a.The probability distribution table for the first six attempts is shown below:
X P(X=k)
1 0.44
2 0.56 ×0.44
3 0.56²×0.44
4 0.56³ × 0.44
5 0.56⁴ ×0.44
6 0.56⁵×0.44
b. the probability is 0.1399.
c. the quarterback can expect to throw about 2.27 passes before completing one.
d. the probability is 0.1865.
e. the probability is 0.7349.
what is probability?The possibility or chance of an event occurring is measured by probability. The expression is given as a number between 0 and 1, with 0 denoting impossibility and 1 denoting certainty. Compared to occurrences with a probability closer to 0, those with a probability closer to 1 are more likely to occur.
a. To construct a probability distribution table for the number of passes attempted before the quarterback has a completion, we can use the geometric probability distribution, which is given by:
P(X=k) = [tex](1-p)^{k-1}[/tex]×p
where X is the number of attempts before the completion, p is the probability of completion on each attempt, and k is the number of attempts.
The probability distribution table for the first six attempts is shown below:
X P(X=k)
1 0.44
2 0.56 ×0.44
3 0.56²×0.44
4 0.56³ × 0.44
5 0.56⁴ ×0.44
6 0.56⁵×0.44
b. The probability that the quarterback throws 3 incomplete passes before he has a completion is given by:
P(X=3) = (1-0.44)³⁻¹× 0.44 × (1-0.44)⁰
= 0.56²×0.44
= 0.1399
Therefore, the probability is 0.1399.
c. The expected number of passes that the quarterback can throw before he completes a pass is given by the formula:
E(X) = 1/p
where p is the probability of completion on each attempt.
In this case, p = 0.44, so the expected number of passes is:
E(X) = 1/0.44
= 2.27
Therefore, the quarterback can expect to throw about 2.27 passes before completing one.
d. The probability that it takes more than 5 attempts before the quarterback completes a pass is given by:
P(X > 5) = 1 - P(X <= 5)
= 1 - [P(X=1) + P(X=2) + P(X=3) + P(X=4) + P(X=5)]
= 1 - [0.44 + (0.56 × 0.44) + (0.56² ×0.44) + (0.56³ × 0.44) + (0.56⁴×0.44)]
= 0.1865
Therefore, the probability is 0.1865.
e. If the quarterback throws 8 passes on the opening drive, the probability that he completes at least half of them is given by the binomial probability distribution, which is given by:
P(X ≥ 4) = 1 - P(X < 4)
where X is the number of completed passes and the probability of completion on each attempt is p = 0.44.
Using the binomial probability distribution table or calculator, we can find:
P(X≥4) = 1 - [P(X=0) + P(X=1) + P(X=2) + P(X=3)]
= 1 - [0.56⁸ + (8× 0.56⁷×0.44) + (28 × 0.56⁶ × 0.44²) + (56× 0.56⁵×0.44³)]
= 0.7349
Therefore, the probability is 0.7349.
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A makeup artist purchased some lipsticks and wants to wrap them individually with gift wrap. Each lipstick has a radius of 0.6 inch and a height of 2.4 inches. How many total square inches of gift wrap will the makeup artist need to wrap 4 lipsticks? Leave the answer in terms of π.
Answer:
The formula for the surface area of a cylinder is:
S = 2πrh + 2πr^2
where S is the total surface area, r is the radius of the base, and h is the height.
For one lipstick, the surface area is:
S = 2π(0.6)(2.4) + 2π(0.6)^2
S = 2.88π + 0.72π
S = 3.6π
To wrap 4 lipsticks, we need to multiply this surface area by 4:
S = 4(3.6π)
S = 14.4π
Therefore, the makeup artist will need approximately 14.4π square inches of gift wrap to wrap 4 lipsticks.
Answer:
Step-by-step explanation:
Total surface area of a cylinder = 2πr(r + h)
2 π (.6) (.6 + 2.4)
2 π .6 (3)
1.2π (3)
3.6 π square inches
Mulitply by four for four lipsticks:
3.6π × 4 = 14.4π sq inches
If ƒ (x) = 3x²+1 — 1, what is the value of f(−1), to the nearest ten-thousandth (if necessary)?
Answer:
To find the value of f(-1), we need to substitute -1 for x in the given function:
f(x) = 3x² + 1 - 1
f(-1) = 3(-1)² + 1 - 1
f(-1) = 3(1) + 0
f(-1) = 3
Therefore, f(-1) is equal to 3.
