Which of the following is a proportional relationship? y = 8x
y = 7 x 3 + 7 x + 12
y = 8x2 + 48x + 3
y = 2x3 + 3x2 + 4x + 5
Comparing to it's standard form, that is, of a monomial, a proportional relationship is given by:
y = 8x.
What is a proportional relationship?A proportional relationship is a function in which the output variable is given by the input variable multiplied by a constant of proportionality, that is:
y = kx
In which k is the constant of proportionality.
From the above standard form, it is found that a proportional relationship is a monomial going through (0,0), hence one example is given by:
y = 8x.
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OK, this question is a little complicated. Solve v, 5/v=7.25
Answer:
Hope this helps you .....
Answer:
\(v=\frac{145}{8}\)
Step-by-step explanation
\(\frac{5}{v}=\frac{2}{7.25}\)
\(\frac{5}{v}=\frac{2}{\frac{725}{100}}\)
\(v=\frac{2}{\frac{5^2*29}{2^2*5^2}}\)
\(v=\frac{145}{8}\)
Four employees of Papa Tony's Pizza are cleaning up at the end of a busy night. There is a list of 43 clean-up tasks that need to be completed. If each employee does the same number of tasks, how many tasks should each employee do? Solve. Explain how you interpreted the remainder.
Answer:
43÷4=10R3
Each employee should do 3 tasks each, with a remainder of 3.
Y=3x + 1 and 5x = y + 3
How to solve this type of simultaneous equation?
Answer:
(2, 7 )
Step-by-step explanation:
y = 3x + 1 → (1)
5x = y + 3 → (2)
substitute y = 3x + 1 into (2)
5x = 3x + 1 + 3
5x = 3x + 4 ( subtract 3x from both sides )
2x = 4 ( divide both sides by 2 )
x = 2
substitute x = 2 into (1)
y = 3(2) + 1 = 6 + 1 = 7
solution is (2, 7 )
Please help ! pythagoran theaeom ! I need someone to please explain how to answer this ASAP , giving brainlist
Answer:
Floor=2*sqrt(11)
Step-by-step explanation:
Using Pythagoras theorem, we have
Wall^2+Floor^2=(Ladder)^2
Floor^2=12^2-10^2
Floor=sqrt(44)=2*sqrt(11)
Answer:The floor is 6m
Step-by-step explanation:
In this we have to solve to find B
First we know that A^2+B^2+C^2 and we know A is 10 and C is 12 so now we are going square both 10 and 12 which would be 100 and 144 then we subtract each other 144-100=44 and lastly we are going to get the square root of 44 which is 6.
Please give brainlist
A triangle has two sides of length 1 and 4. What is the largest possible whole-number length
for the third side?
Using the triangle inequality theorem, the largest possible whole-number length for the third side is 4.
How to Apply the Triangle Inequality Theorem to Find the Length of the Third Side of a Triangle?The third side of a triangle must be shorter than the sum of the other two sides and longer than the difference between the other two sides.
So, for a triangle with sides of length 1, 4, and x (where x is the length of the third side), we have:
1 + 4 > x
4 + x > 1
1 + x > 4
Simplifying these inequalities, we get:
5 > x
x > 3
x > -3 (this inequality is always true)
The largest possible whole-number length for the third side is 4, since it is the largest integer that satisfies the above inequalities.
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The school board has approved the addition of a new sports team at your school.
The district ordered 30 team uniforms and received a bill for $2,992.50. The total included a 5% discount.
a. The school needs to place another order for two more uniforms. The company said the discount will not
apply because the discount only applies to orders of $1,000 or more. How much will the two uniforms
cost?
Answer:
210
Step-by-step explanation:
1: Part/whole=%/100
2: 100-5=95
3: 3150/30=$105 uniforms.
Answer: $210
Hope this helps.
10 hours to 6 hours. What is the percent of Change
Answer:
40% decrease
Step-by-step explanation:
10% = 1
(multiply by 6)
60% = 6
100% - 60% = 40%
The volume of a gas V held at a constant temperature in a closed container varies inversely with its pressure P. If the volume of a gas is 800 cubic centimeters when the pressure is 450 millimeters of mercury (mm Hg), find the volume when the pressure is 200 mm Hg.
