Select the correct rational numbers.

Answer: Let us assume speed of jet in still air =x

speed of wind =y

Jet flying against the wind

Relative speed of the jet = speed of jet in still air -speed of the wind=x-y

distance covered =3426

time =6 hours

distance = speed * time

3426=(x-y)*6

x-y =3426/6

x-y=571——(1)

Jet flying with the wind

Relative speed of the jet = speed of jet in still air +speed of the wind=x+y

distance covered =4026

time =6 hours

distance = speed * time

4026=(x+y)*6

x+y =4026/6

x+y=671———-(2)

solving 1 and 2 we get

x+y=671

x-y=571

x=621

y=50

speed of jet in the still air =x= 621 miles per hour

Step-by-step explanation:

1) The probability that a randomly chosen penny weighs less than 2.4 grams is; 0.00621.

2) The probability that the mean weight of 15 pennies is less than 2.4 grams is; 0

The central limit theorem in statistics tells us that the sampling distribution of the mean will usually be normally distributed, provided that the sample size is large enough.

We are given the following parameter;

Population mean; μ = 2.4 grams

Standard deviation; σ = 0.04 grams

1) The probability that a randomly chosen penny weighs less than 2.4 grams is: P(X < 2.4)

Formula for z-score is;

z = (X - μ)/σ

z = (2.4 - 2.5)/0.04

z = -2.5

The p-value from z-score calculator is; p = 0.00621.

2) The standard deviation for these 15 pennies will now be;

σ' = 0.04/√15

σ' = 0.0103

The probability that the mean weight of 15 pennies is less than 2.4 grams is expressed as;

P(X' < 2.4)

z = (2.4 - 2.5)/0.0103

z = -9.709

The p-value from z-score calculator is; p = 0

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In the given equation [12.5x + 5y = C] the constant C is always 50 with different given values of x and y.

So, the values of C are:

Calculate as follows:

(A) When x = -2 and y = 15.

(B) When x = 0 and y = 10.

(C) When x = 2 and y = 5.

(D) When x = 4 and y = 0.

Therefore, in the given equation [12.5x + 5y = C] the constant C is always 50 with different given values of x and y.

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Gabriel owns a stack of nickels which is 2 inches tall and thickness of each nickel is 0.08 inch then number of nickels with Gabriel is equal to 25.

As given in the question,

Gabriel has 2 inches tall stack of nickel

Thickness of each nickel = 0.08inch.

Let 'n' be the number of nickels Gabriel has .

Required equation to get the number of nickel is equal to :

0.08 × n = 2

⇒ n = 2 / 0.08

⇒ n = 200/ 8

⇒ n = 25

Therefore,  Gabriel owns a stack of nickels which is 2 inches tall and thickness of each nickel is 0.08 inch then number of nickels with Gabriel is equal to 25.

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Answer 0.04

Step-by-step explanation:

because 0.08 divided by two is 0.04

The factors of 6x²y-10xy+15x-25​ are (3x-5)(2xy+5).

According to the question,

We have the following expression:

6x²y-10xy+15x-25​

In this expression, we can not use any identity to solve it further.

Now, in order to find the factors of this expression, we will find the common terms from the first two terms and one common factor from the last two terms.

Taking 2xy as a common factor from first two terms and 5x as a common factor from the last two terms:

2xy(3x-5)+5(3x-5)

Taking (3x-5) as a common factor from the above expression:

(3x-5) (2xy+5)

Hence, the factors of 6x²y-10xy+15x-25​ are (3x-5)(2xy+5).

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Based on the given residual plot, as regards the linear model, we can say that; A linear model is not suitable because the residual plot shows a curved pattern.

A residual plot is a plot that shows the difference between the observed response and the fitted response values.

The ideal residual plot is usually called the null residual plot, and it shows a random scatter of points that form an approximately constant width band around the identity line.

When it comes to finding out if a linear model will be suitable, we can say that the points will form a pattern when the model function is not correct.

Now, you might be able to transform variables or even add polynomial and interaction terms in order to remove the pattern.

Now, looking at the given graph, we can say that a linear model is not suitable because from the definitions above, we can see that the residual plot shows a curved pattern.

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The range of the function is y ≤ 3.

The set of a function's potential output values is known as its range.

Given, the graph of the function.

The range of a function is the set of values of y the function can take.

The maximum y value of the function is 3, and the graph is going down both sides infinitely.

Therefore, the range of the function is y ≤ 3.

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Answer:

no

Step-by-step explanation:

the percentage has nothing to do with how many of them there are, forgive me if im wrong

The exact number of books on the shelf cannot be determined based on the information given.

An expression is a grouping of one or more mathematical or logical operators, operands (values, variables, or other expressions), and brackets in mathematics and computer programming that denote a computation that can be evaluated to generate a value.

We know that between 50 and 100 books are stored on a shelf, so let's assume the number of books is some integer value between 50 and 100, inclusive. Let's call this value "n".

Exactly 20% of the books are textbooks, which means there are 0.2n textbooks on the shelf.

Exactly one-seventh of the books are novels, which means there are (1/7)n novels on the shelf.

We know that n, 0.2n, and (1/7)n are all integers because they represent whole numbers of books. We can write this as:

n = a

0.2n = b

(1/7)n = c

where a, b, and c are integers.

From the second equation, we know that 0.2n is a multiple of 1/10. From the third equation, we know that n is a multiple of 7. Therefore, we can rewrite these equations as:

n = 10b

n = 7c

Since n is equal to both 10b and 7c, we know that n must be a multiple of the least common multiple of 10 and 7, which is 70.

So, n must be a multiple of 70, and therefore must be one of the integers 50, 70, or 90. However, we cannot determine which of these three values is the correct one based on the information given, because all three satisfy the conditions in the problem:

If n=50, then 20% of the books (i.e., 10 books) are textbooks, and 1/7 of the books (i.e., 7.14 books, which we round down to 7) are novels.

If n=70, then 20% of the books (i.e., 14 books) are textbooks, and 1/7 of the books (i.e., 10 books) are novels.

If n=90, then 20% of the books (i.e., 18 books) are textbooks, and 1/7 of the books (i.e., 12.86 books, which we round down to 12) are novels.

Therefore, the exact number of books on the shelf cannot be determined based on the information given.

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Answer: A

Step-by-step explanation :

HE ASKED YOU ABOUT AN EQUALTULAR ( TO EQUALED AND OPPSITE ANGLE )

The maximum number of guests that can fill all the standard rooms is twice the number of the standard rooms

Information from the question

each standard room can fill 2 guests

the maximum number of guests that all standard rooms can accommodate = ?

The problem is solved by multiplication

each standard room (1) = 2 guests

all standard rooms = ?

cross multiplying

? * 1 = 2 * all standard rooms

? = all standard rooms times two

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Answer:

Figure A was translated right 4 units and up 2 units

The width across Keala book cover is 40cm

A rectangle is a type of quadrilateral, whose opposite sides are equal and parallel. It is a four-sided polygon that has four angles, equal to 90 degrees

From the question,

The length of the cover

= 22 1/4

= 89/4

The area of the cover

=890 cm²

From the formula

Area of a Rectangle = Length x Breadth

890=89/4×Breadth

Breadth = 890×4/89

Breadth=40cm

Hence, the width of the book cover is 40cm

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Answer: 8

Step-by-step explanation:

(Sum of first 5 quizzes) / 5 quizzes = 8

Sum of 1st 5 quizzes = 8 x 5 = 40

let x = score on the 8th quiz

(40 + 7 + 5 + x) / 8 = 7.5

52 + x = (7.5)(8) = 60

x = 60 - 52 = 8

Answer:

I think the answer is 33?

Answer:

103 N

Step-by-step explanation:

we use the equation: w = mg

where m is mass, W is weight and g is gravitational field strength

w = ?

m= 10.5 kg

g = 9.81 ms‐² (for earth)

so,

w = 10.5 × 9.81

w = 103.005

w ≈ 103 Newtons

The exact arc length of f(x)=√2x+1 is 4.5.

The arc length is the separation between two points along a curve segment. The arc length of a function f(x) is given by the formula,

[tex]L=\int\limits^a_b {\sqrt{1+f'(x)^2}} \, dx[/tex]

Where f'(x) is derivative of function f(x). The arc length is, to put it simply, the distance that passes across the curved line of the circle that forms the arc. It should be noted that the arc's length is greater than the separation of its ends along a straight line.

Finding the arc length of f(x)=√2x+1 0≤x≤4, using the formula,

First finding the derivative of function,

[tex]f'(x)=\frac{d(\sqrt{2x+1})}{dx} \\\\=\frac{2}{2\sqrt{2x+1}} \\\\=\frac{1}{\sqrt{2x+1}}[/tex]

Now, putting the derivative of function f(x) in the formula of arc length L,

[tex]L=\int\limits^a_b {\sqrt{1+f'(x)^2}} \, dx\\\\L=\int\limits^4_0 {\sqrt{1+(\frac{1}{\sqrt{2x+1}})^2}} \, dx\\\\L=\int\limits^4_0 {\sqrt{1+\frac{1}{2x+1}}}\\\\L=\int\limits^4_0 {\sqrt{\frac{2x+1+1}{2x+1}}}\\L=\int\limits^4_0 {\sqrt{\frac{1}{2x+1}}}\\\approx4.5[/tex]

Therefore, the exact arc length of f(x)=√2x+1 is 4.5.

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Answer:

52°

Step-by-step explanation:

This is an equilateral triangle. Therefore all the sides and angles are equal to each other.

We know that,

the sum of the interior angles in a triangle is 180° and in equilateral triangles each angle measured 60° ( 180°/3 ).

Accordingly,

x + 8 = 60

Subtract 8 from both sides.

x = 60 - 8

x = 52°

The probability that the proportion of defective bottles in a sample of 546 bottles would differ from the population proportion by greater than 4% is: 10.9069.

To obtain the correct value, we need to use the formula for the Z score. This formula requires that we subtract the average or mean value from the data point provided and divide the remaining value by the standard deviation.

Here is the formula:

z = (x-μ)/σ

First population proportion = 0.24

The sample proportion, hat p = 0.04

​Z score =

[tex]0.04 - 0.24 / \sqrt 0.24 (1 - 0.24) / 546[/tex]

So, the Z score will

= -10.9469

So, when the z score = - 10.9469, the probability that Z is greater than - 10.9469,  is = 10.9069

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The actual end-of-year payment or present value of this ordinary annuity is equal to $1,482.

For the rate of interest, we have:

Rate of interest, r = APR/12

Rate of interest, r = 0.12/12

Rate of interest, r = 0.01

Next, we would calculate the present value of this ordinary annuity by using this formula:

Present value, PV = [P ÷ [1 - (1 + r)^{-n}]/r]

Where:

Substituting the given parameters into the formula, we have;

Present value, PV = 4,500 ÷ ((1 - (1 + 0.12)^(-4))/(0.12))

Present value, PV = 4,500 ÷ ((1 - (1.12)^(-4))/(0.12))

Present value, PV = 4,500 ÷ ((1 - 0.635518078)/(0.12))

Present value, PV = 4,500 ÷ ((0.364481922)/(0.12))

Present value, PV = 4,500/3.0373

Present value, PV = $1,481.58 ≈ $1,482.

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The solution of the given statement will be inequality c > -60.

Inequality is defined as mathematical statements that have a minimum of two terms containing variables or numbers is not equal.

We have been given the statement "number c divided by 3 is greater than -20".

As per the given statement, we can represent this algebraic form with inequality as:

⇒ c / 3 > -20

Inequality by multiplying both sides of the inequality by 3:

⇒ 3 × c / 3 > 3 × -20

⇒ c > -60

Thus, the solution of the given statement will be inequality c > -60.

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The question seems to be incomplete the correct question would be

Find the solution if a number c divided by 3 is greater than -20.

Answer:

Step-by-step explanation:

The cost of topsoil per ton would be $48.

The cost of pea gravel per ton is  $20.

The cost of mulch per ton is $479.

What is the linear equations in two variable?

A linear equation in two variables is one that is written in the form ax + by + c=0, where a, b, and c are real numbers and the coefficients of x and y, i.e. a and b, are not equal to zero. For example, 10x+4y = 3 and -x+5y = 2 are two-variable linear equation.

We have,

7 tons of topsoil, 6 tons of mulch, and 3 tons of pea gravel for $3270.

5 tons of topsoil, 5 tons of mulch, and 5 tons of pea gravel for $3015.

Let,

cost of topsoil per ton = x

cost of pea gravel per ton = x - 28

cost of mulch per ton = m

7x + 6m + 3(x - 28)  = 3270

7x + 6m + 3x - 84  = 3270

10x + 6m = 3270 + 84

10x + 6m = 3354 -------------(i)

5x + 5m + 5(x - 28)  = 3015

5x + 5m + 5(x - 28)  = 3015

10x + 5m = 3015 - 140

10x + 5m = 2875 -----------(II)

Subtracting equation (II) from (I), we get

   10x + 6m = 3354

-   10x + 5m = 2875

Solving we get

       m = 479

Put m = 479 in equation(I), we get

           10x + 6m = 3354

           10x + 6(479) = 3354

           10x = 480

              x = 480/10

              x = 48

Hence,

The cost of topsoil per ton would be = x = $48.

The cost of pea gravel per ton = x - 28 = 48 - 28 = $20.

The cost of mulch per ton = m = $479.

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The fifth term of the geometric progression is -0.125 and the sum of the first 20 terms is  [tex]\frac{4}{3}(\frac{1-2^{20} }{2^{20} }) }[/tex]

A geometric progression or a geometric sequence is the sequence, in which each term is varied by another by a common ratio.

All terms of a geometric progression have a common multiple called the common ratio.

if a = -2, which is first term

r = -0.5 which is common ration,

Then fifth term = a[tex]r^{4}[/tex]

substitute a and r into the above equation, you have

fifth term = (-2)([tex](-0.5)^{4}[/tex] = - 0.125

sum of G.P when the common ratio is less than 1, we have

[tex]\frac{a(1 - r^{n} )}{1 - r}[/tex]

where n = number of terms = 20

sum = [tex]\frac{-2(1 - (-0.5)^{20}) }{1--0.5}[/tex] =  [tex]\frac{4}{3}(\frac{1-2^{20} }{2^{20} }) }[/tex]

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Using polar coordinates, volume of the given solid is, 32√3π.

What is volume of solid?

An object's space requirement is expressed in terms of its volume. The amount of unit cubes required to completely fill the solid is how much it weighs. We have a total of 30 unit cubes in the solid, so the volume is as follows: 2 units 3 units 1 unit Equals 30 cubic units

We have to find the volume of the solid Inside the sphere x^2 + y^2 + z^2 = 16 and outside the cylinder x^2 + y^2 = 4 using polar coordinates.

So, the volume is

[tex]2\int\limits\int\limits_D {\sqrt{16-x^2-y^2} } \, dA[/tex]

[tex]2\int\limits^2^\pi _0 {\int\limits^4_2 {\sqrt{16-r^2} } rdrdtheta[/tex]

[tex]2\int\limits^2^\pi _0 {(-\frac{1}{3})(16-r^2)_2^4 } \, dtheta[/tex]

[tex]2\int\limits^2^\pi _0 {(-\frac{1}{3})(-2\sqrt{3}) } \, dtheta[/tex]

[tex]\int\limits^2^\pi _0 {16\sqrt{3} } \, dtheta[/tex]

[tex]32\sqrt{3}\pi[/tex]

Hence, the volume of the given solid using polar coordinates is, [tex]32\sqrt{3}\pi[/tex].

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The values of the variables, x and y in the angles formed by the parallel lines that have a common transversal are;

x = 4°, y = 10°

11. x = 9°, y = 12°

12. x = 14°, y = 5°

13. x = 8°, y = 11°

14. x = 16°, y = 23°

15. x = 9°, y = 13°

Parallel lines are lines that maintain the same distance from each other along their lengths.

From the figure, we get;

(29·x - 3) and (15·x + 7) are linear pair angles, therefore;

(29·x - 3) + (15·x + 7) = 180°

44·x + 4 = 180

x = (180 - 4)/44 = 4

x = 4°

(15·x + 7) and (13·y - 17) are same side exterior angles between parallel lines, therefore;

(15·x + 7) + (13·y - 17) = 180°

(15×4 + 7) + (13·y - 17) = 180°

67 + 13·y - 17 = 180°

50 + 13·y = 180

13·y = 180 - 50 = 130

y = 130 ÷ 13 = 10

y = 10°

11. (18·x - 44)° and  (8·x - 10)° are same side exterior angles, therefore;

(18·x - 44)° +  (8·x - 10)° = 180°

26·x - 54 = 180

x = (180 + 54)/26 = 9

x = 9°

(8·x - 10)° and (13·y - 38)° are linear pair angles, therefore;

(8·x - 10)° + (13·y - 38)° = 180°

(8 × 9 - 10)° + (13·y - 38)° = 180°

62 - 38 + 13·y = 180

13·y = 180 - (62 - 38) = 156

y = 156 ÷ 13 = 12

y = 12°

12. (9·x - 2)° and (5·x + 54)° are corresponding angles, therefore;

(9·x - 2)° = (5·x + 54)°

(9·x - 2)° = (5·x + 54)°

9·x - 5·x = 54 + 2 = 56°

4·x = 56°

x = 56° ÷ 4 = 14°

x = 14°

(9·x - 2)° and (10·y + 6)° are linear pair angles, therefore;

(9·x - 2)° + (10·y + 6)° = 180°

(9 × 14 - 2)° + (10·y + 6)° = 180°

124 + 6 + 10·y = 180

10·y = 180 - 130 = 50

y = 50 ÷ 10 = 5

y = 5°

13. The angle to which the angle (8·x - 1)° is an alternate interior angle is a corresponding angle to the angle (11·x - 25)°, therefore;

(8·x - 1)° is congruent to angle (11·x - 25)°

(8·x - 1)° = (11·x - 25)°

11·x - 8·x = 25 - 1 = 24

3·x = 24

x = 24 ÷ 4 = 8

x = 8°

Angles (15·y - 48)° and (8·x - 1)° are linear pair angles, therefore;

(15·y - 48)° + (8·x - 1)° = 180°

(15·y - 48)° + (8 × 8 - 1)° = 180°

(15·y - 48)° + 63° = 180°

15·y + 15° = 180°

15·y = 180° - 15° = 165°

y = 165° ÷ 15 = 11°

y = 11°

14· The angle (4·x + 4)° and (7·x - 44)° are alternate exterior angles, therefore;

(4·x + 4)° = (7·x - 44)°

7·x - 4·x = 44° + 4° = 48°

3·x = 48°

x = 48° ÷ 3 = 16°

x = 16°

The vertical angle to angle 39° is a linear pair angle to the angle (8·y - 43)°

Therefore;

39 + 8·y - 43 = 180°

8·y  = 180 + 43 - 39 = 184

y = 184 ÷ 8 = 23

y = 23°

15. The diagram indicates that the angles (15·x - 26)° and (12·x + 1)° are congruent, therefore;

(15·x - 26) = (12·x + 1)

(15·x - 12·x) = (26 + 1)

3·x = 27

x = 27 ÷ 3 = 9

x = 9°

The vertical angle to (2·x + 1) is therefore;

12·x + 1 = 12 × 9 + 1 = 109

The angle sum property indicates that we have;

28° + 109° + (4·y - 9)° = 180°

(4·y - 9)° = 180° - (28° + 109°) = 43°

(4·y - 9)° = 43°

(4·y)° = 43° + 9° = 52°

y = 52°/4 = 13°

y = 13°

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To make a square using the method of completing the square.

[ (a + b)² = a² + 2ab + b² ]

[ (a - b)² = a² - 2ab + b² ]

x² - 13x + 31 = 0

(x - 13/2)² + (293/4) = 0

The number added to complete the square is 293/4.

Polynomial is an equation written as the sum of terms of the form kx^n.

where k and n are positive integers.

We have,

x² - 13x + 31 = 0

To make a square using the method of completing the square.

[ (a + b)² = a² + 2ab + b² ]

[ (a - b)² = a² - 2ab + b² ]

x² - 2 x (13/2)x + (13/2)² - (13/2)² + 31 = 0

(x - 13/2)² + 169/4 + 31 = 0

(x - 13/2)² + (293/4) = 0

Thus

The number added to complete the square is 293/4.

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Answer:

Here,

Let the age of Adam be x

and ,Brian be y

so,x=y+20.........eqn 1

and ,2(y+2)=x

or,2y+4=x......eqn 2

Now ,

subtracting eqn1 and eqn 2

so, x=y+20

x=2y+4

- - -

______________

0 = -y+16

so,y=16 and x=y+20 =16+20=36 .

so Adam is 36 years old and brian is 16.

By using the formula of acceleration, it can be calculated that

Time taken by an earthworm  to accelerate from a speed of 0.01 m/s to 0.02 m/s over a distance of 0.9 m is 59.88 s

What is acceleration?

At first, it is important to know about velocity

Distance travelled by a body per unit interval of time in a particular direction is called Velocity

The rate of change of velocity is called acceleration.

Acceleration is a vector quantity as the direction is taken into account.

Initial velocity of earthworm (u)= 0.01 m/s

Final velocity of earthworm (v) = 0.02 m/s

Distance (s) = 0.9 m

We know,

[tex]v^2 = u^2 + 2as\\0.02^2 = 0.01^2 + 2 \times a \times 0.9\\0.02^2 - 0.01^2 = 1.8a\\(0.02 + 0.01)(0.02 - 0.01) = 1.8a\\a = \frac{0.03 \times 0.01}{1.8}\\a = 0.000167 \ ms^{-2}[/tex]

Again,

v = u + at

0.02 = 0.01 + 0.000167[tex]\times[/tex] t

t = [tex]\frac{0.02 - 0.01}{0.000167}[/tex]

t = 59.88 s

Time taken by an earthworm  to accelerate from a speed of 0.01 m/s to 0.02 m/s over a distance of 0.9 m is 59.88 s

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