Answer:
6 + 13i – (7 – 15i)
= 6 + 13i - 7 + 15i (distribute the negative sign)
= -1 + 28i (combine like terms)
Therefore, the answer is -1 + 28i in the form of a + bi.
Step-by-step explanation:
The solution is (-6,0). Which statement best describes the flaw in David's reasoning? (В D David's answer is correct, but he should have graphed the lines. David's answer for x should be 0 because x - x (in line two of his work) is 0. David should have stopped when he calculated -6=-6. This means there are no solutions because the slopes are equal. David should have stopped when he calculated -6=-6. This means there are an infinite number of solutions because it is a true statement.
Answer:
Step-by-step explanation:
the anser is 16
3.1 Complete the following statements so that they are true: 3.1.1The angle between the tangent and chord is ... 3.1.2Opposite angles of a cyclic quadrilateral are ... 3.2In the diagram below, two circles have a common tangent TAB. PT is a tangent to the smaller circle. PAQ, QRT and NAR are straight lines. Let Q = 40°. N B 40° 3.2.1 Determine, with reasons, THREE other angles equal to 40°. 3.2.2 If P₁= A4 prove that PTRN is a parallelogram.
paperback books cost a total of $. How much change will Prakash get if he buys 3 hardcover books and 5 paperback books, and gives the clerk $20 bills?
If the cost of one paperback book is less than $1, he would receive even more change.
To solve this problem, we need to know the cost of one paperback book. Unfortunately, that information is missing from the question. Without it, we cannot determine the total cost of the 5 paperback books and therefore cannot calculate Prakash's change.
However, we can make an educated guess based on the fact that the question mentions both paperback and hardcover books. Typically, hardcover books are more expensive than paperbacks, so we can assume that the cost of one paperback book is less than the cost of one hardcover book.
Assuming that each hardcover book costs $10, the total cost of 3 hardcover books would be $30. If Prakash gives the clerk $20 bills, he would pay $60 in total. If we subtract the cost of the 3 hardcover books ($30) from the total amount paid ($60), we are left with $30.
This is the maximum amount of change Prakash could receive if each paperback book costs $1.
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explain step by step
Answer:
(a) $ 315000
(b) $ 3103448.28
Step-by-step explanation:
(a)
tax = 45% of buying price
Buying price = $700000
tax = 45% × 700000
= $ 315000
(b)
Final price = $4500000
145% = 4500000
buying price = 100%
= 4500000/145 × 100
= 3103448.28
Which question was answered with variable data?
Math item stem image
CLEAR CHECK
Answer:
Question 1
only, because there are many cards in a standard deck of playing cards.
Question 2
only, because the snowfall was not the same for every month.
Neither question, because in each data set, there is only one outcome.
Both questions, because each one has more than one answer.
The term "Variable data" refers to data that can vary or change. It typically includes numerical data that can take on different values or measurements, such as temperature, height, weight, or time.the correct answer is "Neither question, because in each data set, there is only one outcome."
Neither question was answered with variable data, because in each data set, there is only one outcome.
The term "variable data" refers to data that can vary or change. It typically includes numerical data that can take on different values or measurements, such as temperature, height, weight, or time.
In this case, neither question involves variable data. Question 1 is about the number of cards in a standard deck of playing cards, which is a fixed quantity and does not vary. Question 2 is about the total snowfall for each month, but each month has a single, fixed value, so there is no variation in the data.
Therefore, the correct answer is "Neither question, because in each data set, there is only one outcome."
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Question 18
YARDWORK Each week Imani and Demond must mow their 4-acre yard. When they use both their 36-inch mower and 42-inch mower, it
takes them 2 hours. When the 36-inch mower is out for repairs, it takes them 3 hours. How long would the job take if the 42-inch mower
were broken?
Answer:
6/12
Step-by-step explanation:
this is because if you do the math it is 6/12
y=3x+10
what is the y-intercept
Answer: (0,10)
Step-by-step explanation:
To find the y-intercept, substitute in 0 for x and solve for y.
Answer:
The y-intercept is 10. Also can be thought of as the point (0, 10).
