Answer:
[tex]z = 0.228[/tex]
Step-by-step explanation:
Given
x: -3 -1 0 1 1 2 4 4 5
n = 9
Required
Determine the z-score x = 2
z score is calculated by
[tex]z = \frac{x - Mean}{SD}[/tex]
First, we need to calculate the mean
[tex]Mean = \frac{\sum x}{n}[/tex]
Mean = \frac{-3- 1 + 0 + 1 + 1 + 2 + 4 + 4 +5}{n}
[tex]Mean = \frac{13}{9}[/tex]
[tex]Mean = 1.44[/tex]
Next is to calculate the standard deviation
[tex]SD = \frac{\sum (x_i - Mean)^2}{n}[/tex]
[tex]SD =\sqrt{ \frac{(-3-1.44)^2+(-1-1.44)^2+(0-1.44)^2+(1-1.44)^2+(1-1.44)^2+(2-1.44)^2+(4-1.44)^2+(4-1.44)^2+(5-1.44)^2}{9}[/tex][tex]SD =\sqrt{ \frac{(-4.44)^2+(-2.44)^2+(-1.44)^2+(-0.44)^2+(-0.44)^2+(0.56)^2+(2.56)^2+(2.56)^2+(3.56)^2}{9}[/tex]
[tex]SD =\sqrt{ \frac{19.7136+5.9536+2.0736+0.1936+0.1936+0.3136+6.5536+6.5536+12.6736}{9}[/tex]
[tex]SD =\sqrt{ \frac{54.2224}{9}[/tex]
[tex]SD =\sqrt{6.02471111111}[/tex]
[tex]SD = 2.455[/tex]
Substitute these values in
[tex]z = \frac{x - Mean}{SD}[/tex]
Where x = 2
[tex]z = \frac{2 - 1.44}{2.455}[/tex]
[tex]z = \frac{0.56}{2.455}[/tex]
[tex]z = 0.228[/tex]
Hence, the z score of x = 2 is o.228
There are 180 girls in a mixed school. if the ratio of girls to Boyd is 4:3,find the total number of students in the school.
Step 1) Set up a proportion
180 girls / x boys = 4 girls / 3 boys
540 = 4x
x = 135 boys
Step 2) Add the number of boys and girls together
180 + 135 = 315
Answer: 315 total students
Find the value of x in the equation below. 2x+8/6=1/3(x+4) A. x = 0 B. no real solutions C. infinitely many solutions D. x = 1
Answer:
x = 0
Step-by-step explanation:
Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :
2*x+8/6-(1/3*(x+4))=0
Simplify 1/3
Equation at the end of step 1 :
(2x + 8/6) - (1/3 * (x + 4)) = 0
STEP 2 :
Equation at the end of step 2
(2x + 8/6) - (x+4)/3 = 0
STEP 3 :
Simplify 4/3
Equation at the end of step 3 :
(2x + 4/3) - (x+4)/3 = 0
STEP 4 :
Rewriting the whole as an Equivalent Fraction
Adding a fraction to a whole
Rewrite the whole as a fraction using 3 as the denominator :
2x = 2x/1 = 2x*3/3
Equivalent fraction : The fraction thus generated looks different but has the same value as the whole
Common denominator : The equivalent fraction and the other fraction involved in the calculation share the same denominator
Adding up the two equivalent fractions
Add the two equivalent fractions which now have a common denominator
Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:
2x * 3 + 4/3 = 6x+4/3
Equation at the end of step 4 :
(6x+4)/3 - (x+4)/3 = 0
STEP 5 : Pulling out like terms
Pull out like factors :
6x + 4 = 2*(3x + 2)
Adding fractions which have a common denominator
Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:
2*(3x+2)-((x+4))/3 = 5x/3
Equation at the end of step 5 :
5x/3 = 0
STEP 6: When a fraction equals zero
Where a fraction equals zero, its numerator, the part which is above the fraction line, must equal zero.
Now, to get rid of the denominator, multiply both sides of the equation by the denominator.
Here's how:
5x/3*3 = 0*3
Now, on the left hand side, the 3 cancels out the denominator, while, on the right hand side, zero times anything is still zero.
The equation now takes the shape :
5x = 0
Solving a Single Variable Equation:
Solve : 5x = 0
Divide both sides of the equation by 5:
x = 0
Find an equation of the line passing through the points (−8,2) with the slope m= 4/3
Answer:
[tex]y=\frac{4}{3}x+\frac{38}{3}[/tex]
Step-by-step explanation:
So we want to find an equation of a line passing through (-8,2) with a slope of 4/3.
To do so, we can use the point-slope form. This is:
[tex]y-y_1=m(x-x_1)[/tex]
So, substitute (-8,2) for x₁ and y₁, and let m be 4/3:
[tex]y-2=\frac{4}{3}(x+8)[/tex]
Distribute the right:
[tex]y-2=\frac{4}{3}x+\frac{32}{3}[/tex]
Add 2 to both sides. Note that 2 can be written as 6/3. Thus:
[tex]y=\frac{4}{3}x+\frac{32}{3}+\frac{6}{3}[/tex]
Simplify:
[tex]y=\frac{4}{3}x+\frac{38}{3}[/tex]
And this is our equation :)
Formulate the quadratic function that contains the points (-2,1), (0,1) and (1,4).
o f(x) = x2 + 2x +1
Of(x) = x2 - 2x + 1
Of(x) = x2 - 2x - 1
o f(x) = x2 + 2x - 1
Answer: A) f(x) = x² + 2x + 1
Step-by-step explanation:
The standard form of a quadratic equation is: y = Ax² + Bx + C
Input (x, y) coordinates into the standard equation to solve for A, B, & C.
(0, 1) → 1 = A(0)² + B(0) + C
1 = C
(-2, 1) → 1 = A(-2)² + B(-2) + C
1 = 4A - 2B + 1
0 = 4A - 2B
(1, 4) → 4 = A(1)² + B(1) + C
4 = A + C + 1
3 = A + B
Solve the system of equations:
0 = 4A - 2B → 1(0 = 4A - 2B) → 0 = 4A - 2B
3 = A + B → 2(3 = A + B) → 6 = 2A + 2B
6 = 6A
1 = A
Input A = 1 into either equation to solve for B:
3 = A + B
3 = 1 + B
2 = B
Now, Input A = 1, B = 2, and C = 1 into the standard equation:
y = (1)x² + (2)x + (1)
y = x² + 2x + 1
Find the unit vector in the direction of (4,-4). Write your answer in component form. Do not approximate any numbers in your answer.
Answer:
[tex](\frac{1}{\sqrt{2} }, \frac{-1}{\sqrt{2} } )[/tex]
Step-by-step explanation:
The unit vector for a nonzero vector, say u, in the direction of u is given by:
û = [tex]\frac{u}{|u|}[/tex] ---------------(i)
Where;
|u| = magnitude of vector u
From the question;
u = (4, -4)
First let's calculate the magnitude of u as follows;
|u| = [tex]\sqrt{(4)^2 + (-4)^2}[/tex]
|u| = [tex]\sqrt{16 + 16}[/tex]
|u| = [tex]\sqrt{32}[/tex] = [tex]4\sqrt{2}[/tex]
Now, substitute u and |u| into equation (i) as follows;
û = [tex]\frac{(4, -4)}{4\sqrt{2} }[/tex]
û = [tex](\frac{4}{4\sqrt{2} }, \frac{-4}{4\sqrt{2} } )[/tex]
û = [tex](\frac{1}{\sqrt{2} }, \frac{-1}{\sqrt{2} } )[/tex]
Therefore, the unit vector is [tex](\frac{1}{\sqrt{2} }, \frac{-1}{\sqrt{2} } )[/tex]
for stella’s lemonade recipe, 18 lemons are required to make 15 cups of lemonade. at what rate are lemons being used in cups of lemonade per lemon? express your answer in simplest form.
Answer:
5/6 cups/lemon
Step-by-step explanation:
(15 cups)/(18 lemons) = (15/18) cups/lemon = 5/6 cups/lemon
The park wanted to put up a new 500 foot fence around the rectangular playground. The length of the fence is going to be 100 foot. what will be the with of the fence?
Answer:
150 feet
Step-by-step explanation:
A rectangle has 2 pairs of equal sides.
One of the sides is 100 feet, meaning another side is 100 feet.
If we subtract 200 feet we are left with 300, which are the last two sides.
Divide 300 by 2 to get each side length.
150 feet
in abc the measure of side c is 3.9cm if def has a dilation of abc with a scale factor of 2.5
Complete Question:
In ABC, the measure of sides c is 3.9 cm If DEF is a dilation ABC with a scale factor of 2.5 what is the measure of side f
Answer:
f = 9.75
Step-by-step Explanation:
From the information given, a sketch of ∆ABC and ∆DEF with their corresponding sides and angles have been attached below.
∆DEF is a dilation of ∆ABC, which is said to be on a scale factor of 2.5.
The scale factor is a whole number, this implies that ∆DEF is an enlargement of ∆ABC.
Since side c = 3.9 cm, in ∆ABC corresponds to side f, in ∆DEF, therefore, the measure of f would be:
f = measure of c × scale factor
f = 3.9 cm × 2.5
f = 9.75
Evaluate the expression if a equals two and be equal six
Answer:
guess
Step-by-step explanation:
i ain't going to cap but idk
Help it’s not b what is the answer plz help
Answer:
c
Step-by-step explanation:
Please see attached picture for full solution.
for history fair a school building a circular wooden stage find the area of the stageif the radius of the stage is 4 meter use 3.14
Answer:
50.24
Step-by-step explanation:
The formula for the area of a circle is
Area = 3.14 (π) x radius squared [tex]4^{2[/tex]
Area = 3.14 (π) x (4 x 4)
Area = 3.14 (π) x 16
Area = 50.24
If A has the coordinate -10 and C has the coordinate 14 and B is the midpoint of a AC, then what is the coordinates of D which is the midpoint of BC?
Answer:
8
Step-by-step explanation:
The midpoint of AC is ...
B = (A +C)/2 = (-10 +14)/2 = 2
The midpoint of BC is ...
D = (B +C)/2 = (2 +14)/2 = 8
The midpoint of BC is 8.
The sum of the sequence of 685+678+671+664+...+6
Answer:
Sum of the sequence (Sn) = 33,859
Step-by-step explanation:
Given:
Sequence = 685+678+671+664+...+6
Find:
Sum of the sequence (Sn)
Computation:
a = 685
d = 678 - 985 = -7
an = 6
an = a+(n-1)d
6 = 685+(n-1)(-7)
-679 = (n-1)(-7)
97 = n-1
n = 98
So,
Sum of the sequence (Sn) = (n/2)[a+an]
Sum of the sequence (Sn) = (98/2)[685+6]
Sum of the sequence (Sn) = (49)(691)
Sum of the sequence (Sn) = 33,859
20 POINTSS!! Choose the fraction(s) equivalent to the given fraction. -1/7 Select all that apply A. -1/7 B. 1/-7 C. 1/7 D. -1/-7
Answer:
A and B.
Step-by-step explanation:
So we want to select the fractions that equal -1/7.
Let's go through each of the answer choices.
A)
A is -1/7, the exact same.
A is correct.
B)
B is 1/-7.
We can move the negative to the top.
So, 1/-7 is equivalent to -1/7.
B is also correct.
C)
C is 1/7
There are no negatives whatsoever.
C is not correct.
D)
We have -1/-7.
Again, move the negative to the top. We will have:
-(-1)/7
The two negatives cancel:
=1/7.
So, D is not correct.
Our answers are A and B.
1 and 2/3 plus 3 and 3/4
2 and 1/5 plus 3 and 7/8
4 and 1/2 plus 2 5/7
3/4 plus 2/3 plus 1/5
anyone?
URGENT
75 points!!
Answer:
Step-by-step explanation:
1 2/3 + 3 3/4 = 1 8/12 + 3 9/12 = 4 17/12 = 5 5/12
4 1/2 + 2 5/7 = 4 7/14 + 2 10/14 = 6 17/14 = 7 3/14
3/4 + 2/3 + 1/5 = 45/60 + 40/60 + 12/60 = 97/60 = 1 37/60
Answer:
Step-by-step explanation:
boom = 1 37/60
2) Mr. Farmer has a greyhound that can run 37.45 miles per hour (mph). He also has a quarter horse that can run 47.5 mph. How much faster can the quarter horse run than the greyhound?
Answer:
About 1.3 times faster.
Step-by-step explanation:
First set up an inequality.
[tex]\frac{37.45}{47.5}[/tex] =[tex]\frac{x}{y}[/tex]
Now divide top and bottom by 37.45 And you would get 1.26..... which is rounded to about 1.3
Please give brainliest thanks
please someone should help me solve it 2x ÷ x^ - 4
Answer:
The answer is
[tex] {2x}^{5} [/tex]Step-by-step explanation:
[tex] \frac{2x}{ {x}^{ - 4} } [/tex]First of all separate the two from the x
That's
[tex] \frac{2(x)}{ {x}^{ - 4} } [/tex]Next we use the rules of indices
Since they have the same base and are dividing we subtract the exponents
That's
[tex] \frac{ {a}^{x} }{ {a}^{y} } = {a}^{x - y} [/tex]So we have
[tex] \frac{2(x)}{ {x}^{ - 4} } = 2( {x}^{1 - - 4)} = 2( {x}^{1 + 4} )[/tex]We have the final answer as
[tex] {2x}^{5} [/tex]Hope this helps you
Find the area to the nearest square foot of the shaded region below, consisting of a square with a circle cut out of it. Use 3.14 as an approximation for π. Need this ASAP
Answer:
22 square feet
Step-by-step explanation:
Area of shaded region = Area of square - Area of circle. The diameter of the circle is also the length of the side of the square as the circumference of the circle is on the circumference of the square.
Area of circle = 3.14 × r × r
r = 10 ÷ 2
= 5
Area of circle = 3.14 × 5 × 5
= 78.5
Area of square = length × length
Area of square = 10 × 10
= 100
Area of shaded region = Square - Circle
= 100 - 78.5
= 21.5
= 22 (to the nearest square foot)
I hope this helps :)
Refer to the sample data for pre-employment drug screening shown below. If one of the subjects is randomly selected, what is the probability that the test result is a false positive? Who would suffer from a false positive result? Why?
Pre-Employment Drug Screening Results
Positive test result Negative test result
Drug Use Is Indicated Drug Use Is Not Indicated
Subject Uses Drugs 38 12
Subject Is Not a drug user 19 29
Answer:
0.193877
Step-by-step explanation:
The data given to us is
Pre-Employment Drug Screening Results
Positive test result Negative test result
Drug Use Is Indicated Drug Use Is Not Indicated
Subject Uses Drugs: 38 12
Subject Is Not a drug user: 19 29
Now the total of this is = 38+19+12+29= 98
Now the probability of false positive is = 19/98= 0.193877
The Subject Is Not a drug user would suffer from a false positive. He is not a user and has a positive result.
Round 7/12 to the nearest hundredth
Answer:
7.00
Step-by-step explanation:
so you have to round to the narest 0.01 the easy way to do it is round to the hundreth place. And you will get your answer which is 7.00
Several children and adults visited a zoo last week. The
number of children was 2 less than 3 times the number of
adults. Let c represent the number of children and a represent
the number of adults. Which equation shows this situation?
A C = 3a-2
B C = 2a-3
C C = 3a +2
DC - 2a + 3
A solid sphere is cut into 10 equal wedges. The volume of each wedge is Solve the formula for r. 15 O Ar= V2 O B. r = 151 O c. r= 15V (27) O D. r= 15V - 27
Answer:
A. r = ∛ 15V / 2π
Step-by-step explanation:
Volume of a sphere = 4/3 π r³
And to be divided into 10 equal wedges parts.
Volume of each wedge = V = 2/15 π r³
find r
V = 2 π r³ / 15
15 V = 2 π r³
15V / 2π = r³
r = ∛ 15V / 2π
The correct option will be option A i.e., r = [tex]\sqrt[3]{\frac{15}{2\pi } }[/tex]
It is given that a solid sphere is cut into 10 equal wedges , with each wedge having volume V = [tex]\frac{2}{15} \pi r^{3}[/tex]
We have to solve it to get the value of radius r.
What is the formula for volume of sphere ?
The volume of sphere is given by V = [tex]\frac{4}{3} \pi r^{3}[/tex] where , r is the radius of the sphere.
As per the question ;
Volume of sphere = [tex]\frac{4}{3} \pi r^{3}[/tex]
To be divided into 10 equal wedges ;
Volume of each wedge of sphere will be ;
V = [tex]\frac{2}{15} \pi r^{3}[/tex]
15 V = 2[tex]\pi r^{3}[/tex]
or
r³ = [tex]\frac{15V}{2\pi }[/tex]
or
r = [tex]\sqrt[3]{\frac{15}{2\pi } }[/tex]
Thus , the correct option will be option A i.e., r = [tex]\sqrt[3]{\frac{15}{2\pi } }[/tex]
To learn more about volume of sphere click here ;
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PLEASE HELP !
Expand the following numbers ;
1.) 1.23 x 10^0
2.) 1.54 x 10^4
3.) 2.5 x 10^-3
4.) 5.67 x 10^-1
5.) 1.00 x 10^8
6.) 1.00 x 10^-8
Answer:
1. 1.23
2. 15400
3. 0.0025
4. 0.567
5. 100000000
6. 0.00000001
Step-by-step explanation:
you just move the decimal point left for negative and right for positive
A square has a side length of 7 feet. Find the area of the square in square feet. Enter only the number.
Answer:
49
Step-by-step explanation:
area if a square: side length x side length (s^2)
7 x 7 = 49
Area of Square is 49 square feet
Area of SquareGiven that;
Side length of square = 7 feet
Find:
Area of Square
Computation:
Area of Square = Side²
Area of Square = 7²
Area of Square = 49 square feet
Find out more information about 'Area of Square'
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What’s 2 1/6 - 1 5/6?
Answer:
2/6 or 1/3
Step-by-step explanation:
7) A jet travels 440 miles in 2 hours. At this rate, how far could the jet Hy
12 hours? What is the rate of speed of the jet?
Answer:
2,640 miles in 12 hours.
Step-by-step explanation:
440/2=220mph
220*12 hours=2,640
rate of speed=220pmh
8x=2x+36 solve for x
Answer:
the anwser is 6
Step-by-step explanation:
Answer:
x<6
Step one Pull out like factors :
6x - 36 = 6 • (x - 6)
Step two: Solve : 6 = 0
This equation has no solution.
A a non-zero constant never equals zero.
Step three: Solve : x-6 = 0
Add 6 to both sides of the equation :
x = 6
Hoped I helped
a company has $25,000 in cash. next month the company anticipates sales revenue of $10,000, equiptment expense of $2,500, insurance costs of $100, and $200 in licensing fees. what is the projected cash flow at the end of the month?
Answer:o
Step-by-step explanation:
What percentage of the data in a standard normal distribution lies between x = .09 and x = 1.2?
Answer:
34.9% of the data in a standard normal distribution lies between x = .09 and x = 1.2.
Step-by-step explanation:
We have to find the percentage of the data in a standard normal distribution that lies between X = 0.09 and X = 1.2.
As we know that the mean and the standard deviation of a standard normal distribution is 0 and 1 respectively.
The z-score probability distribution for the standard normal distribution is given by;
Z = [tex]\frac{X-\mu}{\sigma}[/tex] = [tex]\frac{X-0}{1}[/tex] ~ Standard normal
Now, the percentage of the data in a standard normal distribution that lies between X = 0.09 and X = 1.2 is given by = P(0.09 < X < 1.2)
P(0.09 < X < 1.2) = P(X < 1.2) - P(X [tex]\leq[/tex] 0.09)
P(X < 1.2) = P( [tex]\frac{X-0}{1}[/tex] < [tex]\frac{1.2-0}{1}[/tex] ) = P(Z < 1.2) = 0.8849
P(X [tex]\leq[/tex] 0.09) = P( [tex]\frac{X-0}{1}[/tex] [tex]\leq[/tex] [tex]\frac{0.09-0}{1}[/tex] ) = P(Z [tex]\leq[/tex] 0.09) = 0.5359
The above probabilities are calculated by looking at the value of z = 1.2 and x = 0.09 in the z table which has an area of 0.8849 and 0.5359 respectively.
Therefore, P(0.09 < X < 1.2) = 0.8849 - 0.5359 = 0.349.
Use a definite integral to find the area of the region between the given curve and the x-axis on the interval [0, b].y= 2x^2.
Given :
Given a curve , [tex]y=2x^2[/tex] .
To Find :
The area of the region between the given curve and the x-axis on the interval [0, b] .
Solution :
Now , area under the curve is given by :
[tex]A=\int\limits^b_0 {2x^2} \, dx \\\\A= |_0^b(\dfrac{2}{3}x^{(2+1)})\\\\A=\dfrac{2b^3}{3}[/tex]
( Integration of [tex]x^2[/tex] is [tex]\dfrac{x^3}{3}[/tex] )
Therefore , the region between the given curve and the x-axis on the interval [0, b] is [tex]\dfrac{2b^3}{3}[/tex] .
Hence , this is the required solution .