The mean of all exam scores in the class is found = 71
Normally distribution
A normal distribution is an arrangement of a data set in which most values cluster in the middle of the range and the rest taper off symmetrically toward either extreme.
While data points are referred to as x in a normal distribution, they are called z or z-scores in the z-distribution. A z-score is a standard score that tells you how many standard deviations away from the mean an individual value (x) lies: A positive z-score means that your x-value is greater than the mean.
The z-score is found by;
z = (x - μ)/σ
x = sample mean
μ = mean score
σ = standard deviation
Now, from this,
x = zσ + μ
For p = 80th percentile= 0.8, see z value from z score table.
z = 0.85
x = 85 points
85 = 0.85σ + μ .....eq 1
For p = 30% = 0.3, see the z value from the z score table.
z = -0.3802
x = 65
65 = -0.3802σ + μ .....eq 2
Solving eq 1 and 2.
σ = 16.25
Put in eq 1
μ = 71.19
μ = 71
Thus, the mean of all exam scores in the class is found = 71
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can someone help me answer this please?? Thank you so much is you help!! :)
The value of g(f(x)) will be 3(1-x²) and the value of g(f(2)) will be -9 for the f(x)=4-3x² and g(x)=x-1.
What is Function?A function from a set X to a set Y assigns exactly one element of Y to each element of X. The set X is known as the function's domain, and the set Y is known as the function's codomain.
What are the 4 types of functions?Functions are broadly classified into four categories. Element-based: one-to-one function, many-to-one function, onto function, one-to-one and onto function, into function.
Here, f(x)=4-3x² and g(x)=x-1
g(f(x))=(4-3x²)-1
g(f(x))=4-3x²-1
=3-3x²
=3(1-x²)
g(f(2))=3(1-2²)
=3*-3
=-9
For f(x)=4-3x² and g(x)=x-1, the value of g(f(x)) is 3(1-x²) and the value of g(f(2)) is -9.
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I need the dercreasing intervel and my grade is at risk so pls be correct
Answer: You are correct
The decreasing interval is (-3, infinity)
This is the same as writing [tex](-3, \infty)[/tex]
===============================================
Explanation:
If a < b and f(a) > f(b), then the function is decreasing.
Visually this means that if the graph is going downhill when moving to the right, the function is decreasing.
The graph shown goes downhill throughout its entire domain of (-3, infinity)
Solve for x, y, and z
Using angle sum property we found that ∠ x = 113°, ∠y = 67° and ∠z = 49°
What is angle sum property of a triangle?The angle sum property of triangle states that the sum of all the interior angles of a triangle is 180°.
If ΔABC is a triangle then,
m ∠A + m ∠B + m ∠C = 180°
Given from the figure in the question that 28°, 39° and x° are interior angles of a triangle, then using angle sum property:
28° + 39° + x° = 180°
⇒ 67° + x° = 180°
⇒ x° = 180° - 67° = 113°
∠x and ∠y are on the same line same point therefore their sum will be 180°
⇒ x° + y° = 180°
⇒ 113° + y° = 180°
⇒ y° = 180° - 113° = 67°
Also an exterior angle of a triangle is equal to sum of interior opposite angles.
∴ y ° = 28° + 39° = 67°
Now, 64° , y° and z° are interior angles of same triangle from the figure in the question.
∴ Using angle sum property,
64° + y° + z° = 180°
⇒ y ° + z° = 180° - 64° = 116°
⇒ y° + z° = 116°
⇒ z° = 116° - y° = 116° - 67° = 49°
Therefore ∠x, ∠y , ∠z are 113° , 67° and 49° respectively
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The vertices of triangle SRQ have coordinates S (1, 1), R (3, 4), and Q (7, 0). If triangle SRQ is rotated about the origin 180°, what are the resulting coordinates of the point R?
Answer:
Step-by-step explanation:
its 3 4
R' (-3,-4) are the resulting coordinates of the purpose R.
A rotation may be a transformation in a plane that turns every point of a preimage through a specified angle and direction about a fixed point. The fixed point is named the center of rotation . The quantity of rotation is called the angle of rotation and it is measured in degrees. Use a protractor to live the specified angle counterclockwise.
Using the rule for a 180° rotation to seek out the vertices of the rotated triangle.
T: (x, y) ⇒ (-x, -y)
Given points of triangle: S(1,1) , R (3, 4) and Q (7, 0).
Rotation 180° about the origin.
S (1, 1) → S' (-1,-1)
R (3,4) → R' (-3,-4)
Q (7,0) → Q' (-7,0)
Hence, the coordinate of the R is: R' (-3,-4).
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A box is to be made by cutting a square measuring 4 centimeters on a side from a square piece of cardboard. If the volume of the box is to be 100 cubic centimeters, find the length of a side of the original square. Round the answer to the nearest tenth of a centimeter.
Given the volume of the box is 100 cm^3
And to made the box we need to cut a square measuring 4 centimeters on a side from a square piece of cardboard.
so, the height of the box = 4 cm
so, the volume = height * area of the base
100 = 4 * area of the base
Area of the base = 100/4 = 25 cm^2
so, the side length of the base of the box =
[tex]\sqrt[]{25}=5[/tex]so, the lenght of the a side of the original square = 5 + 2*4 = 5 + 8 = 13 cm
you were in the garden, there are 34 people in the yard. you kill 30. how many people are in the garden?
In linear equation, You are the only person in the garden at the time the 34 people.
What in mathematics is a linear equation?
A linear equation is a first-order (linear) term plus a constant in the algebraic form y=mx+b, where m is the slope and b is the y-intercept.Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.You are the only person in the garden at the time the 34 people are on their homicidal spree.
Alternatively, if the backyard and garden are in the same place, then there are no longer any individuals in the garden because you would officially count as one of the 34 people who are all killed.
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What are the constraints to this problem?
A Virginia Beach farmer has 480 acres of land on which to grow either corn or soybeans.
He figures he has 800 hours of labor available during the crucial summer season. The farmer
can expect a profit of $40 per acre on corn and $30 per acre on soybeans. He knows that
corn requires 2 hours per acre to raise, and soybeans require 1 hour per acre to raise. How
many acres of each should he plant to maximize profit? What is his maximum profit?
He raise corn in [tex]320[/tex] acres and soybeans in [tex]160[/tex] acres to maximize profit and the maximum profit is [tex]\$18,200[/tex].
A Virginia Beach farmer has [tex]480[/tex] acres of land on which to grow either corn or soybeans.
He has labor available during the crucial summer [tex]=800[/tex] hours
The farmer can expect a profit of [tex]\$40[/tex] per acre on corn.
The farmer can expect a profit of [tex]\$30[/tex] per acre on soybeans.
The corn requires hours to raise [tex]=2[/tex] hours per acre.
The soybeans requires hours to raise [tex]=1[/tex] hours per acre.
We have to find how many acres of each should he plant to maximize profit and his maximum profit.
To solve the question we let he plant [tex]x[/tex] acres of corn and [tex]y[/tex] acres of soybeans.
Total land is available for grow either corn or soybeans is [tex]480[/tex] acre.
So the equation should be
[tex]x+y\leq 480\dots\dots Equation (1)[/tex]
He requires [tex]2[/tex] hours to raise corn per acre and [tex]1[/tex] hours to raise soybeans per acre and he has 800 hours of labor available during the crucial summer season.
So the equation should be
[tex]2x+y\leq 800\dots\dots Equation (2)[/tex]
He expect a profit of [tex]\$40[/tex] per acre on corn and [tex]\$30[/tex] per acre on soybeans.
So profit equation should be
[tex]P=40x+30y[/tex]
Now the subject of constraints
[tex]x+y\leq 480[/tex]
[tex]2x+y\leq 800[/tex]
[tex]x,y\geq 0[/tex]
Now solving the equation [tex]1[/tex] and [tex]2[/tex] to find the value of [tex]x[/tex] and [tex]y[/tex].
Multiplying the equation [tex]1[/tex] by [tex]2[/tex].
After multiplying with [tex]2[/tex] the equation [tex]1[/tex]
[tex]2x+2y\leq 960\dots\dotsEquation (3)[/tex]
Now subtracting Equation [tex](3)[/tex] and Equation [tex](2)[/tex].
[tex]2x+2y-(2x+y)\leq 960-800[/tex]
[tex]2x+2y-2x-y\leq 960-800[/tex]
[tex]y\leq 160[/tex]
Now putting the value of [tex]y[/tex] in Equation [tex](1)[/tex]
[tex]x+160\leq 480[/tex]
Subtract [tex]160[/tex] on both side
[tex]x+160-160\leq 480-160[/tex]
[tex]x\leq 320[/tex]
He raise corn in [tex]320[/tex] acres and soybeans in [tex]160[/tex] acres to maximize profit.
The maximum profit
[tex]P=40x+30y\\P=40\times320+30\times180\\P=12,800+5400\\P=18,200[/tex]
The maximum profit is [tex]\$18,200[/tex].
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Consider this equation of a circle. x^2-2x+y^2+6y-4=0
The answer is bellow!!!
