Answer:
To find the dimensions of the fish tank, we can set up the equation:
(width) * (length) * (height) = 1440 cubic inches
Substituting the given expressions for the dimensions of the tank, we get:
(w) * (w + 8) * (18 - w) = 1440
This is a quadratic equation in w, and we can solve it using the quadratic formula:
w = (-(w + 8) +/- sqrt((w + 8)^2 - 4*(18 - w)11440)) / (2*1)
This simplifies to:
w = (-(w + 8) +/- sqrt(w^2 + 16w + 64 - 72w + 5760)) / 2
= (-(w + 8) +/- sqrt(w^2 - 56w + 5760)) / 2
We can further simplify this equation by factoring:
w = (-(w + 8) +/- sqrt((w - 40)(w - 144))) / 2
We can then solve for w by setting each factor equal to zero:
w - 40 = 0 => w = 40
w - 144 = 0 => w = 144
Since the width of the fish tank must be greater than 6 inches, the only valid solution for w is 40 inches. Substituting this value back into the equation for the volume of the tank, we find that the length of the tank is 48 inches (w + 8 = 40 + 8 = 48) and the height of the tank is 12 inches (18 - w = 18 - 40 = 12).
Therefore, the dimensions of the fish tank are:
width: 40 inches
length: 48 inches
height: 12 inches
The correct answer is therefore (a) width: 12 in., length: 20 in., height: 6 in.
Step-by-step explanation:
Christina also invests $10,000, but instead chooses to invest into a passively managed index fund that is linked to the S&P 500, with an expense ratio of 0. 2%. Her investment also earns a 7% rate of return.
a)How much did she make in one year on her investment with the 7% rate of return?
b)How much does she pay in fees for her passively managed index fund?
c)At the end of the year, what’s the total value (AFTER FEES) of Christina’s mutual fund?
a. The return on investment is $700.
b. The payment should be $20.
c. The total value is $10,680.
Calculation of the return on investment, payment and total value:
a. Since the return on investment is 7%
And, the invested amount is $10,000
So, the return on investment should be
= 7% of $10,000
= $700
b. Since the expense ratio is 0.2%
So, here the payment be like
= 0.2% of $10,000
= $20
c. The total value should be
= $10000-$20 +$700
= $10680
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the length of the hypotenuse of a right triangle in 23in.one leg measures 16in.find the length of the other leg. round your answer to two decimal places
Answer:
16.52
Step-by-step explanation:
hyp²= opp²+adj²
let opp =16in
hyp= 23in
adj²=23²-16²
=529 -256
= 273
adj =√273
= 16.52
A man walked a certain distance at a constant rate. If he had gone 1/2 mile per hour faster, he would have walked the distance in four-fifths the time; if he had gone 1/2 mile per hour slower, he would have been 2 1/2 hours longer on the road. How far did he walk?
Answer:
15
Step-by-step explanation:
15
He walked 15
Apply the 45°-45°-90° Triangle Theorem to find the length of the hypotenuse of the triangle
If the length of each leg of the triangle is 15√2 in, what is the length of the hypotenuse(c)?
Answer:
30
Step-by-step explanation:
The 45-45-90 Triangle Theorem states that in the isosceles 45-45-90 triangle, if we designate each leg as [tex]a[/tex], the base, or hypotenuse is [tex]a\sqrt{2}[/tex] . Since we know the leg is [tex]15\sqrt{2}[/tex], the hypotenuse would be:
[tex]15\sqrt{2} * \sqrt{2} =\\15 * 2=\\30[/tex]
Find the slope of the line that passes through (-21, -47) and (-15,-44).
The slope of the line is 1/2 or 0.5
What is slope of a line ?The slope of a line characterizes the direction of a line.
To find the slope of a line when the coordinates of the two points are given you divide the difference of the y-coordinates of 2 points on a line by the difference of the x-coordinates of those same 2 points .
Thus if
A ( x1, y1) and B( x2, y2)
The slope of the line is y2 - y1 / x2-x1
Calculations
Given ;
A ( -21, -47)
B(-15, -44)
slope = 3/6
=1/2 or 0.5
The slope of the line is 1/2 or 0.5
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Please help with the question below
Answer:
A = -5
Step-by-step explanation:
You have 1,312 grams of radioactive kind of lanthanum. If its half-life is 93 minutes, how much will be left after 279 minutes?
If its half-life is 93 minutes, then the amount left after 279 minutes will be equal to 164 grams.
What is Half-life?In radioactivity, the half-life is the amount of time needed for half of a radioactive sample's atomic nuclei to spontaneously decay (convert into different nuclear species by emitter particles and energy) or, alternatively, the amount of time needed for the radioactive material's disintegration rate to drop by half.
As per the given information given in the question,
Initial amount, N₀ = 1312 grams
Time elapsed, t = 279 min
Half-life, [tex]t^1^/^2[/tex] = 93
Then, use the formula of half-life:
N(t) = N₀[tex](\frac{1}{2})^t^/^(^t^)^1^/^2[/tex]
Substitute the values in above equation,
N(t) = 1312[tex](\frac{1}{2})^2^7^9^/^9^3[/tex]
N(t) = 1312(1/2)³
= 1312 × 0.125
N(t) = 164 grams.
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Answer: 164 grams
Step-by-step explanation: I got the answer right on my ixl
A dolphin swims 465,280 feet in 3 hours. Use the formula d = rt, where d represents distance, r represents rate, and t represents time, to answer the following questions. Show your work.
Using distance, rate and time the answer is 155093.3.
What is distance?Distance is the total movement of an object without any regrad to direction. It is the length of the space between two points .
Given question are-
D=rt where d represent distance.
R represent= Rate
T represents= Time
Based on the given conditions formulate :
A dolphin swims= 465,280
Time = 3hour
=465280/3
Evaluate the expression/equation we can get -
155093.3
Thus the answer is
155093.3
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Eric ha already ran 5 mile and i continuing to run at a pace of 1 mile per hour. Je ha only
The required hours will they have ran the same number of miles is 3.
What is distance and speed?Speed distance time is the equation used to make sense of the connection between speed, distance and time. That is speed = distance ÷ time. Or on the other hand to put it one more way distance isolated by speed will give you the time. Given you know two of the sources of info you can resolve the third.
According to question:Eric has already ran 5 miles and is continuing to run at a pace of 1 mile per hour.Erick distance:: 5 + 1x
Similarly for jess,
Jess distance:: 2 + 2x
To cover same number of miles, above two equations will be equate;
5 + x = 2 + 2x
x = 3 hrs
Thus, requierd number of hours is 3.
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Correct question:
Eric has already ran 5 miles and is continuing to run at a pace of 1 mile per hour. Jess has only run 2 miles and is continuing to run at a pace of 2 miles per hour. In how many hours will they have ran the same number of miles?
Derivative of log(tanhx)
Derivative of log(tanhx) = 2cossec(2x)
Let us assume y = log (tan hx)
On differentiating both sides ,
[tex] \frac{dy}{dx \: } = \frac{d \: log(tanhx)}{dx} [/tex]
[tex] \frac{dy}{dx} = \frac{d log( \tan(hx) ) }{d \tan(hx).d \tan(hx) } \times dx[/tex]
[tex] \frac{dy}{dx} = \frac{1}{ \tan(hx) \times \sec( {h}^{2x} ) } [/tex]
[tex] \frac{dy}{dx} = \frac{ \cos(hx) }{ \sin(hx) } \times \frac{1 }{ \cos(h {}^{2} ) } [/tex]
[tex] \frac{dy}{dx} = \frac{2}{2 \sin(hx). \cos(hx) } [/tex]
[tex] \frac{dy}{dx} = \frac{2}{ \sin(h)(2x) } [/tex]
dy/dx = 2 cos sec (2x)
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What is the equation of the vertical asymptote for the graph of the rational function g(x)=6x−1
Solution n(x), where n(x) is the denominator of the function (notice that this only works if t(x) is not zero for the same value of x).When the denominator is equal to zero, you can solve for x to determine the vertical asymptotes.
How can you locate the graphing formula for a vertical asymptote?By finding the solution to the equation n(x) = 0, where n(x) is the denominator of the function (note that this only works if the numerator t(x) is not zero for the same x value), vertical asymptotes can be obtained. For the function, locate its asymptotes. With the equation x = 1, the graph has a vertical asymptote.When the denominator is equal to zero, you can solve for x to determine the vertical asymptotes. This has previously been factored, therefore reduce each component to zero and get the solution. Since the asymptotes are lines, they are represented mathematically by line equations. X = 3 and X = 1 are the vertical asymptotes.To learn more about Vertical asymptotes refer to:
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A contractor needs to buy nails to build a house. The nails come in small boxes and large boxes. Each small box has 50 nails and each large box has 350 nails. The contractor bought 3 more small boxes than large boxes, which altogether had 2950 nails. Write a system of equations that could be used to determine the number of small boxes purchased and the number of large boxes purchased. Define the variables that you use to write the system.
The number of small boxes and large boxes for the given linear equation condition purchased is 10 and 7 respectively.
What is a linear equation?
Equations whose variables have a power of one are called linear equations. One example with one variable is where ax+b = 0, where a and b are real values and x is the variable.
According to the question, a builder needs to purchase nails in order to construct a house.
Both small and large boxes of nails are provided. There are 50 nails in each small box and 350 in each large box.
The contractor purchased 3 more small boxes than large boxes, hence it is assumed that he purchased an 'x' number of large boxes.
He purchased (x+3) small boxes.
So, 50(x+3) + 350(x) = 2950.
50x + 150 + 350x = 2950.
400x = 2950 - 150.
400x = 2800.
x = 7.
∴ The no. of large boxes he purchased is 7.
∴ The no. of small boxes he purchased is 10.
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Using elimination to solve the system of equations.
3x-5y=11
5(x+y)=5
Answer:
3x - 5y = 11
5(x + y) = 5
Expand the second equation:
5x + 5y = 5
Add both equations:
3x - 5y = 11
5x + 5y = 5
8x = 16
Solve for x:
8x = 16
x = 2
Input x in any equation and solve for y:
3(2) - 5y = 11
6 - 5y = 11
-5y = 5
y = -1
Find the measure of the exterior angle. A triangle, with an exterior angle marked as 2 a degrees. Two of its other interior angles are labeled as a plus 10 degrees and 44 degrees.
The measure of an exterior angle of a triangle is equal to the measure of its neighboring interior angle if both measure 90 degrees, according to the theory of supplementary angles.
What are supplementary angles?If the sums of two angles equal 180 degrees, they are said to be supplementary.
However, two angles do not need to be near one another in order to be complementary.
If two angles' measures sum up to 180 degrees, they are said to be supplementary.
A triangle's outside angle complements the neighboring inner angle.
The adjacent internal angle will therefore likewise be 90 degrees if the exterior angle is.
Therefore, the measure of an exterior angle of a triangle is equal to the measure of its neighboring interior angle if both measure 90 degrees, according to the theory of supplementary angles.
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Correct question:
Can the measure of an exterior angle of a triangle ever equal the measure of its adjacent interior angle? Explain in 2-3 sentences.
A freezer in a lab i et o that the temperature change at a rate of -1. 6C every hour. What i the change in the temperature after 4 1/4 hour? Show your work
The change in the temperature after 4 1/4 hour is -6.8 C.
Given :
A freezer in a lab is set so that the temperature changes at a rate of –1.6 C every hour.
Temperature :
Temperature is the degree of hotness or coldness of an object.
The degrees must contain any units like kelvin , centigrade etc .
Change in temperature after 4 1/4 hours = change rate for hour * number of hours.
= -1.6 C * 4 1/4
= -1.6 C * 4.25
= -16 / 10 C * 425 / 100
= -16 * 425 / 10 * 100 C
= -6800 / 1000 C
= -68 / 10 C
= -6.8 C
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WILL GIVE YOU 85 POINTS IF YOU ANSWER THIS QUESTION ASAP
the accompanying table shows the number of math problems completed correctly by students on a recent test. what is the average number of problems completed correctly by all students?
Answer:
B) 69.6
Step-by-step explanation:
at a 25% off sale you buy a game for 45$ what was the original price
Answer:
$60
Step-by-step explanation:
Let x = the original cost
x - .25x = 45
.75x = 45 Divide both sides by .75
x = 60
Is this a function? Explain, why or why not!
X
-2
-4
-6
Y
1
1
1
Edit View Insert Format Tools Table
By using the concept of function, it can be seen that the given table represents a function.
What is a function?
A function from A to B is a rule that assigns to each element of A a unique element of B. A is called the domain of the function and B is called the codomain of the function.
There are different operations on functions like addition, subtraction, multiplication, division and composition of functions.
Here the values under x represents the domain and the values under y represents the Range.
From the table it can be seen that
Every point of the domain maps to unique point on the range.
So this is a function.
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Solve for all possible values of x.
√9x-9 = x + 1
Omg help someone i don’t get this
Answer:
x = 2 , x = 5
Step-by-step explanation:
assuming you mean
[tex]\sqrt{9x-9}[/tex] = x + 1 ( square both sides to clear the radical )
([tex]\sqrt{9x-9}[/tex] )² = (x + 1)² ← expand using FOIL
9x - 9 = x² + 2x + 1 ( subtract 9x from both sides )
- 9 = x² - 7x + 1 ( add 9 to both sides )
0 = x² - 7x + 10 ← factor the quadratic
consider the factors of the constant term (+ 10) which sum to give the coefficient of the x- term (- 7)
the factors are - 2 and - 5 , since
- 2 × - 5 = + 10 and - 2 - 5 = - 7 , then
(x - 2)(x - 5) = 0
equate each factor to zero and solve for x
x - 2 = 0 ⇒ x = 2
x - 5 = 0 ⇒ x = 5
As a check
substitute these values into the equation and if both sides are equal then they are the solutions.
x = 2
left side = [tex]\sqrt{9(2)- 9}[/tex] = [tex]\sqrt{18-9}[/tex] = [tex]\sqrt{9}[/tex] = 3
right side = 2 + 1 = 3
left side = right side , so x = 2 is a solution
x = 5
left side = [tex]\sqrt{9(5)-9}[/tex] = [tex]\sqrt{45-9}[/tex] = [tex]\sqrt{36}[/tex] = 6
right side = 5 + 1 = 6
left side = right side, so x = 5 is a solution
how do you handle data in analytics to gain greater insights into our audience's behaviour? a partition b sample c segment d extract
By using the segment method, you handle data in analytics to gain greater insights into our audience's behavior.
Analytics:
Analytic refers the field of computer science that uses math, statistics, and machine learning to find meaningful patterns in data.
Given,
Here we need to find how do you handle data in analytics to gain greater insights into our audience's behavior.
In order to find the solution for this one, we must know the definition for the terms of the following,
Audience's behavior - attitudes that affect the behavior of an audience towards a brand or category.
Data - information that has been translated into a form that is efficient for movement or processing.
Insights - the capacity to gain an accurate and deep understanding of someone or something.
Here we have divide the full question into segment to solve this.
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for an electron in the state of hydrogen, what is the probability of being in a spherical shell of thickness at distance (a) (b) and (c) from the proton?
Thus, the probability of the electron being in a spherical shell at distance (a) from the proton is e^(-a/a0), at distance (b) is e^(-b/a0), and at distance (c) is e^(-c/a0).
What is meant by probability?Probability is a metric for determining the possibility or chance of an event happening. It is a mathematical concept that measures the unpredictability of an occurrence and is frequently stated as a decimal or fraction. For example, if the probability of flipping a coin and obtaining heads is 0.5, there is a 50% chance of flipping heads. The number of favorable outcomes to the total number of potential outcomes is used to compute probability. In other words, it is the number of ways an event may occur divided by the total number of conceivable outcomes. Probability is used to make predictions and take wise decisions in a variety of disciplines, including mathematics, science, finance, and engineering.
How to solve?
If we assume the electron is in a hydrogen 1s orbital, the probability density function is given by the square of the 1s wavefunction, which is:
p(r) = (1/πa0^3) e^(-r/a0)
P(r, r+δr) = ∫p(r')dV = ∫p(r')4πr'^2dr'
For the given distances (a), (b), and (c), the probabilities are:
P(a) = ∫p(r')4πr'^2dr' = (1/πa0^3) ∫e^(-r'/a0)4πr'^2dr' = (1/πa0^3) * 4π * a0^3 * e^(-a/a0) = e^(-a/a0)
P(b) = e^(-b/a0)
P(c) = e^(-c/a0)
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You use a garden hose to fill a wading pool. if the water level rises 17 centimeters every 5 minutes and you record the data point of (15, y), what is the value of y? use slope to justify your answer.
The line has a 17/5 slope and y has a value of 51 which will be (15, 51).
What is the slope?In mathematics, a line's slope, also known as its gradient, is a numerical representation of the line's steepness and direction.
The general equation for every straight line is y = MX + c, where m is the gradient (or degree of steepness) of the line and c is the y-intercept (the point in which the line crosses the y -axis).
So, the water level rises by 17 cm in 5 minutes.
Then in 15 minutes, the water will rise by:
15 * 17/5
3*17
51
Then (x, y) will be (15, 51).
Obtaining the slope as follows:
Formula: m = y1 - y2/x1 - x2
m = y2 - y1/x2 - x1
m = 17 - y/5 - x
m = 17/5
Therefore, the line has a 17/5 slope and y has a value of 51 which will be (15, 51).
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The number of songs Oliver has downloaded this year, divided by 12, is equal to 6 less than 30. What is an equation that represents this situation, and how many songs has Oliver downloaded?
Answer: 288
Step-by-step explanation: the number of songs downloaded this year will be x
x/12=30-6
= x/12=24
12*24= 288
x=288
Work out the tax increase on this question!!! Please help
Sales Tax added to the cost of the computer is 178.34 pounds
What is sales tax?
Sales tax is a tax imposed by the government on the price of a commodity for the sale of that commodity. Imposing sales tax on a product increases the price of the product. Nowadays, sales tax has been replaced by Goods and Service Tax (GST).
Here, sales tax is added to increase the price of the computer.
Cost of a computer = 964 pounds
Rate of tax added = 18.5 %
Tax added = [tex]\frac{18.5}{100} \times 964[/tex]
= 178.34 pounds
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Select the correct answer. The sum of two consecutive numbers is 157. This equation, where n is the first number, represents the situation: 2n + 1 = 157. What is the first number? A. 77 B. 78 C. 79 D. 80
Answer:
2n + 1 = 157
2n = 157 - 1
2n = 156
n = 156/2
n = 78
Step-by-step explanation:
hope this helps
COLVE IT PLSS HELP WILL GIVE BRAINLIEST IF THE ANSWER IS RIGHT!
Answer:
degree 5monomialStep-by-step explanation:
You want to know if 5x²y²z +10x²y²z is monomial, binomial, or trinomial, and what its degree is.
DegreeThe degree of a term is the sum of the degrees of the variables in the term:
degree = 2 + 2 + 1 = 5
TermsTwo terms are shown. However, the terms are like terms, so can be combined into one term:
15x²y²z
This tells us the expression is a monomial.
__
Additional comment
The terms of a binomial must be unlike. That is, they don't count as separate terms if they can be combined.
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Create a perpendicular bisector of AB and label the intersection point of the lines E. To verify your result, measure AE and EB and the angles between the bisector and AB. Take a screenshot of your work, and paste it below.
The line CD is the bisector line that divides the line segment AB into two equal parts that are AE = EB.
What is coordinate geometry?Coordinate geometry is the study of geometry using the points in space. Using this, it is possible to find the distance between the points, the dividing line is the m:n ratio, finding the mid-point of the line, etc.
Make an opposite bisector of the Stomach muscle and mark the convergence point of line E. To check your outcome, measure AE and EB and the points between the bisector and Stomach muscle.
The line CD is the bisector line that divides the line segment AB into two equal parts that are AE = EB.
The diagram is given below.
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3w^2-12w=-12
use quadratic formula to solve
Answer:
To solve the quadratic equation 3w^2 - 12w = -12, we can use the quadratic formula:
x = (-b +/- sqrt(b^2 - 4ac)) / (2a)
In this case, a = 3, b = -12, and c = -12. Plugging these values into the formula, we get:
w = (-(-12) +/- sqrt((-12)^2 - 43(-12))) / (2*3)
Simplifying, we get:
w = (12 +/- sqrt(144 + 144)) / 6
w = (12 +/- sqrt(288)) / 6
w = (12 +/- sqrt(288)) / 6
w = (12 +/- 16.97) / 6
w = (12 +/- 16.97) / 6
w = 28.97/6 or -4.97/6
w = 4.828 or -0.828
Therefore, the solutions to the equation 3w^2 - 12w = -12 are w = 4.828 and w = -0.828.
Answer:
w = 2
Step-by-step explanation:
[tex]3w^{2} -12w=-12\\3w^{2} -12w+12 = 0\\[/tex]
[tex]\frac{-b + \sqrt{b^{2} - 4ac} }{2a}[/tex]
[tex]\frac{-(-12) + \sqrt{(-12)^{2} - 4(3)(12) } }{2(3)} = 2[/tex]
the registration fee for a car is 0.9% of the sale price of 5400$ how much is the fee
The registration fee is $60.
Given,
Sale Price = $5400
The value of the registration:
Registration fee = 0.9% of $5,400
= (0.9/100) * 5,400
= 60
Therefore, the registration fee is $60.
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Ashley added ice cubes to her iced tea. The change in temperature of her tea was - 15F. If she added 5 ice cubes, what integer represents the change in tea per ice cube?
Answer:
To find the change in temperature per ice cube, you need to divide the total change in temperature by the number of ice cubes. In this case, you would divide -15F by 5 ice cubes to get -3F per ice cube. The negative sign indicates that the temperature of the tea decreased.
Step-by-step explanation: