In a class of 55 students, 15 students liked Maths but not English and 18 students liked English but
not Maths. If 5 students did not like both, how many students liked both subjects? Represent the
above information in a Venn-diagram.​

Answer:

[tex] \frac{4x - 11}{2} \leqslant 3x - 3 < 4 \\ \\ = > \frac{4x - 11}{2} \leqslant 3x - 3 \: and \: 3x - 3 < 4 \\ \\ < = > 4x - 11 \leqslant 6x - 6 \: \: and \: \: 3x < 7 \\ \\ < = > 2x \geqslant - 5 \: \: and \: \: x < \frac{7}{3} \\ \\ < = > \frac{ - 5}{2} \leqslant x < \frac{7}{3} [/tex]

=> the greatest integer is 2

the smallest integer is -2

Answer:

You can use the Pythagorean Theorem to find the length of the hypotenuse of a right triangle if you know the length of the triangle's other two sides, called the legs. You can use the Pythagorean Theorem to find a value for the length of c, the hypotenuse.

The quadratic equation that describes the function is  

f(x) = x² + 4x + 1

A quadratic equation is a equation that is of the form -

y = f{x} = ax² + bx + c

Given is the table that describes the quadratic function h(x) as follows -

{x}                h{x}

−3               −2

−2               −3

−1                −2

0                  1

1                   6

2                  13

3                  22

The quadratic equation is of the form given -

y = ax² + bx + c

For the point (0, 1), we can write -

1 = c                                                      ..... Eq{1}

For the point (1, 6), we can write -

6 = a + b + 1

a + b = 5                                               ...... Eq{2}

For the point (2, 13), we can write -

13 = 4a + 2b + 1

4a + 2b = 12                                               ...... Eq{3}

From Eq{2}, we can write -

a = 5 - b

So, the equation 3 can be written as -

4(5 - b) + 2b = 12

20 - 4b + 2b = 12

20 - 2b = 12

2b = 8

b = 4                                    ...... Eq{4}

then

a = 1                                ...... Eq{5}

So, we can write the quadratic equation as -

f(x) = x² + 4x + 1

Therefore, the quadratic equation that describes the function is  

f(x) = x² + 4x + 1

To solve more questions on quadratic equations, visit the link below -

brainly.com/question/22412845

#SPJ1

Answer:

33

Step-by-step explanation:

because there are 66 squares and 1/2 is shaded so 33

mark me brainliest mark me brainliest

hope this helps you

According to the findings, 40 of the adults who were not parents and 150 of the adults who were parents believed that the park should be expanded.

250 adults, 180 of whom are parents, leaving 70 adults who are not parents (250 - 180). According to the findings, 40 adults without children and 150 adults with children said the park should be expanded. Thus, 180 – 150 = 30 parents.

Parents: YES OR NO Not parents: 40 | 30 of 150

In this exercise, we must determine the values of the voters who supported expanding the parking lot, which requires that we:

In fact, parents will be 150, not 40.

Parents won't be 30 in total; they'll be 40. Instead, a park should be built to accommodate 250 persons, 180 of whom were parents.

The park should be extended, according to 40 of the people who weren't parents.

To learn more about adults refer to:

https://brainly.com/question/30211748

#SPJ1

Answer:  

can u be more specific so i can properly help u  

Explanation:  

pls explain and i will edit my answer  

Answer:

Step-by-step explanation:

ΔSTU is a right triangle.

US and TU are legs, SU is opposite to ∠T.

Use tangent to find the measure of ∠T.

a) The probability that a person will like cake is given as follows: 0.6 = 60%.

b) The probability that a person does not like any of the two desserts is given as follows: 0.1 = 10%.

c) The events are non-mutually exclusive, as the probability of liking both is different of zero.

In a Venn probability, two events are related with each other, as are their probabilities.

The "or probability" is given by:

[tex]P(A \cup B) = P(A) + P(B) - P(A \cap B)[/tex]

The events for this problem are given as follows:

The probabilities for this problem are given as follows:

P(A or B) = 0.9, P(A) = 0.42, P(A and B) = 0.12.

Hence the probability that a person likes cake is given as follows:

0.9 = 0.42 + P(B) - 0.12

0.3 + P(B) = 0.9

P(B) = 0.6.

Probability of 0.90 that people liked cake or pie, hence the probability that a person likes neither is of:

1 - 0.9 = 0.1 = 10%.

(or means at least one of them, and neither is complementary to at least one).

As P(A and B) = 0.12 is different of zero, the events are non-mutually exclusive.

More can be learned about Venn probabilities at https://brainly.com/question/7965468

#SPJ1

Answer:

3 and 4 is correct

Step-by-step explanation:

that's the only 2 numbers that is correct

Answer:

  (a, b, c) = (-3, -2, -4)

Step-by-step explanation:

You want to solve the system of 3 equations in 3 variables shown in the attached figure.

The easiest solution is one provided by a suitable calculator (attached). It tells you ...

The "work" is entering the problem into the calculator.

We notice the sum of 'a' coefficients is zero, so we can add the three equations to get ...

  (4a +5b -6c) +(-3a -2b +7c) +(-a +4b +2c) = (2) +(-15) +(-13)

  7b +3c = -26 . . . . . simplify

Multiplying the third equation by 4 and adding that to the first equation gives ...

  4(-a +4b +2c) +(4a +5b -6c) = 4(-13) +(2)

  21b +2c = -50 . . . . . simplify

Now, we have two equations in two unknowns.

Multiplying the first equation above by 3 and subtracting this last equation eliminates the b term to give ...

  3(7b +3c) -(21b +2c) = 3(-26) -(-50)

  7c = -28 . . . . . simplify

  c = -4 . . . . . . . divide by 7

Using this in the first "ad hoc" equation, we can find b:

  7b +3(-4) = -26

  7b = -14 . . . . . . . . add 12

  b = -2 . . . . . . . . divide by 7

And the values of b and c can go into the last of the original equations to give ...

  -a +4(-2) +2(-4) = -13

  -a = 3 . . . . . add 16

  a = -3 . . . . . multiply by -1

The solution is (a, b, c) = (-3, -2, -4).

__

Additional comment

The given solution is "ad hoc" because we decide how we're going to approach the solution based on the coefficients we see. Here, we are solving by "elimination," performing as little arithmetic as possible.

The third equation suggests we could make a substitution for 'a':

  a = 4b +2c +13

That substitution would give a different set of equations in 'b' and 'c' than the ones shown above.

The second attachment shows a graphical solution to the system. It shows (a, b, c) = (-3, -2, -4). The graphing program requires the use of x and y instead of 'a' and 'b' for the variables.

Four methods of solving the system have been described. Take your pick. The calculator solution was the easiest, requiring each number to be entered once.

Answer:

Step-by-step explanation:

You want the lengths of the segments of the hypotenuse of a right triangle when an altitude of 6 m divides the hypotenuse into parts with the ratio 1:9.

The altitude to the hypotenuse of a right triangle is the geometric mean of the parts it divides the hypotenuse into. If the shorter part is x, then the longer part is 9x, and their geometric mean is ...

  6 = √(x(9x)) = 3√x² = 3x

  x = 2 . . . . . . . divide by 3

The length of the shorter segment is 2 m; the longer one, 18 m.

Step-by-step explanation:

please refer to the sketch

The probability that the area of the triangle is at most 20 is 5/9

Probability is a measure of the likelihood of an event occurring. The probability formula is defined as the possibility of an event happening is equal to the ratio of the number of favorable outcomes and the total number of outcomes. Probability of event to happen P(E) = Number of favorable outcomes/Total Number of outcomes.

Given here: Right triangle XYZ has legs of length XY = 12 and YZ = 6. Point D is chosen at random within the triangle XYZ. Thus area of triangle XYZ is

1/2×12×6=36

Now if the area of the triangle is at most 20 then the required probability is = 20/36

                      =5/9

Hence, The probability that the area of the triangle is at most 20 is 5/9

Learn more about probability here:

https://brainly.com/question/30034780

#SPJ1

Answer: 25.4%

Step-by-step explanation:

1.25.4%

2.24.5%

3.2/3

4.83.3%

5.62.5%

An equation which has one (1) solution include the following: D. |W| = 0.

In Mathematics, an absolute value function can be defined as a type of function that is composed of an algebraic expression, which is placed within absolute value symbols and measures the distance of a point on the x-coordinate to the x-origin (0) of a cartesian coordinate (graph).

Mathematically, an absolute value function can be represented by this mathematical expression:

|x| = x, x ≥ 0.

|x| = x, x < 0.

Generally speaking, an equation or absolute value function would have exactly one (1) solution when there is only one (1) value for the variable (W) that makes the equation to be true as shown below:

|W| = 0

W = ±0

W = 0

Read more on absolute value function here: brainly.com/question/28308900

#SPJ1

Answer:

1/2

Step-by-step explanation:

4/5x=2/5

x=(2/5)/(4/5)

x=(2/5)(5/4)

x=2/4

x=1/2

Answer:

Step-by-step explanation:

The minimum is the smallest value in the data set. The maximum is the largest value in the data set.

We will set the first derivative of the function to zero and solve for x to get the critical point. If we take the second derivative or f''(x), then we can find out whether this point will be a maximum or minimum. If the second derivative is positive, it will be a minimum value.

A minimum or a maximum is called an extreme point. A local extreme point is the smallest or largest value in its neighborhood. If it is also the smallest or largest at the entire domain of the function, it is called a global extreme point. The local minima and maxima can be found by solving f'(x) = 0.

Learn more about maxima and minima at:

brainly.com/question/82347

#SPJ1

Complete question is: What is the difference between Minimum or maximum value?

Answer:

371 children

Step-by-step explanation:

289*$2,5 + 371*$1,5 = $1279

Answer:

Step-by-step explanation:

I believe the answer is D) f(x) = 1 / (x-3)^2

I put that into my graph calculator thing and it matched it perfectly

Step-by-step explanation:

50-20=30

30÷2=15

therefore the sons age is 15

Answer:

43°

Step-by-step explanation:

Answer:

43

Step-by-step explanation:

The value of the function h(x) is x² -  4x +6 and 4-6 x².

Any function's x-intercept, y-intercept, and slope can be calculated using function formulas. You could also determine a quadratic function's vertex. Additionally, the function can be graphed for various x values.

Simply adding the values of the functions f(x) and g will yield the value of the function f(x) and g(x).

Therefore, we get

f(x) = x² and  we have g(x) = 4x - 6

h(x) = f(x) - g(x)

h(x) =   x² -  4x +6

h(x) = f(g(x))

     =  x²( 4x - 6)

     = 4-6 x²

h(x) is the inverse of g(x)

   = inverse of 4x - 6

   = 1/ 4x - 6

To know more about function visit:

brainly.com/question/2477560

#SPJ1

Answer:

Step-by-step explanation:

Answer:

Option A) [tex]3\frac {1}{2}[/tex]

Step-by-step explanation:

In order to find the diameter you need to multiply the radius x 2

Over here the radius is given as 7/4cm

But the diameter is

[tex]\frac{7}{4} X\frac{2}{1}[/tex] = [tex]\frac{7}{2}[/tex]

And when we simply the mixed fractions we only get one possible answer

which is [tex]3\frac{1}{2} = \frac{7}{2}[/tex] Option A)

Answer:

  y = -5x -19

Step-by-step explanation:

You want the equation of the line parallel to y=-5x+3 through point (-3, -4).

The equations of parallel lines differ only in their constant. We can find the new constant by using the values at the given point:

  y = -5x +b

  -4 = -5(-3) +b

  b = -4 -15 = -19 . . . . . . subtract 15

The equation is ...

  y = -5x -19

The value of x is 10°.

What is a measure of an angle?

Since an angle is measured in degrees, the term "degree measure" is used. Since 360 degrees make up one full revolution, it is divided into 360 equal sections. A degree is what the revolution is at each stage.

Here, we have

The measure of ∠AOC is 90°.

3x° + 46° +14° = 90°

3*10° + 46 + 14° = 90°

Hence,  the value of x is 10.

To learn more about the measure of an angle from the given link

https://brainly.com/question/25770607

#SPJ1

The value of x is 10°.

Since an angle is measured in degrees, the term "degree measure" is used. Since 360 degrees make up one full revolution, it is divided into 360 equal sections. A degree is what the revolution is at each stage.

An angle is a measure of the amount of rotation between two rays or lines that share a common endpoint, called the vertex of the angle. The two rays or lines are called the sides of the angle, and the endpoint is called the vertex.

Here, we have

The measure of ∠AOC is 90°.

3x° + 46° +14° = 90°

3*10° + 46 + 14° = 90°

Hence,  the value of x is 10.

To learn more about the measure of an angle from the given link

brainly.com/question/25770607

#SPJ1

Answer:

Step-by-step the answer is  3/4

Kiki is estimated to need more 1/4 glue that James

From the complete question, we have the following highlights:

This means that:

Kiki chose a project that requires 2 1/4 glue while James chose a project that required 2 1/2

The difference (d) is:

d = 2 1/2 - 2 1/4

Evaluate

d = 1/4

Hence, Kiki is estimated to need more 1/4 glue that James

Read more about line plots at:

https://brainly.com/question/24309209

The percentage of people aged 20 to 34 that  have IQs between 125 and 150 of people aged 20 to 34 have IQs between 125 and 150 is 21.94%

Percentage simply means a proportion of the number as a fraction of 100

What percent of people aged 20 to 34 have IQs between 125 and 150?

Let X = Scores on the standard IQ test for the 20 to 34 age group

This implies that  X ~ Normal(x=110, б² = 25)

The z-score probability distribution for the normal distribution is given by;   Z  =   (x-ц)/б ~ N(0,1)

Recall that  population mean = 110 and standard deviation = 25

Now, the percent of people aged 20 to 34 have IQs between 125 and 150 is given by = P(125 < X < 150) = P(X < 150) - P(X  125)

 P(X < 150) = P(  <  ) = P(Z < 1.60) = 0.9452

 P(X  125) = P(    ) = P(Z  0.60) = 0.7258

The above probability is calculated by looking at the value of x = 1.60 and x = 0.60 which has an area of 0.9452 and 0.7258.

Therefore, P(125 < X < 150) = 0.9452 - 0.7258 = 0.2194 or 21.94%

Learn more about percentages on https://brainly.com/question/29306119

#SPJ1