5 bombas deben trabajar durante 4 dias para llenar la piscina.
¿cuántos días demoran en llenar la misma piscina, si trabajan 8 horas diarias?Cada bomba trabaja a un rate (razon de trabajo) R.
Sabemos que 3 bombas, trabajando 5 horas diarias por 10 días (un total de 50 horas), llena una piscina, entonces:
(3R)*50 horas= 1 piscina.
R = (1 piscina)/(150 horas).
Es decir, una sola bomba tarda 150 horas en llenar una piscina.
En el caso de que 5 bombas trabajen, tenemos que para llenar una piscina tienen que trabajar un tiempo T.
5*((1 piscina)/(150 horas))*T = 1 piscina.
(1 piscina)/(30 horas)
Resolviendo para T, obtenemos:
T = 1 piscina*(30 horas)/(1 piscina) = 30 horas.
Y sabemos que trabajan 8 horas diarias, es decir, las bombas deben trabajar durante:
30/8 = 3.75 ≈ 4 días.
5 bombas deben trabajar durante 4 dias para llenar la piscina.
Sí quieres aprender más sobre razones de trabajo.
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i need help with this word problem please! :)
Answer:
Step-by-step explanation:
ASSUMING all family members purchased ride tickets
Let n be the number of family members
148 = 8 + n(16 + 12)
140 = 28n
n = 5
Find the equation of the exponential function represented by the table below:
x y
0 5
1 15
2 45
3 135
y=
Answer:
y=5·3x
Step-by-step explanation:
x=0, y=5:
5=a·b↑0 a=5
x=1, y=15:
15=5·b↑1
b=15/5=3
The equation of the exponential function is y = 5(3)ˣ
What is an exponential function?An exponential function is a Mathematical function in the form f (x) = aˣ, where “x” is a variable and “a” is a constant which is called the base of the function and it should be greater than 0.
Given,
x: 0, 1, 2, 3
y: 5, 15, 45, 135
We have to find the exponential equation:
The exponential function in the form:
y = a × b ˣ
y value of x as 0 is 5.
This is the a value in the equation.
The ratio of values between x as 1 and x as 0 is 15/5 which is equal to 3. This is the value of b in the equation.
Therefore, the equation will become:
y = 5 × 3 ˣ
Hence the equation of the exponential function is y = 5(3)ˣ
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Two decimal for 2597.58333
Answer:
2597. 58000 and this is the ans
Juan has x quarters and y dimes, having a minimum of 16 coins worth at most $3 combined. No less than 4 of the coins are quarters. Solve this system
of inequalities graphically and determine one possible solution.
Answer:
See belowStep-by-step explanation:
Quarter - 25¢, dime - 10¢, total - $3 = 300¢
Inequalities:
x + y ≥ 1625x + 10y ≤ 300x ≥ 4See attached for graphical solution. There are many solutions.
Possible one solution:
5 quarters and 17 dimesA board 120 inches long is divided into 2 sections. If the ratio of the 2 sections is 3:5, what are the lengths of the sections?
15 inches, 105 inches
A
B
24 inches, 96 inches
C 40 inches, 80 inches
D 45 inches, 75 inches
Answer:
D 45 inches, 75 inches
Step-by-step explanation:
3:5 is 3 + 5 = 8 parts
one section is 3/8 of 120 = 45 inches
other section is 5/8 of 120 = 75 inches
D 45 inches, 75 inches
A furniture company charges 0.45 per pound
for shipping
Write an equation for the cost(y) of shipping
x pounds.
Use it to determine the cost of shipping a
12-pound chair.
The cost of the shipping a 12 pound chair is 5.4 all you need to do is 0.45 x 12 =5.4
0.45=Y 5.3=X
HELP LAST ATTEMPT!!!!
Answer:
(6,-2)
Step-by-step explanation:
What is the value of v?
By isosceles triangle theorem,
Angle ZXY = Angle ZYX
The sum of the angles in a triangle is 180 degrees.