1. A contractor is building the base of a circular fountain. On the blueprint, the base of the fountain has a diameter of 40 centimeters. The blueprint has a scale of three centimeters to four feet. What will be the actual area of the base of the fountain, in square feet, after it is built? Round your answer to the nearest tenth of a square foot.
the actual area of the base of the fountain, in square feet, after it is built is approximately 1.3 square feet (rounded to the nearest tenth of a square foot).
How to solve the question?
To find the actual area of the base of the fountain, we need to convert the measurements from the blueprint to the actual measurements.
First, we need to find the radius of the circular base. The diameter of the base is given as 40 centimeters on the blueprint, so the radius is half of that, or 20 centimeters.
Next, we need to convert the scale of the blueprint from centimeters to feet. The scale is given as three centimeters to four feet, which can be simplified to a ratio of 3:4. To convert from centimeters to feet, we need to multiply by a conversion factor of 1 foot/30.48 centimeters, since there are 30.48 centimeters in a foot.
So, to find the actual radius of the circular base in feet, we multiply the blueprint radius (20 centimeters) by the conversion factor:
20 centimeters * (1 foot/30.48 centimeters) = 0.656168 feet
Now that we have the actual radius of the circular base, we can find the actual area of the base. The formula for the area of a circle is A = πr^2, where A is the area and r is the radius. Plugging in the actual radius we just found, we get:
A = π(0.656168 feet)^2 = 1.34977 square feet
Therefore, the actual area of the base of the fountain, in square feet, after it is built is approximately 1.3 square feet (rounded to the nearest tenth of a square foot).
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HELP ASAP if ur good with non-linear and increasing lines and choose 2 of the letter A,B,C,D,E
(Please see the picture!)
Extra points nd brainlist!
Answer:
B and D
Step-by-step explanation:
A and C are linear because they are going in a straight line. E is going downwards, so it is decreasing. That leaves B and D, which have exponential growth.
please help me solve the bonus question
Answer: a = 5 and k = 1/2
Step-by-step explanation:
We are given that the function is defined by:
f(x) = 16 + a(3^(kx))
We need to find the real numbers a and k such that f(0) = 21 and f(4) = 61. Using the given values of f(0) and f(4), we can form a system of two equations:
f(0) = 16 + a(3^(k(0))) = 21
f(4) = 16 + a(3^(k(4))) = 61
Simplifying the first equation, we get:
16 + a(3^0) = 21
16 + a = 21
a = 5
Substituting this value of a into the second equation, we get:
16 + 5(3^(4k)) = 61
5(3^(4k)) = 45
3^(4k) = 9
We know that 3^2 = 9, therefore
4k = 2
=> k = 2/4
=> k = 1/2
Therefore, the real numbers a and k that satisfy the given conditions are a = 5 and k = 1/2. So the function is:
f(x) = 16 + 5(3^(x/2))
The solution to the equation give us an approximate that x = 1.55.
What is the solution to the equation?To solve this equation, we can start by subtracting 4 from both sides to isolate the exponential term:
3.5^x + 4 - 4 = 11 - 4
This simplifies to:
3.5^x = 7
Next, we can take the logarithm of both sides with base 3.5 to eliminate the exponent:
log(3.5^x) = log(7)
Using the property of logarithms that log(a^b) = b*log(a), we can rewrite the left side as:
x*log(3.5) = log(7)
Now, we can solve for x by dividing both sides by log(3.5):
x = log(7) / log(3.5)
Plugging in the values, we get:
x = 0.84509804001 / 0.54406804435
x = 1.55329475566
x ≈ 1.55.
Answered question "Solve the equation 3.5^x + 4 = 11"
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A rectangle has a perimeter of 36 feet. It is twice as long as it is wide. What are the dimensions of the rectangle??
Dimensions of the rectangle are 6 feet and 12 feet.
What is a Rectangle?Rectangle is a quadrilateral whose each pair of opposite sides are equal in length and each two consecutive sides are in right angle to each other. In rectangle one pair of equal opposite sides is called Length and another one is called Width.
What is the formula of Perimeter of a Rectangle?If length of a rectangle is L and width of rectangle is W then the perimeter of that rectangle will be = 2(L+W)
Let W be the rectangle's width.
Here according to question the rectangle is twice as long as it is wide.
So, length of rectangle = 2W
Perimeter will be = 2(W+2W) = 2*(3W) = 6W
So, according to question,
6W = 36
W = 36/6 = 6
Thus the width of the rectangle is = 6 feet.
Then the length = 2*6 = 12 feet.
Hence dimensions of the rectangle are 12 feet and 6 feet respectively.
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Please help me with the volume!! I beg‼️‼️‼️
Answer:
Option D) 400π cubic units.
Step-by-step explanation:
GIVEN :
Radius of cylinder = 5 unitsHeight of cylinder = 16 unitsTO FIND :
Volume of cylinderUSING FORMULA :
[tex]\quad\star{\underline{\boxed{\sf{V_{(Cylinder)} = \pi{r}^{2}h}}}}[/tex]
V = volume π = 3.14 or 22/7r = radius h = heightSOLUTION :
Substituting all the given values in the formula to find the volume of cylinder :
[tex]\quad{\sf{\dashrightarrow{V_{(Cylinder)} = \pi{r}^{2}h}}}[/tex]
[tex]\quad{\sf{\dashrightarrow{V_{(Cylinder)} = \pi{(5)}^{2}16}}}[/tex]
[tex]\quad{\sf{\dashrightarrow{V_{(Cylinder)} = \pi{(5 \times 5)}16}}}[/tex]
[tex]\quad{\sf{\dashrightarrow{V_{(Cylinder)} = \pi{(25)} \times 16}}}[/tex]
[tex]\quad{\sf{\dashrightarrow{V_{(Cylinder)} = \pi \times 25\times 16}}}[/tex]
[tex]\quad{\sf{\dashrightarrow{V_{(Cylinder)} = \pi \times 400}}}[/tex]
[tex]\quad{\sf{\dashrightarrow{V_{(Cylinder)} = 400 \pi}}}[/tex]
[tex]\quad\star{\underline{\boxed{\sf{\pink{V_{(Cylinder)} = 400 \pi \: {units}^{3}}}}}}[/tex]
Hence, the volume of cylinder is 400π cubic units.
—————————————————Given the piecewise function below, evaluate the function as indicated
The evaluation of the functions using piecewise function gives:
f(-9) = 8
f(0) = 2
f(6) = 7
f(-6) = 4
f(3) = 4.5
f(9) = -6
How to evaluate the functions using piecewise function?
To evaluate the functions using piecewise function, we have to the condition they satisfy. That is:
For f(-9), x = -9. Thus, x≤ -6. So use f(x) = (-4/3)x - 4 to evaluate f(-9). That is:
f(-9) = (-4/3)*(-9) - 4
f(-9) = 8
For f(0), x = 0. Thus, -6 x ≤ 6. So use f(x) = (5/6)x + 2 to evaluate f(0). That is:
f(0) = (5/6)*0 + 2
f(0) = 2
For f(6), x = 6. Thus, -6 x ≤ 6. So use f(x) = (5/6)x + 2 to evaluate f(6). That is:
f(6) = (5/6)*6 + 2
f(6) = 7
For f(-6), f(x) = (-4/3)x - 4:
f(-6) = (-4/3)*(-6) - 4
f(-6) = 4
For f(3), f(x) = (5/6)x + 2:
f(3) = (5/6)*3 + 2
f(3) = 4.5
For f(9), x = 9. Thus, x > 6. Use f(x) = -2x + 12:
f(9) = -2*9 + 12
f(9) = -6
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PROJECTILE A firework is launched from the ground. After 4 seconds, it reaches a
maximum height of 256 feet before returning to the ground 8 seconds after it was
launched. The height of the firework f(x), in feet, after x seconds can be modeled
by a quadratic function.
a. What are the zeros and vertex of f(x)?
b. Sketch a graph of f(x) using the zeros and vertex of the function. Interpret the
key features of the function in the context of the situation.
c. Write a quadratic function that represents the situation.
(a) The vertex is (6, 144),(b) When the fireworks are launched at time x = 0 and return to the earth at time x = 12 seconds, respectively, these times are denoted by zeros in the function,.(c) this is the quadratic function that represents the situation f(x) = -4 + 144.
How to deal with this problem?a. To find the zeros and vertex of the quadratic function, we need to first write it in the standard form:
[tex]f(x) = ax^2 + bx + c[/tex]
where a, b, and c are constants.
The vertex of the function is given by:
x = -b/2a
Since the quadratic function is symmetrical around the vertex, we know that the time it takes to reach the maximum height is halfway between the launch time and the time it hits the ground again. So, the time to reach maximum height is (4 + 8)/2 = 6 seconds.
Therefore, we can set up a system of equations using the information given:
f(4) = 0 (the firework is launched from the ground)
f(6) = 256 (the firework reaches its maximum height)
f(12) = 0 (the firework hits the ground again)
Plugging in the values of x and f(x), we get:
16a + 4b + c = 0
36a + 6b + c = 256
144a + 12b + c = 0
Solving this system of equations, we get:
a = -4
b = 48
c = 0
Therefore, the quadratic function that represents the situation is:
[tex]f(x) = -x^2 + 48x[/tex]
The zeros of the function can be found by setting f(x) = 0:
[tex]f(x) = -4x^2 + 48x[/tex]
0 = x(-4x + 48)
x = 0 (the firework is launched from the ground)
x = 12 (the firework hits the ground again)
The vertex can be found using the formula:
x = -b/2a = -48/(-8) = 6
So the vertex is (6, 144).
b. Using the zeros and vertex, we can sketch a graph of f(x):
The quadratic function's graph
Considering the function's primary characteristics in light of the circumstances:
The peak height of the fireworks, which occurs at x = 6 seconds and f(6) = 256 feet, is represented by the function's vertex.
The firework is at ground level at x = 0 (launch time) and x = 12 seconds (when it reaches the ground again), which are represented by zeros in the function.
The graph's form suggests that the firework rises before falling again, which is consistent with the scenario given.
c. The quadratic function that represents the situation is:
[tex]f(x) = -4x^2 + 48x[/tex]
This function can be simplified by factoring out -4:
[tex]f(x) = -4( x^2- 12x)[/tex]
Completing the square:
[tex]f(x) = -4( x^2- 12x + 36 - 36)[/tex]
[tex]f(x) = -4( (x^2-6)- 36)[/tex]
[tex]f(x) = -4(x^2-6) + 144[/tex]
This form of the function shows that the vertex is (6, 144), and that the maximum height is 144 feet.
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anyone know what the area of triangle ABC is?
The area of triangle ABC is 6cm²
What is a triangle?A triangle is a three-sided polygon that consists of three edges and three vertices. It is also known as the trigon and has special names such as the hypotenuse (opposite the right angle) and legs (the other two sides). It can also refer to a percussion instrument consisting of a rod of steel bent into the form of a triangle open at one angle.
The area of the triangle is given as
Area= 1/2absinC
But the CosB = Adj/Hypo
Cos60 = Adj/12
1/2 = Adj/12
corss and multiply to have
2A = 12
Therefore Adj = 6
Therefore base = 6*2 = 12
Applying the formula we have Area= 1/2acsinB
Area = 1/2* 12*12*Cos60
Area = 12*1/2 =6cm²
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* (3) Find the area of the shaded area 2 of each rectangle. 7 cm 8 cm 12 cm
The area of the shaded region is 73.65 cm².
We have,
The shaded region is a triangle.
Base = x
Height = y
Now,
Using the Pythagorean theorem,
y² = 12² + 10²
y² = 144 + 100
y² = 244
y = √244
And,
x² = 8² + 5²
x² = 64 + 25
x² = 89
x = √89
Now,
Area of the shaded region.
= 1/2 x √89 x √244
= 1/2 x 9.43 x 15.62
= 73.65 cm²
Thus,
The area of the shaded region is 73.65 cm².
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Find the degree of the monomial. -3q4rs6
Therefore, the degree of the given monomial is 11.
What is monomial?In algebra, a monomial is an expression consisting of a single term. A term can be a constant, a variable, or the product of a constant and one or more variables. In other words, a monomial is a polynomial with only one term. The degree of a monomial is the sum of the exponents of its variables.
Here,
The degree of a monomial is the sum of the exponents of its variables.
For the monomial -3q⁴rs⁶, the degree would be:
4 + 1 + 6 = 11
Therefore, the degree of the monomial -3q⁴rs⁶ is 11.
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Please help studying for next grade.
98+107÷(82-12)x122
Answer:
284.06
Step-by-step explanation:
To solve this expression using the order of operations (PEMDAS), we must first perform the operations inside the parentheses: 82-12 equals 70. Next, we must perform the multiplication and division from left to right: 107 divided by 70 equals approximately 1.53, and 1.53 times 122 equals approximately 186.06. Finally, we add 98 to get our answer. Therefore, the expression 98+107÷(82-12)x122 simplifies to approximately 284.06.
Answer:
284.06
Step-by-step explanation:
got it right on edge
Two runners run in different directions, 60° apart. Alex runs at 5m/s, Barry runs at 4m/s. Barry passes through X 3 seconds after Alex passes through X. At what rate is the distance between them increasing at the instant when Alex is 20 metres past X?
Answer:
Draw a picture of Angkor Wat
For each of the figures write an absolute value equation to satisfy the given solution set -5 and -1
the given solution set {-5, -1} can be obtained by substituting either of the possible solutions into the absolute value equation and verifying that it holds.
what is an equation ?
In mathematics, an equation is a statement that asserts the equality of two mathematical expressions. An equation typically consists of two expressions separated by an equal sign, with the expression on the left side of the equal sign equal to the expression on the right side of the equal sign.
In the given question,
To write an absolute value equation that satisfies a given solution set, we need to consider the definition of absolute value. The absolute value of a number is its distance from zero the number line. Therefore, an absolute value equation can be written as follows:
|expression| = distance
where the expression is the quantity whose absolute value is being taken, and distance is a non-negative value representing the distance from zero. The equation is satisfied if and only if the expression has a distance from zero that matches the given distance.
For the solution set {-5, -1}, we can write the following absolute value equations for the given figures:
A number line with -5 and -1 marked as solutions:
|x + 3| = 2
This equation is satisfied when x = -5 or x = -1, because |-5 + 3| = 2 and |-1 + 3| = 2.
A number line with -5 and -1 equidistant from zero:
|x| = 5
This equation is satisfied when x = -5 or x = 5, because |-5| = 5 and |5| = 5.
Note that for both figures, the given solution set {-5, -1} can be obtained by substituting either of the possible solutions into the absolute value equation and verifying that it holds.
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What is the volume of a rectangular prism that is 120 centimeters by 2 meters by 1.5 meters in cubic centimeters? 3,600,000 cm 3 3,600 cm 3 36,000 cm 3 3.6 cm 3
The volume of the rectangular prism in cubic centimeters is 3,600,000
What is the volume of the rectangular prismFrom the question, we have the following parameters that can be used in our computation:
Dimension = 120 centimeters by 2 meters by 1.5 meters
The volume of the rectangular prism is the product of the dimensions
i.e.
Volume = Length * width * height
Substitute the known values in the above equation, so, we have the following representation
Volume = 120 * 2 * 1.5
Convert to cm
Volume = 120 * 200 * 150
Evaluate
Volume = 3600000
Hence, the volume in cubic centimeters is 3,600,000
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Find the circumference of a child swimming pool that has a radius of 3 feet
The circumference of a child swimming pool is 6π.
What is circumference?
The circumference of a circle or ellipse in geometry is its perimeter. That is, if the circle were opened up and straightened out to a line segment, the circumference would be the length of the arc. The curve length around any closed figure is more often referred to as the perimeter.
Here, we have
Given: A child swimming pool that has a radius of 3 feet.
We have to find the circumference.
The circumference is diameter x π
The diameter is twice the radius
c = 2πr
c = 2π(3)
= 6π
Hence, the circumference of a child swimming pool is 6π.
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Please explain how to do this (Find the trig ratio) i have no idea :(
The cosine of angle B is: cos(B) = AC / AB = 20/29
Define the Pythagorean Theorem?
The Pythagorean Theorem, a well-known geometric theorem that states that the sum of the squares of the legs of a right-angled triangle is equal to the square of the hypotenuse (the opposite side of the right angle) - that is, in familiar algebraic notation. , a2 + b2 = c2 .
In a right triangle, the cosine of an angle is defined as the ratio of the adjacent side to its hypotenuse. In this case, angle B is the angle we are interested in, and the adjacent side is side AC. Using the Pythagorean theorem, we find the length of side AC:
AC² = AB²+ BC²
AC² = 29² - 21²
AC² = 400
AC = 20
Therefore, the cosine of angle B is:
cos(B) = AC / AB = 20/29
Other trigonometric ratios of angle B can be found using the following formulas:
sin(B) = BC / AB = 21/29
tan(B) = BC / AC = 21/20
csc(B) = AB / BC = 29 / 21
sec(B) = AB / AC = 29/20
bed (B) = AC / BC = 20 / 21
Thus, the trigonometric ratios of angle B are:
sin(B) = 21/29
cos(B) = 20/29
tan(B) = 21/20
csc(B) = 29/21
sec(B) = 29/20
crib(B) = 20/21
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Downtown Mathville is laid out as a 6 x 6 square grid of streets (see diagram below). Your apartment is located at the southwest corner of downtown Mathville (see point H). Your math classroom is located at the northwest corner of downtown Mathville (see point M). You know that it is a 12-block walk to math class and that there is no shorter path. Your curious roommate (we’ll call her Curious Georgia) asks how many different paths (of length 12 blocks – you don’t want to back track or go out of your way) could you take to get from your apartment to the math class. It should also be clear that no shorter path exists. Can you solve Curious Georgia’s math problem?
Answer: 924 paths
Step-by-step explanation:
Since there is no shorter path, we know that the path must consist of 6 blocks to the north and 6 blocks to the east. Thus, the problem is equivalent to finding the number of ways to arrange 6 N's (for north) and 6 E's (for east) in a sequence such that no two N's are adjacent and no two E's are adjacent.
Let's denote N by 1 and E by 0. Then the problem is equivalent to finding the number of 12-digit binary sequences (i.e., sequences consisting of 0's and 1's) such that there are no consecutive 1's or consecutive 0's.
We can solve this problem using dynamic programming. Let F(n,0) be the number of n-digit binary sequences that end in 0 and have no consecutive 0's, and let F(n,1) be the number of n-digit binary sequences that end in 1 and have no consecutive 1's. Then we have the following recurrence relations:
F(n,0) = F(n-1,0) + F(n-1,1)
F(n,1) = F(n-1,0)
with initial values F(1,0) = 1 and F(1,1) = 1.
Using these recurrence relations, we can compute F(6,0) and F(6,1), and the total number of valid sequences is F(6,0) + F(6,1) = 132. Therefore, there are 132 different paths of length 12 blocks from your apartment to the math class.
The table shows Gillian’s Net worth. Assets are shown as positive numbers, and liabilities are shown as negative numbers. Gillian’s net worth is $90,500. Based on the information in the table, what is the number of money Gillian owes for student loan?
Answer:
Step-by-step explanation:
1 Suppose another student says he spends $29 each
week on entertainment. Will the mean and median
increase or decrease?
decreas
2 What is the new mean when the value from problem 1
is included in the data set?
Show your work. For elementary kids
Answer:
Step-by-step explanation:
Consider the two-loop circuit shown below:
Ignore the red and pencil markings, just worry about the printed questions
The variables I₁ and I₂ using the matrix algebra and using the Cramer's rule are I₁ = 1 and I₂ = 1
Writing the system of equations in matrix formFrom the question, we have the following parameters that can be used in our computation:
15I₁ + 5I₂ = 20
25I₁ + 5I₂ - 30 = 0
Rewrite as
15I₁ + 5I₂ = 20
25I₁ + 5I₂ = 30
Rewrite as
I₁ I₂
15 5 20
25 5 30
From the question, the matrix form is
AI = b
Ths matrix A from the above is
[tex]A = \left[\begin{array}{cc}15&5&25&5\end{array}\right][/tex]
Ths matrix B from the above is
[tex]B = \left[\begin{array}{c}20&30\end{array}\right][/tex]
And, we have the matrix I to be
[tex]I = \left[\begin{array}{c}I_1&I_2\end{array}\right][/tex]
Finding I₁ and I₂ using the matrix algebraStart by calculating the inverse of A from
[tex]A = \left[\begin{array}{cc}15&5&25&5\end{array}\right][/tex]
So, we have:
|A| = 15 * 5 - 5 * 25
|A| = -50
The inverse is
[tex]A^{-1} = -\frac{1}{50}\left[\begin{array}{cc}5&-5&-25&15\end{array}\right][/tex]
Recall that
AI = b
So, we have
[tex]I = -\frac{1}{50}\left[\begin{array}{cc}5&-5&-25&15\end{array}\right] * \left[\begin{array}{c}20&30\end{array}\right][/tex]
Evaluate the products
[tex]I = -\frac{1}{50}\left[\begin{array}{c}5 * 20 + -5 * 30&-25 * 20 + 15 *30\end{array}\right][/tex]
[tex]I = -\frac{1}{50}\left[\begin{array}{c}-50&-50\end{array}\right][/tex]
Evaluate
[tex]I = \left[\begin{array}{c}1&1\end{array}\right][/tex]
Recall that
[tex]I = \left[\begin{array}{c}I_1&I_2\end{array}\right][/tex]
So, we have
I₁ = 1 and I₂ = 1
Finding I₁ and I₂ using the Cramer's rule,Recall that the determinant of matrix A calculated in (a) is
|A| = -50
Replace the first column in A with b
So, we have
[tex]AI_1 = \left[\begin{array}{cc}20&5&30&5\end{array}\right][/tex]
Calculate the determinant
DI₁ = 20 * 5 - 30 * 5
DI₁ = -50
Replace the second column in A with b
So, we have
[tex]AI_2 = \left[\begin{array}{cc}15&20&25&30\end{array}\right][/tex]
Calculate the determinant
DI₂ = 15 * 30 - 20 * 25
DI₂ = -50
So, we have
I₁ = DI₁ / |A| = -50/-50 = 1
I₂ = DI₂ / |A| = -50/-50 = 1
So, we have
I₁ = 1 and I₂ = 1
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Angle & segment relationship
Area & Arc Length
BRAINLIEST find the volume and surface area of a hypotenuse of a triangular right base that is 25 m . 7m height 24 m base? 22m length?
Answer:
Volume = (1/2)(7)(24)(22) =
1,848 cubic meters
Surface area = 2(1/2)(7)(24) + 7(22) + 22(24) + 22(25) = 1,400 square meters
Find sin(π/4). Round to 3 decimal places.
Step-by-step explanation:
sin (pi/4) = sqrt(2) / 2 = .707
you either just know this after a time or you can use a calculator (in RADIAN mode)
Answer:
sin(π/4) = sin(45°) = 0.707106781186548 ≈ 0.707 (rounded to 3 decimal places)
Step-by-step explanation:
here are the steps:
Convert π/4 to degrees: π/4 * (180/π) = 45°
Use the definition of sine to find the sine of 45°:sin(45°) = opposite/hypotenuse
In a right-angled triangle with an angle of 45°, the opposite and adjacent sides are equal, so we have:sin(45°) = opposite/hypotenuse = adjacent/hypotenuse = 1/√2
Rationalize the denominator by multiplying both the numerator and denominator by √2:sin(45°) = 1/√2 * √2/√2 = √2/2
Round to 3 decimal places: sin(45°) ≈ 0.707Therefore, sin(π/4) = sin(45°) = √2/2 ≈ 0.707 (rounded to 3 decimal places).
if a1 = 6 and an =5an-1 then find the value of a6
To find the value of a6, we need to first determine the value of a2, a3, a4, and a5 using the given recurrence relation:
a1 = 6
a2 = 5a1 = 5(6) = 30
a3 = 5a2 = 5(30) = 150
a4 = 5a3 = 5(150) = 750
a5 = 5a4 = 5(750) = 3750
Now, we can find a6 using the recurrence relation:
a6 = 5a5 = 5(3750) = 18750
Therefore, the value of a6 is 18750.
The Wills Tower (formerly known as the Sears Tower) in Chicago is about 454 feet tall A model of it has a scale of 2 in 45 feet. How tall is the model?
The model is 64.62 inches tall. The solution has been obtained by using the arithmetic operations.
What are arithmetic operations?
Any real number may be explained using the four basic operations, also referred to as "arithmetic operations." In mathematics, operations like division, multiplication, addition, and subtraction come first, followed by operations like quotient, product, sum, and difference.
We are given that height of tower is 1454 feet and the scale is given as follows:
2 inches = 45 feet
Now, using the division operation, we get
⇒ Height of the model = 1,454 ÷ 45
⇒ Height of the model = 32.31
Now, using the multiplication operation, we get
⇒ Height of the model = 32.31 * 2
⇒ Height of the model = 64.62 inches
Hence, the model is 64.62 inches tall.
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The correct question has been attached below.
Someone please answer this question
Some forms of cardiovascular disease involve the buildup of plaque on the inside walls of blood vessels. The buildup can put added stress on the heart and vessels, reducing or preventing blood flow to vital organs of the body.
Imagine that the diagram is a circular cross section of a blood vessel. What is the area of the inside of the blood vessel (i.e., the yellow part) in square units? Round your answer to the nearest tenth. The equation for the area of a circle is A = πr2, where A is area, π ≈ 3.14, and r is the radius. Recall that the radius is half of the diameter.
Answer:
153.94 cm2
Step-by-step explanation:
Circle area = π * r² = π * 49 [cm²] ≈ 153.94 [cm²]
π ≈ 3.14159265 ≈ 3.14
d = r * 2 = 7 [cm] * 2 = 14 [cm]
MARK AS BRAINLIEST PLS I TOOK 3 HOURS THINKING ABOUT THIS
A suitcase is a rectangular prism whose dimensions are 2 3 foot by 1 1 2 feet by 1 1 4 feet. Find the volume of the suitcase.
The volume of the suitcase is 35/8 cubic feet or approximately 4.375 cubic feet.
What is rectangular prism?A rectangular prism is a three-dimensional solid object that has six faces, where each face is a rectangle. It is also called a rectangular parallelepiped. A rectangular prism is a type of prism because it has a constant cross section along its length.
According to question:A rectangular prism's volume V is determined by:
V = l × w × h
where l denotes the prism's length, w its width, and h its height. Here are the facts:
l = 2 3 ft
w = 1 1/2 ft
h = 1 1/4 ft
When we enter these values into the formula, we obtain:
V = (2 3 ft) × (1 1/2 ft) × (1 1/4 ft)
= (7/3 ft) × (3/2 ft) × (5/4 ft)
= 35/8 ft³
Therefore, the volume of the suitcase is 35/8 cubic feet or approximately 4.375 cubic feet.
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Construct a polynomial function with the following properties: third degree, only real coefficients, −1 and 4+i are two of the zeros, y-intercept is −17 .
The polynomial function with the given properties is:[tex]f(x) = x^3 - 7x^2 + 9x - 17[/tex]
What do you mean by polynomial function?A polynomial function is a function that contains only non-negative integer powers or only positive integer exponents in the equation, such as a quadratic equation, a cubic equation, etc. For example, 2x + 5 is a polynomial whose exponent is 1.
Since the polynomial has real coefficients and one of its zeros is complex, the complex conjugate of 4+ i, which is 4-i, must also be zero. So the three zeros of the polynomial are -1, 4+i and 4-i. To form a polynomial with these zeros, we start by writing the factors of the polynomial:
(x + 1) (x - 4 - i) (x - 4 + i)
We can simplify this expression by multiplying the factors:
[tex](x + 1) (x^2 - 8x + 17)[/tex]
Expanding this, we get:
[tex]x^3 - 7x^2+ 9x - 17[/tex]
Thus, the polynomial function with the given properties is:
[tex]f(x) = x^3 - 7x^2 + 9x - 17[/tex]
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The polynomial function is p(x) = (-17/5)x³ + (34/5)x² + (33/5)x - 16
What do you mean by polynomial function?A polynomial function is a function that contains only non-negative integer powers or only positive integer exponents in the equation, such as a quadratic equation, a cubic equation, etc. For example, 2x + 5 is a polynomial whose exponent is 1.
If -1 is a zero of the polynomial function, then x+1 is a factor of the polynomial. Similarly, if 4+i is a zero, then 4-i is also a zero, because complex roots always occur in conjugate pairs. Therefore, (x+1) and (x - 4 - i)(x - 4 + i) = (x - 4)² + 1 are factors of the polynomial. We can then construct the polynomial function by multiplying these factors:
p(x) = A(x+1)(x - 4 - i)(x - 4 + i)
where A is a constant that we need to determine, and p(x) is the desired third-degree polynomial function.
To determine A, we can use the y-intercept given in the problem. The y-intercept is the value of p(0), so:
p(0) = A(0+1)(0 - 4 - i)(0 - 4 + i) = A(17+4i)
But we also know that p(0) = -17, so:
-17 = A(17+4i)
Solving for A:
A = -17/(17+4i) = (-17/5) + (68/5)i
Therefore, the polynomial function we seek is:
p(x) = [(-17/5) + (68/5)i](x+1)(x - 4 - i)(x - 4 + i)
Expanding the product and simplifying, we get:
p(x) = (-17/5)x³ + (34/5)x² + (33/5)x - 16
This is a third-degree polynomial with only real coefficients, -1 and 4+i are two of the zeros, and the y-intercept is -17.
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