1. The total amount of your emergency fund will be $11,403.75.
2. $8,552.81 is in the CD, and $2,850.94 is in the regular savings account.
What is the total amount of your emergency fund?Your FICA deduction is 7.65% of your gross income:
7.65% of $4,520.00 = $345.98
Your federal tax withholding is 11.75% of your gross income:
11.75% of $4,520.00 = $531.40
Your state tax withholding is 8.5% of your gross income:
8.5% of $4,520.00 = $384.40
Your total deductions are:
= $345.98 + $531.40 + $384.40
= $1,261.78
Your monthly income after deductions is:
= $4,520.00 - $1,261.78
= $3,258.22
Your fixed expenses are 30% of your realized income:
= 30% of $3,258.22
= $977.47
Your monthly savings amount is:
= $3,258.22 - $977.47
= $2,280.75
You saved 5 months' worth in an emergency fund, so the total amount in your emergency fund is:
= 5 x $2,280.75
= $11,403.75
Regenerate response
How much is in the CD and savings account?You placed 75% of your emergency fund in a 60-day CD at a 5.25% APR:
= 75% of $11,403.75 = $8,552.81
You placed the remaining 25% of your emergency fund in a regular savings account at a 3.8% APR:
= 25% of $11,403.75
= $2,850.94.
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50 Points! Multiple choice algebra question. If r(x)=x^3-2x+1, find r(2a^3). Photo attached. Thank you!
Answer:
D
Step-by-step explanation:
Answer:
D. [tex]8a^{9} -4a^{3} +1[/tex]
Step-by-step explanation:
Given [tex]r(x)=x^{3} -2x+1[/tex] and find [tex]r(2a^{3} )[/tex] :
[tex]r(2a^{3} )[/tex] is the same as saying [tex]x=2a^{3}[/tex]So, we have [tex]r(2a^{3} )=(2a^{3})^{3} -2(2a^{3})+1[/tex]Solve for [tex]r(2a^{3} )[/tex] :
1. [tex]r(2a^{3} )=(2a^{3})^{3} -2(2a^{3})+1[/tex]
Start with simplifying [tex](2a^{3})^{3}[/tex][tex](2a^{3})^{3}=2^{3}*(a^{3})^{3}=8*a^{3*3}=8a^{9}[/tex]When you have a quantity raised to a power, or an exponent, you have to distribute the exponent to each term multiplied.When you multiply two terms that are raised to a power, you add the powers.When you divide two terms that are raised to a power, you subtract the power in the numerator from the power in the denominator.When you have a power raised to a power, you multiply the powers.2. [tex]r(2a^{3} )=8a^{9} -2(2a^{3})+1[/tex]
Simplify [tex]2(2a^{3})[/tex]Multiply two times the quantity[tex]2(2a^{3})=4a^{3}[/tex]3. [tex]r(2a^{3} )=8a^{9} -4a^{3}+1[/tex]
Answer:
So, if [tex]r(x)=x^{3} -2x+1[/tex], then [tex]r(2a^{3} )=(2a^{3})^{3} -2(2a^{3})+1=8a^{9} -4a^{3}+1[/tex].
Then the answer is D. [tex]r(2a^{3} )=8a^{9} -4a^{3}+1[/tex]
what is the percent of decrease from 8 to 6
The calculated value of the percent of decrease from 8 to 6 is 25%.
What is the percent of decrease from 8 to 6To find the percent of decrease from 8 to 6, we need to find the difference between the two numbers and express it as a percentage of the original number (8).
The difference between 8 and 6 is 8 - 6 = 2.
To express this difference as a percentage of 8, we can use the formula:
percent decrease = (difference / original number) x 100%
Substituting the values we get:
percent decrease = (2 / 8) x 100% = 0.25 x 100% = 25%
Therefore, the percent of decrease from 8 to 6 is 25%.
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Please help with the answer!
Answer:
Step-by-step explanation:
2.1 so a
Leo is a barber.
He charges £5 for a haircut.
He charges 10% extra for hair gel.
One day 25 customers have a haircut.
16 of these ask for hair gel.