Step-by-step explanation:
This equation is in Slope-Intercept form. The y is all by itself on the left side of the equal sign. On the right, there is an x term. The number next to the x (the co-efficient of x) is the slope. The constant, the number all by itself is the y-intercept.
In the equation,
y = 3x + 10 the slope is 3 and the y-intercept is 10.
This is where the graph crosses the y-axis, the point (0,10)
For any equation you can find the y-intercept by letting x = 0.
y = 3(0) + 10
y = 0 + 10
y = 10
Help me with this please
Answer:
2/3
Step-by-step explanation:
3 times 2/3 will equal 2 (A - B)
4.5 times 2/3 will equal 3 (B - C)
6 times 2/3 will equal 2 (C - D)
to find the fraction just divide any of the numbers on the dialated figure (right side) by it's parallel side
4. a) Verify that DEF is a right triangle.
E(-2, 2)
D(1,4)
F(3,1)
b) Describe another method that you could
use to answer part a).
Answer:To verify whether triangle DEF is a right triangle, we can use the slope formula and the perpendicularity criterion.
a) Verification of DEF as a right triangle:
Calculate the slopes of the two sides:
Slope of DE = (y2 - y1) / (x2 - x1) = (4 - 2) / (1 - (-2)) = 2 / 3
Slope of EF = (y2 - y1) / (x2 - x1) = (1 - 2) / (3 - (-2)) = -1 / 5
Check if the product of the slopes is -1 (perpendicular lines):
(Slope of DE) * (Slope of EF) = (2 / 3) * (-1 / 5) = -2 / 15
Since the product of the slopes is not -1, the sides DE and EF are not perpendicular. Therefore, triangle DEF is not a right triangle.
b) Another method to determine if triangle DEF is a right triangle:
Another method to answer part a) is by calculating the lengths of the three sides DE, EF, and DF. Then, we can check if the Pythagorean theorem holds true.
Calculate the lengths of the sides:
Length of DE = sqrt((x2 - x1)^2 + (y2 - y1)^2) = sqrt((1 - (-2))^2 + (4 - 2)^2) = sqrt(9 + 4) = sqrt(13)
Length of EF = sqrt((x2 - x1)^2 + (y2 - y1)^2) = sqrt((3 - 1)^2 + (1 - 4)^2) = sqrt(4 + 9) = sqrt(13)
Length of DF = sqrt((x2 - x1)^2 + (y2 - y1)^2) = sqrt((3 - (-2))^2 + (1 - 2)^2) = sqrt(25 + 1) = sqrt(26)
Apply the Pythagorean theorem:
If DF^2 = DE^2 + EF^2, then triangle DEF is a right triangle.
DF^2 = (sqrt(26))^2 = 26
DE^2 + EF^2 = (sqrt(13))^2 + (sqrt(13))^2 = 13 + 13 = 26
Since DF^2 equals DE^2 + EF^2, the Pythagorean theorem holds true, indicating that triangle DEF is a right triangle.
Therefore, the two methods of verification provide conflicting results. One method (using the perpendicularity criterion) suggests that DEF is not a right triangle, while the other method (using the Pythagorean theorem) suggests that it is a right triangle. In such cases, it is important to double-check the calculations and verify the accuracy of the given points to resolve the discrepancy.
Step-by-step explanation:
Compare the rates of change of the following items.
y = 0.6z
6
8
00
2
4
OB. The rate of change of item I is equal to the rate of change of item II.
I
II
OA. The rate of change of item II is greater than the rate of change of item I
y
OC. The rate of change of item I is greater than the rate of change of item II
0.6
1.2
1.8
2.4
The rate of change of item I is greater than the rate of change of item II
The rate of change of item I is 0.6
Let us find the rate of change of item II
Rate of change = 1.2-0.6/4-2
=0.6/2
=0.3
So rate of change of item II is 0.3 which is lesser than rate of change of I
the rate of change of item I is greater than the rate of change of item II
Hence, the rate of change of item I is greater than the rate of change of item II
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find a value of c so that p(z ≥ c) = 0.55.
To find a value of c such that P(z ≥ c) = 0.55, we need to use a standard normal distribution table or calculator.From the standard normal distribution table, we find that the z-score corresponding to a right-tailed area of 0.55 is approximately 0.126.
Therefore, we have:
P(z ≥ c) = 0.55
P(z ≤ c) = 1 - P(z ≥ c) = 1 - 0.55 = 0.45
Using the standard normal distribution table, we find that the z-score corresponding to a left-tailed area of 0.45 is approximately -0.126.
So, c = -0.126.
Therefore, the value of c that satisfies P(z ≥ c) = 0.55 is approximately -0.126.
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It is found that 15% of pupils at a school do not jog or swim or cycle, 8% do all three activities, 15% swim and cycle but do not jog, 15% do both jog and swim, 20% swim only, 18% cycle only and 42% do two or more activities
a) Define the cardinality of the complement of set
b) Workout the percentage of pupils who
i) Do both jog and cycle
ii) Swim or cycle
iii) Do not swim
iv) Do not jog, swim and cycle
Step-by-step explanation:
a) The complement of the set of pupils who do not jog or swim or cycle would be the set of pupils who do at least one of these activities.
b) We can use a Venn diagram to help us visualize the information given and answer the questions:
```
_____________
/ \
/ \
jog / A \ swim
/ \
/ \
________/_________ _______\_________
/ \ / \
/ \ / \
cycle B \ / C \ none
/ \ /
/ \____________/
/
/
/
/
/
```
- i) To find the percentage of pupils who do both jog and cycle, we look at the intersection of sets A and B, which is 8%. Therefore, 8% of pupils do both jog and cycle.
- ii) To find the percentage of pupils who swim or cycle, we add the percentages of sets B, C, and D (the parts of the circles that include swimming or cycling), which gives 8% + 15% + 18% = 41%. Therefore, 41% of pupils swim or cycle.
- iii) To find the percentage of pupils who do not swim, we add the percentages of sets A, B, and D (the parts of the circles that do not include swimming), which gives 15% + 8% + 18% = 41%. Therefore, 41% of pupils do not swim.
- iv) To find the percentage of pupils who do not jog, swim, or cycle, we look at the complement of the set of pupils who do at least one of these activities. This is given as 15%, so the percentage of pupils who do not jog, swim, or cycle is 15%.
15% of pupils do not jog, swim or cycle. Of the remaining pupils, 19% both jog and cycle, 61% either swim or cycle, and 39% do not swim. The numbers are based on a full 100% participation rate in regards to these three activities only.
Explanation:The cardinality of a complement of a set refers to the elements that are not in the original set. In context of this question, the complement of the set would be the 15% of pupils who do not partake in jogging, swimming or cycling.
To answer the other parts of the question:
The percentage of pupils who both jog and cycle can be found by adding the percentages of pupils who take part in two or more activities (42%) and then subtracting the percentage of pupils who swim and cycle but do not jog (15%) as well as those who do all three activities (8%). This gives 42% - 15% - 8% = 19%. The percentage of pupils who swim or cycle can be found by adding the percentage of those who swim only (20%), cycle only (18%), do all three activities (8%), as well as those who swim and cycle but do not jog (15%). This gives 20% + 18% + 8% + 15% = 61%. The percentage of pupils who do not swim can be found by subtracting the percentage of those who swim from 100%. This gives 100% - 61% = 39%.The percentage of pupils who do not jog, swim, or cycle is given directly as 15%.Please note that this solution is assuming that all pupils participate in at least one of these activities or none at all and that there are no other activities available.
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In the figure below, Z is the center of the circle. Suppose that QR = 14, SR = 14, UZ = 3x + 5, and VZ = 23. Find the following.
Answer:
x=6
Step-by-step explanation:
VZ=UZ
3x+5=23
3x=18
x=6
Determine the missing dimension of the area is 112 in.²
The missing dimension of the rectangle is 8 inches.
To determine the missing dimension of an area of 112 in.², we need to know at least one of the dimensions. Let's assume we know the length of the rectangle is 14 inches.
We can then use the formula for the area of a rectangle, which is length multiplied by width, to solve for the missing dimension.
We can rearrange the formula to solve for the width by dividing both sides by the length: width = area/length. Plugging in the values we know, we get: width = 112 in.² / 14 in. = 8 inches.
It's important to note that if we had started with the width instead of the length, we would have used the same formula but rearranged it to solve for the length instead. The formula for the area of a rectangle is very useful for solving these types of problems.
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Jackson was solving a two-step equation. Which property justifies the work done between steps one and two?
The work done between steps one and two is justified by applying the Addition Property of Equality.
In step one, we start with the equation 3x - 2 = 10.
To isolate the variable, we can use the Addition Property of Equality, which allows us to add 2 to both sides of the equation.
This yields 3x = 12 (step two).
The Addition Property of Equality states that if the same value is added to both sides of an equation, the equality remains true.
Hence, the property utilized between these steps is the Addition Property of Equality.
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the slope of line that passes through the points (20,30) and (40,14) is
a) -5/4
b) -4/5
c) 4/5
d) 5/4
Answer:
B
Step-by-step explanation:
calculate the slope m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (20, 30 ) and (x₂, y₂ ) = (40, 14 )
m = [tex]\frac{14-30}{40-20}[/tex] = [tex]\frac{-16}{20}[/tex] = - [tex]\frac{4}{5}[/tex]
The distance required for an automobile to stop is directly proportional to the square of its velocity. If a car can stop in 1800 meters from a velocity of 30 kph, what will be the required distance at 28 kph?
In California, each automobile license plate consists of a single digit followed by three letters, followed by three digits. How many distinct license plates can be formed if the first number cannot be zero and the three letters cannot form "DOG"?
Answer: How many distinct license plates can be formed if the first number cannot be zero and the three letters cannot form "DOG"?
Step-by-step explanation:
Since the first digit cannot be 0, there are 9 choices for the first digit.
For the three letters, there are 26 choices for the first letter, 26 choices for the second letter, and 25 choices for the third letter (since we cannot use "D", "O", or "G").
For the last three digits, there are 10 choices for each digit.
Therefore, the total number of distinct license plates can be formed is:
9 x 26 x 26 x 25 x 10 x 10 x 10 = 16,290,000
So there are 16,290,000 distinct license plates that can be formed if the first number cannot be zero and the three letters cannot form "DOG".
{I Hope This Helps! :)}
suppose at a certain college we know 80% of the students like chipotle and 65% of the students like papa john's pizza. moreover, of the students that like chipotle we know 69% like papa john's pizza. suppose we randomly select a student. what is the probability that a student likes papa john's, given they do not like chipotle?
Therefore, the probability that a student likes papa john's given they do not like chipotle is approximately 0.275 or 27.5%.
Bayes' theorem allows us to calculate conditional probabilities, which is the probability of an event occurring given that another event has already occurred. In this case, we want to find the probability that a student likes Papa John's pizza given that they do not like Chipotle.
We start by using the given probabilities to calculate the probability that a student does not like Chipotle, which is the complement of the probability that they do like Chipotle. Then, we calculate the probability that a student likes both Papa John's and Chipotle, and use this to find the probability that a student likes Papa John's given that they do not like Chipotle.
Bayes' theorem is a powerful tool that is used in a wide range of fields, including statistics, probability theory, and machine learning. It provides a systematic way to update probabilities based on new information or evidence, which is a crucial aspect of many real-world applications.
P(B) = 1 - 0.8 = 0.2 (the probability that a student does not like chipotle)
P(A|B) = P(A and B) / P(B) = (0.65 - 0.69*0.8) / 0.2 ≈ 0.275
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Please help with this i need this quick
Answer:
x = 11.0
Step-by-step explanation:
Since this is a right triangle, we can find the measure of x using one of the trigonometric ratios.
If we allow ∠A to represent the reference angle, we see that BC is the opposite side and AB is the hypotenuse. Thus, we can use the sine ratio, which is sin (reference angle) = opposite/hypotenuse.We can plug in everything into the sine ratio and solve for x:sin (27) = BC / AB
sin (27) = 5 / x
x * sin (27) = 5
x = 5 / sin (27)
x = 11.01344632
x = 11.0
leanna needs no more than 2.5 hours to finish her homework. which inequality represents the number of hours, x, leanna needs to finish her homework?
This means that the value of x should not exceed 2.5, as Leanna needs no more than 2.5 hours to complete her homework.
The inequality that represents the number of hours, x, Leanna needs to finish her homework is: x ≤ 2.5.
The inequality x ≤ 2.5 means that the value of x should not exceed 2.5. Since Leanna needs no more than 2.5 hours to finish her homework, we can use this inequality to represent the possible values of x. If x is greater than 2.5, then Leanna would take more than 2.5 hours to finish her homework, which contradicts the given condition. Therefore, the inequality x ≤ 2.5 is the correct representation of the number of hours Leanna needs to finish her homework.
In conclusion, the inequality x ≤ 2.5 represents the number of hours, x, Leanna needs to finish her homework. This means that the value of x should not exceed 2.5, as Leanna needs no more than 2.5 hours to complete her homework.
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Use a double integral to find the area of the region.
The region inside the circle
(x +3)^2 + y^2 = 9
and outside the circle
x^2 + y^2 = 9
The area of the region is (27π/4) square units.
We have,
To find the area of the region inside the circle (x + 3)² + y² = 9 and outside the circle x² + y² = 9, we can use a double integral in polar coordinates.
The region is an annulus (a region between two concentric circles) with the smaller circle centered at (-3,0) and radius 3, and the larger circle centered at the origin and radius 3.
We can rewrite the equations of the circles in polar coordinates as:
(x + 3)² + y² = 9
And,
r² + 2r cos(theta) + 9 = 9
r² + 2r cos(theta) = 0
r = -2 cos(theta)
And,
x² + y² = 9
r² = 9
The region can be described as 0 ≤ r ≤ 3 and -π/2 ≤ θ ≤ π/2 since we are only interested in the part of the region above the x-axis.
The area of the region can be calculated using the following double integral:
A = ∫∫R r dr dθ
where R is the region in polar coordinates.
We can integrate with respect to r first:
A = ∫(-π/2)^(π/2) ∫0³ r dr dθ
= ∫(-π/2)^(π/2) [(1/2) r²]_0³ dθ
= ∫(-π/2)^(π/2) (9/2) dθ
= (9/2) [θ]_(-π/2)^(π/2)
= (9/2) [π - (-π/2)]
= (9/2) (3π/2)
= (27π/4)
Thus,
The area of the region is (27π/4) square units.
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Select the true statement about trend lines.
A. The distance between each point and the line is always the same.
B. The distance from the points to the line should be as small as
possible.
OC. A trend line connects the points.
D. A trend line goes through the first and last points.
The true statement about trend lines include the following: B. The distance from the points to the line should be as small as possible.
What is a trend line?In Mathematics and Statistics, a trend line is sometimes referred to as a line of best fit and it can be defined as a statistical tool which is commonly used in conjunction with a scatter plot, in order to determine whether or not there's any form of correlation (either positive or negative) between a given data.
Generally speaking, the line of best fit or trend line should be very close to the data points as much as possible. This ultimately implies that, a characteristics of a trend line is that the distance from each of the data points to the line must be as small as possible i.e closer to the line.
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Calculate the double integral ∫∫R 2x/1+xy dA, where R = [0,2] x [0,1].
The double integral ∫∫R 2x/(1+xy) dA over R = [0,2] x [0,1] is equal to -4ln(3) + 4.
We have:
∫∫R 2x/(1+xy) dA = ∫[0,2]∫[0,1] 2x/(1+xy) dy dx
Using u-substitution with u = 1 + xy, we have du/dy = x. Solving for x, we get x = du/dy / y. Substituting this into the integral, we get:
∫∫R 2x/(1+xy) dA = ∫[0,2]∫[0,1] 2u/(u) * (1/u) du dx
Simplifying and evaluating the inner integral, we get:
∫∫R 2x/(1+xy) dA = ∫[0,2] (-2ln|1+xy|)[y=0]^{y=1} dx
= ∫[0,2] -2ln(1+x) dx
= [-2(xln(1+x)-x)]_{x=0}^{x=2}
= -4ln(3) + 4
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Find the magnitude of vector AB where A=(-10,-9) and B(-7,4) . Round to the thousandths
Answer:
√((-10 - (-7))^2 + (-9 - 4)^2)
= √((-3)^2 + (-13)^2)
= √(169 + 9) = √178 = 13.342
Two angles, ∠A and ∠B, are complementary. If sin A = 4/7, what is cos B?
A. 74
B. 47
C. 37
D. √44/7
The Value of cos B is,
⇒ cos B = 0.64
We have to given that;
Two angles, ∠A and ∠B, are complementary.
And, sin A = 4/7
Now, We can simplify as;
sin A = 4/7
A = sin⁻¹ 4/7
A = 39.8°
Since, Two angles, ∠A and ∠B, are complementary.
Hence, We get;
∠A + ∠B = 90°
39.8° + ∠B = 90°
∠B = 90 - 39.8°
∠B = 50.2°
Thus, Value of cos B is,
⇒ cos B = cos 50.2° = 0.64
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let $s$ be a subset of $\{1,2,3,...,50\}$ such that no pair of distinct elements in $s$ has a sum divisible by $7$. what is the maximum number of elements in $s$?
The maximum number of elements in $s$ is $\boxed{7}$, which we can achieve by choosing one element from each of the residue classes modulo $7$.
To find the maximum number of elements in $s$, we need to consider the elements of $\{1,2,3,...,50\}$ that are congruent to each residue class modulo $7$. There are seven residue classes modulo $7$, namely $\{0,1,2,3,4,5,6\}$. Since the sum of two elements from the same residue class modulo $7$ will also be in the same residue class modulo $7$, we cannot include more than one element from each residue class in $s$.
We can include one element from the residue class $0$, which gives us one element. For the other six residue classes, we can choose at most one element from each of them without violating the condition that no pair of distinct elements in $s$ has a sum divisible by $7$. This gives us a total of $1+6=7$ elements in $s$.
Therefore, the maximum number of elements in $s$ is $\boxed{7}$, which we can achieve by choosing one element from each of the residue classes modulo $7$.
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x and y intercept for x-2y=32
Answer:
The x-intercept is (32, 0),The y-intercept is (0, -16).------------------------
Set one variable to 0 and solve for the other.
For the x-intercept, set y = 0 and solve for x:
x - 2(0) = 32 x = 32For the y-intercept, set x = 0 and solve for y:
0 - 2y = 32 -2y = 32 y = -16The x-intercept is (32, 0) and the y-intercept is (0, -16).
Whats the answer and how do i show work
The measure of <1 is 147 degree.
Given:
m∠2 = 12x - 15
m∠7 = 3x + 21
Since angles 2 and 7 are alternate Exterior angles, they are congruent.
So, 12x - 15 = 3x + 21
12x - 3x = 21 + 15
9x = 36
x = 4
So, <2 = 12x - 15= 48 - 15 = 33
Now, <1 + <2 = 180 (Linear Pair)
<1 + 33 = 180
<1 = 147 degree
Thus, the measure of <1 is 147 degree.
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when selecting your schedule in school, you can choose from three math courses, four english courses, two science courses, and two history courses. how many choices do you have for your schedule if you need to select one math, one english, one science, and one history course?
You have 48 different choices for your schedule if you need to select one math, one English, one science, and one history course. It's important to note that this calculation assumes that there are no restrictions or prerequisites for the courses, and that all options are available to all students.
When selecting your schedule in school, you have to choose one math course from the three options, one English course from the four options, one science course from the two options, and one history course from the two options. To find out how many different schedule options you have, you need to multiply the number of options for each subject. So, you have:
3 options for math x 4 options for English x 2 options for science x 2 options for history = 48 possible schedule combinations.
Therefore, you have 48 different choices for your schedule if you need to select one math, one English, one science, and one history course. It's important to note that this calculation assumes that there are no restrictions or prerequisites for the courses, and that all options are available to all students.
To determine the number of possible schedules, you need to multiply the number of choices for each subject together. You have three math courses, four English courses, two science courses, and two history courses. The formula for calculating the total number of choices is:
Total choices = (Math choices) x (English choices) x (Science choices) x (History choices)
Total choices = (3) x (4) x (2) x (2) = 48
So, you have 48 different possible schedules when selecting one math, one English, one science, and one history course.
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