]So, the second dropdown option is 3.
i need help with my homework PLEASE CHECK WORK WHEN DONE
Answers
SOLUTION
Given the question in the image, the following are the solution steps to answer the question.
STEP 1: Write the given data
[tex]\begin{gathered} \mu=27 \\ \sigma=2 \\ x=25 \end{gathered}[/tex]STEP 2: Write the formula for calculating the z-score
[tex]z=\frac{x-\mu}{\sigma}[/tex]STEP 3: Calculate the z-score
[tex]z=\frac{25-27}{2}=-\frac{2}{2}=-1[/tex]STEP 4: Find the probability
Using the z-score calculator,
Hello! I need some assistance with this homework question for precalculus, please?HW Q5
Answers
Explanation:
We were given the function:
[tex]g(x)=-1+4^{x-1}[/tex]We are to determine its domain, range and horizontal asymptote. This is shown below:
Domain:
[tex]\begin{gathered} g(x)=-1+4^{x-1} \\ 4^{x-1} \\ when:x=-10 \\ 4^{-10-1}=4^{-11} \\ when:x=1 \\ 4^^{1-1}=4^0=1 \\ when:x=20 \\ 4^{20-1}=4^{19} \\ \text{This shows us that the function is valid for every real number. This is written as:} \\ \left\{x|x∈R\right\} \end{gathered}[/tex]Range:
[tex]\begin{gathered} g(x)=-1+4^{x-1} \\ \begin{equation*} -1+4^{x-1} \end{equation*} \\ when:x=-10 \\ =-1+4^{-10-1}\Rightarrow-1+4^{-11} \\ =-0.9999\approx-1 \\ when:x=1 \\ =-1+4^{1-1}\Rightarrow-1+4^0\Rightarrow-1+1 \\ =0 \\ when:x=5 \\ =-1+4^{5-1}\Rightarrow-1+4^4\Rightarrow-1+256 \\ =255 \\ \text{This shows us that the lowest value of ''y'' is -1. This is written as:} \\ \left\{y|y>−1\right\} \end{gathered}[/tex]Horizontal asmyptote:
For exponential functions, the equation of the horizontal asymptote is given as:
[tex]y=-1[/tex]Melissa standing 40 feet from a tree the angle of elevation from where she is standing on the ground to the top of the tree is 50° how tall is the tree round the final answer to the nearest 10th.
Answers
Given:
• Melissa standing 40 feet from a tree.
,• The angle of elevation from where she is standing on the ground to the top of the tree is 50°.
Required: To determine the height of the tree.
This is achieved thus:
First, we represent the given information diagrammatically as follows:
Using the diagram above, in relation to the given angle, we can determine the height of the tree by using the tangent ratio as follows:
[tex]\begin{gathered} \tan\theta=\frac{opposite}{adjacent} \\ \therefore\tan50\degree=\frac{h}{40} \\ h=40\tan50\degree \\ h\approx47.7ft \end{gathered}[/tex]Hence, the answer is:
[tex]47.7ft[/tex]