From the question, we are to convert 20 quartz to gallons.
Given
1 quartz = 1/4 gallons
20 quartz = x
Cross multiply and find x;
1 * x = 20 * 1/4
x = 20/4
x = 5
Hence 20 quartz is equivalent to 5 gallons
The half-life of a radioactive isotope is the time it takes for quantity of the isotope to be reduced to half its initial mass. Starting with 175 grams of a radioactive isotope, how much will be left rafter 5 half-lives? Round your answer to the nearest gram
Exponential Decay
The model for the exponential decay of a quantity Mo is:
[tex]M=M_o\cdot e^{-\lambda t}[/tex]Where λ is a constant and t is the time.
The half-life of a radioactive isotope is the time it takes to halve its initial mass. It can be calculated by making M = Mo/2 and solving for t:
[tex]\begin{gathered} \frac{M_o}{2}=M_o\cdot e^{-\lambda t} \\ \text{Simplifying:} \\ e^{-\lambda t}=\frac{1}{2} \\ \text{Taking natural log:} \\ -\lambda t=-\log 2 \\ t=\frac{\log 2}{\lambda} \end{gathered}[/tex]It's required to calculate the remaining mass of an isotope of Mo = 175 gr after 5 half-lives have passed, that is. we must calculate M when t is five times the value calculated above.
Substituting in the model:
[tex]M=175gr\cdot e^{-\lambda\cdot\frac{5\log 2}{\lambda}}[/tex]Simplifying (the value of λ cancels out):
[tex]\begin{gathered} M=175gr\cdot e^{-5\log 2} \\ \text{Calculating:} \\ M=175gr\cdot0.03125 \\ M=5.46875gr \end{gathered}[/tex]Rounding to the nearest gram, 5 grams of the radioactive isotope will be left after the required time.
I have tried multiple times but still could not get the correct answer or at least accurate answers
Given:
R is the midpoint of QS.
[tex]RS=5\text{,RT}=13[/tex]The midpoint is the point on a line segment equally distant from the two endpoints.
It gives,
[tex]\begin{gathered} QR=RS\ldots\ldots\text{. R is midpoint of QS} \\ \Rightarrow QR=5 \end{gathered}[/tex]Also,
[tex]\begin{gathered} RS+ST=RT \\ 5+ST=13 \\ ST=13-5 \\ ST=8 \end{gathered}[/tex]So, QT is calculated as,
[tex]\begin{gathered} QT=QR+RE+ST \\ QT=5+5+8=18 \end{gathered}[/tex]Answer: QT = 18
Hi I need help with this
system by applications i belive the answer is A can you check?
Let's use the variable x to represent the cost of a senior ticket and y to represent the cost of a child ticket.
If the cost of 1 senior ticket and 1 child ticket is $18, we have:
[tex]x+y=18[/tex]If 2 senior tickets and 1 child tickets cost $27, we have:
[tex]2x+y=27[/tex]Subtracting the first equation from the second one, we can solve the result for x:
[tex]\begin{gathered} 2x+y-(x+y)=27-18 \\ 2x+y-x-y=9 \\ x=9 \end{gathered}[/tex]Now, solving for y:
[tex]\begin{gathered} x+y=18 \\ 9+y=18 \\ y=18-9 \\ y=9 \end{gathered}[/tex]Therefore the cost of one senior ticket is $9 and the cost of one child ticket is $9.
Correct option: D.
what is 0.554 / 0.041
Answer:
13.5
Step-by-step explanation:
Hello!
Here is your solution after dividing the given decimals.
[tex]0.554[/tex] ÷ [tex]0.041[/tex] = [tex]13.51219[/tex] ← (There is a line passing over all numbers to the right side of the decimal.)
In summary, the final answer is 13.5 ← (Line over 5)
Hope this helps!
What are the coordinates of point B (3,-2) after a 90° clockwise rotation about the origin?
A ball is dropped from a state of rest at time T = 0.The distance traveled after t seconds is s(t) = 16t^2 ft.
