Answers
The value of "x" in the given figure and question is 20 units.
As per the question statement, We are given a figure in which we are supposed to find the value of x.
Before solving the question, if we observe the figure, we can conclude that this question will include the concepts of right angled triangle or specifically Pythagoras Theorem, which states that
\(Perpendicular^{2} + base^{2} = hypotenuse^{2}\) where perpendicular, base and hypotenuse are the three sides of the right angled triangle.
In Triangle RTQ
using Pythagoras Theorem
\(RQ^{2} = TQ^{2} +TR^{2} \\RQ=x\\x^{2} = 16^{2} + TR^{2} \\TR^{2} = x^{2} -16^{2}\)
Now considering triangle SRT
using Pythagoras Theorem
\(SR^{2} = RT^{2} + ST^{2} \\SR^{2} = (x^{2} -16^{2}) +9^{2}\\\)
Now considering triangle RSQ
using Pythagoras Theorem
\(SQ^{2} = SR^{2} +RQ^{2} \\(9+16)^{2} = SR^{2} + RQ^{2} \\(9+16)^{2} = x^{2} -7^{2}+x^{2} \\ (9+16)^{2} =2x^{2} -7^{2} \\25^{2}+7^{2} = 2x^{2}\)
\(2x^{2} =674\)
\(x^{2} =337\\x=\sqrt{337} \\x=18.357\)
Therefore x = 18.357 approx 20 units.
Pythagoras Theorem: The well-known Pythagorean Theorem states that the square on the hypotenuse of a right triangle equals the sum of the squares on its legs.To learn more about Pythagoras Theorem, click on the link given below:
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Related Questions
0.23 divided by 5.05 explain with steps
Answers
Answer:
Step-by-step explanation:
\mathrm{Multiply\:the\:numerator\:and\:denominator\:by:}\:100
\mathrm{Multiply\:the\:quotient\:digit}\:\left(0\right)\:\mathrm{by\:the\:divisor}\:505
\mathrm{Subtract}\:0\:\mathrm{from}\:23
What is the value of x in the equation 1/3x+7=−2?
Answers
Answer:
x = -27
Step-by-step explanation:
\(\frac{1}{3} x+7=-2\\\\\frac{1}{3} x=-2-7\\\\\frac{1}{3} x=-9\\\\x=-27\)
Some sources report that the weights of full-term newborn babies in a certain town have a mean of 7 pounds and a standard deviation of 0.6 pounds and are Normally distributed.
a. What is the probability that one newborn baby will have a weight within 0.6 pounds of the mean—that is, between 6.4 and 7.6pounds, or within one standard deviation of the mean?
b. What is the probability that the average of nine babies' weights will be within 0.6 pounds of the mean; will be between 6.4 and 7.6 pounds?
c. Explain the difference between (a) and (b).
Answers
The probability that a single newborn baby's weight is within 0.6 pounds of the mean is approximately 68.26%.
Similarly, the probability that the average weight of a sample of nine babies is within 0.6 pounds of the mean is also approximately 68.26%. The difference lies in the context of considering an individual versus a sample.
a. To find the probability that one newborn baby will have a weight within 0.6 pounds of the mean, we need to calculate the area under the normal distribution curve between 6.4 and 7.6 pounds. This can be done by finding the z-scores corresponding to these values and then looking up the probabilities in the standard normal distribution table. Alternatively, we can use a statistical calculator or software to find the probability directly. The probability is approximately 0.6826 or 68.26%.
b. To find the probability that the average of nine babies' weights will be within 0.6 pounds of the mean, we need to consider the distribution of sample means. According to the Central Limit Theorem, when the sample size is large enough (in this case, nine babies), the distribution of sample means will be approximately normal regardless of the shape of the population distribution. The mean of the sample means will still be 7 pounds, but the standard deviation of the sample means will be the standard deviation of the population divided by the square root of the sample size (0.6/√9 = 0.2 pounds). Therefore, we can use the same approach as in part (a) to find the probability. The probability is also approximately 0.6826 or 68.26%.
c. The difference between (a) and (b) is in the context. In (a), we are considering the probability of a single newborn baby having a weight within 0.6 pounds of the mean. In (b), we are considering the probability of the average weight of a sample of nine babies being within 0.6 pounds of the mean. The difference arises from the fact that the sample mean has a smaller standard deviation compared to an individual measurement, resulting in a narrower range around the mean.
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Which equation describes the line that passes through the point at (-2,1) and is perpendicular to the line y=1/3x+5 ?
F. y=3 x+7
G. y=1/3x+7
H. y=-3 x-5
J. y=-1/3x-5
Answers
The equation that describes the line that passes through the point at (-2,1) and is perpendicular to the line y=1/3x+5 is J. y=-1/3x-5.
Two lines are perpendicular if their slopes are negative reciprocals of each other. The slope of the line y=1/3x+5 is 1/3. The negative reciprocal of 1/3 is -3. Therefore, the equation of the line that is perpendicular to y=1/3x+5 and passes through the point (-2,1) will have a slope of -3.
We can start by finding the slope-intercept form of the equation of the line that passes through the point (-2,1). The slope-intercept form of an equation of a line is y=mx+b, where m is the slope and b is the y-intercept.
The slope of the line is -3. The y-coordinate of the point is 1. The x-coordinate of the point is -2. Substituting these values into the slope-intercept form of the equation gives us:
y=-3x+b1=(-3)(-2)+b1=6+bb=-5Therefore, the equation of the line that passes through the point (-2,1) is y=-3x-5.
We can check to make sure that this line is perpendicular to y=1/3x+5 by calculating the slopes of the two lines. The slope of y=1/3x+5 is 1/3. The slope of y=-3x-5 is -3. The negative reciprocal of 1/3 is -3. Therefore, the two lines are perpendicular.
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^^
1. 3x2 + 4x2 = 35
2. 3x2 – 28 = 2x2 + 33
3. X2 – 25 = 25
4. 2x2 – 30 = 70
5. 8x2 – 6x2 = 54
6. 3x2 – 6 = 34 – 2x2
7. X2 + 49 = 196
8. 5x2 – 40 = 100
9. 9x2 = 4x2 + 10
10. X2 – 4 = 80
11. X2 + 25 = 100
12. 2x2 + 7 = 67
13. (x2 + 22)= 16
14. (x + 5)2 = 23
15. (x – 4)2 = 11
Answers
Answer:
Step-by-step explanation:
1. 3x2 + 4x2 = 35
2. 3x2 – 28 = 2x2 + 33
3. X2 – 25 = 25
4. 2x2 – 30 = 70
5. 8x2 – 6x2 = 54
6. 3x2 – 6 = 34 – 2x2
7. X2 + 49 = 196
8. 5x2 – 40 = 100
9. 9x2 = 4x2 + 10
10. X2 – 4 = 80
11. X2 + 25 = 100\(\left \{ {{y=2} \atop {x=2}} \right.\)
12. 2x2 + 7 = 67
13. (x2 + 22)= 16
14. (x + 5)2 = 23
15. (x – 4)2 = 11
Mrs. Vo, Mrs. Manuel, Ms. Soun and Mr. Lopez are contestants on a game show. In one of the rounds of the game
show, the contestants have a chance to spin a wheel up to two times in a row to try to get the highest possible sum
without going over 100. The wheel that they spin is divided into 21 equal portions, each containing one element from
the set of numbers containing 1 and all the multiples of 5 less than or equal to 100.
Mr. Lopez goes first. If he spins the wheel twice, getting a 15 and a 50, what is the probability that on Mrs. Vo's first
spin, she gets a number larger than Mr. Lopez's sum? Express your answer as a common fraction.
Answers
Therefore, the probability of Mrs. Vo winning is 1 - 91/300 - 8/21 = 11/30.
What is Probability?Probability refers to the likelihood or chance that a particular event or outcome will occur. It is a mathematical concept that quantifies the degree of uncertainty associated with an event or situation. Probability is typically expressed as a number between 0 and 1, where 0 indicates that an event is impossible, and 1 indicates that it is certain to occur.
by the question.
let's consider the first case: Mrs. Vo spins a number greater than 65 on her first spin. There are a total of 8 numbers greater than 65 on the wheel: 70, 75, 80, 85, 90, 95, 100. Since there are 21 sections on the wheel, the probability of spinning a number greater than 65 on the first spin is 8/21.
The number of possible outcomes for Mrs. Vo's spin is 21, since there are 21 equal portions on the wheel. However, we need to exclude the outcomes that would cause Mrs. Vo's sum to exceed 100, since that would result in an automatic loss. The largest possible outcome on the wheel is 100, so Mrs. Vo cannot spin a number greater than or equal to 35 on her first spin.
The number of outcomes that would give Mrs. Vo a winning sum of at least 66 is the number of outcomes greater than 65, which are 70, 75, 80, 85, 90, 95, and 100. There are 7 such outcomes.
If Mrs. Vo spins a number less than or equal to 65 on her first spin, the probability of this happening is 13/21. The probability of her second spin being between 1 and 35 is 35/100 (since there are 35 numbers between 1 and 35 on the wheel). So, the probability of her total sum being less than or equal to 65 is (13/21) * (35/100) = 91/300.
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(2.1) T/F A system is made of two or more equations.
Answers
True.
A system of equations is a set of two or more equations that are to be solved simultaneously.
A system of equations is a set of two or more equations that are to be solved simultaneously. In linear algebra, a system of equations is typically represented as a set of linear equations in the form:
a11x1 + a12x2 + ... + a1nxn = b1
a21x1 + a22x2 + ... + a2nxn = b2
...
am1x1 + am2x2 + ... + amnxn = bm
where the variables x1, x2, ..., xn are the unknowns, the coefficients aij and the constants bi are given, and the goal is to find a solution vector (x1, x2, ..., xn) that satisfies all the equations in the system.
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suppose net income = $200 , depreciations = $10, and working capital went up by $70. what was cash from operations?
Answers
cash from operations is $140 when net income = $200 , depreciations = $10, and working capital went up by $70.
Cash from Operations = Net Income + Depreciation - Change in Working Capital
Plugging in the values:
Cash from Operations = $200 + $10 - $70
Cash from Operations = $140.
So, cash from operations is $140.
Cash from operations can be calculated by adding non-cash items such as depreciation and subtracting changes in working capital.
This means that the company generated $140 in cash from its operations during the given period. It is important to understand the cash from operations as it represents the cash generated from the day-to-day operations of the business and provides an indication of its ability to generate cash in the future.
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the price of a 7 minute phone call is $2.45.What is the price of a 19 minute phone call
Answers
Answer:
$6.65
Step-by-step explanation:
7 ----- 2.45
19 ---- x
\(x=\frac{(19)(2.45)}{7} =6.65\)
Hope this helps
This number is in scientific notation.
2.4 x 104
Convert the number into standard notation. What is the value?
2.4 x 10-4 =
Answers
Answer:
24
0.00024
hope it helps;)
Answer:
0.00024
Step-by-step explanation:
A jet travels 490 miles in 5 hours. At this rate, how far could the jet fly in 12 hours? What is the rate of speed of the jet?
Answers
Answer: 1,176 miles
Step-by-step explanation:
490 / 5 = 98 miles
98 mph X 12 hours is 1,176
an article marked at rs.8,000 is sold at rs6689.60 allowing some discount and adding vat.8f the rate of discount was double then the rate of vat, find the selling price of the article without vat
Answers
The selling price of the article without VAT is Rs. 6,429.13.
What is Algebraic expression ?
In mathematics, an algebraic expression is a combination of variables, constants, and mathematical operations, such as addition, subtraction, multiplication, and division, that represents a quantity or a relationship between quantities.
Let's assume the rate of discount to be 'x' and the rate of VAT to be 'y'.
According to the problem, the marked price of the article is Rs. 8,000.
After applying the discount, the selling price becomes:
Selling price = Marked price - Discount
Selling price = 8000 - (x÷100) * 8000
Now, we add the VAT to the selling price:
Selling price with VAT = Selling price + (y÷100) * Selling price
Selling price with VAT = [8000 - (x÷100) * 8000] + [(y÷100) * (8000 - (x÷100) * 8000)]
Selling price with VAT = 6689.60 (Given)
We are also given that the rate of discount was double the rate of VAT, i.e.,
x = 2y
Substituting this value in the above equation, we get:
6689.60 = [8000 - (2y÷100) * 8000] + [(y÷100) * (8000 - (2y÷100) * 8000)]
Simplifying this equation, we get:
6689.60 = 8000 * [1 - (2y÷100) + (y÷100) - (2y÷100) * (y÷100)]
6689.60 = 8000 * [1 - (3y÷50) + (y*y÷5000)]
Solving for y, we get:
y = 4
Now, we can calculate the selling price without VAT as follows:
Selling price without VAT = Selling price - (y÷100) * Selling price
Selling price without VAT = 6689.60 - (4÷100) * 6689.60
Selling price without VAT = Rs. 6,429.13
Therefore, the selling price of the article without VAT is Rs. 6,429.13.
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2 + 7c – 4c2 – 3c + 4
Answers
Answer:-4c^2+4c+6
Step-by-step explanation:
Hope that’s what ur looking for:)
Answer:
2 + 7c – 4c2 – 3c + 4
4c∧2 + 4c + 6
Step-by-step explanation:
Is negative 51 over 5 rational or irrational?
Answers
Answer:
it is rational
the probility of alvins mother will server rice with dinner is 0.78 the probilty that she will server carrots is with dinner is 0.30
Answers
The probability of both rice and carrots being served with dinner is 23.4%.
The probability of Alvin's mother serving rice with dinner can be expressed using the formula P(Rice) = 0.78. This means that the probability of Alvin's mother serving rice with dinner is 78%. The probability of Alvin's mother serving carrots with dinner can be expressed using the formula P(Carrots) = 0.30. This means that the probability of Alvin's mother serving carrots with dinner is 30%. To calculate the combined probability of both rice and carrots being served with dinner, we can use the formula P(Rice and Carrots) = P(Rice) * P(Carrots) = 0.78 * 0.30 = 0.2340. This means that the probability of both rice and carrots being served with dinner is 23.4%.
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A diver is standing on a platform 7 ft above the pool.
He jumps from the platform with an initial
upward velocity of 20 ft/s. Use the formula
h(t) =- 16+ + vt + s, where h is his height above the
water, t is the time, v is his starting upward velocity
and s is his starting height. What is the maximum
altitude that the diver reaches? Round to the nearest
whole number.
Answers
Answer:
13 ft
Step-by-step explanation:
We assume your height formula is intended to be ...
h(t) = -16t² +20t +7
This will have its maximum value at ...
t = -b/(2a) = -20/(2(-16)) = 5/8
The height at that time is ...
h(5/8) = (-16(5/8) +20)(5/8) +7 = 10(5/8) +7 = 106/8 = 53/4 = 13 1/4 . . . ft
To the nearest whole foot, the diver will reach a height of 13 ft above the pool.
_____
Additional comments
The standard form quadratic can be described as ...
f(x) = ax² +bx +c
The extreme value occurs at ...
x = -b/(2a)
This can also be written as ...
f(x) = (ax +b)x +c
which can make it easier to evaluate for some numerical value of x.
At the beginning of the month we had a current account of € 467. After withdrawing five identical amounts from the account, we were left with € 88. How Much Money Do We Make Every Time?
Answers
Answer:
€75.80
Step-by-step explanation:
Start with €467.
End up with €88.
Total amount withdrawn:
€467 - €88 = €379
The total amount was withdrawn in 5 equal amounts.
Each amount taken is:
€379 ÷ 5 = €75.80
Find the value of each variable. Write your answer in radical form
Please answer ASAP
I will give brainlist
Numbers 3&4
Answers
Answer:
3.
11² + 11² = x²
121 + 121 = x²
242 = x²
x = √242
x = 11√2
4.
tan(60°) = y/36
√3 = y/36
y = 36√3
tan(30°) = x/36
√3/3 = x /36
x = 36√3/3
x = 12√3
Answer:
Step-by-step explanation:
3) Using the Pythagorean Theorem (A^2+B^2=C^2) We can tell that x^2=11^2+CB^2. If you can find what CB is then you can find x by doing 11^2+CB^2=x^2 and if you square root x^2 you get x.
4) Same thing, y^2+x^2=36^2.
Someone help me please!!
Answers
Answer:
6cm
Step-by-step explanation:
half way point between 8 and 4
Write the equation of the line that passes through the points (7, -4) and (-1,3), first in point-slope form, and then in
slope-intercept form.
The slope of the line is
When the point (7,4) is used, the point-slope form of the line is
The slope-intercept form of the line is
Help pls I’ll give brainly!!!
Answers
Step-by-step explanation:
first we need to calculate the slope, which is needed in both equation forms.
the slope is the ratio "y coordinate change / x coordinate change" when going from one point on the line to another.
I always prefer to go from left to right (but it works exactly the same way in the opposite direction), so I go from (-1, 3) to (7, -4).
x changes by +8 (from -1 to +7).
y changes by -7 (from +3 to -4).
so, the slope is -7/+8 = -7/8
when (7, -4) is used (I think you have a typo in the problem description up there), the point-slope form is
y - y1 = m(x - x1)
with (x1, y1) being the point coordinates, and m bring the slope
y - -4 = -7/8 × (x - 7)
or simplified
y + 4 = -7/8(x - 7)
the slope-intercept form is
y = mx + n
m being the slope, n being the y-intercept (y value for x=0).
we know already
y = -7/8 x + n
we also use the coordinates of a point here to solve for n :
-4 = -7/8 × 7 + n = -49/8 + n
-32/8 = -49/8 + n
17/8 = n
so, the full equation is
y = -7/8 x + 17/8
3. y= (-7/8)x + (17/8)
Complete the steps in solving the quadratic function 7x – 9 = 7x2 – 49x by completing the square.
answer below:
–9 = 7x2 –
⇒ 56 x
–9 +
⇒ 112 = 7(x2 – 8x +
⇒ 16 )
56, 112, 16 in that order
Answers
Answer:
it's actually 28+/-√721/7
Step-by-step explanation:
In the statement, z = 1.42, p > .05, which of the following interpretations is true? a) There is a significant difference between the sample value and the population. b) There is not a significant difference between the sample value and the population. c) There is a marginally significant difference between the sample value and the population.d) The answer cannot be determined from the information given.
Answers
The correct interpretation is b) There is not a significant difference between the sample value and the population.
In the given statement, z = 1.42 and p > .05. The z-value represents the standardized difference between the sample value and the population mean, while the p-value represents the probability of observing a result as extreme as, or more extreme than, the observed result under the null hypothesis (no difference between the sample value and the population mean). A p-value greater than .05 indicates that the difference between the sample value and the population mean is not statistically significant, meaning we cannot reject the null hypothesis.
Based on the provided information (z = 1.42, p > .05), we can conclude that there is not a significant difference between the sample value and the population.
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i need help answering this for homework
Answers
Simplify 6a + 5a - a - 5 + 2a712a-513a-512a
Answers
By arranging similar terms, we have
\(\begin{gathered} 6a+5a+2a-a-5 \\ \text{which gives} \\ 13a-a-5 \end{gathered}\)since 13a minus a is 12a, the answer is
\(12a-5\)which corresponds to option 2 from top to bottom
Sale! 95% OFF
of the original price!
What was the original price of a cruise ticket whose sale price is $46?
$
Answers
The original price of cruise ticket was $920.
How are sales and discounts determined?Identify the initial cost, for instance $90.Obtain the discount (for instance, 20%).Determine the savings: 20% of $90 = $18.To determine the selling price, deduct the savings from the original cost: $90 - $18 = $72.The % discount is first converted to a decimal.
95% /100% = 0.95
Step 2: Next, we enter the discount and selling price into the calculation.
P = (1 − d)x
⇒ 46 = (1 − 0.95) x
Step 3: To determine the original price, we calculate the equation from Step 2.
46 = (1 x 0.95), according to the original equation
46 = (0.05)x
46 / 0.05 = x
x = 920
The cruise ticket originally cost $920.
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Find the extremum of f(x,y) subject to the given constraint, and state whether it is a maximum or a minimum f(x,y)=x^2 +2y^2 −2xy;x+y=15
Answers
There is one critical point which is (5,10), and it is a local minimum which is also the global minimum of f(x,y) subject to the constraint x + y = 15.
Determining the nature of a constraintTo find the extremum of f(x,y) subject to the constraint x + y = 15,
Use the method of Lagrange multipliers.
Let g(x,y) = x + y - 15 be the constraint function.
Find the critical points of the function
\(F(x,y,λ) = f(x,y) - λ*g(x,y), \)
where λ is the Lagrange multiplier.
Taking the partial derivatives of F with respect to x, y, and λ, we get:
\(∂F/∂x = 2x - 2y - λ \\
∂F/∂y = 4y - 2x - λ \\
∂F/∂λ = x + y - 15\)
Setting these partial derivatives equal to zero and solving the system of equations, it becomes,
x = 2y
x = 5
y = 5/2
Substitute x = 5 in the constraint equation x + y = 15, we get
y = 10.
Therefore, the critical point is (5, 10).
To determine whether this critical point is a maximum or a minimum, use the second partial derivative test.
The Hessian matrix of f(x,y) is:
H = [2 -2; -2 4]
Evaluating H at the critical point (5,10)
H(5,10) = [2 -2; -2 4]
The determinant of H(5,10) is 8, which is positive.
Therefore, the critical point (5,10) is a local minimum of f(x,y) subject to the constraint x + y = 15.
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You bake 40 cookies, which is 25 less than the number of donuts you also make. Does the equation "x+25=40" describe the situation? If not, write an equation that does and explain what the variable represents.
Answers
Step-by-step explanation:
This equation does not describe the situation.
Let x be the number of donuts I made.
x-25= 40
(because there is 25 lesser cookies than donuts.
Answer: No; x-25=40
Step-by-step explanation:
40=x-25
cookies equals 25 less than donuts
because donuts is 25 less than cookies
donuts = 65
total = 40 + 40+65=145
Minh has a number cube. It has a different number on each side: 4,5,6,7,8, or 9. Minh will roll the number cube once. What is the probability he will roll a 5
Answers
Answer:
it is a 20 percent chance on all of them
Step-by-step explanation:
Step-by-step explanation:
The number of events = Minh rolls 4 + Minh rolls 5 + Minh rolls 6 + Minh rolls 7 + Minh rolls 8 + Minh rolls 9 = 6 events
The number of required outcome = Minh rolls 5
The probability, P, of an event occurring is defined as follows;
Which gives for the probability, P₅, that when Minh roll the number cube one he will roll a 5, we have
The number of possible outcomes = The number of events = 6
The number of required outcome = 1
Therefore;
Therefore, the probability that Minh will roll a 5 = 1/6.
Rebecca carries a balance on her credit card each month. Today is the first day of the new. 28-day billing cycle. The current balance is x and the APR is 24%.
Rebecca is buying a friend an expensive gift that costs $1,400 that she plans to put on her credit card. This will be her only purchase this month. Sed she will be
making this purchase on the last day of the month. Part A if her finance charge will be $51 write and solve an equation to determine her current balance on her credit card show your work. Part B How much in finance charges can she save by making the purchase on the last day of the billing cycle
Answers
Part A: Rebecca's credit card balance can be calculated using the equation x = (51 - 1) 0.02 if her finance charge is $51.
Part B: By making the purchase on the final day of the billing cycle rather than the first day, Rebecca will be able to avoid paying $27 in finance charges.
How do equations work?
A mathematical statement proving the equality of values between two or more mathematical expressions is called an equation.
Equation symbols (=) are used to represent equations.
A finance charge is what?
The interest and other fees levied on credit cards are included in a finance charge.
Typically, the finance charge is based on a stated APR (annual percentage rate).
The month's billing cycle lasts for 28 days.
Balance at current starting = x.
APR = 24%, or annual percentage rate.
The monthly percentage rate (MPR) equals 2% (24% divided by 12).
The final day's purchase cost $1,400.
$51 is the total finance fee for the month.
($1,400 x 2% x 1/28) = $1 finance fee for the last-minute purchase.
$50 ($51 - $1) serves as the initial balance's finance charge.
The starting balance at this time is x = $2,500 ($50 x 2%).
Current Beginning Balance Equation: x = 51 - 1 0.02
($1,400 x 2%) Equals $28 in total loan charges for the last-minute purchase.
Finance charge savings from buying on the last day equals $27 ($28 - $1).
By buying the $1,400 gift for her friend on the last day of the billing cycle rather than the first, Rebecca can avoid paying $27 in finance charges.
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The inside of a resting cell is slightly negative relative to the outside. This is an example of electrical disequilibrium O failed homeostasis osmotic equilibrium chemical disequilibrium
Answers
The resting cell membrane maintains a slight negative charge inside relative to the outside, creating an electrical disequilibrium. The correct answer is A.
The resting cell membrane maintains a slight negative charge inside relative to the outside, creating an electrical disequilibrium. This phenomenon is crucial for various cellular functions and is achieved through the selective movement of ions across the cell membrane. By actively pumping out positively charged ions like sodium (\(Na^+\)) and taking in negatively charged ions like potassium (\(K^+\)), the cell establishes an electrical potential difference.
This electrical disequilibrium plays a fundamental role in cellular activities such as nerve transmission and muscle contraction. It enables the rapid transmission of electrical signals along nerve cells and facilitates the coordinated contraction of muscle fibers.
The maintenance of this electrical disequilibrium is an example of the cell's remarkable ability to regulate its internal environment, a process known as homeostasis. By actively controlling ion movements, the cell ensures a balance between the intracellular and extracellular environments, allowing for optimal cellular functioning.
Therefore, the slight negative charge inside a resting cell relative to the outside exemplifies electrical disequilibrium and serves as a vital component of cellular homeostasis and proper functioning.
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Note: The question would be as
The inside of a resting cell is slightly negative relative to the outside. This is an example of
a. electrical disequilibrium
b. O failed homeostasis
c. osmotic equilibrium
d. chemical disequilibrium