Using direct variation, the value of x for equation y = 5/-3 (x) is 3/5 when y = -1
What is direct and inverse variation?When x is not equal to zero, an equation of the form y = kx describes the linear function known as direct variation. When x is not equal to zero and k is a nonzero real number constant, the equation of the form xy = k describes the nonlinear function known as inverse variation.
Using direct variation,
y = kx
⇒ 5 = k(-3)
⇒ k = 5 / -3
for y = -1
y = 5/-3 (x)
⇒ -1 = 5/-3 × x
⇒ x = 3/5
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Compute the mean and variance of the following probability distribution. (round your answers to 2 decimal places.) x p(x) 7 0.10 14 0.20 21 0.25 28 0.45 click here for the excel data file
The mean of the probability distribution is 21.35 and the variance of the probability distribution is 51.3275
Given the probability distribution with values of x and corresponding P(x). We need to find the values of [tex]x^2[/tex], x P(x), [tex]x^2[/tex] P(x) to calculate mean and variance.
x P(x) [tex]x^2[/tex] x P(x) [tex]x^2[/tex] P(x)
7 0.10 49 0.7 4.9
14 0.20 196 2.8 39.2
21 0.25 441 5.25 110.25
28 0.45 784 12.6 352.8
-----------------------------------------------------
∑x P(x) = 21.35
∑[tex]x^2[/tex] P(x) = 507.15
Mean = ∑x P(x) = 21.35
and variance = ∑[tex]x^2[/tex] P(x) - [tex](\sum x\ P(x) )^2[/tex] = 507.15 - 455.8225 = 51.3275
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The harmonic mean of two numbers a and b equals 2/ 1/a + 1 / b . As you vary the length of a violin or guitar string, its pitch changes. If a full-length string is 1 unit long, then many lengths that are simple fractions produce pitches that harmonize, or sound pleasing together. The harmonic mean relates two lengths that produce harmonious sounds. Find the harmonic mean for each pair of string lengths.
c. 3/4 and 3/5
The Harmonic Mean for the length of strings 3/4 and 3/5 is 2/3 .
Harmonic mean for 2 numbers "a" and "b" is denoted by
[tex]HM=\frac{2}{\frac{1}{a} +\frac{1}{b} }[/tex].
In the given question ;
Given that ;
the length of the first string is 3/4
Length of the second string is 3/5.
Substituting the values in the formula of harmonic mean
we get,
HM=[tex]\frac{2}{\frac{1}{\frac{3}{4} }+\frac{1}{\frac{3}{5} } }[/tex]
[tex]=\frac{2}{\frac{4}{3} +\frac{5}{3} }[/tex]
Taking LCM of denominator as 3 and solving further we get ;
[tex]=\frac{2}{\frac{5+4}{3} }\\ \\ =\frac{2}{\frac{9}{3} }[/tex]
Rewriting the complex fraction
=2*(3/9)
=6/9
On further simplifying we get ;
=2/3
Therefore , the Harmonic Mean for the length of strings 3/4 and 3/5 is 2/3 .
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A projectile’s motion can be modeled by the quadratic equation: h left parenthesis t right parenthesis space equals space minus g t squared space plus space v subscript 0 t space plus thin space h subscript 0 g is 16 if in feet and 9 if in meters;; t = time in second elapsed from release of projectile; v0= initial velocity; h0 = initial height. Write the equation for a projectile that is dropped (v0 = 0) from a height of 100 ft. When will it hit the ground? Change the equation to reflect that the object is thrown upward from an initial height of 6 ft at 30 ft/sec. When will the object be back at the starting height? Hit the ground?
The projectile motion equation [tex]h(t) = - g \cdot {t}^{2} + v_{0}\cdot {t} + h_{0}[/tex], gives;
First part;
The object will hit the ground in 2.5 secondsSecond part;
The object will be back at the starting point in 1.875 secondsThird part;
The object will hit the ground in approximately 2.06 secondsHow can the projectile motion information be found?The quadratic equation that represents the projectile motion can be presented as follows;
[tex]h(t) = - g \cdot {t}^{2} + v_{0}\cdot {t} + h_{0}[/tex]
g = 16 ft./s² or 9 m/ s²
First part;
When
[tex] v_{0} = 0 \: and \: h_{0} = 100 \: ft.[/tex]
We have;
h(t) = -16•t² + 100
When the object hits the ground, we have;
h(t) = 0, which gives;
0 = -16•t² + 100
Therefore;
16•t² = 100
t² = 100 ÷ 16 = 25/4
t = √(25/4) = 5/2 = 2.5
The time it takes the object to reach the ground is 2.5 seconds.Second part;
The direction in which the object is thrown = Upwards
Initial height of the object, [tex] h_{0} = 6 \: ft[/tex]
Initial speed of the object, [tex] h_{0} = 30 \: ft/sec[/tex]
The equation of the projectile motion is therefore;
h(t) = -16•t² + 30•t + 6
Which gives;
When the object is at its starting height of 6 feet, h(t) = 6, which gives;
6 = -16•t² + 30•t + 6
-16•t² + 30•t = 0
A solution to the above equation is t = 0
The other solution is found as follows;
-16•t² + 30•t = 0
-16•t + 30 = 0
30 = 16•t
t = 30/16 = 1.875
The object will be back at the starting height at 1.875 secondsThird part;
When the object hits the ground, we have;
h(t) = 0, which gives;
0 = -16•t² + 30•t + 6
Which gives;
t ≈ 2.06
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Two people quit work and begin college at the same time. Their salary and education information is given in the table below.
Salary prior to school
Years attending college
Total cost of college
Salary upon graduating
Person A
$18,000
3
$45000
$33,000
Person B
$27,000
4
$30,000
$37,000
Choose the true statement.
a.
Person A recovers their investment in a shorter amount of time.
b.
Person B recovers their investment in a shorter amount of time.
c.
They recover their investments in the same amount of time.
d.
There is too little information to compare the time to recover their investments.
Person B recovers their investment in a shorter amount of time.
What is the recovery time?In order to determine the recovery time, divide the total cost of college by the salary that is earned after graduating from college.
Division is the process of grouping a number into equal parts using another number. The sign used to denote division is ÷. Division is one of the basic mathematical operations.
Recovery time = cost of college / salary after college
Recovery time for person A = $45,000 / $33,000 = 1.36
Recovery time for person B = $30,000 / $37,000 = 0.81
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3. The!perimeter!of!a!rectangle!is!24.!!Find
the dimensions if its length is 4 greater
than its width.
Answer:
the length would be 9.6 and the width would be 2.4
Step-by-step explanation:
9.6×2= 19.2
2.4×2= 4.8
19.2+4.8=24
A project has a critical path with a duration of 20 weeks and a standard deviation of 4 weeks. There is a 35% chance the project will be completed in x weeks or less. What is x? select the closest answer.
According to the question, a project has a duration of [tex]20[/tex] weeks and a standard deviation of[tex]4[/tex] weeks. And the calculated weeks to complete the [tex]35[/tex] percent work is [tex]18.4[/tex].
As per question, the critical path is the longest path from start to finish. It tells the minimum time required to finish the assigned project.
As per the question, the given data is as follows:
Time Duration = [tex]20[/tex] weeks, Standard Deviation = [tex]4[/tex] weeks, Completion = [tex]35[/tex] percent
[tex]Z = \frac{S-T}{var} =18.4[/tex]
The solution for the given question is [tex]18.4[/tex].
What is the critical path?
The critical path is the path for the assigned work and it is the longest path. This phenomena is used to calculate the minimum time for the project completion.
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2(4w-1)=-10(w-3)+4 solve the question
Answer:
w = 2
Step-by-step explanation:
[tex]2\cdot \:4w-2\cdot \:1\\= 8w-2\cdot \:1\\= 8w-2\\-10\left(w-3\right)+4\\= - 10w - \left(-10\right)\cdot \:3\\= -10w+10\cdot \:3\\-10w + 30\\= -10w + 30+4\\= -10w + 34\\8(w)-2=-10w+34\\8(w) - 2+2 =-10w+34+2\\8(w)=-10w+36\\18(w)=36\\\frac{18(w)}{18} = \frac{36}{18}\\= 2[/tex]
Answer:w=2
Step-by-step explanation:
8w-2=-10w+30+4
8w-2=-10w+34
Add 10 w both sides
18w-2=34
add 2 both sides
18w=36
Divide by 18
W=2
Por favor help me . I’m struggling on this specific topic and need to know how to resolve it. Thanks in advance
Using the graph of h we get (a) Value of function h at x=5 is 8
(b) Limit of h(x) at x=5 does not exist
(c) Value of function h at x=7 is 4
(d) Limit of h(x) at x=7 does not exist
(e)Limit of h(x) at x=8 is 5
What is limit of a function how to find limit using graph?Limit : Limit is the value that a function output approaches as the input approaches to a certain value.
For any function g(x) , [tex]\lim_{x \to \22} g(x)[/tex] refers to the value that the g(x) approaches as the x approaches to 2 from either left hand side or from right hand side
From any graph we can easily see that to what value g(x)=y on the curve is approaching when the x is approaching to some value on x axis and if the graph is splitting into different functions on the value of x where x is approaching then the limit does not exist for that value of x.
For given graph h(x)
We can see value of value of function h at x=5 is 8 and value of function h at x=7 is 4
As the graph of h(x) has a hole in the graph when x=5, breaking its function into two different function on x=5 then or limit of h(x) at x=5 does not exist
As the graph of h(x) has a hole in the graph when x=7, breaking its function into two different function on x=7 then or limit of h(x) at x=7 does not exist
As the graph is not breaking at x=8or we can say that graph of g(x)is approaching to 5 as x approaches to 8 then limit of h(x) at x=8 is equal to g(1) that is 5
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The sum of an integer and 6 times the next consecutive integer is -50. Find the
value of the greater integer.
Answer:
Submit Answer
Dar
The value of the greater integer is -8.
Given,
The sum of an integer and 6 times the next consecutive integer = -50
We have to find the value of the greater integer:
Let's take x as the integer.
Next consecutive integer be (x + 1)
Now,
x + 6(x + 1) = -50
x + 6x + 6 = -50
7x + 6 = -50
7x = -50 - 6
7x = -56
x = -56/7
x = -8
The value of x is -8.
Now,
x + 1 = -8 + 1 = -7
That is,
-8 + (6 × -7) = -50
-8 -42 = -50
Here, the integers are of negative values.
So, the value of greater integer be -8.
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Suppose a balloon is filled with 5000 cm³ of helium. It then loses one fourth of its helium each day. How much helium will be left in the balloon at the start of the tenth day?c. How can you write a formula for this sequence?
The sequence can be expressed by the formula: v(n) = 5000 . (3/4)ⁿ⁻¹. Helium left at the start of the 10th day is 375.42 cm³
1st day:
Helium is filled with 5000 cm³ of helium.
We can write v(1) = 5000 cm³
2nd day:
The balloon losses 1/4 of helium volume. In other word, the remaining volume of helium is:
(1 - 1/4) = 3/4 of its initial volume.
We can write:
v(2) = 3/4 . 5000 = 3750 cm³
We can continue this process:
v(3) = 3/4 . 3750 = 2812.5
Notice that each day remaining volume of helium forms a geometric sequence, with v(1) = 5000 and a common ratio (r) = 3/4.
Recall the formula for the nth term of a geometric sequence:
v(n) = v(1) . rⁿ⁻¹
To find the explicit formula, substitute v(1) = 5000 and (r) = 3/4:
v(n) = 5000 . (3/4)ⁿ⁻¹
Tenth day means n = 10. Substitute these parameters into the formula:
v(10) = 5000 . (3/4)¹⁰⁻¹
v(10) = 5000 . (3/4)⁹
= 375.42 cm³
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A bakery sells an average of 14 dozen cupcakes a day to about 50 customers. what is their average sale rate, in cupcakes per customer?
i also need the answer really quick!!!
Answer:
3.36
Step-by-step explanation:
→ How much is a dozen
12
→ Multiply by 14
168
→ Divide by 50
168 ÷ 50 = 3.36
on Tuesday the shop receives x cents by selling bottles of water at 45 cents each. In terms of x, how many bottles were sold
the bottles were sold equal x / 45
What is the sum of the polynomials? 1.3t3 t2 â€"" 42t 8 1.3t3 t2 â€"" 6t 8 1.9t3 8.4t2 â€"" 42t 1.9t2 â€"" 42t 8
The sum of the polynomials is [tex]\bold{4.5t^3 + 12.3t^2-132t+24}[/tex].
Given polynomials are:
[tex]1.3t^3+t^2-42t+8\\ 1.3t^3+t^2-6t+8 \\1.9t^3+8.4t^2-42t \\1.9t^2-42t+8[/tex]
To find the sum of the polynomials, add the coefficients of the terms of same degree in each polynomials. That is add the terms containing [tex]t^3[/tex] , then terms of [tex]t^2[/tex], then terms of t and finally the constant terms of the polynomials.
So we get, [tex](1.3t^3+t^2-42t+8)+(1.3t^3+t^2-6t+8 )+(1.9t^3+8.4t^2-42t )+(1.9t^2-42t+8)\\ = (1.3+1.3+1.9)t^3+(1+1+8.4+1.9)t^2+(-42-6-42-42)t+(8+8+8)\\=\bold{4.5t^3 + 12.3t^2-132t+24}[/tex]
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Recipe a four minestrone soup requires 4 cups of tomatoes a different recipe recipe be for minestrone soup requires 14 cups of tomatoes which recipe requires more tomatoes how much more
Answer:
The recipe with 14 cups of tomatoes requires more tomatoes. This is because it needs 10 cups more of tomatoes than the recipe with 4 cups.
Please help with the question on the photo :)
Answer:
Explanation:
a) To work out the average or mean age we must first calculate the total age.
19 x 2 = 38
20 x 3 = 60
21 x 1 = 21
22 x 4 = 88
23 x 1 = 23
Total = 230
Then... Divide the number of players with this figure
Number of players = 2 + 3 + 2 + 4 + 1 = 11
230/11 = 20.9 is the average age of the players
b) We know the average will now be 22 and we know the number of players is now 12.
So... 22 x 12 = 264 (This will be the new total age of all the players)
We know the previous total was 230
So 264-230 = 34 (years old)
I hope this helps you! :)
Help please??? Quick
Answer:2.5
Step-by-step explanation:
5/2=2.5
in a school canteen, a cup of tea costs 80p. Write down an expression for the cost in pence of y cups of tea
The expression is f(y) = 80y.
We have a school canteen.
We have to write down an expression for the cost in pence of y cups of tea.
What is a function in Mathematics?A function in mathematics is a relation involving two variables, such that one variable is dependent on the other for its value.
According to the question -
Number of cups of tea = y
Cost of one cup = 80 pence.
Therefore, the function representing the cost in pence of y cups of tea =
f(y) = 80y
Hence, the expression is 80y.
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Find the distance between pair of parallel lines with the given equations.
y=2x+3 y=2x-7
The distance between pair of parallel lines with the following equation
y=2x+3 y=2x-7 [tex]2{\sqrt 5}[/tex] units
Definition of parallel linesParallel lines are any two or more lines that lie in the same plane but never cross one another. Both have the same slope and are equally distant from one another. No matter how far we extend a parallel line, it will always remain straight.
The fundamental characteristics listed below make it simple to recognize parallel lines.
Straight lines which are always the same distance apart from one another are known as parallel lines.No matter how far apart they are from one another, the parallel lines can never intersect.The slope of a line which is perpendicular to both the lines will be [tex]-\frac{1}{2}[/tex].
Check what are the y-intercept of any one of the two lines & write the equation of the perpendicular line through it.
The y-intercept of line y = 2x-7 is (0, -7).
So, the equation of any line with slope [tex]-\frac{1}{2}[/tex] and a y-intercept of −7 is
y = [tex]-\frac{1}{2}x-7[/tex]
The perpendicular intersects or meets the line y = 2x -7 at (0,-7).
Now, to find the point of intersection of the perpendicular & the other line, solve the two equations.
Solve for x:
2x + 3 = [tex]-\frac{1}{2}x-7[/tex]
[tex]\frac{5}{2} x[/tex] = -10 (combine them like terms)
x = -4 (multiply each side by 2\5)
Find y:
y = [tex]-\frac{1}{2}.(-4)-7[/tex]
= -5
so, the point is (-4,-5).
Now using the Distance Formula, find the distance between the points (-4,-5) and (0,−7).
[tex]{\displaystyle d={\sqrt {\left(x_{2}-x_{1}\right)^{2}+\left(y_{2}-y_{1}\right)^{2}}}[/tex]
[tex]={\sqrt {\left(0-(-4\right)^{2}+\left(-7-(-5\right))^{2}}}[/tex]
[tex]={\sqrt {4^2 +(-2)^2}}[/tex]
[tex]=2{\sqrt 5}[/tex]
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solve each proportion.
3/7=12/x
The value of x in the equation 3/7 = 12/x is equal to 28.
Proportion is a type of mathematical equation that is used to determine the value of the quantities that are not known by forming two equal ratios.
Ratios can be defined as an expression that is used to compare the size of two numbers in relationship to each other to determine how big is one number from the other.
The given proportion can be solved as follows:
3/7 = 12/x
3x = 12 × 7
3x = 84
If 3x is equal to 84, then x will be equal to:
x = 84/3
x= 28
Therefore, the proportion is solved as the value of x is found to be 28.
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oiytrewsdfvbnmoijhugytfr
Answer:
kribble
Step-by-step explanation:
Answer: rftyguhjiomnbvfdswertyio
Step-by-step explanation:
pyploliguatd
What is the value of your total assets if you have a car worth $4,000, you owe $1500 on the car loan, and you have a baseball card collection valued at $750?
The total asset is $4750
How to find the total asset ?The worth of the car is valued at the worth of has $4000 and you he have a baseball card collection valued at $750.
The capital is also know as the equity which means the net worth.
Liabilities are everything a business owes, now and in the future.
Assets are everything a business owns. Assets may be current or fixed assets
Therefore,
Total Assets - Total Liabilities = Capital
Where
Base ball card collection = $750
Total assets = ?
Capital = $4000
Hence,
Total Assets = $4000 + $750
Total Assets = $4750
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Jenny is 12 years older than Steve, Five years ago, Jenny was four times older that Steve was then. How old are Jenny and Steve now?
say Steve is x ,then jenny will be x + 12
five years ago Steve's age was x - 5 and Jenny's age was x + 12 - 5= x + 7
since jenny was four times Steve's age 5 years ago the equation will be
x + 7 = 4(x - 5)
= x + 7 = 4x - 20
putting like terms together, we will have
4x - x = 20 + 7
= 3x = 27
this means 3x ÷ 3= 27 ÷ 3
x = 9
this means Steve is 9 years old and Jenny is 21 years old
Δ A B C is a right isosceles triangle with hypotenuse AB. M is the midpoint of AB. Write a coordinate proof to show that CM is perpendicular, to AB.
It is proved that CM will be perpendicular to AB if M is midpoint of AB.
It is given that ΔABC is a right isosceles triangle with hypotenuse AB and M is midpoint of AB.
We have to prove that CM is perpendicular to AB.
What is an isosceles triangle ?
An isosceles triangle ΔABC is a triangle that has at least two sides of equal length i.e., AC= BC
As per the question ;
ΔABC is a right isosceles triangle with hypotenuse AB.
⇒ AC = BC (by the definition of isosceles triangle)
Also ;
M is midpoint of AB.
⇒ CM = CM (reflexive property)
So ;
ΔACM ≅ Δ BCM (by SSS)
∠A = 45° and ∠B = 45° because of right isosceles triangle.
Also ;
∠ACM = ∠BCM
because they are corresponding angles of congruent triangles
i.e.,
∠ACB = 90°
Now ;
∠ACM + ∠BCM = ∠ACB
because they are adjacent angles.
∵
∠ACM = ∠BCM , so ;
∠ACM + ∠ACM = ∠ACB
2∠ACM = 90°
∠ACM = 45 °
∵
∠A = 45 ° and ∠ACM = 45°
⇒ ∠AMC = 90°
because the sum of angles in a triangle is 180°.
So ,
If ∠AMC = 90° , then CM is perpendicular to AB because perpendicular lines form 90° angles.
Thus , CM will be perpendicular to AB if M is midpoint of AB.
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Write an equation of a circle with the given center and radius. Check your answers.
center (0,0) , radius 10
The equation of the circle with radius 10 and center at (0 , 0) is x^2 + y^2 = 100.
The general form of the equation of circle is given by (x - h)^2 + (y - k)^2 = r^2, where (h , k) is the location of the center and r is the radius of the circle.
Given the radius and center of the circle, substitute these values to the general form of the equation of the circle.
(x - h)^2 + (y - k)^2 = r^2
where (h , k) = (0 , 0)
r = 10
(x - 0)^2 + (y - 0)^2 = 10^2
x^2 + y^2 = 100
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Factor the polynomial by its greates
9b³ +24b³
||
Answer:
Step-by-step explanation:
=the highest common factor is [tex]3b^{3}[/tex]
therefore you can divide each and every term of the expression and take it out of the brackets.
[tex]=3b^{3} (3+8)\\=3bx^{3} (11)[/tex]
Although I still see no use of factorising because there are only like times that is what I put on table. Please ask if you have questions
Determine the truth value of the given conditional statement. If true, explain your reasoning. If false, give a counterexample.
If {x⁴=16}, then x=2.
A function assigns the values. The given statement "If {x⁴=16}, then x=2" is true.
What is a Function?A function assigns the value of each element of one set to the other specific element of another set.
The given statement "If {x⁴=16}, then x=2" is true. This is because we solve the equation x⁴=16 for the value of x as shown below, then the value of x will be 2, as shown below.
x⁴ = 16
x⁴ = 2 × 2 × 2 × 2
x × x × x × x = 2 × 2 × 2 × 2
x = 2
As it is seen that the value of x is 2. Although, the given statement may be false if the value of x is -2 because still the value of x⁴ = 16, but the only two options available are true and false. Thus, we can conclude that the given statement is true.
Hence, The given statement "If {x⁴=16}, then x=2" is true.
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Use the given information to determine whether LM is a perpendicular bisector, median, and/or an altitude of Δ J K L .
Δ J L M ≅ ΔK L M
LM is the perpendicular bisector, median, and altitude of Δ JKL.
Since Δ JLM ≅ ΔKLM, we can prove JM ≅ MK and [tex]\angle[/tex] LMJ ≅ [tex]\angle[/tex] LMK. Since [tex]\angle[/tex] LMJ ≅ [tex]\angle[/tex] LMK and they are a linear pair, then we know they are right angles and LM ⊥ JK.
What is meant by CPCTC?CPCTC is an abbreviation for "corresponding parts of congruent triangles are congruent," and it states that if two or more triangles are congruent, their corresponding angles and sides are also congruent.
CPCTC is frequently used at or near the end of a proof in which the student is asked to demonstrate that two angles or two sides are congruent. It means that if two triangles are proven to be congruent, the three pairs of sides that correspond must also be congruent, as must the three pairs of angles that correspond.
Since Δ JLM ≅ ΔKLM, we can prove JM ≅ MK and [tex]\angle[/tex] LMJ ≅ [tex]\angle[/tex] LMK. Since [tex]\angle[/tex] LMJ ≅ [tex]\angle[/tex] LMK and they are a linear pair, then we know they are right angles and LM ⊥ JK.
Therefore, we know that JM ≅ MK by CPCTC, making M the midpoint of JK. Therefore, LM is the perpendicular bisector, median, and altitude of ΔJKL.
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Cory studied for his math test on Monday and Tuesday. He spent a total of 75 minutes studying. He spent an extra 15 minutes studying on Tuesday. How long did he study on Monday and Tuesday
Answer:
90 minutes...
Step-by-step explanation:
75+15....
Solve each equation. 7(a+1)-3 a=5+4(2 a-1)
The the solution of the linear equation in one variable 7(a+1)-3 a=5+4(2a-1) is at a = 3/2.
According to the given question.
We have a linear equation in one variable.
7(a+1)-3 a=5+4(2a-1)
As we know that, the linear equations in one variable is an equation which is expressed in the form of ax+b = 0, where a and b are two integers, and x is a variable and has only one solution.
Thereofre, the solution of the linear equation in one variable 7(a+1)-3 a=5+4(2a-1) is given by
7(a+1) -3a = 5 + 4(2a - 1)
⇒ 7a + 7 - 3a = 5 + 8a - 4 (by distributive rule)
⇒ 4a + 7 = 1 + 8a
⇒ 7 - 1 = 8a - 4a
⇒ 6 = 4a
⇒ 6/4 = a
⇒ a = 3/2
Hence, the the solution of the linear equation in one variable 7(a+1)-3 a=5+4(2a-1) is at a = 3/2.
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A pair of parallel interstate gas power lines run 10 meters apart and are equally distant from relay station A. The power company needs to locate a gas-monitoring point on one of the lines exactly 12 meters from relay station A. Draw a diagram showing the locus of possible locations (there should be two.)
Explanation would be appreciated!
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