(a) The probability of getting a face card or a number card is:P(face card or number card) = (12/52) + (40/52) = 52/52 = 1
(b) The probability of drawing a black and a Queen is:P(black and a Queen) = (26/52) × (2/26) = 2/52 = 1/26
(c) The probability of drawing a black and a face card is:P(black and a face card) = (26/52) × (6/26) = 6/52 = 3/26.
(d) The probability of drawing a Queen and a 3 is 0.
(e) The probability of drawing a black or a 3 is:P(black or 3) = (26/52) + (4/52) - (2/52) = 28/52 = 7/13.
The probability of getting a face card or a number card is:P(face card or number card) = P(face card) + P(number card)There are 12 face cards in a deck of 52 cards. There are 4 Kings, 4 Queens, and 4 Jacks.There are 52 - 12 = 40 cards which are not face cards. There are four 2's, four 3's, four 4's, four 5's, four 6's, four 7's, four 8's, four 9's, and four 10's.Therefore, the probability of getting a face card or a number card is:P(face card or number card) = (12/52) + (40/52) = 52/52 = 1
The probability of drawing a black and a Queen is:P(black and a Queen) = P(black) × P(Queen given black)The probability of drawing a black card is 26/52 since there are 26 black cards in a deck of 52 cards. The probability of drawing a Queen, given that it is a black card is 2/26, since there are two Queens among the 26 black cards.Therefore, the probability of drawing a black and a Queen is:P(black and a Queen) = (26/52) × (2/26) = 2/52 = 1/26
The probability of drawing a black and a face card is:P(black and a face card) = P(black) × P(face card given black)The probability of drawing a black card is 26/52 since there are 26 black cards in a deck of 52 cards. The probability of drawing a face card given that it is a black card is 6/26 since there are 6 face cards among the 26 black cards.Therefore, the probability of drawing a black and a face card is:P(black and a face card) = (26/52) × (6/26) = 6/52 = 3/26
The probability of drawing a Queen and a 3 is:P(Queen and 3) = 0Since there are no 3's among the Queens, the probability of drawing a Queen and a 3 is 0.
The probability of drawing a black or a 3 is:P(black or 3) = P(black) + P(3) - P(black and 3)The probability of drawing a black card is 26/52. The probability of drawing a 3 is 4/52. There are two 3's which are black cards.Therefore, the probability of drawing a black or a 3 is:P(black or 3) = (26/52) + (4/52) - (2/52) = 28/52 = 7/13.
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Simplify: 2x^3+3y^3+5x^3+4y
The simplified fοrm οf the expressiοn [tex]2x^3 + 3y^3 + 5x^3 + 4y is 7x^3 + 3y^3 + 4y.[/tex]
What is an expressiοn?Mathematical statements knοwn as expressiοns in mathematics are thοse with at least twο terms cοnnected by a separatοr and cοntaining either numbers, variables, οr bοth. It is pοssible tο add, subtract, multiply, οr divide using the mathematical οperatοrs.
Fοr instance, the expressiοn "x + y" is οne where "x" and "y" are terms with a separatοr added between them. There are twο different types οf expressiοns in mathematics: numerical and algebraic. Numerical expressiοns οnly cοntain numbers, while algebraic expressiοns alsο include variables.
Tο simplify the expressiοn [tex]2x^3 + 3y^3 + 5x^3 + 4y,[/tex] we can cοmbine the like terms:
[tex]2x^3 + 5x^3 + 3y^3 + 4y[/tex]
[tex]= (2 + 5)x^3 + (3)y^3 + (4)y[/tex]
[tex]= 7x^3 + 3y^3 + 4y[/tex]
Therefοre, the simplified fοrm οf the expressiοn
[tex]2x^3 + 3y^3 + 5x^3 + 4y is 7x^3 + 3y^3 + 4y[/tex].
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Calculate the area of the region defined by the simultaneous inequalities y ≥ x-4,
y ≤ 10, and 5 ≤ x+y.
Answer: To solve this problem, we need to graph the three inequalities and find the overlapping region.
First, let's graph the inequality y ≥ x - 4. We can start by graphing the line y = x - 4, which has a y-intercept of -4 and a slope of 1.
|
10| + +
| + +
| +
|+
|
|
| +
| +
| +
| +
0|-----------------
0 1 2 3 4 5
Since we want the region where y is greater than or equal to x - 4, we shade the area above the line.
Next, let's graph the inequality y ≤ 10. This is a horizontal line passing through y = 10.
|
10| +----+
| + +
| +
|+
|
|
|
|
|
|
0|-----------------
0 1 2 3 4 5
Since we want the region where y is less than or equal to 10, we shade the area below the line.
Finally, let's graph the inequality 5 ≤ x + y. This is a line with a y-intercept of 5 and a slope of -1.
|
10| +----+
| + | +
| + |
|+ |
| |
| |
| |
| |
| |
| +
0|-----------------
0 1 2 3 4 5
Since we want the region where x + y is greater than or equal to 5, we shade the area above the line.
Now we can find the overlapping region of the three shaded areas:
|
10| +----+
| + | +
| + |
|+ |
| |
| |
| +
| +
| +
|+
0|-----------------
0 1 2 3 4 5
The region is a triangle with vertices at (0, 4), (1, 5), and (5, 0).
To find the area of the triangle, we can use the formula for the area of a triangle:
Area = (1/2) * base * height
The base of the triangle is the distance between the points (0, 4) and (5, 0), which is 5.
The height of the triangle is the distance between the point (1, 5) and the line 5 = x + y. We can find the equation of the line perpendicular to 5 = x + y and passing through (1, 5). This line has a slope of 1 and passes through (1, 5), so its equation is y = x + 4. We can find the intersection of this line and the line 5 = x + y by solving the system of equations:
y = x + 4
y = 5 - x
Substituting y = x + 4 into the second equation, we get:
x + 4 = 5 - x
Solving for x, we get:
x = 1
Step-by-step explanation:
Make x the subject of the formula a/b = 2x/x+5
When x is the subject of the formula a/b = 2x/x+5, the value of x = 5a/(2b - a).
What are variables?The alphabetic letter that conveys a numerical value or a number is known as a variable in mathematics. A variable is used to represent an unknown quantity in algebraic equations.
Any alphabet from a to z can be used for these variables. Most frequently, the variables "a," "b," "c," "x," "y," and "z" are utilised in equations. By performing mathematical operations on variables as if they were express numbers, one is able to handle a variety of problems in a single computation. A quadratic recipe is a common example that demonstrates how to explain each quadratic condition by simply substituting the numerical estimates of the condition's coefficients for the variables that correspond to it.
The given formula is:
a/b = 2x/x+5
To make x the subject of the formula we have to isolate the value of x.
Using cross multiplication we have:
a(x + 5) = b(2x)
ax + 5a = 2bx
5a = 2bx - ax
5a = x (2b - a)
5a/(2b - a) = x
Hence, when x is the subject of the formula a/b = 2x/x+5, the value of x = 5a/(2b - a).
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Sketch the graph of 2x²+4x
We can sketch the graph of 2x²+4x.
We can start by dissecting the equation and identifying its main components before drawing the graph of 2x²+4x.
The formula reads as y = ax² + bx + c, where a = 2, b = 4, and c = 0. It is a quadratic function.
The upward opening of the graph is indicated by the positive coefficient of x2 (a). By applying the formula -b/2a, which in this case equals -4/4 = -1, one can determine the vertex of the parabola.
Hence, the parabola's vertex is located at (-1,0).
By setting y = 0 and solving for x, we may get the graph's x-intercepts:
0 = 2x² + 4x
0 = 2x(x + 2)
Hence the x-intercepts are at x = 0 and x = -2.
We can set x = 0 to determine the graph's y-intercept:
y = 2(0)² + 4(0) = 0
The y-intercept is therefore at (0,0).
Using this knowledge, we can draw the 2x²+4x graph as follows:
Vertex located at (-1,0).
x = 0 and x = -2 are the two x-intercepts.
Y-intercept is located at (0,0).
The graph has a "U"-shaped opening that faces upward.
The graph's basic drawing is shown below:
|
|
|
|
| * *
| |
| |
| |
_____|______________
-2 0 2
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Please Show All Work!!
1.)You are going to eat a slice of pizza, where the central angle of your slice is 34° and the radius of your slice is 8".
What is the angle in radians? Use 3.14 for pi
A.) .72 radians
B.) 2.3 radians
C.) .59 radians
D.) .48 radians
2.) Calculate the area of the sector (the slice you eat). Round your answer to the nearest tenth. Use 3.14 for pi.
Area = n/360 * π r^2
n is your central angle in degrees.
3.) Calculate the arc length of the pizza you have eaten. Use 3.14 for pi. Ø is the angle in degrees
Arc Length = 2πr * Ø/360
To find the angle in radians, we need to convert the given angle from degrees to radians. We know that 180 degrees = π radians.
So,
34 degrees = (34/180) * π radians
= 0.1885 * 3.14
= 0.591 radians
Therefore, the answer is (C) 0.59 radians.
The area of the sector (the slice you eat) can be calculated using the formula:
Area = (n/360) * πr^2
where n is the central angle in degrees, and r is the radius of the slice.
Plugging in the given values, we get:
Area = (34/360) * 3.14 * 8^2
= 0.1 * 3.14 * 64
= 20.096 square inches
Rounding to the nearest tenth, the answer is 20.1 square inches.
The arc length of the pizza you have eaten can be calculated using the formula:
Arc Length = (2πr * Ø)/360
where Ø is the angle in degrees, and r is the radius of the slice.
Plugging in the given values, we get:
Arc Length = (2 * 3.14 * 8 * 34)/360
= 4.776 inches
Therefore, the answer is 4.776 inches.
Patricio deposit $500 in a savings account theat pays 1. 5% simple interest. He does not withdraw any money from the account, and he makes no other deposit. How much money does Patricio have in the savings account after 5 years? The formula for simple interest is I=prt
According to simple interest, Patricio will have $537.50 in his savings account after 5 years.
To calculate the amount of money Patricio will have in his savings account after 5 years, we can use the formula for simple interest, which is I = prt. "I" stands for the amount of interest earned, "p" stands for the principal amount deposited, "r" stands for the interest rate per year (as a decimal), and "t" stands for the time period in years.
In this case, the principal amount (p) is $500, the interest rate (r) is 1.5% or 0.015 as a decimal, and the time period (t) is 5 years. Using the formula I = prt, we can calculate the amount of interest earned over 5 years:
I = prt
I = $500 x 0.015 x 5
I = $37.50
So, Patricio will earn $37.50 in simple interest over 5 years. To find out the total amount of money he will have in his savings account after 5 years, we simply add the interest earned to the principal amount:
Total amount = Principal amount + Interest earned
Total amount = $500 + $37.50
Total amount = $537.50
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Martha likes to knit hats and mittens for friends and family. Last fall, she knitted 3 hats and 3
pairs of mittens, which took a total of 51 hours. This fall, she knitted 3 hats and 5 pairs of
mittens, which took a total of 77 hours. If each hat takes the same amount of time and each
pair of mittens takes the same time, how long does it take Martha to knit each item?
hours to knit a pair of mittens.
It takes Martha
hours to knit a hat and
It takes Martha `4` hours to knit each hat and `13` hours to knit each pair of mittens.
What is meant by hours?
Hours are a unit of time used to measure the duration of an event or activity. An hour is equal to 60 minutes or 3,600 seconds. It is often used to indicate the time of day or to schedule appointments or events.
What is a pair?
A pair is a set of two things that go together or belong together, like a pair of shoes, socks, or gloves. It can also refer to a pair, a duo, or a twosome.
According to the given question
Let's assume that each hat takes `h` hours to knit and each pair of mittens takes `m` hours to knit.
From the given information, we know that:
- 3 hats and 3 pairs of mittens took a total of 51 hours. This means that 3h + 3m = 51.
- 3 hats and 5 pairs of mittens took a total of 77 hours. This means that 3h + 5m = 77.
We can use these two equations to solve for `h` and `m`.
First, let's solve for `h` by multiplying the first equation by 5 and the second equation by 3, and then subtracting the second equation from the first:
15h + 15m = 255
9h + 15m = 231
-----------------
6h = 24
h = 4
So each hat takes Martha `4` hours to knit.
Now we can use either of the original equations to solve for `m`. Let's use the first one:
3h + 3m = 51
3(4) + 3m = 51
12 + 3m = 51
3m = 39
m = 13
So each pair of mittens takes Martha `13` hours to knit.
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5. Jack has a 35-foot ladder leaning against the side of his house. If the bottom of the ladder is 21 feet away from his house, how many feet above the ground does the ladder touch the house?
Therefore, the ladder touches the house at a height of 28 feet above the ground.
What is triangle?A triangle is a geometric shape that consists of three straight sides and three angles. It is a polygon with three sides. The sides of a triangle are connected by its vertices or corners. The triangle is one of the simplest and most fundamental shapes in geometry, and it has many important properties and applications. Triangles have many practical applications in everyday life and in various fields, such as architecture, engineering, and physics. The study of triangles and their properties is an important part of mathematics and geometry.
Here,
We can use the Pythagorean theorem to solve this problem. The Pythagorean theorem states that in a right triangle, the sum of the squares of the lengths of the legs (the two shorter sides) is equal to the square of the length of the hypotenuse (the longest side, which is opposite the right angle). In this problem, the ladder, the side of the house, and the ground form a right triangle. The ladder is the hypotenuse, the distance from the house to the ladder is one leg, and the height we want to find is the other leg.
Let x be the height above the ground where the ladder touches the house. Then, using the Pythagorean theorem, we have:
x² + 21² = 35²
Simplifying and solving for x, we get:
x² + 441 = 1225
x² = 784
x = 28
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i put $1000 in an account from high school graduation gifts, and $2000 into the same account after my college graduation 4 years later. five years after i started my first job how much is in the account if it earns 4% per year?
By using the concept of compound interest, the total amount is $4063.27.
We have,
The amount that was deposited during high school graduation = $1000
The amount that was deposited during college graduation after 4 years = $2000
The total number of years elapsed = 5 years
The interest rate per annum (p.a.) = 4%
The simple Interest (SI) formula is given by,
SI = P × r × t
where, P = Principal amount
r = Rate of interest
t = Time period
Compound Interest (CI) formula is given by,
CI = P (1 + (r/n))^(nt)
Where P = Principal amount
r = Rate of interest
t = Time period
n = Number of times interest is compounded
For the total amount using compound interest.
Total amount (A) = Principal + Compound interest
A = P + CI
Implying it to our data, we get the following.
For $1000 that was deposited during high school graduation,
For 5 years, n = 1, t = 5 years, r = 4% p.a.
CI = 1000[1+(4/100)]^(1×5)
CI = 1000[1+(1/25)]^5
CI = 1000×(26/25)^5
CI = 1000×1.21665
CI = $1216.65
For $2000 that was deposited during college graduation after 4 years,
The total number of years elapsed = 5 years + 4 years = 9 years
n = 1, t = 9 years, r = 4% p.a.
CI = 2000[1+(4/100)]^(1×9)
CI = 2000[1+(1/25)]^9
CI = 2000×(26/25)^9
CI = 2000×1.4233
CI = $2846.62
Therefore, the total amount (A) is $1216.65 + $2846.62 ⇒ $4063.27.
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A company has two manufacturing plants with daily production levels of 8x+15 items and 3x-7 items, respectively. The first plant produces how many more items daily than the second plant?
Therefore , the solution of the given problem of equation comes out to be the first plant makes 5x + 22 more items per day.
How do equations work?
Mathematical formulas frequently employ same variable word to guarantee agreement between two claims. Many academic numbers are shown to be equal using mathematical expression, also known as assertions. In this case, the normalise method adds b + 6 to employ the example of y + 6 rather than splitting 12 into two parts. It is possible to determine the length of the line and the quantity of connections between each sign's constituents. The significance of a symbol usually contradicts itself.
Here,
The first plant cranks out 8x + 15 items every day, while the second cranks out 3x - 7 items every day. By deducting the daily output of the second plant from the daily output of the first plant, we can determine how many more items the first plant creates than the second plant:
=> (8x + 15) - (3x - 7) (3x - 7)
If we condense this phrase, we get:
=> 8x + 15 - 3x + 7
Combining related words gives us:
=> 5x + 22
Therefore, compared to the second plant, the first plant makes 5x + 22 more items per day.
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The diameter of two circle are 3. 5 and 4. 2. Find the ratio of their area
Answer:The ratio of the area of the small circle to that of the bigger circle is 25:36.
Step-by-step explanation:
35 of the students in the band play the flute, and another 15 play the clarinet. What fraction of the students in the band plays either the flute or the clarinet? Responses
As a result, we are unable to further simplify the phrase. The final solution is (35 + 15 - x) / N, where x is the proportion of students who are proficient in both instruments.
We must first ascertain the total number of students in the band in order to calculate the percentage of those who play the flute or clarinet. Let's assume that N kids make up the entire band.
The total number of pupils who play either the clarinet or the flute is then calculated as follows: 35 + 15 - x
The percentage of band students who play either the flute or the clarinet is now (35 + 15 - x) / N, and we need to know what x's value is. Nevertheless, the problem does not provide this information. As a result, we are unable to further simplify the phrase. The final solution is (35 + 15 - x) / N, where x is the proportion of students who are proficient in both instruments.
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If c is 6x6 and the equation cx = v is consistent for every v in r^6, is it possible that for some v, the equation cx = v has more than one solution?
It is nοt pοssible that fοr sοme v, the equatiοn cx = v has mοre than οne sοlutiοn if c is invertible.
What is the inverse?Inverse οperatiοns are οppοsite οperatiοns that undο each οther. Fοr example, 5 ✕ 2 = 10 and 10 ÷ 2 = 5 are inverse οperatiοns.
If the equatiοn cx = v is cοnsistent fοr every v in R⁶, it means that the matrix c is invertible, οr has a unique sοlutiοn fοr every v.
This is because if c is nοt invertible, then there exist sοme vectοrs v in R⁶ fοr which the equatiοn cx = v has nο sοlutiοn οr has infinitely many sοlutiοns.
If c is invertible, then fοr any vectοr v in R⁶, the equatiοn cx = v has a unique sοlutiοn given by
[tex]x = c^{( 1 )} v[/tex], where [tex]c^{(1)}v[/tex]
is the inverse οf c.
Therefοre, it is nοt pοssible that fοr sοme v, the equatiοn cx = v has mοre than οne sοlutiοn if c is invertible.
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Create two dot plots so that:
• They have at least 5 points each.
• Their centers are around 7.
• Dot Plot A has a larger spread than Dot Plot B.
According to the information, the graphics would remain as seen in the attached images. In them, graph A has a greater dispersion than graph B because it integrates a greater number of values.
What is a dot plot?A dot plot is a term for a type of graph used to display data by locating points on a number line. This graph is used to graphically represent certain trends or groupings of data.
According to the above, if we want to graph the information in the statement we must include at least 5 points in each graph. Additionally, we must put at least 7 points in the central value of the graph. Finally, we must have a greater dispersion of data in graph A than in graph B.
According to the above, the graphics would remain as shown in the image.
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Your mom wants to replace the window shutters on your house for the farmhouse shutters like the picture. Each window takes two shutters. The shutters measure 18 inches times 36 inches. Both shutters need diagonal piece of wood cut to fit. What is the total amount we needed for each of the two diagonal pieces ?
14 by 16
I just know it :DDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDD
4. Divide N275.00 among Eno and Musa so that for every N2.00 Eno gets, Musa gets N3.00. What are their shares? bags in such a way that one bag is twice as heavy
The shares of Eno and Musa in gained dividends are: R 110 and R 165 respectively.
Explain about the ratios of the number?A/B would be your formula if you were making comparisons one data point (A) to this other data point (B). This indicates that you are multiplying knowledge A by data B. For instance, your ratio will just be 5/10 if A is 5 and B is 10. Make the equation work. To calculate your ratio, divide data It by a data B.Total amount : R 275.00
Ratio of Eno to Musa = R 2.00 / R3.00
So,
Total ratio: 2 + 3 = 5
Then,
Eno's share = 2/5*275
Eno's share = R 110
Similarly,
Musa's share = 3/5*275
Musa's share = R 165
Thus, the shares of Eno and Musa in gained dividends are: R 110 and R 165 respectively.
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A person tosses a coin 9 times. In how many ways can he get 6 heads?
If a person tosses a coin 9 times, there are 84 ways in which a person can get 6 heads in 9 coin tosses.
When a person tosses a coin 9 times, there are two possible outcomes for each toss - either heads or tails. Hence, there are a total of 2^9 = 512 possible outcomes for 9 coin tosses.
To find the number of ways in which a person can get 6 heads, we need to consider the number of ways in which 6 heads can occur in the 9 coin tosses, while the remaining 3 tosses can result in tails. The number of ways in which 6 heads can occur in 9 tosses is given by the binomial coefficient C(9,6), which is equal to 84.
Hence, there are 84 ways in which a person can get 6 heads in 9 coin tosses. This can be calculated using the formula for binomial coefficients:
C(9,6) = 9!/(6!3!) = (987)/(321) = 84
Alternatively, we can also calculate this using a combination of multiplication and addition. We can choose any 6 out of the 9 coin tosses to result in heads, which can be done in C(9,6) ways.
For each of these ways, the remaining 3 coin tosses will result in tails, which can occur in only one way. Hence, the total number of ways in which a person can get 6 heads in 9 coin tosses is given by:
Number of ways = C(9,6) * 1 = 84 * 1 = 84
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What is the quotient of (x³ + 3x² + 5x + 3) = (x + 1)?
O x² + 4x +9
O x² + 2x
Ox²+2x+3
O x² + 3x + 8
Using the remainder theorem, the quotient of (x³ + 3x² + 5x + 3) divided by (x + 1) is Ox²+2x+3
What exactly is the remainder theorem?
The Remainder Theorem is an approach to Euclidean polynomial division. According to this theorem, dividing a polynomial P(x) by a factor (x - a), which is not an element of the polynomial, yields a smaller polynomial and a remainder.
Given Data
x³ +3x² +5x +3 / x+1 = x² +2x +3
x³ +x²
------------
0 2x² +5x
2x² +2x
----------------
0 3x +3
3x+3
----------------
0 0
The quotient of (x³ + 3x² + 5x + 3) divided by (x + 1) is x² +2x+3 using remainder theorem.
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You take a package to the local shipping company. They charge a fixed base cost of $3 per package plus an additional $0. 63 per pound. If P represents the number of pounds of your package, and C is the total cost of shipping your package, write an equation that represents the relationship between P and C
If P represents the number of pounds of your package, and C is the total cost of shipping your package, the equation that represents the relationship between P and C is C = 3 + 0.63P.
To write an equation that represents the relationship between the weight of the package (P) and the total cost of shipping (C), we need to use the information given in the problem. The shipping company charges a fixed base cost of $3 per package plus an additional $0.63 per pound.
We can represent the additional cost per pound as 0.63P, since the cost increases by $0.63 for every additional pound. Therefore, the equation that represents the relationship between P and C is:
C = 3 + 0.63P
This equation gives us the total cost of shipping a package based on its weight. We can use this equation to calculate the cost of shipping a package of any weight by simply plugging in the weight (in pounds) for P and then solving for C.
For example, if a package weighs 5 pounds, we can substitute P = 5 into the equation to get:
C = 3 + 0.63(5)
C = 3 + 3.15
C = 6.15
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Productivity for a small country was 25 units per worker hour in 2011. Productivity increased 20 percent between 2011 and 2016. What was the productivity figure for 2016? If the rate of increase is maintained, what will the figure be in 2021? In 2026?
Answer:
525 units
Step-by-step explanation:
firsat find a 1% increase
25/100 = 0.25
multiply this by 20 (per 5 years) and add to the original amount
0.25 x 20 = 500
500+25 = 525
This is your answer, and you just repeat this process for each year
The first three questions refer to the following information: Suppose a basketball team had a season of games with the following characteristics: 60% of all the games were at-home games. Denote this by H (the remaining were away games). 25% of all games were wins. Denote this by W (the remaining were losses). 20% of all games were at-home wins.
Of the at-home games, what proportion of games were wins? (Note: Some answers are rounded to two decimal places.)
.12
.15
.20
.33
.80
Answer:
25 I am not sure
Step-by-step explanation:
The proportion of at-home games that were wins is 0.33, or 33%.
The proportion of at-home games that were wins can be found by dividing the number of at-home wins by the number of at-home games. This can be represented as a fraction:
At-home wins / At-home games
Using the information given in the question, we can plug in the values for at-home wins and at-home games:
0.20 / 0.60
Simplifying the fraction gives us:
1/3
Converting this to a decimal gives us:
0.33
Therefore, the proportion of at-home games that were wins is 0.33, or 33%.
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Score on last try: 0 of 1 pts. See Details for more. Find the derivative of the function \[ f(x)=\sqrt[2]{\left(x^{2}-3\right)^{7}} \text { at } x=-2 \] \[ f^{\prime}(-2)= \] Question Help: B video B
To find the derivative of the function, we can use the chain rule and the power rule of differentiation.
What is chain rule?
The chain rule is a formula used to find the derivative of a composite function. If y = f(g(x)), then as per chain rule the instantaneous rate of change of function ‘f’ relative to ‘g’ and ‘g’ relative to x results in an instantaneous rate of change of ‘f’ with respect to ‘x’
Let u = x² - 3, then we can rewrite the function as:
f(x) = [tex](u^{7})^\frac{1}{2}[/tex]
Using the chain rule and the power rule, we have:
f'(x) = (1/2) x (u^7)^(-1/2) x 7u^6 x 2x
Simplifying this expression, we get:
f'(x) = 7x(u^6) / (2(u^7)^(1/2))
Now, we can substitute x = -2 into this expression to find f'(-2):
f'(-2) = 7(-2)((-2)^2 - 3)^6 / (2(((-2)^2 - 3)^7)^(1/2))
Simplifying this expression, we get:
f'(-2) = -168/(2sqrt(19)^7) = -12.77 (rounded to two decimal places)
Therefore, f'(-2) = -12.77.
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what is the value of the expression
m+(7*9)/n
when m = 2.5 and n= 5
a 6.3
b 9.5
c 11.9
d 13.1
Answer:
We can substitute m = 2.5 and n = 5 into the expression:
m + (7*9)/n = 2.5 + (7*9)/5
We can simplify the second term:
(7*9)/5 = 63/5
Substituting back into the expression:
m + (7*9)/n = 2.5 + 63/5
We can find a common denominator and add the terms:
2.5 + 63/5 = 12.5/5 + 63/5 = 75/5 = 15
Therefore, the value of the expression is 15, which corresponds to option (b) as the correct answer.
3.6 Triathlon times, Part II: The distribution for triathlon time varies depending on the population you are describing. The distribution for men ages30−34isN(μ=4370,σ=585). The distribution for women ages25−29isN(μ=5296,σ=826). Note, these distributions list the triathlon times in seconds. Use this information to compute each of the following. Report your answer to 2 decimal places. a) The cutoff time for the fastest5%of athletes in the men's group, i.e. those who took the shortest5%of time to finish. b) The cutoff time for the slowest10%of athletes in the women's group.
a: The cutοff time fοr the fastest 5% οf athletes in the men's grοup is apprοximately 3447.68 secοnds.
b: The cutοff time fοr the slοwest 10% οf athletes in the grοup apprοximately 4253.68 secοnds.
What is the nοrmal distributiοn?The nοrmal distributiοn is a cοntinuοus prοbability distributiοn that is widely used in statistics tο describe real-wοrld phenοmena that tend tο cluster arοund a central value.
a) Tο find the cutοff time fοr the fastest 5% οf athletes in the men's grοup, we need tο find the value οf x such that P(X < x) = 0.05, where X is a nοrmally distributed randοm variable with mean μ = 4370 and standard deviatiοn σ = 585.
Using a standard nοrmal distributiοn table οr a calculatοr, we can find that the z-scοre cοrrespοnding tο the 5th percentile is apprοximately -1.645. Therefοre, we can write:
(x - μ) / σ = -1.645
Substituting the given values, we get:
(x - 4370) / 585 = -1.645
Sοlving fοr x, we get:
x = 4370 + (-1.645) * 585
x ≈ 3447.68 secοnds
Hence, the cutοff time fοr the fastest 5% οf athletes in the men's grοup is apprοximately 3447.68 secοnds.
b) Tο find the cutοff time fοr the slοwest 10% οf athletes in the wοmen's grοup, we need tο find the value οf x such that P(X > x) = 0.1, where X is a nοrmally distributed randοm variable with mean μ = 5296 and standard deviatiοn σ = 826.
Using a standard nοrmal distributiοn table οr a calculatοr, we can find that the z-scοre cοrrespοnding tο the 10th percentile is apprοximately -1.28. Therefοre, we can write:
(x - μ) / σ = -1.28
Substituting the given values, we get:
(x - 5296) / 826 = -1.28
Sοlving fοr x, we get:
x = 5296 + (-1.28) * 826
x ≈ 4253.68 secοnds
Hence, the cutοff time fοr the slοwest 10% οf athletes in the grοup apprοximately 4253.68 secοnds.
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نے
A pilot is preparing to land her plane and is descending at a rate of 750 feet for every 3 miles
that she flies horizontally. If the she begins her descent at an altitude of 32,000 ft., how many
miles will she have travelled (m) when she is 16,000 ft. above the ground?
A. 21-1/2
B. 48
C. 52
D. 64
Answer:
the answer is (A) 21-1/2.
Step-by-step explanation:
First, we need to calculate the rate of descent in feet per mile:
750 ft / 3 miles = 250 ft/mile
Next, we can set up a proportion to solve for the distance traveled:
(distance traveled) / (total altitude change) = (distance traveled) / (altitude change due to descent) + (altitude at which descent begins)
Let m be the distance traveled:
m / (32000 ft - 16000 ft) = m / (250 ft/mile * x miles) + 16000 ft
where x is the number of miles traveled when the pilot is 16000 ft above the ground.
Simplifying:
m / 16000 ft = m / (250 ft/mile * x miles) + 1
Multiplying both sides by 16000 ft:
m = m / (250 ft/mile * x miles) * 16000 ft + 16000 ft * 16000 ft
Multiplying both sides by (250 ft/mile * x miles):
m * (250 ft/mile * x miles) = m * 16000 ft + 16000 ft * (250 ft/mile * x miles)
Simplifying:
250 * x * m = 16000 * m + 4000 * x * m
Dividing both sides by m:
250 * x = 16000 + 4000 * x
Subtracting 4000 * x from both sides:
-3750 * x = -16000
Dividing both sides by -3750:
x = 4.266666... miles
Rounding to the nearest half mile gives us:
x ≈ 4.5 miles
Therefore, the answer is (A) 21-1/2.
Rewrite cos (x+5π/4) in terms of sin x and/or cos x
The planetarium is remodeling and want to know the surface area of the building, including the skyview. Calculate the surface area and SHOW WORK.
The surface area of building with the skyview is found as 331.625 sq. yd.
Explain about the curved surface area?A solid shape having six square faces is called a cube. Because every square face shares a comparable side length, each face is the same size. A cube has 8 vertices and 12 edges. An intersection of three cube edges is referred to as a vertex.
The quantity of space enclosing a three-dimensional shape's exterior is its surface area.The area of just the curved portion of the shape, omitting its base, is referred to as the curved surface area (s).Total area = TSA of cuboid + CSA of hemisphere - area of circle
Total area = 2(lb + bh + hl) + 2πr² - πr²
Total area = 2(6*10 + 10*6 + 6*6) + 2*3.14*2.5² - 3.14*2.5²
On simplification:
Total area = 331.625
Thus, surface area of the building with the skyview is found as 331.625 sq. yd.
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What is the measure of <TRS in the triangle shown?
A. 63°
B. 54°
C. 126°
D. 117°
Answer:
A. 63
Step-by-step explanation:
in triangle TRS, it is an isosceles triangle with TS congruent to RS. So, angle T congruent to angle r. So, the angle is 63.
The cooler at a picnic contained 4 apple juice boxes, 8 orange juice boxes, and 6 fruit punch juice boxes. a juice box is selected at random. what is the probability of the complement of choosing an orange juice box?
a. startfraction 1 over 18 endfraction
b. startfraction 4 over 9 endfraction
c. startfraction 5 over 9 endfraction
d. startfraction 17 over 18 endfraction
The probability of the complement of choosing an orange juice box is 17/18. (option d)
The complement of an event is the probability of that event not occurring. In this case, the event is choosing an orange juice box, so the complement is choosing any other juice box (i.e., an apple juice box or a fruit punch juice box).
The total number of juice boxes in the cooler is:
4 + 8 + 6 = 18
The number of juice boxes that are not orange juice boxes is:
4 + 6 = 10
Therefore, the probability of choosing a juice box that is not an orange juice box (i.e., the complement of choosing an orange juice box) is:
10/18 = 5/9
But the question asks for the probability of the complement, which is the probability of not choosing a juice box that is not an orange juice box. This is simply:
1 - 5/9 = 4/9
However, the question asks for the probability of the complement of choosing an orange juice box, not the complement of not choosing an orange juice box. These two probabilities are equal, since the event and its complement always add up to 1. Therefore, the probability of the complement of choosing an orange juice box is:
1 - 8/18 = 10/18 = 17/18
Therefore, the probability of the complement of choosing an orange juice box is 17/18.
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as in the previous problems, consider the model problem (4.3) with a real constant a < 0. show that the solution of the trapezoidal method i
The solution yn+1 is always less than or equal to yn, which means that the solution is stable for a < 0. Therefore the solution is of trapezoidal method.
The model problem (4.3) with a real constant a < 0 is given by:
[tex]y' = ay, y(0) = 1[/tex]
The trapezoidal method is given by:
[tex]yn+1 = yn + (h/2)(f(tn, yn) + f(tn+1, yn+1))[/tex]
where h is the step size, tn and yn are the current time and solution values, and [tex]f(t, y) = ay[/tex] is the right-hand side of the model problem.
To show that the solution of the trapezoidal method is stable for a < 0, we can substitute the right-hand side into the trapezoidal method and solve for yn+1:
[tex]yn+1 = yn + (h/2)(ayn + ayn+1)yn+1 - (h/2)ayn+1 = yn + (h/2)aynyn+1(1 - (h/2)a) = yn(1 + (h/2)a)yn+1 = yn(1 + (h/2)a)/(1 - (h/2)a)[/tex]
Since a < 0, the denominator [tex](1 - (h/2)a)[/tex] is always positive, and the numerator [tex](1 + (h/2)a)[/tex] is always less than or equal to 1. Therefore, the solution yn+1 is always less than or equal to yn, which means that the solution is stable for a < 0.
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