Answer:
60
Step-by-step explanation:
5 * 12 = 60
Sara can weed a garden in 30 minutes. When her brother Hamdan helps her, they can weed
the same garden in 20 minutes. How long would it take Hamdan to weed the garden if he
worked by himself?
Step-by-step explanation:
Hello!The answer is:It will take 42.35 minutes to weed the garden together.
Why?
To solve the problem, we need to use the given information about the rate for both Laura and her husband. We know that she can weed the garden in 1 hour and 20 minutes (80 minutes) and her husband can weed it in 1 hour and 30 minutes (90 minutes), so we need to combine both's work and calculate how much time it will take to weed the garden together.
So, calculating we have:
Laura's rate:
\frac{1garden}{80minutes}
80minutes
1garden
Husband's rate:
\frac{1garden}{90minutes}
90minutes
1garden
Now, writing the equation we have:
Laura'sRate+Husband'sRate=CombinedRateLaura
′
sRate+Husband
′
sRate=CombinedRate
\frac{1}{80}+\frac{1}{90}=\frac{1}{time}
80
1
+
90
1
=
time
1
\frac{1*90+1*80}{7200}=\frac{1}{time}
7200
1∗90+1∗80
=
time
1
\frac{170}{7200}=\frac{1}{time}
7200
170
=
time
1
\frac{17}{720}=\frac{11}{time}
720
17
=
time
11
\frac{17}{720}=\frac{1}{time}
720
17
=
time
1
\frac{17}{720}*time=1
720
17
∗time=1
time=1*\frac{720}{17}=42.35time=1∗
17
720
=42.35
Hence, we have that it will take 42.35 minutes to weed the garden working together.
Have a nice day!If the integral of the product of x squared and e raised to the negative 4 times x power, dx equals the product of negative 1 over 64 times e raised to the negative 4 times x power and the quantity A times x squared plus B times x plus E, plus C , then the value of A B E is
Answer:
[tex]A + B + E = 32[/tex]
Step-by-step explanation:
Given
[tex]\int\limits {x^2\cdot e^{-4x}} \, dx = -\frac{1}{64}e^{-4x}[Ax^2 + Bx + E]C[/tex]
Required
Find [tex]A +B + E[/tex]
We have:
[tex]\int\limits {x^2\cdot e^{-4x}} \, dx = -\frac{1}{64}e^{-4x}[Ax^2 + Bx + E]C[/tex]
Using integration by parts
[tex]\int {u} \, dv = uv - \int vdu[/tex]
Where
[tex]u = x^2[/tex] and [tex]dv = e^{-4x}dx[/tex]
Solve for du (differentiate u)
[tex]du = 2x\ dx[/tex]
Solve for v (integrate dv)
[tex]v = -\frac{1}{4}e^{-4x}[/tex]
So, we have:
[tex]\int {u} \, dv = uv - \int vdu[/tex]
[tex]\int\limits {x^2\cdot e^{-4x}} \, dx = x^2 *-\frac{1}{4}e^{-4x} - \int -\frac{1}{4}e^{-4x} 2xdx[/tex]
[tex]\int\limits {x^2\cdot e^{-4x}} \, dx = -\frac{x^2}{4}e^{-4x} - \int -\frac{1}{2}e^{-4x} xdx[/tex]
[tex]\int\limits {x^2\cdot e^{-4x}} \, dx = -\frac{x^2}{4}e^{-4x} +\frac{1}{2} \int xe^{-4x} dx[/tex]
-----------------------------------------------------------------------
Solving
[tex]\int xe^{-4x} dx[/tex]
Integration by parts
[tex]u = x[/tex] ---- [tex]du = dx[/tex]
[tex]dv = e^{-4x}dx[/tex] ---------- [tex]v = -\frac{1}{4}e^{-4x}[/tex]
So:
[tex]\int xe^{-4x} dx = -\frac{x}{4}e^{-4x} - \int -\frac{1}{4}e^{-4x}\ dx[/tex]
[tex]\int xe^{-4x} dx = -\frac{x}{4}e^{-4x} + \int e^{-4x}\ dx[/tex]