106 + 2 same angles (-106) = 180 (-106) (Subtract 106 by both sides)
2 same angles (/ 2) = 74 (/ 2) (Divide 2 by both sides)
V = 37
Answer:
The value of v is 37°.
Step-by-step explanation:
Given that △ XYZ is an isosceles triangle where both sides have the equal angles. The total angle of △ is 180°. Let ∠ZXY and ∠ZYX be the same angles:
Let ∠ZXY = v, ∠ZYX = v, ∠ XZY = 106°,
∠ZXY + ∠ZYX + ∠XZY = 180°
v + v + 106° = 180°
2v + 106° = 180°
2v = 180° - 106°
2v = 74°
v = 74 ÷ 2
v = 37°
How long will it take for an investment to triple in value if it earns 81% compounded continuously? Round your answer to three decimals.
A. 0.678 years
B. 0.856 years
C. 1.356 years
D. 1.366 years
The number of years it would take an investment to triple with continuous compounding is 1.356 years.
The formula for calculating future value of an investment when there is continuous compounding is FV = A x [tex]e^{r}[/tex] x N
Where:
A= amount e = 2.7182818 N = number of years r = interest rateFV = future value FV / A = 3N = log(3) / log(e) / 0.81 = 1.356 years
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GEOMETRY HOMEWORK HELP! PLS!!
Answer:
x = 37°
Step-by-step explanation:
Given the triangle with two given exterior angles, m ∠107° and m ∠110°:
We can use the exterior angle theorem where it states that the measure of each exterior angle of a triangle is equal to the sum of the measures of the opposite and remote interior angles.
Start by finding the supplement of m ∠110°, that will serve as the other remote interior angle.
The supplement of ∠110° is:
∠110° + y = 180°
Where y = represents the other unknown interior angle.
Subtract ∠110° from both sides:
∠110° - ∠110° + y = 180° - ∠110°
y = 70°
Therefore, the other remote interior angle is y = 70°. Now, we can determine the value of x by establishing the following equation:
107° = x° + 70°
Subtract 70 from both sides:
107° - 70° = x° + 70°- 70°
x = 37°
A breakfast cereal producer makes its most popular product by combining just raisins and flakes in each box of cereal. The amounts of flakes in the boxes of this cereal are normally distributed with a mean of 370\,\text{g}370g370, start text, g, end text and a standard deviation of 24\,\text{g}24g24, start text, g, end text. The amounts of raisins are also normally distributed with a mean of 170\,\text{g}170g170, start text, g, end text and a standard deviation of 7\,\text{g}7g7, start text, g, end text.
Let T=T=T, equals the total amount of product in a randomly selected box, and assume that the amounts of flakes and raisins are independent of each other.
Find the probability that the total amount of product is less than 575\,\text{g}575g575, start text, g, end text.
You may round your answer to two decimal places.
P(T<575)\approx
Using the normal distribution, it is found that there is a 0.9192 = 91.92% probability that the total amount of product is less than 575 g.
In a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
It measures how many standard deviations the measure is from the mean. After finding the z-score, we look at the z-score table and find the p-value associated with this z-score, which is the percentile of X.When two normal variables are added, the mean is the sum of the means while the standard deviation is the square root of the sum of the variances.In this problem, the product is composed by flakes and raisins, and we have that:
[tex]\mu_F = 370, \sigma_F = 24, \mu_R = 170, \sigma_R = 7[/tex]
Hence, the distribution for the total amount of product has mean and standard deviation given by:
[tex]\mu = \mu_F + \mu_R = 370 + 170 = 540[/tex]
[tex]\sigma = \sqrt{\sigma_F^2 + \sigma_R^2} = \sqrt{24^2 + 7^2} = 25[/tex]
The probability that the total amount of product is less than 575 g is the p-value of Z when X = 575, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{575 - 540}{25}[/tex]
[tex]Z = 1.4[/tex]
[tex]Z = 1.4[/tex] has a p-value of 0.9192.
0.9192 = 91.92% probability that the total amount of product is less than 575 g.
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Find positive numbers x and y satisfying the equation xy=20 such that the sum 4x+y is as small as possible.
-(b-z)-(-2b+z)-(-3b-z)
Step-by-step explanation:
4b + z I think lol I honestly looked it up
SUBTRACT the given polynomials : (x + 2) - (8x + 4)
A}7x + 2
B}7x - 2
C}-7x - 2
D}-7x + 2
WELP ;-;
The equivalent expression for the subtraction (x + 2) - (8x + 4) is -7x - 2
Option C is correct
The given polynomial expression is:
(x + 2) - (8x + 4)
Expand the expression by removing the parenthesis
x + 2 - 8x - 4
Collect like terms
x - 8x + 2 - 4
-7x - 2
Therefore, the equivalent expression for the subtraction (x + 2) - (8x + 4) is -7x - 2
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what does (-x)+(-x)+(-x)=
Answer: -3x
Step-by-step explanation:
(-x)+(-x)=-2x
-2x+(-x)=-3x
1.8.3 practice - functions
3. Water freezes at 0 Celsius and 32 Fahrenheit. Water boils at 100 Celsius and 212 Fahrenheit.
Answer:
A. C(F) = 5/9F -(17 7/9)
B. slope: 5/9
C. y-intercept: -17 7/9
Step-by-step explanation:
A.The question tells us that the independent variable is the temperature in degrees Fahrenheit. Then the given ordered pairs are ...
(F, C) = (32, 0) and (212, 100)
The slope can be found from the slope formula:
m = (y2 -y1) / (x2 -x1)
m = (100 -0)/(212 -32) = 100/180 = 5/9
The y-intercept can be found from the slope-intercept equation for a line:
y = mx +b
b = y -mx
Using the first point, we have ...
b = 0 -(5/9)(32) = -160/9 = -17 7/9
Using the found values for m and b, the slope-intercept equation can be written ...
C(F) = 5/9F -(17 7/9)
__
B.The slope was found in part A to be 5/9. This means each degree Fahrenheit corresponds to 5/9 of a degree Celsius.
__
C.The y-intercept was found in part A to be -17 7/9. This means 0 °F corresponds to -17 7/9 °C.
What is the Bill of Rights?
The first amendment to the Constitution, which is actually a group of ten amendments
The list of laws that people of the United Stated needed to follow
The document that replaced the Constitution
The document that replaced the Articles of Confederation
Answer:
The first amendment to the Constitution, which is actually a group of ten commandments
Step-by-step explanation:
The first amendment to the Constitution is actually a group of ten amendments called the Bill of Rights. The Bill of Rights guarantees all Americans certain freedoms, such as freedom of religion, freedom of the press, freedom of speech, the right to bear arms, and the right to a fair trial.
SOMEONE PLEASE HELP MEEEEE
Answer:
Area = 23.12 cm²
perimeter = 24.28 cm
Step-by-step explanation:
top shaded region is circular arc with 90° sector angle
so perimeter of arc is 90 / 360 * 2πr
here radius of arc is half the length of square side
r = 6.8/2 = 3.4
top area shaded perimeter = 90/360 * 2 * 3.14 * 3.4
= 1/4 * 2 * 3.14 * 3.4
= 5.338
bottom region perimeter is also same
total perimeter of shaded region is = side + side + two arcs
= 6.8 + 6.8 + 2 * 5.338
= 13.6 + 10.676
= 24.276
= 24.28
Area of top shaded region is 90/360 * πr²
A = 1/4 * 3.14 * 3.4²
= 9.0746
bottom shaded region area is half of area of square - area of bottom arc
= 6.8 * 3.4 - 9.0746
= 23.12 - 9.0746
= 14.0454
so total area of shaded region is 9.0746 + 14.0454
= 23.12
or you can just calculate area as half of area of total square = 6.8² / 2
= 23.12
WHAT is the next sequence
Answer: its 21
Step-by-step explanation:
the sequence goes up by 1 each time
Answer:
21
Step-by-step explanation:
a1=1
a2=a1+2
a3=a2+3
a4=a3+4
...
a(n)=a(n-1)+n
write the equation of a line that is perpendicular to 2x+4y= 14 a need goes through (4,6)
This can be simplified to 2x-y = 2
Solving for y leads to y = 2x-2
========================================================
Explanation:
Anything perpendicular to Ax+By = C is of the form Bx-Ay = D
The given equation 2x+4y = 14 tells us that A = 2, B = 4, C = 14.
