Given: A team of 3 employees is preparing 20 reports. Mary takes 30 minutes to complete a report. Matt takes 45 minutes to complete a report.
All reports are completed in 4 1/2 hours. To Find: How long does it take the third team member to complete a report?Solution: Let the third employee takes x minutes to complete a report work done by Mary in 1 minute = 1/30Work done by Matt in 1 minute = 1/45Work done by the third employee in 1 minute = 1/x Total work done by all three in 1 minute = 1/30 + 1/45 + 1/x (As all are working together) a Total number of reports to be prepared = 20Therefore, total work = 20Now,
we know that all reports are completed in 4 1/2 hours = 9/2 hours∴ Total time = 9/2 x 60 = 270 minutes according to the problem statement, Total work = Total time x Total work done by all three in 1 minute20 = 270 (1/30 + 1/45 + 1/x)Solving the above equation for x, we get :x = 90 minutes therefore, it takes the third team member 90 minutes to complete a report.
Answer: 90 minutes.
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Let's represent the third team member as t. Mary takes 30 minutes to complete a report, while Matt takes 45 minutes to complete a report.
Thus, it takes the third team member 3 hours to complete a report.
Therefore, we can use the information given to form an equation. We are given that the team is preparing 20 reports, so:
30 minutes/report × M reports + 45 minutes/report × N reports + T minutes/report × O reports = 4.5 hours
To make the equation simpler, let the unit conversion 4.5 hours to minutes:
4.5 hours × 60 minutes/hour = 270 minutes
Thus:
30M + 45N + TO = 270
O= 20 - M - N
From the third team member: TO = T × 20
Therefore:
30M + 45N + T × 20 = 270
Solving for T:
30M + 45N + 20T = 270
T = (270 - 30M - 45N)/20
We know that there are only three members in the team, and that M and N have already been defined, so we can substitute these values:
T = (270 - 30(20) - 45(0))/20
T = 3
Thus, the time taken by the third team member is 3 hours to complete a report.
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Is the equation cosine theta - sine theta =1 an identity? Explain
what is the degree form for 3π/4 radians? enter your answer in the box.
The degree form for 3π/4 radians is 135°.The degree form for 3π/4 radians is 135°. To convert radians to degrees, we multiply the radian measure by the conversion factor of 180°/π.
In this case, we have (3π/4) * (180°/π) = (3 * 180°) / 4 = 540° / 4 = 135°. Therefore, 3π/4 radians is equivalent to 135° in the degree form.
To convert an angle from radians to degrees, we use the conversion factor of 180°/π. This conversion factor represents the relationship between a full circle (360°) and 2π radians.
In this case, we want to convert the angle 3π/4 radians to degrees. We multiply the radian measure (3π/4) by the conversion factor (180°/π):
(3π/4) * (180°/π) = (3 * 180°) / 4 = 540° / 4 = 135°
By canceling out the common factor of π and simplifying the expression, we find that 3π/4 radians is equal to 135°.
Therefore, the degree form of the angle 3π/4 radians is 135°.
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Timothy wanted to get some exercise. He walked 12 blocks in 10 minutes. What was his average speed of his walk?
Answer: 1.2 blocks
Step-by-step explanation:
Timothy walks 12 blocks in 10 minutes so it can be written as
12 blocks = 10 minutes
divide both sides by 10
1.2 blocks per minute
Janice wants to go to the Sadie Hawkins dance. The probability of a random boy saying yes is 45%. How many does she need to be willing to ask to have a 99.7% chance of going?
Janice needs to be willing to ask at least 16 boys to have a 99.7% chance of getting a "yes" and going to the Sadie Hawkins dance.
To determine how many boys Janice needs to be willing to ask in order to have a 99.7% chance of getting a "yes" and going to the Sadie Hawkins dance, we can use the concept of probability and the binomial distribution.
The probability of a random boy saying yes is 45%, which means the probability of a boy saying no is 55%. Let's assume Janice asks "n" boys.
The probability of at least one boy saying yes can be calculated using the complement rule. The complement of the event "at least one boy saying yes" is the event "all boys saying no."
The probability of all "n" boys saying no is (0.55)^n, as the probability of each boy saying no is 55%.
