Question 1

A tiling pattern is defined by the pattern rule equation 'n = 6 + 4p`,

where `p is the position number and 'n' is the number of tiles.

How many tiles would there be in position 22?

let's rewrite:

as:

The factors of 10 that sum to 7 are 2 and 5, therefore:

The expression "F = {(x, y) : φ(x, y, p)}" represents a set of ordered pairs (x, y) that satisfy a condition defined by the function φ. The interpretation and nature of the set F depend on the specific function φ and the parameter p, which determine the relationship between the variables x, y, and p.

The expression "F = {(x, y) :  φ(x, y, p)}" represents a set F consisting of ordered pairs (x, y) that satisfy a particular condition defined by the function  φ, which takes the variables x, y, and p as inputs.

To fully understand the meaning of F, we need to delve into the function  φ and its relationship with the variables x, y, and p. The function φ could represent a wide range of mathematical relationships or conditions that determine the inclusion of certain pairs (x, y) in the set F.

For instance, let's consider a specific example where vraphi(x, y, p) is defined  φ(x, y, p) = \(x^2 + y^2 - p^2.\)In this case, F = {(x, y) : \(x^2 + y^2 - p^2\)= 0} represents a set of ordered pairs (x, y) that satisfy the equation \(x^2 + y^2 - p^2 = 0.\) This equation represents a circle with radius p centered at the origin (0, 0). Consequently, F corresponds to all the points lying on the circumference of this circle.

It is important to note that the specific meaning and implications of F heavily rely on the nature of the function  φ and the parameter p. Different functions and parameters will yield distinct sets F with their own unique characteristics and interpretations.

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A) The distance that a force of 3 newtons would stretch the rubber band is; 0.015 m

B) The amount of work it takes to stretch the rubber band this far is; 0.0225 J

From Hookes's law, as long as the elastic limit is not exceeded the extension is directly proportional to the force applied.

F = Ke

Where;

F = force

K = force constant

e = extension

Thus,  for a restoring force of magnitude 2 newtons ;

2 N = K(1 × 10⁻²) m

K = 2 N /(1 × 10⁻²) m

K = 200 N/m

a) For a force of 3 newtons, we have;

3N = 200 N/m × a

Where a is the extension in meters

a = 3N/200 N/m

a = 0.015 m

b) The formula to find the work done is;

P.E = ¹/₂Ke²

P.E = ¹/₂ * 200 * 0.015²

P.E = 0.0225 J

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Step-by-step explanation:

sqrt(x + 2) - 15 = -3

sqrt(x + 2) = 12 (add 15 to both sides)

x + 2 = 12² = 144 (square both sides)

x = 142.

Answer:

x = 142

Step-by-step explanation:

√x+2 - 15 = -3 (Given)

√x+2 = 12 (Add 15 on both sides)

x + 2 = 144 (Square both sides to get rid of the radical)

x = 142 (Subtract 2 on both sides)

Answer:

Calculate the amount of total value in each case substituting x or d by 7 and compare the amounts:

f(7) = 100*7 + 1000 = $1700

g(7) = 1000*(1.1)^7 = $1948.72 (rounded)

As we see the option 2 is better choice and the difference is:

$1948.72 - $1700 = $248.72

Step-by-step explanation:

For partb

The height of the building is approximately 86.6025403784 feet.

Amari is standing 50 feet from the base of a building. From where he stands, the angle formed between the top of the building and the ground at his feet is 60°.

The right triangle has been formed in the scenario such that the base of the right triangle is formed by the ground, height of the right triangle is formed by the building and the hypotenuse of the right triangle is formed by the line connecting Amari and the top of the building.

Hence, we can make use of trigonometric ratios to calculate the height of the building. Let us assume that the height of the building is h.By definition,

tan 60 = h/50tan 60 = (√3) / 1h/50 = (√3) / 1h = 50 × (√3)h ≈ 86.6025403784

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Using Trigonometry, the value of x in the right triangle is 17.1

Since we have a right angle triangle ; The angle L can be obtained thus ;

L = 180 - (90+67)

L = 23

Using Trigonometry:

Sin23° = opposite/ hypotenuse

Opposite= 6.7

hypotenuse= x

Sin23° = 6.7/x

x = 6.7/sin(23°)

x = 17.14

Therefore, the value of x to the nearest tenth is 17.1

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Answer:

10\(x^{2}\)+x-21

Step-by-step explanation:

you just do (5x-7)(2x+3) and foil it out

The total amount payable at the end of 4 years is 406

In this given sum we are provided with the values of principal , rate of interest , and the number of years , we are asked to calculate the amount payable after 4 years that is the matured amount which is calculated with the addition of the principal amount and the simple interest. For that we had to first find out the amount of interest and then we need to add that with the principal amount to get the matured amount or the amount that is payable at the end of 4 years.

here we have to apply the formulla of simmple interest :

(principal × rate of interest × no. of years )/ 100

In the given sum principal (p) = 350 , rate of interest (r) = 4% pa , no. of years (n) = 4

Simple interest = pnr/100

= (350 × 4 × 4)/100  = 56

Matured Amount = Principal + Interest

= 350 + 56 = 406

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Answer:

1

Step-by-step explanation:

 The method I used is elimination.

 x - 2y = 1

-x - 4y = -7         To find y, we need to cancel the x by using it's opposite. This also affects the other numbers in the equation. This makes positive 4 into a negative and positive 7 into a negative.

   Now we are left with,   -2y = 1

                                           -4y = -7

   Add and you get,         -6y = -6

   Divide      -6y/-6     =  -6/-6

      Our answer is, y = 1.

Answer:

A=-80

B=175

C=64

Step-by-step explanation:

I USED SUBTRACTION

In this probability case, the correct statements are:

A) There are 2 black socks.

C) There is at most 1 gray sock.

E) It is likely that a black sock is selected.

D) It is impossible to select a red sock.

Given that the probability of selecting a  black, white, or gray sock is 1, we can deduce that the total number of socks in the bag is "16".

Statement A  is correct because it state s that there are 2 black socks.

Statement C  is correct because it states that there is at most 1 gray sock, which means there can be either   0 or 1 gray sock.

Statement E   is correct because it states that it is likely to select a black sock.   Since the probability of selecting a white sock is 3/4, the probability of selecting a black  sock is higher  than that.

Statement   D is correct because  it states that it is impossible to select a red sock. The given information does not  mention any red socks, so the probability of selecting a red sock is 0.

Statement B is incorrect because it states that there are 12 white socks.

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Full Question:

Although part of your question is missing, you might be referring to this full question:

A bag contains 16 socks.One sock is chosen at random.The probability of selecting a black,white,or gray sock is 1.The probability of selecting a white sock is 3/4.Selecting a gray sock is less likely than selecting a black sock.Which statements describe the situation?Choose all the correct answers.

A There are 2 black socks.

C There is at most 1 gray sock.

E It is likely that a black sock is selected.

B There are 12 white socks.

D It is impossible to select a red sock.

Answer:

x=-pie/12

sinxcosx=-1/4

multiply both sides by 2

sin2x = 2sinxcosx we know

now equation will be

sin2x = -1/2

2x=-pie/6

x=-pie/12

Answer:

Answer should be 50.....

Answer:

d = 5 is a solution to the equation 13 - d = 8

Step-by-step explanation:

We have to solve 13 - d = 8

Now,

13 - d = 8,

We add d on both sides,

13 - d + d = 8 + d

13 = 8 + d

we subtract 8 from both sides,

13 - 8 = 8 - 8 + d

5 = d

d = 5

Hence the answer is 5

The unit rate of the equation y = -4x + 2 is -4

From the question, we have the following equation

y = -4x + 2

The above equation is a linear equation

Linear equations are represented as

y = mx + c

Where

When the equations y = mx + c and y = -4x + 2 are compared, we have

Unit rate, m = -4

Y-intercept, c = 2

Note that all linear equations have a constant rate of change

Hence, the unit rate in the linear equation is -4

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the answer for this question is  i don't know

So , bye

(a) This differential equation can be written in the form (*) with P(x) = 1, Q(x) = 2x, and n = 2.

(b) The substitution u = 1/y will transform it into the linear equation Du/dx +  0u = -2x

(c)Using the substitution in part (b), we rewrite the initial condition in part  u(1) = 1/y(1) = 1/4.

(d) the linear equation in part (b) is y = 1/(C - x) and  the solution that satisfies the initial condition in part (c) U(x) = -y⁻¹ = -x + C,

(e) Finally, solve for y(x) = 1/(1/4 + 1 - x) = 4/(5 - x).

What is  Bernoulli differential equation?

A Bernoulli differential equation is a type of non-linear ordinary differential equation of the form:

dy/dx + P(x)y = Q(x)yⁿ

where P(x) and Q(x) are functions of x and n is a constant. The equation is named after the Swiss mathematician Jakob Bernoulli.

These types of differential equations are important in various fields of science, such as physics, engineering, and economics. They are non-linear, meaning that the dependent variable y appears in both linear and non-linear terms, making them difficult to solve in general.

a) This differential equation can be written in the form (*) with P(x) = x, Q(x) = 2x, and n = 2.

b) The substitution u = y⁻¹ will transform it into the linear equation du/dx - xu = -2x.

c) Using the substitution in part (b), we rewrite the initial condition as u(1) = 1/4.

d) Now we solve the linear equation in part (b). The characteristic equation is given by d/dx(e\(\mathrm{(\int -xdx))}\) = -xe\(\mathrm{(\int -xdx))}\) which has the general solution u(x) = Ce\((-x^2/2)\).

Using the initial condition, we find C = 1/4, so u(x) = 1/4e\((-x^2/2)\).

e) Finally, we solve for y. From u = y⁻¹, we have y = 1/u = 4e\((-x^2/2)\).

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Answer:

The answer is A, 72

Answer:

x = 65

Step-by-step explanation:

the sum of the interior angles of a quadrilateral = 360°

sum the angles and equate to 360

x + 95 + 118 + 82 = 360

x + 295 = 360 ( subtract 295 from both sides )

x = 65

Answer:

\(\sqrt{-14} = i\sqrt{14}\)

Step-by-step explanation:

There is no real solution only in complex numbers

Answer:.

Step-by-step explanation:

Answer:

Step-by-step explanation:

Simplify parentheses : 0.5x+0.3=2.1x+9-5.5

Combine like terms : 0.5x+0.3=2.1x+3.5

Isolate the variable : -1.6x=3.2

Divide by -1.6 on both sides : x=-2

Answer:  the answer is in the picture

have a nice one

Step-by-step explanation:

The measure of side n is √(m^2 - 64).

According to the given question.

We have a right angle triangle.

Here, we have to find the measure n.

Since, the given triangle is divided into two right angle triangles.

Now in the right angled triangle with the side measure m, n and 8.

By the Pythagoras theorem we can say that

m^2 = 8^2 + n^2

⇒ m^2 = 64 + n^2

⇒ m^2 -64 = n^2 ...(i)

⇒ n = √(m^2 - 64)

Hence, the measure of side n is √(m^2 - 64).

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Answer:

percent- 85%

fraction- 17/20 (simplified) or written like this:  \(\frac{17}{20}\)

decimal- 0.85

Step-by-step explanation:

I hope this helps you! Good luck and have a great day. ❤️✨

Answer:

The p-value of the test is 0.0014 < 0.01, meaning that the data indicates that the true average unrestrained compressive strength is less than the design value of 3200.

Step-by-step explanation:

We want to determine whether the data indicate that the true average unrestrained compressive strength is less than the design value of 3200.

At the null hypothesis, we test if the mean is at the design value of 3200, so:

\(H_0: \mu = 3200\)

At the alternate hypothesis, we test if it is less than the design value of 3200, so:

\(H_a: \mu < 3200\)

The test statistic is:

\(t = \frac{X - \mu}{\frac{s}{\sqrt{n}}}\)

In which X is the sample mean, \(\mu\) is the value tested at the null hypothesis, s is the standard deviation of the sample and n is the size of the sample.

3200 is tested at the null hypothesis:

This means that \(\mu = 3200\)

The sample average unrestrained compressive strength for 50 specimens of a particular type of brick was computed to be 3120 psi, and the sample standard deviation was 180.

This means that \(n = 50, X = 3120, s = 180\)

Test statistic:

\(t = \frac{X - \mu}{\frac{s}{\sqrt{n}}}\)

\(t = \frac{3120 - 3200}{\frac{180}{\sqrt{50}}}\)

\(t = -3.14\)

P-value of the test and decision:

The p-value of the test is the probability of finding a sample mean below 3120, which is the p-value of t = -3.14, using a one-tailed test, with 50 - 1 = 49 degrees of freedom.

With the help of a calculator, the p-value of the test is 0.0014

The p-value of the test is 0.0014 < 0.01, meaning that the data indicates that the true average unrestrained compressive strength is less than the design value of 3200.

Step-by-step explanation:

x - number of senior citizen tickets sold

y - number of child tickets sold

1st day: 3x + 6y = 102

2nd day: x + 12y = 184

2 (3x + 6y = 102)

= 6x + 12y = 204

-1 (x + 12y = 184)

= -x - 12y = -184

6x + 12y = 204

-x - 12y = -184

= 5x = 20

x = 4

3(4) + 6y = 102

= 12 + 6y = 102

= 6y = 90

y = 15

Answer:

One senior ticket is $ 4.00 and one child ticket is $ 15.00

Hope this helps! :D

Answer:

Step-by-step explanation:

3x -8 = 2x + 5

x - 8 = 5

x = 13

3(13) - 8 + 2(13) + 5

39 - 8 + 26 + 5

31 + 31 = 62