[tex]\int xe^{-4x} dx = -\frac{x}{4}e^{-4x} -\frac{1}{4}e^{-4x}[/tex]
So, we have:
[tex]\int\limits {x^2\cdot e^{-4x}} \, dx = -\frac{x^2}{4}e^{-4x} +\frac{1}{2} \int xe^{-4x} dx[/tex]
[tex]\int\limits {x^2\cdot e^{-4x}} \, dx = -\frac{x^2}{4}e^{-4x} +\frac{1}{2} [ -\frac{x}{4}e^{-4x} -\frac{1}{4}e^{-4x}][/tex]
Open bracket
[tex]\int\limits {x^2\cdot e^{-4x}} \, dx = -\frac{x^2}{4}e^{-4x} -\frac{x}{8}e^{-4x} -\frac{1}{8}e^{-4x}[/tex]
Factor out [tex]e^{-4x}[/tex]
[tex]\int\limits {x^2\cdot e^{-4x}} \, dx = [-\frac{x^2}{4} -\frac{x}{8} -\frac{1}{8}]e^{-4x}[/tex]
Rewrite as:
[tex]\int\limits {x^2\cdot e^{-4x}} \, dx = [-\frac{1}{4}x^2 -\frac{1}{8}x -\frac{1}{8}]e^{-4x}[/tex]
Recall that:
[tex]\int\limits {x^2\cdot e^{-4x}} \, dx = -\frac{1}{64}e^{-4x}[Ax^2 + Bx + E]C[/tex]
[tex]\int\limits {x^2\cdot e^{-4x}} \, dx = [-\frac{1}{64}Ax^2 -\frac{1}{64} Bx -\frac{1}{64} E]Ce^{-4x}[/tex]
By comparison:
[tex]-\frac{1}{4}x^2 = -\frac{1}{64}Ax^2[/tex]
[tex]-\frac{1}{8}x = -\frac{1}{64}Bx[/tex]
[tex]-\frac{1}{8} = -\frac{1}{64}E[/tex]
Solve A, B and C
[tex]-\frac{1}{4}x^2 = -\frac{1}{64}Ax^2[/tex]
Divide by [tex]-x^2[/tex]
[tex]\frac{1}{4} = \frac{1}{64}A[/tex]
Multiply by 64
[tex]64 * \frac{1}{4} = A[/tex]
[tex]A =16[/tex]
[tex]-\frac{1}{8}x = -\frac{1}{64}Bx[/tex]
Divide by [tex]-x[/tex]
[tex]\frac{1}{8} = \frac{1}{64}B[/tex]
Multiply by 64
[tex]64 * \frac{1}{8} = \frac{1}{64}B*64[/tex]
[tex]B = 8[/tex]
[tex]-\frac{1}{8} = -\frac{1}{64}E[/tex]
Multiply by -64
[tex]-64 * -\frac{1}{8} = -\frac{1}{64}E * -64[/tex]
[tex]E = 8[/tex]
So:
[tex]A + B + E = 16 +8+8[/tex]
[tex]A + B + E = 32[/tex]
I need HELP PLZZZZZ!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
7 C
Step-by-step explanation:
We want to find the y value for an x value of -9
The y value for the x value of -9 is 7
Tannis' first machine could throw a car 27 meters. She studied her first machine and built a better one. Her second machine could throw a car 7 times as far. How far does the second machine throw a car?
Choose 1 answer:
(Choice A)
The machine throws the car 189 meters, because 27×7=189.
(Choice B)
The machine throws the car 3 meters, because 27÷7=3 remainder 6.
(Choice C)
The machine throws the car 4 meters, because 27÷7=3 remainder 6.
Help please just right the ratio for all
Michael Bob had a net income of $10,000 a month. His car note was $560 a month. What percent of his income was his car payments
Which graph is a function of x?
Answer:
A vertical line through the origin
Step-by-step explanation:
Can you please help it’s hard!
Answer:
F
Step-by-step explanation:
Cuale es la distancia entre dos puntos (6,-7)(-2,8)
Answer:
17
Step-by-step explanation:
Use the distance formula to determine the distance between the two points.
[tex]d = \sqrt{(x_{2} -x_{1})^{2} + (y_{2} - x_{1})^{2} }[/tex]
d = distance
[tex](x_{1}, y_{1})[/tex] = coordinates of the first point
[tex](x_{2}, y_{2})[/tex] = coordinates of the second point
Answer: The distance between the points (6,-7)(-2,8) is 17.
Step-by-step explanation:
To calculate the distance between two points, we apply the following formula:
[tex]\boldsymbol{\sf{d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2 } }}[/tex]
The points are:
(x₁, y₁) = 6, -7(x₂, y₂) = -2. 8We substitute in the formula and solve:
[tex]\boldsymbol{\sf{d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2 } }}\\ \\ \boldsymbol{\sf{d=\sqrt{(-2-6)^2+(8-(-7))^2 } }}\\ \\ \boldsymbol{\sf{d=\sqrt{(-8)^2+15^2}=\sqrt{64+225 } }}\\ \\ \boldsymbol{\sf{d=\sqrt{289}=17 }}[/tex]
The distance between the points (6,-7)(-2,8) is 17.
I need the answer or work this either pass or fail please !
Step-by-step explanation:
DAG = DG
120=120°
DHG + DG =360°
DHG +120° =360°
DHG+120°-120°=360°-120°
DHG°=240°
Find the length of side y.
y=_ft
Answer:
x= 0.22947
Step-by-step explanation:
Step-by-step explanation:
x=0 22 im not sure though ok
Practice polynomials
solve and show your work
3x^2-14x-5
Answer:
( − 5 ) ( 3 + 1 )
Step-by-step explanation:
Use the sum-product pattern: 3 2 − 1 4 − 5
3 2 + − 1 5 − 5
Common factor from the two pairs: 3 2 + − 1 5 − 5
( 3 + 1 ) − 5 ( 3 + 1 )
Rewrite in factored form
Answer:
Step-by-step explanation:
Standard form:
3x2 − 14x − 5 = 0
Factorization:
(x − 5)(3x + 1) = 0
Solutions based on factorization:
x − 5 = 0 ⇒ x1 = 5
3x + 1 = 0 ⇒ x2 = −1
3
≈ −0.333333
Extrema:
Min = (2.333333, −21.333333)
Answer:
(3 x + 1 ) ( x − 5 )
According to Cavalieri’s Principle, if all of the following have the same height, which pair would NOT have the same volume? Explain why.
Answer:
Pair 2.
Step-by-step explanation:
For the volumes to be the same the base areas must also be the same.
For Pair 2 the areas are 25π and 24π while the other 2 pairs have both base areas = 25π.
If you rolled two dice, what is the probability
that you would roll a sum of 11?
Give your answer as a simplified fraction. Enter
the number that belongs in the green box.
second
first
1 2 3 4 5 6
1 1,1 1,2 1,3 1,4 1,5 1,6
22,1 2,2 2,3 2,4 2,5 2,6
33,1 3,2 3,3 3,4 3,5 3,6
4 4,1 4,2 4,3 4,4 4,5 4,6
55,1 5,2 5,3 5,4 5,5 5,6
6 6,1 6,2 6,3 6,4 6,5 6,6
Enter
Answer:
2/36 or 1/18 simplified
Step-by-step explanation:
you have all the combinations listed which is good.
probability = number of successful events / number of total events
look for the sums that are 11 and count them (there are 2 - 5,6 and 6,5).total the number of all events (36)so you then get the 2/36there are
I need help it’s confusing to me.Someone pls help
Answer:
cylinder volume= 1005.30965cm²
rectangular prism volume= 384cm²
total volume: 1005.30965+384= 1389.31cm²
round off to the nearest two decimal places
a) 32,369
b) 99,004
Answer:
a = 32,37
b=99
Step-by-step explanation:
a = 32,369
The third decimal place is greater (or equal) than 5, so we need to add one unit to the second place.
= 32,37
b = 99,004
The third decimal place is lesser than 5, so we can simply delete it.
= 99,00
Since only zero in every decimal places are not relevant, we can remove them:
= 99
Marie had 12 pizzas. She wanted to give each person of a 1/4
pizza. How many people would receive a piece of pizza?
Answer:
48 people.
Step-by-step explanation:
Each person gets 1/4 of a pizza meaning that one pizza can serve 4 people. If one pizza can serve 4 people, 12 pizzas can serve 48 people, because 4x12=48.
An experimenter is studying the effects of temperature, pressure, and type of catalyst on yield from a certain chemical reaction. She considers 6 different temperatures, 5 different pressures, and 4 different catalysts are under consideration.
a. If any particular experimental run involves the use of a single temperature, pressure, and catalyst, how many experimental runs are possible?
b. How many experimental runs are there that involve use of the lowest temperature and two lowest pressures?
c. Suppose that five different experimental runs are to be made on the first day of experimentation. If the five are randomly selected from among all the possibilities, so that any group of five has the same probability of selection, what is the probability that a different catalyst is used on each run?
Answer:
a) 120 possible experimental runs
b) 8 possible experimental runs
c) 0
Step-by-step explanation:
a. For the experiment, there are 6 different temperatures (T), 5 different pressures (P), and 4 different catalysts (C). We can find the total number of combinations using the product rule.
N = T × P × C
N = 6 × 5 × 4 = 120
b) If we use only the lowest temperature, we have T = 1, and if we use the two lowest pressures, we have P = 2. We can find the total number of combinations using the product rule.
N = T × P × C
N = 1 × 2 × 4 = 8
c) If we perform 5 experimental runs with 4 possible catalysts, it is not possible to use a different catalyst each time. At least, 1 catalyst must be repeated twice. Then, the event "a different catalyst is used on each run" has a probability of 0.
Find the surface area of the rectangular prism to the nearest hundredth.
Answer:
340
Step-by-step explanation:
2(10*8)=160
2(8*5)=80
2(5*10)=100
160+80+100=340
Find the value of X. Please help!!!
Answer:
x = 9
Step-by-step explanation:
The triangle given is an isosceles triangle because it has two equal sides. By implication, the two base angles that are opposite the two equal sides are equal to each other.
Therefore,
80° + 2(m<2) = 180° (sum of triangle theorem)
80 + 2(5x + 5) = 180
80 + 10x + 10 = 180
Add like terms
90 + 10x = 180
90 + 10x - 90 = 180 - 90 (substraction property of equality)
10x = 90
10x/10 = 90/10 (division property of equality)
x = 9
Bill Board is "lording" his SAT score over his friend, Rhoda Dendron, who took the ACT. "You only got a 25 in math," he chortled, "while I got a 300 in math." Given that the SAT has a μ of 500 and a σ of 100, and the ACT has a μ of 20 and a σ of 5, what is wrong with Bill’s logic (give the answer in both z scores and percentile ranks).
Answer:
Rhoda, whose ACT has a z-score of 1, scored in the 84th percentile in the ACT, compared to Bill, whose SAT has a z-score of -2, who scored in the 2nd percentile on the SAT. Due to the higher percentile(higher z-score) on her test, Rhoda did better on her respective test than Bill, and thus, his logic is wrong.
Step-by-step explanation:
Z-score:
In a set 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]
The Z-score 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. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Bill:
Scored 300, so [tex]X = 300[/tex]
SAT has a μ of 500 and a σ of 100.
His z-score is:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{300 - 500}{100}[/tex]
[tex]Z = -2[/tex]
[tex]Z = -2[/tex] has a p-value of 0.02.
This means that Bill, whose SAT score has Z = -2, scored in the 2nd percentile.
Rhoda
Scored 25, so [tex]X = 25[/tex].
ACT has a μ of 20 and a σ of 5
Her z-score:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{25 - 20}{5}[/tex]
[tex]Z = 1[/tex]
[tex]Z = 1[/tex] has a p-value of 0.84
This means that Rhoda, whose ACT score has Z = 1, scored in the 84th percentile.
What is wrong with Bill’s logic ?
Rhoda, whose ACT has a z-score of 1, scored in the 84th percentile in the ACT, compared to Bill, whose SAT has a z-score of -2, who scored in the 2nd percentile on the SAT. Due to the higher percentile(higher z-score) on her test, Rhoda did better on her respective test than Bill, and thus, his logic is wrong.
4(-8x + 5) = -32.x - 26
solve the equation
Answer:
-46
Step-by-step explanation:
4(-8x + 5) = -32x - 26
-32x + 20 = -32x - 26
-32x + 32x = -26 - 20
x = -46
Answer:
-32x+20=-32x-26
20=-26
so unequal or undefined
hope this helps
have a good day :)
Step-by-step explanation:
Which type of triangle, if any, can be formed with sides measuring 8 inches, 8 inches, and 3
inches?
A. a scalene triangle
B. an equilateral triangle
C. an isosceles triangle
D. no triangle
Answer:
the answer is C
Step-by-step explanation:
Which type of triangle, if any, can be formed with sides measuring 8 inches, 8 inches, and 3
inches?
A. a scalene triangle
B. an equilateral triangle
C. an isosceles triangle
D. no triangle
Someone please help me
Answer:
48
Step-by-step explanation: 1 foot is 12 inches. Since the feet are going up by ones, you can say 1=12, 2=24 (+12), 3=36(+12), 4=48(+12)
Hope this helps
Answer and Step-by-step explanation:
The answer is 48.
Each value of y is a multiple of 12, so for when there is 4 feet, you multiply 12 by 4 to get 48.
For when it is 1 foot, you multiply 12 by 1 to get 12.
For when it is 2 feet, you multiply 12 by 2 to get 24.
For when it is 3 feet, you multiply 12 by 3 to get 36
For when it is 5 feet, you multiply 12 by 5 to get 60.
If you were to continue, the y-values (aka the inches) will always be a multiple of 12.
#teamtrees #PAW (Plant And Water)
which expression is equivalent to (5^-2) ^5 x 5^4
Answer:
6.4 × 10 ^-5
Step-by-step explanation:
(0.04)^5 × 625 = 6.4 × 10^-5 (6.4e-5)
A boy is flying two kites at the same time. He has 450 ft of line out to one kite and 390 ft to the other. He estimates the angle between the two lines to be 34 degrees. Approximate the distance between the kites.
Answer:
[tex]C=252.2ft[/tex]
Step-by-step explanation:
From the question we are told that:
First Kite Distance [tex]A=450ft[/tex]
Second Kite Distance [tex]B=390ft[/tex]
Angle [tex]\theta=34\textdegree[/tex]
Generally the equation for Distance X between the kites is mathematically given by
Using Cosine Rule
[tex]C^2=A^2+B^2-2abCos \theta[/tex]
Therefore
[tex]C^2=(450)^2+(390)^2-2(450)(390)Cos 34[/tex]
[tex]C^2=63607.81[/tex]
[tex]C=\sqrt(63607.81)[/tex]
[tex]C=252.2ft[/tex]
Which value of x will make the inequality true?
X - 4 >-2
A)-4
B)-1
C)0
D)5
[tex]\boxed{D)\:5}[/tex] ✔
[tex]\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\orange{:}}}}}[/tex]
[tex]\sf\purple{A)\:-4}[/tex] ❌
[tex]x - 4 < - 2 \\ = - 4 - 4 < - 2 \\ = - 8 < - 2[/tex]
[tex]\sf\purple{B)\:-1}[/tex] ❌
[tex]x - 4 < - 2 \\ = - 1 - 4 < - 2 \\ = - 5 < - 2[/tex]
[tex]\sf\purple{C)\:0}[/tex] ❌
[tex]x - 4 < - 2 \\ = 0 - 4 < - 2 \\ = - 4 < - 2[/tex]
[tex]\sf\red{D)\:5}[/tex] ✅
[tex]x - 4 > - 2 \\ = 5 - 4 > - 2 \\ = 1 > - 2[/tex]
[tex]\circ \: \: { \underline{ \boxed{ \sf{ \color{green}{Happy\:learning.}}}}}∘[/tex]
Mary makes trail mix with bulk nuts and dried fruit. She spends $4.50 on the dried fruit. Mixed nuts cost $2.50 per pound. She has a total of $12 to spend. What are the possible number of pounds of nuts she can buy?
Answer: 3 pounds
Step-by-step explanation: 12 - 4.50 = 7.50 7.50/2.50=3
Please help me solve this math problem and explain it. Will give BRANIEST!
(X^2+2xy+y^2)^2
Answer:
I'm sorry hindi ko po alam eh
Which approach is the best to find the volume of a cube?
A
Measure the length of one side and multiply the length by 3.
B
Measure the length of one side and multiply the length by itself.
© Count the number of 1-cubic-centimeter unit cubes that fit inside the cube.
D
Count the number of 1-square-centimeter unit squares that cover the cube.