how to find (a) and (b)?​

The value of q is 0.35.

The value of p is 0.16.

The value of r is 0.27.

The value of P(A given NOT B) is approximately 0.4211.

To calculate the values of p, q, and r, we can use the information provided in the Venn diagram and the probabilities of events A and B.

Given:

P(A) = 0.43

P(B) = 0.62

P(A∩B) = 0.27

Calculating the value of p:

The value of p represents the probability of event A occurring without event B. In the Venn diagram, p corresponds to the region inside A but outside B.

We can calculate p by subtracting the probability of the intersection of A and B from the probability of A:

p = P(A) - P(A∩B)

= 0.43 - 0.27

= 0.16

Therefore, the value of p is 0.16.

Calculating the value of q:

The value of q represents the probability of event B occurring without event A. In the Venn diagram, q corresponds to the region inside B but outside A.

We can calculate q by subtracting the probability of the intersection of A and B from the probability of B:

q = P(B) - P(A∩B)

= 0.62 - 0.27

= 0.35

Therefore, the value of q is 0.35.

Calculating the value of r:

The value of r represents the probability of both event A and event B occurring. In the Venn diagram, r corresponds to the intersection of A and B.

We are given that P(A∩B) = 0.27, so the value of r is 0.27.

Therefore, the value of r is 0.27.

Finding the value of P(A given NOT B):

P(A given NOT B) represents the probability of event A occurring given that event B does not occur. In other words, it represents the probability of A happening when B is not happening.

To calculate this, we need to find the probability of A without B and divide it by the probability of NOT B.

P(A given NOT B) = P(A∩(NOT B)) / P(NOT B)

We can calculate the value of P(A given NOT B) using the provided probabilities:

P(A given NOT B) = P(A) - P(A∩B) / (1 - P(B))

= 0.43 - 0.27 / (1 - 0.62)

= 0.16 / 0.38

≈ 0.4211

Therefore, the value of P(A given NOT B) is approximately 0.4211.

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Answer: You can do this!

Step-by-step explanation: For D. The x= -1 and the y= 1 for E same thing the x= 7 and the y= 1 so look for the 7 on the x-axes and the one on the y-axes get it. I believe that you got this!

Hope this helped love<3

V is a vector space with the operations of addition and scalar multiplication.

Since f(t) and g(t) are real numbers, you're utilizing the fact that the real numbers themselves are commutative in that step, which truly confused me when I first learned about it and after.

Let V denote the set of all differentiable real-valued functions defined on the real line.

You only need to mention that real-number addition is commutative. Since f is not a number until you evaluate, you couldn't do it before you did.

On a different note, you cannot say that

f+g=f(t)+g(t)

but you can say that (f+g)(t)=f(t)+g(t)

So  V is a vector space with the operations of addition and scalar multiplication.

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Answer:

40

Step-by-step explanation:

The first triangle is 1/2 the size of the bigger triangle, you would just multiply 20 by the ration you have which is 2 and you get 40

Answer:

128 + 72 = 200

Step-by-step explanation:

Start from the ones. And go next to tens and last find the hundreds.

see image.

Answer:

B

Step-by-step explanation:

The best - well, only way- is to check a few points.

Namely -1 (unless your eyesight is really poor!), 0, 1, 2, and 3.

\(f(x) = 2^x\\f(-1) = 2^-^1 = \frac12\\f(0) =2^0 =1\\f(1)= 2^1=2\\f(2)=2^2=4\\f(3)=2^3= 8\)

Now you can mark all these points in each graph (well, you could if they were on paper and not on a screen) and see which one of the lines passes through all of them. Spoiler alert, it's the B graph.

A represents \(2(2^x) = 2^{x+1}\), B is the one you want, C is \(\frac{2^x}2 = 2^{x-1}\) and D looks like \(4^x = 2^2^x\)

The first five terms of the geometric sequence is 6, 18, 54, 162 and 486

Geometric progression is given by:

\(nth\ term=ar^{n-1}\)

where a is the first term, r is the common ratio

Given that first term is 6, and common ratio is 3, Hence a = 6, r = 3

\(First\ term=6\\\\Second \ term=6(3)^{2-1}=18\\\\Third \ term=6(3)^{3-1}=54\\\\Fourth \ term=6(3)^{4-1}=162\\\\Fifth \ term=6(3)^{5-1}=486\)

The first five terms of the geometric sequence is 6, 18, 54, 162 and 486

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Answer:

The domain would be -3≤x≤2 and the range would be -5≤y≤4

Step-by-step explanation:

The domain is where the x values cover, so since on the graph the points range from having -3 as the x value to 2, x would be anything between or equal to these values.

The domain is where the y values cover, so since on the graph the points range from having -5 as the y value to 4, y would be anything between or equal to these values.

Sammy's total trip was 75 miles. To find the total length of Sammy's trip, we can use the information given in the question.

We know that Sammy traveled 15 miles by bus, and this distance represents twenty percent of his total trip.

Let's denote the total length of his trip as "T" (in miles).

We can set up a proportion to solve for T:

(15 miles) / (T) = (20 percent) / 100

To solve for T, we can cross-multiply and then divide:

15 * 100 = 20 * T

1500 = 20T

T = 1500 / 20

T = 75

So, Sammy's total trip was 75 miles.

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The number of square meters that the space that Araceli rents is, is 30. 66 square meters.

The space that Araceli rents has a rectangular space so to find the area of the rectangular space that Araceli rents, we need to multiply the length by the width.

The given width is 4. 2 meters and the length is 7. 3 meters.

The area of the space in square meters is therefore :

Area = Length × Width

Area = 7. 3 meters × 4. 2 meters

Area = 30. 66 square meters

In conclusion, the space that Araceli rents has an area of 30. 66 square meters.

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We have to find the value of z and x.

We assume that lines g and h are parallel.

Then, z and the angle with measure 85° are consecutive interior angles.

As they are conscutive interior angles, their measures add 180°.

Then, we can write:

Then, we can relate the angle with measure z with the angle with measure (6x-109). They are vertical angles and, therefore, they have the same measure.

Then, we can write:

Answer: z = 95 and x = 34.

Given that 16 families went on a trip and the cost of the trip was Rs. 2,16,352.The amount paid by each family is to be determined by unitary method Hence each family paid Rs.13522

Now, let's solve this by using the method of unitary method. To find the cost of 1 family trip, we will divide the total cost of the trip by the number of families.2,16,352 / 16 = 13,522 So, the cost of the trip per family is Rs. 13,522.Hence, each family paid Rs. 13,522 for the trip.

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Answer:

Step-by-step explanation

1. The total cost of the trip for all 16 families is Rs 2,16,352.
2. To find out how much each family paid, we need to divide the total cost by the number of families: Rs 2,16,352 ÷ 16.
3. When we do the division, we get the result: Rs 13,522.

Now let's check if this result is correct:

1. If each family paid Rs 13,522 for the trip, then the total cost for all 16 families would be: 16 × Rs 13,522 = Rs 2,16,352.
2. This is exactly the same as the total cost given in the problem statement.

So we have shown that each family paid **Rs 13,522** for the trip

Answer:

x is 9

Step-by-step explanation:

The correct options are -

When something is bought on credit, an initial payment is made in the form of a down payment.

Given is that Renata is purchasing a condominium for $125,000. She wants to put down a down payment of 20%.

We can calculate the amount she is putting in down payment as -

{x} = 20% of 125000

{x} = 20/100 x 125000

{x} = 20 x 1250

{x} = 25000

Therefore, the correct options are -

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P(1.6,-2.9) are the coordinates of circumcentre of the triangle

The circumcenter of a triangle is the point where the perpendicular bisectors of the sides of that particular triangle intersect.

Let L(3,−6), M(5,−3), N(8,−6) be the vertices of the given △LMN.

Let P(x,y) be the circumcentre of △LMN. Then,

PL = PM = PN

Also, PL² = PM² = PN²

PL² = PM²

(x-3)² + (y-(-6))² = (x-5)² + (y-(-3))²

(x-3)² + (y+6)² = (x-5)² + (y+3)²

x²-6x+9 + y²+12y+36 = x²-10x+25 + y²+6y+9

4x + 6y = -11   ---- (1)

Also, PM² = PN²

(x-5)² + (y-(-3))² = (x-8)² + (y-(-6))²

(x-5)² + (y+3)² = (x-8)² + (y+6)²

x²-10x+25 + y²+6y+9 = x²-16x+64 + y²+12y+36

6x - 6y = 27   ---- (2)

Solve (1) and (2) simultaneously by elimination:

6 × (4x + 6x = -11)

4 × (6x - 6y = 27)

24x + 36y = -66

24x - 24y = 108

subtract:

         60y = -174

         y = -174/60

         y = -2.9

Put y = -2.9 into (1):

4x + 6x = -11

4x + 6(-2.9) = -11

4x - 17.4 = -11

4x = 6.4

x = 1.6

Thus, the coordinates of the circumcentre of △LMN are P(1.6, -2.9)

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There is no significant difference between the mean scores of Education and Nursing students in mathematics.

Null hypothesis (H₀): There is no significant difference between the mean scores of Education and Nursing students in mathematics.

Alternative hypothesis (H₁): There is a significant difference between the mean scores of Education and Nursing students in mathematics.

We will use significance level (α) of 0.01.

Given:

Sample mean for Education students (x₁) = 88.50

Sample mean for Nursing students (x₂) = 90.25

Standard deviation for the Education student sample (s₁) = 7.5

Standard deviation for the Nursing student sample (s₂) = 8.2

Sample size for Education students (n₁) = 25

Sample size for Nursing students (n₂) = 29

The t-test statistic for two independent samples is:

t = (x1₁ - x2) / sqrt((s₁² / n₁) + (s₂² / n₂))

t = (88.50 - 90.25) / sqrt((7.5² / 25) + (8.2² / 29))

t ≈ -0.8187

In this case, df = 24.

The critical value for α = 0.01 and df = 24 is approximately ±2.797.

Since |-0.8187| < 2.797, the absolute value of the t-test statistic is smaller than the critical value.

Therefore, we fail to reject the null hypothesis.

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Using quadratic function concepts, it is found that the true statements about the equation are:

A quadratic function is given according to the following rule:

\(y = ax^2 + bx + c\)

\(x_v = -\frac{b}{2a}\)

\(y_v = -\frac{\Delta}{4a}\)

\(\Delta = b^2 - 4ac\)

\(x_1 = \frac{-b + \sqrt{\Delta}}{2a}\)

\(x_2 = \frac{-b - \sqrt{\Delta}}{2a}\)

In this problem, the function is:

\(f(x) = x^2 - 6x + 2\)

The coefficients are \(a = 1, b = -6, c = 2\).

Since a > 0, the graph has a minimum value.

For the extreme value, we have that:

\(x_v = -\frac{b}{2a} = \frac{6}{2} = 3\)

\(\Delta = b^2 - 4ac = (-6)^2 - 4(1)(2) = 28\)

\(y_v = -\frac{\Delta}{4a} = -\frac{28}{4} = -7\)

Hence:

The extreme value is at the point (7,-3).

The solutions are:

\(x_1 = \frac{6 + \sqrt{28}}{2} = \frac{6 + 2\sqrt{7}}{2} = 3 + \sqrt{7}\)

\(x_2 = \frac{6 - \sqrt{28}}{2} = \frac{6 - 2\sqrt{7}}{2} = 3 - \sqrt{7}\)

The solutions are \(3 \pm \sqrt{7}\).

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To find the missing angle measure, we need to use the fact that the sum of angles in a triangle is 180 degrees. Let's denote the missing angle as x. We know that one angle is 38 degrees and another angle is 12.5 degrees.Therefore, the missing angle measure is 129.5 degrees.

By subtracting these two angles from 180 degrees, we get:

180 - 38 - 12.5 = 129.5

Without additional information, it is not possible to determine the remaining parts of the triangle. We would need the lengths of at least one side or the measures of other angles to solve for the missing parts.

The given information states that AC is equal to AB minus mzB. Without knowing the values of AB and mzB, we cannot determine the exact length of AC. We would need additional information to solve for the length of AC.Therefore, the missing angle measure is 129.5 degrees.

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The probability that the teacher will choose two girls would be = 1/6

Probability is defined as the expression that shows the possibility of an outcome of an event which may or may not happen.

The total number of students in the class = 9

The total number of girls = 4

The total number of boys = 5

The formula for finding probability = No of favourable outcome/Total number of outcomes.

The probability that teacher choose first girl = 4/9

One girl is selected we must reduce the number of girls available for selection to 4 - 1 = 3.

We must also reduce the number of children available for selection 9 - 1 = 8.

The probability that teacher choose second girl = 3/8

Thus, the probability = 4/9 × 3/8 = 1/6

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The approximate height of the tree is given as follows:

45.6 ft.

The geometric mean theorem states that the length of the altitude drawn from the right angle of a triangle to its hypotenuse is equal to the geometric mean of the lengths of the segments formed on the hypotenuse.

The altitude segment for this problem is given as follows:

14.5 ft.

The bases are given as follows:

5.2 ft and x ft.

Hence the value of x is given as follows:

5.2x = 14.5²

x = 14.5²/5.2

x = 40.4 ft.

Hence the height of the three is given as follows:

5.2 + 40.4 = 45.6 ft.

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The answer of the given question is (a) TR = p(40 - (4/3)p), or TR = 40p - (4/3)p² , (b)  TC = 9q + (3/10)q² + 30 , (c) π = 40p - (4/3)p² - 9q - (3/10)q² - 30 , (d) TR ≈ 342.67 , (e) the profit when 20 units are produced is approximately RM188.27 , (f)  the profit when 7 units are produced is approximately -RM24.44, indicating a loss , (g) the output required to obtain a profit of RM100 is approximately 8.78 units.

An equation is  mathematical statement that asserts yhe equality of two expressions. It typically consists of variables, constants, and mathematical operations like addition, subtraction, multiplication, and division, among others. Equations are often used to solve problems, to model real-world phenomena, and to describe mathematical relationships.

(a) The total revenue is given by TR = p x q. Substituting the demand equation q = 40 - (4/3)p, we get TR = p(40 - (4/3)p), or TR = 40p - (4/3)p².

(b) The total cost is given by TC = q x AC. Substituting the given average cost function, we get TC = 9q + (3/10)q² + 30.

(c) The profit is given by π = TR - TC. Substituting the expressions we found in parts (a) and (b), we get π = 40p - (4/3)p² - 9q - (3/10)q² - 30.

(d) At the break even point, the firm earns zero profit, so we set π = 0 and solve for q. Substituting the expression we found in part (a) for p, we get:

0 = 40p - (4/3)p² - 9q - (3/10)q² - 30

0 = 40(40/3 - (3/4)q) - (4/3)(40/3 - (3/4)q)² - 9q - (3/10)q² - 30

0 = 533.33 - 51.25q - 0.22q^2

Solving for q using the quadratic formula, we get:

q = (51.25 ± sqrt(51.25² - 4(-0.22)(533.33))) / 2(-0.22)

q ≈ 22.75 or q ≈ 206.58

We reject the solution q ≈ 206.58 because it is outside the relevant range of output, which is between 0 and 40. Therefore, the total output at the break even point is approximately 22.75 units. To find the total revenue at the break even point, we substitute q = 22.75 into the demand equation from part (a) and get:

p = (40/3) - (3/4)q

p ≈ 15.08

TR = p x q

TR ≈ 342.67

(e) To find the profit when 20 units are produced, we substitute q = 20 into the expression for profit we found in part (c) and get:

π = 40p - (4/3)p² - 9q - (3/10)q² - 30

π ≈ 188.27

Therefore, the profit when 20 units are produced is approximately RM188.27.

(f) To find the profit when 7 units are produced, we substitute q = 7 into the expression for profit we found in part (c) and get:

π = 40p - (4/3)p² - 9q - (3/10)q² - 30

π ≈ -24.44

Therefore, the profit when 7 units are produced is approximately -RM24.44, indicating a loss.

(g) To find the output required to obtain a profit of RM100, we set the profit equation equal to 100 and solve for q:

Profit = TR - TC

100 = pq - ACq

100 = (40-(4/3)p)*q - (9+(3/10)q+30/q)*q

100 = (40-(4/3)p - 9q - 3q²/10)

Multiplying by 10 and rearranging terms, we get a quadratic equation in q:

3q² + 91q - 310 = 0

Solving for q using the quadratic formula, we get:

q = (-91 ± sqrt(91² - 43(-310)))/(2*3)

q ≈ 8.78 or q ≈ -29.44

Since the quantity produced cannot be negative, the output required to obtain a profit of RM100 is approximately 8.78 units.

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Do u have a screenshot

Step-by-step explanation:

Answer:

---------------------------------------

Let the cost of the meal be x.

Adding a tip of 19%:

Answer:

Wyatt should multiply with 1.19.

Step-by-step explanation:

Forming the expression,

→ 1 + (19% of 1)

Now the required number is,

→ 1 + (19% of 1)

→ 1 + ((19/100) × 1)

→ 1 + (19/100)

→ 1 + 0.19 = 1.19

Hence, required number is 1.19.

Answer:

Choice a: \(x>5\)

Step-by-step explanation:

All you have to do on this one is add the 7 on both sides.

\(x-7>8\\x>5\)

So the answer is anything greater than 5.

Therefore , the solution of the given problem of equation comes out to be the new line equation is y  = 4x + 22.

The analogous symbol (=) is used in arithmetic equations to signify equality between two statements. It is shown that it is possible to compare various numerical factors using mathematical techniques, which have served as manifestations of reality. For example, the equal sign divides the number 12 or even the solution y + 6 = 12 onto two different halves. How many characters already appear on either end of such a symbol can be calculated. Conflicting symbol meanings occur frequently.

Here,

Given :

The graph shows straight line is

=> y =mx + c where m is the slope

b) y =4x  + 7

where 4 is the gradient or slope of the line

c) y = 4x + 7

point (0,15)

new equation is :

=> y - 15 = 4 (x -0 ) + 7

=> y  = 4x + 22

Therefore , the solution of the given problem of equation comes out to be the new line equation is y  = 4x + 22.

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Answer:

7.11

Step-by-step explanation: Area=lengthxwdth

64=lengthx9

64/9=length

7.11=length