To find the number of boys Janice needs to ask to have a 99.7% chance of going, we want the complement probability (all boys saying no) to be 0.003. Therefore:
(0.55)^n ≤ 0.003
Taking the logarithm of both sides:
n * log(0.55) ≤ log(0.003)
Solving for "n":
n ≥ log(0.003) / log(0.55)
Using a calculator:
n ≥ 15.154
Since Janice can't ask a fraction of a boy, we need to round up the value of "n" to the nearest whole number.
Therefore, Janice needs to be willing to ask at least 16 boys to have a 99.7% chance of getting a "yes" and going to the Sadie Hawkins dance.
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Show me the work to 4x-4<8 and 9x+5>23. The answer is already shown. (Geometry )
Answer:
transpose -4 to left
and 5 to left
subtract and and after transpose you will have a sign change
then you can divide
12/4,18/9
so,
x<2,x>3
13. Which graph best represents -5y = -6x + 15?
А
Help ASAP !!!
A new car is valued at $28,000. It increases 9% per year. What is the total value of the car two year after purchase?
Answer:
$33,040
Step-by-step explanation:
Hope this helps and have a wonderful day!!!
Answer:
$30520
Step-by-step explanation:
Find the distance between the set of points (-4,5) and (4,0)
Answer:
√89
Step-by-step explanation:
√(4+4)2+(0-5)2
√(8)2+(-5)2
√64+25
√89
The illustration below shows the graph of yyy as a function of xxx.
Complete the following sentences based on the graph.
Initially, as xxx increases, yyy
.
Afterward, the slope of the graph of the function is equal to
for all xxx between x=3x=3x, equals, 3 and x=5x=5x, equals, 5.
The slope of the graph is equal to
for xxx between x=5x=5x, equals, 5 and x=9x=9x, equals, 9.
The greatest value of yyy is y=\:y=y, equals
, and it occurs when x=\:x=x, equals
.
answer in the picture
Answer:
The illustration below shows the graph of yyy as a function of xxx.
Complete the following sentences based on the graph.
Initially, as xxx increases, yyy
Step-by-step explanation:
The measure of ∠CBD is 45% of the measure of ∠ABC. Find the value of x.
Answer:
x = 49.5°
Step-by-step explanation:
∠ABC = 90°
∠CBD = 45%∠ABC
∠CBD = 0.45(90)
∠CBD = 40.5°
x = ∠ABC - ∠CBD
x = 90 - 40.5
x = 49.5°
WILL MARK BRANLIEST
What is true about the decimal form of an irrational number ?
A) The decimal both repeats and terminates
B) The decimal does not repeat or terminate
C) The decimal repeats
D) The decimal terminates
Therefore, the decimal representations of irrational numbers satisfy conditions 1 and 2; that is, irrational numbers are decimals that do not terminate and do not repeat. Knowing these properties, it is now possible for us to construct irrational numbers in decimal form at will.
for spanish people
Por lo tanto, las representaciones decimales de números irracionales cumplen las condiciones 1 y 2; es decir, los números irracionales son decimales que no terminan y no se repiten. Conociendo estas propiedades, ahora es posible para nosotros construir números irracionales en forma decimal a voluntad.
please help its for a grade!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
9514 1404 393
Answer:
2x+4y=56; 5x+2y=64adult: $10; child: $7budget is not high enoughStep-by-step explanation:
See the attached.
Daniel is baking cookies but does not have all of the he needs. The ratio of flour:sugar in his recipe is 3:2cups. If he only has 1.5cups of sugar, how much flour should he use to keep the ratio the same?
Answer:
Step-by-step explanation:
3:2 = 2.5:1.5
half of 2 is 1 so if you had 1.5 it would only be half. For a better explanation, 1 minute is 60 seconds half of a minute is 30 seconds. if you have 45 seconds it would be 3/4 of a second. this is hard for me to explain so if you need more examples just tell me in the comments.
i hope this helps
have a nice day/night
mark brainliest please:)
Draw the pipeline diagram (on the next page) for the following programs. Please note whether it
is a multi cycle CPU or a single cycle CPU
Program 1
Given a Single Cycle CPU where each stage is fixed at 200 ps (a 1000ps clock cycle), draw the pipeline diagram for the program below data
num: .word 12 .text
la $s0, num
lw $t0, 0($s0)
addi $t1, $t0, 3
Program 2
Given a Multi Cycle CPU where each stage is fixed at 200 ps (a 1000ps clock cycle), draw thepipeline diagram for the program below data
num: .word 12
.text
la $s0, num
lw $t0, 0($s0)
addi $t1, $t0, 3
1. What is the total length of time to run Program 1?
2. What is the total length of time to run Program 2?
3. What hazards, if any, exist in Program 1?
4. What hazards, if any, exist in Program 2?
The steps to draw a pipeline diagram for a given program are:
Understand the CPU architecture Identify the instructions in the programAssign cycle numbers Draw the pipeline stagesRepresent the pipeline stages Represent the instructions Handle hazards (if applicable)Review and finalizeWhat is the process?Understand the CPU architecture: This involves knowing pipeline stages, their durations, and relevant instructions/hazards. Step 2: Identify program instructions. Each instruction goes through pipeline stages.
Assign cycle numbers sequentially to each instruction. Visualize pipeline progress over time. Draw pipeline stages. Draw a horizontal line divided into cycles to represent time. Each cycle = 1 clock cycle duration. Place cycle numbers below the line.
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Is rolling a 5 on a traditional number cube
1. Impossible
2. Unlikely
3. Likely
4. Certain
Answer:
3. Likely
Step-by-step explanation:
Please help me guys, do not give me the wrong answer please explain it to me please, please.
Answer:
Where is ur question??
plss put ur question I will give correct answer
A 30, Y-connected alternator is rated at 1,600KVA, 13.5KV. The armature effective AC resistance per phase is 1.50. The percentage regulation for a load of 1,280kW at unity power factor is 3.5%. Determine: (a) synchronous reactance of the alternator (b) %VR at full-load 0.8pf leading (c) What is the effect on %VR value if taken at half-load lagging pf? Justify and explain briefly your answer on one(1) sentence.
(a) The synchronous reactance of the alternator is 0.001953125 Ω.
The synchronous reactance [tex]X_{s}[/tex] of the alternator can be calculated using the formula:
[tex]X_{s} = (Vt^2) / (3 * VL * S_{base})[/tex]
where [tex]V_{t}[/tex] is the rated line-to-line voltage of the alternator, VL is the rated line-to-neutral voltage of the alternator (which is the same as the rated voltage for a Y-connected alternator), and S_base is the apparent power rating of the alternator (which is equal to the rated power factor of the alternator times the rated apparent power). Substituting the given values, we get:
[tex]X_{s} = (13.5^2) / (3 * 13.5 * 1600) = 0.001953125[/tex] Ω
Therefore, the synchronous reactance of the alternator is 0.001953125 Ω.
(b) The percentage voltage regulation at full-load 0.8 power factor leading is 23.15%.
The percentage voltage regulation (%VR) at full-load 0.8 power factor leading can be calculated using the formula:
%VR = (E - Vl) / Vl * 100%
where E is the generated voltage of the alternator, and Vl is the terminal voltage of the alternator at full-load 0.8 power factor leading. We can assume that the armature resistance and inductance are negligible compared to Xs for this calculation. Using the given values, we first calculate the apparent power S of the load:
S = P / pf = 1280 / 0.8 = 1600 kVA
Since the load is at unity power factor, the current drawn from the alternator is also 1600 A. Therefore, the voltage drop across Xs is:
Vx = Xs * I = 0.001953125 * 1600 = 3.125 V
The generated voltage E is equal to the terminal voltage Vl plus the voltage drop across Xs:
E = Vl + Vx
The percentage voltage regulation is then:
%VR = (E - Vl) / Vl * 100% = (Vl + Vx - Vl) / Vl * 100% = Vx / Vl * 100%
Substituting the given values, we get:
%VR = 3.125 / 13.5 * 100% = 23.15%
Therefore, the percentage voltage regulation at full-load 0.8 power factor leading is 23.15%.
(c) If the %VR value is taken at half-load lagging power factor, it will be higher than the %VR value at full-load 0.8 power factor leading. This is because the load impedance at half-load lagging power factor has a lower magnitude than the load impedance at full-load 0.8 power factor leading, which means that the voltage drop across [tex]X_{s}[/tex] will be a larger fraction of the terminal voltage, resulting in a larger %VR value.
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Can someone help me with this problem
Answer:
51 degrees
Step-by-step explanation:
As we already know that this triangle is a right triangle.
To find x, you need to subtract both angles.
90 - 39
= 51
[48 (72-12) -225] ÷ 9
someone pls help
Answer:
295
Step-by-step explanation:
Answer:
295!
Step-by-step explanation:
72 - 12 = 60
48 x 60 = 2880
2880 - 225 = 2655
2655 / 9 = 295
Have you ever heard of PEMDAS? It is the order in which to solve equations like this one. Here's what it stands for:
Parenthesis
Exponents
Multiplication
Division
Addition
Subtraction
I hope this is helpful for future math equations similar to this one.
The U.S. Energy Information Agency reported that the mean monthly household electric bill in the United States in a recent year was $110.14. Assume the amounts are normally distributed with standard deviation $20.00. a. Find the 7th percentile of the bill amounts. b. Find the 62nd percentile of the bill amounts c. Find the median of the bill amounts.
a) The 7th percentile of the bill amounts is given as follows: $80.64.
b) The 62nd percentile of the bill amounts is given as follows: $116.24.
c) The median of the bill amounts is given as follows: $110.14.
How to obtain probabilities using the normal distribution?We first must use the z-score formula, as follows:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
In which:
X is the measure.[tex]\mu[/tex] is the population mean.[tex]\sigma[/tex] is the population standard deviation.The z-score represents how many standard deviations the measure X is above or below the mean of the distribution, and can be positive(above the mean) or negative(below the mean).
The z-score table is used to obtain the p-value of the z-score, and it represents the percentile of the measure represented by X in the distribution.
The mean and the standard deviation for this problem are given as follows:
[tex]\mu = 110.14, \sigma = 20[/tex]
The median is the same as the mean, hence it is given as follows:
$110.14.
The 7th percentile is X when Z = -1.475, hence:
-1.475 = (X - 110.14)/20
X - 110.14 = -1.475 x 20
X = $80.64.
The 62nd percentile is X when Z = 0.305, hence:
0.305 = (X - 110.14)/20
X - 110.14 = 0.305 x 20
X = $116.24.
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Given a set of linear equalities in several variables, we know that we can find a satisfying assignment in polynomial time. For example, given the equalities 211X1 + 212X2+...+ almxm = 221X1 + a22x2+...+ a2mdm = C2 an1X1 + An2x2+...+ AnmIm = Cn we know that we can solve this (i.e. find a set of xis so that all the equalities are satisfied) in polynomial time in n and m. ?. Suppose we now have a set of linear inequalities 211X1 + 212X2+...+ alm&m < 221X1 + A2222+...+ a2mX m
Solving a set of linear inequalities in several variables is an NP-hard problem, meaning there is no known polynomial-time algorithm to find a satisfying assignment.
Unlike linear equalities, solving a set of linear inequalities in several variables is an NP-hard problem. This means that there is no known polynomial-time algorithm to find a satisfying assignment for all instances of such problems. The complexity arises from the fact that there are infinitely many potential solutions, making it challenging to determine whether a feasible assignment exists or not. To find a satisfying assignment for linear inequalities, algorithms typically use heuristics or approximation techniques that do not guarantee optimality or completeness. Various methods, such as linear programming or constraint satisfaction algorithms, can be employed, but they may have exponential time complexity in the worst case. Therefore, solving a set of linear inequalities generally requires more computational resources and time compared to solving linear equalities.
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An element with a mass of 840 grams decays by 22.9% per minute. To the nearest minute, how long will it be until there are 70 grams of the element remaining?
Answer:10
Step-by-step explanation:believe me bro
To the nearest minute, it will be 10 minutes until there are 70 grams of the element remaining.
How to find the time it took for an element to decay to a certain mass?The time the element took to decay can be found by using the following formula:
[tex]F=P(1-r)^{t}[/tex]
Where:
F is the remaining mass.P is the original mass of the element.r is the rate at which the element is decaying.t is the time it took for the element to decay.We can find the answer by substituting the values.
[tex]F=P(1-r)^{t}\\\Rightarrow 70=840(1-0.229)^{t}\\\Rightarrow \frac{70}{840} =(1-0.229)^{t}\\0.0833=(1-0.229)^{t}\\t=9.56\\\approx10 \text{ minutes}[/tex]
Therefore, we have found that the element will take around 10 minutes to have 70 grams remaining.
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no The sum of two angles in a triangle is 150 degrees. What is the supplement of the third angle of the 2 of 4 triangle? (a) 150 (b) 10 (c) 30 (d) 85
The measure of the third angle, C, is 30 degrees. So, the correct answer is (c) 30.
Let's assume the three angles of the triangle are A, B, and C, where A, B, and C are measured in degrees.
We know that the sum of the angles in a triangle is 180 degrees. Therefore, we can write the equation:
A + B + C = 180
The obtain of two angles is 150 degrees, we can set up another equation:
A + B = 150
To obtain the measure of the third angle, which we'll call C, we can subtract the sum of the other two angles from 180:
C = 180 - (A + B)
Substituting the value of the sum of two angles (150 degrees), we have:
C = 180 - 150
C = 30
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Which expression is equivalent to -6(-2\3 +2x)
-4-12x
-4+2x
4-12x
4+12x
Answer:
4 - 12x
Step-by-step explanation:
Use the distributive property.
-6(-2/3 +2x) =
= -6 × -2/3 + (-6) × 2x
= 4 - 12x
6n-18n-18=6 slove by factoring
Answer:n=−2
Step-by-step explanation:
find the slope of the points 2,8 and 12,55
Answer:
m = 4.7
Step-by-step explanation:
If you plug in these values in the slope formula, this is what happens:)
Answer:
47/10x
**Do not leave your answer as a decimal, slope is usually in fraction form**
Step-by-step explanation:
Slope Formula: [tex]\frac{\text{rise}}{\text{run}} / \frac{y_2 - y_1}{x_2 - x_1}[/tex] In this formula, subtract the 1st coordinate from the second. So, the 2nd y coordinate goes first, place a "minus" sign, and then the 2nd y-coordinate. This is the same for the x coordinates.
Finding the Answer: To find the answer, we just plug the numbers correctly into the equation, just as I explained above. We would do 55-8 first, which is 47, and then 12-2 which is 10.
Combined, the answer is 47/10x. You always place an x after the slope, which can be used to plug in other numbers. The answer cannot be simplified anymore, so this is simplfied.
Which equation best represents the graph?
Home Internet Access According to a study, 76% of adults ages 18-29 years had broadband Internet access at home in 2011. A researcher wanted to estimate the proportion of undergraduate college students (18-23 years) with access, so she randomly sampled 180 undergraduates and found that 157 had access. Estimate the true proportion with 99% confidence. Use a graphing calculator and round the answers to at least three decimal places
The 99% confidence interval for the true proportion of undergraduate college students with home internet access is: 0.872 ± 0.057 or (0.815, 0.929).
To estimate the true proportion of undergraduate college students (18-23 years) with home internet access, we can use a confidence interval.
The point estimate for the proportion is 157/180 = 0.872. To find the margin of error, we can use the formula:
Margin of error = z* (sqrt(p_hat*(1-p_hat)/n))
where z* is the critical value for the desired confidence level, p_hat is the sample proportion, and n is the sample size.
For a 99% confidence level, the critical value is 2.576. Plugging in the values, we get:
Margin of error = 2.576 * (sqrt(0.872*(1-0.872)/180)) = 0.057
Therefore, the 99% confidence interval for the true proportion of undergraduate college students with home internet access is:
0.872 ± 0.057 or (0.815, 0.929)
This means that we are 99% confident that the true proportion of undergraduate college students with home internet access falls between 0.815 and 0.929.
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Write the equation of the circle ?
Center (-1,0)
Radius:4
Answer:
(x+1)^2 + y ^2 = 16
Step-by-step explanation:
center: (-1,0)
radius=4
(x-h)^2 + (y-k)^2 = r^2
(h,k) = center
plug in the center
(x+1)^2 + (y+0) ^2 = r^2
r^2 = (4)^2
r^2=16
(x+1)^2 + y^2 = 16
Select the correct answer from each drop-down menu.
Consider the equation below.
x^3 - 3x^2 - 4 = 1/x-1 +5
The solutions to the equation are approximately x =
0.91 and x= *blank*
Answer:
The solution is x = + 0.77 , -0.77
Step-by-step explanation:
The equation is
[tex]x^3 - 3x^2 - 4 = \frac{1}{x} -1 +5\\x^4 -3x^3 -4x = 1-4x\\x^4 - 3x^3 = 1\\x^3 (x-3) = 1\\\\x^4 -3x^3 -1 = 0\\x^4 -3x^3 -1[/tex]
The solutions to the equation is
x = + 0.77 , -0.77
Answer:
0.91 and 3.69
Step-by-step explanation: