The point of intersection is (17/9, -4/9, 29/9). The process of finding the point of intersection between a line and a plane involves substituting the parametric equations of the line into the equation of the plane.
To find the point of intersection between the line and plane, we need to substitute the parametric equations of the line into the equation of the plane. This gives us:
2 + 2(4t) - (2 - 3t) + 1 = 0
Simplifying, we get:
9t + 1 = 0
Therefore, t = -1/9. We can substitute this value of t into the parametric equations of the line to find the coordinates of the point of intersection:
x = 1 + 2(-1/9) = 17/9
y = 4(-1/9) = -4/9
z = 2 - 3(-1/9) = 29/9
So the point of intersection is (17/9, -4/9, 29/9). The process of finding the point of intersection between a line and a plane involves substituting the parametric equations of the line into the equation of the plane. This allows us to solve for the value of the parameter that corresponds to the point of intersection. Once we have this value, we can substitute it back into the parametric equations of the line to find the coordinates of the point. It is important to note that not all lines intersect with all planes, and some may intersect at multiple points or not intersect at all. Therefore, it is important to carefully analyze the equations and properties of both the line and plane before attempting to find their point of intersection.
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Complete the square to re-write the quadratic function in vertex form:
Answer: y=−(x−5/2)^2−3/4
find the taylor polynomial t3(x) for the function f centered at the number a. f(x) = xe−7x,
The Taylor polynomial t3(x) for the function f(x) = xe−7x centered at a is:
t3(x) = f(a) + f'(a)(x-a) + f''(a)(x-a)2/2! + f'''(a)(x-a)3/3!
To find the Taylor polynomial t3(x), we need to compute the first three derivatives of f(x):
f(x) = xe−7x
f'(x) = e−7x − 7xe−7x
f''(x) = 49xe−7x − 14e−7x
f'''(x) = −343xe−7x + 147e−7x
Next, we evaluate these derivatives at x = a and simplify:
f(a) = ae−7a
f'(a) = e−7a − 7ae−7a
f''(a) = 49ae−7a − 14e−7a
f'''(a) = −343ae−7a + 147e−7a
Now, we plug these values into the formula for t3(x):
t3(x) = ae−7a + (e−7a − 7ae−7a)(x-a) + (49ae−7a − 14e−7a)(x-a)2/2! + (−343ae−7a + 147e−7a)(x-a)3/3!
We can simplify this expression to obtain the final form of t3(x):
t3(x) = ae−7a + (x-a)e−7a(1-7(x-a)) + (x-a)2e−7a(49a-7) + (x-a)3e−7a(-343a+147)/6
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The diameter of a planet at its equator is 5110 kilometers Estimate using scientific notation
Answer:
5.11 × 10^3 km
Step-by-step explanation:
5,110 km ÷ 1,000 = 5.11 × 10^3 km
Therefore, the diameter of the planet at its equator in scientific notation is 5.11 × 10^3 km.
write a function computenum that takes one integer parameter and returns 9 times the parameter. ex: computenum(3) returns 27.
The function `computenum` is a simple Python function that takes an integer parameter and returns the product of the parameter and 9. This means that the function returns a value that is nine times the value of the input parameter.
The `computenum` function can be implemented in Python using a single line of code, as shown below:
```python
def computenum(num):
return num * 9
```
This code defines a function called `computenum` that takes a single parameter called `num`. The function body consists of a single line of code that multiplies `num` by 9 and returns the result. When the function is called with an integer argument, it returns the product of that argument and 9. This function can be used in various contexts where a value needs to be multiplied by 9.
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which value of r indicates a stronger correlation than 0.40?
A value of r greater than 0.40 indicates a stronger correlation than 0.40.
The correlation coefficient, denoted as "r," measures the strength and direction of the linear relationship between two variables. The value of r ranges from -1 to 1. When the absolute value of r is closer to 1, it indicates a stronger correlation. In this case, a value of r greater than 0.40 suggests a stronger positive correlation than 0.40.
This means that as one variable increases, the other variable tends to increase as well, and the relationship between the variables is more pronounced. For example, if the correlation coefficient is 0.60, it indicates a stronger positive correlation than 0.40. Similarly, if the correlation coefficient is 0.90, it indicates an even stronger positive correlation. On the other hand, if the correlation coefficient is negative, such as -0.60 or -0.90, it indicates a stronger negative correlation.
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find the first four nonzero terms of the taylor series about 0 for the function t3sin(5t). t3sin(5t)≈
To find the Taylor series about 0 for the function t3sin(5t), we need to compute its derivatives up to the fourth order at x = 0. First, let's compute the first four derivatives:
f(t) = t^3sin(5t)
f'(t) = 3t^2sin(5t) + 5t^3cos(5t)
f''(t) = 6tsin(5t) + 30t^2cos(5t) - 25t^3sin(5t)
f'''(t) = 6sin(5t) + 90tcos(5t) - 75t^2sin(5t)
f''''(t) = 450cos(5t) - 270t sin(5t)
Next, we evaluate these derivatives at x = 0:
f(0) = 0
f'(0) = 0
f''(0) = 0
f'''(0) = 6
f''''(0) = 450
Finally, we can write the Taylor series about 0 for t3sin(5t) as:
t^3sin(5t) ≈ 0 + 0t + 0t^2 + (6/3!)t^3 + (450/4!)t^4
≈ (1/3!)t^3 + (1/4)t^4
Therefore, the first four nonzero terms of the Taylor series about 0 for t3sin(5t) are (1/3!)t^3 and (1/4!)t^4. These terms approximate the function t3sin(5t) near x = 0 with increasing accuracy as x gets closer to 0.
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Please Help me on this, I'm a bit stuck on this one! Thanks if you do!
Answer:
z = 56
Step-by-step explanation:
124 and Z form a straight line so they will add to 180
124+z = 180
z = 180-124
z = 56
Answer:
z = 56°
Step-by-step explanation:
We know that vertically opposite angles are equal.
∴ y = 124°
We know that angles in a straight line are added up to 180°.
∴ y + z = 180
124 + z = 180
z = 180 - 124
z = 56°
x = 56° ( vertically opposite angles ⇒ x = z )
Which problem situation corresponds to the equation 84 - 8x = 52 ?
Corresponds to the equation 84 - 8x = 52 is one where there is a total of 84 items and each item costs 8 dollars less than the previous one. The goal is to determine how many items can be purchased with a budget of 52 dollars. Therefore, In this situation, you gave marbles to 4 friends, with each friend receiving 8 marbles.
Situation, You have 84 marbles in a jar. You want to divide the marbles into equal groups to give away to your friends. After distributing the marbles, you have 52 marbles remaining in the jar. How many friends did you give the marbles to....
Equation , The equation representing this situation is 84 - 8x = 52, where x represents the number of friends you gave the marbles to, and 8 represents the number of marbles in each group.
1. Write down the equation: 84 - 8x = 52
2. To find the value of x, we will first isolate the term containing x. To do this, we need to move the constant term (84) to the other side of the equation by subtracting it from both sides: -8x = 52 - 84
3. Perform the subtraction: -8x = -32
4. Now, to solve for x, we will divide both sides of the equation by -8: x = -32 / -8
5. Perform the division: x = 4
Therefore, In this situation, you gave marbles to 4 friends, with each friend receiving 8 marbles.
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Find the area lying outside r=4sinθ and inside r=2+2sinθ.
The area lying outside r=4sinθ and inside r=2+2sinθ is approximately 10.81 square units.
To find the area lying outside r=4sinθ and inside r=2+2sinθ, we need to first graph these two polar curves.
r=4sinθ is a cardioid, while r=2+2sinθ is a limacon with an inner loop.
The area we are looking for is the shaded region between these two curves.
To find the area, we need to integrate the difference between the outer curve (r=4sinθ) and the inner curve (r=2+2sinθ) from θ=0 to θ=2π:
Area = ∫(4sinθ)^2 - (2+2sinθ)^2 dθ from θ=0 to θ=2π
This simplifies to:
Area = ∫(16sin^2θ - 4 - 8sinθ - 4sin^2θ) dθ from θ=0 to θ=2π
Area = ∫(12sin^2θ - 8sinθ - 4) dθ from θ=0 to θ=2π
Using trigonometric identities and integration techniques, we can solve for the area:
Area = 4π - 8/3
Therefore, the area lying outside r=4sinθ and inside r=2+2sinθ is approximately 10.81 square units.
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In Example 5.4 and Exercise 5.5, we considered the joint density of Y1, the proportion of the capacity of the tank that is stocked at the beginning of the week, and Y2, the proportion of the capacity sold during the week, given bya Find the marginal density function for Y2.b For what values of y2 is the conditional density f (y1|y2) defined?c What is the probability that more than half a tank is sold given that three-fourths of a tank is stocked?
The probability that more than half a tank is sold given that three-fourths of a tank is stocked is P(Y2 > 1/2 | Y1 = 3/4) = ∫ f(y1=3/4 | y2) dy2, with integration limits from 1/2 to the upper limit of the domain of Y2.
a) To find the marginal density function for Y2, we need to integrate the joint density function f(y1, y2) with respect to y1 over its domain. The marginal density function for Y2 is given by:
f_Y2(y2) = ∫ f(y1, y2) dy1
b) The conditional density f(y1|y2) is defined for values of y2 for which the marginal density function f_Y2(y2) is positive. In other words, we need to find the range of y2 values for which f_Y2(y2) > 0.
c) The probability that more than half a tank is sold given that three-fourths of a tank is stocked can be found using the conditional density f(y1|y2). Let Y1 = 3/4 and Y2 > 1/2. Then the probability is given by:
P(Y2 > 1/2 | Y1 = 3/4) = ∫ f(y1=3/4 | y2) dy2, with integration limits from 1/2 to the upper limit of the domain of Y2.
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For the pair of functions, write the composite function and its derivative in terms of one input variable.c(x) = 3x2 − 7; x(t) = 2 − 6tc(x(t)) = ?dc dt = ?.
The composite function is c(x(t)) = 3(2-6t)^2 - 7, and its derivative with respect to t is dc/dt = -72 + 216t.
To write the composite function, we substitute the expression for x(t) into c(x), giving c(x(t)) = 3(2-6t)^2 - 7.
To find the derivative of this composite function with respect to t, we use the chain rule:
dc/dt = (dc/dx) * (dx/dt)
where (dc/dx) is the derivative of c(x) with respect to x, and (dx/dt) is the derivative of x(t) with respect to t.
Taking the derivative of c(x) = 3x^2 - 7 with respect to x, we get:
dc/dx = 6x
And taking the derivative of x(t) = 2 - 6t with respect to t, we get:
dx/dt = -6
Substituting these values into the chain rule formula, we get:
dc/dt = (6x) * (-6)
Since x(t) = 2-6t, we can substitute that expression for x to get:
dc/dt = (6(2-6t)) * (-6)
Simplifying, we get:
dc/dt = -72 + 216t
So the composite function is c(x(t)) = 3(2-6t)^2 - 7, and its derivative with respect to t is dc/dt = -72 + 216t.
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WILL GIVE BRAINLIEST AND 100 POINTS PLS HELP A small tree that is 6 feet tall casts a 4-foot shadow, while a building that is 27 feet tall casts a shadow in the same direction. Determine the length of the building's shadow.
12 feet
14 feet
15 feet
18 feet
Answer:
should be 18 ft
Step-by-step explanation:
6÷4= 1.5
27÷1.5= 18
Find the coordinates of all the points whose distance from (-3,-4) is the square root of 10 and whose distance from (1,0) is the square root of ten
The points whose distance from (-3,-4) is the square root of 10 and whose distance from (1,0) is the square root of 10 are given by the circle (x+3)^2 + (y+4)^2 = 2, which has center (-3,-4) and radius sqrt(2).
The problem involves finding all points that are equidistant from two given points. These points will lie on the perpendicular bisector of the line segment joining the two given points.
First, we find the midpoint of the line segment joining (-3,-4) and (1,0), which is ((-3+1)/2, (-4+0)/2) = (-1,-2).The line passing through (-1,-2) and perpendicular to the line joining (-3,-4) and (1,0) can be found by finding the negative reciprocal of the slope of that line. The slope of the line joining (-3,-4) and (1,0) is (0-(-4))/(1-(-3)) = 4/4 = 1. So the slope of the perpendicular line is -1/1 = -1.
Now we have the slope and a point on the perpendicular line, so we can find its equation using point-slope form: y - (-2) = (-1)(x - (-1)) => y = -x - 1.
Next, we find the points that are a distance of sqrt(10) from (-3,-4) and also from (1,0). Let (x,y) be a point on the line y = -x - 1. The distance from (-3,-4) to (x,y) is sqrt((x-(-3))^2 + (y-(-4))^2), which simplifies to sqrt(x^2 + y^2 + 6x + 8y + 25). Similarly, the distance from (1,0) to (x,y) is sqrt((x-1)^2 + y^2). Setting these two expressions equal to sqrt(10) and squaring both sides, we get the equation x^2 + y^2 + 6x + 8y + 15 = 0.
We can complete the square to rewrite this equation as (x+3)^2 + (y+4)^2 = 2. This is the equation of a circle centered at (-3,-4) with radius sqrt(2). The coordinates of all points equidistant from (-3,-4) and (1,0) are given by the points on this circle.
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Jeremiah needed dog food for his new puppy. He compared the prices and sizes of three types of dog food.
Canine Cakes Bark Bits Woofy Waffles
Size- (pounds) 16. 50 40
Cost- $24 $82 $48
Part A: Calculate the corresponding unit rate for each package.
Part B: Determine the best buy using the unit rates found in Part A. Explain your answer.
if Jeremiah wants to get the most dog food for his money, he should buy the Woofy Waffles.
For Part A,
According to the given data in the table,
To calculate the unit rate for each package,
Simply divide the cost by the size.
So, for Canine Cakes,
The unit rate would be $24 ÷ 16 pounds = $1.50 per pound.
For Bark Bits,
The unit rate would be $82 ÷ 50 pounds = $1.64 per pound.
And for Woofy Waffles,
The unit rate would be $48 ÷ 40 pounds = $1.20 per pound.
For Part B,
To determine the best buy using the unit rates found in Part A.
The best buy is the package with the lowest unit rate,
because that means you're getting the most product for your money.
In this case,
The package with the lowest unit rate is Woofy Waffles,
At $1.20 per pound.
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ali is a professional basketball player who has determined that he makes nine 3pt shots per every ten attempts. what is the probability that out of 25 shots he misses 4?
The probability that Ali misses 4 shots out of 25, given that he has a 3-point shooting percentage of 9/10 or 0.9, is approximately 0.1394, or about 13.94%.
What is probability?The probability of an event occurring is defined by probability. There are numerous real-life scenarios in which we must forecast the outcome of an occurrence.
We can use the binomial distribution to find the probability that Ali misses 4 shots out of 25, given that he has a 3-point shooting percentage of 9/10 or 0.9.
Let X be the number of missed shots out of 25 attempts. Since each shot is either a miss or a make, this is a binomial distribution with n = 25 and p = 1 - 9/10 = 1/10. We want to find P(X = 4), which is:
P(X = 4) = (25 choose 4) * (1/10)⁴ * (9/10)²¹
where "25 choose 4" is the number of ways to choose 4 shots out of 25.
Using a calculator, we can evaluate this expression to find:
P(X = 4) ≈ 0.1394
Therefore, the probability that Ali misses 4 shots out of 25, given that he has a 3-point shooting percentage of 9/10 or 0.9, is approximately 0.1394, or about 13.94%.
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We need to write 5 3/4 as a decimal.
The decimal form of the given number which is 5 3/4 is 5.75.
Given number = 5 3/4.
The given number is a fractional number, which is looking like a mixed fraction.
To write the mixed fraction into decimal form first, we have to write it into normal fraction, later we divide it to get the required decimal form.
To convert mixed fraction into normal fraction,
5 3/4 = ((4*5) + 3) / 4 = 23/4
So, the fraction is 23/4.
To convert the fraction into a decimal, we have to divide the numerator by the denominator as shown below,
23/4 = 5.75
From the above analysis, we can conclude that the decimal form of 5 3/4 is 5.75.
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find the first partial derivatives of f(x,y)=3x−4y3x 4y at the point (x,y)=(3,1). ∂f∂x(3,1)= ∂f∂y(3,1)=
The first partial derivatives of f(x,y) at the point (3,1) are:
∂f/∂x(3,1) = 3
∂f/∂y(3,1) = -12
To find the first partial derivatives of f(x,y) at the point (3,1), we need to find the partial derivative with respect to x and y, respectively, and then substitute x=3 and y=1.
So, let's begin with the partial derivative with respect to x:
∂f/∂x = 3 - 0 (since the derivative of 3x with respect to x is 3, and the derivative of 4y with respect to x is 0)
Now, we can substitute x=3 and y=1 into this expression:
∂f/∂x(3,1) = 3 - 0 = 3
So, the partial derivative of f(x,y) with respect to x at the point (3,1) is 3.
Next, let's find the partial derivative with respect to y:
∂f/∂y = 0 - 12y^2 (since the derivative of 3x with respect to y is 0, and the derivative of 4y with respect to y is 12y^2)
Now, we can substitute x=3 and y=1 into this expression:
∂f/∂y(3,1) = 0 - 12(1)^2 = -12
So, the partial derivative of f(x,y) with respect to y at the point (3,1) is -12.
Therefore, the first partial derivatives of f(x,y) at the point (3,1) are:
∂f/∂x(3,1) = 3
∂f/∂y(3,1) = -12
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when a coin is tossed three times, what is the probability that all three tosses are heads? the possible outcomes for the coin tosses are{hhh,ttt,htt,hht,thh,tth,hth,tht}
The probability of getting all three tosses to head is 1/8.
We have,
When a coin is tossed, there are two possible outcomes:
heads (H) or tails (T).
Since there are three tosses, the total number of possible outcomes.
2³ = 8.
The probability of getting heads on one toss is 1/2.
The probability of getting heads on all three tosses is the product of the probabilities of getting heads on each individual toss:
P(HHH) = P(H) x P(H) x P(H) = (1/2) x (1/2) x (1/2) = 1/8.
Therefore,
The probability of getting all three tosses to head is 1/8.
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Which description explains how the graph of f(x)=x√ could be transformed to form the graph of g(x)=x+9
Answer:
To transform the graph of f(x)=x√ into g(x)=x+9, we need to apply a horizontal shift to the right by 9 units. This can be done by replacing x in f(x) with x-9 to get g(x)=(x-9)√. The resulting graph will be the same as the graph of f(x), but shifted 9 units to the right.
arenthesize an Arithmetic Expression Suppose you are given a sequence of n nonnegative numbers separated by n-1 addition (+) and and multiplication (x) operators, e.g., 2x3 x 0+6+2 x 5 +4. Depending on how you parenthesize the expression it may evaluate to different values, e.g., for the expression above: ((2 x 3) x (0 + 6)) + (2 x (5 + 4)) 54 (2 x 3) (0+ (6 + 2) (5 + 4))) 432 (2 x (3 x 0)) + (6 + ((2 x 5) + 4)) 20 = = Suppose the n numbers are given in the array A[1: n), where for 1
To parenthesize an arithmetic expression with n nonnegative numbers and n-1 addition and multiplication operators, determine the different ways to parenthesize the expression and evaluate each expression to find the different possible values.
To parenthesize an arithmetic expression with a given sequence of n nonnegative numbers separated by n-1 addition (+) and multiplication (x) operators, follow these steps:
1. Identify the sequence of numbers and operators: In the example provided, the sequence is 2x3x0+6+2x5+4.
2. Determine the possible parenthesizations: You can parenthesize the expression in different ways to get different results, such as:
- ((2x3)x(0+6))+(2x(5+4)) = 54
- (2x3)((0+(6+2))(5+4)) = 432
- (2x(3x0))+(6+((2x5)+4)) = 20
3. Evaluate each parenthesized expression: Calculate the values of each expression by following the order of operations (PEMDAS) - Parentheses, Exponents, Multiplication, and Division (from left to right), and Addition and Subtraction (from left to right).
In summary, to parenthesize an arithmetic expression with n nonnegative numbers and n-1 addition and multiplication operators, determine the different ways to parenthesize the expression and evaluate each expression to find the different possible values.
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Can you explain your answer please?
Answer:
A. 24 inches
Step-by-step explanation:
A cube is defined by having all three lengths being of equal size,
[tex]V = L^3[/tex]
so to find length from the volume of a cube, you must take the cube root of the volume.
[tex]\sqrt[3]{V} = L[/tex]
[tex]\sqrt[3]{216} = 6[/tex]
That means each side of the cube has a length of 6 inches.
The formula for the perimeter is give below the cube diagram.
[tex]P = 4L[/tex]
Which means we just take the length we found above and multiply it by 4.
[tex]4*6 =24[/tex] inches
Therefore 24 inches is your answer.
find the upper and lower bound approximation within 0.005 of pi
The upper bound approximation for pi within 0.005 is 3.150 and the lower bound approximation is 3.140.
we can use the fact that pi is approximately equal to 3.14159. To find the upper and lower bound approximations, we need to add or subtract 0.005 from this value.
For the upper bound approximation, we add 0.005 to 3.14159, which gives us 3.14659. Since pi is greater than this value, we need to round up to the nearest hundredth, giving us 3.150.
For the lower bound approximation, we subtract 0.005 from 3.14159, which gives us 3.13659. Since pi is less than this value, we need to round down to the nearest hundredth, giving us 3.140.
the upper and lower bound approximations for pi within 0.005 are 3.150 and 3.140 respectively.
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An arithmetic sequence contains the terms a2 = 17, a4 = 41, and a7 = 77. Which formula represents the nth term of the sequence?
The arithmetic sequence is solved and the nth term is Aₙ = 5 + ( n - 1 )12
Given data ,
Let the terms of the AP be represented as
a₂ = 17, a₄ = 41, and a₇ = 77
So , a + d = 17
Now , a₂ + 2d = 41
On simplifying , we get
2d = 24
Divide by 2 on both sides , we get
d = 12
So , the first term is a = a₂ - 12
a = 5
So , the nth term of AP is Aₙ = 5 + ( n - 1 )12
Hence , the arithmetic progression is solved
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I’m the bridge shown, the steel beams that are used to create the outer edges form an isosceles trapezoid.
The perimeter of the isosceles trapezoid is equal to 456 feet which makes the option c correct.
What is an Isosceles trapezoidThis is a trapezoid in which the base angles are equal and therefore the left and right side lengths are also equal. The opposite angles are supplementary which implies they sum up to 180°.
We shall first find the length of the left and right sides which are of same length as follows:
3x - 2 = 2x + 3
3x - 2x = 3 + 2
x = 5
PQ = 6(25) - 10 = 140
QR = 3(25) - 22 = 53
RS = 9(25) - 15 = 210
PS = 2(25) + 3 = 53
perimeter of the Isosceles trapezoid = 140ft + 53ft + 210ft + 53ft
perimeter of the Isosceles trapezoid = 456ft.
Therefore, the perimeter of the isosceles trapezoid is equal to 456 feet which makes the option c correct.
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What is the product of (five to the -1st power )( five to the -3rd power)
The product of (five to the -1st power) and (five to the -3rd power) can be calculated using the properties of exponents. So, the product of (five to the -1st power) and (five to the -3rd power) is equal to 1/625.
When multiplying two expressions with the same base (in this case, five) and different exponents, you can simply add the exponents together. So, for this problem, you will add the exponents -1 and -3, resulting in an exponent of -4.
Therefore, the product of (five to the -1st power) and (five to the -3rd power) is equal to five to the -4th power. To express this as a positive exponent, you can rewrite it as a fraction with the exponent in the denominator: 1/(five to the 4th power). Now, calculate the value: 1/(5^4) = 1/625.
In conclusion, the product of (five to the -1st power) and (five to the -3rd power) is equal to 1/625.
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if a table is in 1nf and its primary key is not a composite key, then the table is also in 2nf. group of answer choices true false
True. If a table is in 1NF (First Normal Form) and its primary key is not a composite key, then the table is also in 2NF (Second Normal Form).
1NF requires that a table has no repeating groups, and all entries in a column are of the same data type. In other words, each attribute must have a single value, and there can't be multiple instances of the same attribute within a single row. This ensures that the table is well-structured and organized. 2NF builds on the requirements of 1NF and mandates that a table should have no partial dependencies. This means that each non-primary key attribute must be fully functionally dependent on the entire primary key, and not just a part of it. When the primary key is not a composite key, it means that it consists of a single attribute. In this case, all non-primary key attributes would be fully functionally dependent on the primary key by default, as there are no other components in the primary key for partial dependency to occur. Therefore, if a table with a non-composite primary key is in 1NF, it will also satisfy the conditions for 2NF.
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Exercise 2.2 Concise Elective Ma 1. In a certain class, 12 students study History, 13 study Government and 15 study Akan. Each student in the class studies at least one of the three subject, 6 students study two of the three subjects and 3 students studies all three subjects. Find (i) the number of students who are in the class (ii) those who study only one subject
(q22) Find the area of the shaded region.
The area between the functions f(x) = 2 · x + 6 and g(x) = 2 · x² + 2 is equal to 8.333 square units. (Right choice: C)
How to determine the area between two curves
In this question we must determine the area between the functions f(x) = 2 · x + 6 and g(x) = 2 · x² + 2, this can be done by using the following definite integral:
A = ∫²₋₁ [f(x) - g(x)] dx
A = ∫²₋₁ f(x) dx - ∫²₋₁ g(x) dx
A = ∫²₋₁ (2 · x + 6) dx - ∫²₋₁ (2 · x² + 2) dx
A = x²|²₋₁ + 6 · x|²₋₁ - (2 / 3) · x³|²₋₁ - 2 · x|²₋₁
A = 2² - (- 1)² + 6 · [2 - (- 1)] - (2 / 3) · [2³ - (- 1)³] - 2 · [2 - (- 1)]
A = 1 + 18 - 14 / 3 - 6
A = 8.333
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Solve this problem, ASAP
The maximum area that can be enclosed with 92 yards of fencing material is 1058 square yards.
How to calculate the areaSolving the equation for W, we get:
W = 92 - 2L
Substituting this value of W into the area equation, we have:
Area = L * (92 - 2L)
Area = 92L - 2L²
In our case, a = -2 and b = 92. Substituting these values, we get:
L = -92 / (2 * -2)
L = -92 / -4
L = 23
Substituting this value of L back into the equation for W, we have:
W = 92 - 2(23)
W = 92 - 46
W = 46
Therefore, the dimensions of the rectangular garden that maximize the enclosed area are L = 23 yards and W = 46 yards.
Area = L * W
Area = 23 * 46
Area = 1058 square yards
So, the maximum area that can be enclosed with 92 yards of fencing material is 1058 square yards.
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He pays $4 for parking and $12 for each pizza he buys. If he plays a total of $52 how many pizzas did he buy
Answer:
4 pizzas
Step-by-step explanation:
first of all, subtract parking fee from total:
52 - 4 = 48.
now divide by 12:
48/12
4.
so he he pays for 4 pizzas at $12 each (4 X 12 = 48).
and he pays $4 for parking.
48 + 4 = 52.