The variation equation is xy = a^3
How to determine the equation?An inverse variation is represented as:
xy = k
Where k is the constant of variation
When y = a and x =a^2, we have:
k = a * a^2
Evaluate
k = a^3
Substitute k = a^3 in xy = k
xy = a^3
Hence, the equation is xy = a^3
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Answer both 2 and 3 please
2.
1 day = 24h
1h = 60min
We have 4h 20min
[tex]4h + 20min = 4h+\dfrac{20}{60}h=4h+\dfrac{1}{3}h=4\dfrac{1}{3}h=\dfrac{13}{3}h[/tex]
[tex]\dfrac{\frac{13}{3}}{24}=\dfrac{13}{3}\cdot\dfrac{1}{24}\\\\\huge\boxed{(D)\ \dfrac{13}{72}}[/tex]
3.
6:51PM + 9min → 7:00PM
7:00PM + 27min → 7:27PM
9min + 27min = 36min
[tex]36min=\dfrac{36}{60}h=\dfrac{3}{5}h[/tex]
[tex]\huge\boxed{(C)\ \dfrac{3}{5}}[/tex]
two consecutive odd integers such that 4 times the larger is 29 more than 3 times the smaller
Answer:
21
Step-by-step explanation:
a,a+2,..
4(a+2)=29+3a
4a+8=29+3a
4a-3a=29-8
a=21
A fishing gear shop from boulder, co bought $23,000 worth of fishing rods from a liquidator in pasadena, ca. the shop sold the fishing rods for $49,000, making a profit of $250 per fishing rod. there were __?__ fishing rods involved.
Subtraction is a mathematical operation that reflects the removal of things from a collection. The boulder.co bought 104 fishing rods.
What is subtraction?Subtraction is a mathematical operation that reflects the removal of things from a collection. The negative symbol represents subtraction.
Given the cost price of all the fishing rods is $23,000, also the selling price of all the fishing rod is $49,000. Therefore, the total profit from this transaction is,
Profit = $49,000 - $23,000 = $26,000
Since the profit on a single fishing rod is $250, while the total profit is $26,000. Therefore, the number of fishing rods can be written as,
Number of Fishing rod = Total profit/ Profit per rod
= $26,000 / $250
= 104
Hence, the boulder.co bought 104 fishing rods.
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Study the table.
x
y
–2
8
–1
2
0
0
1
2
2
8
Which best describes the function represented by the data in the table?
linear with a common ratio of 4
linear with a common second difference of 4
quadratic with a common ratio of 4
quadratic with a common second difference of 4
Answer:
quadratic with a common second difference of 4
Step-by-step explanation:
quadratic equations: Quadratic equations are the polynomial equations of degree 2 example - a[tex]x^2\\[/tex]+ b[tex]x[/tex] + c = 0.
[tex]\begin{array}{cc}x&y\\-2&8\\-1&2\\0&0\\1&2\\2&8\end{array}\right][/tex]
from the table it is clear that,
function is y = 2[tex]x^2\\[/tex]
so the function is not linear as the equation specifies.
formula to find second difference of a quadratic equation:
f(x + 2) - 2f(x + 1) + f(x)
therefore;
[tex]2(x+2)^2[/tex] - [tex]4(x+1)^2[/tex] + [tex]2x^2[/tex]
[tex]2(x^2 + 4x + 4) - 4(x^2 + 2x+ 1 ) + 2x^2[/tex]
[tex]2x^2 + 8x + 8 - 4x^2 - 8x - 4 + 2x^2[/tex]
[tex]4x^2 - 4x^2 + 8x - 8x +8 - 4[/tex]
4
therefore, the answer is quadratic with a common second difference of 4
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Find the measure of one interior angle of a regular 21-gon.
A. 160
B. 162.9
C. 165.6
D. 165
Expand & simplify
3(t+5)+5(t−6)
Answer:
8t - 15
Explanation:
⇒ 3(t+5)+5(t−6)
distribute inside parenthesis
⇒ 3(t) + 3(5) + 5(t) + 5(-6)
multiply the variables
⇒ 3t + 15 + 5t - 30
collect like terms
⇒ 3t + 5t + 15 - 30
add/ subtract like terms
⇒ 8t - 15
Solution: 8t-15
Detailed explanation:
First the problem asks us to expand
[tex]\tt 3(t+5)=3\cdot t +3\cdot5=3t+15[/tex]
Similarly
[tex]\tt 5(t-6)=5\cdot t -5\cdot 6=5t-30[/tex]
Therefore
[tex]\tt 3t+15+5t-30[/tex]
Upon combining like terms
[tex]\tt 8t+15-30[/tex]
Upon doing this further
[tex]\tt 8t-15[/tex]
1. Michael Murphy is employed at Agilent Technologies. He has family medical coverage through the group medical plan that Agilent provides for its employees. The annual premium cost for Michael's family is $5,260. The company pays 70 percent of the cost. How much is deducted from his weekly paycheck for medical insurance? (Note: 52 weeks in a year)
$28.12
$29.74
$30.35
$32.66
None of these choices are correct.
2. Brenda Baker has a group health insurance policy from her job at a bank. Her annual premium is $3,500. The policy has a $500 deductible and pays 80% of all medical costs with a stop-loss provision of a limit of $4,000 for out-of-pocket expenses, after the deductible is paid. If Brenda had medical bills totaling $12,000, how much were her out-of-pocket medical costs, including her premiums?
$5,900
$6,300
$6,700
$6,900
None of these choices are correct.
Addition is one of the four fundamental mathematical operations. The correct option is E, None of these choices are correct.
What is Addition?Addition is one of the four fundamental mathematical operations, the others being subtraction, multiplication, and division. When two whole numbers are added together, the total quantity or sum of those values is obtained.
1. The annual premium cost for Michael's family is $5,260. The company pays 70% of the cost. Therefore, the cost he needs to may is,
30% of $5,260
= 0.30 × $5260
= $1578
Since the premium is needed to be paid in 52 week, therefore, the premium cost per week will be,
Premium cost = $1578/52 = $30.35
Hence, the correct option is C, $30.35.
2. Brenda annual premium is $3,500. Also, her medical bills is totaling to $12,000. Therefore, the total amount that is paid by the Brenda in purchasing Insurance and paying the bill is,
Amount Brenda spend = $3,500 + $12,000 = $15,500
The policy has a $500 deductible and pays 80% of all medical costs with a stop-loss provision of a limit of $4,000 for out-of-pocket expenses, after the deductible is paid. Therefore, the amount that she can get is,
Amount she can get = $500 + $4,000 = $4,500
Now, the amount that she needs to pay from her pocket is,
Amount = $15,500 - $4, 500 = $11,000
Hence, the correct option is E, None of these choices are correct.
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Brainliest!
Which system is represented in the graph?
y>x²-2x-3
y > x + 3
Oy
y
Oy2x²-2x-3
y ≤ x + 3
Oy>x²-2x-3
y
Answer:
y ≥ x² -2x -3y ≤ x +3Step-by-step explanation:
When matching graph to inequality, the first things to look for are the nature of the boundary line (solid or dashed), and the direction of shading relative to the boundary line (above or below, left or right).
Boundary lineThe boundary line of the solution set of an inequality will be solid if the line is included in the solution. That is, the inequality will include the "or equal to" case. The corresponding inequality symbols are ≤ or ≥.
The boundary line of the solution set will be dashed if the line is not included in the solution. The corresponding inequality symbols are < or >.
ShadingThe shading will be above the boundary line if the solution set includes larger y-values than those on the boundary. This will be the case when the inequality is of the form y > ( ) or y ≥ ( ).
For inequalities of the form y < ( ) or y ≤ ( ), the shading will be below the boundary line.
Similarly, the shading for an inequality of the form x > ( ) will be right of the boundary line, where x-values are greater. For inequalities of the form x < ( ), the shading will be to the left of the boundary line.
ApplicationIn the given graph, both boundary lines are solid, so both inequalities will include the "or equal to" case. This eliminates choices A, B, D.
The shading is above the quadratic boundary line, and below the linear boundary line, so the inequalities can be expected to be of the forms ...
y ≥ x² +...y ≤ x +...These forms match choice C:
y ≥ x² -2x -3y ≤ x +3Kevin earns $240,000 a year as a surgeon. He contributes $20,500 to
his pre-tax 401(k) retirement account and pays the government 28% of his
remaining salary per year. How much is his net pay?
Using proportions, it is found that his net pay is of $158,040.
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three.
His first discount is for the retirement account, hence the taxable amount is:
T = 240000 - 20500 = $219,500.
He pays 28% of that in taxes, hence his net pay is of 100 - 28 = 72% of $219,500, hence:
N = 0.72 x 219500 = $158,040.
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Trout Street and Salmon Street are the same distance from the boardwalk to the intersection of 1st Street, Trout Street, and Salmon Street as shown in the diagram. Abby walks down 1st Street and stops when she reaches the boardwalk.
How far of a walk does she have to get to Trout Street?
Abby's walk to Trout Street is _______ yards.
Answer:
800
Step-by-step explanation:
I did it on the test
Answer:
800
Step-by-step explanation:
I just fifnished test
How do I solve an endless amount of numbers with a common ratio
..........
etc. 10+1+0.1+0.01+0.001....
Answer:
11 .21 add the number together
Notice that the given sum is equivalent to
[tex]10 + 1 + \dfrac1{10} + \dfrac1{10^2} + \dfrac1{10^3} + \cdots \\\\ ~~~~~~~~~~~~ = 10 \left(1 + \dfrac1{10} + \dfrac1{10^2} + \dfrac1{10^3} + \dfrac1{10^4} + \cdots\right)[/tex]
or 10 times the infinite geometric series with ratio 1/10.
To compute the infinite sum, consider the [tex]n[/tex]-th partial sum
[tex]S_n = 1 + \dfrac1{10} + \dfrac1{10^2} + \cdots + \dfrac1{10^{n-1}}[/tex]
Multiply both sides by the ratio.
[tex]\dfrac1{10} S_n = \dfrac1{10} + \dfrac1{10^2} + \dfrac1{10^3} + \cdots + \dfrac1{10^n}[/tex]
Subtract this from [tex]S_n[/tex] to eliminate all but the outermost terms,
[tex]S_n - \dfrac1{10} S_n = 1 - \dfrac1{10^n} \implies S_n = \dfrac{10}9 \left(1 - \dfrac1{10^n}\right)[/tex]
As [tex]n\to\infty[/tex], the exponential term will decay to 0, leaving us with
[tex]1 + \dfrac1{10} + \dfrac1{10^2} + \cdots = \dfrac{10}9[/tex]
Then the value of the sum we want is
[tex]10\times\dfrac{10}9 = \boxed{\dfrac{100}9}[/tex]
What is the research hypothesis when using anova procedures?
When using ANOVA procedures, the research hypothesis is: there is no significance difference within the mean values of the groups.
What is a Research Hypothesis in ANOVA Procedure?ANOVA procedure compares the mean values of different groups that are administered with treatments. The research hypothesis, such as the null hypothesis would be stated as: no significance difference in the mean values within the groups.
Thus, we can conclude that the research hypothesis when using the ANOVA procedures can be stated as a null hypothesis, which states that: there is no significance difference within the mean values of the groups.
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10 1/9 rounded to the whole or half
Answer:
Your answer is 68. Hope you got a big score!
4
Which equation represents a linear function that has a slope of 5 and a y-intercept of -6?
4
O y=-6x+²/
O y=x-6
Oy=x+6
Oy=6x+
k
Answer:
y = 5x - 6
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
here m = 5 and c = - 6 , then
y = 5x - 6 ← equation of line
The equation represents a linear function with a slope of 5 and a y-intercept of -6 is y = 5x - 6.
The equation of a linear function is typically written in the form "y = mx + b," where "m" represents the slope and "b" represents the y-intercept.
Given that the slope is 5 and the y-intercept is -6, the equation becomes:
y = 5x - 6
Here's the calculation:
The slope (m) is 5, and the y-intercept (b) is -6. Therefore, the equation becomes:
y = 5x - 6
This equation represents a linear function with a slope of 5 and a y-intercept of -6.
Hence the equation represents a linear function with a slope of 5 and a y-intercept of -6 is y = 5x - 6.
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Find the 12th term in the arithmetic sequence an = 3 − 6(n − 1)
Answer:
-63
Step-by-step explanation:
3 - 6(12 - 1) = 3 - 6(11) = 3 - 66 = -63
which one is it? I will give you twenty points, if you will answer
Answer:
A fraction equivalent to [tex]\frac{1}{2}[/tex] on the number line is [tex]\frac{3}{6}[/tex].
Drag the dot to [tex]\frac{3}{6}[/tex] on the number line.
Step-by-step explanation:
3 is half of 6. To check if this is correct multiply [tex]\frac{1}{2}[/tex] and 3.
[tex]\frac{1}{2}*3=\frac{3}{6}[/tex]
Hope this helps!
If not, I am sorry.
Laboratory tests show that the lives of
light bulbs are normally distributed with
a mean of 750 hours and a standard
deviation of 75 hours. Find the
probability that a randomly selected
light bulb will last between 750 and 825
hours.
Answer in percentage!!!
This result is approximate.
=========================================================
Explanation:
mu = 750 = mean
sigma = 75 = standard deviation
The raw scores or x values are x = 750 and x = 825
Let's compute the z score for each x value
z = (x - mu)/sigma
z = (750 - 750)/75
z = 0
and
z = (x - mu)/sigma
z = (825 - 750)/75
z = 1
Therefore P(750 ≤ x ≤ 825) is equivalent to P(0 ≤ z ≤ 1) in this context.
Use a z score table to determine that
P(z ≤ 0) = 0.5
P(z ≤ 1) = 0.84314 approximately
So,
P(a ≤ z ≤ b) = P(z ≤ b) - P(z ≤ a)
P(0 ≤ z ≤ 1) = P(z ≤ 1) - P(z ≤ 0)
P(0 ≤ z ≤ 1) = 0.84314 - 0.5
P(0 ≤ z ≤ 1) = 0.34314 approximately
The value 0.34314 then converts to 34.314% which rounds to 34%
Or you could use the empirical rule as shown below. The pink section on the right is marked 34% which is approximate. This pink section is between z = 0 and z = 1.
Which piecewise defined function is shown on the
graph?
f(x) =
f(x)
f(x)=
f(x) =
DONE
x+ 2, if 0 < x <4
x-3,if 4 < x <8
x+2, if 0≤x≤4
x-3,if 4 ≤x≤8
Intro
x+2, if 0 < x≤4
x-3, if 4 < x≤8
[x+2,if 0≤x <4
x-3, if 4 < x <8
10
8
20
2
9
8
x
10
Answer: (4)
Step-by-step explanation:
The first part has a closed hole at x=0 and an open hole at x=4, so it should be [tex]0 \leq x < 4[/tex].
This eliminates all the options except for (4).
The piecewise function that represents the graph will be f(x) = x + 2, 0 ≤ x < 4 and f(x) = x - 3, 4 ≤ x < 8. Then the correct option is D.
What is a function?A function is an assertion, concept, or principle that establishes an association between two variables. Functions may be found throughout mathematics and are essential for the development of significant links.
A function that is based on a series of intervals is known as a specific goal. The absolute value serves as a frequent illustration. Other piecewise functions include the Boolean stepping, rectangle, and triangle functions.
The slope of the line is one. And the y-intercept is 2 and -3. Then the equation of the line is given as,
f(x) = x + 2, 0 ≤ x < 4
f(x) = x - 3, 4 ≤ x < 8
The piecewise function that represents the graph will be f(x) = x + 2, 0 ≤ x < 4 and f(x) = x - 3, 4 ≤ x < 8. Then the correct option is D.
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The point stope form of the equation of the line that passes through (-4,-3) and (12, 1) is y-1 = (x-12). What is
the standard form of the equation for this line?
Answer:
x-4y = 8
Step-by-step explanation:
The standard form for the equation of a line is Ax+By=C where A is a positive integer and B and C are integers
First we need to find the slope
m = ( y2-y1)/(x2-x1)
m = (-3-1) / (-4-12)
=-4/-16
= 1/4
The point slope form is
y-1 = 1/4(x-12)
Multiply each side by 4
4(y-1 )= 4*1/4(x-12)
4(y-1) = x-12
4y -4 = x-12
Subtract 4y from each side
4y-4-4y = x-4y -12
-4 = x-4y -12
Add 12 to each side
-4+12 = x-4y -12+12
8 = x-4y
x-4y = 8
The standard form is x-4y = 8
Given that a function, h, has a domain of -3 ≤ x ≤ 11 and a range of 1 ≤ h(x) ≤ 25 and that h(8) = 19 and h(-2) = 2, select the statement that could be true for h.
A.
h(-3) = -1
B.
h(13) = 18
C.
h(2) = 16
D.
h(8) = 21
The true statement is h(2)=16.
What is domain and range?The domain of a function is the set of values that we are allowed to plug into our function. The range of a function is the set of values that the function assumes.
Given:
domain of -3 ≤ x ≤ 11 and a range of 1 ≤ h(x) ≤ 25,
Also, h(8) = 19 and h(-2) = 2,
Now,
2=h(-2)< h(2)<h(8) =19
h(8)=19≠21
h(13)> h(8) =19
h(-3)< h(-2) =2 [1 ≤ h(x) ≤ 25]
Hence, h(2)=16
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Situation:
A 45 gram sample of a substance that's
used to preserve fruit and vegetables has
a k-value of 0.1109.
N-Noe-kt
No - initial mass (at time t - 0)
N = mass at time t
k - a positive constant that depends on
the substance itself and on the units
used to measure time
t-time, in days
Find the substance's half-life, in days.
Round your answer to the nearest tenth.
Enter the correct answer.
+00
DONE
A function assigns the values. The half life of the substance is 6.25 days.
What is a Function?A function assigns the value of each element of one set to the other specific element of another set.
Given the function for the substance as [tex]N= N_o e^{-kt}[/tex], therefore, the half life of the substance can be written as,
[tex]N= N_o e^{-kt}\\\\\dfrac{N}{N_o}= e^{-kt}[/tex]
Since we need to find the half life, therefore, the ratio of the initial mass and the mass after half-life will be 1/2.
[tex]\dfrac12= e^{-kt}\\\\\ln (0.5) = -kt[/tex]
Given the value of k is 0.1109, therefore,
[tex]\ln (0.5) = -kt\\\\\ln (0.5) = -(0.1109)t\\\\t = 6.25[/tex]
Hence, the half life of the substance is 6.25 days.
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Solve x+ 2y = -2 I’m really confused
Answer:
y=−1/2x−1
Step-by-step explanation:
I put it in slope intercept form as I assume that is what the question is asking.
The quotient of a number p and 38
Answer:
[tex] \frac{p}{38} [/tex]
The required quotient of a number p and 38 is 38/p, as of the given condition
What is arithmetic?In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication, and division,
here,
In the quesiton, we have to determine the quotient of a number p and 38.
So, divide 38 by p to determine the quotient.
= 38/p
Thus, the required quotient of a number p and 38 is 38/p.
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Find the values of a and b if 5+3√3/7+4√3 = a + √3b
The values of a and b are :
[tex]a = \sqrt{3} \\ \\ •\sqrt{3} b = - 1 \\ \\ b = \frac{ - 1}{ \sqrt{3} }. [/tex]
I need help with this
Step-by-step explanation:
please mark me as brainlest
one gym membership charges $10 a month with a sign-up fee of $45. Another gym does not charge patrons a sign-up fee but costs $25 a month. at what month is the total cost of both memberships the same?
Answer:
3 months
Step-by-step explanation:
HELP PLEASE
which choice is equivalent to the quotient below? √15/3√3
A. √5/3
B. √5/9
C. √5/√3
D. √4
Answer:
A - [tex]\sqrt{5}[/tex]
Step-by-step explanation:
[tex]\sqrt{15} = \sqrt{5} *\sqrt{3} \\\frac{\sqrt{5} *\sqrt{3}}{3*\sqrt{3}} = \frac{\sqrt{5}}{3}[/tex]
Answer: √5/3
Step-by-step explanation:
A plant was 8 in. tall last week, and grew x in. this week. 1. Which expression represents how tall, in inches, the plant is now? A. x + 8 B. 8x Explain your thinking. 2. For the expression not chosen, describe a scenario the expression might represent.
Answer:
Step-by-step explanation:
Solution
Total growth (2 weeks) = x + 8
Explanation
During the second week, the plant is already 8 inches tall. It adds x to its total growth. 8x is not the same thing.
Meaning of 8x
For plants, 8x could mean the amount of growth that took place in 8 weeks. x is the amount of growth that takes place in 1 week. You have to think that the growth (x) for each week is the same
Which of the following graphs represents the solution set
x>5?
Answer:
Graph A is correct.
Step-by-step explanation:
Graph A is the graph with the open circle and the arrow pointing to the right.
Nitrogen and oxygen are the most abundant gases in Earth’s atmosphere. A nitrogen molecule is 0.00000000003 meters larger than an oxygen molecule.
Which statements describe writing 0.00000000003 in scientific notation?
The exponent is negative , The exponent represents the number of places the decimal moves. , Option A and D is the correct answer.
The complete question is
Which statements describe writing 0.00000000003 in scientific notation? Check all that apply.
A.The exponent is negative.
B. The exponent is positive.
C.The coefficient is 0.3.
D.The exponent represents the number of places the decimal moves.
E.The decimal moves to the right.
What is meaning of Scientific Notation ?Scientific Notation means writing a decimal number in the form of 10ˣ .
It is given that
A nitrogen molecule is 0.00000000003 meters larger than an oxygen molecule.
= 3 × 10⁻¹¹
(scientific notation)
The exponent is negative , The exponent represents the number of places the decimal moves. , Option A and D is the correct answer.
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