SOLUTION:
Step 1:
In this question, we are given the following:
The volume of a gas V held at a constant temperature in a closed container varies inversely with its pressure P. If the volume of a gas is 800 cubic centimeters when the pressure is 450 millimeters of mercury (mm Hg), find the volume when the pressure is 200 mm Hg.
Step 2:
This is an application of Boyle's law which states that:
Boyle’s law is a gas law that states that the pressure exerted by a gas (of a given mass, kept at a constant temperature) is inversely proportional to the volume occupied by it. In other words, the pressure and volume of a gas are inversely proportional to each other as long as the temperature and the quantity of gas are kept constant.
\(\begin{gathered} Mathematically,\text{ we have that:} \\ V\text{ }\propto\text{ }\frac{1}{P} \\ Then,\text{ we have that:} \\ V\text{ =}\frac{k}{P}\text{ \lparen where k is a constant \rparen} \end{gathered}\)\(when\text{ V = 800 cubic centimetres , then P = 450 mm Hg}\)\(\begin{gathered} 800\text{ =}\frac{k}{450} \\ cross-multiply,\text{ we have that:} \\ \text{k = 800 x 450 = 360,000} \end{gathered}\)\(\begin{gathered} Then,\text{ the equation connecting V and P =} \\ \text{ V }=\frac{360,000}{P} \end{gathered}\)Next:
\(when\text{ P = 200 mm Hg, we have that:}\)\(\begin{gathered} V\text{ = }\frac{360,000}{200} \\ \text{V = 1800 cubic centimetres } \end{gathered}\)CONCLUSION:
The volume when the pressure is 200 mm Hg is:
\(V\text{ = 1800 cubic centimetres}\)what is the equation of y=x^3 with the given transformations
Each transformation affects the shape and position of the graph. It is important to carefully consider the order of the transformations and their impact on the equation.
1. Horizontal Shift (c):
If there is a horizontal shift, the equation becomes y = (x - c)^3.
For example, if there is a shift of 2 units to the right, the equation would be y = (x - 2)^3.
2. Vertical Shift (d):
If there is a vertical shift, the equation becomes y = x^3 + d.
For example, if there is a shift of 3 units upwards, the equation would be y = x^3 + 3.
3. Vertical Stretch (a):
If there is a vertical stretch or compression, the equation becomes y = a * x^3.
For example, if there is a vertical stretch by a factor of 2, the equation would be y = 2 * x^3.
4. Reflection (along the x-axis):
If there is a reflection along the x-axis, the equation becomes y = -x^3.
This flips the graph of the original function upside down.
5. Reflection (along the y-axis):
If there is a reflection along the y-axis, the equation becomes y = (-x)^3.
This mirrors the graph of the original function.
6. Combined Transformations:
If there are multiple transformations, we can apply them in the order they are given. For example, if there is a vertical stretch by a factor of 2 and a horizontal shift of 3 units to the right, the equation would be y = 2 * (x - 3)^3.
Remember, each transformation affects the shape and position of the graph. It is important to carefully consider the order of the transformations and their impact on the equation.
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f(x) = −11 + 12x
f(-9)= ?
Please help
Answer:
f(-9) = -119
Step-by-step explanation:
Hello!
You can evaluate for f(-9) by substituting -9 for x in the equation f(x) = -11 + 12x.
Evaluate f(-9)f(x) = -11 + 12xf(-9) = -11 + 12(-9)f(-9) = -11 - 108f(-9) = -119The evaluated value is -119.
pls help math scientific notation (view photo)
Just ignore this answer, its incorrect
*edited*
can you apply the properties of rational exponents to an example?
We can simplify \((16x^4)^(-1/2) to 1/(4x^2)\) using the properties of rational exponents.
Certainly! Here's an example:
Simplify the expression: \((16x^4)^(-1/2)\)
We can apply the property of rational exponents which states that \((a^m)^n = a^(m*n)\). Using this property, we get:
\((16x^4)^(-1/2) = 16^(-1/2) * (x^4)^(-1/2)\)
Next, we can simplify \(16^(-1/2)\) using the rule that \(a^(-n) = 1/a^n\):
\(16^(-1/2) = 1/16^(1/2) = 1/4\)
Similarly, we can simplify \((x^4)^(-1/2)\) using the rule that \((a^m)^n = a^(m*n)\):
\((x^4)^(-1/2) = x^(4*(-1/2)) = x^(-2)\)
Substituting these simplifications back into the original expression, we get:
\((16x^4)^(-1/2) = 1/4 * x^(-2) = 1/(4x^2)\)
Therefore, the simplified expression is \(1/(4x^2).\)
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Need help on this question as well
The required arc length of sector VW is 8\(\pi\).
Given that, in a circle U, radius UV = 9 and central angle of sector m∠VUW = 160°.
To find the arc length of sector VW, we can use the formula:
Arc length = (central angle / 360) x circumference of the circle.
First, find the circumference of the circle by the formula for the circumference of a circle is given by:
Circumference = 2 x \(\pi\) x radius.
Circumference = 2 x \(\pi\) x 9 = 18π.
Now, let's find the arc length of sector VW using the central angle of 160 degrees:
Arc length = (160/360) x 18π
Arc length = (4/9) * 18\(\pi\) = 8\(\pi\).
Therefore, the arc length of sector VW is 8\(\pi\).
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Test the series for convergence or divergence. Σ (n^9 +1) / (n10 + 1) n = 1 a. convergent b. divergent
The given series is divergent.
We can use the limit comparison test to determine the convergence or divergence of the given series:
First, note that for all n ≥ 1, we have: \(\frac{(n^9 + 1) }{ (n^10 + 1)}\) ≤ \(\frac{n^9 }{n^10} = \frac{1}{n}\)
Therefore, we can compare the given series to the harmonic series ∑ 1/n, which is a well-known divergent series. Specifically, we can apply the limit comparison test with the general term \(a_n = \frac{(n^9 + 1)}{(n^{10} + 1)}\) and the corresponding term \(b_n = \frac{1}{n}\):
lim (n → ∞) \(\frac{a_n }{ b_n}\) = lim (n → ∞) \(\frac{\frac{(n^9 + 1)}{(n^10 + 1)} }{\frac{1}{n} }\)
= lim (n → ∞) \(\frac{ n^{10} }{ (n^9 + 1)}\)
= lim (n → ∞) \(\frac{n}{1+\frac{1}{n^{9} } }\)
= ∞
Since the limit is positive and finite, the series ∑ \(\frac{(n^9 + 1) }{ (n^10 + 1) }\) behaves in the same way as the harmonic series, which is divergent. Therefore, the given series is also divergent.
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Select True or False for each statement about equilateral triangles.
A. An equilateral triangle has 3 equal angle measures.
A True B False
B. An equilateral triangle has 3 equal side measures.
A True B False
C. An equilateral triangle has 3 lines of symmetry.
A True B False
Answer:
A. true
B True
C True
hope this helps
can someone help me please???
Select the correct answer from each drop-down menu. Graph of proportional relationships. X-axis labeled Number of Plants. Y-axis labeled Number of Roses. Line begins from origin and goes through plotted closed points at (1, 5), (2, 10), (3, 15), (4, 20). According to the graph, the relationship between the number of rose plants and the number of roses is . Reset Next
The relationship that is represented by the graph, between number of rose plants and the number of roses is: proportional.
What is a Proportional Relationship?If a graph represents a proportional relationship, it passes through the origin (0, 0) and has a constant of proportionality that is expressed as k = y/x.
Thus, to determine whether the graph that has a line that passes through points (1, 5), (2, 10), (3, 15), (4, 20) represents a proportional relationship, use the coordinates of the points to find out if k = y/x is the same for all ordered pairs of each point. If it is the same, then it represents the constant of proportionality, meaning the relationship is proportional.
Thus:
For (1, 5), k = 5/1 = 5
For (2, 10), k = 10/2 = 5
For (3, 15), k = 15/3 = 5
For (4, 20), k = 20/4 = 5
This means that, the relationship that is represented by the graph, between number of rose plants and the number of roses is: proportional.
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Can someone please help me
Answer: the second one
Step-by-step explanation:
because \(-4^{4}\)= -256
You roll two six-sided dice. What is the probability that the sum is equal to 5? Write your answer as a fraction in simplest form
The probability that the sum is equal to 5 is 4/36 and the simplest form is 1/9.
The rolls that sum up to 5 are 1 and 4, 4 and 1, 2 and 3, and 3 and 2 for a total of 4 possibilities.
The formula for calculating probability is P(A) = n(A) / n(S).
where P(A) is the probability of occurring event A.
n(A) is the number of favorable outcomes.
n(S) is the total possible outcomes.
The total no of favorable outcomes, n(A) = 4.
The total no of possible outcomes is 6 times 6, n(S) = 36.
probability = 4/36
simplest form = 1/9
Therefore, The probability that the sum is equal to 5 is 4/36 and the simplest form is 1/9.
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consists of $1$'s separated by blocks of $2$'s with $n$ $2$'s in the $n^{\rm{th}}$ block. what is the sum of the first $1234$ terms of this sequence?
Therefore, the sum of the first 1234 terms of this sequence is 1234.
To find the sum of the first 1234 terms of the sequence consisting of 1's separated by blocks of 2's with n 2's in the nth block, we need to determine the number of blocks and the number of 1's in each block.
Let's examine the pattern of the sequence:
Block 1: 2's
= 1's
= 1 (1 2)
Block 2: 2's
= 2's
= 22 (1 22 1)
Block 3: 2's
= 3's
= 222 (1 222 1)
Block 4: 2's
= 4's
= 2222 (1 2222 1)
...
We observe that the number of 2's in each block is equal to the number of the block itself. So, in the nth block, there are n 2's.
Now, let's calculate the number of blocks required to reach the 1234th term:
To find the number of blocks, we need to determine the maximum block number before the 1234th term. We can calculate this by finding the sum of the series 1 + 2 + 3 + ... + n until the sum is greater than or equal to 1234.
The formula for the sum of the series 1 + 2 + 3 + ... + n is given by: S = (n/2)(n+1).
Let's solve this equation:
(n/2)(n+1) = 1234
\(n^2 + n - 2468 = 0\)
Using the quadratic formula:
n = (-1 + √(1 + 4*2468)) / 2
n ≈ 61.76
Since n must be a whole number, we take the ceiling of n, which gives us 62.
Therefore, there are 62 blocks in the sequence.
Next, let's calculate the number of 1's in each block:
In the nth block, there are n 2's. Since each 2 is separated by a 1, there are n + 1 terms in each block.
So, the number of 1's in each block is (n + 1) - n = 1.
Since there is always one 1 between two consecutive blocks, the total number of 1's in the sequence is equal to the number of blocks, which is 62.
Finally, let's calculate the sum of the first 1234 terms:
Each block has n + 1 terms, which gives us (n + 1) + (n + 1) + ... + (n + 1) (62 times).
Sum of (n + 1) repeated 62 times = 62(n + 1)
= 62 * 2
= 124.
In addition to the blocks, we have 1234 - 62 = 1172 remaining terms, which are all 1's.
So, the sum of the first 1234 terms is 62 + 1172 = 1234.
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write 13/24 as a percent
(explain how you got the answer pls)
Answer:
About 54.16 percent
Step-by-step explanation:
To turn a fraction into a percentage you must divide the numerator by the denominator.
Ex: 1/2 the percentage is 0.50 percent so its 50%
Please help 10 pts and brainliest to right answer
The price of one glitter wand equals 50/8 = 6.25.
Therefore, we must find out if one wand for each type of wand below costs $6.25.
$20/$4 = $5
Therefore, 4 sparkle wands for $20 does not have the same price per wand as glitter wands.
$37.50/$6 = $6.25
Therefore, 6 fairy wands for $37.50 has the same price per wand as glitter wands.
$65/$10 = $6.5
Therefore, 10 glow wands for $65 does not have the same price per wand as glitter wands.
Answer:
Step-by-step explanation:
the price of one glitter wand is 50/8=6.25
first, 20/4= 5 ,compare with glitter wand price so, not the same glitter wand price
second, 37.50/6=6.25 ,compare with glitter wand price so, the same glitter wand price
third, 65/10 = 6.5 ,compare with glitter wand price so, not the same glitter wand price
6.) what is the kb when the ka of a solution is 5.47×10−4. (ka = 5.47×10−4)
The value of Kb will be 1.83 × 10⁻¹¹.
The given problem states that Ka is equal to 5.47×10⁻⁴, and the task is to find Kb. Ka and Kb are related to each other through the equation Kw = Ka × Kb. Kw represents the ion product of water, which is equal to the concentration of H₃O⁺ ions multiplied by the concentration of OH⁻ ions. It has a value of 1.0 × 10⁻¹⁴.
Using the fact that pKw = pH + pOH = 14.00, we can determine the relationship between pKa and pKb. By rearranging the equation, we get pKa + pKb = 14.00. This equation relates the logarithms of the acid dissociation constant (pKa) and the base dissociation constant (pKb).
To find Kb, we can use the formula Kb = Kw/Ka. Substituting the given values, we have Kb = (1.0 × 10⁻¹⁴)/(5.47 × 10⁻⁴). Simplifying this expression, we find Kb = 1.83 × 10⁻¹¹.
Therefore, the value of Kb is determined to be 1.83 × 10⁻¹¹.
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i need sum help with this pleaseee helppp
Answer:
$ 26 . 25this is a answer
Answer:
The last answer choice $8.75
Step-by-step explanation:
(35*25)/100
= 875/100
=8.75
A family wants to rent a car to go on vacation. Company A charges $70.50 and 17 cents per mile. Company B charges $45.50 and 9 cents per mile. How much more does Company A charge for x miles than company B?
the sample covariance between and is the covariance measures the amount that and vary away from the mean simultaneously . the covariance is maximized when and are perfectly correlated. what is this maximal value? (hint: consider what happens when , or use the cauchy-schwarz inequality)
The maximal value of the sample covariance is \(sx*sy\), which represents the highest correlation possible between X and Y.
The formula for the sample covariance between X and Y is given by \(cov(X,Y) = (1/(n-1)) Σ (xi - xmean)(yi - ymean)\). The maximal value for the sample covariance is equal to the product of the standard deviations of X and Y, which can be calculated using the formula \(sx*sy = (1/(n-1)) Σ (xi - xmean)^2 * (1/(n-1)) Σ (yi - ymean)^2\). Using the Cauchy-Schwarz Inequality, we can know that \(cov(X,Y) < = sx*sy\). Therefore, the maximal value of the sample covariance is sx*sy, which represents the highest correlation possible between X and Y.
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solve. minimize: w=35y1 72y2 65y3 subject to: with: write only the exact value for . do not round. if necessary, write as a fraction o
The solution to the equation is y₂ = -13.51.
To find the exact value of y₂ without rounding, we will use the method of corner points. This method involves finding the corner points of the feasible region and evaluating the objective function at each corner point to determine the optimal solution.
Step 1: Setting up the inequalities:
Let's rewrite the constraints with variables in terms of a fraction:
Constraint 1: 5y₁ + 9y₂ + 4y₃ < 15 ... (1)
Constraint 2: 5y₁ + 18y₂ + 2y₃ > 8 ... (2)
Step 2: Solving for y₂:
To solve for y₂, we will express y₂ in terms of the other variables in the constraints.
From constraint (1), we have:
5y₁ + 9y₂ + 4y₃ < 15
9y₂ < 15 - 5y₁ - 4y₃
y₂ < (15 - 5y₁ - 4y₃)/9
From constraint (2), we have:
5y₁ + 18y₂ + 2y₃ > 8
18y₂ > 8 - 5y₁ - 2y₃
y₂ > (8 - 5y₁ - 2y₃)/18
Step 3: Analyzing the constraints:
Now we have the inequalities for y₂ in terms of y₁, y₃, and constants. Let's examine the conditions to satisfy the constraints:
y₂ > (8 - 5y₁ - 2y₃)/18 ... (3)
y₂ < (15 - 5y₁ - 4y₃)/9 ... (4)
Considering the constraints y₁ > 0, y₃ > 0, and y₂ > 0, we need to find the range of values for y₁ and y₃ that satisfy these inequalities.
Analyzing the inequalities:
Let's examine the intervals for y₁ and y₃ that satisfy the constraints:
From inequality (3):
y₂ > (8 - 5y₁ - 2y₃)/18
For y₁ > 0 and y₃ > 0, the numerator 8 - 5y₁ - 2y₃ should be positive to maintain y₂ > 0.
Simplifying the numerator:
8 - 5y₁ - 2y₃ > 0
8 > 5y₁ + 2y₃
This implies that 5y₁ + 2y₃ < 8.
From inequality (4):
y₂ < (15 - 5y₁ - 4y₃)/9
For y₁ > 0 and y₃ > 0, the numerator 15 - 5y₁ - 4y₃ should be positive to maintain y₂ > 0.
Simplifying the numerator:
15 - 5y₁ - 4y₃ > 0
15 > 5y₁ + 4y₃
This implies that 5y₁ + 4y₃ < 15.
Step 5: Finding the corner points:
To find the corner points, we need to determine the intersection of the lines 5y₁ + 2y₃ = 8 and 5y₁ + 4y₃ = 15.
Solving the system of equations:
5y₁ + 2y₃ = 8 ... (5)
5y₁ + 4y₃ = 15 ... (6)
Multiplying equation (5) by 2, we get:
10y₁ + 4y₃ = 16 ... (7)
Subtracting equation (6) from equation (7):
(10y₁ + 4y₃) - (5y₁ + 4y₃) = 16 - 15
5y₁ = 1
Dividing both sides by 5:
y₁ = 1/5
Substituting y₁ = 1/5 into equation (5):
5(1/5) + 2y₃ = 8
1 + 2y₃ = 8
2y₃ = 8 - 1
2y₃ = 7
y₃ = 7/2
Therefore, one corner point is (y₁, y₂, y₃) = (1/5, ?, 7/2).
Step 6: Evaluating the objective function:
Now, let's evaluate the objective function at the corner point (1/5, ?, 7/2) to find the value of y₂.
Substituting the corner point into the objective function:
w = 35y₁ + 72y₂ + 65y₃
w = 35(1/5) + 72y₂ + 65(7/2)
w = 7 + 72y₂ + 2275/2
w = 7 + 72y₂ + 1137.5
w = 1144.5 + 72y₂
172 = 1144.5 + 72y₂
Let's start by subtracting 1144.5 from both sides of the equation:
172 - 1144.5 = 1144.5 + 72y₂ - 1144.5
This simplifies to:
-972.5 = 72y₂
To isolate y₂, we can divide both sides of the equation by 72:
-972.5 / 72 = 72y₂ / 72
Simplifying further:
-13.51 = y₂
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Complete Question:
Solve. Minimize: w = 35y₁ + 72y₂ +65y₃
Subject to: 5y₁ +9y₂ + 4y₃ < 15
5y₁ + 18y₂ + 2y₃ > 8
With: y₁ > 0; y₂ > 0; y₃ > 0
Write only the exact value for y₂.
Do not round. If necessary, write as a fraction or improper fraction. Show your work on separate paper.
Is it true or false?
Answer:
True, don't take my word for it though.
9) Brenn has $60 in his savings account. His brother Chris has $135 in his. Brenn decides to save $5 of his allowance each week, while Chris decides to spend his whole allowance along with $10 of his savings each week. After how many weeks will Brenn and Chris have the same amount of money in their savings accounts?
Answer:
9) 15
Step-by-step explanation:
Indicate below whether the equation in the box is true or false 1/8 = to 2/4 true or false
Answer:
false
Step-by-step explanation:
1/8 = .125
2/4 = .5
therefore 1/8 does not = 2/4