a) The probability that they actually use drugs, if an employee tests positive for drug use is 69%
b) The probability that a nondrug user will test positive for drug use twice in a row is 0.25%
c) The probability that someone who tests positive twice in a row is not a drug user is 23%
What is Bayes' theorem in probability?Based on past knowledge of circumstances that might be relevant to the event, Bayes' theorem estimates the likelihood of an event.
The theorem explains how a degree of belief, stated as a probability, should logically alter to account for the presence of relevant data using Bayesian probability interpretation.
The question state that
Pr(D) = 0.10
Pr(D') = 0.90
Pr (P/D) = 0.98 ( (2% False negatives means for drug users, 2% will get a negative result, so 98% will get positive result)
Pr(P/D') = 0.05
a) The probability that they actually use drugs, if an employee tests positive for drug use Pr(D/P) = Pr(D)*Pr (P/D) / Pr(D)*Pr (P/D)+Pr(D')*Pr(P/D')
⇒ Pr(D/P) = (0.10*0.98)/(0.10*0.98 + 0.90*0.05)
⇒ Pr(D/P) = 0.098/(0.098+0.045)
⇒ Pr(D/P) = 0.098/0.143
⇒ Pr(D/P) ≈ 0.6853
⇒ Pr(D/P) ≈ 69%
b) The probability that a nondrug user will test positive for drug use twice in a row Pr (P*2/D') = Pr(P/D')*Pr(P/D')
⇒ Pr (P*2/D') = 0.05*0.05
⇒ Pr (P*2/D') = 0.0025
⇒ Pr (P*2/D') = 0.25%
c) The probability that someone who tests positive twice in a row is not a drug user Pr (D'/P*2) = Pr(D')*Pr (P*2/D') / Pr(D')*Pr (P*2/D')+Pr(D)*Pr (P*2/D)
⇒ Pr (D'/P*2) = (0.90*.0.05²)/(0.90*0.05²+0.10*0.98²)
⇒ Pr (D'/P*2) = 0.00225/ 0.00225+0.09604
⇒ Pr (D'/P*2) = 0.00225/0.09829
⇒ Pr (D'/P*2) ≈ 0.2289
⇒ Pr (D'/P*2) ≈ 23%
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find the arc length?
The length of the Arc of the circle is 17.00 units
How to find the length of arc?We should know that the arc of the circle is part of the circumference of the circle cut off by the radii of the circle.
The length of the arc is given by
L=[tex]\frac{A}{360} *2*\pi *r[/tex] where A= angle made by the radii
[tex]\pi[/tex]=3.14, radius =10, L-length of arc = x
Applying the values in the formula we have
x=(x/3*2*3.14*10)÷360
Simplifying the expression
62.8x=1080x
Taking the ratio of both sides we have
62.8x:1080x
= 17.00 units
Therefore the length of the arc is 17.00 units
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Let Sn be the number of lattice paths in the Cartesian plane that start at (0,0), end at (n,n), contain no points above the line y = x, and are composed only of steps (0, 1), (1,0), and (1, 1), i.e. 1, +, and /. So = 1. Consider the generating function S(x):=∑_(n=0)^[infinity]▒〖SnX^n〗. Prove that 1 + (x – 1)S(x) + xS(x)2 = 0.
A formal power series that encodes the coefficients of a sequence of numbers is a generating function.
Here, the coefficients of the sequence {Sₙ} are encoded by the generating function S(x). where Sₙ is the number of lattice paths as described above.
Here we will use the fact that the generating function for a sequence satisfies a functional equation that relates the generating function to the sequence itself to prove that 1 + (x – 1)S(x) + xS(x)² = 0,
Here, the functional equation is
S(x) = 1 + xS(x) + xS(x)²
This equation implies that
The term 1 on the right-hand side corresponds to the fact that to reach the point (0,0) (the starting point), there is exactly one way which is to stay at the starting point.
The term xS(x) corresponds to the fact that by taking a step in the positive x-direction and then following a path to (n-1, n-1) we can reach any point (n,n)
The term xS(x)² corresponds to the fact that by taking a step in the positive x-direction and then following a path to (n-2, n-2), and then taking another step in the positive x-direction and following a path to (n-1, n-1) we can reach any point (n,n)
Thus, 1 + (x – 1)S(x) + xS(x)² = 0. Hence proved.
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What is the equation of this function after it is reflected over the x-axis?
Answer:
Below
Step-by-step explanation:
Multiplying the equation by -1 will flip it around the x - axis
so 3(x-2)^3
sweet-fit jeans has a factory that makes two styles of jeans; super-fit and super-hug. each pair of super-fit takes 20 minutes to cut and 30 minutes to sew and finish. each pair of super-hug takes 20 minutes to cut and 55 minutes to sew and finish. the plant has enough workers to provide at most 18,999 minutes per day for cutting and at most 40,999 minutes per day for sewing and finishing. the profit on each pair of super-fit is $6.50 and
The profit earned per day is $6674.695 at point (449.93,500.02).
Let the number of pair of super-fit jeans = x
Let the number of pair of super-hug jeans = y
We know that x,y≥0.
Total time provided for cutting per day = 18,999 minutes
Total time provided for sewing and finishing per day = 40,999 minutes
Therefore, the inequalities are:
20x+20y ≤ 18,999
30x+55y ≤ 40,999
The shaded region is the feasible region and the point of intersection is (449.93,500.02).
The profit on Super-fit jeans = $6.50
The profit on super-hug jeans = $7.50
To maximise the profit in a day, we maximize z = (6.50 x x) + (7.50 x y)
The maximum profit is obtained at (449.93,500.02).
Therefore, z = (6.50 x 449.93) + (7.50 x 500.02)
z = 2924.545 + 3750.15
z = 6674.695
The profit earned per day is $6674.695.
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the ration of hugs to kisses at the family reunion was 4:1 if there were 148 hugs how many kisses were there
There were 37 kisses at the family reunion. Probability is used to make predictions and inform decision-making.
Probability is a measure of the likelihood of an event occurring. It is expressed as a number between 0 and 1, where 0 indicates that the event is impossible, and 1 indicates that the event is certain to occur.
To find the number of kisses at the family reunion, you can set up the ratio 4 hugs : 1 kiss as a proportion and solve for the number of kisses. Here's how you can do this:
First, cross-multiply to find the total number of hugs and kisses:
4 hugs * 1 kiss = 148 hugs
4 kisses = 148 hugs
Then, divide both sides of the equation by 4 to find the number of kisses:
4 kisses / 4 = 148 hugs / 4
1 kiss = 37 hugs
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Aid!! It's for today
Using theory about stereotypes and different associated thoughts, we have to:
''A girl who has a boy-friend cannot have frie-nds'', this affe-cts us because the thought promotes restrictions on the freedoms of a woman when she has a boy-friend. ''A boy should not show his affection or be tender'', this affects us because it is a thought that promotes stereotypes that do not allow the proper development of people. ¿What is a stereotype?A stereotype, basically, can be defined as an idea that is already pre-established and accepted, it is applied to different individuals.
¡Hope this helped!
Use the pair of functions to find f(g(x)) and g(f(x)) . Simplify your answers.
f(x)=sqrt(x)+8 , g(x)=x^2+1
f(g(x))=
g(f(x))=
The solution to the given composite functions are;
f(g(x)) = √(x² + 1) + 8
g(f(x)) = [√(x) + 8]² + 1
How to solve composite functions?
Composite functions are usually formed when one function is used as the input of another function.
We are given the functions;
f(x) = √(x) + 8
g(x) = x² + 1
1) f(g(x)); This simply means we will put the entire g(x) function for x in f(x) to get;
f(g(x)) = √(x² + 1) + 8
2) g(f(x)); This simply means we will put the entire f(x) function for x in g(x) to get; g(f(x)) = [√(x) + 8]² + 1
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-3x^2-6x+24 factor this equation by any means
Step-by-step explanation:
-3x² - 6x + 24
this is an expression, not an equation.
for an equation this would have to look like e.g.
-3x² - 6x + 24 = 0
anyway, yes, we can factor this expression :
-3x² - 6x + 24 = -3(x² + 2x - 8) = -3(x + 4)(x - 2)
why ?
x² + 2x - 8 corresponds to
(x + a)(x + b) = x² + (a+b)x + ab
so which factors a and b multiply to ab = -8 and add to (a+b) = 2 ?
-8 has the factors
4, -2
-4, 2
8, -1
-8, 1
only (4, -2) covers the both criteria.
therefore, the correct factorization is
-3(x + 4)(x - 2)
an fda representative randomly selects 8 packages of ground chuck from a grocery store and measures the fat content (as a percent) of each package. assume that the fat contents have an approximately normal distribution. the resulting measurements are given below.fat contents (%)12 15 16 1315 13 15 13step 1 of 2 : calculate the sample mean and the sample standard deviation of the fat contents. round your answers to two decimal places, if necessary.
We calculated sample mean 14 and standard deviation 1.32
What is sample mean?A sample mean refers to the average of all values included in the data list.
How to calculate sample mean and standard deviation from the list of data?When we have a list of data set, we can calculate the mean value of the data set by adding all the values and divided by the amount of data.
We are given, 8 packages of ground chuck
number of samples, N = 8
fat contents (%) for 8 packages, X= 12, 15, 16, 13, 15, 13, 15, 13
Sum of X= ∑X= 112
sample mean= sum of all data values/ number of data items in the sample
X= ∑X/N
sample mean X = 112/8 =14
we calculate X² for 8 sample = 144, 225, 256, 169, 225, 169, 225, 169
∑X² = 1582
standard deviation is calculated by using the formula bellow
√[∑X²/N-(∑X/N)²] = √[1582/8-(112/8)²]
standard deviation = 1.32
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use the factor theorem to determine whether is a factor of . specifically, evaluate at the proper value, and then determine whether is a factor.
According to factor theorem, if f(x) is a polynomial of degree n ≥ 1 and 'a' is any real number, then, (x-a) is a factor of f(x), if f(a)=0.
The factor theorem states
[tex]$(x-a)$ is a factor of $f(x) \Leftrightarrow f(a)=0$[/tex]
f(x)=4 x^3-3 x^2-8 x+4
we have (x-2)[tex]\Rightarrow a=2[/tex]
& [tex]f(2)=4 \times 2^3-3 \times 2^2-8 \times 2+4 \\& f(2)=4 \times 8-3 \times 4-16+4 \\& f(2)=32-12-16+4 \\& f(2)=8 \neq 0\end{aligned}[/tex]
[tex]$\therefore x-2$ is not a factor of $4 x^3-3 x^2-8 x+4$[/tex]
however by the remainder theorem when
[tex]$f(x)=4 x^3-3 x^2-8 x+4$[/tex] is divided by [tex]$(x-2)$[/tex] the remainder is 8
the factor theorem being a special case of the remainder theorem
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Answer:
Step-by-step explanation:
Use the factor Theorem to determine whether x =3 is a factor of P (x)=x-2x2-6. Specifically, evaluate P at the proper value, and then determine whether X-3 is a factor. P (UI) - 0 P 0 1 - 3 is a factor of P (*) O +- 3 is not a factor of P (x) This problem has been solved!
Find the length of the triangle.
The height of the triangle that has an area of 7 ⁷/₈ square cm will be 3 cm.
What is the area of the triangle?The polygonal shape of a triangle has a number of sides and three independent variables. Angles in the triangle add up to 180°.
Assume 'h' is the height of the triangle and 'b' be the base of the triangle.
Then the area of the triangle is given as,
A = (1/2) × h·b
The area of the triangle is 7 ⁷/₈ cm² and the base length of the triangle is 5 ¹/₄ cm.
Convert the mixed fraction number into a fraction number. Then we have
7 ⁷/₈ = 63/8
5 ¹/₄ = 21/4
The height of the triangle is given as,
63/8 = (1/2) x h x (21/4)
Simplify the equation, then we have
63/8 = (1/2) x h x (21/4)
63/8 = (21/8)h
21h = 63
h = 3 cm
The height of the triangle that has an area of 7 ⁷/₈ square cm will be 3 cm.
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28. For any of the vehicles listed in the table,
how many days can you rent the vehicle
before it would be less expensive to rent
for the week?
Answer:
small car: 2
medium car: 2
luxury car: 2
Small van: 2
Large van: 3
Step-by-step explanation:
just multiply the amount per day by numbers increasing from 1 till you get a number that is larger than the week. I swear whoever made this car rental will not be in business much longer lol.
For 2 days, vehicle can be given to rent before it would be less expensive to rent.
What is algebra?Algebra is a study of mathematical expressions, in which numbers and quantities are represented in formulas and equations by letters and other universal symbols.
Given that,
Rent for small car,
For 1 day = $100.
For 1 week = $250
The maximum days in which small car could be given to rent,
= 250 / 100 = 2.5 ≅ 2 days.
Similarly, for medium car = 290 / 110 = 2.7 ≅ 2 days.
For luxury car = 325 / 120 = 2.54 ≅ 2 days.
For small van = 350 / 150 = 2.3 ≅ 2 days.
And for large can = 390 / 170 = 2.28 ≅ 2 days.
Each car can be rented for 2 days before it would be less expensive for the week.
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Match the inequality on the left with the appropriate graph on the right
Answer:
i got the last two but i am confused on the first two
Step-by-step explanation:
good luck
have fun
bye
If you flip three coins, the probability of getting three heads is 0.125. Which of the following statements follows from this?
answer choices
O If you flip three coins 1000 times, you will get three heads exactly 125 times.
O If you flip 3 coins 10 times and never get three heads, the probability of getting three heads in the next set of 10 flips is slightly greater than 0.125.
O If you have 20 sets of three coin flips, then at least one set of flips will be three heads.
O If you flip 3 coins 5000 times, the percentage of time you get three heads will be very close 12.5%.
O If you get 3 heads two times in a row, the probability of getting 3 heads again on the next toss of 3 coins is nearly zero.
Using the given provided probability value of getting three heads, The statement which best follow the given condition is If you flip 3 coins 5000 times, the percentage of time you get three heads will be very close to 12.5%.
What do you mean by probability?
The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.
According to the given question:
Assume you have a fair coin, which means it will likely land tails up 50% of the time and heads up 50% of the time. Let's say you flip it three times, each time independently. What is the likelihood that it will land heads up first, followed by a tails up landing?
The solution is 1/8, or 12.5%.
coin flipped = 3 times.
probability of getting three heads = 0.125
Since, This probability explains the chances of landing three heads which is 0.125 which in terms of percentage is 12.5% .
So, The statement is If you flip 3 coins 5000 times, the percentage of time you get three heads will be very close 12.5%.
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Please help will mark Brainly
Answer:
120 children
Step-by-step explanation:
c=children
a=adults
c+a=237
1.75c+2a=444
(c+a=237)*2 ==> make a in the equation equal to 2a
2c+2a=474
- (1.75c+2a=444) ==> eliminate a from the equation
2c-1.75c + 2a-2a = 474-444
2.00c-1.75c = 30
0.25c = 30
4 * 0.25c = 4 * 30 ==> remove decimals by multiplying each side by 4
c = 120 children
tara has 5/8 gallons of glue. She uses 2/5 of the glue to make blue slime, 1/5 of the glue to make green slime, and the rest of the glue to make purple slime. How many gallons of glue does tara use to make purple slime
Answer:
We can say that he used a total of 5/8 gallons of glue
let x - glue to make purple slime
5/8 = 2/5 + 1/5 + x
5/8 = 3/5 + x (LCD of 5 and 8 is 40)
25/40 = 24/40 + x
25/40 - 24/40 = 24/40 - 24/40 + x (subtract 24/40 both sides)
x = 1/40
CHECKING:
5/8 = 2/5 + 1/5 + 1/40
5/8 = 3/5 + 1/40
25/40 = 24/40 + 1/40
25/40 = 25/40
Therefore, the glue to make purple slime is 1/40 gallons.
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Step-by-step explanation:
heart and star pls <3 brainliest will be appreciated <3(っ◔◡◔)っ -{ elyna s }-in non-degenerate cases of the logistic regression model, the maximum likelihood estimator always exists and is always unique. assume the design matrix is of full rank.
For regression and classification predictive modeling, the Maximum Likelihood Estimation framework can be used as a foundation for estimating the parameters of numerous machine learning models.
The logistic regression model is a part of this.
Is MLE always present?For species distribution models, maximum likelihood is a common parameter estimation method. A popular species distribution model, the Poisson point process, does not always have maximum likelihood estimates.
In logistic regression, how is the maximum likelihood determined?At the end of the day, the most extreme probability gauge for p is the mean of the y variable from the N draws. According to the result, p=n1/N=y is the value of p that maximizes the above log-likelihood function.
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Question 1 of 10
For the x-values 1,2,3, and so on, the y-values of a function form a geometric sequence that increases in value. What type of function is it?
A. Increasing linear
B. Decreasing linear
C. Exponential growth
D. Exponential decay
The type of function is it is C . Exponential growth .
Given :
For the x-values 1,2,3, and so on, the y-values of a function form a geometric sequence that increases in value .
If for values of x values of y increases and forms a geometric sequence then it would be an exponential growth function because geometric sequence is an exponential function and since, it is increasing hence, an exponential growth.
Option B is incorrect because because y is not decreasing
Option C and D are incorrect because geometric sequence can never be linear since, it gives common ratio.
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The price of an item has been reduced by 95%. The original price was $65
The new price of the item is equivalent to $3.25.
What is percentage?In mathematics, a percentage is a number or ratio that represents a fraction of 100. A percentage is a dimensionless number i.e. it has no unit of measurement.Given is that the price of an item has been reduced by 95%. The original price was $65
Assume the new price to be $[x]. So, we can write -
x = 65 - {95% of 65}
x = 65 - {(95/100) x 65}
x = 65 - {6175/100}
x = 65 - 61.75
x = 3.25
Therefore, the new price of the item is equivalent to $3.25.
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A rock falls from a tower that is 352 feet high. As it is falling, its height is given by the formula h=352-16t^(2). How many seconds (in tenths ) will it take for the rock to hit the ground (h)=(0)?
The rock will take 10.25 seconds to hit the ground, as the amount determined by the formula h=352-16t^(2).
The given equation is h=352-16t^(2). This equation can be used to calculate the time it will take for a rock to hit the ground after it has been dropped from a tower that is 352 feet high. The equation states that the rock's height (h) is equal to 352 minus 16 times the square of the time (t). To find the time it will take for the rock to hit the ground (h=0), we can rearrange the equation to solve for t. The rearranged equation is t=sqrt((352-0)/16), which simplifies to t=10.25. This means that the rock will take 10.25 seconds to hit the ground. This can also be expressed in tenths of a second as 102.5, which is the same as 10.25 seconds.
t= sqrt((352-0)/16)
t= sqrt(22)/4
t= 10.25
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help meeeee last question
The number of cubical boxes that can contain in the rectangular box is 36.
What is the volume of a cuboid?Volume is defined as the space occupied by an object.
The volume of a cuboid is (length×width×height).
Given, Length of the rectangle box is 16 cm and the width of the box is
12 cm.
We know the volume of a cube is (side)³.
Therefore, given that the volume of a cubical 64 cm³ and we know (4)³ is 64.
Hence the height of the rectangular box is 3 layers so (4×3) = 12 cm
So, the volume of the rectangular box is (16×12×12) cm³ = 2304 cm³.
Therefore, The maximum number of boxes that can be contained is
= (2304/64)
= 36.
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Solve the following equation for x
You bought 12 red apples and 15 green apples to make some pies.
What is the ratio of the number of red apples to the total number of apples?
Answer:
4.9
Step-by-step explanation:
Review of logarithms (logs)
For each of the following equations, write down the
name of the operation that occurs in the equation and
the name of the inverse operation that helps you
solve the equation.
Equation
x+10=25
2x=28
4²=64
Name of operation
Name of inverse
operation
The operations, along with their inverses are given as follows:
x + 10 = 25: Operation of addition, the inverse is of subtraction.2x = 28: Operation of multiplication, the inverse is the division.4^x = 64: The operation is the exponential, the inverse is the logarithm.How to solve the operations?The operations are solved applying the inverse operations.
The first operation is solved as follows:
x + 10 = 25
x = 25 - 10
x = 15.
Hence the addition operation was solved applying the subtraction operation, which is the inverse operation of the addition.
The second operation is solved as follows:
2x = 28
x = 28/2
x = 14.
Hence the multiplication operation was solved applying the division operation, which is the inverse operation of the multiplication.
The third operation is given as follows:
4^x = 64.
log4(4^x) = log4(64)
x = 3. (as 4³ = 64, hence log4(64) = 3).
Hence the exponential operation was solved applying the logarithm operation, which is the inverse operation of the exponential.
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Let X1,82 be independent random variables representing lifetimes (in hours) of two key components of a device that fails when and only when both components fail. Say each Xi has an exponential distribution with mean 1000. Let Y1 = min(X1,X2) and Y2 = max(X1,X2), so that the space of Y1,Y2 is 0 < y1 < y2 <. (a) Find G(y1, y2) = P(Y1 = 71,Y2 = y2).
To find the probability that Y1 = 71 and Y2 = y2, we can write G(y1, y2) = P(Y1 = 71, Y2 = y2).
To find the probability that Y1 = 71 and Y2 = y2, we need to consider the possible values of X1 and X2 that could lead to these values of Y1 and Y2. The probability density functions (PDFs) of an exponential distribution with mean 1000 is f(x) = 1/1000 * e^(-x/1000). Therefore, the probability of this event is
P(X1 = 71, X2 = y2) = f(71) * f(y2) = 1/1000 * e^(-71/1000) * 1/1000 * e^(-y2/1000).Another possibility is that X1 = y2 and X2 = 71. The probability of this event is
P(X1 = y2, X2 = 71) = f(y2) * f(71) = 1/1000 * e^(-y2/1000) * 1/1000 * e^(-71/1000).Since these two events are mutually exclusive and exhaust all possible ways that Y1 can equal 71 and Y2 can equal y2, the probability of these events occurring is the sum of these probabilities. Therefore,
G(y1, y2) = P(Y1 = 71, Y2 = y2) = P(X1 = 71, X2 = y2) + P(X1 = y2, X2 = 71) = (1/1000 * e^(-71/1000) * 1/1000 * e^(-y2/1000)) + (1/1000 * e^(-y2/1000) * 1/1000 * e^(-71/1000)) = 2/1000^2 * e^(-(71 + y2)/1000).Note that this expression is only valid when 0 < 71 < y2 < ∞ since these are the conditions under which Y1 can equal 71 and Y2 can equal y2.
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F.ds = 4 pi, F.ds = 9 pi Use Green's Theorem to determine the circulation of F around C1, assuming that curl (F) = 2 on the shaded region. F. ds =
F.ds = 4 pi, F.ds = 9 pi
circulation of F around C1, assuming that curl (F) = 2 on the shaded region. F. ds =
c1-9 (52-12-12) π+9л+4л=(207+12)л=219л
Green's Theorem =Green's Theorem states that a line integral around the boundary of the plane region D can be computed as the double integral over the region D. where the path integral is traversed anti-clockwise. Green's Theorem Area
Therefore, the line integral defined by Green's theorem gives the area of the closed curve. Therefore, we can write the area formulas as: A = − ∫ c y d x. A = ∫ c x d y. Green's theorem relates a line integral around a simply closed plane curve C and a double integral over the region enclosed by C. The theorem is useful because it allows us to translate difficult line integrals into more simple double integrals, or difficult double integrals into more simple line integrals.
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write an equation of the line that is parallel to the graph of 3x-5=y and whose y intercept is (0,7).
Parallel lines always have the same slope and different y-intercepts.
Slope-intercept form: [tex]y=mx+b[/tex]
m = slopeb = y-interceptSolving the QuestionWe're given:
[tex]3x-5=y[/tex]b = (0,7)We can see that in [tex]y=3x-5[/tex] that the slope of the line is 3. Parallel lines have the same slope, so therefore:
m = 3
We're also given that the y-intercept is (0,7).
b = 7
Plug m and b into slope-intercept form:
[tex]y=3x+7[/tex]
Answer[tex]y=3x+7[/tex]
A marina is in the shape of a coordinate grid. Boat A is docked at (4.2, −2) and Boat B is docked at (−5.2, −2). The boats are ____ units apart. (3 points)
6.2
7.2
9.4
13.4
Answer:
so (-5.2,-2) and (4.2,-2) are 9.4 units apart away from each other
Step-by-step explanation:
so (4.2,-2) and (-5.2,-2) add together and get 9.4
Last year the depth of the river was 4.2 feet deep. This year it dropped 24%. Find the depth of the river this year to cross it.
The depth of the river is 3.192 feet.
How to illustrate the percentage?A percentage is a value or ratio that may be stated as a fraction of 100. If we need to calculate a percentage of a number, we should divide it's entirety and then multiply it by 100.
The percentage therefore refers to a component per hundred. Per 100 is what the word percent means. It is represented by %.
Since last year the depth of the river was 4.2 feet deep and year it dropped 24%. The depth will be:
= 4.2 - (24% × 4.2)
= 4.2 - 1.008
= 3.192 feet
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Timmy has a collection of 95 coins consisting of dimes and nickels in his bank, The total value of his bank is $6.50. How many dimes are in his collection? How many nickels are in his collection?
Timmy has a collection of 95 coins consisting of dimes and nickels in his bank, The total value of his bank is $6.50. We can infer that he has 60 nickels and 35 dimes.
Define equation.In algebra, an equation is a declaration of equivalence that includes one or more variables or unknowable quantities.
Given,
Timmy has a collection of 95 coins consisting of dimes and nickels in his bank, The total value of his bank is $6.50.
Set d and n to the appropriate numbers.
Timmy has 95 coins in total, all of which are dimes and nickels, as far as we know.
Equation,
So d + n = 95
His bank is worth a total of $6.50.
A nickel is worth $0.05, while a dime is worth $0.10.
So
0.10d + 0.05n = $6.50
Take note that we have just produced an equation system that we can solve.
The two equations exist.
D + n = 95
and
0.10d + 0.05n = 6.50.
The replacement approach is probably going to be the simplest way to solve this problem out of all the options available to us.
First, we'll want to change the second equation's terms so that one of the variables is defined.
d+ n = 95
Take d off on both sides.
n = 95 - d
Now, let's define "n."
After defining one of the variables, we can now enter (or replace) its value in the other equation. After replacing it, we can find a solution for the other variable.
0.10d + 0.05n = 6.50
n = 95 - d
0.10d + 0.05(95 - d) = 6.50
We now determine d.
0.10d + 0.05(95 - d) = 6.50
distribution of the 0.05 in step 1
0.05 × 95 = 4.75
and
0.05 × -d = -0.05d
0.10d + 4.75 - 0.05d = 6.50
Step 2: Add like terms together (0.10 - 0.05) to get 0.05
0.05d + 4.75 = 6.50
step 3: Take 4.75 off of each side.
0.05d = 1.75
step 4: Subtract 0.05 from both sides.
0.05d / 0.05 = d and 1.75 / 0.05 = 35
d = 35
Now that we know the value of one variable, we can use it to solve for the second variable by plugging it into one of the equations ( note that the equation that we use does not matter, we will acquire the same answer )
d + n = 95
d = 35
35 + n = 95
Take 35 off both sides.
n = 60
We can infer that he has 60 nickels and 35 dimes.
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