Quadrilateral PQRS is transformed using the rule (x, y) - (x, y - 7). Which graph shows this transformation?

(a) The probability that a point chosen randomly inside the rectangle is in the square is 0.6.

(b) The probability that a point chosen randomly inside the rectangle is outside the square is 0.4.

The probability that a point chosen randomly inside the rectangle is in each given shape is calculated as follows;

The area of the triangle is calculated as follows;

area = ¹/₂ x base x height

area = ¹/₂ x 4 x 5

area = 10 sq.units

The area of the rectangle is calculated as follows;

area = 4 x 4

area = 16 sq.units

The probability that a point chosen randomly inside the rectangle is in the square is calculated as;

P = outcome / total possible outcome

P = ( 10 ) / 16

P = 0.625 ≈ 0.6

The probability that a point chosen randomly inside the rectangle is outside the square;

P = 1 - p(inside)

P = 1 - 0.6

P = 0.4

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Answer: i think c

Step-by-step explanation:

Cost of apples, y, varies directly with pounds

of apples purchased, x.

y = kx

k is constant of proportion

Four pounds of apples cost $5

5 = 4k

k = 5/4 = 1.25

10 = 8k

k = 10/8 = 1.25

As it should be, k is a constant equal to 1.25

y = 6(1.25) = $7.50 for 6 pounds of apples

Answer:

the answer is D

Step-by-step explanation:

i took the test on edg your welcome

Answer:

x=45

Step-by-step explanation:

i hope its right good luck :)

i think im wrong

Step-by-step explanation:

We define 3 events

A = event that driver is above speed limit

B = event that driver is below limit

T = event that the gun detected him

At 95%

P(A) = 1-0.95 = 0.05

P(B) = 0.95

P(T|A) = 0.98

P(A|T) = 0.02

P(T|B) = 1-0.99 = 0.01

P(B|T) = 0.99

1. For answer a

P(TnA) = P(A) x P(T|A)

= 0.05 x 0.98

= 0.049 is the probability gun detected speeding and the driver was speeding

2. For answer b

P(TnB) = P(B) x P(T|B)

= 0.95x0.01

= 0.0095 is probability that gun deects speeding and driver was not speeding

3. For answer c

We solve this using bayes theorem

P(B|T) = P(B) x P(T|B) / (P(B)*P(T|B)) + (P(A) +P(T|A))

= 0.095x0.01 divided by (0.95x0.01)+(0.05*0.98)

= 0.0095 divided by 0.0585

= 0.16239

= 0.1624 to 4 decimal places.

Answer:

B. 15.2 inches.

The average rate of change of the function over the interval 0 < x < 60 is -2/3.

In mathematics, a function is a relation between a set of inputs and a set of outputs, such that each input is related to exactly one output. In other words, a function is a process that takes one or more inputs and produces an output. Functions are essential in mathematics, as they allow us to express relationships between variables and to model real-world situations. For example, a function can be used to calculate the area of a rectangle given its length and width.

This can be found by taking the difference between the y-values at the endpoints of the interval (41-17 = 24) and dividing it by the difference between the x-values (60-0 = 60). 24/60 = 2/3, and since the y-values are decreasing, the rate of change is negative, so the average rate of change is -2/3.

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We need to know about density to solve this problem. The density of the piece of metal is 5.9 g/\(cm^{3}\), so option (c) is the correct answer.

Density is a substance's mass per unit volume. The symbol commonly used for density is ρ. Density can be calculated by dividing the mass by volume. In this question we know that mass of the metal piece is 124 grams and the volume is given to be 21 cubic centimeters. The density can be calculated by dividing the mass by volume of the metal piece.

density =mass/ volume= 124/21=5.90 g/\(cm^{3}\)

Therefore the density of the piece of metal is 5.9 g/\(cm^{3}\) , so option (c) is the correct answer.