So Bx-Ay = D updates to 4x-2y = D.
We'll plug in the coordinates of the given point (x,y) = (4,6) to solve for D.
4x-2y = D
D = 4x-2y
D = 4(4)-2(6)
D = 16-12
D = 4
So 4x-2y = D updates to 4x-2y = 4
Optionally, we can divide each term by 2 to go from 4x-2y = 4 to 2x-y = 2
If we wanted to solve for y, then we'd get y = 2x-2
How long would it take 100,000 grams of
radioactive iodine, which has a half-life of 60 days, to decay to
25,000 grams? Use the formula N = N() where N is the final amount of the substance, N, is the initial amount, and #
represents the number of half-lives.
Answer:
t = 2 half-lives = 2*60 days = 120 days
hope this helps
Step-by-step explanation:
Rice is being poured into a cylindrical container with radius 4.5 inches so
that the height of the rice is increasing at a constant rate of 0.5 inches per
second. At what rate is the volume of rice in the container increasing at
the instant when the height is the same as the radius? (=2ℎ)
Please help
asked:the istant of height is the same as the radius
given facts:cylindrical container with radius 3.5 inches height of rice increasing 0.5 inches per second
solve hidden given:(4.5+o.5+2)
what operation to be used: addition and subtraction
solve+4.5+05+2=6.0
chec: 6.0-4.5=1.5
What is the relationship between the 9 in the hundreds place and the 9 in the tens place in 2,743,995?
Hundred and tenths are the relationship of 9 in the number
Answer:
The 9 in the hundreds column is ten times greater than the 9 in the tens column.
Step-by-step explanation:
work out the value of 10²-4³ give ypur answer as a power of 6
Answer: 36
Step-by-step explanation: 10^2 is 100 and 4^3 is 64, and 100-64=36
In Brad's golf bag, he has 3 times more white golf balls than yellow golf balls. He has 18 white golf balls in his bag.
Which equation can be used to find how many yellow golf balls, y, Brad has in his bag?
A.
3 + y = 18
B.
18 + y = 3
C.
3y = 18
D.
18y = 3
Answer:
C
Step-by-step explanation:
Read the short scenario and answer the question that follows.
Lisa's credit card balance this month is $969.16. Her APR (annual percentage rate) is 15.24 %. The minimum payment due is $20.00.
If she pays only the minimum each month and does not add any more charges, how long will it take her to pay off the entire balance?
Choose the correct answer below.
A.
about 10 years
B.
about 6 years
C.
about 3 years
D.
about 1 year
Answer:
B
Step-by-step explanation:
Use the amortisation formula:
A = P (r(1+r)^n)/((1+r)^n - 1)
swap in your numbers
p = 969.16
A = 20
n = 0.1524/12
20 = 969.16((0.1524/12) (1+(0.1524/12))^n) / ((1+(0.1524/12))^n - 1)
Then solve for n
n = 72 months
n = 6 years
Y = ___x + ____
Find the equation of the line.
Find The slope of the line represented by the points in the table (use your notes to get the formula it needed).
4.
Number
of Hours
1
2.
3
4
Cost
($)
$17
$29
$41
$53
1, 7, 13, 19, 25
Find the 20th linear term
Answer:
I think that the answer to your question is 115
Which expression is NOT equal to 729?
3 × 3 × 3 × 3 × 3 × 3
63
9 × 9 × 9
36
Answer:
6^3
Step-by-step explanation:
3 × 3 × 3 × 3 × 3 × 3=729
6^3=216
3 × 3 × 3 × 3 × 3 × 3=729
3^6=729
Hope this helps :)
3 × 3 × 3 × 3 × 3 × 3
63
9 × 9 × 9
36
