Find the area of the figure

The amplitude of subsequent oscillations is 0.093 m.

The spring stiffness is quantified by the spring constant, or k. For various springs and materials, it varies. The stiffer the spring is and the harder it is to stretch, the bigger the spring constant.

Given that,

Mass of a block, m = 1.2 kg

Spring constant of the spring, k = 14.0 N/m

While the block is sitting at rest, a student hits it with a hammer and almost instantaneously gives it a speed of 32.0 cm/s or 0.32 m/s

We need to find the amplitude of the subsequent oscillations.

We can use the conservation of energy here. Initially, the kinetic energy of the block is maximum and then it gets converted to the potential energy of the spring.

Mathematically,

[tex]\frac{1}{2} mv^2=\frac{1}{2}kv^2[/tex]

A is the amplitude of subsequent oscillations.

[tex]A=\sqrt{(\frac{mv^2}{k} )} \\\\A=\sqrt{\frac{(1.2)(0.32)^2}{14} } \\\\A=0.093m[/tex]

So, the amplitude of subsequent oscillations is 0.093 m.

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i) The profit/loss when no cars are produced is a loss of 6600 Rupees.

II) The break even point is at 20 cars

III) The profit/loss if 400 cars are produced is;  a loss of 13400Rupees.

(i) When no cars are produced, x = 0.

Thus, plugging this value into the function p(x) = -x² + 350x - 6600, we have;

p(0) = -0² + 350(0) - 6600 = -6600.

Therefore, the profit/loss when no cars are produced is a loss of 6600 thousand Rupees.

(ii) The break-even point is the point at which the profit is zero, i.e., p(x) = 0. Setting p(x) = 0 and solving for x, we find that;

-x² + 350x - 6600 = 0

x = 20

Therefore, the break-even point is x = 20 cars. T

(iii) If 400 cars are produced, the profit can be found by plugging this value into the function p(x) = -x² + 350x - 6600.

We find that p(400) = -400² + 350(400) - 6600

= -160000 + 140000 + 6600 = -13400. Therefore, the profit/loss if 400 cars are produced is a loss of 13400 Rupees.

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Answer:

I inch = 7.2 miles

Step-by-step explanation:

Proportion method is applied:

                     1.5 inches on a map = 10.8 miles of actual distance

                  ∴ 1 inches on the map = x miles of the actual distance

Cross-multiplication is applied:

(1.5 inches)(x miles) = (1 inch)(10.8 miles)

x needs to be isolated and made the subject of the equation:

x miles = [tex]\frac{(1 inch)(10.8 miles)}{1,5 inches}[/tex]

Inches in the numerator and denominator will cancel eachother out:

x miles = [tex]\frac{10.8 miles}{1.5}[/tex]

         x miles = 7.2 miles

∴ Scale on the map:

                  1 inch = 7.2 miles

Answer: 245 yds

Step-by-step explanation:

61 1/4 times 4 = 245

Answer:

Fourth option: √65/4

Step-by-step explanation:

Since the angles are similar, each of the angles of ΔEFG must be equal to each of the corresponding angles of ΔHIJ

Specifically, m ∠J in ΔHIJ = m∠G in Δ EFG

Let's first find ∠G

Since EFG is a right triangle,

tan(G) = EF/FG = √65/4

tan J must be the same as tan G  = √65/4

This is the fourth  option

The value of tanJ is in the right angled triangle HIJ√65 / 4

An equation is an expression that contains numbers and variables linked together by mathematical operations of addition, subtraction, multiplication, division and exponents. An equation can either  be linear, quadratic, cubic, depending of the degree of the variable.

Two triangles are similar if their corresponding angles are equal to each other.

Given that triangle EFG and triangle HIJ are similar, hence:

Angle G = Angle J

tanJ = tanG = √65 / 4

The value of tanJ is  √65 / 4

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The instructor chose to use the highest score now mode, hence the score of the second attempt would be used that is 10/10.

In statistics, the value that consistently appears in a particular set is referred to as the mode. The mode or modal value in a data set is sometimes referred to as the value or number that occurs most frequently in the data set. In addition to mean and median, it is one of the three measures of central tendency.

The scores at different attempts are:

First attempt: 2/10 = 0.2

Second attempt: 10/10 = 1

Third attempt: 3/10 = 0.3

The instructor chose to use the highest score now mode, hence the score of the second attempt would be used that is 10/10.

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In response to the query, x is equal to 60°, 120°, 240°, and 300°. These four options are the answer to the equation.

A mathematical equation is a statement that two amount or values are equal, such as 6 x 4 = 12 x 2. 2. A noun that counts. An equation is applied when several or more factors must be considered jointly in order to understand or explain the whole situation.

This equation can be solved using the trigonometric identity:

[tex]sinx = \sqrt{ (1 - cos^2x)}[/tex]

This identity can be used as a substitution in the equation:

5 sinx - 5 cosx = 2

5 [tex]\sqrt{(1 - cos^2x) }[/tex] - 5 cosx = 2

5 sqrt[tex](1 - cos^2x)[/tex]) = 7 + 5 cosx

Squaring both sides:

25([tex]1 - cos^2x[/tex]) = 49 + 70 cosx + 25 [tex]cos^2x[/tex]

25 - 25 [tex]cos^2x[/tex] = 49 + 70 cosx + 25 [tex]cos^2x[/tex]

0 = 74 + 45 cosx

45 cosx = -74

cosx = -74/45 = -2/3

The inverted cosine function can be used to determine that x = cos-1(-2/3). x must be within the range of 0° to 360°, hence x must be 300°.

5 sin - 5 cos - 5(-1/2) = 5 sqrt(3)/2 + 5/2 = 2 + 2.5 = 2.5

Since the left side of the equation is not equal to 2, x = 300° is not a solution to the equation.

We can repeat this process for the other solutions to the equation:

x = 60°, x = 120°, x = 240°, and x = 300°

These are the four solutions to the equation for 0° <= x < 360°.

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The solution to the system of equations is (13/3, 16/3).

The graph is given below.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

Example:

2x + 4 = 8 is an equation.

We have,

y = 14x - 2 _____(1)

y = x + 1 ______(2)

Now,

The graph of the equation is given below.

Now,

From (1) and (2).

14x - 2 = x + 1

14x - x = 1 + 2

13x = 3

x = 13/3

And,

y = x + 1

y = 13/3 + 1

y = 16/3

So,

The solution is (13/3, 16/3)

Thus,

The solution is (13/3, 16/3).

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Answer:

Step-by-step explanation:

Answer:

Around 11:15 am

Step-by-step explanation:

Let h represents the number of hours the plumber works

Since the plumber charges $65 fee plus $75 per hour, the bill can be calculated by:

→ bill = 65 + 75h

Since the bill is $195.25

→ 195.25 = 65 + 75h

→ 75h = 130.25

→ h = 1.74

1.74 implies that the plumber worked almost 1 hour and 45 minutes. Since the plumber started at 9:30, the repair was completed around 11:15 am.

The cumulative distribution function (CDF) of U is also well known and is given by:

F(u) = 1 - [tex]e^{(-u/2)}[/tex] × γ(1/2, u/2)

where γ is the lower incomplete gamma function.

What is the chi-squared distribution?

The chi-squared distribution is a continuous probability distribution that is widely used in statistics and other fields.

The random variable U = Y1^2 + Y2^2 has a well-known distribution called the chi-squared distribution with two degrees of freedom. The density function of U is given by:

[tex]f(u) = (1 / (2 \times \pi)) \times e^{(-u/2)} \times (u/2)^{(1/2 - 1)}[/tex]

where e is the base of the natural logarithm and π is the mathematical constant pi. This distribution has a positive support on the interval [0, +∞).

The cumulative distribution function (CDF) of U is also well known and is given by:

F(u) = 1 - [tex]e^{(-u/2)}[/tex] × γ(1/2, u/2)

where γ is the lower incomplete gamma function.

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Answer: 115%

Step-by-step explanation:

100% = 1

10%=0.1

5%=0.05

100%+10%+5%=115%

1+0.1+0.05=1.15

Answer: 15

Step-by-step explanation:

x+x*15/100

x(1+.15)

1.15x

Answer:

3?

Step-by-step explanation:

im not sure sorry

The people that are eating record toys are 48

From the question, we have the following parameters that can be used in our computation:

People at the movies = 80

People are eating popcorn = 2/5

Using the above as a guide, we have the following:

Record toys = (1 - People are eating popcorn) * People at the movies

Substitute the known values in the above equation, so, we have the following representation

Record toys = (1 - 2/5) * 80

Evaluate

Record toys = 48

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Answer:

  x = 5

Step-by-step explanation:

You want the length of x in the figure showing similar triangles.

The bottom edge of the triangle is 2/3 of the left edge.

The similar triangles have the same ratio of side lengths. That means x is 2/3 of (3+4.5):

  (2/3)(7.5) = 5

The length x is 5 units.

Answer: The public debt in 2007 would be 6,783,231,062,743.62 + 595,821,633,586.70 = 7,379,052,696,330.32

Step-by-step explanation:

Answer:

21+15+9=45/4=that the answer

The weight of the robot is within the error limit of 0.3%.

Given is that a robot building club organizes competitions by weight categories called classes each class permit a percent error of 0.3%. In the 5 kg class one robot weighs 4.925 kg.

Let -

{x} = 0.3% of 5

{x} = 0.3/100 x 5

{x} = 3/1000 x 5

{x} = 15/1000

{x} = 3/200

{x} = 0.015                                                                            .... Eq { 1 }

Now -

For the weight of the robot to be under the weight limit -

4.925 ≤ (5 - x)

4.925 ≤ (5 - 0.015)

4.925 ≤ 4.985                                                       ..... Eq { 2 }

which is true.                              

Therefore, the weight of the robot is within the error limit of 0.3%.

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Answer: 0

Step-by-step explanation:

Using GEMDAS

- Grouping

- Exponents

- Multiplication

- Division

- Addition

- Subtraction

[5-6+1]

= [-1+1] because you add/subtract from left to right

= [0] because -1+1=0.

Answer is 0

Answer:

x=2

Step-by-step explanation:

4x+4=12

   -4   -4

_______

4x=8

_____

4     4

x=2

The expression 6j^2 - 4j 12 can be rewritten as [tex]$-24(j\frac{1}{2})^2 -12$[/tex]where , and [tex]$q=-12$[/tex]. Thus,[tex]$\frac{q}{p}=-24$[/tex].

The expression[tex]$6j^2 - 4j 12$[/tex] can be rewritten in the form [tex]$c(j p)^2 q$[/tex], where c, p, and q are constants. To do this, we can factor out a common factor from the expression. In this case, the common factor is j. Then, we can rewrite the expression as [tex]$j(6j - 12)$[/tex] which simplifies to [tex]$-24j^2 -12$[/tex]. Dividing both sides by j, we can rewrite the expression as [tex]$-24(j\frac{1}{2})^2 -12$[/tex] where [tex]$c=-24$[/tex], [tex]$p=\frac{1}{2}$[/tex] and [tex]$q=-12$[/tex]. Thus, [tex]$\frac{q}{p}=-24$[/tex]. To summarize, the expression [tex]$6j^2 - 4j 12$[/tex] can be rewritten in the form [tex]$c(j p)^2 q$[/tex] where c, p, and q are constants, and [tex]$\frac{q}{p}=-24$[/tex].

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Answer: -1

Step-by-step explanation:

When the graph g hits g=2, the y is -1

The values of a = 17 and b = - 56

that make the following piece wise defined function both continuous and differentiable everywhere.

A continuous function in mathematics is one that doesn't change value unexpectedly due to discontinuities, or breaks in the function's continuity. A continuous function in mathematics is a function that causes the value of the function to continuously vary as a result of a continuous variation of the argument, or a change without a leap. Thus, there aren't any discontinuities—rapid changes in value.

conditions are:

1.

f(x) is continuous if,

[tex]\lim_{x \to \ 5^{-}}f(x)[/tex] = [tex]\lim_{x \to \ 5^{+}}f(x)[/tex] = f(5)

2.

differentiable if,

[tex]\lim_{x \to \ 5^{-}}f^'(x)[/tex] = [tex]\lim_{x \to \ 5^{+}}f^'(x)[/tex]

for 1st condition:

⇒ [tex]\lim_{x \to \ 5^{-}}f(x) = \lim_{x \to \ 5^{+}}f(x)[/tex]

⇒ [tex]\lim_{x \to \ 5^{-}}(-3x -6) = \lim_{x \to \ 5^{+}}(-2x^2+ax+b)[/tex]

⇒ (-3 × (-5) - 6) = - 2(5)² + a(5) + b

⇒ - 21 = - 50 + 5a + b

⇒ 5a + b = 29 ................... (1)

For 2nd condition:

⇒ [tex]\lim_{x \to \ 5^{-}}f^'(x) = \lim_{x \to \ 5^{+}}f^'(x)[/tex]

⇒ [tex]\lim_{x \to \ 5^{-}} \frac{d}{dx} (-3x - 6) = \lim_{x \to \ 5^{+}} \frac{d}{dx}(-2x^2 + ax + b)[/tex]

⇒ - 3 = - 4x + a

⇒ - 3 = - 4 (5) + a

⇒ a = 17

Substitute a = 17 in equation (1) we get:

5(17) + b = 29

or, b = - 56

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The complete question is as follows:

Check the picture below.

The percent change of an object is the ratio of its final value to its initial value.

The percentage of an item's final value versus its starting value is its percent change. By dividing the difference in data by the starting value, you can get the percent change.

"Rate" simply refers to the quantity divided by another number, typically 100, 1,000, or another multiple of 10. A rate per 100 is known as a percentage.

Percentage Change is the difference that results from deducting the old value from the new value, dividing by the old value, and multiplying the result by 100 to represent it as a percentage. In most cases, multiplying a fraction by 100 results in a percent conversion.

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Answer: The sample space of possible outcomes is:

{SM, SJ, MJ, MS, JS, JM}.

There are 6 possible outcomes in the sample space, and 1 of these outcomes results in the first student being a boy (Franklin, represented by "F").

Therefore, the probability of the first student being a boy is P(A) = 1/6.

Step-by-step explanation:

Answer:

Top one is 3/8

Middle is 4/7

Bottom is 1/3

Step-by-step explanation:

The polynomial  n² + 6n - 1 can be factored as,

(n + 3 + √10)(n - 3 + √10)(3n - 2).

We know that if x = a is one of the roots of a given polynomial x - a = 0 is a factor of the given polynomial.

To confirm if x - a = 0 is a factor of a polynomial we replace f(x) with f(a) and if the remainder is zero then it is confirmed that x - a = 0 is a factor.

Given, A product of two polynomials (n² + 6n - 1)(3n - 2).

Now, The quadratic expression n² + 6n - 1 can be factored as,

n² + 6n - 1.

[- 6 ± √(36 + 4)]/2.

= [- 6 ± √40]/2.

= [- 6 ± 2√10]/2.

= - 3 ± √10.

Therefore, (n² + 6n - 1)(3n - 2)

= (n + 3 + √10)(n - 3 + √10)(3n - 2).

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Step-by-step explanation:

mortgages, lines of credit, checking and savings accounts, auto loans and the convenience of electronic banking and Automated Teller Machines (ATMs)

Step-by-step explanation:

Banks and credit unions offer a variety of financial services, including:

Checking and savings accounts

Personal loans

Mortgages

Credit cards

Investment products (e.g. mutual funds, individual retirement accounts (IRAs))

Foreign currency exchange

Online and mobile banking

Wire transfers

Automated teller machines (ATMs)

Insurance products (e.g. life, auto, homeowners)

Wealth management services

Small business banking services.

Note that the exact services offered may vary depending on the institution.