ANSWERS
(a) 68 ft
(b) 136 ft/s
(c) 128 ft/s
EXPLANATION
(a) The time interval is from 4s to 4.5s, so the distance the ball travels from 4s to 4.5s is,
[tex]\Delta s=16\cdot(4.5)^2-16(4)^2=68ft[/tex](b) As stated, the average velocity is the quotient between the distance traveled and the time,
[tex]\frac{\Delta s}{\Delta t}=\frac{68ft}{0.5s}=136ft/s[/tex](c) Here we have to find the distance as we did in part b and then divide by the time interval,
[tex]\begin{cases}\lbrack4,4.01\rbrack\to\Delta s=1.28016\to V=1.28016/0.01=128.16ft/s \\ \lbrack4,4.001\rbrack\to\Delta s=0.128016\to V=0.128016/0.001=128.016ft/s \\ \lbrack4,4.0001\rbrack\to\Delta s=0.01280016\to V=0.01280016/0.0001=128.0016ft/s \\ \lbrack3.9999,4\rbrack\to\Delta s=0.01279984\to V=0.01279984/0.0001=127.9984ft/s \\ \lbrack3.999,4\rbrack\to\Delta s=0.127984\to V=0.127984/0.001=127.984ft/s \\ \lbrack3.99,4\rbrack\to\Delta s=1.2784\to V=1.2784/0.01=127.84ft/s\end{cases}[/tex]As we can see in the middle values, as the time interval is shorter - the difference approaches 0, the value of the velocity is closer to 128ft/s.
Hence, the estimated instantaneous velocity at t = 4 is 128 ft/s
Help I’ll give extra points!10. Camilla is saving to purchase a new pair of bowling shoes that will cost at least $39. She hasalready saved $19. What is the least amount of money she needs to save for the shoes?11. Suppose you earn $20 per hour working part time at a tax office. You want to earn at least$1,800 this month, before taxes. How many hours must you work?For problem 12, translate the phrase intoalgebraic inequality.12. A tour bus can seat 55 passengers. A minimum of 15 people must register for the tour to bookthe bus.
the least amount of money she needs to save is 20
the number of hours you must work is at least 90hours
Explanation:
10) The pair of shoes cost at least $39
at least $39 means: the cost is ≥ 39
≥ means greater than or equal to
Amount saved = $19
Let the least amount of money = x
x + 19 ≥ 39
x ≥ 39-19
x ≥ 20
This means the least amount of money she needs to save is 20
11) Let the number of hours worked = x
Amount earned per hour = $20
Amount to be earned this month is at least $1,800
This means amount to be earned this month ≥ 1800
[tex]\begin{gathered} 20\times x\text{ }\ge\text{ 1800} \\ 20x\text{ }\ge\text{ 1800} \\ \text{Divide through by 20} \\ x\text{ }\ge\text{ }\frac{1800}{20} \\ x\text{ }\ge\text{ 90} \end{gathered}[/tex]This means the number of hours you must work is at least 90hours
If the two triangles shown below are similar based on the giveninformation, complete the similarity statement, otherwise choose the"Not Similar" button.А18 in9 inHB7 in14 inACAB-ANot Similar
1) Two triangles are similar if they have congruent angles and proportional sides (for each corresponding leg).
2) So let's check whether there are similar triangles by setting a proportion:
[tex]\begin{gathered} \frac{HC}{CA}=\frac{JH}{CB} \\ \frac{9}{18}=\frac{7}{14} \\ Simplify\text{ both:} \\ \frac{1}{2}=\frac{1}{2} \end{gathered}[/tex]3) So yes they are similar, i.e. ΔCAB ~ΔHGJ
consider the function f(x) = x^1/2 and the function G, shown below. g(x)= f(1/4 • x) = (1/4 •x)^1/2how will the graph of the function g differ from the graph of the function f?
ANSWER
The graph of function g is the graph of function f stretched horizontally by a factor of 4.
EXPLANATION
Function g(x) is a transformation of function f(x), obtained by multiplying the variable, x, by 1/4. This is described as a horizontal stretch by a factor of 4.
Hence, the graph of function g is the graph of function f stretched horizontally by a factor of 4.
Find the surface area and the volume of the figure below round your answer to the nearest whole number
The shape in the questionis a sphere having
Radius = 10ft
Finding the Surface area
The surface area of a square is given as
[tex]\text{Surface Area of sphere = 4}\pi r^2[/tex]putting the value for radius
[tex]\begin{gathered} \text{Surface Area of sphere = 4 }\times\frac{22}{7}\times\text{ 10}\times10 \\ \text{Surface Area of sphere = }\frac{4\text{ }\times22\times10ft\times10ft}{7} \\ \text{Surface Area of sphere = }\frac{8800ft^2}{7} \\ \text{Surface Area of sphere = 1257.14ft}^2 \\ \text{Surface Area of sphere }\cong1257ft^2\text{ ( to the nearest whole number)} \end{gathered}[/tex]The surface area of the sphere = 1257 square feet
Finding the volume
The volume of a sphere is given as
[tex]\text{volume of sphere = }\frac{4}{3}\pi r^3[/tex]putting the value of radius
[tex]\begin{gathered} \text{Volume of sphere = }\frac{4}{3}\times\frac{22}{7}\text{ }\times10ft\text{ }\times10ft\text{ }\times10ft \\ \text{Volume of sphere = }\frac{88000ft^3}{21} \\ \text{Volume of sphere = 4190.47ft}^3 \\ \text{Volume of sphere}\cong4190ft^3\text{ (to the nearest whole number)} \end{gathered}[/tex]Therefore, the volume of the sphere = 4190 cubic feet
I really need help solving this practice from my prep guide in trigonometry
Given: Different angles in degrees and in terms of pi. The different angles are:
[tex]\begin{gathered} a)714^0 \\ b)\frac{23\pi}{5} \\ c)120^0 \\ d)\frac{31\pi}{6} \end{gathered}[/tex]To Determine: The equivalence of the given angles
The equivalent of degree and pi is given as
[tex]\begin{gathered} 2\pi=360^0 \\ \pi=\frac{360^0}{2} \\ \pi=180^0 \\ 360^0=2\pi \\ 1^0=\frac{2\pi}{360^0} \\ 1^0=\frac{1}{180}\pi \end{gathered}[/tex][tex]\begin{gathered} a)714^0 \\ 1^0=\frac{1}{180}\pi \\ 714^0=\frac{714^0}{180^0}\pi \\ 714^0=3\frac{29}{30}\pi \\ 714^0=\frac{119\pi^{}}{30} \end{gathered}[/tex][tex]\begin{gathered} b)\frac{23\pi}{5} \\ 1\pi=180^0 \\ \frac{23\pi}{5}=\frac{23}{5}\times180^0 \\ \frac{23\pi}{5}=828^0 \end{gathered}[/tex][tex]\begin{gathered} c)120^0 \\ 1^0=\frac{\pi}{180} \\ 120^0=120\times\frac{\pi}{180} \\ 120^0=\frac{2\pi}{3} \end{gathered}[/tex][tex]\begin{gathered} d)\frac{31\pi}{6} \\ 1\pi=180^0 \\ \frac{31\pi}{6}=\frac{31}{6}\times180^0 \\ \frac{31\pi}{6}=930^0 \end{gathered}[/tex]ALTERNATIVELY
A revolution is 360 degree
[tex]\begin{gathered} a)714^0 \\ \text{Multiples of 360 degre}e \\ 2\times360^0=720^0 \\ \text{equivalent of 714 degre}e\text{ would be} \\ 720^0-714^0=6^0 \end{gathered}[/tex][tex]undefined[/tex][tex]\begin{gathered} a)714^0=\frac{119\pi}{30} \\ b)\frac{23\pi}{5}=828^0 \\ c)120^0=\frac{2\pi}{3} \\ d)\frac{31\pi}{6}=930^0 \end{gathered}[/tex]Examine the graph and write a statement about the data. Use specific information from the graph.
This bar graph represents the percentage of the public's trust in the Federal Government from year 1960 to 2015. The public trust was highest in year 1960 at 74% and it was at its lowest in 2015 at 18%.
A local deli kept track of the sandwiches it sold for three months. The polynomials below model the number of sandwiches sold, where s represents days. Ham and Cheese: 4s^3-28s^2+33s+250Pastrami: -7.4s^2+32s+180Write a polynomial that models the total number of these sandwiches that were sold.
we are given that the following polynomials model the number of sandwiches sold per day:
[tex]\begin{gathered} HC=4s^3-28s^2+33s+250 \\ P=-7.4s^2+32s+180 \end{gathered}[/tex]The total amount of sandwiches is equivalent to the sum of both polynomials:
[tex]4s^3-28s^2+33s+250-7.4s^2+32s+180[/tex]Associating like terms:
[tex]4s^3+(-28s^2-7.4s^2)+(33s+32s)+(250+180)[/tex]Adding like terms:
[tex]4s^3-35.4s^2+65s+430[/tex]Since we can simplify any further, this is the polynomial that models the total amount of sandwiches.
I had $70 and my mother gave me $10 and my father gave me $30 and aunt and uncle gave me $150 and I had another $7 how much do I have
Initial money = 70
then add
10 + 30 + 150 + 7 = 197
Now add both results
70 + 197 = 267
Answer is
You have $267
A park in a subdivision is triangular shaped. Two adjacent sides of the park are 533 feet and 525 feet. The angle between the sides is 53 degrees. To the nearest unit, what is the area of the park in square yards?A. 27,935B. 24,831C. 37,246D. 12,415thank you ! :)
Given:
Length of the two adjacent sides = 533 feet and 525 feet
Angle between the two sides = 53 degrees
Let's find the area of park.
Let's make a sketch representing this situation:
Let's first find the length of the third side.
Apply the cosine rule.
We have:
[tex]\begin{gathered} a=\sqrt{533^2+525^2-2(533)(525)cos53} \\ \\ a=\sqrt{284089+275625-336805.7777} \\ \\ a=\sqrt{222908.2223} \\ \\ a=472.13\text{ ft} \end{gathered}[/tex]Now, apply the Heron's formula to find the area:
[tex]A=\sqrt{s(s-a)(s-b)(s-c)}[/tex]Where:
a = 472.13
b = 533
c = 525
Let's solve for s:
[tex]\begin{gathered} s=\frac{472.13+533+525}{2} \\ \\ s=\frac{1530.13}{2} \\ \\ s=765.1\text{ } \end{gathered}[/tex]• Therefore, the area will be:
[tex]\begin{gathered} A=\sqrt{765.1(765.1-472.13)(765.2-533)(765.1-525)} \\ \\ A=\sqrt{765.1(292.97)(232.1)(240.1)} \\ \\ A=111738.81\text{ ft}^2 \end{gathered}[/tex]The area in square feet is 111,738.81 square feet.
Now, let's find the area in square yards.
Apply the metrics of measurement.
Where:
1 square yard = 9 square feet
Thus, we have:
111,738.81 square feet =
[tex]\frac{111738.81}{9}=12415.4\approx12415\text{ square yards}[/tex]Therefore, the area of the park in square yards is 12,415 square yards.
ANSWER:
12,415 square yards.
a triangular pyramid has four faces h = b = 1. What is the pryimands surface area?(There's no image)(
Let's find the area of one face
[tex]A=\frac{bh}{2}[/tex]Where h = b = 1.
[tex]A=\frac{1\cdot1}{2}=\frac{1}{2}[/tex]Given that there are four faces, we have to multiply the area above by 4
[tex]S=4\cdot\frac{1}{2}=2[/tex]Hence, the answer is 2 square units.Ryan bought 3 1/2 boxes of paper clips. Allan bought 1 3/4 more boxes than Ryan.
Colin bought 1 1/2 times as many boxes as Allan How many boxes did Colin buy?
Answer:
Colin bought 7 7/8 boxes
Step-by-step explanation:
Let R represent the number of boxes bought by Ryan and A represent the number of boxes bought by Allan
R = 3 1/2
Convert to improper fraction:
3 1/2 = (3 x 2 + 1)/2 = 7/2
Allan bought 1 3/4 more boxes than Ryan
A = R + 1 3/4
Convert 1 3/4 to improper fraction:
1 3/4 7/4
So A = 7/2 + 7/4 = 14/4 + 7/4 = 21/4
Colin bought 1 1/2 times as many boxes as Allan
C = 1 1/2 x A
Convert 1 1/2 to improper fraction:
1 1/2 = 3/2
So C = 3/2 x 21/4
= 63/8 = 7 7/8 boxes
4j+2=h solve for j please help
To solve for j'
4j + 2 = h
subtract 2 from both-side of the equation
4j + 2-2 = h -2
4j = h-2
divide both-side of the equation by 4
4j/4 = h-2/4
[tex]j=\frac{h-2}{4}[/tex]40. Coach Hesky bought 3 new uniforms for his basketball team. He spent a total of $486. If the same amount was spent on each uniform, how much did he spend per player? .
new uniforms = 3
Total amount spent = $486
Amount spent per player = $486 /3 = $162
I need help with review on functions
The answer is Option 2
Its not a function
The domain and range of the function is shown at the various endpoints of the graph.
At every point you can always identify a value for x (the input value) and also a corresponding value for y (the output value).
Please note the endpoints marked in blue.
These are the endpoints, and for every point, you will have (x, y).
However, note that at the endpoints, the values of y remains the same.
For every relation to be a function, there must be exactly one corresponding y value for every x value. As shown by the blue markings on the graph, the x values on the horizontal axis both have the same y value (which is zero).
Hence, the relationship shown by the graph is not a function
Not a timed or graded assignment. Need a quick answer tho. Thank you
ANSWER:
Difference of squares
[tex]8x-7[/tex]STEP-BY-STEP EXPLANATION:
We have the following quotient:
[tex]\frac{64x^2-49}{8x+7}[/tex]We factor, knowing that the numerator is a difference of squares, therefore:
[tex]\begin{gathered} a^2-b^2=(a+b)(a-b) \\ \text{ in this case} \\ a=8x \\ b=7 \\ 64x^2-49=(8x+7)(8x-7) \\ \text{ Replacing:} \\ \frac{(8x+7)(8x-7)}{8x+7}=8x-7 \end{gathered}[/tex]Suppose that $6000 is placed in an account that pays 19% interest compounded each year. Assume that no withdrawals are made from the account.
We are going to use the formula for the compound interest, which is
[tex]A=P\cdot(1+\frac{r}{n})^{nt}[/tex]A = the future value of the investment
P = the principal investment amount (the initial deposit or loan amount)
r = the annual interest rate (decimal)
n = the number of times that interest is compounded per unit t
t = the time the money is invested or borrowed for
Replacing the values in the first question we have:
[tex]\begin{gathered} A=P\cdot(1+\frac{r}{n})^{nt} \\ A=6000,r=0.19,n=1,t=1 \\ A=6000\cdot(1+\frac{0.19}{1})^1=7140 \end{gathered}[/tex]Answer for the first question is : $7140
Then, replacing the values in the second question we have:
[tex]\begin{gathered} A=P\cdot(1+\frac{r}{n})^{nt} \\ A=6000,r=0.19,n=1,t=2 \\ A=6000\cdot(1+\frac{0.19}{1})^2=8497 \end{gathered}[/tex]Answer for the second question is : $8497
Two question I want to verify my answerSolve for y in terms of x 2x =1-5yAnd Simplify the given expression Write answer with a positive exponent (X^-3/y^4)^-4
Part 1
we have
2x =1-5y
solve for y
step 1
Adds 5y both sides
2x+5y=1
step 2
subtract 2x both sides
5y=-2x+1
step 3
Divide by 5 on both sides
y=-(2/5)x+1/5
Part 2
we have the expression
[tex](\frac{x^{-3}}{y^4})^{-6}=(\frac{y^4}{x^{-3}})^6=(y^4x^3)^6=y^{(24)}x^{(18)}[/tex]What is the x values that satisfies the linear equations on the graph?
In the linear equations shown on the coordinate grid, the values of x that satisfies both equations is 2 (option b).
The graph of both equations intersect at the point where x equals 2.
the value of y is directly proportional to the value of x. if y = 45 when x = 180 what is the value of y = 90
We have a direct proportionality between y and x.
If "k" is the constant of proportionality, the equation for this situation is:
[tex]y=kx[/tex]To find the constant of proportionality, we solve that equation for k:
[tex]k=\frac{y}{x}[/tex]And since when y=45, x=180, substituting these values to find k:
[tex]\begin{gathered} k=\frac{45}{180} \\ k=0.25 \end{gathered}[/tex]Now, we substitute the value of k into the equation of proportionality:
[tex]y=0.25x[/tex]And in this equation, we can substitute any value of the variables, and find the value of the other variable.
In this case, we have y=90, so we substitute that value and solve for x:
[tex]\begin{gathered} 90=0.25x \\ \frac{90}{0.25}=x \\ 360=x \end{gathered}[/tex]Answer: when y=90, x=360
Multiply each term inside the parentheses by the factor outside the parentheses 2(x - 4) = 2 x + 2(-4) Multiply Simplify.2(×-4)=2x+2(-4)
We have the expression:
[tex]2(x-4)=2x+2(-4)[/tex]We solve as follows:
[tex]2x-8=2x-8[/tex]If we want to simplify further, we will get:
[tex]2x=2x\Rightarrow x=x\Rightarrow0=0[/tex]***
In order to simplify the expression:
[tex]2(x-4)=2x+2(-4)[/tex]We multiply 2 times x and add 2 times -4, that is:
[tex]2x+2(-4)=2x+2(-4)[/tex]Now, we multiply 2 times -4 in both sides, that is:
[tex]2x-8=2x-8[/tex]A 33-inch piece of steel is cut into three pieces so that the second piece is twiceas long as the first piece, and the third piece is one inch more than five times thelength of the first piece. What is the length of the first piece?
Let;
x = the length of the first piece
y=the length of the second piece
z=the length of the third piece
From the question;
"the second piece is twice as long as the first piece" can be written in equation as:
y = 2x
"the third piece is one inch more than five times the length of the first piece"
can be written as :
z= 5x+ 1
Total length of the 3 pieces = 33
This implies:
x + y + z =33
substitute y=2x and z=5x+1 into the above
x + 2x + 5x+1 = 33
8x + 1 = 33
subtract 1 from both-side of the equation
8x = 33 -1
8x = 32
divide both-side of the equation by 8
x= 32/8
x= 4
The length of the first piece is 4-inches
15. Find m<1.
Observing the given figure n< 1 can be found using the Vertical angel theorem to be 132.75 degrees
What is vertical angle theorem?The vertical angle theorem is used when two straight lines intersect, at their point of intersection four angles are formed. The angles opposite to each other are equal
How to find m< 1 using vertical angle theoremThe figure shows
(x² - 6x)⁰
(x/2 + 42)°
From vertical angle theorem
(x² - 6x)⁰ = (x/2 + 42)°
solving for x by multiplying out by 2
2x² - 12x = x + 84
2x² - 12x - x - 84 = 0
2x² - 13x - 84 = 0
factorizing the parabolic equation gives
(x + 4)(2x-21)
using the positive value of x
x = 21/2
substituting x = 21/2 into (x/2 + 42) gives
= 47.25
sum of angles at a point = 360 degrees
2 * 47.25 + 2 * m< 1 = 360
2 * m< 1 = 360 - 94.5
m< 1 = 265.5/2
m< 1 = 132.75
Learn more on vertical angles here: https://brainly.com/question/68367
#SPJ1
divide fraction2*1/3 / 7*3/8 =
Step-by-step explanation:
3.999 is the correct answer
