Answer:
y = 1/8 x - 9/2
Step-by-step explanation:
slope of line q = 1/8
y-(-2)= 1/8(x-2)
y+2 = 1/8 x - 1/4
y = 1/8 x - 1/4 - 2
y = 1/8 x + (-1-8)/2
y = 1/8 x -9/2
in october 2012, apple introduced a much smaller version of the apple ipad, known as the ipad mini. weighing less than 11 ounces, it was 50% lighter than the standard ipad. battery tests for the mini ipad showed that battery life is uniformly distributed between 8.5 and 12 hours. what is the value of 'a'? answer to one decimal.
a) The Probability density function of given uniform distribution example is
F(x) = 1/3.5 for 8.5 < x< 12
Uniform distribution in Statistics is a type of probability distribution in which all possible outcomes have equally likely chance to occur. It is generally represented by U(x,y) where
x ---> minimum value and y---> maximum value
Probability density function is a probability function which defines the density of continuous random variable lying between specified range
values. It is denoted by f( a<X<b)
Probability density function for uniform distribution is F(x) = 1/(b-a) for a<x<b where a and b are parameters of uniform distribution.
We have following informations,
weigh of mini iPad = 11 ounces or 50% lighter than standard iPad.
Assume that the battery of iPad is uniformly distributed between 8.5 hours to 12 hours.
this implies a = 8.5 , b = 12
F(x) = 1/(12 - 8.5) = 1/3.5 for 8.5<x<12
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#Complete Qestion :
In October 2012, Apple introduced a much smaller variant of the Apple iPad, known as the iPad Mini. Weighing less than 11 ounces, it was about 50% lighter than the standard iPad. Battery tests for the mini ipad showed that battery life is uniformly distributed between 8.5 and 12 hours. what is the value of 'a'? answer to one decimal. Assume that the battery life of the iPad Mini is uniformly distributed between 8.5 and 12 hours.
a) What is the probability that the battery life for an iPad Mini will be 10 hours or less?
at 9:30 am andrew left exeter for portsmouth, cycling at 12 mi/h. at 10:00 am stacy left portsmouth for exeter, cycling at 16 mi/h. the distance from exeter to portsmouth is 20mi.find the time they meet
Stacey meets Andrew 1.5 hours after she starts travelling at 11:30 AM and Andrew meets Stacey 2 hours after he starts travelling at 11:30 AM.
How to solve this problem?
Stacey and Andrew in the mentioned problem will meet in a time frame only when the both have travelled equal distances in respect to another.
Given, speed at which Andrew was travelling = 12 mi/h
Speed at which Stacey was travelling = 16 mi/h
Let the time taken by Stacey be = t hours
Therefore, the time taken by Andrew = (t + 0.5) hours
When Stacey overtakes Andrew, they must have covered the same distance, therefore:
16t = 12×(t + 0.5) ⇒ 16t = 12t + 6 ⇒ 4t = 6 ⇒ t = 6/4 ⇒ t = 3/2 ⇒ t = 1.5
Therefore, Stacey meets Andrew 1.5 hours after she starts travelling at 11:30 AM and Andrew meets Stacey 2 hours after he starts travelling at 11:30 AM.
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help help help helppp
The coordinate of image of P is (-6,-4)
What in math is a coordinate?
a pair of numbers that utilize the horizontal and vertical breakups from the two reference axes to define a point's location on a coordinate plane. generally expressed by the x-value and y-value pair (x,y).
P (-2,2)
Translation (x,y)=(x-4,y-6)
x= -2
y= 2
x-4= -6
y-6= -4
Hence the coordinate of image of p is (-6,-4)
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Given that X is directly proportional to y2. if x=4 units and y=3 units ,then find the value of y when x= 3 units
Answer:
y = 2.60 (to 3sf)
Step-by-step explanation:
Since x is directly proportional to y², then x = ky², where k is a constant.
When x = 4, y = 3,
4 = k(3)²
4 = 9k
9k = 4
∴[tex]k =\frac{4}{9}[/tex]
∴ When x = 3,
[tex]\frac{4}{9}y^{2} = 3[/tex]
∴y = 2.60 (to 3sf)
at a certain clothing store, the clothes are displayed on racks. the clothes on each rack have similar prices, but the prices among the racks are very different. to estimate the typical price of a single piece of clothing, a consumer will randomly select four pieces of clothing from each rack. what type of sample is the consumer selecting? responses a census a census a cluster sample a cluster sample a simple random sample a simple random sample
The clothing in the store is separated into strata, each of which is a rack of items with comparable prices. An illustration of the use of a stratified random sample is the mean price calculated using the randomly chosen articles of clothing from the strata.
Describe a random sample.In the random sampling method of sampling, each sample has an equal chance of being chosen. In order to fairly represent the entire population, a sample is chosen at random. From a pool of 250 employees, 25 names could be chosen at random to represent a simple random sample. The sample in this case is random, and the population in this case is the employees since each has an equal chance of being chosen.
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Shandra is preheating her oven before using it to bake. The initial temperature of the oven is 65° and the temperature will increase at a rate of 10° per minute after being turned on. What is the temperature of the oven 8 minutes after being turned on? What is the temperature of the oven tt minutes after being turned on?
Answer:
x=145 at 8 minutes
im not sure what tt means but please read my note at the end.
Step-by-step explanation:
if the initial temp is 65 and it increases at a rate of 10 per min the use
65+10(x)
let x be the number of minutes
65+10(8)
65 +80= 145
after 8 minutes the oven will be at 15 degrees. im not sure what tt is suppose to mean, but to find any other solution just plug it into x multiply x by 10 and add it to 65
simplify (4i+1)^2
show all work
The simplified answer is 8i-15.
What do you mean by iota?
Iota is a mathematical concept that is represented by the symbol i and has the value of [tex]i^{2}=-1[/tex] , or i =[tex]\sqrt{-1}[/tex] . It is an imaginary unit number that is denoted by i. You could have run into instances when the discriminant is negative while attempting to solve quadratic equations.
According to the given question,
We have: [tex](4i+1)^{2}[/tex]
Now, we will solving this by formula,
[tex](a+b)^{2}=a^{2} +b^{2}+2ab[/tex]
Putting the values in it,
[tex](4i+1)^{2}=(4i)^{2}+1^{2}+2(4i)(1)\\=16i^{2} +1+8i\\ =16(-1)+8i+1\\=8i-16+1\\=8i-15[/tex]
Therefore, the required answer is 8i-15.
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5-(40/5)
Step A: 5+ (4)
Step B: 5+8
Step C: 13
In which step did the student first make an error? Be sure to include the correct value of
the expression in simplest form in your answer.
Explain your answer.
Answer:
5 - [tex]\frac{40}{5}[/tex] = 5 - 8 = -3
Step-by-step explanation:
The first mistake made by the student is in Step A where the problem was not copied down correctly.
a comic book costs $3.99. it is marked up 45%. what is the final price of the comic book after it is marked up?
The final price of the comic book after it is marked up is $5.79.
Since we have given that
Cost of a comic book including tax = $ 3.99
According to the question, it is given that it is marked up 45%,
=3.99 × (100+45)÷100
=3.99 × 145/100
=399 × 1.45
=5.79
Hence, the final price of the comic book after it is marked up is $5.79.
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HELP PLEASE ASAP!!!!!!!!
The missing angle is as follows:
m∠C = 30 degrees.How to find congruent triangle?When two triangles are congruent they will have exactly the same three sides and exactly the same three angles.
In other words, two triangles are said to be congruent if all three corresponding sides are equal and all the three corresponding angles are equal.
Therefore, the triangle ABC is congruent to EDF.
Hence,
∠A = ∠D
∠B = E
∠C = ∠F
Therefore,
m∠C = x
m∠F = 2x - 30
Hence,
m∠C = m∠F
x = 2x - 30
x - 2x = -30
-x = -30
x = 30
m∠C = 30 degrees
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The formula d=16f^2 describes the number of feet d a skydiver falls in t second of free fall. How far does a skydiver fall after 1.5 second?
The skydiver falls a distance of 36 feet after 1.5 seconds.
What is the distance?Distance is a measurement of how far apart two things or points are, either numerically or occasionally qualitatively. The distance can refer to a physical length in physics or to an estimate based on other factors in common usage.Distance is the sum of an object's movements, regardless of direction. The distance can be defined as the amount of space an object has covered, regardless of its starting or ending position.Now, we have:
d=16t²t=1.5 secondsTo calculate distance:
d = 16 * 1.5*1.5d= 36 feetTherefore, the skydiver falls a distance of 36 feet after 1.5 seconds.
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Hi if someone could help me I would be very grateful.
I submitted a photo of the questions
Answer:
5/12
6/15
10/18
Step-by-step explanation:
suppose the insect population doubled after 15 hours. how long (in hours) will it take the insect population to grow to eight times its initial size? (simplify your answer completely.)
Using population growth modeling it is concluded that the population of insects after 1 hour will be about 1.05 times.
What is growth and decay modeling?The method used to calculate the growth and decay of insects or bacteria are called growth and decay modeling.
Let us assume n₀ is the initial population, then the total population n(t) after t time is given by the formula:
n(t) = n₀ [tex]e^{rt}[/tex], where r = the relative rate of growth.
Suppose an initial number of insects is x and after 15 hours it becomes 2x.
2x = x[tex]e^{15r}[/tex]
[tex]e^{15r}[/tex] = 2
Take the log of both sides of the equation
ln [tex]e^{15r}[/tex]= ln 2
15r = ln 2
r = 0.693147/15
Now, population after 1-hour = x [tex]e^{r}[/tex]
= 1.047
≈ 1.05
Hence the population of insects after 1 hour will be about 1.05 times.
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Each month Edna spends all her income on rent, on travel and on other living expenses She spends 1/3 of her income on rent. she spends 1/5 of her income on travel. She spends $420 of her income on other living expenses. Work out her income each month.
Answer:I think $1064
Step-by-step explanation:
First you multiply 1/5 by 420 and then add, so 1/5 x 420 = 84 & 420 + 84 = 504. Then you multiply 1/3 by 420 and also add, so 1/3 x 420 = 140 & 420 + 140 = 560. After you add both totals to get your final answer, so 504 + 560 = 1064. Her income each month is $1064.
Evaluate the expression.
Do not round your answer.
1/5(3+2+ 5)² =
Answer:
20
Step-by-step explanation:
do parenthesis first
1/5(3+2+ 5)² =
1/5(10)² =
then exponent
1/5(10)² =
1/5(100) =
20
Which inequality represents the phrase "nine less than two
times a number is no more than 45?"
The expression of the inequality is [tex]9 < 2x\le45[/tex]. It can be obtained using the operations of inequality.
What is inequality?
In matmathematics if two numbers are not equal even then there is a relationship. This relationship can be defined by inequality relationship.
According to the pharase, 9 is less than two times a number. Hence, consider the number is x and its two times means 2x. Now, 9 should be less than this number. Hence, 9<2x. Now, again the number 2x is not more than 45. Means, it can be equal to 45. Hence, it will give the expression [tex]2x\le45[/tex].
Now, combine the two expressions as follows:
9<2x
[tex]2x\le45[/tex]
[tex]9 < 2x\le45[/tex]
Hence, the expression of the inequality is [tex]9 < 2x\le45[/tex].
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If a+4/a = 4 then find the value of a^5-1/a^5
pls answer this one as quick as possible.
Value of [tex]a^5-\frac{1}{a^5}[/tex] is 31.97.
What do you mean by algebraic expression?
In mathematics, an expression that incorporates variables, constants, and algebraic operations is known as an algebraic expression (addition, subtraction, etc.). Terms comprise expressions.
There are 3 main types of algebraic expressions which include:
Monomial Expression
Binomial Expression
Polynomial Expression
An algebraic expression which is having only one term is known as a monomial.
Given expression:
a + 4/a = 4
We need to simplify the above expression and will find the value of a.
[tex]a+\frac{4}{a}=4[/tex]
⇒ [tex]\frac{a^2+4}{a}=4[/tex]
⇒ [tex]a^{2}+4=4a[/tex]
⇒ [tex]a^2-4a+4=0[/tex]
⇒ [tex]a^2-2a-2a+4=0[/tex]
⇒ a(a-2) -2(a-2) = 0
⇒ (a-2)(a-2) = 0
⇒ a = 2
Now, substitute this value of a in expression , [tex]a^5-\frac{1}{a^5}[/tex]
[tex]2^5-\frac{1}{2^5}[/tex]
= 32 - 1/32
= [tex]\frac{1024-1}{32} =1023/32 = 31.97[/tex]
Therefore, value of [tex]a^5-\frac{1}{a^5}[/tex] is 31.97.
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Clay asks Donte to play the following number puzzle:
Pick a number
Add 4
Multiply by 2
Subtract 3
Add your original number
Donte’s final result is 32. Which number did he start with?
Group of answer choices below
A. 7
B. 9
C. 4
D. 23
E. 0
Expand and simplify (3x + 4)(2x + 3)
Answer:
6x^2+17x+12
Step-by-step explanation:
(3x+4) * (2x+3)
3x * 2x = 6x^2
3x * 3 = 9x
+4 * 2x = +8x
+4 * +3 = +12
6x^2+ 9x+8x +12
Simplify:
6x^2+17x+12
help meeeeeeeeeeeeee pleaseeeeeeeeee!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Describe the relationship as parallel intersecting or skew AB or BC
Based on the image attached, the relationship are:
a). AB and BC - Both the segments are said to be perpendicular and they are intersecting at the point B.
b). AE and BF - Both segments are said to be parallel
c). EF and ED - Both are skew
d). Plane ABC and plane ABF - Both of the planes do intersect at point AB
e). Plane AED and plane BFC - Both of the given planes are known to be parallel
How do you know if lines are parallel intersecting or skew?if the ratio equality is accurate, parallel. If the lines are not parallel or if you can solve them as a system of simultaneous equations, the lines will intersect. If two crossing lines have a zero dot product, they are perpendicular.
If the lines are not parallel or intersecting, they are said to skew. Lines that are parallel never cross.
Therefore,
if lines are in the same plane, do not intersect, and are parallelif lines only meet at one point, then they are intersecting.If lines are on two distinct planes and don't intersect, they skew.Learn more about parallel intersection from
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Given the following function, find the vertex, y=5x^2-8x+6
Answer:
The vertex is (0.8, 2.8)------------------------------------
GivenFunction y = 5x² - 8x + 6Find the x-coordinate of the vertexx = - b/(2a)x = - (-8)/(2*5) = 8/10 = 0.8Find the y-coordinate of the vertexy = 5(0.8²) - 8(0.8) + 6 = 2.8Tell whether x and y show a positive, negative, or no relationship
Answer:
negative, as the points are slowly making their way "down" the graph :)
These points are linear.
Find the slope.
x 56 7 8 9
y| 11 | 16 | 21 | 26 | 31
Hint: First calculate the change
between each y-value.
[?]
Slope =
The slope is m = 5.
What is slope?
The change in y coordinate relative to the change in x coordinate is referred to as a line's slope in mathematics. The symbols Δy and Δx stand for the net change in the y-coordinate and the net change in the x-coordinate, respectively. where "m" denotes a line's gradient. tanθ then represents the slope of a line.
We have to find the slope of the points given.
First to find the change between each y - value.
16 - 11 = 5
21 - 16 = 5
26 - 21 = 5
31 - 26 = 5
So the change between each y - value is 5.
Now, to find the slope of the points.
Since,
Slope = m = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
[tex]m_1=\frac{16-11}{6-5}= \frac{5}{1} =5\\ m_2=\frac{21-16}{7-6}=\frac{5}{1} =5\\ m_3=\frac{26-21}{8-7}=\frac{5}{1}=5\\m_4=\frac{31-26}{9-8}=\frac{5}{1} =5[/tex]
Hence, the slope of the given points is 5.
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Answer:
The answer is 5
Step-by-step explanation:
Though there is also a bottom number, just put a 1 in the bottom number
2 3/5 times 3 1/3
NEED ASAP
Answer:
Answer is: 8 2/3 but improper is 26/3
if the interest for 5 years on Rs 3000 is Rs 525, find the interest on Rs 2200 for 6 years at the same rate of interest.
Using the formula of simple interest, the interest on Rs 2200 for 6 years at the same rate of interest is Rs 462.
In the given question,
The given principal amount = Rs 3000
The given time = 5 years
Interest amount = 525
Now finding the rate of interest.
As we know that the formula of simple interest.
I = P*R*T/100
525 = 3000*R*5/100
Multiply by 100 on both side we get
52500 = 15000*R
Divide by 15000 on both side
R = 52500/15000
R = 3.5
In the question we have to find the interest on Rs 2200 for 6 years at the same rate of interest.
To find the interest put the value in I = P*R*T/100
As given P=2200, R=3.5%, T=6 years
I = P*R*T/100
I = 2200*3.5*6/100
I = 462
Hence, the interest on Rs 2200 for 6 years at the same rate of interest is Rs 462.
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15. Find mACB. help me please
The measure of the angle ACB is 87°.
What does the term angle mean?Angles produced by two beams are included in the plane that contains the rays. The intersection of two planes may also produce an angle. Dihedral angles are the name given to them. It is also possible to determine the angle between two crossing curves using the angle created by the rays that are perpendicular to each intersecting curve at that point.
An angle can also refer to a measurement of a rotation or an angle. This number represents the length-to-radius ratio of a circular arc.
When two crossing lines in a plane are not perpendicular to one another, Euclid defined a plane angle as the inclination between those intersecting lines.
In triangle ADE and triangle ACB, the triangles are similar.
So,
∠AED/ ∠ABC = ∠DAE/∠CAB
∠AED = ∠ABC
11x-2 = 6x + 13
11x - 6x = 13 + 2
5x = 15
x = 15/5
x = 3
So, the measure of angle ABC is
∠ ABC = 6(3)+13
∠ ABC = 18+13
∠ ABC = 31°
Now, consider triangle ABC, the sum of all angles = 180°
So, 62° + 31° + ∠ACB = 180°
∠ACB + 93° = 180°
∠ACB = 180° - 93°
∠ACB = 87°
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ESSENTIAL
Chuck
Match up each scenario with the equation that models the word problem.
Skate rental charges an additional $3.
Jeff is 3 years less than Tony's age.
Marie buys balloons for a party that
are $3.00 each.
Intro
y=x+3
y=x-3
y = 3x
Done
En this is the answer
The following are the equations which matches the given word problems:
a. Skate rental charges an additional $3 :
y = x+3
b. Jeff is 3 years less than Tony's age:
y=x-3
c. Marie buys balloons for a party that are $3.00 each:
y = 3x
Given, we have the word problems:
a. Skate rental charges an additional $3 :
here, based on the fixed charge, additional charge is taken as $3.
let the total charge be represented as y and
x represent the fixed charge,
hence the equation we get is:
y = x+3
b. Jeff is 3 years less than Tony's age.
let y represent the age of Jeff
and x represent the age of Tony.
hence we frame the equation as:
y = x - 3
c. Marie buys balloons for a party that are $3.00 each:
let the cost of the balloon be represented as y
and x represent the number of balloons Marie wants to buy for $3 each.
hence the equation we frame is:
y = 3x
Hence we get the required equations.
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a positive integer divisor of 12! is chosen at random. the probability that the di-visor chosen is a perfect square can be expressed asmn, wheremandnare relativelyprime positive integers. what ism n?
The probability that the divisor chosen is a perfect square is found to be 1/22 which is m:n.
What exactly is meant by probability?Probability is synonymous with possibility. It is a mathematical branch that deals with the occurrence of a random event. The value ranges from zero to one. Probability has been introduced in mathematics to predict the likelihood of events occurring.Given: Randomly, a positive integer divisor of 12! is selected.
Prime factorization of 12! = 2¹⁰ × 3⁵ × 5² × 7¹ × 11
Total divisors of 12! = 11 × 6 × 3 × 2 × 2
Each number in the prime factorization must have an even exponent in order to construct a perfect square divisor. In the prime factorization, the divisor cannot have any factors of 7 and 11 because there is only one of each in 12!. There are 6 × 3 × 2 perfect squares as a result.The probability that the divisor chosen is a perfect square is given as:
(6 × 3 × 2)/(11 × 6 × 3 × 2 × 2)
= 1/22
=m/n
Therefore, the probability that the divisor chosen is a perfect square is found to be 1/22 which is m:n.
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gold miners in alaska have found, on average, 12 ounces of gold per 1,000 tons of dirt excavated with a standard deviation of 3 ounces. assume the amount of gold found per 1,000 tons of dirt is normally distributed. if the miners excavated 1,000 tons of dirt, how little gold must they have found such that they find that amount or less only 15% of the time?
Miners excavated 1000 tons of dirt, and they found 8.892 ounces of gold.
Let X stand for the random variable determining how much gold is discovered for every 1,000 tonnes of dirt dug up. After that, we learn that:
X ~ N (12, 3²)
Let K be the required amount of discovered gold. 15% of the time, less than K worth of gold is discovered. Next, we have:
P (X ≤ K) = 0.15
When we transform this into a typical normal variable, we get:
P [Z ≤ (K - 12) / 3] = 0.15
From the common normal tables, we can deduce:
P (Z ≤ -1.036) = 0.15
Comparing the two equations above, we obtain:
(K - 12) / 3 = -1.036
K = 12 - (1.036 * 3) = 12 - 3.108 = 8.892
As a result, 8.892 ounces of gold are needed.
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