In a group of 105 students, 70 students passed Mathematics, 60 students passed History and 45 students passed Geography; 30 students passed Mathematics and History, 35 students passed History and Geography, 25 passed Mathematics and Geography and 15 passed all three subjects. Draw a Venn Diagram to illustrate this information. Find the number of students who
a) Passed at least one subjects
b) Passed exactly two subjects
c) Passed Geography and failed Mathematics
d) Passed all three subjects e) Failed Mathematics given that they passed History
answer pls
Answers
a) Passed at least one subject: 100 students
b) Passed exactly two subjects: 90 students
c) Passed Geography and failed Mathematics: 20 students
d) Passed all three subjects: 15 students
e) Failed Mathematics given that they passed History: 30 students.
To solve this problem, let's draw a Venn diagram to visualize the information given:
In the Venn diagram above, the circles represent the three subjects: Mathematics (M), History (H), and Geography (G). The numbers outside the circles represent the students who did not pass that particular subject, and the numbers inside the circles represent the students who passed the subject. The numbers in the overlapping regions represent the students who passed multiple subjects.
Now, let's answer the questions:
a) Passed at least one subject:
To find the number of students who passed at least one subject, we add the number of students in each circle (M, H, and G), subtract the students who passed two subjects (since they are counted twice), and add the students who passed all three subjects.
Total = M + H + G - (M ∩ H) - (M ∩ G) - (H ∩ G) + (M ∩ H ∩ G)
Total = 70 + 60 + 45 - 30 - 25 - 35 + 15
Total = 100
Therefore, 100 students passed at least one subject.
b) Passed exactly two subjects:
To find the number of students who passed exactly two subjects, we sum the students in the overlapping regions (M ∩ H, M ∩ G, and H ∩ G).
Total = (M ∩ H) + (M ∩ G) + (H ∩ G)
Total = 30 + 25 + 35
Total = 90
Therefore, 90 students passed exactly two subjects.
c) Passed Geography and failed Mathematics:
To find the number of students who passed Geography and failed Mathematics, we subtract the number of students in the intersection of M and G from the number of students who passed Geography.
Total = G - (M ∩ G)
Total = 45 - 25
Total = 20
Therefore, 20 students passed Geography and failed Mathematics.
d) Passed all three subjects:
To find the number of students who passed all three subjects, we look at the overlapping region (M ∩ H ∩ G).
Total = (M ∩ H ∩ G)
Total = 15
Therefore, 15 students passed all three subjects.
e) Failed Mathematics given that they passed History:
To find the number of students who failed Mathematics given that they passed History, we subtract the number of students in the intersection of M and H from the number of students who passed History.
Total = H - (M ∩ H)
Total = 60 - 30
Total = 30
Therefore, 30 students failed Mathematics given that they passed History.
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Related Questions
A person observes the top of a radio antenna at an angle of elevation of 5 degrees after getting 1 mile closer to the antenna the angle of elevation is 10 degrees how tall is the antenna to the nearest tenth of a foot?
Answers
The height of the antenna is approximately 5.1 feet.
1. Let's assume the height of the antenna as 'h' feet.
2. We have two angles of elevation: 5 degrees and 10 degrees.
3. When the person is 1 mile closer to the antenna, the change in the angle of elevation is 10 - 5 = 5 degrees.
4. We can use the tangent function to find the height of the antenna. The tangent of an angle is equal to the opposite side divided by the adjacent side.
5. The opposite side is the change in height, which is h feet (since the person moved closer by 1 mile, the change in height is equal to the height of the antenna).
6. The adjacent side is the horizontal distance from the person to the antenna. We can use trigonometry to find this distance.
7. In a right triangle, the tangent of an angle is equal to the ratio of the opposite side to the adjacent side.
tan(5 degrees) = h / x (where x is the horizontal distance in miles)
8. Similarly, after moving closer, the tangent of the angle becomes:
tan(10 degrees) = h / (x - 1)
9. We can solve these two equations simultaneously to find the value of h.
10. Rearranging the equations, we get:
h = x * tan(5 degrees)
h = (x - 1) * tan(10 degrees)
11. Setting the two expressions for h equal to each other, we have:
x * tan(5 degrees) = (x - 1) * tan(10 degrees)
12. Solving this equation for x, we find:
x = tan(10 degrees) / (tan(10 degrees) - tan(5 degrees))
13. Substitute the value of x back into one of the earlier equations to find h:
h = x * tan(5 degrees)
14. Calculate the value of h using a calculator:
h ≈ 1 * tan(5 degrees) ≈ 0.0875 miles ≈ 0.0875 * 5280 feet ≈ 461.4 feet
15. Rounded to the nearest tenth of a foot, the height of the antenna is approximately 5.1 feet.
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Mohammed Corporation's comparative balance sheet for current assets and liabilities was as follows:
Dec. 31, 20Y2 Dec. 31, 20Y1
Accounts receivable $20,900 $20,000
Inventory 61,800 62,500
Accounts payable 19,700 18,600
Dividends payable 24,000 22,000
Adjust net income of $98,500 for changes in operating assets and liabilities to arrive at net cash flow from operating activities.
Answers
The net cash flow from operating activities would be $100,800.
What is the net cash flow from operating activities?Change in accounts receivable:
= $20,900 - $20,000
= $900
Change in inventory:
= $61,800 - $62,500
= -$700
Change in accounts payable:
= $19,700 - $18,600
= $1,100
Change in dividends payable:
= $24,000 - $22,000
= $2,000
Change in operating assets and liabilities:
= Change in accounts receivable + Change in inventory - Change in accounts payable - Change in dividends payable
= $900 + (-$700) + $1,100 + $2,000
= $2,300
Net cash flow from operating activities:
= Net income + Change in operating assets and liabilities
= $98,500 + $2,300
= $100,800.
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What is the symbol ~, if you're trying to find the probability of ~A?
the addition probability
the probability of the event not happening
the multiplication probability
None of these choices are correct.
Answers
The symbol ~ (tilde) is commonly used to represent the negation or complement of an event. When we refer to ~A, it means "not A" or "the complement of A." In terms of probability, ~A represents the event not happening or the event A occurring.
Michelle has $15 and wants to buy a combination of dog food to feed at least four dogs at the animal shelter. A serving of dry food costs $1, and a serving of wet food costs $5.
1, Write the system of inequalities that models this scenario
2, Describe the graph of the system of inequality’s including shading and the types of lines graphed. Provide a description of the solution set.
Answers
Answer:
Step-by-step explanation:
1. The system of inequalities that models this scenario can be represented as:
Let x be the number of servings of dry food.
Let y be the number of servings of wet food.
The cost constraint:
1x + 5y ≤ 15
The minimum number of dogs constraint:
x + y ≥ 4
2. The graph of the system of inequalities would be a shaded region in the coordinate plane.
To graph the inequality 1x + 5y ≤ 15, we can first graph the equation 1x + 5y = 15 (the corresponding boundary line) by finding two points on the line and connecting them. For example, when x = 0, y = 3, and when y = 0, x = 15. Plotting these points and drawing a line through them will represent the equation 1x + 5y = 15.
Next, we need to shade the region below the line because the inequality is less than or equal to (≤). This shaded region represents the solutions that satisfy the cost constraint.
To graph the inequality x + y ≥ 4, we can again find two points on the line x + y = 4 (the corresponding boundary line). For example, when x = 0, y = 4, and when y = 0, x = 4. Plotting these points and drawing a line through them will represent the equation x + y = 4.
Lastly, we shade the region above the line x + y = 4 because the inequality is greater than or equal to (≥). This shaded region represents the solutions that satisfy the minimum number of dogs constraint.
The solution set is the overlapping region where the shaded areas of both inequalities intersect. This region represents the combination of servings of dry food and wet food that Michelle can purchase within her budget ($15) to feed at least four dogs at the animal shelter.
The inequalities D + W > 4 and D + 5W ≤ 15 model the problem. The graph represents these inequalities, with the overlap of shaded regions showing possible food serving combinations.
Explanation:
Let's define D as the number of servings of dry food and W as the number of servings of wet food. The system of inequalities that models this scenario is:
D + W > 4: Michelle needs enough food for at least four dogs.D + 5W ≤ 15: Michelle cannot spend more than $15.The graph will show the solution sets to the inequalities. D and W must both be non-negative, hence the graphed area is in the first quadrant. The first inequality requires shading above a line that connects (0,4) and (4,0). This line is solid since numbers equal to 4 are included. The second inequality requires shading below a line that connects (0,3) and (15,0). This is also a solid line because Michelle can spend exactly $15. The overlapping region of the graph is the solution set, quantifying the combinations of dry and wet food servings that Michelle can buy.
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Calculate:
1+2-3+4+5-6+7+8-9+…+97+98-99
Answers
The value of the given expression is 1370.
To calculate the given expression, we can group the terms in pairs and simplify them.
We have the following pattern:
1 + 2 - 3 + 4 + 5 - 6 + 7 + 8 - 9 + ... + 97 + 98 - 99
Grouping the terms in pairs, we can see that each pair consists of a positive and a negative term. The positive term increases by 1 each time, and the negative term decreases by 1 each time. Therefore, we can rewrite the expression as:
(1 - 3) + (2 + 4) + (5 - 6) + (7 + 8) + ... + (97 + 98) - 99
The sum of each pair in parentheses simplifies to a single term:
-2 + 6 - 1 + 15 + ... + 195 - 99
Now, we can add up all the terms:
-2 + 6 - 1 + 15 + ... + 195 - 99 = 1370
As a result, the supplied expression has a value of 1370.
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What the meaning of statement this?
Answers
A set S is T-finite if it satisfies Tarski's finite set condition, which states that for every nonempty subset X of P(S), there exists a maximal element u in X such that there is no v in X with u as a proper subset of v and u is distinct from v. If a set does not satisfy this condition, it is considered T-infinite.
In set theory, a set S is said to be T-finite if it satisfies a particular property called Tarski's finite set condition. This condition states that for every nonempty subset X of the power set of S (denoted as P(S)), there exists a maximal element u in X such that there is no element v in X that properly contains u (i.e., u is not a proper subset of v) and u is distinct from v.
To understand this concept, let's break it down further:
T-finite set: A set S is T-finite if, for any nonempty subset X of P(S), there exists an element u in X that is maximal. This means that u is not properly contained in any other element in X.
Maximal element: In the context of Tarski's finite set condition, a maximal element refers to an element u in X that is not a proper subset of any other element in X. In other words, there is no v in X such that u is a proper subset of v.
Distinct elements: This means that u and v are not the same element. In the context of Tarski's finite set condition, u and v cannot be equal to each other.
T-infinite set: A set S is T-infinite if it does not satisfy Tarski's finite set condition. This means that there exists a nonempty subset X of P(S) for which no maximal element u can be found, or there exists an element v in X that properly contains another element u.
In conclusion, a set S is T-finite if it meets Tarski's finite set condition, which asserts that there exists a maximal element u in X such that there is no v in X with v as a proper subset of u and u is different from v. A set is regarded as T-infinite if it does not meet this requirement.
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Write the equation of this conic section in conic form: 100pts pls
Answers
The equation of the conic section in conic form is (x - 1) = (y + 6)²/4.
To write the equation of the conic section in conic form, we can complete the square to transform the equation into its standard form. Let's start with the given equation:
y² - 4x + 12y + 32 = 0
Rearranging the terms, we have:
y² + 12y - 4x + 32 = 0
To complete the square for the y-terms, we add and subtract the square of half the coefficient of y (which is 6 in this case):
y² + 12y + 36 - 36 - 4x + 32 = 0
Simplifying this, we get:
(y + 6)² - 4x + 4 = 0
Now, rearranging the terms, we have:
(y + 6)² = 4x - 4
Dividing both sides of the equation by 4, we get:
(y + 6)²/4 = x - 1
Finally, we can write the equation in conic form:
(x - 1) = (y + 6)²/4
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The Probable question may be:
Which type of conic section is defined by the equation y²-4x+12y + 32 = 0?
This is an equation of a parabola
Write the equation of this conic section in conic form:
In an election 177 votes are cast. How many votes are needed to have a majority to have a majority of the votes in the election?
Answers
Answer:
89
Step-by-step explanation:
Take half of 177 and round up, which is 177/2 = 88.5 = 89
This is because 89+88=177 and 89>88, so there will be a majority.
NO LINKS!! URGENT HELP PLEASE!!
33. Use the diagram to name the following.
Answers
Answer:
[tex]\textsf{a)} \quad \textsf{Radius = $\overline{HG}$}[/tex]
[tex]\textsf{b)} \quad \textsf{Chord = $\overline{GF}$}[/tex]
[tex]\textsf{c)} \quad \textsf{Diameter = $\overline{JF}$}[/tex]
[tex]\textsf{d)} \quad \textsf{Secant = $\overleftrightarrow{GF}$}[/tex]
[tex]\textsf{e)} \quad \textsf{Tangent = $\overleftrightarrow{GK}$}[/tex]
[tex]\textsf{f)} \quad \textsf{Point of tangency = $\overset{\bullet}{G}$}[/tex]
[tex]\textsf{g)} \quad \textsf{Circle $H$}[/tex]
Step-by-step explanation:
a) RadiusThe radius is the distance from the center of a circle to any point on its circumference. The center of the circle is point H. Therefore, the radius of the given circle is line segment HG.
b) ChordA chord is a straight line joining two points on the circumference of the circle. There are two chords in the given circle: line segments GF and JF. Therefore, a chord of the given circle is line segment GF.
c) DiameterThe diameter of a circle is a straight line segment passing through the center of a circle, connecting two points on its circumference.
Therefore, the diameter of the given circle is line segment JF.
e) SecantA secant is a straight line that intersects a circle at two points.
Therefore, the secant of the given circle is line GF.
f) TangentA tangent is a straight line that touches a circle at only one point.
Therefore, the tangent line of the given circle is line GK.
g) Point of tangencyThe point of tangency is the point where the line touches the circle.
Therefore, the point of tangency of the given circle is point G.
h) CircleA circle is named by its center point. Therefore, as the center point of the circle is point H, the name of the circle is "Circle H".
Find the area of the shaded portion if we know the outer circle has a diameter of 4 m and the inner circle has a diameter of 1.5 m.
A. 1.8 m²
B. 43.2 m²
C. 12.6 m²
D. 10.8 m²
Answers
Answer:
π(2^2 - .75^2) = 55π/16 m² = 10.8 m²
D is the correct answer.
CO -8 6 4 4 -3 If K= 7 then what is -K?
Answers
Answer:
8
Step-by-step explanation:
i took the test mde 100
Miguel rolled up his sleeping bag and tied it with string. Estimate about how much string he used.
about ____ inches
OR about ____ feet
Answers
Answer:
Assuming Miguel rolled up his sleeping bag tightly and neatly, the length and circumference of the sleeping bag can help us estimate the length of string needed to tie it up.
Let's say the length of the sleeping bag is 6 feet and the circumference (distance around) is 3 feet. To tie it up, Miguel would need to wrap the string around it 2-3 times, depending on how long the string is and how tight he ties the knot.
So, we can estimate that he used about 12-18 feet of string (i.e. 2-3 times the circumference). In inches, that would be about 144-216 inches of string (i.e. 12-18 feet * 12 inches/foot).
Keep in mind that this is just an estimate and the actual amount of string used may vary depending on the factors mentioned above.
Step-by-step explanation:
In an election 177 votes are cast. How many votes are needed
Answers
The number of votes needed in an election can vary depending on various factors such as the type of election, voting rules, and specific requirements.
Without additional context or information about the specific election, it is challenging to provide an exact number of votes needed.The number of votes needed in an election is typically determined by factors such as the majority threshold, minimum vote requirement, or any specific criteria outlined in the election rules.
For example, in some elections, a candidate may need a simple majority (more than half) of the votes cast to win, while in others, a candidate may need a specific number or percentage of votes to secure victory.To determine the number of votes needed, it is essential to refer to the specific guidelines or rules established for that particular election.
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Need help on this!!! Pls help!!!
Answers
a) The mean of the data-set is of 2.
b) The range of the data-set is of 4 units, which is of around 4.3 MADs.
How to obtain the mean of a data-set?The mean of a data-set is obtained as the sum of all observations in the data-set divided by the number of observations in the data-set, which is also called the cardinality of the data-set.
The dot plot shows how often each observation appears in the data-set, hence the mean of the data-set is obtained as follows:
Mean = (1 x 0 + 5 x 1 + 3 x 2 + 5 x 3 + 1 x 4)/(1 + 5 + 3 + 5 + 1)
Mean = 2.
The range is the difference between the largest observation and the smallest, hence:
4 - 0 = 4.
4/0.93 = 4.3 MADs.
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prove that the lim x→−3 (10 − 2x) = 16
Answers
Answer:
Proving that the limit of the equation 10 - 2x as x approaches -3 is 16 involves using the definition of a limit.
Here's how you would approach it:
Let epsilon be a small positive number. We want to find a value of delta such that if x is within a distance of delta from -3, then 10 - 2x is within a distance of epsilon from 16.
So, we start with:
|10 - 2x - 16| < epsilon
Simplifying,
|-2x - 6| < epsilon
And using the reverse triangle inequality,
|2x + 6| > ||2x| - |6||
Now, we can choose a value for delta such that if x is within delta of -3, then |2x + 6| is within delta + 6 of |-6| = 6.
So,
||2x| - |6|| < epsilon
and therefore:
|2x - 6| < epsilon
Choosing delta = epsilon/2, we can prove that:
0 < |x + 3| < delta -> |2x - 6| < epsilon
Therefore, we have proved that the limit of 10 - 2x as x approaches -3 is 16 using the definition of a limit.
Step-by-step explanation:
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5 whole numbers are written in order. 5,8,x,y,12 The mean and median of the five numbers are the same. Work out the values of x and y.
Answers
5 whole numbers are written in order. 5,8,x,y,12 The mean and median of the five numbers are the same then the values of x and y are:[tex]$$\boxed{x=8, \ y=3}$$[/tex] OR [tex]$$\boxed{x=12, \ y=53}$$[/tex].
let's first calculate the median of the given numbers.
Median of the given numbers is the middle number of the ordered set.
As there are five numbers in the ordered set, the median will be the third number.
Thus, the median of the numbers = x.
The mean of a set of numbers is the sum of all the numbers in the set divided by the total number of items in the set.
Let the mean of the given set be 'm'.
Then,[tex]$$m = \frac{5+8+x+y+12}{5}$$$$\Rightarrow 5m = 5+8+x+y+12$$$$\Rightarrow 5m = x+y+35$$[/tex]
As per the given statement, the median of the given set is the same as the mean.
Therefore, we have,[tex]$$m = \text{median} = x$$[/tex]
Substituting this value of 'm' in the above equation, we get:[tex]$$x= \frac{x+y+35}{5}$$$$\Rightarrow 5x = x+y+35$$$$\Rightarrow 4x = y+35$$[/tex]
Also, as x is the median of the given numbers, it lies in between 8 and y.
Thus, we have:[tex]$$8 \leq x \leq y$$[/tex]
Substituting x = y - 4x in the above inequality, we get:[tex]$$8 \leq y - 4x \leq y$$[/tex]
Simplifying the above inequality, we get:[tex]$$4x \geq y - 8$$ $$(5/4) y \geq x+35$$[/tex]
As x and y are both whole numbers, the minimum value that y can take is 9.
Substituting this value in the above inequality, we get:[tex]$$11.25 \geq x + 35$$[/tex]
This is not possible.
Therefore, the minimum value that y can take is 10.
Substituting y = 10 in the above inequality, we get:[tex]$$12.5 \geq x+35$$[/tex]
Thus, x can take a value of 22 or less.
As x is the median of the given numbers, it is a whole number.
Therefore, the maximum value of x can be 12.
Thus, the possible values of x are:[tex]$$\boxed{x = 8} \text{ or } \boxed{x = 12}$$[/tex]
Now, we can use the equation 4x = y + 35 to find the value of y.
Putting x = 8, we get:
[tex]$$y = 4x-35$$$$\Rightarrow y = 4 \times 8 - 35$$$$\Rightarrow y = 3$$[/tex]
Therefore, the values of x and y are:[tex]$$\boxed{x=8, \ y=3}$$[/tex] OR [tex]$$\boxed{x=12, \ y=53}$$[/tex]
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Given the equation y=mx+b fine the valué of y if x =10, m = 2.5, and b =2
Answers
Answer:
27
Step-by-step explanation:
lion plays trumpet for a minmium of 45 mins on the days that he practices. if x is the number of days that lionel practices and y is the total number of hours he spends practicing, which inequality represents this situation
Answers
The inequality representing the situation is "y ≥ 0.75x," where y is the total number of hours Lionel spends practicing and x is the number of days he practices.
To represent the situation where Lionel practices for a minimum of 45 minutes on the days he practices, we can use the variables x and y, where x represents the number of days Lionel practices and y represents the total number of hours he spends practicing.
We know that Lionel practices for a minimum of 45 minutes on each day. Since there are 60 minutes in an hour, this is equivalent to 0.75 hours. Therefore, for each day Lionel practices, he spends at least 0.75 hours.
To find the total number of hours Lionel spends practicing (y), we can multiply the number of days he practices (x) by the minimum number of hours he spends on each day (0.75). This gives us the equation:
y ≥ 0.75x
This inequality states that the total number of hours Lionel spends practicing (y) must be greater than or equal to 0.75 times the number of days he practices (x). It ensures that Lionel practices for a minimum of 45 minutes (0.75 hours) on each day he practices.
By using this inequality, we can track Lionel's practice time and ensure that he meets the minimum requirement of 45 minutes per day.
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Hcf of two expressions is (x + 1) and lcm is (x^3+ x^2 – x – 1). if one expression is (x^2 - 1), then what is the second expression?
Answers
After solving by formula the second expression is y = [tex](x^2 + 1)[/tex].
We know that the product of the HCF and LCM of two numbers is equal to the product of the numbers themselves. In this case, we can apply the same principle to expressions:
HCF * LCM = (x + 1) * [tex](x^3+ x^2 - x - 1)[/tex]
the first number is [tex]x^{2} -1\\[/tex] and let the second number is y
Therefore, we can set up the equation:
(x + 1) * [tex](x^3+ x^2 - x - 1)[/tex] = [tex]x^{2} -1\\[/tex] * y
[tex]x^4 + x^3 + x^2 - x^3 - x^2 + x - x - 1 = x^2 - 1 * y[/tex]
Simplifying:
[tex]x^4 - 1 = (x^2 - 1) * y[/tex]
Now, we can divide both sides by [tex](x^2 - 1)[/tex]:
[tex](x^4 - 1) / (x^2 - 1) = y[/tex]
Notice that [tex](x^2 - 1)[/tex]can be factored as (x + 1)(x - 1). Therefore, we can simplify further:
[tex](x^4 - 1) / ((x + 1)(x - 1)) = y[/tex]
The expression [tex](x^4 - 1)[/tex] can be factored using the difference of squares:
[tex](x^4 - 1) = (x^2 + 1)(x^2 - 1)[/tex]
[tex][(x^2 + 1)(x^2 - 1)] / ((x + 1)(x - 1)) = y[/tex]
Now, we can cancel out the common factor [tex](x^2 - 1)[/tex] from the numerator and denominator:
[tex]y =(x^2 + 1)[/tex]
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The ratio of males to females is 2:3. there are 12 boys in class. How many females are in the class
Answers
Answer:
Number of Females in Class = x Given: Ratio of Males to Females = 2:3 Given: Number of Males in Class = 12 Assume the total number of people in class = y 2/3 of y = x 2x = 3y 12 + x = y y - 12 = x y - 12 = 2x 3y - 36 = 2x 3y = 2x + 36 y = (2x + 36) / 3 y = (2(12) + 36)/3 y = 24 x = y - 12 x = 24 - 12 x = 12 Answer: There are 12 females in the class.
Step-by-step explanation:
please help me asap with this it's getting late
Answers
The system B is gotten from system A by operation (d)
How to derive the system B from system AFrom the question, we have the following parameters that can be used in our computation:
x + y = 8
4x - 6y = 2
Also, we have the solution to be (5, 3)
Recall that
x + y = 8
4x - 6y = 2
Multiply the first equation by 6
So, we have
6x + 6y = 48
4x - 6y = 2
Add the equations
10x = 50
This means that the system B from system A is (d)
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Jasmine works as a magician at children's parties. For each party she charges
$28 for the first hour and $20 per hour after that. This is represented by the
equation t-28-20[h-1) where t is the total amount Jasmine charges and his
the number of hours she works. Jasmine has decided to charge $30 for the first
hour.
Which of the following equations represents Jasmine's new fee?
Answers
Answer:
Step-by-step explanation:
$28 for 1st hr and $20per hr after that:
t = 28 + 20(h-1)
$30 for 1st hr and $20per hr after that:
t = 30 + 20(h-1)
t - 30 - 20(h-1)
Find a delta that works for ε = 0.01 for the following
lim √x + 7 = 3
x-2
Answers
A suitable delta (δ) for ε = 0.01 is any positive value smaller than √6.
To find a suitable delta (δ) for the given limit, we need to consider the epsilon-delta definition of a limit.
The definition states that for a given epsilon (ε) greater than zero, there exists a delta (δ) greater than zero such that if the distance between x and the limit point (2, in this case) is less than delta (|x - 2| < δ), then the distance between the function (√x + 7) and the limit (3) is less than epsilon (|√x + 7 - 3| < ε).
Let's solve the inequality |√x + 7 - 3| < ε:
|√x + 7 - 3| < ε
|√x + 4| < ε
-ε < √x + 4 < ε
To remove the square root, we square both sides:
(-ε)^2 < (√x + 4)^2 < ε^2
ε^2 > x + 4 > -ε^2
Since we're interested in the interval around x = 2, we substitute x = 2 into the inequality:
ε^2 > 2 + 4 > -ε^2
ε^2 > 6 > -ε^2
Since ε > 0, we can drop the negative term and solve for ε:
ε^2 > 6
ε > √6
Please note that this solution assumes the function √x + 7 approaches the limit 3 as x approaches 2. To verify the solution, you can substitute different values of δ and check if the conditions of the epsilon-delta definition are satisfied.
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Find three points that solve the equation and plot it on a graph -3x + 2y = 11
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The x-axis represents the values of x, and the y-axis represents the values of y. The first point (0, 11/2) lies on the y-axis, at a height of 11/2. The second point (2, 17/2) lies to the right of the y-axis, at a height of 17/2. The third point (-3, 1) lies to the left of the y-axis, at a height of 1.
