A = hours for plan A
B = hours for plan B
Monday: 6A + 5B = 7
Tuesday: 2A + 3B = 3
use elimination by multiplying the 2nd equation by 3.
Doing that we get 3(2A + 3B = 3) = 6A + 9B = 9
So the two equations are now:
6A + 9B = 9
6A + 5B = 7
Subtract and we have 4B = 2
B = 2/4 = 1/2 of an hour
Now put 1/2 back into either equation to solve for A
6A + 5(1/2) = 7
6A + 5/2 = 7
6A = 14/2 -5/2
6A = 9/2
divide by 6 to get A = 9/12 = ¾ hours
Plan A = 3/4 hour
Plan B = 1/2 hour
Final answer:
By setting up and solving a system of equations, we find that Plan A lasts for 45 minutes per session and Plan B lasts for 30 minutes per session.
Explanation:
Solving for the Duration of Workout Plans
We have information regarding the total duration of workouts and the number of clients for two consecutive days. To find the duration of each workout plan, we use a system of equations. Let A represent the duration of Plan A and B represent the duration of Plan B. The equations based on the given information are:
6A + 5B = 420 minutes (7 hours on Monday)
2A + 3B = 180 minutes (3 hours on Tuesday)
Multiplying the second equation by 3 gives us:
6A + 9B = 540
Subtracting the first equation from this result gives us:
4B = 120 minutes, therefore, B = 30 minutes
Now we substitute B = 30 in the first equation:
6A + 150 = 420, which simplifies to 6A = 270, hence A = 45 minutes
Thus, Plan A lasts for 45 minutes and Plan B lasts for 30 minutes.
HELPPPPPPPPPPPP ASAP!!!!!!!!!!
Read the following statement: If the sum of two angles is 90°, then the angles are complementary. The hypothesis of the statement is:
there are two angles.
the sum of two angles is 90°.
the angles are complementary.
Angles are complementary if their sum is 90°.
Brian is waiting at a park across the street from the hockey arena for his dad to pick him up. It rained most of the morning, and the streets still have puddles. At which point should Brian stand to be as far as possible from each street to avoid getting splashed? Explain your answer.
To avoid getting splashed from puddles on the street, Brian should stand in the middle of the park. This would distance him completely from the immediate spray zone of passing vehicles, like being further away from the shore reduces the impact of sprays from waves.
Explanation:To avoid getting splashed by cars driving through the puddles, Brian should stand in the middle of the park. By doing so, he establishes the maximum possible distance between himself and any part of the street. Staying as far away from the streets reduces the risk of any water reaching him when cars pass by.
Think of it like Jill delivering her flyers and retracing her steps: the farthest spot from her house during her journey was at the midpoint of her travel route.
Also consider Peter's driving scenario: The farther he is from other cars, the less likely he is to get affected by their maneuvers. In a similar way, Brian, being in the middle of the park would keep him away from the splash zone of passing cars.
Lastly, akin to Julian and his father on their surfboards, being away from the impact point of the waves (which is near the shore) they get least affected by the spray. This analogy can be compared to Brian's situation with the puddles.
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Solve this quadratic equation. x ^2 + 2x - 22 = 0
Answer:
[tex]x=-1+\sqrt{23}\; ,\;-1-\sqrt{23}[/tex]
Step-by-step explanation:
Roots of quadratic equations [tex]ax^{2}+bx+c=0[/tex] calculated as:
[tex]x=\frac{-b\pm\sqrt{b^{2}-4ac}}{2a}[/tex]
First, compare [tex]ax^{2}+bx+c=0[/tex] with [tex]x^{2}+2x-22=0[/tex]
here a = 1 , b = 2 and c = -22
Now, plug the value of a,b and c in [tex]x=\frac{-b\pm \sqrt{b^{2}-4ac}}{2a}[/tex]
[tex]x=\frac{-2\pm \sqrt{2^{2}-4(1)(-22)}}{2(1)}[/tex]
[tex]x=\frac{-2\pm \sqrt{4+88}}{2}[/tex]
[tex]x=\frac{-2\pm \sqrt{92}}{2}[/tex]
[tex]x=\frac{-2\pm 2\sqrt{23}}{2}[/tex]
[tex]x=-1\pm \sqrt{23}[/tex]
Hence, [tex]x=-1+\sqrt{23}\; ,\;-1-\sqrt{23}[/tex]
The sum of three consecutive odd integers is 69. find the integers
What is the value of x?
x =
Answer: The value of x is 2 units.
Explanation:
Since we have given that
AB and CD are two chords that are intersected externally at point E.
As we know the relation regarding the above i.e.
[tex]EA\times EB=EC\times ED[/tex]
Here,
EB=x+1
EA=x+1+11 = (x+12)
EC=x+4
ED=x+4+1 = (x+5)
Now, we put the values in the relation given above :
[tex](x+1)(x+12)=(x+4)(x+5)\\\\x^2+13x+12=x^2+9x+20\\\\12+13x=20+9x\\\\13x-9x=20-12\\\\4x=8\\\\x=\frac{8}{4}=2\\\\x=2\ units[/tex]
Hence, the value of x is 2 units.
Answer:
x = 2 is the answer.
Step-by-step explanation:
When two chords AE and ED are drawn from an external point E to a circle then by theorem we know the relation
AE×BE = DE×CE
AE = x + 1 + 11 = x + 12
BE = x + 1
CE = x + 4
DE = x + 4 + 1 = x + 5
Now putting these values in the formula
(x + 12)(x + 1) = (x + 4)(x + 5)
x² + 12x + x + 12 = x² + 5x + 4x + 20
13x + 12 = 9x + 20
13x - 9x = 20 - 12
4x = 8
x = 2
x = 2 is the answer.
Copy and complete the table on the previous page into a Word document. Title your journal "Pythagorean Theorem". Discuss any relationships you see in the table? Then, look at the equation below and calculate whether a2 + b2 is >, <, or = to c2 based on the numbers you recorded in your table.
I attached the chart (in blue) and the assignment! Can someone please help, I don't understand!
PLEASE HELP!!!
A building manager installs sensors to see how often people turn off the lights when they leave a room. After a month, the manager has a sample size of 400, a sample mean of 47%, and a sample standard deviation of 4%. What is the confidence level for a confidence interval of 46.6% to 47.4%?
A. 68%
B. 85%
C. 99.7%
D. 95%
Answer: 95%
Step-by-step explanation:
A P E X
Option A. is the correct answer. Using the empirical rule and the provided narrow interval, the confidence level for the confidence interval of 46.6% to 47.4% is most likely 68%.
The question is asking to find the confidence level for a given confidence interval. In the scenario, a building manager finds that 47% of the time, people turn off the lights when they leave the room, with a sample standard deviation of 4%. To calculate the confidence level for the interval of 46.6% to 47.4%, we'd typically use a Z-score or t-score formula along with the sample size to determine which confidence level corresponds to the given interval. However, the provided question does not give us enough information to perform a calculation; thus, it is likely that the question expects us to understand the empirical rule (also known as the 68-95-99.7 rule).
Based on the empirical rule, the intervals corresponding to one, two, and three standard deviations from the mean (for a normal distribution) contain approximately 68%, 95%, and 99.7% of the data, respectively. Since the given confidence interval, 46.6% to 47.4%, is quite narrow and is likely to correspond to a plus or minus one standard deviation from the sample mean, the correct confidence level would be approximately 68% (Answer A). This assumption is due to the small range of the interval (0.4%) compared to the sample standard deviation (4%).
How do you convert .444444444 to a fraction?
which one of the following sets of numbers represents the lengths of the sides of a right triangle ?
a. 13 35 37
b. 6 9 10
c. 5 12 13
d. 9 40 42
5, 12, 13 are the sides representing lengths of sides of a right triangle.
What is Pythagoras theorem?The theorem attributed to Pythagoras that the square on the hypotenuse of a right-angled triangle is equal in area to the sum of the squares on the other two sides.
Given that, lengths of sides of triangles.
If a triangle is a right triangle, then it should follow Pythagoras theorem,
Using Pythagoras theorem,
13² = 169
12² + 5² = 144 + 25 = 169
Therefore, 13² = 12² + 5² is following Pythagoras theorem.
Hence, 5, 12, 13 are the sides representing lengths of sides of a right triangle
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What is the length of side PQ?
Answer: The length of PQ = 64
Step-by-step explanation:
We are given that ΔPQR and ΔABC are similar right triangles .
Since, we know that the corresponding sides of similar triangles are proportional.
Therefore, we get
[tex]\dfrac{PQ}{AB}=\dfrac{QR}{BC}\\\\\Rightarrow\dfrac{PQ}{16}=\dfrac{80}{20}\\\\\Rightarrow\ PQ=4\times16\\\\\Rightarrow\ PQ=64[/tex]
Hence, the length of side PQ = 64 units
If the following object is translated right two units and down three units. Where will the translation be located?
recursive function f(n+1)=1/3 f(n) if f (3)=9 what is f(1)
Perform the operation(s) and write the answer in simplest from.
2 2/5+3 1/4
A.)5 1/3
B.)25/9
C.)5 13/20
D.)12 5/9
How do you simplify squats roots
100 point reward with certified answer. 4 basic algebra questions, must show work. If the answers are wrong your response will be deleted and the points taken back. Good luck!
Submit a positive integer. the winner is the person who submits the lowest number that isn't submitted by anyone else.
You are given the mass of CaH₂ which is 14 grams and H₂O which is 28 grams. You are required to find the maximum volume of H₂ gas at STP. The balanced chemical reaction is CaH₂ + 2H₂O → Ca(OH)₂ + H₂. Note that for every one mole of CaH₂, 2 moles of H₂O is needed to completely react and produce Ca(OH)₂ + H₂. So the CaH₂ and H₂O are at equal proportions. At STP, temperature is at 0°C(273K) and pressure at 1 atm. The molar mass of CaH₂ is 42 grams per mole.
14g CaH₂(1mol CaH₂/42 grams CaH₂)(1mol H₂/1mol CaH₂) = 0.333 moles H2
The ideal gas equation is PV = nRT, with R(gas constant) = 0.08206 L-atm/mol-K. get the equation for volume, we have
V = nRT/P
V = (0.333mol H₂)(0.08206 L-atm/mol-K)(273K)/1atm
V = 7.47L
The answer is a positive integer.
What is the frequency of the function y = cos5x?
Final answer:
The frequency of the function y = cos5x is 5/2π.
Explanation:
The given function is y = cos5x. To find the frequency of this function, we need to determine the coefficient of x in the argument of the cosine function. In this case, the coefficient is 5, which means the argument of the cosine function will complete 5 full cycles in an interval of 2π.
The frequency of a function is the reciprocal of the period. The period is found by dividing 2π by the coefficient of x. So, the period of the given function is 2π/5, and the frequency is the reciprocal of the period, which is 5/2π.
Therefore, the frequency of the function y = cos5x is 5/2π.
The box plot shows the total amount of time, in minutes, the students of a class spend reading each day
What information is provided by the box plot? 10 Points
1. The mean for the data
2. The median for that data
3. The number of students who provided information
4. The number of students who read for more than 21.15 minutes
Hey, really need help with this question, thanks. Find the derivative of f(x) = -10/x at x = -12.
Find an equation for the nth term of the arithmetic sequence. a18 = 97, a20 = 281
Final answer:
To find the nth term equation of an arithmetic sequence, we first determined the common difference to be 92 by given terms, and then found the first term by using the formula for arithmetic sequences. The nth term equation for the sequence is: an = -1489 + (n-1)(92).
Explanation:
To find the nth term equation of the arithmetic sequence, we need to determine the common difference and the first term of the sequence. Since we know the 18th term, a18 = 97, and the 20th term, a20 = 281, we can find the common difference, d, by subtracting the two given terms and dividing by the number of terms between them:
d = (281 - 97) / (20 - 18) = 184 / 2 = 92.
Once we have the common difference, we can use the following formula to find the first term (a1):
an = a1 + (n-1)d.
Let's substitute n = 18 and d = 92 into the formula:
97 = a1 + (18-1)(92)
a1 = 97 - (17)(92) = -1489.
Now we can write the equation for the nth term of the arithmetic sequence:
an = -1489 + (n-1)(92).
you spend $124.00 shopping, but the store is offering a 30% discount. what is the total cost after the discount? round to the nearest cent
The coordinates of quadrilateral PQRS are P(0, 0), Q(a + c, 0), R(2a + c, b), and S(a, b). How can you use coordinate geometry to show that one pair of opposite sides is parallel?
Answer:
Apply the Distance Formula to show that opposite sides pq and rs are congruent
What is sum of the area under the standard normal curve to the left of z = -1 and to the right og z = 1.25?
Factor: 24x^3−81
x^3 is x to the third power
Write an equation for the line perpendicular to 2x−3y = 5 and containing (−2, 1).
Hello:
the equation is : y = ax+b
the slope is a : a×(2/3) = -1......(
perpendicular to a line : 2x-3y =7 with a slope of 2/3 because : y = (2/3)x-7/3)
a = -3/2 y=(-3/2)x+b
the line that passes through (-2, 1) : 1 =
(-3/2)(-2)+b
b = -2
the equation is : y = (-3/2)x-2
Anderson has $50 in his savings account. He deposits $5 every week. His father also deposits $20 into the account every time Anderson mows the lawn. His savings account balance can be shown with the following expression:
50 + 5w + 20m
Part A: Identify a coefficient, a variable, and a constant in this expression. (3 points)
Part B: If Anderson saves for 10 weeks and mows the lawn 2 times, how much will he have in his account? Show your work to receive full credit. (4 points)
Part C: If Anderson had $85 in his savings account, would the coefficient, variable, or constant in the expression change? Why? (3 points)
We are given the equation of the savings (s) as:
s = 50 + 5 w + 20 m
Part A.
Coefficient = 5 and 20
Variable = w and m
Constant = 50
Part B.
w = 10
m = 2
Therefore the total savings is:
s = 50 + 5 (10) + 20 (2)
s = $140
Part C.
The coefficient and the constant values are considered as fixed value because they do not change. Therefore only the variable value would change, however the expression 50 + 5 w + 20 m would still be the same. That is only the values of the variable change.
what is the difference of m and 7 increased by 15
The expression which represents a difference of m and 7 increased by 15 will be (m - 7) + 15.
What is an expression?A mixture of variables, numbers, addition, subtraction, multiplication, and division are called expressions.
An expression is a mathematical proof of the equality of two mathematical expressions.
A statement expressing the equality of two mathematical expressions is known as an equation.
The difference between m and 7 is
m - 7
Increased also referred for addition so
Increased by 15 is ( m - 7) + 15
Hence "The expression which represents a difference of m and 7 increased by 15 will be (m - 7) + 15".
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what is 67912 to the nearest 10
the last digit is the ones place, if it is 5 or higher you would round up
under 5 you round down
so to the nearest 10 the number would be 67910
how to express -8+4-2+1 in sigma notation