Using proportions, it is found that it took 15 days for the students to finish the project.
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct or inverse proportional, can be built to find the desired measures in the problem.
In this problem, we have that:
100% of the project is done by 5 students in 15 days.After the 3 students left, 2 students will have a time of x days to do 100 - (9/15) = 40% of the project.The compound rule of three is given as follows:
1 project - 5 students - 15 days
0.4 project - 2 students - x days
Increasing the number of students, the number of days is reduced, hence the measures are inverse proportional and the rule of three is given by:
[tex]\frac{15}{x} = \frac{2}[5} \times \frac{1}{0.4}[/tex]
[tex]\frac{15}{x} = \frac{2}{2}[/tex]
15/x = 1
x = 15 days.
It took 15 days for the students to finish the project.
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What is the slope of a line perpendicular to the line whose equation is 3x + y = -9.
Fully simplify your answer.
Considering the definition of perpendicular line, the slope of a line perpendicular to the line whose equation is 3x+y= -9 is [tex]\frac{1}{3}[/tex].
Linear equationA linear equation o line can be expressed in the form y = mx + b.
where
x and y are coordinates of a point.m is the slope.b is the ordinate to the origin and represents the coordinate of the point where the line crosses the y axis.Perpendicular linePerpendicular lines are lines that intersect at right angles or 90° angles.
Two nonvertical lines are perpendicular if the slope of one is the negative reciprocal of the slope of the other. In other words, if you multiply the slopes of two perpendicular lines, you get –1.
Equation of perpendicular line in this caseIn this case, the line is 3x+y=-9. Expressed in the form y = mx + b, you get: y= -9 - 3x or, what is the same, y= -3x -9
If you multiply the slopes of two perpendicular lines, you get –1. In this case, the line has a slope of -3. So:
(-3)× slope perpendicular line= -1
slope perpendicular line= (-1)÷ (-3)
slope perpendicular line= [tex]\frac{1}{3}[/tex]
Finally, the slope of a line perpendicular to the line whose equation is 3x+y= -9 is [tex]\frac{1}{3}[/tex].
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An industrial machine produces widgets, but it has a 0.07 defective rate. what is the probability that the machine produces fewer than 5 defective widgets in a production run of 100 items?
The probability that the machine produces fewer than 5 defective widgets in a production run of 100 items is 0.10
What is the probability?A probability refers to the ratio of favorable events to the n number of total events.
Also, it means the chance that a particular event (s) will occur expressed on a linear scale from 0 to 1 which can also be expressed as a percentage between 0 and 100%.
Given data
An industrial machine produces 5 widgets.
It has a 0.07 defective rate.
Defective rate fewer than 5
Total Probability = P of 4 defective + P for 3 defective + P for 2 defective + P for 1 defective.
Total Probability = 4/100 + 3/99 + 2/98 + 1/97
Total Probability ≈ 0.10
Therefore, the required probability for fewer than 5 defective rate is 0.10
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the x and y intercept
necesito la respuesta, urgente
The value of the function f(x) = ( 8x² - 2x + 4 ) / 2 when x = -3/5 is 101/25.
Hence, f(-3/5) = 101/25.
What is the value of the function at f(-3/5) ?Given the function; f(x) = ( 8x² - 2x + 4 ) / 2
To determine the value of the function when x = -3/5, we simply replace the variable x with -3/5 in the function.
f(x) = ( 8x² - 2x + 4 ) / 2
f(-3/5) = ( 8(-3/5)² - 2(-3/5) + 4 ) / 2
Divide each term by 2
f(-3/5) = 4(-3/5)² - (-3/5) + 2
f(-3/5) = 4(9/25) - (-3/5) + 2
f(-3/5) = 36/25 +3/5 + 2
f(-3/5) = ( 36 + 3×5 + 2×25 ) / 25
f(-3/5) = ( 36 + 15 + 50 ) / 25
f(-3/5) = 101/25
The value of the function f(x) = ( 8x² - 2x + 4 ) / 2 when x = -3/5 is 101/25.
Hence, f(-3/5) = 101/25.
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Which describes the combined variation shown in the equation F = kxy/z?
1) F varies directly with x, and inversely with y
and z.
2)F varies directly with z, and inversely with x
and y.
3)F varies directly with y, and inversely with x and z.
4) F varies directly with x and y, and inversely
with z.
Answer:
option 4
Step-by-step explanation:
F = [tex]\frac{kxy}{z}[/tex]
k is the constant of variation
• if the variables are on the numerator they vary directly
• if the variables are on the denominator they vary inversely
In this case F varies directly with x and y ( variables on numerator ) and inversely with z ( variable on denominator )
A 400 L tank is filled with pure water. A copper sulfate solution with a concentration of 20 g/L flows into the tank at a rate of 4 L/min. The thoroughly mixed solution is drained from the tank at a rate of 4 L/min. a. Write a differential equation (initial value problem) for the mass of the copper sulfate. b. Solve the differential equation
(a) Let [tex]C(t)[/tex] denote the amount (in grams) of copper (II) sulfate (CuSO₄) in the tank at time [tex]t[/tex] minutes. The tank contains only pure water at the start, so we have initial value [tex]\boxed{C(0)=0}[/tex].
CuSO₄ flows into the tank at a rate
[tex]\left(20\dfrac{\rm g}{\rm L}\right) \left(4\dfrac{\rm L}{\rm min}\right) = 80 \dfrac{\rm g}{\rm min}[/tex]
and flows out at a rate
[tex]\left(\dfrac{C(t)\,\rm g}{400\,\mathrm L + \left(4\frac{\rm L}{\rm min} - 4\frac{\rm L}{\rm min}\right) t}\right) \left(4\dfrac{\rm L}{\rm min}\right) = \dfrac{C(t)}{100} \dfrac{\rm g}{\rm min}[/tex]
and hence the net rate of change in the amount of CuSO₄ in the tank is governed by the differential equation
[tex]\boxed{\dfrac{dC}{dt} = 80 - \dfrac C{100}}[/tex]
(b) This ODE is linear with constant coefficients and separable, so we have a few choices in how we can solve it. I'll use the typical integrating factor method for solving linear ODEs.
[tex]\dfrac{dC}{dt} + \dfrac C{100} = 80[/tex]
The integrating factor is
[tex]\mu = \exp\left(\displaystyle \int \frac{dt}{100}\right) = e^{t/100}[/tex]
Distributing [tex]\mu[/tex] on both sides gives
[tex]e^{t/100} \dfrac{dC}{dt} + \dfrac1{100} e^{t/100} C = 80 e^{t/100}[/tex]
and the left side is now the derivative of a product,
[tex]\dfrac d{dt} \left[e^{t/100} C\right] = 80 e^{t/100}[/tex]
Integrate both sides. By the fundamental theorem of calculus,
[tex]e^{t/100} C = e^{t/100}C\bigg|_{t=0} + \displaystyle \int_0^t 80 e^{u/100}\, du[/tex]
The first term on the right vanishes since [tex]C(0)=0[/tex]. Then
[tex]e^{t/100} C = 8000 \left(e^{t/100} - 1\right)[/tex]
[tex]\implies \boxed{C(t) = 8000 - 8000 e^{-t/100}}[/tex]
What is the perimeter of kite OBDE?
12 units
22 units
38 units
58 units
By definition of perimeter, direct observation and Pythagorean theorem, the perimeter of kite OBDE is 38 units. (Correct choice: C)
How to determine the perimeter of a kite OBDE
In geometry, the perimeter is the sum of the lengths of the sides of a figure. Herein we must determine the perimeter of a quadrilateral, the kite OBDE, that is, the sum of the lengths of its four sides:, which can be found both by direct observation or by the use of the Pythagorean theorem.
Please notice that the quadrilateral has an axis of symmetry passing through the points O and D, which implies that OB = OE and BD = DE. The length of sides BD and DE is 6 units and the length of the sides OB and DE are:
OB = DE = 0.5 · √(24² + 10²)
OB = DE = 13
Lastly, the perimeter of kite OBDE is p = 2 · 6 + 2 · 13 = 38 units.
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Answer: C. 38 units
Step-by-step explanation: TRUST ME!!! Answer is correct on Edge!!! :)
Just did it and got it correct!
Please help and explain!!!
Answer:
Option A
Step-by-step explanation:
The solution is in the image
The mean if four numbers is 25 if three numbers are 36, 12 and 24 what is the fiurth number
correct answer is 28.
If the mean of four numbers is 25 and three numbers are 36, 12 and 24 then fourth number is 28.
Find fourth number?given terms are:
first number =36
second number=12
third number=24
fourth number=?
let us assume the fourth number be x.
what is mean?we know the formula to find mean is:
Mean=addition of given terms / total number of terms
According to given statement, we put the values in above equation and we get,
25=(36+12+24+x) / 4
By rearranging, we get
36+12+24+x=100
72+x=100
x=100-72
x=28
so, the fourth number is 28.
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If the top ten nations were randomly selected to march, one after another, into the stadium at the closing ceremonies, in how many ways could the nations have marched in?
Step-by-step explanation:
1. Entrance of Head of State and IOC President
2. Playing of the national anthem
3. The parade of the athletes
4. The symbolic release of doves
5. Olympic Laurel Award
6. Official Speeches
7. Opening of the Games
8. Raising the Olympic flag and playing the Olympic Anthem
9. Athletes, judges and coaches’ oath
10. Lighting of the Olympic flame
11. The artistic programme
What value of z* should be used to construct an 88% confidence interval of a population mean?
Z = 1.555 should be used
If we seek an 88% confidence interval, that means we only want a 12% chance that our interval does not contain the true value.
Assuming a two-sided test, that means we want a 6% chance attributed to each tail of the Z-distribution.
the zα/2 value of z0.06.
This z value at α/2=0.06 is the coordinate of the Z-curve that has 6% of the distribution's area to its right, and thus 94% of the area to its left. We find this z-value by reverse-lookup in a z-table.
What is Z-distribution?The standard normal distribution, also called the z-distribution, is a special normal distribution where the mean is 0 and the standard deviation is 1.
Any normal distribution can be standardized by converting its values into z-scores. Z-scores tell you how many standard deviations from the mean each value lies.
Why is z-score used?The standard score (more commonly referred to as a z-score) is a very useful statistic because it
(a) allows us to calculate the probability of a score occurring within our normal distribution and
(b) enables us to compare two scores that are from different normal distributions.
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If m ABD = 61, and m DBC = 59, then m ABC = ? PLS ASAP
Given that angle ABD and angle DBC are adjacent angle, the value of angle ABC is 120 degrees.
What is the value of angle ABC?Given the data in the question;
Angle ABD = 61°Angle DBC = 59°Angle ABC = ?Since angle ABD and angle DBC are adjacent angle, there addition will give us the value of angle ABC.
∠ABD + ∠DBC = ∠ABC
We substitute in the given values
61° + 59° = ∠ABC
∠ABC = 120°
Given that angle ABD and angle DBC are adjacent angle, the value of angle ABC is 120 degrees.
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what is the Pythagorean theorem
Answer:
a^2+b^2=c^2
Step-by-step explanation:
leg1=a
leg2=b
hypotenuse=c
a^2+b^2=c^2
Answer:
u see this is how the Pythagorean theorem works a^2 + b^2 = c^ i hope this helps have a great day bye please mark as brainliest :D
Step-by-step explanation:
The average of 15,19,23,41,and Z is 20. What is the value of x
The value of x from the given data is 2
Calculating the average of numbersMean is the ratio of sum of numbers to the total samples. Given the following data
15,19,23,41, and Z
The mean is calculated as
Mean = 15+19+23+41+z/5
Since the mean the of the data is given as 20. Substitute
20 = 15+19+23+41+z/5
Cross multiply
20*5 = 15+19+23+41+z
100 = 15+19+23+41+z
100 = 98 + z
z = 100- 98
z = 2
Hence the value of x from the given data is 2
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Prepare a grid with magic number 30. You can choose any set of numbers in sequence but the numbers should not be repeated.
The grid of numbers with a row and column sum of 30 is
3 15 12
17 11 2
10 4 16
How to prepare the grid?The grid in the question has a row sum and column sum of 15
The question implies that we create a similar grid with a row sum and column sum of 30
Represent the grid as follows:
a b c
d e f
g h j
So, we have the following sum of rows
a + b + c = 30
d + e + f = 30
g + h + j = 30
And, we have the following sum of rows
a + d + g = 30
b + e + h = 30
c + f + j = 30
Using trial by error, we have:
3 + 15+ 12 = 30
17 + 11 + 2 = 30
10 + 4 + 16 = 30
When the columns are added, we have
3 + 17 + 10 = 30
15 + 11 + 4 = 30
12 + 2 + 16 = 30
Hence, the grid of numbers is
3 15 12
17 11 2
10 4 16
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How much money do I need now if I am going to recieve $5000 every 6 months (starting in 6 months) for 10 years if the interest rates are 4%/a compounded semi-annually?
By using the compound interest model, the initial deposit required to receive $ 5 000 every 6 months is $ 125 000.
How many money should be deposited in the beginning to receive a certain amount periodically
In this problem we must apply the compound interest model, which represent a periodic accumulation of interest according to the following formula:
C' = C · (1 + r/100)ˣ (1)
Where:
C - Initial depositr - Interest rateC' - Resulting moneyx - Period indexIf we know that x = 1, r = 4, C = x and C' = x + 5 000, then the initial deposit is:
x + 5 000 = x · (1 + 4/100)
x + 5 000 = 1.04 · x
0.04 · x = 5 000
x = 125 000
By using the compound interest model, the initial deposit required to receive $ 5 000 every 6 months is $ 125 000.
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In a scale drawing of a painting, 2 centimeters represents 7 inches.
The height of the real painting is 35 inches. What is the height of the painting in the scale drawing?
The height of the painting in the scale drawing is 10 centimeters if the height of the real painting is 35 inches given that in a scale drawing of a painting, 2 centimeters represents 7 inches. This can be obtained by using the ratio of scale drawing to the real drawing.
Find the height of the painting in the scale drawing:Here in the question it is given that,
In a scale drawing of a painting, 2 centimeters represents 7 inchesThe height of the real painting is 35 inchesThus we can say that, scale of the painting is 2 cm : 7 in
Ratio of scale drawing and real painting is 2 : 7
⇒ Similarly here height of the painting in the scale drawing to the height of the painting in the real drawing will be in the ratio 2 : 7.
We can say that,
2 cm/7 in = x cm/35 in
where x is the height of the painting in the scale drawing
2 cm × 35 in /7 in = x cm
x = 2 × 5 cm
x = 10 cm
Hence the height of the painting in the scale drawing is 10 centimeters if the height of the real painting is 35 inches given that in a scale drawing of a painting, 2 centimeters represents 7 inches.
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Which function has exactly one zero?
Answer:
Step-by-step explanation:
Answer:
i think no 3 hasexactly one 0
The expression x2y - 2xy - 24y can be factored by first factoring out a common factor of y. After the common factor is removed, the remaining factor is a\
The remaining factor of x^2y - 2xy - 24y is (x - 6)(x + 4)
How to determine the remaining factor?The expression is given as:
x^2y - 2xy - 24y
Factor out y from the expression
y(x^2 - 2x - 24)
Expand the equation
y(x^2 + 4x - 6x - 24)
Factorize
y(x - 6)(x + 4)
Hence, the remaining factor of x^2y - 2xy - 24y is (x - 6)(x + 4)
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A population of rabbits has 20 offspring per pair of rabbits. a population of cheetahs has 2 offspring per pair of cheetahs. which population will be more affected by genetic drift?
Cheetahs population will be more affected by genetic drift
What is genetic drift?Genetic drift is the change in a population's frequency of an existing gene variant brought on by chance. Gene variations may totally vanish due to genetic drift, hence reducing genetic variation. Additionally, it may lead to the considerably greater frequency and even fixation of previously rare alleles.
What causes genetic drift?Random drift is a result of recurrently small populations, drastic population reductions known as "bottlenecks," and founder events in which a new population is created from a small number of individuals.
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I need help pls and thank you
Answer:
12 in, 7 in
Step-by-step explanation:
The area of a rectangle is the product of length and width. Here, you are given the area, and an additional relation between length and width.
SetupThe two relations between length and width described by this problem are ...
A = LW . . . . . . . dimensions are of a rectangle
L = W +5 . . . . . . length is 5 inches more than width
A = 84 . . . . . . . . area in square inches
SolutionSubstituting for L and A in the area formula, we have ...
84 = (W +5)(W)
We can solve this as a quadratic in any of several ways. One of those ways is by factoring.
Essentially, we're looking for factors of 84 that differ by 5. We can consider different factorizations of 84 to see what we get:
84 = 84×1 = 42×2 = 28×3 = 21×4 = 14×6 = 12×7
The differences between the factors in these pairs are 83, 40, 25, 17, 8, 5.
This means the last pair, with a difference of 5, is the one we're looking for.
W+5 = 12, W = 7
The rectangle is 12 inches long and 7 inches wide.
__
Additional comment
As a quadratic in standard form, we would have ...
W² +5W -84 = 0 ⇒ (W +12)(W -7) = 0 ⇒ W = {7, -12}
If you were to solve this by completing the square, you would have ...
(W +2.5)² = 90.25 ⇒ W = -2.5 ±9.5 = {7, -12}
A conical circus tent has a 20 ft central pole that supports it. the slant height of the tent is 26 ft long. explain how to find the angle the tent pole makes with the sides of the tent.
The angle the pole makes with the tent is 39.7°.
What is an angle?An angle is a figure in Euclidean geometry created by two rays, called the sides of the angle, that share a common termination, called the vertex of the angle. Angles formed by two rays are located in the plane containing the rays.Trigonometric ratio: the trigonometric ratio is used to demonstrate the relationship between the sides and angles of a right-angled triangle.
Let θ represent the angle the pole makes with the tent.
Using trigonometric ratios:
cos(θ) = 20/26θ = 39.7°Therefore, the angle the pole makes with the tent is 39.7°.
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The dashed triangle is the image of the solid triangle. The center of dilation is (6, 6).
What is the scale factor used to create the dilation?
Enter your answer as an integer or decimal in the box.
The two right triangles are graphed on a coordinate plane. The horizontal x-axis ranges from negative 10 to 10 in increments of 1. The vertical y-axis ranges from negative 10 to 10 in increments of 1. A dashed triangle has vertices at begin ordered pair 6 comma 6 end ordered pair, begin ordered pair 6 comma 9 end ordered pair, and begin ordered pair 9 comma 6 end ordered pair. A solid triangle has vertices at begin ordered pair 6 comma 6 end ordered pair, begin ordered pair 6 comma negative 9 end ordered pair, and begin ordered pair negative 9 comma 6 end ordered pair.
Answer:
The scale factor is 1/5.
Step-by-step explanation:
You can find the side length of triangles by looking at the points or it might be easier to see if you look at the graphs that I have attached. I can see that the legs of the small triangle are 3 and the legs of the large triangle are 15. What do I need to multiple 3 by to get 15? 5. That is the scale factor from the little triangle to the big triangle. If I go the other way, the scale factor is the reciprocal of 5 or 1.5
Given the function defined in the table below, find the average rate of change,
in simplest form, of the function over the interval 12 ≤ ≤ 36.
0
12
36
48
60
37
34
31
28
25
22
The average rate of change of [tex]f(x)[/tex] on [tex]12\le x\le36[/tex] is the difference quotient
[tex]\dfrac{f(36) - f(12)}{36 - 12} = \dfrac{28 - 34}{24} = \boxed{-\dfrac14}[/tex]
Seema had 150 marbles.rani had 20 marbles more than seema.alok had 50 marbles lass than rani how many marbles did rani have
Answer:
120
Step-by-step explanation:
seema 150 marbles
rani 20 more marbles
alok 50 less marble
150+20=170_rani
170-50=120_alok
1,615×10 to the 2 power
simplifying 1,615×10 to the 2 power would give 161500
Simplifying the index form
Index notation is known as a way of representing numbers (constants) and variables (e.g. x and y) that have been multiplied by themselves a number of times.
Index notations, or indices are use to simplify expressions or solve equations involving powers.
For instance;
8 × 8 × 8 × 8
8 is multiplied by itself 4 times
In index form , it is written as 8 ^4, that is, 8 to the 4 power
From the information given, we have to simply 1,615×10 to the 2 power
It can be written as;
= 1, 615 × 10 × 10
= 1, 615 × 100
= 161500
Thus, simplifying 1,615×10 to the 2 power would give 161500
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.
Let’s assume the following statements are true: Historically, 75% of the five-star football recruits in the nation go to universities in the three most competitive athletic conferences. Historically, five-star recruits get full football scholarships 93% of the time, regardless of which conference they go to. If this pattern holds true for this year’s recruiting class, answer the following:
a. Based on these numbers, what is the probability that a randomly selected five-star recruit who chooses one of the best three conferences will be offered a full football scholarship?
b. What are the odds a randomly selected five-star recruit will not select a university from one of the three best conferences? Explain.
c. Explain whether these are independent or dependent events. Are they Inclusive or exclusive? Explain.
The probability that a randomly selected five-star recruit who chooses one of the best three conferences will be offered a full football scholarship is 69.75%.
What is the computation for the above solution?
Note that this is simple probability.
Hence probability of the 75% football starts selected randomly where the chance is 93% =
75% x 93%
= 69.75%
What are the odds a randomly selected five-star recruit will not select a university from one of the three best conferences?The chance that 25% of the five-star recruit will not select a university form one of the three best conferences is explained as follows:
Because only 75% stand the chance of being selected into the three ivy leagues, this means that 25% stand no chance.
Recall that the total population is 100%.
Are these are independent or dependent events. Are they Inclusive or exclusive?From the statement of problem given, it is clear that the events are mutually exclusive. Recall "Historically, five-star recruits get full football scholarships 93% of the time, regardless of which conference they go to.
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does anyone know how to do this? pls help
Answer:
-3
Step-by-step explanation:
If you reflect over the y-axis and then move 2 units to the left(x-2), then ABCD will be 3 units above EHGF. Since you need to move it down 3 units to map ABCD onto EHGF, you will need to do y-3, which is the same as y+-3
10. There are 355 students at Median Middle School. If there 8% of the students were absent on Tuesday, how many students were absent? How many were present?
To solve this question, we simply need to divide the total amount of students by 8% to find out how many students were absent and how many were present.
However, we can't simply multiply it by 8%, so we need to turn that into a decimal.
8% - 0.08
Multiply:
355 x 0.08
= 28.4
Round:
28 kids were absent
Subtract:
355 - 28
= 327
This means that 28 kids were absent, and 327 kids were present.
Will has twice as many stamps in his collection as Carlton and Ashley do in their collections combined. If Ashley has 30 stamps and she has a third as many as Carlton has, how many stamps are in Will’s collection?
Taking into account the definition of a system of linear equations, 240 stamps are in Will’s collection.
System of linear equationsA system of linear equations is a set of two or more equations of the first degree, in which two or more unknowns are related.
Solving a system of equations consists of finding the value of each unknown so that all the equations of the system are satisfied. That is to say, the values of the unknowns must be sought, with which when replacing, they must give the solution proposed in both equations.
Number of stamps that are in Will’s collectionIn this case, a system of linear equations must be proposed taking into account that:
W: Number of stamps that are in Will’s collectionC: Number of stamps that are in Carlton’s collectionA: Number of stamps that are in Ashley’s collectionOn the other hand, you know that:
Ashley has 30 stamps and she has a third as many as Carlton has → A= [tex]\frac{1}{3}[/tex]C → 30= [tex]\frac{1}{3}[/tex]CWill has twice as many stamps in his collection as Carlton and Ashley do in their collections combined. → W= 2(C + A)So, the system of equations to be solved is
[tex]\left \{ {{30=\frac{1}{3}C } \atop {W=2(C+30)}} \right.[/tex]
There are several methods to solve a system of equations, it is decided to solve it using the substitution method, which consists of clearing one of the two variables in one of the equations of the system and substituting its value in the other equation.
Solving the first equation:
30= [tex]\frac{1}{3}[/tex]C
30÷[tex]\frac{1}{3}[/tex]= C
90= C
Substituting the value in the second equation:
W= 2(90 + 30)
W= 2×120
W=240
Finally, 240 stamps are in Will’s collection.
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