He worked 43 hours to earn Rs. 23250
His basic pay is Rs. 18000 for a basic 36 hours a week. His salary is
Rs. 23250. This proves that he has worked extra time. So the amount earned in the extra hours equals Rs. 23250 - Rs. 18000 = Rs.5250.
Amount per hour earned in basic pay = 18000/36 = Rs.500 a hour.
∴ Amount per hour earned in extra hours = 1.5 x 500 = 750 per hour.
So number of hours he worked in extra time = Rs.5250/750 = 7 hours.
Thus total number of hours = 36 + 7 = 43 hours.
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what is the volume of a triangular pyramid that is 5 feet tall and has a base area of 9 square feet
The volume of the triangular prism as described is; 15 cubic foot.
What is the volume of the triangular pyramid?A triangular pyramid simply refers to any geometric solid with a triangular base, and all three lateral faces are also triangles with a common vertex
It follows from the formula for calculating the volume of a triangular prism that;
Volume = (1/3) × base area × height.
Consequently,
volume of the prism is; = (1/3) ×9 × 5
Volume = 15 cubic foot
Therefore, volume of the triangular prism as described is; 15 cubic foot.
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A set of n = 25 pairs of scores (x and y values) has a pearson correlation of r = 0. 80. how much of the variance for the y scores is predicted by its relationship with x?
The amount of variance for y that is predicted by its relationship with x is 64%.
How much variance is predicted?
Variance measures the rate of dispersion of a data point around the dataset. It can be calculated by finding the square of the standard deviation of a dataset. Variance measures the variation of a data set.
Correlation is a statistical measure used to measure the linear relationship that exists between two variables. The greater the correlation coefficient is closer to one, the greater the linear relationship that exists between the two variables. A positive correlation occurs when the two variables move in the same direction.
Variance = (correlation coefficient²) x 100
(0.80²) x 100
0.64 x 100 = 64%
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A straight line passes through the points (1,3) and (2,2). What is the x-intercept of this line?
Answer:
x-int: (4, 0)
Step-by-step explanation:
First, we need to find the equation of the line.
The equation of a line is y = mx + b, where m is the slope and b is the y-intercept.
Thus, we need to find the slope first by using the slope formula:
[tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} } \\[/tex] or change in y / change in x
So we have: [tex]\frac{3-2}{1-2}=\frac{1}{-1}=-1=m[/tex]
We must plug in the slope to find the y-intercept:
[tex]3=-1(1)+b\\3=-1+b\\4=b[/tex]
So the equation of the line is y = -x + 4
The x-intercept means that the y coordinate is 0 so we can use the equation:
[tex]0=-x+4\\-4=-x\\4=x[/tex]
Each day of the week mrs uses 3/4 of a gallon of gas what is the amount she uses in five days?
Answer:
3.75
Step-by-step explanation:
3/4 times 5 =3 3/4
Two balls are drawn in succession out of a box containing red and white balls. Find the probability that at least 1 ball was red, given that the first ball was replaced before the second draw. Not replaced before the second draw.
The probability that at least 1 ball was red, given that the first ball was replaced before the second draw is 28.5%; and the probability that at least 1 ball was red, given that the first ball was not replaced before the second draw is 22.5%.
What is probability?Probability is an area of mathematics that deals with numerical descriptions of how probable an event is to occur or how likely a statement is to be true.To find the probability that at least 1 ball was red, given that the first ball was replaced before the second draw. Not replaced before the second draw:
2 + 5 = X7 = X(2/7 + 2/7) /2 = X(0.285 + 0.285) /2 = X0.285 = X(2/7 + 1/6 ) /2 = X(0.28 + 0.16) /2 = X0.451/2 = X0.225 = XTherefore, the probability that at least 1 ball was red, given that the first ball was replaced before the second draw is 28.5%; and the probability that at least 1 ball was red, given that the first ball was not replaced before the second draw is 22.5%.
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The complete question is given below:
Two balls are drawn in succession out of a box containing 2 red and 5 white balls. Find the probability that at least 1 ball was red, given that the first ball was (Upper A )Replaced before the second draw. (Upper B )Not replaced before the second draw.
Find two positive numbers satisfying the given requirements. the product is 242 and the sum is a minimum. (smaller value) (larger value)
The two positive numbers satisfying the given requirements are 15.56 and 15.56
For given question,
Let x and y be two positive numbers satisfying the given requirements.
⇒ xy = 242 .............(1)
The sum of given two positive numbers is a minimum.
Let the sum of given two positive numbers is S.
⇒ x + y = S ............(2)
From equation(1),
⇒ y = 242/x
Substitute above value of y in equation (2),
⇒ x + y = S
⇒ S = x + (242 / x)
Now, for above equation we find the derivative of x with respect to x.
⇒ 0 = 1 - [tex]\frac{242}{x^{2} }[/tex]
⇒ 242/x² = 1
⇒ x² = 242
⇒ x = ±15.56
Since the numbers are positive, x = 15.56
For x = 15.56
⇒ y = 15.56
Therefore, the two positive numbers satisfying the given requirements are 15.56 and 15.56
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Find the nth taylor polynomial for the function, centered at c. f(x) = ln(x), n = 4, c = 5
The nth taylor polynomial for the given function is
P₄(x) = ln5 + 1/5 (x-5) - 1/25*2! (x-5)² + 2/125*3! (x-5)³ - 6/625*4! (x - 5)⁴
Given:
f(x) = ln(x)
n = 4
c = 3
nth Taylor polynomial for the function, centered at c
The Taylor series for f(x) = ln x centered at 5 is:
[tex]P_{n}(x)=f(c)+\frac{f^{'} (c)}{1!}(x-c)+ \frac{f^{''} (c)}{2!}(x-c)^{2} +\frac{f^{'''} (c)}{3!}(x-c)^{3}+.....+\frac{f^{n} (c)}{n!}(x-c)^{n}[/tex]
Since, c = 5 so,
[tex]P_{4}(x)=f(5)+\frac{f^{'} (5)}{1!}(x-5)+ \frac{f^{''} (5)}{2!}(x-5)^{2} +\frac{f^{'''} (5)}{3!}(x-5)^{3}+.....+\frac{f^{n} (5)}{n!}(x-5)^{n}[/tex]
Now
f(5) = ln 5
f'(x) = 1/x ⇒ f'(5) = 1/5
f''(x) = -1/x² ⇒ f''(5) = -1/5² = -1/25
f'''(x) = 2/x³ ⇒ f'''(5) = 2/5³ = 2/125
f''''(x) = -6/x⁴ ⇒ f (5) = -6/5⁴ = -6/625
So Taylor polynomial for n = 4 is:
P₄(x) = ln5 + 1/5 (x-5) - 1/25*2! (x-5)² + 2/125*3! (x-5)³ - 6/625*4! (x - 5)⁴
Hence,
The nth taylor polynomial for the given function is
P₄(x) = ln5 + 1/5 (x-5) - 1/25*2! (x-5)² + 2/125*3! (x-5)³ - 6/625*4! (x - 5)⁴
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Pls help as soon as possible
Answer:
12
Step-by-step explanation:
6*6 = 36
36/3 = 12
Answer:
12
Step-by-step explanation:
Given expression:
[tex]\dfrac{1}{3}x^2[/tex]
To evaluate the given expression for x = 6, substitute x = 6 into the expression and simplify:
[tex]\begin{aligned}x=6 \implies \dfrac{1}{3}(6)^2 & = \dfrac{1}{3}(6 \cdot 6)\\\\& = \dfrac{1}{3}(36)\\\\& = \dfrac{36}{3}\\\\& = \dfrac{3 \cdot 12}{3}\\\\& = \dfrac{\diagup\!\!\!\!3 \cdot 12}{\diagup\!\!\!\!3}\\\\& = 12\end{aligned}[/tex]
A ribbon is 5 m long. A piece of length 3 4/5 m is cut from it. What is the length of the remaining piece?
Answer:
1.2 meters long
Step-by-step explanation:
3(4/5)m=3.8m
5m-3.8m=1.2m
Which function represents the following graph?
X
The last one because the other ones only go to the positive side and not the negative too since the cube root
A car is known to be 88% likely to pass inspection at a certain motor vehicle agency inspection office. what is the probability that at least 90 cars pass inspection if a random sample of 100 cars is taken at this motor vehicle agency inspection office?
Using the normal distribution, there is a 0.3228 = 32.28% probability that at least 90 cars pass inspection.
Normal Probability DistributionThe z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score measures how many standard deviations the measure is above or below the mean. Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.The binomial distribution is the probability of x successes on n trials, with p probability of a success on each trial. It can be approximated to the normal distribution with [tex]\mu = np, \sigma = \sqrt{np(1-p)}[/tex].The parameters for the binomial distribution are given by:
n = 100, p = 0.88.
Hence the mean and the standard deviation for the approximation are:
[tex]\mu = np = 100 \times 0.88 = 88[/tex][tex]\sigma = \sqrt{np(1-p)} = \sqrt{100 \times 0.88 \times 0.12} = 3.25[/tex]The probability that at least 90 cars pass inspection, using continuity correction, is P(X > 89.5), which is one subtracted by the p-value of Z when X = 89.5, hence:
Z = (89.5 - 88)/3.25
Z = 0.46
Z = 0.46 has a p-value of 0.6772.
1 - 0.6772 = 0.3228.
0.3228 = 32.28% probability that at least 90 cars pass inspection.
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The sum of fice consecutive positive intergers is 2020. Find the largets of these numbers.
Answer:
3, 7, 14
Step-by-step explanation:
Please answer the one this exercises if you can send photos sent it pls and you have to use quadratic function for these Thanks
The expression of the equation will be:
x² - 8x = x(x - 8)
x² - 10x = x(x - 10)
x² - 5x = x(x - 5)
x² - 3x = x(x - 3)
How to compute the equation?It should be noted that an equation simply means the expression of the variables that are given.
In this case, the following can be represented:
x² - 8x = x(x - 8)
x² - 10x = x(x - 10)
x² - 5x = x(x - 5)
x² - 3x = x(x - 3)
This is illustrated above.
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Find the median of the data set. round your answer to the nearest tenth if necessary. 13,13,15,15,15,15,17,17,19,20
Answer:
Hey Desmariesin7587, the median of the data set that you gave is 15.9
Step-by-step explanation:
Since the amount of values in the data set was not even, I could not find a middle number. Instead, I added up all of the values and divided the total sum by the amount of values that there were; in this case, 10.
----------------------
Have a great day,
Nish
You are playing a game with three cards. At the start, all three cards are face down. You know that a different real number is written on every card, but you do not know what the numbers are. The rules of the game are as follows: You can choose any card and turn it over (assuming that you have not already turned it over). You can either keep the card, or discard it. If you discard a card, then you cannot go back to it; you must choose a new card. If the card you have kept has the largest real number on it, then you win the game. If you use the optimal strategy, then what is the probability that you win the game
concluding, the idea is discarding cards until we get,at least, a 6, in that case, the smallest probability of winning the game is 0.59, which is more than in half of the cases.
How to find the probability?
Now, we know that there are 52 cards in a normal deck, if we only keep the ones with real numbers, there are 40.
These numbers go from 1 to 10.
5.5 is the average real number in the cards, so, having a 6 or more in a card is what we expect.
This means that if the card that we turn up is smaller than 6, we discard it.
If the card has the value 6 or larger, we keep it.
In this case, the probability of losing is if one of the other cards has a value larger than 6.
The probability that a random card has a value larger than 6 is:
p = (number of cards with a value larger than 6)/(total number of cards)
p = (16/39)
(The quotient is 39 instead of 40, because we already know one of the cards)
This means that if keep the 6, the probability of winning is:
1 - 16/39 = 0.59
If instead, we got a 7, obviously we keep it, in that case the probability of winning is:
1 - 12/39 = 0.69
And so on, concluding, the idea is discarding cards until we get,at least, a 6, in that case, the smallest probability of winning the game is 0.59, which is more than in half of the cases.
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Need help with my math please. 31-41.
Step-by-step explanation:
31) the answer is (98765x9) +3=888888
why if u look at the equation is descending and if u verify the cinjecture u will find out is correct
41)½+¼+⅛+1/16+1/32=1-1/32
just d same reason with (31)
Find the 45th term of the arithmetic sequence an = 2 + 4(n − 1).
145
182
178
264
The 45th term of the arithmetic sequence is 178. Option C
How to determine the term
Given the arithmetic sequence formula as;
an = 2 + 4(n − 1)
we have n = 45
Let's substitute the value of 'n' into the formula;
a = 2 + 4( 45 - 1)
expand the bracket
a = 2 + 4(44)
a = 2 + 176
a = 178
The 45th term is 178
Thus, the 45th term of the arithmetic sequence is 178. Option C
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A depository institution holds $164 million in required reserves and $9 million in excess reserves. Its remaining assets include $417 million
in loans and $137 million in securities.
If the institution's only liabilities are transactions deposits, calculate the required reserve ratio.
(Enter your response rounded to the nearest integer.)
The required reserve ratio is 0.226 or 22.6%.
Given that a depository institution holds $164 million in required reserves and $9 million in excess reserves and Its remaining assets include $417 million in loans and $137 million in securities.
The following equality always holds.
Total liabilities=Total assets
It is given that the institution's only liabilities are transaction deposits.
This means:
Total transaction deposits=Total assets
Total transaction deposits=Required reserves + Excess reserves + Loans + Securities
Total transaction deposits=$164+$9+$417+$137
Total transaction deposits=$727
Calculate the required reserve ratio as follows:
Required reserve ratio=(Required reserves)/(Total transaction deposits)
Required reserve ratio=($164 million)/($727 million)
Required reserve ratio=0.226 or 22.6%.
Hence, the required reserve ratio when a depository institution holds $164 million in required reserves and $9 million in excess reserves and Its remaining assets include $417 million in loans and $137 million in securities is 0.226 or 22.6%.
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Isabel made $176 for 8 hours at work At the same rate, how many hours would she have to work to make 374
Answer:
17 hours
Step-by-step explanation:
We first want to figure out how much money shes making per hour.
We can simply divide 176 by 8 getting us 22
Since we know she makes 22 dollars an hour we can divide 374 by 22 getting us 17.
Now we know it would take 17 hours to make 374 dollars
If you want to double check you can simply multiply 17 by 22 which would get you 374
Answer: 17 hours
Step-by-step explanation
Solve following equation:
[tex]4x+10=-2+4[/tex]
Step-by-step explanation:
4x + 10 = -2 + 4
4x = -2 + 4 - 10
4x = -8
x = -2
[tex]\huge\text{Hey there!}[/tex]
[tex]\huge\textbf{Equation:}[/tex]
[tex]\mathsf{4x + 10 = -2+ 4}[/tex]
[tex]\huge\textbf{Simplify it:}[/tex]
[tex]\mathsf{4x + 10 = 2}[/tex]
[tex]\huge\textbf{Subtract 10 to both sides:}[/tex]
[tex]\mathsf{4x + 10 - 10 = 2 - 10}[/tex]
[tex]\huge\textbf{Simplify it:}[/tex]
[tex]\mathsf{4x = 2 - 10}[/tex]
[tex]\mathsf{4x = -8}[/tex]
[tex]\huge\textbf{Divide 4 to both sides:}[/tex]
[tex]\mathsf{\dfrac{4x}{4} = \dfrac{-8}{4}}[/tex]
[tex]\huge\textbf{Simplify it:}[/tex]
[tex]\mathsf{x = \dfrac{-8}{4}}[/tex]
[tex]\mathsf{x = -2}[/tex]
[tex]\huge\textbf{Therefore, your answer should be:}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
Put the following equation in standard form and determine the quadratic, linear, and constant coefficients. -3x2 - 8 = 5x - 7
Answer:
-3x² -5x -1 = 0-3 (quadratic)-5 (linear)-1 (constant)Step-by-step explanation:
The equation will be in standard form when terms are listed in order of decreasing degree, and the right side of the equation is 0.
Standard formWe can subtract the right-side expression from both sides to get standard form.
-3x² -8 -(5x -7) = 5x -7 -(5x -7)
-3x² -8 -5x +7 = 0 . . . . . . . simplify a bit
-3x² -5x -1 = 0 . . . . . . . . . collect terms
The standard form equation can be written ...
-3x² -5x -1 = 0
CoefficientsThe quadratic coefficient is the coefficient of the term with degree 2. The quadratic coefficient is -3.
The linear coefficient is the coefficient of the term with degree 1. The linear coefficient is -5.
The constant coefficient is the coefficient of the term with no variables. The constant is -1.
__
Additional comment
We can make the leading coefficient positive by multiplying the equation by -1. This gives ...
3x² +5x +1 = 0
with quadratic, linear, and constant coefficients 3, 5, 1.
This is a legitimate answer to this question. In the case of linear equations, the "standard form" has the constant on the right side of the equal sign, and the leading coefficient is required to be positive. A negative leading coefficient can sometimes lead to errors (when the sign is overlooked), so having a positive leading coefficient is often preferred.
Given that………………………..
[tex]\sum^{\infty}_{n=1} (a/b)^n=5 \\ \\ =\frac{a/b}{1-\frac{a}{b}}=5 \\ \\ \frac{a}{b-a} =5 \\ \\ \frac{a}{b}=\frac{5}{6}[/tex]
So, we need to find
[tex]\sum^{\infty}_{n=1} n(5/6)^n
[/tex]
Let this sum be S.
Then,
[tex]S=(5/6)+2(5/6)^2 +3(5/6)^3+\cdots \\ \\ \frac{5}{6}S=(5/6)^2 + 2(5/6)^3+\cdots \\ \\ \implies \frac{1}{6}S=(5/6)+(5/6)^2+(5/6)^3+\cdots=5 \\ \\ \implies S=\boxed{30}[/tex]
each side of a 4ft x 6ft rectangular flower bed was lengthened by the same amount. the area of the new flower bed is twice the area of the old one. Find the new dimensions.
The new dimensions of the flower bed are 4√2 and 6√2
How to determine the new dimensions?The dimensions of the initial rectangular flower bed are given as:
Length = 4ft
Width = 6 ft
The area of the new flower bed is twice the area of the old one.
This means that
New Area = Old Area * 2
Substitute the dimensions of the old area in the above equation
New Area = 4 * 6 * 2
Express 2 as √2 * √2
This gives
New Area = 4 * 6 * √2 * √2
Rewrite the above equation as:
New Area = 4√2 * 6√2
The area of a rectangle is
Area = Length * Width
This means that:
Length = 4√2 ft
Width = 6√2 ft
Hence, the new dimensions of the flower bed are 4√2 and 6√2
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Answer: 6x8
Step-by-step explanation:
(4+x)(6+x)=2*24
x^2+10x+24=48
subtract 48 on both sides
x^2+10x-24=0
Solve using the quadratic formula
-10±√(100+96)÷2
simplifies to
-(10±14)÷2 = 2, -12
-12 doesn't work though because the sides can't be negative.
So x=2
To check, add both sides by 2:
2(4x6)=6x8=48
The volume of the square-based pyramid shown is 72 m³. If the area of its
base is 36 m2, what is the height (h) of the pyramid?
base,
Answer:
Height = 6m
Step-by-step explanation:
[tex]\frac{1}{3}[/tex] × 36 = 12
72 ÷ 12 = 6
find the missing length 25 and 65
Answer: 60.
Step-by-step explanation:
Let in a right triangle one of the legs is 25, and the hypotenuse is 65.
Hence, the other leg is: [tex]\sqrt{65^2-25^2}=\sqrt{4225-625}=\sqrt{3600}=60.[/tex]
Please help!!!!! Please explain too, I want to understand it!
Find the slope of the line shown below
Answer:
[tex] \frac{3}{2} [/tex]
Step-by-step explanation:
From the attached photo, we can deduce:
(2,2) as (x1,y1)
(-2,-4) as (x2,y2)
Slope Formula =
[tex] \frac{y1 - y2}{x1 - x2} [/tex]
Now we can substitute these values into the formula to find the slope.
Slope of line =
[tex] \frac{2 - ( - 4)}{2 - ( - 2)} \\ = \frac{2 + 4}{2 + 2} \\ = \frac{6}{4} \\ = \frac{3}{2} (reduced \: to \: simplest \: form)[/tex]
A town is mapped on a coordinate grid. The library is located at point (-3, 9) and the museum is located at
point (8, 2).
Where is the midpoint of the line segment whose endpoints are the library and the museum?
O (-5.5, 5.5)
O (-5.5, 3.5)
O (2.5, 3.5)
O (2.5, 5.5)
Applying the Midpoint Formula, the midpoint of the line segment whose endpoints are the library and the museum is calculated as: D. (2.5, 5.5).
What is the Midpoint Formula?To find the coordinates of the midpoint between two endpoints on a coordinate plane, the midpoint formula that is used is expressed as: M[(x2 + x1)/2, (y2 + y1)/2].
Given the following coordinates:
The library is located at point (-3, 9)
The museum is located at point (8, 2), therefore, let:
(-3, 9) = (x1, y1)
(8, 2) = (x2, y2)
Midpoint = M(x, y)
Substitute the values into M[(x2 + x1)/2, (y2 + y1)/2]:
M(x, y) = [(8 + (-3))/2, (2 + 9)/2]
M(x, y) = (5/2, 11/2)
M(x, y) = (2.5, 5.5)
Thus, the midpoint of the line segment whose endpoints are the library and the museum is calculated as: D. (2.5, 5.5).
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Answer:
Its D (2.5, 5.5) On Edg 2022-23
Step-by-step explanation:
Hope This Helps:))
The ratios of teachers:male students :female students is 2:17:18 the total number of students is 665 find the number of teachers
Answer: 38 teachers.
Step-by-step explanation:
Let the share ratio be x.
So, quantity of teachers = 2x, quantity of male students = 17x,
quantity of female students = 18x.
17x+18x=665
35x=665
Divide the left and right sides of the equation by 35:
х=19.
2x=2*19
2x=38.
Solve using the quadratic formula.
n2 + 2n + 1 = 0
Write your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth.
n = ____
or n = ____
i wasnt ever smart lol please help quick
Answer:
-1
Step-by-step explanation:
n^2+2n = -1
n(n+2) = -1