6. a. Sixty students in a class took an examination in Physics and Mathematics. If 17 of them passed Physics only, 25 passed in both Physics and Mathematics and 9 of them failed in both subjects, find i. the number of students who passed in Physics ii. the probability of selecting a student who passed in Mathematics 17​

Since ABCD is a square, and AC is the diagonal of the square, therefore, then,  angle BAC would be Option B. 45°

A square is known as a quadrilateral with four interior angles of 90° each, and four equal sides.

Properties of a square include

Angle BAC is half the angle of the diagonal

= 90/2 = 45°

Thus, since ABCD is a square, and AC is the diagonal of the square, therefore, then, angle BAC would be Option B. 45°

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The symbolic representation for the given statement " If two angles are not congruent, then they have the same measure" is ~q → p. So, option A is correct.

It is given that,

p - "Two angles have the same measure"

q - "The angles are congruent"

Statement: " If two angles are not congruent, then they have the same measure"

So, symbolically it is written as,

The hypothesis "two angles are not congruent" is represented by ~q and the conclusion "they have the same measure" is represented by p.

That is,

The representation is "If ~q then p i.e., ~q → p. So, option A is correct".

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The smallest perimeter and dimensions of rectangle having area of 169 [tex]inches^{2}[/tex] is 52 inches , length 16 inches and breadth also 16 inches.

Given that the area of rectangle is 169 [tex]inches^{2}[/tex].

We have to find the smallest perimeter and dimensions of the rectangle.

let the length of rectangle be x inches and breadth be y  inches.

We know that area of rectangle is the product of its length and breadth. So,

Area=xy

169=xy

y=169/x

Perimeter of rectangle =2(x+y)

Put the value of y=169/x in the perimeter.

P=2(x+169/x)

P=2x+338/x

Differentiate both sides with respect to x.

dP/dx=2-338/[tex]x^{2}[/tex]

Again differentiate it with respect to x.

[tex]d^{2} P/dP^{2}[/tex]=676/[tex]x^{3}[/tex]

Because the second derivative is greater than 0 so the perimeter is minimum.

Put dP/dx=0 to get the value of x.

dP/dx=0

2-338/[tex]x^{2}[/tex]=0

2=338/[tex]x^{2}[/tex]

[tex]x^{2}[/tex]=169

x=[tex]\sqrt{169}[/tex]

x=13

Put the value of x in y=169/x

y=169/13

=13

To calculate the perimeter, put the values of x and y in P=2(x+y)

P=2(13+13)

=2*26

=52 inches.

Hence The smallest perimeter and dimensions of rectangle having area of 169 [tex]inches^{2}[/tex] is 52 inches , length 16 inches and breadth also 16 inches.

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Answer:

D

Step-by-step explanation:

if you look the point on the y axis is -3 which is your starting point

in y=mx+b m is the slope

The measure of angle GFD of the circumscribed circle is; A: 40°

From the figure, we can apply the arc angles summation formula to get;

Major angle ∠FED + Minor angle ∠FED = 360°

We are given that Major arc FD measures 280°. Thus;

280° + Minor angle ∠FED = 360°

Minor angle ∠FED = 360° - 280°

Minor angle ∠FED = 80°

Also, we know that;

∠FED + ∠FGD = 180°

Thus, putting ∠FED = 80° gives us;

80° + ∠FGD = 180°

Subtract 80° from both sides using subtraction property of equality to get;

∠FGD = 180° - 80°

∠FGD = 100°

Now, GF and GD are the tangents to the circle from the same point G. Thus, we can say that;

GD = GF

Therefore,

∠FDG = ∠GFD = x

(This is because ∠FDG and ∠GFD are the angles opposite to equal sides.

In triangle FGD, we have sum of interior angles = 180°

Therefore, we have the expression;

∠FDG + ∠FGD + ∠GFD = 180° (due to the fact that sum of angles in a triangle is equal to 180°)

x + 100° + x = 180°

2x = 180° - 100°

2x = 80°

x = 40°

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Answer:

40

Step-by-step explanation:

I did a thing and it worked

Using excel, we can determine that the likelihood that a randomly picked steel plate measuring 1 foot by 1 foot contains two or fewer faults is 0.862.

This is further explained below.

Generally, the characteristic or condition of being probable; the degree to which something is likely to occur or be the case. the likelihood of anything happening or something is the case.

In conclusion, In this section, we will make the assumption that the number of defects found in a steel plate measuring 1 foot by 1 foot has a Poisson distribution with a mean of 1.28.

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The total surface area, in m², of the sunshade is 0.4344 m²

A pyramid can have a squared base, rectangular base or other polygons. The formula we can to find the total surface area of a squared pyramid is

Surface Area = P x l/2

Where

Given that a sunshade on one set of equipment has a square base of 120 cm and a height of 50 cm. That means that the length L of the base will be  120 cm and half of it will be 60 cm

To find the slant height l, we will use Pythagoras theorem.

[tex]l^{2}[/tex] = 60² + 50²

[tex]l^{2}[/tex] = 3600 + 2500

[tex]l^{2}[/tex] = 6100

l = √6100

l = 78.1 cm

convert it to meter

l = 78.1/100

l = 0.781 m

The perimeter P of the base = 4 x 120/100 = 4.80 m

The Surface Area = P x l/2

Substitute all the necessary parameters into the formula

Surface Area = 4.80 x 0.781/2  

Surface Area = 1.8744 m²

If the sunshades are open-bottomed square based pyramids, this means that the base is not included. That is, the area of the base should be taken away from the answer above.

Area of the base = 120/100 x 120/100 = 1.44 m²

The total surface area, in m², of the sunshade will 1.8744 - 1.44

The total surface = 0.4344 m²

Therefore, the total surface area, in m², of the sunshade is 0.4344 m²

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Answer:

Maybe the answer must be 90°

Answer:

20%

Step-by-step explanation:

To find the percentage of change find the difference between the two numbers, divide by the original number, then multiply by 100.

Find difference

90-72=18

Divide difference by original

18/90=0.2

Multiply by 100

0.2*100=20

"An arithmetic sequence is a linear function whose domain is restricted to the set of non-negative integers."  

The general form an arithmetic sequence is:

       [tex]a_{n} = a_{1} + (n- 1) d[/tex]

So, the statement provided is True.

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Answer:

B. (-6)(-6)

Step-by-step explanation:

-  X - = +

and 6 x 6 = 36.

Question 4

[tex]\sin 30^{\circ}=\frac{y}{14\sqrt{3}}\\\\\frac{1}{2}=\frac{y}{14\sqrt{3}}\\\\\boxed{y=7\sqrt{3}}\\\\\\\\\cos 30^{\circ}=\frac{x}{14\sqrt{3}}\\\\\frac{\sqrt{3}}{2}=\frac{x}{14\sqrt{3}}\\\\\boxed{x=21}[/tex]

Question 5

[tex]\cos 45^{\circ}=\frac{x}{28}\\\\\frac{1}{\sqrt{2}}=\frac{x}{28}\\\\x=\frac{28}{\sqrt{2}}\\\\\boxed{x=14\sqrt{2}}\\\\\\\\\sin 45^{\circ}=\frac{y}{28}\\\\\frac{1}{\sqrt{2}}=\frac{y}{28}\\\\y=\frac{28}{\sqrt{2}}\\\\\boxed{y=14\sqrt{2}}[/tex]

Answer:

1/2=20/40 19/20=38/40

Step-by-step explanation:

so the first option

Let [tex]n=abcba[/tex] be such a number. If 18 divides [tex]n[/tex], then both 2 and 9 divide [tex]n[/tex].

To be divisible by 2, we must have [tex]a\in\{2,4,6,8\}[/tex]. Meanwhile we can have [tex](b,c)\in\{0,1,2,\ldots,9\}^2[/tex].

To be divisible by 9, we the sum of the digits of [tex]n[/tex] must itself be divisible by 9, or

[tex]2a+2b+c=9k[/tex]

for some integer [tex]k[/tex].

The largest value of [tex]2a+2b+c[/tex] is 2•8 + 2•9 + 9 = 43, so we must have [tex]k\in\{1,2,3,4\}[/tex].

I'm not sure what the best way to get the final count may be, but there are 44 such numbers. It's rather tedious to do by hand.

• If [tex]k=1[/tex], then [tex]2a+2b+c=9[/tex], and we can do this in 4 ways.

For example,

2•2 + 2•0 + 5 = 9 [tex](n = 20502)[/tex]

• If [tex]k=2[/tex], then [tex]2a+2b+c=18[/tex] and can be done in 16 ways.

2•2 + 2•3 + 8 = 18 [tex](n = 23832)[/tex]

• If [tex]k=3[/tex], then [tex]2a+2b+c=27[/tex] and can be done in 18 ways.

2•2 + 2•7 + 9 = 27 [tex](n = 27972)[/tex]

• If [tex]k=4[/tex], then [tex]2a+2b+c=36[/tex] and can be done in 6 ways.

2•6 + 2•8 + 8 = 36 [tex](n = 68886)[/tex]

Using the Fundamental Counting Theorem, there are 15 ways to travel from Andy's house to Willie's house.

It is a theorem that states that if there are n things, each with [tex]n_1, n_2, \cdots, n_n[/tex] ways to be done, each thing independent of the other, the number of ways they can be done is:

[tex]N = n_1 \times n_2 \times \cdots \times n_n[/tex]

For this problem, the parameters are:

[tex]n_1 = 3, n_2 = 5[/tex].

Hence the number of ways is:

N = 3 x 5 = 15.

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The purpose of the graphic is to show the relationship between different educational qualifications and unemployment rate.

This is a situation in which employable individuals look for jobs and are unable to find one.

The key findings in this graphic is that the higher the level of education, the lesser the unemployment rate.

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Based on the given parameters, the 15 ft rope will reach the swimmer

From the question, we have the following equation:

sin 55 = 10/x

Multiply both sides of the equation by x

x * sin 55 = 10/x * x

Evaluate the product

x * sin 55 = 10

Divide both sides by sin 55

x = 10/sin 55

Evaluate sin 55

x = 10/0.8192

Evaluate the quotient

x = 12.21

From the question, the lifeguard tosses a ring in a 15ft rope to the swimmer

15 is greater than 12.21

This means that the 15 ft rope will reach the swimmer

Hence, the 15 ft rope will reach the swimmer

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Using the binomial distribution, the probabilities are given as follows:

a) 0.4159 = 41.59%.

b) 0.5610 = 56.10%.

c) 0.8549 = 85.49%.

The formula is:

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

The parameters are:

For this problem, the values of the parameters are:

n = 3, p = 0.76.

Item a:

The probability is P(X = 2), hence:

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 2) = C_{3,2}.(0.76)^{2}.(0.24)^{1} = 0.4159[/tex]

Item b:

The probability is P(X < 3), hence:

P(X < 3) = 1 - P(X = 3)

In which:

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 3) = C_{3,3}.(0.76)^{3}.(0.24)^{0} = 0.4390[/tex]

Then:

P(X < 3) = 1 - P(X = 3) = 1 - 0.4390 = 0.5610 = 56.10%.

Item c:

The probability is:

[tex]P(X \geq 2) = P(X = 2) + P(X = 3) = 0.4159 + 0.4390 = 0.8549[/tex]

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Answer:

(2, -1).

Step-by-step explanation:

y = 1/4x^2 - x - 1

First convert to vertex form:

y = 1/4(x^2 - 4x) - 1

y = 1/4[(x - 2)^2 - 4] - 1

y =  1/4(x - 2)^2 - 2

The formula for the focus of the parabola y = a(x - h)^2 + k is (h, k+1/4a)

So here it is:

(2, -2+1/ 4*1/4)

=  (2, -1).

When it comes to resource allocation, it's not a one sentence answer. The explanation for how to go about this is given below. But first, lets look at what Profit Allocation means.

This simply means the process of distributing profit to various areas of the business such that all parts are (human and non-human  components) are satisfied and operating at equilibrium.

There are five steps to aligning your budget and resource demands when planning for support resource allocation.

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Answer:

  x = 7

Step-by-step explanation:

The integer values of x that satisfy |x| < 9 are ...

  {-8, -7, -6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7. 8}

Of these values, the only one listed as an answer choice is ...

  x = 7

__

Additional comment

The expression |x| means "the absolute value of x". It is the value of x with the sign made positive. That is |-10| = 10, a number greater than 9. Of course, |13| = 13, also a number greater than 9.

The taxi fare for a journey of n miles in dollars is 1 + 2n

Linear equations are equations that have constant average rates of change, slope or gradient

The given parameters about the taxi fares are given as

First two miles = $5

Additional mile = Increment of $2

Let the number of miles be n

So, we have:

2 miles = $5

Additional miles = (n - 2) * 2

Add the above expressions

5 + (n - 2)* 2

Represent the value with f(n)

So, we have:

f(n) = 5 + (n - 2)* 2

Expand the bracket

f(n) = 5 + 2n - 4

Collect the like terms

f(n) = 5 - 4+ 2n

Evaluate the like terns

f(n) = 1 + 2n

Hence, the taxi fare for a journey of n miles in dollars is 1 + 2n

So, the complete parameters are:

First two miles = $5

Additional mile = Increment of $2

n miles  1 + 2n

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The correct answer is x = 9

What is a parallelogram in math?

Diagonals of a parallelogram bisect each other.

For quadrilateral LMNO to be a parallelogram, LP must equal PN, and OP must equal PM.

Set OP equal to PM and solve for x.

PM = OP

3x - 9 = 18

Add 9 to both sides.

3x = 27

Divide both sides by 3.

x = 9

Therefore, the value of x = 9

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The complete question is -

Determine the value of x that would make quadrilateral LMNO a parallelogram.

3

9

11

18

Answer: x=9

Step-by-step explanation:

Answer:

Step-by-step explanation:

add 4 more rows like in the pattern and you will get your answer

Answer:

36 squares.

Step-by-step explanation:

Number of squares in each step is triangular number. This form a triangular series.

1 , 3 , 6 , 10........

Number of squares in each step is given by

  [tex]\sf \dfrac{n*(n+1)}{2}[/tex]  here , n is the step or term.

n = 8

[tex]\sf Number \ of \ squares \ in \ 8^{th} \ step = \dfrac{8 * (8+1)}{2}[/tex]

                                             [tex]\sf = \dfrac{8*9}{2}\\\\ = 4*9\\\\=36 \ squares[/tex]