When the dimensions of a two gallon container are tripled, the container can hold up to 54 gallons of liquid, since the volume will increase 27 times.
Explanation:The question is about how a two gallon container can hold when all of its dimensions are tripled. In mathematics, when dimensions of a cube (or a rectangular prism, which the container can be assumed to be) are increased proportionally, the volume, which is proportional to the cube of the dimensions, increases by the cube of that same factor.
In this case, the dimensions of the container have all been tripled (a three-fold increase) which results in the volume of the space inside the container increasing by 3³ = 27 times. Therefore, the two gallon container, when its dimensions are tripled, can hold 2 gallons x 27 = 54 gallons. It's important to understand this is a principle of geometry and works irrespective of the units of measurement used (gallons, liters, cubic centimeters, etc.)
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The parking lot has 40 cars and 3 4 of the cars have in-state license plates. How many cars have in-state license plates?
3/4 *40 =30.
So 30 cars have in state license
To find how many cars have in-state license plates, multiply the total number of cars (40) by the fraction (3/4). The answer is 30 cars have in-state license plates.
To find the number of cars with in-state license plates, we need to calculate 3/4 of the total number of cars in the parking lot.
First, identify the total number of cars: 40 cars.Then, determine the fraction of cars with in-state license plates: 3/4.Multiply the total number of cars by this fraction: (3/4) * 40.Perform the multiplication: (3/4) * 40 = 30.Therefore, 30 cars in the parking lot have in-state license plates.
Correct question :
The parking lot has 40 cars and 3/4 of the cars have in-state license plates. How many cars have in-state license plates?
A supervisor has asked her team to improve its average talk Time Performance the team's average talk time is 13 minutes per call in the average for the call center is 8 minutes per call the following week the supervisor reports the following results John's went from 15 minutes to 16.5 minutes George's went to from 15 minutes to 14 minutes Paul's went from 12 minutes to nine minutes and Ringoes went from 12 minutes to 2 minutes whose performance improve the most While most likely giving the best service to customers?
Answer:
john
Step-by-step explanation:
I found a place that will give me 20% discount if i spend over $50.My nill $75.How much money will i save?
A number is increased by 50% and then the result is decreased by 50%. What is the percent of decrease from the original number to the final number?
Final answer:
To find the percent of decrease, calculate the difference between the original and final numbers, divide by the original number, and multiply by 100. In this case, the percent of decrease is 25%.
Explanation:
To find the percent of decrease from the original number to the final number, we need to calculate the difference between the original number and the final number, then divide that difference by the original number and multiply by 100 to get the percentage.
Let's assume the original number is x. When the number is increased by 50%, it becomes 1.5x. When the result is decreased by 50%, it becomes 0.5 times 1.5x, which is 0.75x.
The decrease from the original number to the final number is x - 0.75x = 0.25x. To find the percent of decrease, we divide the decrease by the original number (0.25x / x) and multiply by 100 to get 25%. Therefore, the percent of decrease from the original number to the final number is 25%.
Final answer:
The overall percent change from the original number to the final number, after increasing by 50% and then decreasing by 50%, is a 25% decrease.
Explanation:
To find the percentage decrease from the original number to the final one after the series of increases and decreases described, we need to follow a couple of steps:
First, we increase the original number by 50%. If the original number is x, its increased value is x + 0.5x = 1.5x.
Next, we decrease this new number by 50%. The decreased value is 1.5x - (0.5 × 1.5x) = 1.5x - 0.75x = 0.75x.
To find the percentage change from the original value, we calculate (final value - initial value) / initial value × 100%. Using the value obtained from the second step, this becomes (0.75x - x) / x × 100% = -0.25x/x × 100% = -25%.
Therefore, the overall percent change is a 25% decrease from the original number.
Expand
6
∑ 3n
n=2
a.2+3+4+5+6
b.3+6+9+12+15
c.6+9+12+15+18
d.3+6+9+12+15+18
Answer:
Step-by-step explanation:
d.3+6+9+12+15+18 sum 6 terms multiple of 3
Factor q^3-125 completely.
The expression [tex]\(q^3 - 125\)[/tex] can be completely factored as [tex]\((q - 5)(q^2 + 5q + 25)\)[/tex] using the difference of cubes formula, where [tex]\(q\)[/tex] is the variable and 5 is the cube root of 125.
The given expression [tex]\(q^3 - 125\)[/tex] can be factored using the difference of cubes formula, which is[tex]\(a^3 - b^3 = (a - b)(a^2 + ab + b^2)\)[/tex]. In this case, [tex]\(a = q\)[/tex] and [tex]\(b = 5\)[/tex], as [tex]\(125 = 5^3\)[/tex].
Applying the difference of cubes formula, the factorization becomes:
[tex]\[ q^3 - 125 = (q - 5)(q^2 + 5q + 25) \][/tex]
This is the complete factorization of [tex]\(q^3 - 125\).[/tex]
The question probable may be:
Factorize: [tex]q^3[/tex]-125
The expression q^3-125 is factored completely as (q - 5)(q^2 + 5q + 25), using the difference of cubes formula.
Explanation:To factor the expression q^3-125 completely, we recognize that it represents a difference of cubes since 125 is a perfect cube (5^3).
The difference of cubes can be factored using the formula a^3 - b^3 = (a - b)(a^2 + ab + b^2). In our case, a = q and b = 5.
The factored form of the expression is therefore (q - 5)(q^2 + 5q + 25).
Remember that factoring expressions is essential for simplifying equations and solving algebraic problems efficiently.
Manager 1 has 7 years of service, averaged $5000 per day in sales, had a customer Service Rating of 5 and had 83% of projects completed on time.
u didnt ask a question here you dummy thicc sassy block of cheesy
Manager 1, with 7 years of service, achieved an average daily sales of $5,000, maintained a high customer service rating of 5, and successfully completed 83% of projects on time Business involves the production, exchange, or provision of goods and services in pursuit of profit, contributing to economic growth and sustainability.
Manager 1's performance is evaluated based on several key metrics. First, their 7 years of service indicate experience and commitment to the company. Second, the daily sales average of $5,000 reflects their effectiveness in generating revenue. The customer service rating of 5 signifies exceptional customer satisfaction, indicating effective communication and problem-solving skills. Lastly, the 83% on-time project completion rate demonstrates efficiency in managing tasks and meeting deadlines. These attributes collectively suggest that Manager 1 is a valuable asset to the company, with a strong track record of delivering results and maintaining high standards of customer service.
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For the following question, find the length of the missing side leave. Your answer in simplest radical form.
Please help I’m so confused on this lesson!
The length of the missing side is √445 meters.
For a right triangle, the Pythagorean theorem states that the square of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides (the legs).
In this case, we are given the lengths of the two legs, which are 11 meters and 18 meters. We need to find the length of the hypotenuse, which is the missing side.
Steps to solve:
Step 1: Substitute the given values into the Pythagorean theorem:
[tex]a^2 + b^2 = c^2[/tex]
where:
a = 11 meters (shorter leg)
b = 18 meters (longer leg)
c = the missing side (hypotenuse)
Step 2: Evaluate the equation:
[tex]11^2 + 18^2[/tex]= [tex]c^2[/tex]
121 + 324 = [tex]c^2[/tex]
445 = [tex]c^2[/tex]
Step 3: Take the square root of both sides to solve for c:
c = √445
The length of the missing side is √445 meters
Let u= ln x and v=ln y. Write ln(x^3y^2) in terms of u and v.
a. 3u + 2v
Step-by-step explanation:To solve this problem, we need to apply some properties of logarithms. Properties are useful to simplify complicated expressions. Here we need to use a very useful property of logarithms called the logarithm of a product is the sum of the logarithms, that is:
[tex]log_{b}(MN)=log_{b}(M)+log_{b}(N)[/tex]
From the function, it is then true that:
[tex]ln(x^{3}y^{2})=ln(x^{3})+ln(y^{2})[/tex]
The other property we must use is Logarithm of a Power:
[tex]log_{b}M^{n}=nlog_{b}M[/tex]
Then:
[tex]ln(x^{3}y^{2})=ln(x^{3})+ln(y^{2}) \\ \\ ln(x^{3}y^{2})=3ln(x)+2ln(y)[/tex]
Since:
[tex]u=ln(x) \\ v=ln(y)[/tex]
Then:
[tex]ln(x^{3}y^{2})=3u+2v[/tex]
Finally, the correct option is:
a. 3u + 2v
Answer:
A edge
Step-by-step explanation:
Are the polygons similar? If they are, choose the correct similarity statement and scale factor.
The similarity is ΔRST ~ Δ UVW and Scale Factor is 5/6.
What is Similarity?If two triangles have an equal number of corresponding sides and an equal number of corresponding angles, then they are comparable. Similar figures are described as items with the same shape but varying sizes, such as two or more figures.
Given:
From the Two Triangles we can see that
<VUW = <SRT = 32
and, SR / VU = TR / WU
10/ 12 = 15/ 16
5/6 = 5/6
So, By SAS similarity Criteria both Triangles are Similar.
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I'm taking a chance on a spinner with 20 outcomes how likely is to land on an even number
Answer:
50% chance
Step-by-step explanation:
You would have a 50% chance of landing on a even number
If a equation of a line y=5x-3 is changed to y=1/5x-3, how is the graph effected? A.The line shifts up B.The line becomes steeper C.The line becomes less steep D.The line now decreases from left to right
Answer:
Option C.
Step-by-step explanation:
we have
[tex]y=5x-3[/tex] -----> equation of a line with slope [tex]m=5[/tex]
Is changed to
[tex]y=(1/5)x-3[/tex] ----> equation of a line with slope [tex]m=1/5[/tex]
Compare the slopes
The slope becomes smaller
therefore
The line becomes less steep
see the attached figure to better understand the problem
If r(x) = 2 – x2 and w(x) = x – 2, what is the range of (wor)(x) ?
The term (wor)(x) is unclear and needs clarification to accurately find the range. If it refers to the composition of the two functions (w◦r)(x) or (r◦w)(x), different ranges can be obtained.
Explanation:To find the range of (w or r)(x), we first need to evaluate this expression. Our given functions are r(x) = 2 - x² and w(x) = x - 2.
However, the function (wor)(x) is not clearly defined in this case since the term "or" does not have a traditional mathematical operation associated with it in this context. This question may well be referring to the composition of the two functions (w◦r)(x) or (r◦w)(x), but without clear instruction, a definitive answer cannot be given.
If it refers to (w◦r)(x), this means w(r(x)) which equals w(2-x²) = (2 - x²) - 2 = -x².
If it refers to (r◦w)(x), this means r(w(x)) = r(x-2) = 2 - (x - 2)².
Each of these composited functions would have a different range. Please clarify the meaning of (wor)(x) so a definitive answer can be provided.
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Find the rectangular coordinates of the point with the polar coordinates (8, 3 divided by 2 pi ). (1 point) (0, -8) (0, 8) (8, 0) (-8, 0)
Answer:
(x,y) = (0,-8)
Step-by-step explanation:
We know that a point in polar coordinates is represented by
(r, θ)
Where r is the distance from the origin and θ is the angle.
Rectangular coordinates can be found by
x = r*cos(θ)
y = r*sin (θ)
x = r*cos(θ) = 8* cos (3π/2)
y = r*sin (θ) = 8 sin(3π/2)
x = 8* cos (3π/2) = 8*0 = 0
y = 8* sin (3π/2) = 8*(-1) = -8
(x,y) = (0,-8)
Correct option is (A) (0,-8)
Now any point in polar coordinates is represented by
(r, θ)
where 'r' is the distance from the origin
and 'α' is the angle.
Rectangular coordinates can be found by using the formula:
[tex]x=r*cos(\alpha )\\y=r*sin(\alpha )[/tex]
Thus the x coordinate would be given as :
[tex]x=r*cos(\alpha )\\x=8*cos(\frac{3\pi }{2} )\\x=8*0\\x=0\\[/tex]
Similarly the y coordinate would be given as :
[tex]y=r*sin(\alpha )\\y=8*sin(\frac{3\pi }{2} )\\y=8*(-1)\\y=-8\\[/tex]
Thus (x, y) = (0,-8) is the required coordinates
HELP!!!!!!!!!!!!!!!
Find the smallest positive integer $a,$ greater than 1000, such that the equation
\sqrt a - \sart a-x has a rational root.
The smallest positive integer [tex]a[/tex] greater than 1000 such that [tex]\sqrt{a} - \sqrt{a-x}[/tex] has a rational root is [tex]a = 1024[/tex].
To find the smallest positive integer [tex]a[/tex] greater than 1000 such that the equation [tex]\sqrt{a} - \sqrt{a-x} = 0[/tex] has a rational root, we need to analyze the condition given in the equation.
We start from the original equation:
[tex]\sqrt{a} - \sqrt{a-x} = 0[/tex]
This implies that:
[tex]\sqrt{a} = \sqrt{a-x}[/tex]
Squaring both sides will remove the square root:
[tex]a = a - x[/tex]
So, we simplify this to:
[tex]x = 0[/tex]
In this case, it suggests that for the equation to have a rational root, [tex]x[/tex] must be equal to zero, which is a trivial case and not within the scope of finding a number greater than 1000.
Next, we need to find conditions under which [tex]\sqrt{a} - \sqrt{a-x}[/tex] has non-trivial rational roots. We realize that for other values of [tex]x[/tex], the right-hand side requires that [tex]a - x[/tex] must also be a perfect square in order for [tex]\sqrt{a-x}[/tex] to yield a rational number.
Assume [tex]a = n^2[/tex] where [tex]n[/tex] is any integer. Therefore:
[tex]\sqrt{a} = n[/tex]
Then we rewrite the original equation in terms of a new term, say [tex]m[/tex], where:
[tex]a - x = m^2[/tex]
Substituting this, we find that:
[tex]n^2 - m^2 = x[/tex]
This indicates that [tex]x[/tex] must also be a perfect square if we want to maintain the rationality in all cases.
We need to follow this procedure to find the smallest positive integer greater than 1000:
Start with [tex]n = 32[/tex] since [tex]32^2 = 1024 > 1000[/tex]. Test to see if [tex]x = n^2 - m^2[/tex] for some integer [tex]m[/tex] yields a rational number in various scenarios. If [tex]m = 31[/tex], then [tex]x = 32^2 - 31^2 = 1024 - 961 = 63[/tex] (which is rational). If [tex]m = 30[/tex], then [tex]x = 32^2 - 30^2 = 1024 - 900 = 124[/tex] (also rational).While checking values yields rational results, the lowest value of [tex]a[/tex] that successfully gives a rational root while being above 1000 appears to be [tex]1024[/tex].
PLEASE HELP WILL GIVE BRAINLIEST
What is the point and slope of the line represented by the equation below?
y + 3 = -2(x - 8)
A. slope = -2; point = (8, -3)
B. slope = -2; point = (3, -8)
C. slope = -2; point = (-8, 3)
D. slope = 2; point = (-3, 8)
Answer:
A. slope = -2; point = (8, -3)
Step-by-step explanation:
Compare to the point-slope form for slope m and point (h, k).
y -k = m(x -h)
You see that k = -3, m = -2, h = 8, so ...
the slope is -2the point is (h, k) = (8, -3)How long would it take for a ball dropped from the top of a 256-foot building to hit the ground
If the Laffite family deposits $8500 in savings account at 6.75% interest, compounded continuously, how much will be in the account after 25 years
Answer:
Option b
Step-by-step explanation:
We have a compound interest problem. With an annual interest rate of 0.675 and an initial payment of 8500, with t = 25 years
Then you must use the annual compound interest formula, which is represented by a growing exponential function:
[tex]y = e ^{ht}[/tex]
Where:
h is the interest rate of 0.675
y is the money in the savings account as a function of time
Then substitute the values in the formula and we have:
[tex]y = e ^{0.675(25)}[/tex]
[tex]y = 45,950.57[/tex]
Plato Help Please 35points
Stephanie is planning to build a boxed garden in her yard. She has not decided on the exact size of the garden, but Stephanie knows she wants the garden to be a rectangle with the length and width in a specific ratio. She also knows the cost of the materials needed to make the garden. Stephanie uses this information to create the following function to model the total cost, C), in dollars, to build a boxed garden that is x feet wide.
C(x)=2x^2+32
What is the average rate of change in the total cost to build the boxed garden as the width increases from 2 feet to 4 feet?
A.$6 per foot
B.$12 per foot
C.$18 per foot
D.$16 per foot
In the equation x is the feet of width.
If the original width is 2 feet, then X^2 = 2^2 = 4
If the width changes to 4 feet, then x^2 becomes 4^2 = 16
The change is 16 - 4 = 12
The answer should be B. $12 per foot.
Answer:
Option B is correct.
Step-by-step explanation:
Given the function which represent the total cost in dollars to build a boxed garden that is x feet wide.
[tex]C(x)=2x^2+32[/tex]
we have to find the average rate of change in the total cost to build the boxed garden as the width increases from 2 feet to 4 feet.
[tex]C(2)=2(2)^2+32=8+32=40[/tex]
[tex]C(4)=2(4)^2+32=32+32=64[/tex]
[tex]\text{Average rate of change=}\frac{C(4)-C(2)}{4-2}[/tex]
[tex]=\frac{64-40}{2}=\frac{24}{2}=$12 per foot[/tex]
Hence, option B is correct.
Complete the statement: A prime number is a whole number greater than 1 whose only factors are ______ and _______.
first blank- zero (0)
second balnk- the prime number
Answer:A prime number is a whole number greater than one whose only factors are 1 and itself
Colin drove 45 minutes to the airport. He arrived 90 minutes before his flight departed, and then he spent 70 minutes in the air. Once he landed, Colin spent 20 minutes gathering his luggage, and then he drove 35 minutes to his hotel. What must be true of any expression that represents the total time that Colin spent traveling from his house to the hotel?
Answer:
it took a total of 260 minutes or 4 hours and 20 minutes from Collin's house to his hotel.
Step-by-step explanation:
As each of the activities described is an independent activity that does not overlap, we can easily sum up the durations of each to find the total time Collin took from his house to the hotel.
We add it as follows :
he drove to the airport for 45 minutes + he waited at the airport for the flight to depart for 90 minutes + his fight duration was 70 minutes + upon landing, he gathered his luggage for 20 minutes + he drove to the hotel for 35 minutes.
So, 45+90+70+20+35 = 260 minutes
Answer:
The numbers can be added in any order.
Step-by-step explanation:
Just got this quiz question right.
Hope this helps :)
Let u=ln x and v= ln y. Write ln( √x · y^2) in terms of u and v.
Answer:
C
Step-by-step explanation:
We can use 2 properties of logarithms to write this:
1. ln(x*y) = lnx + ln y
2. ln(a^b) = b ln a
Using property 1, we can write as:
[tex]ln(\sqrt{x} *y^{2})\\=ln(\sqrt{x} )+ln(y^2)\\=ln(x^{\frac{1}{2}})+2lny\\=\frac{1}{2}lnx+2lny[/tex]
We know u = lnx and v = ln y, we simply substitute it now:
[tex]\frac{1}{2}lnx+2lny\\=\frac{1}{2}u+2v[/tex]
the correct answer is C
Answer:
c
Step-by-step explanation:
Please help me out!!!!!!!!
the correct answer would be 46°
It would be 46° but since there is an x = ? The "?" would be replaced with 46°
I hope this helps! ^^ You can just put 46° For your answer.
A real estate broker's base salary is $18,000. She earns a 4% commission on total sales. How much must she sell to earn $55,000 total?
The salary of the real estate broker = $18,000
Commission earned on total sales = 4% or 0.04
Total income earnings = $55,000
Let the total sales be = x
Equation becomes :
[tex]18000+0.04x=55000[/tex]
[tex]0.04x=55000-18000[/tex]
[tex]0.04x=37000[/tex]
[tex]x=925000[/tex]
Hence, the real estate broker must sell $925,000 worth of real estate to earn $55,000.
Find the lowest common denominator for these fractions and then add and simplify. 2/3 and 1/6
Answer:
Step-by-step explanation:
12 is the common denominator
The answer will be 6!!
need quick help with math!!!
[tex] \frac{5 - \sqrt{2} }{ \sqrt{3} } \\ \\ = \frac{5 - \sqrt{2} }{ \sqrt{3} } \times \frac{ \sqrt{3} }{ \sqrt{3} } \\ \\ = \frac{(5 - \sqrt{2} ) \sqrt{3} }{( { \sqrt{3} )}^{2} } \\ \\ = \frac{5 \sqrt{3} - \sqrt{6} }{3} [/tex]
Whats the distance between the 2 points? (use Pythagorean Theorem)
Your horizontal value (x) is 3 because 5.5-2.5 = 3
Your vertical value (y) is 3.5 because 4.5-1 = 3.5
Pythagoras Theorem
[tex]c^{2}= \sqrt{a^{2}+b^{2} }[/tex]
a = 3
b = 3.5
[tex]c^{2}= \sqrt{3^{2}+3.5^{2} }[/tex]
c = 4.60977222
c = 4.61 to 2d.p.
Bo's gross annual income is $45,408. He is paid semimonthly and has 6% deducted from his paychecks for his 403(b). His employer matches his deduction, up to 3%. How much was deposited into Bo's 403(b) each payday?
113.52
157.18
170.28
227.04
170.28 is the answer
Answer:
170.28
Step-by-step explanation:
Got it right on the test.
Solve each equation (quadratic pattern)
[tex]2^{2x} -2^{x} =12[/tex]
[tex]3^{2x} + 3^{x+1} =4[/tex]
[tex]4^{x} + 6[/tex] · [tex]2^{x} +8 = 0[/tex]
[tex]9^{x} = 3^{x} +6[/tex]
Answer: x = 2
Step-by-step explanation:
[tex]2^{2x}-2^x-12=0\\\\\text{Let u = }2^x\\\\u^2-u-12=0\\(u-4)(u+3)=0\\\\u-4=0\quad and\quad u+3=0\\u=4\qquad and\quad u=-3\\\\\text{Substitute u with }2^x\\2^x=4\qquad and \quad 2^x=-3\\2^x=2^2\quad and\quad \text{not possible}\\\boxed{x=2}[/tex]
********************************************************************************
Answer: x = 0
Step-by-step explanation:
[tex]3^{2x}+3^{x+1}-4=0\\\\3^{2x}+3^x\cdot3^1-4=0\\\\\text{Let u = }3^x\\u^2+3u-4=0\\\\(u+4)(u-1)=0\\\\u+4=0\quad and\quad u-1=0\\u=-4\qquad and\quad u=1\\\\\text{Substitute u with }3^x\\3^x=-4\qquad and\quad 3^x=1\\\text{not possible}\ and\quad 3^x=3^0\\.\qquad \qquad \qquad \qquad \boxed{x=0}[/tex]
********************************************************************************
Answer: No Solution
Step-by-step explanation:
[tex]4^x+6\cdot 2^x+8=0\\\\2\cdot 2^x+6\cdot 2^x+8=0\\\\\text{Let u = }2^x\\2u+6u+8=0\\8u+8=0\\8u=-8\\u=-1\\\\\text{Substitute u with }2^x\\2^x=-1\\\text{not possible}[/tex]
********************************************************************************
Answer: No Solution
Step-by-step explanation:
[tex]9^x=3^x-6\\\\3\cdot 3^x=1\cdot 3^x-6\\\\\text{Let u = }3^x\\\\3u=u-6\\2u=-6\\u=-3\\\\\text{Substitute u with }3^x\\3^x=-3\\\text{not possible}[/tex]
If x = 5, what additional information is necessary to show that triangle DAC is congruent to triangle BAC by SAS
Answer:
Lengths of AD and AB. They must be same for theorem SAS
Answer:
[tex]\overline{\rm AD} = \overline{\rm AB}[/tex]
Step-by-step explanation:
Two figures are congruent if they have the same shape and size, although their position or orientation are different. The congruence criteria correspond to the postulates and theorems that state what are the minimum conditions that two or more triangles must meet in order to be congruent. One of the congruence criteria is:
SAS (Side-Angle-Side): Two triangles are congruent if they have two sides and the angle determined by them respectively equal.
So, considering the previous information and the data provided by the problem. Then, the additional information necessary to show that triangle DAC is congruent to triangle BAC is:
[tex]\overline{\rm AD} = \overline{\rm AB}[/tex]