To find the equation of the plane that passes through the point (0, 9, 0) and is perpendicular to the vector n = -2i ÷ 4k, we first need to find the normal vector of the plane.
Since the plane is perpendicular to the given vector, the normal vector will be parallel to it. So, we can take the given vector and multiply it by -1 to get a vector in the opposite direction, which will be normal to the plane.
n = -2i ÷ 4k = -1/2i ÷ k
Multiplying by -1 gives us:
n = 1/2i ÷ k
Now we can use the point-normal form of the equation of a plane:
r · n = d
where r is the position vector of any point on the plane, n is the normal vector, and d is the distance of the plane from the origin (since the normal vector is normalized, d will be the signed distance of the plane from the origin).
Substituting the given point (0, 9, 0) and the normal vector n = 1/2i ÷ k into the equation, we get:
(0, 9, 0) · (1/2i ÷ k) = d
0 + 9(1/2) + 0 = d
d = 4.5
So the equation of the plane is:
x/2 + z/2 = 4.5
or, multiplying by 2 to eliminate fractions:
x + z = 9
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If JM=10 and LM=14, what is KM?
Write your answer as a whole number or as a decimal rounded to the nearest hundredth.
KM =
The calculated value of the length of segment KM is 11.83
Calculating the length of KMFrom the question, we have the following parameters that can be used in our computation:
JM = 10
LM = 14
Using the similar triangle ratio, we have
JM/KM = KM/LM
substitute the known values in the above equation, so, we have the following representation
10/KM = KM/14
So, we have
KM^2 = 10 * 14
Evaluate
KM^2 = 140
This gives
KM = 11.8321595662
As a decimal rounded to the nearest hundredth, we have
KM = 11.83
HEnce, the value of KM is 11.83
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Find the area of a triangle that has sides of 7, 9, and 12 inches
The area of the triangle is approximately 31.3049 square inches.
The area of a triangle can be found using the formula: A = (1/2)bh, where b is the length of the base of the triangle, and h is the height (or perpendicular distance from the base to the opposite vertex).
However, in this case, we don't have the height. Instead, we can use
Heron's formula, which only requires the lengths of the three sides of the triangle:
A = √[s(s-a)(s-b)(s-c)],
where a, b, and c are the lengths of the sides of the triangle, and s is the semiperimeter (half the perimeter): s = (a + b + c)/2.
Using the given values, we have:
s = (7 + 9 + 12)/2 = 14
A = √[14(14-7)(14-9)(14-12)]
A = √[14(7)(5)(2)]
A = √(980)
A ≈ 31.3049 square inches
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For the differential equation
s′′+bs′+6s=0,
find the values of b that make the general solution overdamped, underdamped, or critically damped.
(For each, give an interval or intervals for b for which the equation is as indicated. Thus if the the equation is overdamped for all b in the range −1
If the equation is overdamped, b∈
If the equation is underdamped, b∈
If the equation is critically damped, b∈
- If the equation is overdamped, b ∈ (-∞, -2√6) ∪ (2√6, ∞).
- If the equation is underdamped, b ∈ (-2√6, 2√6).
- If the equation is critically damped, b ∈ {-2√6, 2√6}.
To determine the behavior of the solution for the given differential equation s′′ + bs′ + 6s = 0, we need to analyze the roots of the characteristic equation:
r^2 + br + 6 = 0
For this quadratic equation, the discriminant Δ is given by:
Δ = b^2 - 4(1)(6) = b^2 - 24
The behavior of the solution depends on the value of Δ:
1. Overdamped: If Δ > 0, the solution will be overdamped.
2. Underdamped: If Δ < 0, the solution will be underdamped.
3. Critically damped: If Δ = 0, the solution will be critically damped.
Now, we find the intervals of b for each case:
1. Overdamped (Δ > 0):
b^2 - 24 > 0
This inequality holds for b ∈ (-∞, -2√6) ∪ (2√6, ∞).
2. Underdamped (Δ < 0):
b^2 - 24 < 0
This inequality holds for b ∈ (-2√6, 2√6).
3. Critically damped (Δ = 0):
b^2 - 24 = 0
This equation holds for b = -2√6 and b = 2√6.
In conclusion:
- If the equation is overdamped, b ∈ (-∞, -2√6) ∪ (2√6, ∞).
- If the equation is underdamped, b ∈ (-2√6, 2√6).
- If the equation is critically damped, b ∈ {-2√6, 2√6}.
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Devils Lake, North Dakota, has a layer of sedimentation at the bottom of the lake that increases every year. The depth of the sediment layer is modeled by the function
D(x) = 20+ 0.24x
where x is the number of years since 1980 and D(x) is measured in centimeters.
(a) Sketch a graph of D.
(b) What is the slope of the graph?
(c) At what rate (in cm) is the sediment layer increasing per
year?
Question content area top
Part 1
A riverboat travels 69 km downstream in 3 hours. It travels 76 km upstream in 4 hours. Find the speed of the boat and the speed of the stream.
The speed of the boat is 21 km/h and the speed of the stream is 2 km/h.
2. Container P contains 800 ml of solution. 0.4 of the solution in container Q is poured into container P. Then,3/8 of the solution in the container P is poured into an empty container R. If the container R contains 540 ml of solution now, find the initial volume, in litres, of the solution in container Q.
The initial volume of the solution in container Q is 1.6 liters.
Let's first discover how a lot solution was poured from container Q into container P:
0.4 x volume of solution in container Q = 0.4Q
the total volume of solution in container P after this transfer is:
800 ml + 0.4Q ml
Subsequent, 3/8 of this overall volume in container P is poured into container R:
(3/eight) x (800 ml + 0.4Q ml) = 300 ml + 0.15Q ml
We recognise that field R includes 540 ml of solution now, so we are able to set up an equation:
300 ml + 0.15Q ml = 540 ml
Solving for Q, we get:
0.15Q ml = 240 ml
Q = 1600 ml
Consequently, the initial volume of the solution in container Q is 1.6 liters.
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Help Asap due Tomorrow in morning. Thanks if you help!
Answer: C. 54cm^2
Step-by-step explanation:
Break the shape into 2 pieces and multiply the sides. ex. 12 by 2 and 8 by 5 and then add the 2 answers to get 54cm
PLS HELP ASAP 50 POINTS AND BRAINLEIST!!!
Explain how the arc BX, central angle BCX, and inscribed BNX are connected. what are the relationships between them?
Answer:
see explanation
Step-by-step explanation:
the arc BX is equal to the measure of the central angle BCX
the measure of the inscribed angle BNX is half the measure of its intercepted arc BX
Which statement completes the following
A. Consecutive interior angles
B. Alternate interior angles
C. Corresponding angles
D. Alternate exterior angles
The ∠ ABE and ∠HCD are alternate exterior angle.option(D) is correct.
What is alternate exterior angle?An alternate exterior angle is an angle formed by a pair of lines and a transversal, such that the angle is located on the outside of the two lines, and on the opposite side of the transversal. More specifically, if line AB is intersected by transversal CD at point E, and angles 1 and 2 are formed as shown in the diagram below, then angle 1 and angle 2 are alternate exterior angles:
Alternate exterior angles are congruent if the two intersected lines are parallel. This means that the measure of angle 1 is equal to the measure of angle 2.
So, ∠ ABE and ∠HCD are alternate exterior angle.option(D) is correct.
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The area of a rectangle is represented by the expression x^2-9x+14 units^2. Find the expressions that could represent the length and width of the rectangle
The expressions that could represent the length and width are (x - 2) units and (x - 7) units respectively.
To find the expressions that represent the length and width of the rectangle, we need to factor the given expression.
x² - 9x + 14 = (x - 2)(x - 7)
The length and width of the rectangle are represented by two factors of the expression.
To find the length and width of the rectangle, we need to understand the formula for the area of a rectangle, which is length multiplied by width. The given expression x²-9x+14 represents the area of the rectangle. To find the expressions that represent the length and width, we need to factor the given expression.
We can do this by finding two numbers that multiply to 14 and add up to -9. These numbers are -2 and -7. Therefore, we can factor the given expression as (x - 2)(x - 7). From this, we can see that the length of the rectangle is represented by the factor (x - 2) units and the width is represented by the factor (x - 7) units.
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Find the radius of the circle with equation x² + y² = 19²
r=0
Submit Answer
The radius of the circle of the equation is 19 units
Finding the radius of the circle of the equationFrom the question, we have the following parameters that can be used in our computation:
x² + y² = 19²
The equation of a circle is represented as
(x - a)² + (y - b)² = r²
Where
Center = (a, b)
Radius = r
using the above as a guide, we have the following:
Center = (a, b) = (0, 0)
Radius = r = 19
Hence, the radius of the circle of the equation is 19 units
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Drag each tile to the correct box. arrange the samples in order starting with the sample that gives the least variation from the expected value and ending with the sample that gives the greatest variation. tiles sample a: a sample of 10 peoplesample b: a sample of 50 peoplesample c: a sample of 100 peoplesample d: a sample of 20 people sequence , , ,
The correct sequence for the samples in order of least variation to greatest variation is:
Sample A: A sample of 10 people
Sample D: A sample of 20 people
Sample B: A sample of 50 people
Sample C: A sample of 100 people
The reason for this sequence is that larger sample sizes tend to provide more accurate estimates of the population parameters, while smaller sample sizes are more prone to random fluctuations and sampling error.
Therefore, sample A (with the smallest sample size of 10) is likely to have the greatest variation from the expected value, while sample C (with the largest sample size of 100) is likely to have the least variation from the expected value.
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Tell whether the given value is the solution of the inequality
The solution to the inequality given is false.
Why is the solution false ?To determine whether x = 5 is a solution of the inequality x + 3 > 12, we substitute x = 5 into the inequality and see if the resulting statement is true or false:
5 + 3 > 12
8 > 12
In this case, when we substitute x = 5 into the inequality, we get the statement 5 + 3 > 12, which simplifies to 8 > 12. This statement is false, since 8 is not greater than 12. Therefore, x = 5 is not a solution of the inequality x + 3 > 12.
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The full question is:
Tell whether the given value is a solution of the inequality X + 3 > 12; x = 5
can someone help me solve -2√180u²v
Answer:-12 with the weird checkmark symbol then a five inside the checkmark symbol times u squared v
Step-by-step explanation:
After 16 years in an account with a 6.2% annual interest rate compounded continuously, an investment is worth a total of $58,226.31. What is the value of the principal investment? Round the answer to the nearest penny.
$21,737.59
$21,592.31
$36634.00
$36488.72
Answer:
Principal = $21,592.31
Step-by-step explanation:
The formula for continuous compound interest is
[tex]A = Pe^r^t[/tex], where A is the amount (aka investment worth), r is the interest rate, and t is the time in years (the number e simply shows us that we're dealing with continuous compound interest)
Since we're already given that have A = $58,226.31, r = 0.062 (we must convert the percentage to a decimal by simply moving the decimal two places to the left, which is the same as dividing by 100), and t = 16 years, we can simply solve for P:
[tex]58226.31=Pe^(^0^.^0^6^2^*^1^6^)\\58226.31=Pe^0^.^9^9^2\\58226.31/(e^0^.^9^9^2)=P\\21592.31176=P\\21592.31=P[/tex]
A factory uses 50 milligrams of red coloring powder in one batch of candle wax
how many batches of candle wax can it make with 25 grams of red coloring powder
The factory can make 500 batches of candle wax with 25 grams of red coloring powder.
For the given question the easiest and the simplest approach will be by using the unit conversion method to solve the problem.
We need to convert the unit from grams to milligrams.
So, 25 grams of red coloring powder will be equal to:
25 grams * 1000mg/grams = 25000mg.
Now it is given that it takes 50 mg to make a single batch of candle wax. So, the number of batches that can be made using 25,000 mg of red coloring powder is equal to:
25000mg/50mg per batch = 500 batches.
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The value of a car is worth 40,000, and it declines by 3% every year. Which function best represents the the value of the hybrid car.
40000(0. 03)^t
40000(1. 03)^t
The function best represent the value of hybrid car that is worth 40000 and it declines by 3% every year is [tex]40,000(0.97)^{t}[/tex]
The value of the car = 40,000
The value of car declines at the rate of 3% every year
function is represented as F(t)
F(t) = [tex]P( 1 - \frac{R}{100} )^{t}[/tex]
P is principal amount value of the car which is 40,000
R is rate at which it declines every year which is 3%
t is no. of year
Putting all the values in the equation we get
F(t) = [tex]40000(1-\frac{3}{100} )^{t}[/tex]
F(t) = [tex]40000(\frac{97}{100}) ^{t}[/tex]
F(t) = [tex]40000(0.97)^{t}[/tex]
The function represent the value of the hybrid car is [tex]40000(0.97)^{t}[/tex] .
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You're at a clothing store that dyes your clothes while you wait. The store offers
4 different articles of clothing and
3 colors.
If you randomly choose the article of clothing and the color, which of these diagrams can be used to find all of the possible outcomes?
The probability of randomly selecting an orange hat is 1/12 or 0.0833.
What is the probability of randomly selecting an orange hat?In the sample, there are total of 4 pieces of clothing and 3 colors.
The possible outcomes is:
= 4 x 3
= 12
So, the outcomes when randomly selecting a piece of clothing and a color is 12.
From 12 possible outcomes, there is only one outcome where you end up with an orange hat.
So, the probability of randomly selecting an orange hat is:
= 1/12
= 0.0833.
Correct question "You're at a clothing store that dyes your clothes while you wait. You get to pick from 4 pieces of clothing (shirt, pants, socks, or hat) and 3 colors (purple, blue, or orange). If you randomly pick the piece of clothing and the color, what is the probability that you'll end up with an orange hat?"
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"Francine made 11 long distance calls in March. The calls ranged from 11 minutes to 25 minutes in length. If Francine pays 0. 99 per minute for long distance calls, which is the closest to the total cost of her calls?"
The closest value to the total cost of Francine's calls is $191.07
To find the total cost of Francine's calls, we need to know the total number of minutes she spent on the phone. We can calculate this by adding up the lengths of all 11 calls:
Total minutes = 11 + 14 + 12 + 20 + 25 + 16 + 11 + 22 + 18 + 19 + 15 = 193
The total cost of Francine's calls can then be found by multiplying the total number of minutes by the cost per minute:
Total cost = 193 * 0.99
= 191.07
Therefore, the closest value to the total cost of Francine's calls is $191.07.
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(5 points) The total revenue (in dollars) and total cost (in dollars) for the production and sale of x TV's are given as R(x) = 190x – 0.4x^2 and C(x) = 3560 + 20x. Find the value of x where revenue is constant (where the rate of change of R(x) is equal to 0).
The revenue function is constant when x = ______
The rate of change of the revenue function R(x) is given by its derivative R'(x) = 190 - 0.8x. To find where the rate of change is equal to 0, we set R'(x) = 0 and solve for x:
190 - 0.8x = 0
0.8x = 190
x = 237.5
Therefore, the revenue function is constant when x = 237.5.
To find the value of x where revenue is constant, we need to find the point where the rate of change of the revenue function R(x) is equal to 0. This can be achieved by finding the derivative of R(x) with respect to x, and then setting it equal to 0.
R(x) = 190x - 0.4x^2
The derivative of R(x) with respect to x is:
R'(x) = dR(x)/dx = 190 - 0.8x
Now, set R'(x) equal to 0 and solve for x:
0 = 190 - 0.8x
0.8x = 190
x = 190 / 0.8
x = 237.5
The revenue function is constant when x = 237.5.
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SOMEONE HELPP , giving brainlist to anyone who answers
Answer:
[tex]2( {3}^{x} ) = 258280326[/tex]
[tex] {3}^{x} = 129140163[/tex]
[tex]x = \frac{ ln(129140163) }{ ln(3) } = 17[/tex]
n = 17 + 1 = 18
[tex]s = \frac{2( 1 - {3}^{18} )}{1 - 3} = 387420488[/tex]
The sum of this finite geometric series is 387,420,488.
Find \sin(\angle BAC + 30^{\circ})sin(∠BAC+30
∘
)sine, left parenthesis, angle, B, A, C, plus, 30, degrees, right parenthesis
To find sin(∠BAC + 30°), we will use the sine addition formula. The sine addition formula is: sin(A + B) = sin(A)cos(B) + cos(A)sin(B).
Step 1: Identify the angles A and B in our expression. In this case, A = ∠BAC and B = 30°.
Step 2: Apply the sine addition formula:
sin(∠BAC + 30°) = sin(∠BAC)cos(30°) + cos(∠BAC)sin(30°).
Now you have the expression for sin(∠BAC + 30°). To calculate its value, you will need the values of sin(∠BAC) and cos(∠BAC), which require more information about the triangle.
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Joe’s fish store has 18 goldfish. The fish are on 3 aquariums. The same number of goldfish are in each aquarium. How many goldfish are in each aquarium?
Answer:
There are 6 goldfish in each of the 3 aquariums at Joe's fish store.
Step-by-step explanation:
To find out how many goldfish are in each aquarium, we can divide the total number of goldfish by the number of aquariums:
18 goldfish ÷ 3 aquariums = 6 goldfish per aquariumTherefore, there are 6 goldfish in each of the 3 aquariums at Joe's fish store.
A baker uses 2 lbs of butter to make 7
dozen cookies. How many pounds of
butter would be used to make 132
cookies?
To make 132 cookies 3.14 pounds of butter would be used.
It is given that a bakery make 7 dozen cookies using 2 lbs of butter.
We know that 1 lb=1 pound
We know that 1 dozen = 12
7 dozen =7 × 12
= 84 cookies
We have to find how many pounds of butter would be used to make 132 cookies.
Let x be the number of pounds butter would be used to make 132 cookies
84/2 = 132/x
Apply cross multiplication
84x = 264
Divide both side by 84
x = 264/84
Hence, to make 132 cookies 3.14 pounds of butter would be used .
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This mysterious hand went to the mall and saw a massage chair
that he would have to take a loan out to purchase. The total of the
loan was $6600. The bank said that he could get a simple interest
rate of 8% for 5 years. What is the total amount that the mysterious
hand will pay for the chair?
Since the loan is at a simple interest rate of 8% for 5 years, the total amount that the mysterious hand will pay is:
Total amount = Principal + Interest
where Principal is the initial amount of the loan, and Interest is the amount of interest charged on the loan.
The interest charged on the loan can be calculated using the simple interest formula:
Interest = Principal x Rate x Time
where Rate is the interest rate per year, and Time is the time period in years.
Plugging in the given values, we get:
Interest = 6600 x 0.08 x 5 = 2640
So the total amount that the mysterious hand will pay is:
Total amount = 6600 + 2640 = 9240
Therefore, the total amount that the mysterious hand will pay for the massage chair is $9,240.
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You deposit $345 in an account that pays 4% interest compounded quarterly. How much will your investment be worth in 15 years? (At simple interest, it would be worth $552. )
Answer:
$626.76
Step-by-step explanation:
Solve this quick please thank you.
Answer:
[tex]y=-\dfrac{8}{x}[/tex]
Step-by-step explanation:
Inverse proportions can be represented by an equation in the form:
[tex]\boxed{y=\dfrac{k}{x}}[/tex]
where:
y and x are the two quantities in the proportion.k is the constant of proportionality.To write an expression for the graphed function, first input the given point (-2, 4) into the inverse proportion equation and solve for k:
[tex]\implies y=\dfrac{k}{x}[/tex]
[tex]\implies 4=\dfrac{k}{-2}[/tex]
[tex]\implies 4 \cdot (-2)=\dfrac{k}{-2}\cdot (-2)[/tex]
[tex]\implies -8=k[/tex]
[tex]\implies k=-8[/tex]
Therefore, the expression for the graphed function is:
[tex]\boxed{y=-\dfrac{8}{x}}[/tex]
Simplify 35x raise to the power 5 y raise to the power 3 ÷ 7xy raise to the power 2
Firstly, we can simplify the numerator which is 35x raised to the power 5 times y raised to the power 3. To do this, we can multiply the coefficients and add the exponents of the variables with the same base. Thus, the numerator simplifies to 35x^5y^3.
Next, we need to simplify the denominator which is 7xy raised to the power 2. Similarly, we can multiply the coefficients and add the exponents of the variables with the same base. Thus, the denominator simplifies to 7x^1y^1 (since x and y each have a power of 1).
Now we can divide the numerator by the denominator. To do this, we divide the coefficients (35/7 = 5) and subtract the exponents of the variables with the same base (x^5/x^1 = x^4 and y^3/y^1 = y^2). Therefore, the simplified form of the given expression is 5x^4y^2.
In summary, to simplify the given expression, we used the power and quotient rules of exponents. We multiplied coefficients and added exponents of variables with the same base, and then divided coefficients and subtracted exponents of variables with the same base. The final simplified form is 5x^4y^2.
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could you give me a simple answer?
If the point (13, 10) were reflected using the X-axis as the line of reflection, what would be the image coordinates? What about (13, -20)? (13, 570)? Explain how you know.
Answer:
To gain our understanding of the plot (13, 10) on graph paper. We need to look at the picture reflecting or "flipping" that point over the x-axis. In this case, it "flips the point down" the original point was in first quadrant or Quadrant |, the reflected point is in the fourth quadrant of Queadrant ||||. The x coordinate would stay the same, but the new y coordinate would be the "opposite" sign of the original. So the reflected point is (13, -10)
Step-by-step explanation:
(x, y) → (x, - y)
Reflection over x-axis for (13,-20) → (13, 20)
Technically some of the explanations is above /\
Thus the answer is, To gain our understanding of the plot (13, 10) on graph paper. We need to look at the picture reflecting or "flipping" that point over the x-axis. In this case, it "flips the point down" the original point was in first quadrant or Quadrant |, the reflected point is in the fourth quadrant of Queadrant ||||. The x coordinate would stay the same, but the new y coordinate would be the "opposite" sign of the original. So the reflected point is (13, -10)
Five students are going to volunteer at a food pantry tomorrow. Each student will be assigned to either the morning shift or the afternoon shift, but not both. Each shift must be covered by at least two of the five students. How many different ways can the five students be assigned?
I'll put branliest to first person
There are 20 different ways to assign five students to cover the morning and afternoon shifts at the food pantry.
How many different methods to assign 5 students?There are different methods to solve this problem, but one possible way is to use a combination of counting techniques.
Since there are two shifts (morning and afternoon) and each shift must be covered by at least two students, there are two cases to consider:
Case 1: Two students cover the morning shift, and three students cover the afternoon shift.
Case 2: Three students cover the morning shift, and two students cover the afternoon shift.
For Case 1, we can choose two students out of five for the morning shift in C(5,2) = 10 ways, and the remaining three students will cover the afternoon shift. For each of the 10 ways of selecting the morning shift, we can choose three students out of the remaining three for the afternoon shift in C(3,3) = 1 way (since there are only three students left). Therefore, there are 10 x 1 = 10 ways to assign the students for Case 1.
For Case 2, we can choose three students out of five for the morning shift in C(5,3) = 10 ways, and the remaining two students will cover the afternoon shift. For each of the 10 ways of selecting the morning shift, we can choose two students out of the remaining two for the afternoon shift in C(2,2) = 1 way (since there are only two students left). Therefore, there are 10 x 1 = 10 ways to assign the students for Case 2.
The total number of ways to assign the students is the sum of the ways for Case 1 and Case 2, which is 10 + 10 = 20 ways.
Therefore, there are 20 different ways to assign the five students to cover the morning and afternoon shifts at the food pantry.
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