The table shows information about the lengths of time, in minutes, it took some

pupils to do their maths homework last week.

Frequency

Length of time (1)

0
5

10
24

25
12

30
8

2

Draw a histogram for

the information in the table.

Frequency density

0+

10

20

30

Length of time (1)

40

50

There are 46 elements in total for 4 sets A, B, C, and D.

Consider 4 sets A, B, C, and D.

Each set has 15 elements.

The pair-wise intersection has 4 elements.

The three-way intersection has 3 elements.

There are 2 elements in the intersection of all sets.

So,

P(A) = P(B) = P(C) = P(D) = 15

P(A ∩ B) = P(A ∩ C) = P(A ∩ D) = P(B ∩ C) = P(B ∩ D) = P(C ∩ D) = 4

P(A ∩ B ∩ C) = P(A ∩ B ∩ D) = P(A ∩ C ∩ D) = P(B ∩ C ∩ D) = 3

P(A ∩ B ∩ C ∩ D) = 2

The total number of elements are:

P (A U B U C U D) = P(A) + P(B) + P(C) + P(D) - P(A ∩ B) - P(A ∩ C) - P(A ∩ D)- P(B ∩ C) - P(B ∩ D) - P(C ∩ D) + P(A ∩ B ∩ C) + P(A ∩ B ∩ D) + P(A ∩ C ∩ D) + P(B ∩ C ∩ D) - P(A ∩ B ∩ C ∩ D).

P (A U B U C U D) = 15 + 15 + 15 + 15 - 4 - 4 - 4 - 4 - 4 - 4 + 3 + 3 + 3 + 3 - 2

= 60 - 24 + 12 - 2

= 60 + 12 - 24 - 2

= 72 - 26

= 46

Therefore there are 46 elements.

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From the trigonometric function sec θ = 13/12, two more functions are derived -

Option C: cos θ = 12/13

Option D: tan θ = 5/12

What is trigonometric function?

Simply put, trigonometric functions also referred to as circular functions are the functions of a triangle's angle. This means that these trig functions provide the relationship between the angles and sides of a triangle.

The given trigonometric function is -

sec θ = 13/12

Sec function is written as the ratio of hypotenuse to adjacent.

sec θ = 1/cos θ

Cos function is written as the ratio of adjacent to hypotenuse.

cos θ = 12/13

To find the opposite, apply the Pythagoras theorem -

(Opposite)² = (Hypotenuse)² - (Adjacent)²

(Opposite)² = (13)² - (12)²

(Opposite)² = 169 - 144

Opposite = √25

Opposite = 5

Tan function is written as the ratio of opposite to adjacent.

tan θ = 5/12

Therefore, from sec function, cos and tan function are obtained.

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Both Guillermo's and Cara's solutions are incorrect due to the incorrect substitution of values of a variable to find the dependent one.

Guillermo's solution is incorrect because he did not substitute the value of 'b' from the first equation into the second equation. Instead, he directly added 0.49b to both sides and solved for a, which gives an incorrect result.

Cara's solution is also incorrect because she did not substitute the value of 'a' from the first equation into the second equation. Instead, she used the equation a + b = 7 to solve for the value of b, which gave her an incorrect result.

We can find the correct solution as follows -

The system of equations is,

⇒ a + b = 7   .. (i)

And 1.29a + 0.49b = 6.63 .. (ii)

Now, we will solve the system of equations as follows -

⇒ a + b = 7  

⇒ a = 7 - b .. (i)

And, ⇒ 1.29a + 0.49b = 6.63 .. (ii)

Substitute the value of a from (i) in (ii), we get;

⇒ 1.29a + 0.49b = 6.63

⇒ 1.29(7 - b) + 0.49b = 6.63

⇒ 9.03 - 1.29b + 0.49b = 6.63

⇒ - 0.8b = 6.63 - 9.03

⇒ - 0.8b = - 2.4

⇒ 0.8b = 2.4

⇒ b = 2.4 / 0.8

⇒ b = 3

And, From (i);

⇒ a = 7 - b .. (i)

⇒ a = 7 - 3

⇒ a = 4

Hence, 4 pounds of apples and 3 pounds of bananas were bought.

Thus, both of their solutions are incorrect.

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The complete question is -

FIND THE ERROR In the system a + b = 7 and 1.29a + 0.49b = 6.63, a represents pounds of apples and b represents pounds of bananas a person bought. Guillermo and Cara are finding and interpreting the solution. Is either correct? Explain your reasoning.

a. Guillermo: 1.29a + 0.49b = 6.63 ⇒ 1.29a +0.49(a + 7) = 6.63 ⇒ 1.29a + 0.49a + 3.43 = 6.63 ⇒ 1.78a = 3.2 ⇒ a = 1.8

a + b = 7, so b = 5.2. The solution (1.8, 5.2) means that 1.8 pounds of apples and 5.2 pounds of bananas were bought.

b. Cara: 1.29a + 0.49b = 6.63 ⇒ 1.29(7-b) + 0.49b = 6.63 ⇒ 9.03- 1.29b + 0.49b = 6.63 ⇒ -0.8b = -2.4 ⇒ b=3

The solution b = 3 means that 3 pounds of apples and 3 pounds of bananas were bought. volunteers. The ratio of boys to girls is 7:5.​

The displacement vector of the object is (-3, 9) and the work done is 30 Joules

The term called vector in math is defined as a quantity or phenomenon that has two independent properties such as magnitude and direction.

Here we know that the value of force F is (-1, 3) and the point is (3, -9)

Then the displacement from origin to (3, -9) is calculated as,

=> d = (0-3, 0-(-9))

Then the value of d is ( -3, 9)

Here the formula to Work done is written as,

=> F x d

=> (-1, 3) x (-3, 9) = 3 + 27

=> 30 joules.

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Answer:

2

Step-by-step explanation:

count the grids, A is 4, B is 8, so scale =2

There are other methods to write a division issue, such as using a / or a to denote "divided by." As a result, in the equation 473 / 2 = 1 the divisor is the quotient, the remainder is 236, and the divisor is 2.

Divide the dividend's first digit, which should be on the left, by the divisor, then write the result as the quotient on top. Write the difference below after subtracting the outcome from the digit. Bring down the dividend's next digit (if present).

Long division strategy: lengthy division techniques. The same symbols are used for long division as they are for short division: dividend (the number being divided) under the "bus stop," divisor (the number the dividend is being divided by), quotient (the solution) on top, and each place value aligned with the dividend.

Dividend Divisor = Quotient + Remainder is the formula for dividing two numbers.

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The complete question is "Divide the given numbers 473 and 6 using our free online Long Division Calculator and determine the Quotient and Remainder as Q 78 R 5 instantly without any hurdles."

ΔABC and ΔDEF are not similar because corresponding angles are not equal.

Now, According to the question:

In triangle ABC :

The measure of angle A is 35º and

The measure of angle B is 20°.

In triangle DEF:

The measure of angle D is 35º and

The measure of angle F is 125

We know that :

Sum of interior angles of triangle is 180°

Now, In ΔABC:

∠A + ∠B + ∠C = 180°

35 +  20 + ∠C = 180°

55° +  ∠C = 180°

∠C = 180° - 55°

∠C = 125°

Now,  In ΔDEF:

∠D + ∠E + ∠F = 180°

35 + ∠E + 125 = 180°

160  + ∠E = 180°

∠E = 180° - 160°

∠E = 20°

So, ∠C ≠ ∠E  as ∠C = 125° and ∠E =20°

Hence, No, Triangles are not similar .

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Answer:

x ≥ 10

Step-by-step explanation:

A solid dot on 10 means 10 is included.

An arrow pointing to the right of 10 means all numbers greater than 10 are included.

Answer: x ≥ 10

Answer:10 =< x

Step-by-step explanation:
Shaded circle means include that number so it is a <= or >= sign
Goes to x.
Think about it a bit, not quite sure if 50 is involved in this inequality

Part E: The area that Jordan can walk around is equal to the area of a circle with a radius of 6 feet is 113 square feet.

Part A: Wendell cannot make a triangular garden using pieces A, B, and F because the sum of the lengths of the two shorter sides of a triangle (in this case, pieces A, B, and F) must be greater than the length of the longest side (in this case, piece F, which is 2 feet long) in order for the triangle to be a valid one. Since the sum of the lengths of pieces A and B is 12 feet, which is greater than the length of piece F, it is not possible to make a triangular garden using these pieces.

Part B: Wendell cannot make a triangular garden using pieces D, E, and F because the sum of the lengths of the two shorter sides of a triangle (in this case, pieces D, E, and F) must be greater than the length of the longest side (in this case, piece D, which is 8 feet long) in order for the triangle to be a valid one. Since the sum of the lengths of pieces E and F is 5 feet, which is less than the length of piece D, it is not possible to make a triangular garden using these pieces.

Part C: Wendell can make a rectangular garden with the pieces of wood he has by using pieces A and C or pieces B and D. He cannot use pieces E and F because they are not long enough to make up one of the sides of a rectangle.

Part  D: Wendell can not create two triangular gardens using all six pieces of wood as the sum of the lengths of the two shorter sides of a triangle must be greater than the length of the longest side, and he only have 3 pieces with length greater than 3 feet which is required to create one triangle.

Wendell can create two rectangular gardens using all six pieces of wood by using pieces A and C, and pieces B and D.

Part E: The area that Jordan can walk around is equal to the area of a circle with a radius of 6 feet (since the chain is 12 feet long).

The formula to calculate the area of a circle is πr^2

where π is approximately 3.14 and

r is the radius of the circle,

so the area that Jordan has to walk around is approximately

3.14 x 6² =113 square feet.

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The initial fee charged to customers for using the gym, given the graph showing the charges to customers is $ 20.

To find the initial membership fee, you should look at the y - intercept of the graph.

The y - intercept is the point where the x vale is 0 and this case this point shows the cost when the customers have not worked out in the gym for any hour yet.

This y - intercept is therefore $ 20 as this is the point on the graph where the value of x is 0.

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The question is:

What is the initial fee charged to customers for using the gym?

A rectangular prism has a volume of  2x ^ 3 + 19x ^ 2 + 24x

the volume of the rectangular prism is

The area contained by an object's limits in three-dimensional space is referred to as its volume.

Thus, a rectangular prism having the following dimensions: 2x length, (x2) width, and (x + 2) height

L x B x H = volume

= x× (x +8 )(2x + 3)

= x(x + 8)(2x + 3)

(2x + 3) * x ^ 2 + 8x(2x + 3)

2x ^ 3 + 19x ^ 2 + 24x

The area contained by an object's limits in three-dimensional space is referred to as its volume.

A rectangular prism's volume is thus 2x ^ 3 + 19x ^ 2 + 24x

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Conditions which help us to differentiate the properties of rectangle, rhombus , and square are:

Rectangle : Opposite sides are congruent with measure of each of the angle 90°.

Rhombus : Parallelogram whose diagonals are perpendicular.

Square: All four sides are congruent with measure of each of the angle 90°.

Different conditions of rectangle , rhombus, and square are:

The given question is incomplete, I answer the question in general according to my knowledge:

What are the conditions which differentiate rhombus, rectangle, and square from each other?

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The probabilities for this problem are given as follows:

It is a distribution with two bounds, given by a and b, in which each possible outcome is equally as likely.

The probability of finding a value of at lower than x is:

[tex]P(X < x) = \frac{x - a}{b - a}[/tex]

The bounds for this problem are given as follows:

a = 2, b = 70.

Hence the probability of less than 30 seconds is given as follows:

P(X < 30) = (30 - 2)/(70 - 2)

P(X < 30) = 0.4118 = 41.18%.

The uniform distribution is a continuous distribution, meaning that the probability of an exact value is of 0.

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Answer:

A. 500 people will go out to the park when its 100F is incorrect.

Answer:

-20

Step-by-step explanation:

Answer: b to the power of 3 / 8 Have a nice day!

Answer:

Step-by-step explanation:

12.7% = 12.7/100 = 0.127

The linear functions f(x) and g(x) are neither parallel nor perpendicular.

To obtain whether they are parallel of perpendicular, first we must obtain the slope of each line.

Given two points, the slope of a line is calculated as the change in y divided by the change in x.

Hence, the slope for each line is obtained as follows:

They would be:

Hence they are neither.

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The values of x and y on solving the two simultaneous equations are x = 1 and y = 3.

The simultaneous equations to be solved are 4x + 2y = 10 and x + 2y = 7.

Rearranging the above equations, we have,

- 4x - 2y = - 10 -----(A)

x + 2y = 7  -------(B)

Solving them, we have, -3x = -3

x = 1 ------(C)

Substituting (C) in (B), we have,

1 + 2y = 7

2y = 6

y = 3 ------(D)

Now, let us substitute the x and y values in (A) and (B) and then check.

4x + 2y = 10

4 + 2(3) = 10

A is checked.

x + 2y = 7

1 + 2(3) = 7

B is checked.

Thus, the values of x and y are checked to be correct.

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The altitudes, the medians, and the angle-bisectors are distinct for the congruent sides but coincident for the base. Hence, 7 lines.

Now, According to the question:

Altitude. A line segment joining a vertex of a triangle with the mid-point of the opposite side. An altitude is a perpendicular line segment drawn from a vertex of a triangle to the opposite side. It divides the opposite sides into two equal parts.

A Median of a triangle is a straight line segment which is drawn from the vertex of a triangle to the middle point of the opposite side. It splits the opposite side of the triangle into two equal line segments. That means we know that it's a median if we have got those equal line segments.

The altitudes, the medians, and the angle-bisectors are distinct for the congruent sides but coincident for the base. Hence, 7 lines.

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The probability that  a product attains a good review is 0.6125

The given information can be tabulated as follows.

Success type          High             Moderate              Low            Total

                               0.40                   0.35                 0.25             1

Good reviews          0.95                    0.60                0.10

Combined prob       0.4*0.95             0.35*0.6          0.25*0.1

                                0.38                    0.21                  0.025       0.6125

A)the likelihood that a product will receive a favorable review = Prob it is successful and receives a favorable review + Prob it is moderately successful and receives a favorable review + Prob it is unsuccessful and receives a favorable review = 0.6125

B) If a new design receives positive feedback, there is a 0.62 percent chance that it will be a highly successful product.

C) Chance of not receiving a favorable review: (0.40*0.05)

+0.35(0.4) +(0.25)*0.9\s= 0.385

Prob for successful but not receiving a favorable evaluation is 0.40(0.05) = 0.02; required prob is 0.0519.

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Three letters will be selected from five letters. The number of possible selections is 10.

A combination is a method of picking elements from a collection where the order of selection is irrelevant. Assume we have three numbers P, Q, and R. The number of ways we can choose two numbers from each set is determined by combination.

Suppose we want to pick k elements from a set of n elements, then the number ways it can be chosen is:

C(n,k) = n! / k! (n-k)!

Where n! is n factorial.

In this case, there are 5 letters and we want to select three letters. Hence, k = 3, and n = 5.

C(5,3) = 5! / 3! (5-3)!

C(5,3) = 5! / (3! 2!) = 10

Thus, there are 10 possible selections.

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There are a total of 10 slips.

8 slip with 3 on it

2 slips with 9  on it

value = Probability of 3 x 3 + Probability of 9 x 9.

=  (8 / 11)  x 3 + (2/ 11)  x 9

24 / 11 + 24 / 11 = 4.36

probability

The area of mathematics known as probability deals with numerical descriptions of how likely it is for an event to happen or for a claim to be true. A number between 0 and 1 is the probability of an event, where, broadly speaking, 0 denotes the event's impossibility and 1 denotes its certainty.

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Answer: Ordinal numbers are a designation of something's place in a series by a number, such as first or third.  Ordinal numbers can function as pronouns, nouns, and adjectives.

Answer:

Step-by-step explanation:

It means what place something is in. For example the ordinal of 1 is 1st 2 is 2nd and 3 is 3rd and so on. I hope this helps.

Answer:-√ 5

Step-by-step explanation:

4√ 20 = 8√ 5
3√ 45 = 9√ 5
8√ 5 - 9√ 5 = -√ 5

Answer:

y = - [tex]\frac{1}{3}[/tex] x + [tex]\frac{5}{3}[/tex]

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

here m = - [tex]\frac{1}{3}[/tex] and c = [tex]\frac{5}{3}[/tex] , then

y = - [tex]\frac{1}{3}[/tex] x + [tex]\frac{5}{3}[/tex] ← equation of line

Answer: 24x+ (-12y)= -36

Step-by-step explanation:

Answer:

VALUES (5,6,12)

Step-by-step explanation: