Answer:
The number is -9
Step-by-step explanation:
Let x be the number we do not know.
The you would set up the equation like
2x + 3 = x - 6
+6
2x+9 = x
-2x
9 = -1 x
/-1
=-9
To check math:
2(-9) + 3 = -9 - 6
-18 + 3 = -15
-9 - 6 = -15
Mrs. Holmes’s physics class uses 3D-printing software to create miniature bridges that can hold at least 5 pounds. Teams will print multiple parts of the bridges and then assemble the parts. One team wants at least 6 inches between the bridge's upper and lower rail. The lower rail of the bridge contains points (2, 10) and (16, 3). Will the bridge meet the team's specifications if the upper rail contains points (5, 1)? If yes, how far apart are the rails? Let every unit represent an inch. Round your answer to the nearest hundredth, if needed.
Answer:
I litteraly have the same problem and no clue how to do I
Step-by-step explanation:
13. When feeding, a juvenile whale shark filters about 600 cubic meters of water through its
mouth each hour. About 2.8 kilograms of food are filtered out from the water each hour.
120
a. Graph the function that represents the amount a of water filtered by the whale shark as a
function of the number of minutes.
m
b. The whale shark feeds for 7.5 hours each day. Graph the function that represents the amount f
of food (in pounds) filtered by the whale shark as a function of the number d of days.
Answer:214.29
Step-by-step explanation:600 divided by 2.8
possibly the answer
Question 4 of 10
For f(x) = 2x+ 1 and g(x)=x²-7, find (f+ g)(x).
OA. 2x³ - 6
OB. x²+2x+8
OC. 2x² - 15
O D. x²+2x-6
Answer:
D
Step-by-step explanation:
Function f is adding to function g, therefore combine the two into one and combine like terms to solve.
What is the fractional equivalent of the repeating decimal n = 0.1515... ? Answer the questions to find out.
1. How many repeating digits does the number represented by n have? (2 points)
ill give 25 points and maybe brainlist
The fractional equivalent of the repeating decimal n = 0.15.15.. is
15/99. And the number represented by n has two repeating digits that is 15.
Given, repeating decimal n = 0.1515..
We must come up with a strategy to eliminate the recurring portion before converting what is left into a fraction. We can benefit from the repetition on our behalf.
set x = 0.151515 ...eq(1)
the 15 is a recurring number means that those two digits keep repeating forever.
so
100x = 15.151515.. eq(2)
Subtract eq(2) from eq(1).
100x = 15.151515
x = 0.151515
we get, 99x = 15
hence x = 15/99
Therefore, the equivalent of the repeating decimal is 15/99.
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read the attachment.
Answer: C, D
Step-by-step explanation:
Answer C is correct because 2/5 is 0.4 and 0.55 is greater than 0.4.
Answer D is correct because 2/5 is 0.4 and 3/4 is 0.75 therefore 0.75 is greater than 0.4.
Answer:
C and D
Step-by-step explanation:
On the number line, the first point is 2/5. 2 divided by 5 gets you .4, so that's why it's at .4. .55 is the next point. .55 is a bigger number than .4, so it would be an answer.
3 divided by 4 gets you .75. 3/4=.75. 2/5=.4. .75 is greater than .4. 3/4 is greater than 2/5
How many times smaller is 1.9 × 10^3 than 4.085 × 10^5?
1.9 × 10^3 is 215 times smaller than 4.085 × 10^5.
The basic formula for the area of a rectangle is length x width, but the basic formula for volume is length x width x height. The calculation does not change depending on how you refer to different measurements. For example, you can use depth instead of height.
Every 3D object occupies a certain space. This space is measured by its volume. Volume is defined as the space occupied within the bounds of an object in three-dimensional space. Also called the capacity of the object. The volume of an object is the amount of space it fills. Large capacity is measured in cubic meters m3. Smaller volumes are measured in cubic centimeters cm3 or cubic millimeters mm3.
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The question is in the photo. Complete C and D.
x = -12
Explanations:Given the following equation
[tex]-\frac{1}{2}x=6[/tex]We are to find the variable x. To do that, we will multiply both sides by -2 as shown:
[tex]\begin{gathered} -\frac{1}{2}x\times-2=6\times-2 \\ x=6\times-2 \\ x=-12 \end{gathered}[/tex]This shows that the value of x for the equation to be true is -12
Check
If x = -12, on substiituting;
[tex]\begin{gathered} =-\frac{1}{2}(-12) \\ =\frac{-12}{-2} \\ =\text{ 6} \end{gathered}[/tex]Since the result is equivalent to 6, this shows that the solution x = -12 is correct.
a poster of area 15360 cm215360 cm2 has blank margins of 10 cm10 cm wide on the top and bottom and 6 cm6 cm wide on the sides. find the dimensions that maximize the printed area. (use decimal notation. give your answers as whole or exact numbers.)
The dimensions that maximize the area are, 96cm and 84cm.
What is area?
The measurement that expresses the size of a region on a plane or curved surface is called area. Surface area refers to the area of an open surface or the boundary of a three-dimensional object, whereas the area of a plane region or plane area refers to the area of a form or planar lamina.
Let the height of poster be h and breadth be b,
bh = 15630cm square........(1)
Height of the printed area=h-10-10 = h - 20
(decrement of 10 from top and bottom)
the breadth of the printed area b-6-6 = b-12
(decrement of 9 from both sides)
for maximum printed area:
A=(h-20)(b-12) should be maximum
[tex]A = (h - 20)(\frac{15360 }{h}-12)[/tex]
From equation (1)
[tex]A = 15360-12h-\frac{307200}{h} +240[/tex]
A = 15600 - 12h - (307200/h)
differentiate with respect to h (it should be=0)
[tex]\frac{dA}{dh}= 0-12 + \frac{307200}{h^2}[/tex]
[tex]12 = \frac{307200}{h} \\h = 160 cm[/tex]
from equation (1),
[tex]bh = 15630cm^2\\b = 96cm[/tex]
dimension of printed area,
= h - 20
= 160 - 20
= 140 cm
= b - 12
= 96 - 12
= 84 cm
Therefore, the dimensions that maximize the area are, 96cm and 84cm.
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Write the function in vertex form.
y = 3x² - 8x + 13
The function is y=
Answer:
y = 3(x - [tex]\frac{4}{3}[/tex] )² + [tex]\frac{23}{3}[/tex]
Step-by-step explanation:
the equation of a parabola in vertex form is
y = a(x - h)² + k
given
y = 3x² - 8x + 13
using the method of completing the square
the coefficient of the x² term must be 1 so divide first 2 terms by 3
y = 3(x² - [tex]\frac{8}{3}[/tex] x) + 13
add/subtract ( half the coefficient of the x- term )² to x² - [tex]\frac{8}{3}[/tex] x
y = 3(x² + 2(- [tex]\frac{4}{3}[/tex] )x + [tex]\frac{16}{9}[/tex] - [tex]\frac{16}{9}[/tex] ) + 13
= 3(x - [tex]\frac{4}{3}[/tex] )² + 3(- [tex]\frac{16}{9}[/tex] ) + 13
= 3(x - [tex]\frac{4}{3}[/tex] )² - [tex]\frac{16}{3}[/tex] + [tex]\frac{39}{3}[/tex]
= 3(x - [tex]\frac{4}{3}[/tex] )² + [tex]\frac{23}{3}[/tex] ← in vertex form
A rock climber completing a two-minute training session climbed 12 meters higher on the wall during the second minute of the session. at the end of the two-minute session, the climber was back to the same spot she was at when the session started. what value represents the climber's change in elevation during the first minute of the training session
The value represents the climber's change in elevation during the first minute of the training session is 1/5.
Given,
During the second minute of a two-minute training session, a rock climber completed a 12-meter ascent up the wall. The climber returned to the identical location she had been in at the beginning of the two-minute session.
Let x be the distance climbed by the climber is x m
During the first minutes(60 seconds): distance climbed =[tex]\frac{x}{60}[/tex]
In the 2nd minute, they climbed 12 m higher than in the 1st minute.
Now, the distance climbed by the climbed in the Second minute = [tex]\frac{x+12}{60}[/tex]
Now, the change in the elevation during the first minute of the training session= [tex]\frac{x+12}{60}-\frac{x}{60} = \frac{12}{60}=\frac{2}{10}=\frac{1}{5}[/tex]
Hence, the value represents the climber's change in elevation during the first minute of the training session is [tex]\frac{1}{5}[/tex]
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Explain what the slope and intercept mean in each situation.
A graph represents the perimeter, y, in units, for an equilateral triangle with side length x units. The slope of the line is 3 and the y-intercept is 0.
The amount of money, y, in a cash box after x tickets are purchased for carnival games. The slope of the line is 14 and the y-intercept is 8.
The number of chapters read, y, after x days. The slope of the line is 54 and the y-intercept is 2.
The graph shows the cost in dollars, y, of a muffin delivery and the number of muffins, x, ordered. The slope of the line is 2 and the y-intercept is 3.
The slope intercept form of the each situation is given by
a) y = 3x + 0
b) y = 14x + 8
c) y = 54x + 8
d) y = 2x + 3
What is slope intercept form?
Slope intercept form- The equation of the line in slope-intercept form is given by:
y = mx + c
Here,
(x, y) = Every point on the line
m = Slope of the line
c = y-intercept of the line
a) In situation one
slope of the line = 3 and y- intercept = 0 =c
The equation becomes y = 3x+ 0
y = 3x
b) slope of the line = 14 and y intercept = 8
y = 14x + 8
c) slope of the line = 54 and y- intercept = 2
y = 54x + 2
d) slope of the line = 2 and y- intercept = 3
y = 2x + 3
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Please answer the questions in the photo ( will mark brainliest )
The reason for the required step using property of equality are as follow:
1. Subtraction property of equality.
2. Subtraction property of equality.
3. Addition property of equality.
As given in the question,
The reason for the required step using property of equality are as follow:
1. 3x + 3 = 5 + x
3x - x + 3 = 5
2x + 3 = 5
Here
Subtraction property of equality is applied.
If x, y, and z are real numbers and x = y
then
x - z = y - z
2. 2x + 3 = 5
2x = 5-3
2x = 2
Here Subtraction property of equality is applied.
If a, b, and c are real numbers and a = b, then
a - c = b - c
3. -x - 1 = 3
-x = 3 + 1
-x = 4
Here Addition property of equality is applied.
If x, y and z are real numbers and x = y, then
x + z = y + z
Therefore, the reason for the required step using property of equality are as follow:
1. Subtraction property of equality.
2. Subtraction property of equality.
3. Addition property of equality.
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GAME DESIGN A computer software designer is creating a new video game. The designer wants to create a secret passage that is halfwaybetween the castle and the bridge. Where should the secret passage be located?
Answer:
8.5 and 10.5
Step-by-step explanation:
add your x1 and x2 coordinate and divide them by 2 to get your x.
and for the y add your y1 and y2 coordinate and divide them by 2 to get your y.
The x1, x2, y1, and y2 in this situation would be (5,14) (being the bridge)
and (12,7) being the castle.
x1 = 5
x2 = 12
y1 = 14
y2 = 7
Solve |x +31-1 = (x + 2)2 by graphing
After plotting the equation on the graph, we know that the value of |x| on line "(x + 2)2" is -0.125 and 0.142.
What is a graph?In mathematics, a graph is a visual representation or diagram that shows data or values in an ordered way. The relationships between two or more things are frequently represented by the points on a graph. In mathematics, "graph" can refer to (at least) two different things. In elementary mathematics, the term "graph" designates a plot or a function graph. A graph is, in the language of mathematicians, a set of points and the connections between some subset of those points (which may be empty).So, solving "|x| +31-1 = (x + 2)2" by graph:
Graph both the equations, "|x| +31-1" and "(x + 2)2" on the graph.(Refer to the graph attached below)
Now, according to the graph, we know that the value of |x| on line "(x + 2)2" is -0.125 and 0.142.Therefore, after plotting the equation on the graph, we know that the value of |x| on line "(x + 2)2" is -0.125 and 0.142.
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NEED HELP ASAP!!! what’s the two column proof for 13x-11+8x-25=90??
The value of x = 6 of the given expression '13x-11+8x-25 = 90' using the two-column proof.
What are expressions?An expression in mathematics is made up of numbers, variables, and functions (such as addition, subtraction, multiplication or division, etc.) You can think of expressions as being similar to phrases. A phrase in language may contain an action on its own, but it does not constitute a complete sentence. You must substitute a number for each variable and carry out the arithmetic operations in order to evaluate an algebraic expression. Since 6 + 6 equals 12, the variable x in the example above is equal to 6.So, the value of x:
Now, the value of x in expression'13x-11+8x-25 = 90' by two columns proof:(Refer to the image attached below)
x = 6Therefore, the value of x = 6 of the given expression using the two-column proof.
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A line passes through the points (-4,-3) and (2, 6). Determine the slope of the line.
• m = 2/3
O The slope is undefined.
Om = 0
Om =3/2
[tex](\stackrel{x_1}{-4}~,~\stackrel{y_1}{-3})\qquad (\stackrel{x_2}{2}~,~\stackrel{y_2}{6}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{6}-\stackrel{y1}{(-3)}}}{\underset{run} {\underset{x_2}{2}-\underset{x_1}{(-4)}}} \implies \cfrac{6 +3}{2 +4} \implies \cfrac{ 9 }{ 6 } \implies {\Large \begin{array}{llll} \cfrac{ 3 }{ 2 } \end{array}}[/tex]
3.State the domain and range for the function y = 4^x+ 3.
The domain of the function is (-∝,∝) and the range is (3,∝) .
We know that the given function is of the form [tex]y=4^x+3\\[/tex] .
So the possible values of x or the domain will be all real values of x.
Now we know from the properties of indices that for all and any real value of x , [tex]4^x > 0[/tex] so the value of y will always be greater than 3 .
For higher values of x the value of y will be higher.
So the range of the function will include all real values greater than 3
The incoming dataset that a function will accept is its domain in mathematics. Domain(f), where f stands for the operation, is another way to express it.
The relationship between the dependent variable y and the regression coefficient x defines the function
A value is said to be in the domain of a function f if it successfully facilitates the production of a sharp number y using another value for x.
So domain : {x | x∈(-∝,∝)}
range : {y | y∈ (3,∝)}
Hence the domain of the function is {x | x∈(-∝,∝)} and the
range is {y | y∈ (3,∝)} .
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g(n) = 3n - 4f(n) = n^3 - 2nFind (gºf)(n)
hello
let's get the functions out first
[tex]g(n)=3n-4[/tex][tex]f(n)=n^3-2n[/tex][tex]g\cdot f(n)=\text{ ?}[/tex][tex]\begin{gathered} g.f(n)=(3n-4)\cdot(n^3-2n) \\ g\mathrm{}f(n)=3n^4-6n^2-4n^3+8n \\ g\mathrm{}f(n)=3n^4-4n^3-6n^2+8n \end{gathered}[/tex]Evaluate the following expression, given that x = -6 and y =12.
|2x+5| - 8y
The value of expression |2x+5| - 8y is -89 when x = -6 and y =12
What is Expression?Expression is a combination of numbers, variables and Operators.
The given expression is mod two x plus 5 minus eight y.
|2x+5| - 8y
This expression has addition, subtraction and multiplication operators.
Given value of x is minus six and y is equal to twelve.
x=-6 and y=12
plug in values of x and y in expression
|2(-6)+5|-8(12)
|-12+5|-96
|-7|-96
The value in mod will be always taken as positive
7-96
-89
Hence the value of expression |2x+5| - 8y is -89 when x = -6 and y =12.
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Transpose and solve for x
15x³=723
Answer:
x = 241 1/3
————
5 1/3
Step-by-step explanation:
Answer:
x = ^3(square root )of 18075 or 5.24875253...
-----------------------
5
Step-by-step explanation:
isolate the variable by deviding each side by factors that dont contain the variable
hope this helped have a good day ^^
To win the recycling contest, you must collect between 83 and 87 pop tabs each week, inclusive. Suppose you collected 82, and, 84 pop tabs during the first two weeks of competition. Write and solve a compound inequality to find the possible values for the number of pop tabs that need to be collected during the third and final week of the competition in order to win the contest.
As per the compound inequality, the possible values for the number of pop tabs that need to be collected during the third and final week of the competition in order to win the contest is 83 ≤ (82 + 84 + n)/3 ≤ 87; 83 ≤n ≤ 95.
Compound inequality:
A compound inequality is an inequality that merges two inequalities either by using "and" or "or".
Given,
In the recycling contest, you must collect between 83 and 87 pop tabs each week, inclusive for winning.
And suppose you collected 82, and, 84 pop tabs during the first two weeks of competition.
Here we nee to find the possible values for the number of pop tabs that need to be collected during the third and final week of the competition in order to win the contest.
Let us consider n be the number of pop tabs.
So, it can be written using the compound inequality,
=> 83 ≤ (82 + 84 + n) /3 ≤ 87
To cancel the fraction we have to multiply 3 with all of them, then we get,
=> 83 x 3 ≤ (82 + 84 + n) ≤ 87 x 3
=> 249 ≤ (166 + n) ≤ 261
To find the value of n we have to subtract 166, then we get,
=> 249 - 166 ≤ n ≤ 261 - 166
=> 83 ≤ n ≤ 95
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Where can I find angles measurements that is Missing each set of supplemenry angles?
Remember that
If the sum of two angles is equal to 180 degrees, then the angles are supplementary
so
In this problem
Let
x ----> the missing angle
x+34.6 =180 degrees -----> by form a linear pair (supplementary angles)
solve for x
x=180-34.6
x=145.4 degreesHELP PLEASE
complete the paragraph proof
given: <1 and <2 are complementary and <2 and <3 are complementary.
prove: <1 congruent <3
it is ________ that <1 and <2 are complementary and <2 and <3 are complementary. By the definition of ________ , m<1+ m<2=90 degrees and m<2+m<3 =90 degrees. By the ____________ property, m<1+m<2=m<2+m<3.
Then,m<1= _____________ by the subtraction property. Therefore, <1 congruent <3 by the ________
The following proof of complementary angle is given below:
it is given that <1 and <2 are complementary and <2 and <3 are complementary. By the definition of complementary angle , m<1 + m<2 = 90 degrees and m<2 + m<3 =90 degrees. By the substitution property, m<1 + m<2 = m<2 + m<3.
Then, m<1 = m<3 by the subtraction property. Therefore, <1 congruent <3 by the complementary angle.
What is a complementary angle?Complementary angle is a pair of angles that sum to a right angle. A right angle is half of the angle formed by a single straight line which is equivalent to 90 degrees.
Given: <1 and <2 are complementary and <2 and <3 are complementary.
prove: <1 congruent <3
The proof of <1 congruent <3 is m<1 + m<2 = m<2 + m<3 by substitution effect and m<1 = m<3 by Subtraction effect
Therefore, the proof of <1 congruent <3 is given by <1 and <2 are complementary and <2 and <3 are complementary.
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ames determined that these two expressions were equivalent expressions using the values of x = 4 and x = 6. Which statements are true? Check all that apply. 7 x + 4 and 3 x + 5 + 4 x minus 1 When x = 2, both expressions have a value of 18. The expressions are only equivalent for x = 4 and x = 6. The expressions are only equivalent when evaluated with even values. The expressions have equivalent values for any value of x. The expressions should have been evaluated with one odd value and one even value. When x = 0, the first expression has a value of 4 and the second expression has a value of 5. The expressions have equivalent values if x = 8.
The statements are true about the given expressions include the following:
When x = 2, both expressions have a value of 18.The expressions have equivalent values for any value of x.The expressions have equivalent values if x = 8.How to determine whether the expressions are equivalent?In order to determine whether these expressions are equivalent, we would evaluate the two expressions based on each of the statements:
"When x = 2, both expressions have a value of 18"
7x + 4 = 7(2) + 4 = 14 + 4 = 18.
3x + 5 + 4x - 1 = 3(2) + 5 + 4(2) - 1 = 6 + 5 + 6 - 1 = 18.
"The expressions are only equivalent for x = 4 and x = 6." is false has demonstrated above.
"The expressions have equivalent values for any value of x." is true.
Let x = 1;
7x + 4 = 7(1) + 4 = 7 + 4 = 11.
3x + 5 + 4x - 1 = 3(1) + 5 + 4(1) - 1 = 3 + 5 + 4 - 1 = 11.
Let x = 10;
7x + 4 = 7(10) + 4 = 70 + 4 = 74.
3x + 5 + 4x - 1 = 3(10) + 5 + 4(10) - 1 = 30 + 5 + 40 - 1 = 74.
"The expressions should have been evaluated with one odd value and one even value." is false because all values of x are solutions.
"When x = 0, the first expression has a value of 4 and the second expression has a value of 5." is false because the two expressions are equivalent expressions.
In conclusion, "The expressions have equivalent values if x = 8." is true because the two expressions are equivalent expressions.
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x = -5y + 4 3x + 15y = -1
Answer: UNDEFINED
Step-by-step explanation:
x=-5y+4 5y=-x+4 y=-1/5x+4/5
3x+15y= -1 15y=-3x-1 y=-1/5x-1/15
COMBINED: -1/5x+4/5=-1/5x-1/15 FIND COMMON DENOMINATOR=15
-3/15x=-3/15x-13/15
0=-13/15 UNDEFINED
The options are relational/irrational and is equal to an integer/has a square root in its denominator
because, the quotient has an integer in its denominator
Explanation
A rational number is a number that is expressed as the ratio of two integers
[tex]\frac{p}{q}[/tex]hence
for
[tex]\frac{20}{\sqrt{16}}[/tex]we can solve the root in the denominator, so we have
[tex]\begin{gathered} \frac{20}{\sqrt{16}} \\ \frac{20}{\sqrt[]{16}}=\frac{20}{4} \end{gathered}[/tex]so, as the number can be expressed as the ratio of two integers ( 20 and 4) we can conclude
[tex]\text{the quotient }\frac{20}{\sqrt[]{16}}\text{ is a rational number}[/tex]because, the quotient has an integer in its denominator
I hope this helps you
Hello I need help with A please make it easy and simple to understand
distanceSolution:
Given that a toy car placed on the floor travels at a constant acceleration for 3 seconds reaching a velocity of 4v m/s, we have
It slows down with a constant deceleration of 0.5 m/s² for 4 seconds before hitting a wall and stopping. This is as shown below:
Thus, the velocity-time graph for the toy car is as shown below:
The total distance traveled by the toy car is evaluated by calculating the area of the triangle ABC. Thus,
[tex]\begin{gathered} \text{Total distance traveled = }\frac{1}{2}\times7\times4 \\ =14\text{ meters} \end{gathered}[/tex]Hence, the
Can someone help me with this ??
-7e + 8 = -13
Pls help Lila's mom is decorating her room and placed acircular rug near her window for story time.How much space does this rug take up if its diametermeasures 25 feet?
Step1: Write the area of the circular Rug
The area of the circle is
[tex]\Pi r^2[/tex]From the question the diameter is 25feet, hence the radius is
[tex]\begin{gathered} \text{radius}=\frac{diameter}{2} \\ =\frac{25}{2} \end{gathered}[/tex]Step2: substitute the value into the formula
[tex]\begin{gathered} \text{area of circular rug=area of a circle=}\Pi r^2 \\ =\frac{22}{7}\times\frac{25}{2}\times\frac{25}{2} \\ =\frac{13750}{28} \\ =491.07ft^2 \end{gathered}[/tex]Hence the area of the circular rug is 491.07 square feet
The will take approximately 491square feetyou
3. Smartphones come with an app that keeps track of the amount of time that the phone is being used. For teenagers, the distribution of amount of time they use their phone is approximately normal with mean = 7.75 hours per day and standard deviation = 1.25 hours per day.
(a) What percent of teenagers use their phone less than 5 hours per day?
(b) What percent of teenagers use their phone more than 10 hours per day?
(c) What proportion of teenagers use their phone between 6 to 8 hours per day?
(d) What is the 75th percentile of this distribution?
Using the normal distribution, it is found that:
a) 1.39% of teenagers use their phone less than 5 hours per day.
b) 3.59% of teenagers use their phone more than 10 hours per day.
c) 49.85% of teenagers use their phone between 6 to 8 hours per day.
d) The 75th percentile of the distribution is of 8.59 hours.
Normal Probability DistributionThe z-score of a measure X of a variable that has mean represented by [tex]\mu[/tex] and standard deviation represented by [tex]\sigma[/tex] is given by the fraction presented as follows:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score measures how many standard deviations the measure X is above or below the mean of the distribution, depending if the z-score is positive or negative.From the z-score table, the p-value associated with the z-score is found, and it represents the percentile of the measure X in the distribution.The mean and the standard deviation of the daily amounts they use their phone are given as follows:
[tex]\mu = 7.75, \sigma = 1.25[/tex]
The proportion that use their phone for less than 5 hours a day is given by the p-value of Z when X = 5, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
Z = (5 - 7.75)/1.25
Z = -2.2
Z = -2.2 has a p-value of 0.0139.
Thus the percentage is of 1.39%.
The proportion that use their phone for more than 10 hours a day is one subtracted by the p-value of Z when X = 10, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
Z = (10 - 7.75)/1.25
Z = 1.8
Z = 1.8 has a p-value of 0.9641.
1 - 0.9641 = 0.0359 = 3.59% (percentage).
The proportion between 6 and 8 hours a day is the p-value of Z when X = 8 subtracted by the p-value of Z when X = 6, hence:
X = 8:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
Z = (8 - 7.75)/1.25
Z = 0.2
Z = 0.2 has a p-value of 0.5793.
X = 6:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
Z = (6 - 7.75)/1.25
Z = -1.4
Z = -1.4 has a p-value of 0.0808.
0.5793 - 0.0808 = 0.4985 = 49.85% (percentage).
The 75th percentile is X when Z = 0.675, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
0.675 = (X - 7.75)/1.25
X - 7.75 = 0.675 x 1.25
X = 8.59 hours.
Learn more about the normal distribution at https://brainly.com/question/4079902
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