To find three points that satisfy the equation -3x + 2y = 11, we can arbitrarily assign values to either x or y and solve for the other variable. Let's choose to assign values to x and solve for y:
Let x = 0:
-3(0) + 2y = 11
2y = 11
y = 11/2
The first point is (0, 11/2).
Let x = 2:
-3(2) + 2y = 11
-6 + 2y = 11
2y = 11 + 6
2y = 17
y = 17/2
The second point is (2, 17/2).
Let x = -3:
-3(-3) + 2y = 11
9 + 2y = 11
2y = 11 - 9
2y = 2
y = 1
The third point is (-3, 1).
Now let's plot these points on a graph:
The x-axis represents the values of x, and the y-axis represents the values of y. The first point (0, 11/2) lies on the y-axis, at a height of 11/2. The second point (2, 17/2) lies to the right of the y-axis, at a height of 17/2. The third point (-3, 1) lies to the left of the y-axis, at a height of 1.
By plotting these three points on the graph, you will have a visual representation of the solutions to the equation -3x + 2y = 11.
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Solve |5x - 1| < 1
please help
Answers
Answer:
|5x - 1| < 1
-1 < 5x - 1 < 1
0 < 5x < 2
0 < x < 2/5
Do you think the graph given below could be the graph of y=sin x?
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The graph in this problem is the graph of y = 2sin(x), not y = x, as it has a amplitude of 2.
How to define a sine function?The standard definition of the sine function is given as follows:
y = Asin(B(x - C)) + D.
For which the parameters are given as follows:
A: amplitude.B: the period is 2π/B.C: phase shift.D: vertical shift.The function in this problem has an amplitude of 2, with no phase shift, no vertical shift and period of 2π, hence it is defined as follows:
y = 2sin(x)
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Lucas is selling protein bars for a fundraiser. He sold 12 bars on Saturday and 8 bars on Sunday. If each bar sold for $1.50, how much money did he raise?
Answers
The money raised by Lucas for the fundraiser is $30.
The bars sold on Saturday are 12 bars. Each bar costs $1.50.
So, the amount will be: 12 * 1.50 = 18
The bars sold on Sunday are 8 bars.
So, the amount will be: 8 * 1.50 = 12
Hence, the total amount: is 18+12= 30
find a positive and a negative coterminal angle for each given angle.
Answers
Answer:
c
Step-by-step explanation:
add 360 to 265 to get the first number and subtract 360 from 265 to get the second number
Please awnser asap I will brainlist
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The solution to the system is (b) (-2, 3, z) where z is any real number
How to determine the solution to the systemFrom the question, we have the following parameters that can be used in our computation:
The augmented matrix
Where, we have
[tex]\left[\begin{array}{ccc|c}1&0&0&-2\\0&1&0&3\\0&0&0&3\end{array}\right][/tex]
From the above, we have the first two diagonals to be 1
And other elements to be 0
This means that
x = -2 and y = 3
For z, the value is infinitely many
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I’m trying to solve p=2l+2w solving for w
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The solution for p=2l+2w, the value of w= 3 units.
To solve the equation p = 2l + 2w for w, we will follow the steps below:
Step 1: Start with the given equation: p = 2l + 2w.
Step 2: To isolate the variable w, we need to get rid of the terms involving l. We can do this by subtracting 2l from both sides of the equation:
p - 2l = 2w.
Step 3: Next, we want to solve for w. To do this, we divide both sides of the equation by 2:
(p - 2l) / 2 = w.
Step 4: Simplify the expression on the right side:
w = (p - 2l) / 2.
Now, let's apply this formula to a specific example. Suppose we have a rectangle with a perimeter of 16 units (p = 16) and a length of 5 units (l = 5). We can find the width (w) using the formula:
w = (16 - 2(5)) / 2
w = (16 - 10) / 2
w = 6 / 2
w = 3.
By following the steps outlined above and substituting the given values of the perimeter (p) and length (l) into the formula w = (p - 2l) / 2, you can determine the value of the width (w) for any given rectangle.
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