[tex]\qquad \qquad \textit{inverse proportional variation} \\\\ \textit{\underline{y} varies inversely with \underline{x}} ~\hspace{6em} \stackrel{\textit{constant of variation}}{y=\cfrac{\stackrel{\downarrow }{k}}{x}~\hfill } \\\\ \textit{\underline{x} varies inversely with }\underline{z^5} ~\hspace{5.5em} \stackrel{\textit{constant of variation}}{x=\cfrac{\stackrel{\downarrow }{k}}{z^5}~\hfill } \\\\[-0.35em] ~\dotfill[/tex]
[tex]\stackrel{\textit{"y" varies inversely with }x^2}{y = \cfrac{k}{x^2}}\hspace{5em}\textit{we also know that} \begin{cases} x=4\\ y=\frac{11}{4} \end{cases} \\\\\\ \cfrac{11}{4}=\cfrac{k}{4^2}\implies \cfrac{11}{4}=\cfrac{k}{16}\implies \cfrac{(11)(16)}{4}=k\implies 44=k~\hfill \boxed{y=\cfrac{44}{x^2}} \\\\\\ \textit{when x=2, what's "y"?}\qquad y=\cfrac{44}{2^2}\implies y=\cfrac{44}{4}\implies y=11[/tex]
Answer:
y = 11 when x = 2
Step-by-step explanation:
This is indirect proportionality where:
y ∝ [tex]\frac{1}{x^{2}}[/tex]
This means:
[tex]y_{1} x_{1}^{2} = y_{2}x_{2}^{2}[/tex]
Substitute the following values in the above equation to solve for [tex]y_{2}[/tex]
[tex]y_{1} = \frac{11}{4}[/tex]
[tex]y_{2} = ?[/tex]
[tex]x_{1} = 4[/tex]
[tex]x_{2} = 2[/tex]
= [tex](\frac{11}{4})(4^{2}) = y_{2}(2^{2})[/tex]
= [tex](\frac{11}{4})(16) = y_{2}(4)[/tex]
= [tex]44 = 4y_{2}[/tex]
= [tex]y_{2} =\frac{44}{4}[/tex]
∴ y = 11
The budget for a project on voting trends includes $3200 for hiring undergraduateâ students, graduateâ students, and faculty members to conduct interviews on the day before an election. Each undergraduate student will conduct 30 interviews forâ $100. Each graduate student will conduct 32 interviews forâ $150. Each faculty member will conduct 33 interviews forâ $200. No more than 20 interviewers can be hired. How many of each type of interviewer should be hired in order to maximize the number ofâ interviews? What is the maximum number ofâ interviews?A)___undergraduateâ students, __ graduateâ students, and___ faculty members should be hired to maximize the number of interviews
By the help of inequality properties The maximum number of interviews is 644.
Let x = number of undergraduate students hired, y = number of graduate students hired, z = number of faculty members hired, n = number of interviews
The objective function is:
Maximize n = 30x + 32y + 33z
The constraints are:
x + y + z ≤ 20
100x + 150y + 200z ≤ 3200
x, y, z integers and ≥ 0 The solution is x = 0, y = 16, z = 4, n = 644
0 undergraduate students, 16 graduate students, and 4 faculty members should be hired to maximize the number of interviews. The maximum number of interviews is 644.
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Pablo received $200 dollars for his high school graduation. He wants to save his money to buy a new laptop that cost $700 for when he attends
college. Each month, he adds $125 to his laptop savings. Write an equation in slope intercept form for m, the number of months that it will take Pablo to save $700.
Let's call the number of months that it takes Pablo to save $700 as "m". The amount of money Pablo has saved after "m" months can be represented by the equation:
y = 200 + 125m
where y is the total amount of money saved after "m" months.
To find the number of months it will take Pablo to save $700, we can set y equal to $700 and solve for m:
700 = 200 + 125m
500 = 125m
m = 500 / 125 = 4
So it will take Pablo 4 months to save $700.
The equation in slope-intercept form is:
y = 125m + 200
where m is the number of months and y is the total amount of money saved. The slope of the line is 125, which represents the amount added to the savings each month, and the y-intercept is 200, which represents the initial amount of money Pablo received for graduation.
An initial deposit of $1200 is put into an account that earns 5% interest, compounded annually. Each year, an additional deposit of $1200 is added to the account.
Through the aid of future value If no withdrawals or new deposits are made, the account's value following the tenth deposit should be $15,093.47.
The implied value of an asset as of a particular date in the future based on a growth rate assumption is known as the Future Value (FV). This area of mathematics examines how random events happen. The value might be between 0 and 1. The mathematical idea of probability aids in predicting the possibility of specific events. In general, probability relates to how probable something is to happen. The interest rate assumption, or the rate of return on the initial amount of capital invested, or the present value, determines the projected future value (PV).
Calculation of the value:
The initial deposit is $1.200
The rate of interest is 5%
Now the future value be like
[tex](1200\times\frac{(1+0.05)^9-1}{0.05} )\times(1+0.05)+1,200\\\\\(1200\times(\frac{1.5513-1}{0.05} )\times(1+0.05)+1,200\\\\(1200\times11.0265)\times(1.05)+1,200\\\\13893.4711+1,200\\$15,093.47[/tex]
Through the aid of future value If no withdrawals or new deposits are made, the account's value following the tenth deposit should be $15,093.47.
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the standard deviation is a resistant measure of spread. t/f
True, the standard deviation is a resistant measure of spread.
The standard deviation is calculated as the square root of the variance of the data set. Variance is calculated as the average of the squared differences between each data point and the mean of the data set. The standard deviation is the square root of this average.
In mathematical terms, the standard deviation can be calculated using the following formula:
σ = √(1/n ∑(x - μ)²)
Where σ is the standard deviation, n is the number of data points in the data set, x is the value of the i-th data point, and μ is the mean of the data set.
The standard deviation is an important measure because it gives an idea of how much the individual values in a data set differ from the mean.
In summary, the standard deviation is a resistant measure of spread because it gives a robust measure of the spread of the data in a set and is not easily influenced by outliers or extreme values.
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8x+12y=−96 into slope intercept from
Write using positive exponents
x^3 * x^5
Answer: easy, the answer is x^6 (look at the image for the solution and make sure to give me brainliest)
Step-by-step explanation:
for each circle find the exact circumference in terms of pi 3mm 7mm
The AB intersects circle P if PA is 7mm and PB is 3mm it must exit the circle, and it has 2 contact points.
PA is longer than the radius of the circle so Point A must be outside of the circle.
What is the meaning of intersecting circles?Two or more circles intersect at one point. Two circles can be tangent to each other in two different ways.
here, we have,
We have given that,
AB lies in the same plane as circle P, which has a radius of 6 mm.
PB is less than the radius of the circle so Point B must be inside the circle.
Since the ray is going from A to B it is coming inside the circle and continuing in the other direction.
Therefore, it must exit the circle, giving us 2 contact points.
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The median and the height of an isosceles trapezoid are equal in length. One diagonal of the trapezoid has length $12$. What is the area of the trapezoid?
The area of the isosceles trapezoid is 72 square units.
What is isosceles trapezoid ?A quadrilateral having at least one set of parallel sides and equal length non-parallel sides is called an isosceles trapezium. To put it another way, it is a trapezium whose two non-parallel sides are congruent. The trapezoid's parallel sides are referred to as the bases, and the segments that link the bases are referred to as the legs. The angle between the bases of an isosceles trapezoid determines its height.
Given:
[tex]\[d = 12 \quad \text{(length of one diagonal)}\][/tex]
Let;
[tex]\[h = \text{height of the trapezoid}\][/tex]
[tex]\[a = \text{smaller base of the trapezoid}\][/tex]
[tex]\[b = \text{larger base of the trapezoid}\][/tex]
Using the given information that the height and median are equal, we have:
[tex]Median(m)=\frac{1}{2} {(a+b)}\\\\Height(h)=\frac{1}{2} {(a+b)}\\\\2h=a+b ........(1)[/tex]
[tex]\[\text{Area} = \frac{1}{2} \cdot (a + b) \cdot h\][/tex]
[tex]\[\text{Area} = m \cdot h\] = h^2 ............(2)[/tex] (∵ [tex]Median(m)=\frac{1}{2} {(a+b)}[/tex] and m=h)
Now,
[tex]\[ d = \sqrt{h^2 + \frac{(a+b)^2}{4}} \][/tex] for isosceles trapezoid,
[tex]\[ 12^2 = h^2 + \frac{(a+b)^2}{4}}[/tex]
[tex]\[ 12^2 = h^2 + \frac{(2h)^2}{4}}[/tex] (∵from eq (1))
[tex]\[ 12^2 = h^2 + {(h)^2}}\\ \\144= 2h^2\\\\h^2=72 ..........(2)[/tex]
Lastly, we may change the values of "a," "b," and "h" in the following formula to find the area as;
[tex]\[\text{Area} = \frac{1}{2} \cdot (a + b) \cdot h\][/tex]
[tex]\[\text{Area} = \frac{1}{2} \cdot (2h) \cdot h\][/tex]
[tex]\[\text{Area} = h \cdot h\] = h^2 = 72 sq units[/tex]
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please answer thank you!!!!!!!!!
The measure of the angle formed by 2 secants that have a common point outside a circle is 1/2 the difference of the measure of the further intercepted arc and the closer intercepted arc. That means that half of the the measure of arc ABC - measure of arc XYZ is the measure of angle X. Substituting the given values gives you the equation x = 1/2 (125-45)
Then you can solve.
x = 1/2 (80)
x = 40
The measure of angle X is 40 degrees
Suzanna has $20. Candy bars
cost $0.50. How many candy
bars can she buy and still
have more than $7 left?
Answer:
Step-by-step explanation:
Divide 20 by 0.50. This gets you 40 meaning she can buy 40 candy bars with her $20 if they are $0.50 each. In order to have $7 left over then she would buy 14 candy bars.
Can I please have some help? THanks
By using the function rule, the missing values in table should be completed as follows;
x -2 -1 0 1 2
y -16 -6 4 14 24
How to complete the table?In order to use the given linear function to complete the table, we would have to substitute each of the values of x (x-values) into the linear function and then evaluate as follows;
When the value of x = -2, the y-value of this linear function is given by;
-10x + y = 4
y = 10x + 4
y = 10(-2) + 4 = -16.
When the value of x = -1, the y-value of this linear function is given by;
y = 10x + 4
y = 10(-1) + 4
y = -6.
When the value of x = 0, the y-value of this linear function is given by;
y = 10x + 4
y = 10(0) + 4
y = 4.
When the value of x = 1, the y-value of this linear function is given by;
y = 10x + 4
y = 10(1) + 4
y = 14.
When the value of x = 2, the y-value of this linear function is given by;
y = 10x + 4
y = 10(2) + 4
y = 24.
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9th grade math i need help in
The fourth term in the sequence is 7.
What is Geometric Progression?Geometric progression is a sequence of numbers such that the ratio of two consecutive numbers is the same for whole sequence.
This ratio is common ratio.
Given is the first term of a sequence.
c(1) = 56
Also, there is given an nth term of the sequence.
c(n) = c(n - 1) [tex]\frac{1}{2}[/tex]
This means that every term in the sequence is the half of the preceding term.
So this is a geometric sequence with a common ratio of 1/2.
nth term of a geometric sequence = a. rⁿ⁻¹, where a is the first term and r is the common ratio.
Given, first term = 56 and we found r = 1/2
c(4) = 56 × ([tex]\frac{1}{2}[/tex])⁴⁻¹ = 7
Hence the fourth term in the given sequence is 7.
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The base of a right rectangular prism and a rectangular pyramid is 4 [tex]cm^{2}[/tex]. The height of the pyramid is 3 times larger than the prism. How does the volume of the pyramid compare to the volume of the prism?
Question 3 options:
A) The volume of the pyramid is 3 times larger than the prism.
B) The volume of both shapes are the same.
C) The volume of the pyramid is 9 times larger than the prism.
D) The volume of the pyramids is 1/3 times larger than the prism.
Yhe volume of both the prism and the pyramid are the same. The right response is B, which states, "The volume of both shapes is the same."
What is the straightforward meaning of volume?
Three-dimensional space is occupied by everything. Here, the volume of the space is calculated. A three-dimensional object's volume is the area included inside its bounds. It is also referred to as an object's capability occasionally.
[tex]\mathrm{h_{py} = 3 \times h_p}[/tex]
The volume of the prism is given by:
[tex]V_p[/tex] = base area × height = 4 cm² × [tex]h_p[/tex]
The volume of the pyramid is given by:
[tex]\mathrm{V_{py}}[/tex] = (1/3) * base area * height = (1/3) * 4 cm² * [tex]h_{py[/tex]
Using the equation for [tex]h_{py[/tex] from above, we can substitute:
[tex]\mathrm{V_{py}}[/tex] = (1/3) * 4 cm² * 3 * [tex]h_p[/tex] = 4 cm² * [tex]h_p[/tex] = [tex]V_p[/tex]
So the volume of both the prism and the pyramid are the same. The right response is B, which states, "The volume of both shapes is the same."
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Round 1.587 to the hundredths
place.