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Answer:

y = In | cos(2x + c ) | + c

Step-by-step explanation:

y" + (y')^2 + 4 = 0

substituting u = y'

u' + u^2 + 4 = 0

hence : u' = - (u^2 + 4 )

       \(\frac{u'}{-(u^2 + 4)}\) = 1 ------- (1)

integrating both sides of the equation 1

\(1/2 \int\limits^1_1 {\frac{2du}{(u^2+4)} } \, = x + c\)

x + c = \(- \frac{1}{2} arc tan (\frac{u}{2} )\)   hence  u = -2 tan(2x + c )

remember u = y'

y' = -2 tan(2x + c) ------ (2)

integrating both sides of the equation 2

y = ∫ \(\frac{-sin u}{cos u } du\)

therefore Y = In | cosu | + c

 y = In | cos(2x + c ) | + c

The value of x is 4.

To determine the value of x, we can use the concept of similarity between shapes.

Similar shapes have corresponding sides that are proportional to each other.

Given the dimensions of the first shape as 5, x, and 5, and the dimensions of the second shape as 30, 24, and 30, we can set up the following proportion:

5/x = 30/24

To solve for x, we can cross-multiply:

30 · x = 5 · 24

30x = 120

Dividing both sides of the equation by 30:

x = 120 / 30

x = 4

Therefore, the value of x is 4.

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Answer: 35

Step-by-step explanation: i first divided 12 and 125 since there is 125 cards in total and 12 different cards which gives you 10 point something. There is 3 multiples of 4 so i multiplied 3x10 which gives you 30 and the closest answer is 35. You're welcome

Answer:

35

Step-by-step explanation:

got it right

Answer:

Question: **Actuarial Mathematics, Survival Models** Calculate The Probability That A Life Aged 0 Will Die Between Ages 19 And 36, Given The Survival Function S0(x) = (1/10), 0 X 100 Answer: 0.1.

Step-by-step explanation:

The value of the constant c which would make the function continuous for all values of r is c = \(\frac{5}{3}\).

We are given that f(x) = \(\left \{ {{x-c,x < 5} \atop {4x+2c,x > 5}} \right.\)

since we are given that the function f is continuous at x = 5, then we can Lim f (x) = Lim f (x) = f (5) .......(1)

x---->5⁻       x---->5⁺

now then that we have equate f(5) we can proceed as given below

Lim f (x) = Lim (x² = c) = 5² = c = 25-c

x---->5⁻       x---->5⁺

and from the above solution we can get,

Lim f (x) = Lim (4x + 2c) = 4.5 + 2c

x---->5⁻       x---->5⁺

then we can solve for =20 + 2c

then we get f(5) when we solve for 20 + 2c

now from .....(1) we can put the values for the following, we get

then we get, 25 - c = 20 + 2c

when we solve for c we get, 3c = 5

therefore we know that, c = \(\frac{5}{3}\)

therefore we get the solution for the function as the value of the constant c which would make the function continuous for all values of r is c = \(\frac{5}{3}\).

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Answer:

Dessert 1 is 10 million

Step-by-step explanation:

Do 12 million divided by six and you get 2 million. Then do 2 million times 5 and you get 10 million and this works because 10 million is five times more than 2 million and they add up to get 12 million.

Please give me brainliest

Answer:

The maximum height that the object will reach is of 9 feet.

Step-by-step explanation:

Vertex of a quadratic function:

Suppose we have a quadratic function in the following format:

\(f(x) = ax^{2} + bx + c\)

It's vertex is the point \((x_{v}, f(x_{v})\)

In which

\(x_{v} = -\frac{b}{2a}\)

If a<0, the vertex is a maximum point, that is, the maximum value happens at \(x_{v}\), and it's value is \(f(x_{v})\)

In this question:

\(f(t) = -16t^{2} + 16t + 5\)

So

\(a = -16, b = 16\)

The instant of the maximum height is:

\(t_{v} = -\frac{16}{2*(-16)} = 0.5\)

The maximum height is:

\(f(0.5) = -16*(0.5)^2 + 16*0.5 + 5 = 9\)

The maximum height that the object will reach is of 9 feet.

Answer:

24

Step-by-step explanation:

Answer:

40

Step-by-step explanation:

40

The probability of forming this committee with equal representation is approximately 0.570 or 57.0%.

The total number of individuals in the ATU COVID-19 team of Marshalls is 50 (13+15+10+12). To form an executive committee of 16 with equal representation, we need to choose 4 individuals from each group (4 lecturers, 4 students, 4 administrative staff, and 4 medical personnel).
Using the combination formula, we can calculate the number of ways to choose 4 individuals from each group:
C(13,4) × C(15,4) × C(10,4) × C(12,4) = 715 × 1,455 × 2,385 × 4,095 = 7,976,476,875
Therefore, there are 7,976,476,875 possible ways to form the executive committee with equal representation.
To calculate the probability of forming this committee, we need to divide the number of possible ways by the total number of ways to choose any 16 individuals from the ATU COVID-19 team of Marshalls:
C(50,16) = 13,983,816
The probability of forming the executive committee with equal representation is:
7,976,476,875 / 13,983,816 = 0.570

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Answer:

9 m²

Step-by-step explanation:

The perimeter of a square is 4x, where is the length of one side (because all the sides have the same length).

This means that 4x = 12, so x = 3, in other words the length of one side of the square is 3 m.

To work out the area of the square, multiply the length and the width together: 3 x 3 = 9 m²

Hope this helps!

to paint the room, 2 gallons of paint will be needed

Explanation

to find the number of gallons we need to do a

so

Step 1

a)let

replace

so,the answer is

to paint the room, 2 gallons of paint will be needed

I hope this helps you

Answer:

Is 03.841

Step-by-step explanation:

To find the critical value needed to test the claim that the sentence is independent of the plea, we need to perform a chi-square test of independence. The critical value is based on the significance level (α) and the degrees of freedom.

In this case, the given significance level is 0.05. Since the table represents a 2x2 contingency table (two categories for plea and two categories for sentence), the degrees of freedom (df) can be calculated as (number of rows - 1) * (number of columns - 1) = (2 - 1) * (2 - 1) = 1.

To find the critical value at a significance level of 0.05 with 1 degree of freedom, we consult a chi-square distribution table or use statistical software.

The critical value for a chi-square test with 1 degree of freedom and a significance level of 0.05 is approximately 3.841.

Therefore, the correct answer is 03.841.

To solve the present problem, we need to remember some properties of the number, such as:

From this, we are able to determine the following:

From this, we are able to answer 4. is <

About number 5. we have:

This allows us to answer number 5. as >

About number 6. we can just check the integer part of the numbers because 34<64, and from this, we answer 6. is <

From the above solution, we have the following answers:

Step-by-step explanation:

736 / 365 = 2R6

So even if the first 365 students all have different birthdays, and the next 365 students also all have different birthdays, then there are 2 students for every birthday.  The last 6 students therefore share a birthday with at least 2 other students.  So there are at least 3 students who share a birthday.

Yes, we can prove that at least three students have a birthday on the same day of the year.

What is algebra?

Algebra is the study of mathematical symbols and the rules for manipulating these symbols in formulas.

We have,

Total number of students = 736

So,

In a year there are 365 days.

And we have 736 students,

So,

Two students have birthday on same day = 365 × 2 = 730

NOw,

Students left = 736 - 730 = 6

So,

These 6 Students  share birthday with othe 6 Students .

So, yes there are at least three students who have a birthday on the same day of the year

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Answer:

54

Step-by-step explanation:

ratio is 7:9

7=42

9=?

9×42÷7

Step 1 : Let's review the information given to us to answer the problem correctly:

• Container A = 800 ml - 6 ml per minute

• Container B = 1,000 ml - 10ml per minute

Step 2: Let's write the equation to solve the problem, as follows:

Let x to represent the number of minutes both containers have the same amount of water

Container A = Container B

800 - 6x = 1,000 - 10x

Like terms:

-6x + 10x = 1,000 - 800

4x = 200

Dividing by 4 at both sides:

4x/4 = 200/4

x = ?

I think you can calculate the value of x without problems.

The ordered pairs of the function, h(x) = 3x², are (1,3) and (-1,3).

According to the question,

We have the following information:

h(x) = 3x²

Now, we will look at the options to know the correct option of ordered pairs.

Now, in the options, there are only two values of x (1 and -1). So, we will solve the given function using these two values and we will find the value of h(x).

h(x) = 3x²

h(1) = 3*1*1

h(1) = 3

So, the first ordered pair is (1,3).

When x = -1:

h(x) = 3x²

h(-1) = 3*-1*-1

h(-1) = 3

Now, the second ordered pair of the function is (-1,3).

Hence, the correct options are A and C.

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Where Rectangle ABCD and A’B’C’D’ are similar.

a. the scale factor from ABCD to A’B’C’D’ is 1/2

b. What is the scale factor from A’B’C’D’ to  ABCD is 2

In mathematics, a scale factor is the ratio of matching measurements of an item to a representation of that thing. The copy will be bigger if the scaling factor is a full number. The duplicate will be smaller if the scaling factor is a fraction.

When the scale factor is less than one, you are going from big to small. You are dilating negatively.

When you are going from small to big, you scale factor is reversed. In this case, we had 1/2 in a, in b it became 2/1 which = 2.

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Full Question:

Rectangle ABCD and A’B’C’D’ are similar.

a. What is the scale factor from ABCD to A’B’C’D’?

b. What is the scale factor from A’B’C’D’ to ABCD?

See attached image.

Answer:

Remi bought 3 notebooks

Step-by-step explanation:

Let n = number of notebooks.

2 pencils cost 2 * £0.24 = £0.48

3 pens cost 3 * £0.37 = £1.11

3 sharpeners cost 3 * £0.77 = £2.31

n notebooks cost n * £1.40 = £1.4n

The total cost is £9 - £0.90 = £8.1

0.48 + 1.11 + 2.31 + 1.4n = 8.1

1.4n + 3.9 = 8.1

1.4n = 4.2

n = 3

Answer: Remi bought 3 notebooks.

The number of notebooks Remi would need to buy is 2.

Let's solve this problem step by step.

First, let's calculate the total cost of the items Remi bought.

The cost of 2 pencils would be 2 * £0.24 = £0.48.

The cost of 3 pens would be 3 * £0.37 = £1.11.

The cost of 3 sharpeners would be 3 * £0.77 = £2.31.

Let's assume the number of notebooks Remi bought is 'x'.

The cost of 'x' notebooks would be x * £1.40 = £1.40x.

So, the total cost of all the items would be:

£0.48 + £1.11 + £2.31 + £1.40x = £0.48 + £1.11 + £2.31 + £1.40x = £4.90 + £1.40x.

According to the given information, Remi paid with £9 and received 90p change.

Therefore, we can set up the equation:

£9 - £4.90 - £1.40x = 90p.

To simplify the equation, we need to convert 90p to pounds. Since £1 = 100p, 90p = 90/100 = £0.90.

Now, let's solve the equation:

£9 - £4.90 - £1.40x = £0.90.

Combining like terms, we get:

£4.10 - £1.40x = £0.90.

Now, let's isolate the 'x' term:

£4.10 = £0.90 + £1.40x.

Subtracting £0.90 from both sides, we get:

£3.20 = £1.40x.

Now, let's isolate 'x':

x = £3.20 / £1.40.

x ≈ 2.29.

Since we can't have a fraction of a notebook, we need to round the value to the nearest whole number.

So, Remi bought approximately 2 notebooks.

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Answer:

Infinite solutions.

Step-by-step explanation:

Use the elimination method:

15x - 5y = -20

-3x + y = 4              Multiply this equation by 5:

-15x + 5y = 20         Now add this to the first equation:

0 = 0

So the 2 equations are the same and there are infinite solutions.