Answer:
A
Step-by-step explanation:
x² - 2x + y² + 6y - 4 = 0 ( add 4 to both sides )
x² - 2x + y² + 6y = 4
using the method of completing the square
add ( half the coefficient of the x / y terms )² to both sides
= x² + 2(- 1)x + 1 + y² + 2(3)y + 9 = 4 + 1 + 9
(x - 1)² + (y + 3)² = 14 ← in standard form
a ladder 16 ft long rests against a vertical wall. let theta be the angle between the top of the ladder and the wall and let x be the distance from the bottom of the ladder to the wall. if the bottom of the ladder slides away from the wall, how fast (in ft/rad) does x change with respect to theta when
If the bottom of the ladder slides away from the wall, then x changes by 12cosθ with respect to theta and when θ = π/6, x changes by 6[tex]\sqrt{3}[/tex] inches with respect to θ.
Here, we are given that a ladder 16 ft long rests against a vertical wall and theta is the angle between the top of the ladder and the wall.
We know that, sin of an angle = opposite / hypotenuse
Thus, sinθ = x/16
⇒ x = 16 sinθ
The rate of change of x with respect to θ will be given by dx/dθ
dx/dθ = d/dθ (12sinθ)
= 12 d/dθ (sinθ)
= 12cosθ
Now, we need to find the value of dx/dθ when θ = π/6,
= 12 cosπ/6
= 12 ([tex]\sqrt{3}[/tex]/2)
= 6[tex]\sqrt{3}[/tex]
Thus, when θ = π/6, x changes by 6[tex]\sqrt{3}[/tex] inches with respect to θ.
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Your question was incomplete. Check for full content below-
A ladder 12 feet long rests against a vertical wall. Let θ be the angle between the top of the ladder and the wall, and let x be the distance from the bottom of the ladder to the wall. If the bottom of the ladder slides away from the wall, how fast does x change with respect to θ when θ = π/6?
You overhear your friend explaining how to find intercepts to a
classmate. Your friend says, "When you want to find the x-intercept, just substitute 0 for x
and continue to solve the equation."
Is your friend's explanation correct?
The friend's explanation is not correct.
They are mixing up x and y intercepts.
To find the y intercept, plug in x = 0 to find y.
To find the x intercept, plug in y = 0 and solve for x.
Question 5 of 10Which inequality represents all values of x for which theproduct below is defined?x-5.X+2A. X2-2B. X55O C. X25O D. X20SUBMIT
Answer:
[tex]x\ge-2[/tex]Explanation: The product has two square-roots being multipled together, the inside of each of the root must be greater than or equal to zero, this in Mathematics can be written as follows:
[tex]\begin{gathered} \sqrt[]{x-5}\times\sqrt[]{x+2} \\ \end{gathered}[/tex]Therefore, applying the condition leads us to the following conclusion:
[tex]\begin{gathered} \sqrt[]{x-5}\times\sqrt[]{x+2} \\ \therefore\rightarrow \\ x-5\ge0\rightarrow x\ge5 \\ x+2\ge0\rightarrow x\ge-2 \end{gathered}[/tex]
Therefore it follows that x must be:
[tex]x\ge-2[/tex]
which one?Please help its extra credit!
Answer:
12 weeks
Step-by-step explanation:
if 280=420
then 8=×
cross multiply
280×=420×8
280×=3360
divide both sides with the co efficient of x
280×/280=3360/280
leaving the answer to be 12
A musicians hair was originally 3 inches long. She asked her hair dresser to cut 5/6 of it off. How many inches did she have cut off?
Answer: 2.5 inches
Step-by-step explanation: 3*5/6= 2.5
Alan sees this offer.
Refurbished phone
45% OFF
Now only £88
How much was the phone before the discounted price?
The cost of the phone before the discounted price is $160.
Given that, Refurbished phone 45% OFF now only £88.
What is the discount?Discount is the reduction in the price of goods or services offered by shopkeepers at the marked price. The List price or Marked price is the price of an article as declared by the seller or the manufacturer, without any reduction in price. Selling price is the actual price at which an article is sold after any reduction or discounts in the list price.
Let the original price of the phone be x.
Now, x - 45% of x = 88
⇒ x - 45/100 × x = 88
⇒ x - 0.45x = 88
⇒ 0.55x = 88
⇒ x = 88/0.55
⇒ x = 160
Therefore, the cost of the phone before the discounted price is $160.
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seven more then a number is equal to 18. what is the number
Answer:11
Step-by-step explanation:
Which is true add a short explanation why it is true thank you if u help
Answer:[tex]\sqrt{36} > 5 \\[/tex]
Step-by-step explanation:
because [tex]\sqrt{36} =6[/tex]
Therefore 6 > 5
write an equation of a line that passes through the point (2,-2) and is parallel to the line 5x-2y=4
The equation of line is y= 5/2x -7.
What is equation of line?The slope of the line and a point on the line may be used to create the equation of a line. To better comprehend how the equation for a line is formed. The slope of the line, which can be stated as a numeric integer, fraction, or the tangent of the angle it forms with the positive x-axis, is the line's inclination with respect to the positive x-axis. The coordinate system's point with the x coordinate and the y coordinate is referred to as the point.
One of the significant forms used to express a straight line algebraically is the two point form.
Written as, y- y1= m (x- x1), where m is slope.
Given:
a line passes through the point (2, -2) and parallel to 5x-2y = 4
Now, writing the given equation of line in the form of slope intercept form
5x- 2y=4
2y = 5x -4
y= 5/2x -2
Here the slope is 5/2 and the required line will also have the same slope as parallel line.
then, m=5/2
Now using y=mx +c
put y=-2 and x=2
-2 = 5/2(2) + c
-2 -5 = c
c=-7
Hence, the equation of line is y= 5/2x -7.
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y = x + 3
y = x² - 2x + 3
Answer:
y=3 / y=6
x=0 / x=3
Step-by-step explanation:
Follow the steps given in the picture attached above.
You are completing a math assignment. The number of questions you complete and the time it takes you to complete them have a proportional relationship, as shown in the table.
Number of questions 4 and 7
Time (in minutes) 6 and ?
How much time does it take to complete 7 questions ?
Answer choices
3 min
5 min, 30 sec
9 min
10 min, 30 sec
I think your answer is 10 minutes and 30 seconds. . .
Step-by-step explanation:What I did was I took 6 and 7 and multiplied them together, then i divided 42 by 4, and got 10.5. which would give you 10 minutes and 30 seconds.
6*7=42/4=10.5 (aka 10min 30sec)
While birdwatching, Natalie saw 8 robins. If 40% of the birds she saw were robins, how many birds did Natalie see in all?
40% of 8 is 3.2
hope this helped
can someone helpp me with this i will give brainlest :)
Answer:
Step-by-step explanation:
1slice=280 and 6 slices so 280x6 so 0x6=0 then 80x6=6+6x4=48x10=480
then 200x6= 6x2=12x100=1200
add all 0+480+1200=1680
sry i'm not used to showing work i usually do it all in my head
What is the value of x in this figure?
x = 22
x = 68
x = 90
I don't know.
I’LL MARK BRAINLIEST!! Graph - 5x + 10y = 20
Answer:
Step-by-step explanation:
See screenshot
:]
lol I'm improve my rank so brainliest would help a lot :]
Please someone help me please i need help with this question answer asap
Answer:
y = - [tex]\frac{1}{3}[/tex] x + [tex]\frac{8}{3}[/tex]
Step-by-step explanation:
the perpendicular bisector of AB passes through the midpoint of AB at right angles.
find the midpoint using the midpoint formula
with A (- 2, 0 ) and B (0, 6 )
midpoint = ( [tex]\frac{-2+0}{2}[/tex] , [tex]\frac{0+6}{2}[/tex] ) = ( [tex]\frac{-2}{2}[/tex] , [tex]\frac{6}{2}[/tex] ) = (- 1, 3 )
find the gradient m of AB using the gradient formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = A (- 2, 0 ) and (x₂, y₂ ) = B (0, 6 )
m = [tex]\frac{6-0}{0-(-2)}[/tex] = [tex]\frac{6}{0+2}[/tex] = [tex]\frac{6}{2}[/tex] = 3
given a line with gradient m then the gradient of a line perpendicular to it is
[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{3}[/tex]
the equation of a line in gradient- slope form is
y = mx + c ( m is the gradient and c the y- intercept )
here m = - [tex]\frac{1}{3}[/tex] , then
y = - [tex]\frac{1}{3}[/tex] x + c ← is the partial equation
to find c substitute (- 1, 3 ) into the partial equation
3 = [tex]\frac{1}{3}[/tex] + c ⇒ c = 3 - [tex]\frac{1}{3}[/tex] = [tex]\frac{8}{3}[/tex]
y = - [tex]\frac{1}{3}[/tex] x + [tex]\frac{8}{3}[/tex] ← equation of perpendicular bisector
Mark is looking at a blueprint of a skateboard that shows the ramp's length that is 11.4 inches. If the scale on the blueprint is 1 inch: 6 feet, find the actual length of the ramp.
(Someone answer Asap please.)
Applying the scale factor the actual dimension of the ramp in the blueprint Mark was looking at was found to be 0.158 inches
What is scale factor?Scale factor represent the amount the image is increased or reduced in the map.
How to find the actual length of the rampinformation from the question include
the scale on the blueprint is 1 inch: 6 feet
the ramp's length that is 11.4 inches
finding the scale factor
1 inch ⇒ 6feet = 72 inches
the scale factor is 1/72
finding the actual dimension
1 inch ⇒ 72 inches
? = 11.4 inches
cross multiplying gives
72 * ? = 1 * 11.4
? = 1/72 * 11.4
? = 0.158 inches
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How do you solve an equation like this?
Answer:
Step-by-step explanation:
[tex]\displaystyle\\(64x^\frac{2}{3})^{-\frac{1}{3}} =\\\\(4^3x^\frac{2}{3})^{-\frac{1}{3}}=\\\\ 4^{3*(-\frac{1}{3})}x^ {\frac{2}{3}*(-\frac{1}{3} )}=\\\\ 4^{-1}x^{-\frac{2}{9} }=\\\\\frac{1}{4} x^{-\frac{2}{9} }=\\\\\frac{1}{4} (\frac{1}{x^\frac{2}{9}} } )=\\\\\frac{1}{4\sqrt[9]{x^2} }[/tex]
The wholesale price for a necklace is $10.the mark up percent is 200%.what is the mark up
The mark up is $30.
What is markup?As stated, markup is the distinction between a product's selling price and its cost price. Retail minus Cost is markup. The term "markup" describes the discrepancy between a product's selling price and its actual cost. It is specified as a percentage over the price. In other words, the seller makes a profit when the price of the commodity or service is higher than the overall cost. A unit's gross profit, which is the sales price less the cost to create or buy it for resale, is divided by its cost to determine the markup %. The markup percentage is computed as (12 - 8) / 8 and is equal to 50% if an item costs the business $8 to produce but is sold for $12.
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carmen pulled transactions from the month of march to see if there is an association between coffee and breakfast sandwich purchases. after running through confidence and expected confidence calculations, she calculated the lift ratio at 1.52. what association does a calculated lift ratio of 1.52 reflect?
A lift ratio of 1.52 implies that identifying a person who purchases coffee and a breakfast sandwich is 52% better than guessing that a random person will purchase a breakfast sandwich.
What is the lift ratio about?Stronger relationships are indicated by higher lift values.We divide the confidence ratio by the support of the consequent to arrive at the lift ratio.
Lift ratios greater than one are typically thought to imply a significant link between the components. Lift ratios below 1 indicate that a purchase of the items is unlikely. Lift is simply the ratio of target response divided by the average response.
Carmen analyzed data from the month of March to see if there was a link between coffee and breakfast sandwich purchases. She calculated the lift ratio to be 1.52 after running confidence and expected confidence calculations.
In this case, she wants to know the association between coffee and breakfast sandwich purchases. There's 52% better off than a random individual.
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The coordinates of the endpoints of QR are Q(6, 2) and R(18, 18). Point S is on QR and divides it such that QS:RS is 3:1. What are the coordinates of S? Write your answers as integers or decimals.
Check the picture below.
[tex]\textit{internal division of a line segment using ratios} \\\\\\ Q(6,2)\qquad R(18,18)\qquad \qquad \stackrel{\textit{ratio from Q to R}}{3:1} \\\\\\ \cfrac{Q\underline{S}}{\underline{S} R} = \cfrac{3}{1}\implies \cfrac{Q}{R} = \cfrac{3}{1}\implies 1Q=3R\implies 1(6,2)=3(18,18)[/tex]
[tex](\stackrel{x}{6}~~,~~ \stackrel{y}{2})=(\stackrel{x}{54}~~,~~ \stackrel{y}{54}) \implies S=\underset{\textit{sum of the ratios}}{\left( \cfrac{\stackrel{\textit{sum of x's}}{6 +54}}{3+1}~~,~~\cfrac{\stackrel{\textit{sum of y's}}{2 +54}}{3+1} \right)} \\\\\\ S=\left( \cfrac{ 60 }{ 4 }~~,~~\cfrac{ 56}{ 4 } \right)\implies {\Large \begin{array}{llll} S=(15~~,~~14) \end{array}}[/tex]
Simplify: 18c - 49 + 1 -2c
Answer:
16c - 48
Step-by-step explanation:
combine like terms : 18c - 2c - 49 + 1
then you get 16c - 48