Answer:
1.59
Step-by-step explanation:
Rounding to the hundredths has the same meaning as rounding to the second decimal place. Since the third decimal place is 7, we have to round up the decimal. Therefore the rounded value would be 1.59
I hope this makes sense to you. I am generally good with following up with additional questions. Feel free to leave a comment if you have any questions or you can also message me as well!
Original Problem:
Solve the equation for x.
5³x-2 = 125²x
a. Solve using the change of
base formula:
Log by=log y/ log b
b. Solve using a different
method.
C. Verify your solution(s) by
substituting your value back
into the original equation.
The solution of the equation is,
⇒ x = - 2/3
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
The expression is,
⇒ 5³ˣ⁻² = 125²ˣ
a) Now, We can solve the expression by using change of base formula:
⇒ [tex]log_{b} y = \frac{log y}{log b}[/tex]
Hence, We get;
⇒ 5³ˣ⁻² = 125²ˣ
⇒ 5³ˣ⁻² = 5⁶ˣ
Take log both side we get;
⇒ log 5³ˣ⁻² = log 5⁶ˣ
⇒ (3x - 2) log 5 = 6x log 5
⇒ (3x - 2) = 6x
⇒ - 2 = 6x - 3x
⇒ - 2 = 3x
⇒ x = - 2/3
b) Solve for another method as;
⇒ 5³ˣ⁻² = 125²ˣ
⇒ 5³ˣ⁻² = 5⁶ˣ
By comparing,
⇒ 3x - 2 = 6x
⇒ 3x - 6x = 2
⇒ - 3x = 2
⇒ x = - 2/3
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How to Convert 30x+120y=420 into y=mx+b form?
Answer:
y=-0.25x+3.5
Step-by-step explanation:
Ik this
Which rule describes the relationship between the x-and y- coordinates
on the following graph?
PLS ANSWER FAST
Answer:
The answer is B.
Step-by-step explanation:
Method #1 use point slope formula to solve for m of slope.
Method #2 Plug in x-values into option A or B to see you get your dots.
Answer to all seven questions pls
Answer:
1. 7 or S
2. 2 or E
3. 5 or A
4. 3 or I
5. 9 or the shaded-in letter
6. 11 or T
7. 20 or E
Step-by-step explanation:
1. 7 times 2 is 14, and 7 times 3 is 21
2. 2 times 5 is 10, and 2 times 6 is 12
3. 5 times 3 is 15, and 5 times 5 is 25
4. 3 times 2 is 6, and 3 times 5 is 15
5. 9 times 4 is 36, and 9 times 3 is 27
6. 11 times 2 is 22, and 11 times 3 is 33
7. 20 times 3 is 60, and 20 times 1 is 20.
Emma created the poster shown below... What would be the dimensions of the poster at fraction 1 over 4 times its current size?
Answer:
6w by 9L
Step-by-step explanation:
24 x 1/4=6
36 x 1/4=9
write an expression for w more
than
a number 28
Answer:
W > 28
W has to be greater than 28
25 points! the radius r of a sphere with volume v is given by r= (3v/4π)
find the radius of a ball that hold 66 cubic centimeters of air.
Answer:
To find the radius of a ball that holds 66 cubic centimeters of air:
1. Substitute the given volume into the equation r= (3v/4π): r = (3*66/4π).
2. Simplify the equation: r = (198/4π).
3. Calculate the value of 4π: 4π = 12.57.
4. Divide 198 by 12.57: r = 15.75.
5. The radius of the ball that holds 66 cubic centimeters of air is 15.75 cm.
Answer:
Step-by-step explanation:
To find the radius of a sphere that holds 66 cubic centimeters of air, we can use the formula provided in the question:
r = (3v/4π)
where v is the volume of the sphere. We are given that the volume of the sphere is 66 cubic centimeters, so we can substitute this value into the formula:
r = (3 x 66) / (4 x π)
Simplifying this expression:
r = 198 / (4π)
Using a calculator to evaluate this expression:
r ≈ 15.8267
Therefore, the radius of the sphere that holds 66 cubic centimeters of air is approximately 15.8267 centimeters.
Compare 5/8 and 1/3 please hurry!
Answer:5/8
Step-by-step explanation:
Lowest common denominator is 24
15/24 > 8/24
5/8>1/3
What is 576 square root by division method?
Answer:
√576 = 24
Step-by-step explanation:
You want to find the square root of 576 by the long division method.
MethodThe attachment shows the result of applying the method.
The dividend is marked off in 2-digit groups working outward from the decimal point. An overline is typically used. Here, 76 is the group closest to the decimal point, and the next "group" is 5The integer part of the square root of the leftmost 2-digit group is written as the leftmost digit of the root. Here the integer part of the square root of 5 is 2, so that is the first root digit.The quotient digit is appended to the divisor, and the result is multiplied by the root digit. For the first step here, the digit 2 is appended to 0, and multiplied by the root digit 2. The product, 4, is subtracted from the dividend so far, and the next 2-digit group is appended to the result to form the next "dividend."The root so far is doubled and written as the first digits of the new divisor. This will be 2·2 = 4, with space left to append the next root digit: 4_.The next root digit is the largest integer that can be appended to the divisor, and multiplied by that divisor to obtain a value that is at most equal to the "dividend." Here, the second digit of the root is 4, and 44 · 4 = 176. This value is subtracted from the dividend resulting from step 3. Here, they are equal, so the difference is zero, and we're done. If there are more digits and/or the difference is not zero, then the process is repeated from step 3.The root of 576 is 24.
How do you find the square root of 22 using heron's formula method?
(No spam for the points plss"
Answer:
we can't find it by herons formula. but here is your answer.....
Step-by-step explanation:
[tex]\\\sqrt{22}\\\\we can do by long division method \\ the actual value of \sqrt{22} = 4.69041575982343.\\well \sqrt{22} itself is in the simplest form[/tex]
HURRY PLEASE!!!
You want to fill half of the green cylinder with MONEY!
How many cubic centimeters of MONEY will half of this cylinder hold?
1.1 meters = 110 cm
Don't put the comma in your answer.
The Cylinder can hold 138, 160 cm³.
What is Volume?Each thing in three dimensions takes up some space. The volume of this area is what is being measured. The space occupied within an object's borders in three dimensions is referred to as its volume.
Given:
Height= 1.1 m = 110 cm
Radius= 20 cm
Now, Volume of Cylinder
= πr²h
= 3.14 x 20 x 20 x 110
= 3.14 x 44000
= 138, 160 cm³
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PLEASE HELP. NEED ANSWER ASAP. CANT FAIL.
There are two imaginary roots and one real root of the equation
What is the root of an equation?Generally, In mathematics, the root of an equation is a value that satisfies the equation. In other words, it is the value of the variable for which the equation is true. For example, in the equation x^2 - 4 = 0, the roots are +2 and -2, because when either of these values is substituted for x, the equation becomes true.
There are different methods for finding roots of an equation, depending on the type of equation. For example, some equations can be solved by factoring, while others require the use of more advanced techniques such as the quadratic formula or numerical methods like the Newton-Raphson method.
In general, finding the roots of an equation is an important task in mathematics and has many practical applications in fields such as engineering, physics, and finance.
The roots of the equation are
x=-2,3+2 i, 3-2 i
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How do you find the lower quartile range?
Answer:
q1= n/4
is the formulato fine lower quartile
please help!! write a compound inequality
The compound inequality is x < 1 or x >= 3
How to determine compound inequalityFrom the question, we have the following parameters that can be used in our computation:
The number line
From the number line, we have the following readings
x is less than 1 (exclusive of 1)
x is greater than or equal to 3 (inclusive of 3)
Using the above as a guide, we have the following:
x < 1 or x >= 3
Hence, the solution is x < 1 or x >= 3
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Find the next three terms in the following arithmetic sequence.
-4, 5, 14, 19 …
The next three terms in the following arithmetic sequence -4, 5, 14, 19 … include the following:
Term 5 = 32.
Term 6 = 41
Term 7 = 50
How to calculate an arithmetic sequence?Mathematically, the nth term of an arithmetic sequence can be calculated by using this expression:
aₙ = a₁ + (n - 1)d
Where:
d represents the common difference.a₁ represents the first term of an arithmetic sequence.n represents the total number of terms.Next, we would determine the common difference as follows.
Common difference, d = a₂ - a₁
Common difference, d = 5 - (-4)
Common difference, d = 9
Next, we would determine the next three terms as follows:
a₅ = a₁ + (n - 1)d
a₅ = -4 + (5 - 1)9
a₅ = 32
a₆ = a₁ + (n - 1)d
a₆ = -4 + (6 - 1)9
a₆ = 41
a₇ = a₁ + (n - 1)d
a₇ = -4 + (7 - 1)9
a₇ = 50
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Shondra takes notes in class.
Three entries in Shondra’s notes are not in the right place. What can Shondra do to correct her notes?
Step-by-step explanation:
What notes are you speaking of?