Work out the total amount that Leo charges his customers that day.
f(x) = 4(1+ 0.1/0.5)^0.5x is
Answer:
f(x) = 4(1.095)^x.
Step-by-step explanation:
The function f(x) = 4(1+0.1/0.5)^0.5x can be simplified using the order of operations, which is PEMDAS (parentheses, exponents, multiplication and division, and addition and subtraction).
First, we can simplify 0.1/0.5 to get 0.2.
Next, we can simplify (1 + 0.2) to get 1.2.
Then, we can simplify (1.2)^0.5 to get approximately 1.095.
Finally, we can multiply 4 by 1.095^x to get the simplified function:
He makes 8.50 an hour plus 3 every oil change that he performs last week he worked 36hours n performed 17 oil changes how much money did he make
Answer:
$357
Step-by-step explanation:
Hours = h
Oil changes = o
Money = m
m = 8.5h + 3o
Now we can substitute:
m = 8.5(36) + 3(17)
m = 306 + 51
m = 357
What is the perimeter of the triangle?
Answer:
40 units
Step-by-step explanation:
a = 8
b = 15
To find c, we can use the formula: [tex]a^{2} +b^{2} =c^{2}[/tex]
[tex]8^{2} +15^{2} =x^{2}[/tex]
64 + 225 = c^2
289 = c^2
c = 17
a + b + c = perimeter
8 + 15 + 17 = 40
Answer:
40 units
Step-by-step explanation:
You want the perimeter of the triangle shown in the graph.
DimensionsYou can count the grid squares to find the horizontal and vertical dimensions of the triangle. You find they are 8 units and 15 units, respectively.
The length of the slant side is the hypotenuse of a right triangle with sides 8 and 15. If you don't recognize this {8, 15, 17} Pythagorean triple, you can find the hypotenuse using the Pythagorean theorem:
c² = a² +b²
c² = 8² +15² = 64 +225 = 289
c = √289 = 17
The long side of the triangle is 17 units.
PerimeterThe perimeter of the triangle is the sum of the lengths of its sides:
P = 8 + 15 + 17 = 40
The perimeter is 40 units.
__
Additional comment
A "Pythagorean triple" is a set of three integer side lengths that form a right triangle. The triple is "primitive" if the numbers have no common factor. There are a few Pythagorean triples that regularly show up in algebra, trig, and geometry problems. Some of them are ...
{3, 4, 5}, {5, 12, 13}, {7, 24, 25}, {8, 15, 17}, {9, 40, 41}
You will also see multiples of these, for example, 2·{3, 4, 5} = {6, 8, 10}.
The smallest is {3, 4, 5}, and it is the only set that is an arithmetic sequence (has constant differences between lengths). In every case, the sum of the numbers is even. (A right triangle cannot have integer side lengths and an odd perimeter value.)
PLEAE HELP ME!!! I need this quickly!
Find the exact value of the expressions cos(alpha + beta) sin(alpha + beta) and tan(alpha + beta) under the following conditions. sin(alpha) = 24/25 a lies in quadrant I, and sin(beta) = 15/17 B lies in quadrant II.
We can use the trigonometric identities to find the exact values of the expressions.
First, we can find cos(alpha) and cos(beta) using the Pythagorean identity:
cos(alpha) = sqrt(1 - sin^2(alpha)) = sqrt(1 - (24/25)^2) = 7/25
cos(beta) = -sqrt(1 - sin^2(beta)) = -sqrt(1 - (15/17)^2) = -8/17 (since beta is in quadrant II, where cosine is negative)
Next, we can use the sum formulas for sine and cosine to find sin(alpha + beta) and cos(alpha + beta):
sin(alpha + beta) = sin(alpha)cos(beta) + cos(alpha)sin(beta) = (24/25)(-8/17) + (7/25)(15/17) = -117/425
cos(alpha + beta) = cos(alpha)cos(beta) - sin(alpha)sin(beta) = (7/25)(-8/17) - (24/25)(15/17) = -24/85
Finally, we can use the quotient identity for tangent to find tan(alpha + beta):
tan(alpha + beta) = sin(alpha + beta) / cos(alpha + beta) = (-117/425) / (-24/85) = 39/85
Therefore, cos(alpha + beta) sin(alpha + beta) = (-24/85)(-117/425) = 936/7225, and tan(alpha + beta) = 39/85.
