During the summer, Olympic swimmer Adam Johnson swims every day. On sunny summer days, he goes to an outdoor pool, where he may swim for no charge. On rainy days, he must go to a domed pool. At the beginning of the summer, he has the option of purchasing a $15 season pass to the domed pool, which allows him use for the entire summer. If he doesn't buy the season pass, he must pay $1 each time he goes there. Past meteorological records indicate that there is a 60% chance that the summer will be sunny (in which case there is an average of 6 rainy days during the summer) and a 40% chance the summer will be rainy (an average of 30 rainy days during the summer).
Before the summer begins, Adam has the option of purchasing a long-range weather forecast for $1. The forecast predicts a sunny summer 80% of the time and a rainy summer 20% of the time. If the forecast predicts a sunny summer, there is a 70% chance that the summer will actually be sunny. If the forecast predicts a rainy summer, there is an 80% chance that the summer will actually be rainy. Assuming that Adam's goal is to minimize his total expected cost for the summer, what should he do? Also find EVSI and EVPI
Adam should purchase the long-range weather forecast for $1. By doing so, he will have the best chance of minimizing his total expected cost for the summer.
The expected value of the sample information (EVSI) is the expected cost if Adam does not purchase the forecast and goes with the meteorological records, which is $16.6 ($15 for the season pass plus an average of $1.6 per rainy day).
The expected value of perfect information (EVPI) is the expected cost if Adam purchases the forecast and uses it to make the decision, which is $15.6 ($15 for the season pass plus an average of $0.6 per rainy day).
Thus, purchasing the long-range weather forecast is the best decision for Adam, as it will save him $1 in expected costs and allow him to minimize his total expected cost for the summer.
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Simplify the following expression by combining like terms 3y+8+4y+2
(a) Show the following o-fields are equal to each other: i. B= o({(-20,x); r < R}); ii. B2 = o({(-0,2); 2 € R}); [Note either of them can be taken as the definition of the Borel sigma field on the real line.]
The following o-fields are equal to each other because they both represent the Borel sigma field on the real line:
i. B= o({(-20,x); r < R})
ii. B2 = o({(-0,2); 2 € R})
Note that the Borel sigma field on the real line is the smallest sigma field containing all the open intervals on the real line. This means that any set that can be constructed from countable unions, intersections, and complements of open intervals is in the Borel sigma field.
In the first o-field, B= o({(-20,x); r < R}), the set {(-20,x); r < R} is an open interval on the real line, so it is in the Borel sigma field. Similarly, in the second o-field, B2 = o({(-0,2); 2 € R}), the set {(-0,2); 2 € R} is also an open interval on the real line, so it is also in the Borel sigma field.
Since both o-fields contain sets that are in the Borel sigma field, they are both equal to the Borel sigma field on the real line. Therefore, B= o({(-20,x); r < R}) = B2 = o({(-0,2); 2 € R}).
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Find the slope of each line defined below and compare their values.
Equation of Line A:
y-1=
-1/2 (2
(x + 10)
-
Select values from Line B:
The slope of Line A is
of Line A is
X
-10
-5
0
5
Y
-3
0
3
6
and the slope of Line B is
the slope of Line B.
Therefore the slope
The slope of line A is -1/2 and the slope of line B is -3/5. The slope of line A is greater than the slope of line B.
What is slope?
A line's steepness and direction are measured by the line's slope. Without actually using a compass, determining the slope of lines in a coordinate plane can assist in forecasting whether the lines are parallel, perpendicular, or none at all.
First, let's rewrite the equation of line A in slope-intercept form (y = mx + b) where m is the slope and b is the y-intercept -
y - 1 = - 1/2(x + 10)
y = 1/2(x + 10) + 1
y = 1/2x + 6
So, the slope of line A is - 1/2.
For line B, we can use the formula for finding the slope of a line given two points (m = (y2 - y1) / (x2 - x1)).
Let's use the first and last points to find the slope -
m = (-3 - 6) / (-10 - 5) = -9 / -15 = 3/5
So, the slope of line B is 3/5.
Therefore, the slope of line B is smaller as compared to slope of line A.
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Let B1 be the basis {(1,2,3),(2,−1,2)}={u1,u2} and B2 be the basis {(0,5,4),(1,−8,−5)}={v1,v2}. Show that these two bases span the same subspace of R3
The two bases B1 and B2 span the same subspace of R3.
Let B1 be the basis {(1,2,3),(2,−1,2)}={u1,u2} and B2 be the basis {(0,5,4),(1,−8,−5)}={v1,v2}. We want to show that these two bases span the same subspace of R3.
To do this, we need to show that any vector in the subspace spanned by B1 can also be written as a linear combination of vectors in B2, and vice versa.
Let x be a vector in the subspace spanned by B1. Then x = a*u1 + b*u2 for some scalars a and b. Substituting the values of u1 and u2, we get:
x = a*(1,2,3) + b*(2,−1,2)
= (a+2b, 2a-b, 3a+2b)
Now we want to express x as a linear combination of v1 and v2:
x = c*v1 + d*v2
= c*(0,5,4) + d*(1,−8,−5)
= (d, 5c-8d, 4c-5d)
Setting the two expressions for x equal to each other, we get the following system of equations:
a+2b = d
2a-b = 5c-8d
3a+2b = 4c-5d
Solving this system of equations, we can find values of c and d that satisfy the equations. This shows that any vector in the subspace spanned by B1 can also be written as a linear combination of vectors in B2.
Similarly, we can show that any vector in the subspace spanned by B2 can also be written as a linear combination of vectors in B1.
Therefore, the two bases B1 and B2 span the same subspace of R3.
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A line passes through points (-3, 1) and (2, - 3) What is the slope of the line parallel to the graph?
Answer:
To find the slope of the line passing through (-3, 1) and (2, -3), we can use the slope formula:
slope = (y2 - y1) / (x2 - x1)
where (x1, y1) = (-3, 1) and (x2, y2) = (2, -3).
slope = (-3 - 1) / (2 - (-3))
= -4 / 5
So, the slope of the line passing through (-3, 1) and (2, -3) is -4/5.
To find the slope of a line parallel to this line, we need to remember that parallel lines have the same slope. Therefore, the slope of the parallel line is also -4/5.
Select the correct answer.
Answer:
c.4√6
Step-by-step explanation:
= √2 x 2 x 2 x 2 x 2 x 3
= √24 x 2 x 3
= 4√6
solve every thing here do not draw anything on the graph
The median height is less than the mean height.
Option 3 is correct.
What is Median?The midway value in a given set of figures or data is referred to as the median. To get the average value for a given group of integers, three different metrics are employed in mathematics. The terms are median, mode, and mean. The term "measures of central tendency" refers to these three metrics.
As per the given graph:
Total number of plants = 80
Frequency v/s height of plant is given.
The mean height is 41.9 cm.
To find the median:
Total observations (n) = 25 + 20 + 13 + 10 + 2 + 10
= 80 plants
For median interval:
(n/2) = (80/2)
= 40 plants
Hence, the median interval will be the one where frequency reach 40.
∴ Median lies in the interval of height (30-40) cm.
Hence, the median height is less than the mean height.
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7th garde math question pt 2 pls answer a s a p i ready grade f level
Answer:
45
Step-by-step explanation:
3² · (12-2) ÷ 2
= 9 · (10) ÷ 2
= 90 ÷ 2
= 45
So, the answer is 45
Answer: 135
Step-by-step explanation: use a calculator/online calculator
Pls help guys I give brainliest
Dylan has two measuring jugs, A and B, which hold a combined volume of 800ml. Dulan fill jug A with water. He then fills jug B by pouring in water from jug A. After this, there is 200 ml of water remaining in jug A. Work out the volune of each measuring jug
Jug A has a vοlume οf 400 ml and jug B has a vοlume οf 400 ml.
What is the equatiοn in twο variables?An equatiοn in twο variables is an equatiοn that invοlves twο variables, typically x and y, and relates them with cοnstants and mathematical οperatiοns such as additiοn, subtractiοn, multiplicatiοn, and divisiοn.
Let's represent the vοlume οf jug A by x and the vοlume οf jug B by y.
We knοw that the cοmbined vοlume οf the twο jugs is 800 ml:
x + y = 800 (equatiοn 1)
We alsο knοw that after pοuring water frοm jug A tο jug B, there is 200 ml οf water remaining in jug A. This means that jug B cοntains x ml οf water:
y = x (equatiοn 2)
We can substitute equatiοn 2 intο equatiοn 1 tο eliminate y:
x + y = 800
x + x = 800
2x = 800
x = 400
Nοw that we knοw that the vοlume οf jug A is 400 ml, we can use equatiοn 2 tο find the vοlume οf jug B:
y = x
y = 400
Therefοre, the vοlume οf jug B is alsο 400 ml.
Hence, jug A has a vοlume οf 400 ml and jug B has a vοlume οf 400 ml.
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y = 4* Reflect it across the y-axis, translate it to the right 3 units, and vertically stretch it by a factor of 2
y = -2x + 14
To reflect the equation y = 4 across the y-axis, we need to change the sign of the x-term. Since there is no x-term in the original equation, we can simply add a negative x-term to get the reflected equation: y = -x + 4.
Next, to translate the equation to the right 3 units, we need to subtract 3 from the x-term. This gives us the translated equation: y = -(x - 3) + 4.
Finally, to vertically stretch the equation by a factor of 2, we need to multiply the entire equation by 2. This gives us the final transformed equation: y = 2(-x + 3) + 8.
In summary, the equation y = 4 reflected across the y-axis, translated to the right 3 units, and vertically stretched by a factor of 2 is y = -2x + 14.
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Identify the numbers of Solutions.
9t6-14+³ +4+- 1 = 0
There are ___ Solutions.
Answer:
"t3" was replaced by "t^3".
1 more similar replacement(s).Step by step solution :
STEP 1:Equation at the end of step 1 (((9 • (t6)) - (2•7t3)) + 4t) - 1 = 0
STEP 2 :Equation at the end of step 2: ((32t6 - (2•7t3)) + 4t) - 1 = 0
STEP 3:Checking for a perfect cube 3.1 9t6-14t3+4t-1 is not a perfect cube
Trying to factor by pulling out : 3.2 Factoring: 9t6-14t3+4t-1
Thoughtfully split the expression at hand into groups, each group having two terms:
Group 1: 4t-1
Group 2: -14t3+9t6
Pull out from each group separately:
Group 1: (4t-1)
(1)Group 2: (9t3-14) • (t3)
Factoring by pulling out fails : The groups have no common factor and can not be added up to form a multiplication.Polynomial Roots Calculator : 3.3
Find roots (zeroes) of : F(t) = 9t6-14t3+4t-1
Polynomial Roots Calculator is a set of methods aimed at finding values of t for which F(t)=0 Rational Roots Test is one of the above mentioned tools. It would only find Rational Roots that is numbers t which can be expressed as the quotient of two integersThe Rational Root Theorem states that if a polynomial zeroes for a rational number P/Q then P is a factor of the Trailing Constant and Q is a factor of the Leading CoefficientIn this case, the Leading Coefficient is 9 and the Trailing Constant is -1. The factor(s) are: of the Leading Coefficient : 1,3 ,9 of the Trailing Constant : 1 Let us test .... P Q P/Q F(P/Q) Divisor -1 1 -1.00 18.00 -1 3 -0.33 -1.80 -1 9 -0.11 -1.43 1 1 1.00 -2.00 1 3 0.33 -0.17 1 9 0.11 -0.57 Polynomial Roots Calculator found no rational roots Equation at the end of step 3: 9t6 - 14t3 + 4t - 1 = 0
STEP 4:Equations of order 5 or higher: 4.1 Solve 9t6-14t3+4t-1 = 0In search of an interavl at which the above polynomial changes sign, from negative to positive or the other wayaround.Method of search: Calculate polynomial values for all integer points between t=-20 and t=+20 Found change of sign between t= -1.00 and t= 0.00 Approximating a root using the Bisection Method :We now use the Bisection Method to approximate one of the solutions. The Bisection Method is an iterative procedure to approximate a root (Root is another name for a solution of an equation).The function is F(t) = 9t6 - 14t3 + 4t - 1At t= 0.00 F(t) is equal to -1.00 At t= -1.00 F(t) is equal to 18.00 Intuitively we feel, and justly so, that since F(t) is negative on one side of the interval, andpositive on the other side then, somewhere inside this interval, F(t) is zero Procedure :(1) Find a point "Left" where F(Left) < 0(2) Find a point 'Right' where F(Right) > 0(3) Compute 'Middle' the middle point of the interval [Left,Right](4) Calculate Value = F(Middle)(5) If Value is close enough to zero goto Step (7)Else : If Value < 0 then : Left <- MiddleIf Value > 0 then : Right <- Middle(6) Loop back to Step (3)(7) Done!! The approximation found is MiddleFollow Middle movements to understand how it works : Left Value(Left) Right Value(Right)
0.000000000 -1.000000000 -1.000000000 18.000000000
0.000000000 -1.000000000 -1.000000000 18.000000000
-0.500000000 -1.109375000 -1.000000000 18.000000000
-0.500000000 -1.109375000 -0.750000000 3.508056641
-0.500000000 -1.109375000 -0.625000000 0.454410553
-0.562500000 -0.473213613 -0.625000000 0.454410553
-0.593750000 -0.050185024 -0.625000000 0.454410553
-0.593750000 -0.050185024 -0.609375000 0.191316528
-0.593750000 -0.050185024 -0.601562500 0.067944440
-0.593750000 -0.050185024 -0.597656250 0.008233857
-0.595703125 -0.021135877 -0.597656250 0.008233857
-0.596679688 -0.006491229 -0.597656250 0.008233857
-0.596679688 -0.006491229 -0.597167969 0.000861241
-0.596923828 -0.002817510 -0.597167969 0.000861241
-0.597045898 -0.000978764 -0.597167969 0.000861241
-0.597106934 -0.000058919 -0.597167969 0.000861241
-0.597106934 -0.000058919 -0.597137451 0.000401122
-0.597106934 -0.000058919 -0.597122192 0.000171092
-0.597106934 -0.000058919 -0.597114563 0.000056084
-0.597110748 -0.000001418 -0.597114563 0.000056084
-0.597110748 -0.000001418 -0.597112656 0.000027333
-0.597110748 -0.000001418 -0.597111702 0.000012957
-0.597110748 -0.000001418 -0.597111225 0.000005770 Next Middle will get us close enough to zero: F( -0.597110868 ) is 0.000000379 The desired approximation of the solution is: t ≓ -0.597110868
Note, ≓ is the approximation symbol One solution was found : t ≓ -0.597110868
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There is 1 solution to this equation.
What is equation?An equation is a mathematical statement that two expressions are equal. It consists of two expressions separated by an equals sign (=), and expresses a relationship between the two expressions. Equations can be used to represent a variety of problems and can help solve real-world problems. For example, an equation can be used to calculate the amount of money someone will have after a certain period of time, or to calculate the distance between two points.
In order to answer this question, we must first solve the equation. 9t6-14+³ +4+- 1 = 0 can be written as 9t6 - 11 + 4 - 1 = 0. After simplifying, this equation becomes 9t6 - 7 = 0, which can be further simplified to t6 = 7. Taking the sixth root of both sides, we can determine that t = √7. Therefore, there is 1 solution to this equation.
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Factorise this expression as fully as possible
16t³ + 10t
Factorization of expression 16t³ + 10t is 2t (8t² + 5) .
Factorization or factoring consists of writing a number or another mathematical object as a product of several factors, usually smaller or simpler objects of the same kind. For example, 3 × 5 is a factorization of the integer 15
Given expression
16t³ + 10t
It can be written as
2 × 8 (t . t . t ) + 2 × 5 (t)
Factoring out common factors
2t (8t² + 5)
Hence, 2t (8t² + 5) is factorization of expression 16t³ + 10t
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30 pounds = ___ ounces
1.875
3.75
240
480
30 pounds = 480 ounces
How to convert Pounds to Ounces1 pound (lb) is equal to 16 Ounces (oz).
1 lb = 16 oz
The mass m in ounces (oz) is equal to the mass m in pounds (lb) times 16:
[tex]m_{(oz)} = m_{(lb)} * 16[/tex]
Solution :Convert 30 lb to ounces:
[tex]m_{(oz)} = 30 lb * 16 = 480[/tex] [tex]oz[/tex]
Therefore, 30 pounds converted to ounces is 480 ounces.
Answer: 30 pounds = 480
Step-by-step explanation:
Graph the solution to the inequality on the number line.
|4y+8| <4
Answer:
-3 < y < -1
Step-by-step explanation:
|4y+8| < 4 |4y+8| > -4
4y + 8 < 4 4y + 8 > -4
4y < -4 4y > -12
y < -1 y > -3
So, the answer is -3 < y < -1
The price of an item yesterday $40. Today, the price fell to $26 what is the percentage decrease
Answer:
35%
Step-by-step explanation:
26/40 = 0.65
1-0.65=35
Find the focus.
(y-2)^2=4(x+3)
Answer:
B. (-2,2)
Step-by-step explanation:
An amusement park charges an admission fee of 25 dollars per person. The cost, C (in dollars), of admission for a group of p people is given by the following.
C = 25 p
What is the cost of admission for a group of 3 people?
Answer:
75 dollars.
Step-by-step explanation:
Each person costs 25 dollars and p=3 we just put this into a equation.
25 × 3 = 75
C = 75
Ruth sell oranges. Her average sale for three days was 45 bags. How many bags of oranges does she need to sell on day four to have an average of 50?
The number of bags of oranges that Ruth needs to sell on day 4 to have an average of 50 bags is 65.
Let the number of bags to be sold on day four be = x,
To have an average of 50 bags over 4 days,
The total number of bags Ruth sells in four days must be,
⇒ 4 days × 50 bags/day = 200 bags,
The total number of bags of oranges she sells in 3 days is,
⇒ 3 days × 45 bags/day = 135 bags,
So, to reach a total of 200 bags in 4 days, she needs to sell x bags on the fourth day, which is in equation form as :
⇒ x + 135 = 200
⇒ x = 200 - 135
⇒ 65
Therefore, Ruth needs to sell 65 bags on day four.
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Julie ate lunch at a deli. She ordered a turkey sandwich for $11.73 and a salad for $5.27. The tax was 9.7%. What is the amount of tax for Julie's meal?
Answer:
$1.65
Step-by-step explanation:
9.7%×(11.73+5.27)
0.097×(11.73+5.27)
=1.649
to 2d.p
=1.65
pls give simple working out
due in 10 mins :))))
Answer:
(a) a = 60
(b) a = 75
(c) a = 108
All are corresponding.
Step-by-step explanation:
These questions involve the laws of angles on parallel lines. I like to call them "C", "F" and "Z" angles.
(a) is an example of a "Z" angle. By observation you can see that a is equivalent to the 60 degree angle as they are both internal angles of the "Z" shape created by a line intersecting the pair of parallel lines.
(b) is an example of an "F" angle. a is equivalent to the 75 degree angle because the straight line intersects the pair of parallel lines at the same angle.
(c) is another example of an "F" angle. a is equivalent to the 108 degree angle for the same reason as in question (b).
All the answers are corresponding angles because they are the same as the original. An alternate angle would be where your angle and the original sum to 180, as would be the case in "C" angles (also known as "co-interior" angles).
Feb 23, 12:41:00 PM If f(x)=3x^(5)+4, then what is the remainder when f(x) is divided by x-2 ?
The remainder when f(x)=3x^(5)+4 is divided by x-2 is 100.
The remainder when f(x)=3x^(5)+4 is divided by x-2 can be found using synthetic division.
Step 1: Set up the synthetic division by writing the coefficients of f(x) in a row and the value of x that makes the divisor equal to zero in a box to the left. In this case, the coefficients are 3, 0, 0, 0, 0, and 4 and the value of x is 2.
2|300004
Step 2: Bring down the first coefficient and multiply it by the value in the box. Write the result under the next coefficient and add them together. Repeat this process for all of the coefficients.
2|300004|612244896|36122448100
Step 3: The last number in the bottom row is the remainder. In this case, the remainder is 100.
Therefore, the remainder when f(x)=3x^(5)+4 is divided by x-2 is 100.
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Determine which numbers in the set are solutions of the equation. n-7=12;{17,19,21}
The number 19 is the solution of the equation n-7=12.
How do we find the solution?The equation given is n-7=12. To find the solution, we need to isolate the variable n on one side of the equation. We can do this by adding 7 to both sides of the equation. This gives us:
n-7+7=12+7
Simplifying the equation gives us:
n=19
Now, we can check which numbers in the set {17,19,21} are solutions of the equation. The only number that satisfies the equation is 19. Therefore, the solution of the equation is 19.
Answer: The number 19 is the solution of the equation n-7=12.
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ulas and Applications of A=P(1+(r)/(n))^(nt) Find A when P=2000,r=3%,n=12, and t=9.
The amount of money in the account after 9 years is $2549.68.
The formula A=P(1+(r)/(n))^(nt) is used to calculate the amount of money in an account after a certain amount of time, given the principal amount (P), the interest rate (r), the number of times interest is compounded per year (n), and the number of years (t).
To find A when P=2000, r=3%, n=12, and t=9, we can plug these values into the formula and simplify:
A = 2000(1+(0.03)/(12))^(12*9)
A = 2000(1+0.0025)^(108)
A = 2000(1.0025)^(108)
A = 2000(1.2748)
A = 2549.68
Therefore, $2549.68 is the amount of money in the account after 9 years.
"
Correct question
Ulas and Applications:
If A=P(1+(r)/(n))^(nt)
Find A when P=2000,r=3%,n=12, and t=9.
"
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LINEAR EQUATIONS Multiplicative property of Solve for x 24=(3)/(4)x Simplify your answer as much as x
Using multiplicative property of equations, the solution to the equation is x = 32.
The multiplicative property of equations states that if you multiply both sides of an equation by the same number, the equation will still be true.
In this case, we can use the multiplicative property to solve for x by multiplying both sides of the equation by (4/3) to cancel out the fraction on the right side of the equation.
24 = (3/4)x
(4/3)(24) = (4/3)(3/4)x
32 = x
So the solution to this equation is x = 32.
No need to further simplify your answer since the solution is already in its simplest form.
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Find the missing side
Answer: 30
Step-by-step explanation:
Use Pythagorean's Theorem, a² + b² = c²
18² + 24² = c²
324 + 576 = c²
900 = c²
√900 = c
c = 30
The missing side is 30.
Hope this helps!
PLEASE HELPP. jackie had 2 equal sized bottles. The first bottle contains 1 quart of water. the second bottle contains 5/9 quarts of water what amount of water must jackie pour from the first bottle into the second so that both bottles have tge samw amout of water. Express your answer as a fraction explain your answer using bar models
Jackie needs to pour 2/9of a quart of water from the first bottle to the second bottle to make them have the same amount of water.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
Let us assume that we transfer an amount "x" from the first bottle to the second bottle.
This means that the first bottle will have 1-x quarts of water, while the second bottle will have 5/9 + x quarts of water.
Now, we want to find the value of "x" that makes both bottles have the same amount of water.
We can set up an equation:
1-x = 5/9 + x
We can then solve for "x" by adding "x" to both sides and subtracting 5/9 from both sides:
1 - 5/9 = 2x
4/9 = 2x
x = 2/9
Hence, Jackie needs to pour 2/9 of a quart of water from the first bottle to the second bottle to make them have the same amount of water.
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1. Which of the following are the
possible lengths to complete a
triangle with side lengths of 11 in.
and 14 in.?
The possible length of the third side of a triangle is l < 25
What is triangle?A triangle is a closed, 2-dimensional shape with 3 sides, 3 angles, and 3 vertices. A triangle is also a polygon.
Given that, we need to find the possible lengths to complete a triangle with side lengths of 11 in. and 14 in.
We know that, the triangle inequality states that for any triangle, the sum of the lengths of any two sides must be greater than or equal to the length of the remaining side.
Therefore,
11 + 14 = 25
Let the third side be l,
Therefore,
l < 25
Hence, the possible length of the third side of a triangle is l < 25
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Consider functions f and g.
f(x) = -23
g(x) = |x − 1
What is the value of (go f)(4)?
What is the value of (g • f)(4)?
O A. 9
O B. B. -
O C. -9
O D. 1
The numeric value of the composite function at x = 4 is given as follows:
|f(4) - 1|.
What is the composite function of f(x) and g(x)?The composite function of f(x) and g(x) is given by the following rule:
(f ∘ g)(x) = f(g(x)).
It means that the output of the inside function serves as the input for the outside function.
If g is the outer function, as is the case for this problem, we have that:
(g • f)(x) = g(f(x)).
At x = 4, the numeric value of the composite function is given as follows:
g(f(4)) = |f(4) - 1|.
Missing InformationThe problem is incomplete, hence the composite function is given in general terms.
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