1. Suppose c = -11 + 3i. What two nonzero complex numbers could have been
added together to make c?
2. Find the value of iº.
Answer: To find two complex numbers that add up to c = -11 + 3i, we can set up the following system of equations:
a + b = -11
ai + bi = 3i
Solving for a and b, we can multiply the first equation by i and subtract it from the second equation multiplied by -1 to eliminate b:
ai + bi = 3i
-ai - bi = 11i
0 + 10bi = 14i
Simplifying, we get b = 1.4. Substituting this into the first equation gives:
a + 1.4 = -11
a = -12.4
So the two complex numbers that add up to c are -12.4 + 1.4i and 1.4i.
To find the value of iº, we need to evaluate i raised to the power of 90 degrees (or pi/2 radians) using Euler's formula:
e^(iθ) = cos(θ) + i sin(θ)
So we have:
iº = i^(90°) = e^(iπ/2) = cos(π/2) + i sin(π/2) = 0 + i(1) = i
Therefore, iº = i.
Step-by-step explanation:
If P = 3x² - x + 2 and Q = x² + 5x - 6, then P+ Q =
Answer:
Step-by-step explanation:
If P = 3x² - x + 2 and Q = x² + 5x - 6, then P+ Q = 3x² - x + 2 + x² + 5x - 6 =
4x^2 +4x - 4
D = 16 + 64 = 80
x12 = [tex]\frac{-4+-\sqrt{80} }{8}[/tex]
An investment opportunity is offering an annual interest rate of 12% compounded continuously.
How much should you invest initially if you want to have fifteen thousand dollars after nine years?
Do not include a dollar sign in your answer. Round your answer to the nearest cent.
I
Answer:
data given
interest rate 12%
amount to be received 15ooo
time9years
Step-by-step explanation:
from
A=p[1+r/100]^n
where
A is amount
p is principal
r is rate interest
n number of interist period
now,
15000=p[1+12/100]^8
15000/1.12^8 =p×1.12^8/1.12^8
p=6058.24
p=6058)
: .you should invest 6,058
The amount to be invested initially if you want to have fifteen thousand dollars after nine years is $3947.18.
How to find the compound interest?If n is the number of times the interested is compounded each year, and 'r' is the rate of compound interest annually, then the final amount after 't' years would be:
[tex]a = p(1 + \dfrac{r}{n})^{nt}[/tex]
We are given that:
A=15000
r=0.12
t=9
We need to find P. You can do this by rearranging the formula:
P=ertA
Then plug in the given values and use a calculator:
P=e0.12×915000
P≈3947.18
Therefore, by the given interest rate the answer will be $3947.18.
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Find the slope of the line tangent to the graph of the function at the given value of x.
y = x4 + 2x3 + 2x + 2 at x = -3
Answer:
To find the slope of the line tangent to the graph of the function at x = -3, we need to find the derivative of the function and evaluate it at x = -3.
First, let's find the derivative of the function y = x^4 + 2x^3 + 2x + 2:
y' = 4x^3 + 6x^2 + 2
Now, let's evaluate y' at x = -3:
y'(-3) = 4(-3)^3 + 6(-3)^2 + 2
= -108 + 54 + 2
= -52
Therefore, the slope of the line tangent to the graph of the function y = x^4 + 2x^3 + 2x + 2 at x = -3 is -52.
What does a residual value of –0.8 mean in reference to the line of best fit?
The given point is 0.8 units above the line of best fit.
The given point is 0.8 units below the line of best fit.
The line of best fit is not appropriate to the data.
The line of best fit has a slope of 0.8.
Which equation represents the approximate line of best fit for data, where x represents font size and y represents the number of words on one page?
y = –55x + 407
y = –41x + 814
y = –38x + 922
y = –26x + 723
Answer: A residual value of –0.8 means that the given point is 0.8 units above the line of best fit.
The equation that represents the approximate line of best fit for data, where x represents font size and y represents the number of words on one page is:
y = –38x + 922.
Therefore, the answer is y = –38x + 922.
Step-by-step explanation:
the equation for a projectile's height versus time is h(t)=-16t^2+v0t+h0 a tennis ball machine serves a ball vertically into the air from a height of 2 feet, with an initial speed of 120 feet per second. what is the maximum height, in feet, the ball will attain?
round to the nearest whole foot
Therefore, the maximum height the ball will attain is 221.875 feet.
We are given the equation for the height of a projectile as a function of time:
[tex]h(t) = -16t^2 + v0t + h0[/tex]
where v0 is the initial velocity, h0 is the initial height, and t is the time. We are also given that a tennis ball machine serves a ball vertically into the air from a height of 2 feet, with an initial speed of 120 feet per second. Therefore, we can plug in the values of v0 and h0 into the equation:
[tex]h(t) = -16t^2 + 120t + 2[/tex]
To find the maximum height, we need to find the vertex of this parabola. The x-coordinate of the vertex is given by:
[tex]t = -b/2a[/tex]
where a = -16 and b = 120. Substituting these values, we get:
[tex]t = -120/(2(-16)) = 3.75 seconds[/tex]
To find the corresponding maximum height, we can plug this value of t back into the equation:
[tex]h(3.75) = -16(3.75)^2 + 120(3.75) + 2 = 221.875 feet[/tex]
Therefore, the maximum height the ball will attain is 221.875 feet.
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what is the answer to this equation?
7/10 divided by 1/3
Answer:
To divide fractions, we can multiply the first fraction by the reciprocal of the second fraction.
So, 7/10 divided by 1/3 can be written as:
(7/10) ÷ (1/3) = (7/10) x (3/1)
Multiplying the numerators and denominators, we get:
(7 x 3) / (10 x 1) = 21/10
Therefore, the answer is 21/10, which is an improper fraction. We can simplify it to a mixed number by dividing the denominator into the numerator.
21 ÷ 10 = 2 with a remainder of 1, so the mixed number is:
= 1 1/10
Hence, the answer is 1 1/10 or 11/10.
Step-by-step explanation:
7/10 / (1/3) is equal to 7/10 * 3/1 = (7*3) / (10*1) = 21/10 = 2 1/10
7. A group of students wants to demonstrate that sunlight provides the energy for plants to grow. What is
the control group for the experiment?
A. Some plants will receive less water
B. Some plants will receive fertilizer
C. Some plants will receive no sunlight
D. Some plants will receive no water
I
The control group for the experiment would be option C: some plants will receive no sunlight.
What is control group for experiment ?The control group in an experiment is the group that does not receive the treatment or intervention being tested, so that the effects of the treatment can be compared to a baseline or reference point. In this experiment, the treatment being tested is the provision of sunlight as an energy source for plant growth.
Therefore, the control group should not receive sunlight, so that the effects of sunlight can be compared to the baseline of plant growth without sunlight.
Therefore, the control group for the experiment would be option C: some plants will receive no sunlight.
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What is the approximate distance from the origin to the point (-2, -7, -4)? Round to the nearest tenth
O 3.6 units
O 7.6 units
O 8.3 units
O 9.4 units
The approximate distance from the origin to the point (-2, -7, -4) is 8.3 units.
Distance between two points formula:In three-dimensional space, the distance formula is used to calculate the distance between two points (x₁, y₁, z₁) and (x₂, y₂, z₂) in a three-dimensional coordinate system.
The formula is given by:
d = √[(x₂ - x₁)² + (y₂ - y₁)² + (z₂ - z₁)²]
Here we have
The point (-2, -7, -4)
We need to find the distance between the origin to the point
Let (x₁, y₁, z₁) = (-2, -7, -4) and (x₂, y₂, z₂) = (0, 0, 0)
Using the distance formula,
d = √ [(x₂ - x₁)² + (y₂ - y₁)²+ (z₂ - z₁)² ]
d = √ [(0 - (-2))² + (0 - (-7))²+ (0 - (-4))² ]
d = √ [(2)² + (7)²+ (4)² ]
d = √ [4 + 49 + 16 ]
d = √69 = 8.3066
d = 8.3
Therefore,
The approximate distance from the origin to the point (-2, -7, -4) is 8.3 units.
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Find the area and perimeter of the parallelogram. (Hint: Don't forget your units!)
7 cm
8 cm
4 cm
The area and perimeter of the parallelogram are: 56 square units and 30 units respectively
What is a parallelogram?In Euclidean geometry, a parallelogram is a simple (non-self-intersecting) quadrilateral with two pairs of parallel sides. The opposite or facing sides of a parallelogram are of equal length and the opposite angles of a parallelogram are of equal measure
The parameters that will help us do the math are
base = 7
height = 8
Area = 8*7 = 56 square units
perimeter 2b + 2h
perimeter = 2*7 + 2*8
= 14 +16
P = 30 units
Therefore, the perimeter of the parallelogram and area are 30 units and 56 square units
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Suppose that the function h is defined as follows.
if
-2
-1
h(x)= 0
1
2
Graph the function h.
-3.5
if-2.5
if-1.5
if -0.5
if 0.5 ≤x≤1.5
+
X
Ś
The required graph of the function given; h (x) has been attached.
Define a graph?In mathematics, graph theory is the study of graphs, which are mathematical structures used to represent pairwise interactions between objects. In this definition, a network is made up of nodes or points called vertices that are connected by edges, also called links or lines. In contrast to directed graphs, which have edges that connect two vertices asymmetrically, undirected graphs have edges that connect two vertices symmetrically. Graphs are one of the primary areas of study in discrete mathematics.
Here as per the question the graph of the function, h (x) has been attached.
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A piece of nickel has a mass of 130g and a density of 8.90 g/em. A 60g piece of magnesium has a density of 1.78/cm' Which metal would displace more water form an overflow can?
Since magnesium has a larger volume than nickel, it will displace more water from an overflow can.
To determine which metal would displace more water from an overflow canWe need to compare their volumes.
We can use the formula:
Density = mass / volume
To solve for volume, we rearrange the formula:
Volume = mass / density
For nickel:
Volume = 130g / 8.90 g/cm³ = 14.61 cm³
For magnesium:
Volume = 60g / 1.78 g/cm³ = 33.71 cm³
Therefore, Since magnesium has a larger volume than nickel, it will displace more water from an overflow can.
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if the pink lines are parallel, solve for n
The option that is true about the equations for these two lines iis that they represent the same lines.
How to explain the informationThe trick to questions like this is to get both equations into the slope-intercept form. That is done for our first equation (y = 3x + 5). However, for the second, some rearranging must be done:
5y – 25 = 15x; 5y = 15x + 25; y = 3x + 5
Note: Not only do these equations have the same slope (3), they are totally the same; therefore, they represent the same equation.
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Two lines are described by the equations:
y = 3x + 5 and 5y – 25 = 15x
Which of the following is true about the equations for these two lines?They represent perpendicular lines.
None of the other answers
They represent non-perpendicular, intersecting lines.
They represent the same lines.
They represent parallel lines.
The Chicago white Sox had a home record of 53-28 in the 2021 season. How would you interpret this?
The interpretation of the Chicago white sox data is shown below
Interpreting the Chicago dataThe record 53-28 for the Chicago White Sox in the 2021 season means that they won 53 games and lost 28 games in the home games they played during the season.
This record indicates that the White Sox were a strong team at home, winning more games than they lost.
It also suggests that they had a good advantage playing in their home stadium, as winning a high percentage of home games is generally seen as a positive factor in sports.
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Please help I’m confused
The rational inequality f(x) > 0 has the solution x > - 7
What is a rational inequality?A rational inequality is an inequality in the form of a fraction
Given the function f(x) = (x + 7)/(x² - 4x + 3)
To find the value of x for which the function f(x) > 0, we proceed as follows
Given that f(x) > 0
So, this means that
(x + 7)/(x² - 4x + 3) > 0
This implies that
x + 7 > 0
Subtracting 7 from both sides, we have that
x + 7 - 7 > 0 - 7
x + 0 > - 7
x > - 7
So, f(x) > 0 has the solution x > - 7
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a small bag of flour weighd 20 ounces. a large bag was 19 percent heavier how much does the large bag weigh
Answer:
380 weight
Step-by-step explanation:
please brilliant answer me
Find the volume of a cone with a base diameter of 12cm and a height of 12cm
Answer: 1809.6
Step-by-step explanation: I got to be honest is looked up the cone calculator and I tried 3 three and they all go me 1809.6 (rounded)
A patient takes 110 mg of a drug at the same time every day: Just before each tablet is taken, 5% of the drug present in th
preceeding time step remains in the body. What quantity of the drug remains in the body in the long run?
Hint: First find the quantity of drug present in the body after the second tablet, third tablet, etc to generalize the sequenc
formula for the nth tablet. Then use that sequence to predict the drug remains in the long run.
The requried quantity of drug that remains in the body, in the long run, is 220 mg.
Let's denote the amount of drug in the body just before taking the nth tablet by [tex]D_n[/tex]. We know that [tex]D_0 = 0[/tex](since the patient hasn't taken any tablets yet) and that 5% of the drug is present in the body just before taking a tablet remains in the body. Therefore, we can write:
[tex]D_1 = 110\\D_2 = 0.95 * D_1 + 110 = 203.5\\D_3 = 0.95 * D_2 + 110 = 292.225\\D_4 = 0.95 * D_3 + 110 = 376.81375[/tex]
We can see that the formula for [tex]D_n[/tex] is:
[tex]D_n = 110 * (1 - 0.05)^n + 110 * (1 - (1 - 0.05)^n) / 0.05[/tex]
Simplifying this formula, we get:
[tex]D_n = 220 * (1 - 0.95^n)[/tex]
Now, we want to find the amount of drug that remains in the body in the long run. This means we want to find the limit of [tex]D_n[/tex] as n goes to infinity. Using the formula above, we can see that:
[tex]lim_ {n- > oo} D_n = lim_ {n- > oo} 220 * (1 - 0.95^n) = 220[/tex]
Therefore, the quantity of drug that remains in the body, in the long run, is 220 mg.
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the united states has approximate population of 3.3 x 108 people. Each person in the united states consumes an average of about 14,000 grams of rice per year. how much rice in grams, does the population of the U.S consume each year?
the population of the U.S consumes approximately [tex]4.62 * 10^{12}[/tex] grams of rice each year.
What is marginal utility?
The additional pleasure a consumer has from owning one extra unit of an item or service is known as marginal utility.
We can calculate the total amount of rice consumed in the U.S per year by multiplying the population by the amount of rice consumed per person per year:
Total amount of rice consumed = (Population of the U.S) x (Amount of rice consumed per person per year)
Total amount of rice consumed = [tex](3.3* 10^8) * (14,000)[/tex]
Total amount of rice consumed = [tex]4.62* 10^{12} grams[/tex]
Therefore, the population of the U.S consumes approximately [tex]4.62 * 10^{12}[/tex] grams of rice each year.
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Triangle ABC with vertices at A(−4, −4), B(8, 8), C(2, 6) is dilated to create triangle A′B′C′ with vertices at A′(−2, −2), B′(4, 4), C′(1, 3). Determine the scale factor used.
2
one half
4
one fourth
Answer: there all divided by 2
so it's 2
4. The elevation at ground level is 0 feet. An elevator starts 80 feet below ground level. After
traveling for 20 seconds, the elevator is 30 feet below ground level. Which statement describes
the elevator's rate of change in elevation during this 20-second interval?
A. The elevator traveled upward at a rate
1 rate of 2½ feet per second.
B. The elevator traveled downward at a rate of 2 feet per second.
C. The elevator traveled upward at a rate of 4 feet per second.
D. The elevator traveled downward at a rate of 4 feet per second.
a
Answer:
[tex]m = \frac{ - 30 - ( - 80)}{20 - 0} = \frac{50}{20} = 2 \frac{1}{2} [/tex]
A. The elevator traveled upward at a rate of 2 1/2 feet per second. -30 > -80.
Explain what the constant of proportionality means in the equation y = 5/2 x
Answer:
[tex]y = \frac{5}{2} x[/tex]
[tex] \frac{y}{x} = \frac{5}{2} [/tex]
The constant of proportionality is the ratio of y to x. Here, the ratio of y to x is 5 to 2. We see that y is directly proportional to x.
