2 times y added to 3

To verify the inequality without evaluating the integrals, we can use the properties of integrals.

First, we know that the integral of a positive function gives the area under the curve. Therefore, the integral of √(1-x^2) from -1 to 1 gives the area of a semicircle with radius 1. This area is equal to π/2, which is approximately 1.57.
Next, we can use the fact that the integral of a function over an interval is less than or equal to the product of the length of the interval and the maximum value of the function on that interval. Since the function √(1-x^2) is decreasing on the interval [-1,1], its maximum value is at x=-1, which is √2/2.
Using this property, we have:
∫1 -1 √(1-x^2) dx ≤ (1-(-1)) * √2/2 = √2
Finally, we can use a similar argument to show that the integral is greater than or equal to 2. Therefore, we have:
2 ≤ ∫1 -1 √(1-x^2) dx ≤ √2
To verify the inequality 2 ≤ ∫(1, -1) √(1 - x^2) dx ≤ 2√2 using properties of integrals, let's first establish that the integrand is non-negative on the interval [-1, 1]. Since 0 ≤ x^2 ≤ 1, we have 0 ≤ 1 - x^2 ≤ 1, so √(1 - x^2) is non-negative.
Now, consider the areas of two squares: one with side length 2 and the other with side length √2. The area of the first square is 2² = 4, and the area of the second square is (√2)² = 2. Since the integrand lies between 0 and 1, the area under the curve is less than the area of the first square but more than half of it (as it resembles half of the first square).
Therefore, 2 ≤ ∫(1, -1) √(1 - x^2) dx ≤ 2√2, as the area under the curve is between half of the first square's area and the second square's area.

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Answer:

=144*8/2.5

=1152/2.5

=460.8

Step-by-step explanation:

there you go

Answer:

  XED is 2

  demand will likely be based on price

Step-by-step explanation:

You want the XED for Coke and Pepsi, given that a decrease in price of Pepsi from $2 to $1.75 per liter causes demand for Coke to fall from 6,000 to 4500 liters.

XED is the abbreviation for "cross-elasticity of demand." It is the ratio of the percentage change in the demand for one good to the percentage change in price for another.

  XED = (∆Q/Q)/(∆P/P)

  XED = ((4500 -6000)/(6000))/((1.75 -2.00)/(2.00)) = (2/6000)(-1500/-0.25)

  XED = 2

The XED is positive for substitute goods, and negative for complementary goods (bought together).

The relatively large positive XED for Coke and Pepsi indicates these brands are nearly interchangeable. Consumers will tend to choose one over the other based on price. Apparently, the price of $1.75 per liter of Pepsi is sufficiently low to cause a switch from Coke.

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Answer:

17 seats per row

Step-by-step explanation:

We Know

68 seats in 4 rows

How many seats per row?

We Take

68 ÷ 4 = 17 seats per row

So, there are 17 seats per row.

The answer is:

Work/explanation:

Find the number of seats per row by dividing the number of seats in all 4 rows by the number of rows:

\(\sf{68\div4=17}\)

There are 17 seats per row.

Answer:

2121.8 pounds will be in the account after 2 years.

Step-by-step explanation:

Here's the required formula to find the Amount :

\(\star{\small{\underline{\boxed{\sf{\purple{A = P\bigg(1 + \dfrac{R}{100}\bigg)^{T}}}}}}}\)

Substituting all the given values in the formula to find the Amount :

\(\implies{\small{\sf{Amount = P \bigg(1 + \dfrac{R}{100} \bigg)^{T}}}}\)

\(\implies{\small{\sf{Amount = 2000 \bigg(1 + \dfrac{3}{100} \bigg)^{2}}}}\)

\({\implies{\small{\sf{Amount = 2000 \bigg( \dfrac{100 + 3}{100} \bigg)^{2}}}}}\)

\({\implies{\small{\sf{Amount = 2000 \bigg( \dfrac{103}{100} \bigg)^{2}}}}}\)

\({\implies{\small{\sf{Amount = 2000 \bigg( \dfrac{103}{100} \times \dfrac{103}{100}\bigg)}}}}\)

\({\implies{\small{\sf{Amount = 2000 \bigg( \dfrac{103 \times 103}{100 \times 100}\bigg)}}}}\)

\({\implies{\small{\sf{Amount = 2000 \bigg( \dfrac{10609}{10000}\bigg)}}}}\)

\({\implies{\small{\sf{Amount = 2000 \times \dfrac{10609}{10000}}}}}\)

\({\implies{\small{\sf{Amount = 2000 \times 1.0609}}}}\)

\({\implies{\small{\sf{\underline{\underline{\red{Amount = 2121.8}}}}}}}\)

Hence, the amount is 2121.8 pounds.

\(\rule{300}{2.5}\)

Answer:

B

Step-by-step explanation:

To solve this equation you use the y=mx+b format

Considering that the graph starts at 40 (b) and increase 10 every time that means that the m is 10

Sorry that probably made no sense

Answer:

It says “which” so is it multiple choice??

Also a picture would help!!

Answer: 57

Step-by-step explanation:

1. Multiply 95 and 60

2. You get 5700, then you divide by 100

3. 5700/100 = 57

do you want me to make you a box and whisker plot if so then here

Answer:

Step-by-step explanation:

Given quadratic function:

Points on the graph:

Substitute values of x and y and solve the system of equations:

Subtract eq 2 from eq 1:

Subtract eq 2 from eq 3:

Compare eq 4 and eq 5, solve for a:

Find the value of b using eq 4:

Find the value of c using eq 2:

We now have a, b and c:, the function is:

Answer:

y = -3x² + 7x - 9

Step-by-step explanation:

Given quadratic function:

y = ax² + bx + c

Points on the graph:

(-2,-35), (1,-5), (3,- 15)

Substitute values of x and y and solve the system of equations:

-35 = a(-2)² + b(-2) + c ⇒ -35 = 4a - 2b + c   ⇔ eq 1

-5 = a(1)² + b(1) + c ⇒ -5 = a + b + c               ⇔ eq 2

-15 = a(3)² + b(3) + c ⇒ -15 = 9a + 3b + c       ⇔ eq 3

Subtract eq 2 from eq 1:

-35 - (-5) = 4a - 2b + c - a - b - c

-30 = 3a - 3b

b = a + 10                                                         ⇔ eq 4

Subtract eq 2 from eq 3:

-15 - (-5) = 9a + 3b + c - a - b - c

-10 = 8a + 2b

b = -4a - 5                                                       ⇔ eq 5

Compare eq 4 and eq 5, solve for a:

a + 10 = -4a - 5

a + 4a = -5 - 10

5a = -15

a = -3

Find the value of b using eq 4:

b = -3 + 10

b = 7

Find the value of c using eq 2:

-5 = -3 + 7 + c

c = -5 - 4

c = -9

We now have a, b and c:, the function is:

y = -3x² + 7x - 9

Answer:

Diagonal = 9m

Step-by-step explanation:

area of a rectangle=L×W.-----------(I)

L=2W---------------(ii)

from (1)

32=2W×W

32=2W²

W²=32/2

W²=16

W=√16

W=4

from (ii)

length(L)=2W=2(4)=8m

Width(W)=4m

ii)Diagonal of a rectangle involves the use of Pythagoras theorem

Hyp²=opp²+Adj²

Hyp²=8²+4²

Hyp²=64+16

Hyp²=80

Hyp=√80

Hyp=8.94427191

Hyp=9m

:-The diagonal =9m

1. The sum of the x- and y-intercepts of any tangent line to the curve +V-c is equal to x1, which is equal to c.

2. There is no y-intercept for the given function

3. one equation of the tangent line passing through the origin is y = 4x - 2x^2.

4. The equations for two lines through the origin that are tangent to the curve x^2 - 4x + y + 3 = 0 are y = 4x - 2x^2 and y = -x / (x - 2).

1. To show that the sum of the x- and y-intercepts of any tangent line to the curve +V-c is equal to c, let's consider a general tangent line to the curve at a point (x1, y1).

The equation of a tangent line to a curve at a given point (x1, y1) can be written in the point-slope form as:

y - y1 = m(x - x1)

where m is the slope of the tangent line.

The x-intercept of the tangent line can be found by setting y = 0 and solving for x:

0 - y1 = m(x - x1)

x = x1 - y1/m

The y-intercept of the tangent line can be found by setting x = 0 and solving for y:

y - y1 = m(0 - x1)

y = y1 - mx1

The sum of the x- and y-intercepts can be calculated as:

x + y = (x1 - y1/m) + (y1 - mx1)

= x1 - mx1 + y1 - y1/m

= x1(1 - m) + y1(1 - 1/m)

Since the equation of the curve is +V-c, we can substitute y1 = mx1 + c into the equation:

x + y = x1(1 - m) + (mx1 + c)(1 - 1/m)

= x1 - mx1 + mx1 + c - c/m

= x1

Therefore, the sum of the x- and y-intercepts of any tangent line to the curve +V-c is equal to x1, which is equal to c.

2. To find the equation of the tangent line to the hyperbola 1 at the point (x0, y0), we first need to find the derivative of the hyperbola.

The equation of the hyperbola 1 can be written as:

x^2/a^2 - y^2/b^2 = 1

Differentiating both sides with respect to x, we get:

(2x/a^2) - (2y/b^2)(dy/dx) = 0

Simplifying this equation, we find:

dy/dx = (x/a^2) / (y/b^2)

At the point (x0, y0), the slope of the tangent line is given by dy/dx evaluated at that point:

m = (x0/a^2) / (y0/b^2)

Using the point-slope form of a line, the equation of the tangent line is:

y - y0 = m(x - x0)

Substituting the value of m, we have:

y - y0 = [(x0/a^2) / (y0/b^2)](x - x0)

Simplifying this equation gives the equation of the tangent line to the hyperbola 1 at the point (x0, y0).

To find the y-intercept of the function f(x) = (x^3)/(a^2) - (b^3)/(x), we substitute x = 0 into the equation:

y = (0^3)/(a^2) - (b^3)/(0)

= 0 - undefined

The y-intercept of the function is undefined since the term (b^3)/(0) is undefined.

Therefore, there is no y-intercept for the given function.

3. To find the equations for two lines through the origin that are tangent to the curve x^2 - 4x + y + 3 = 0, we first need to find the slope of the tangent line at the point of tangency.

Differentiating the given equation implicitly with respect to x, we get:

2x - 4 + dy/dx + 0 = 0

dy/dx = 4 - 2x

At the point of tangency, the slope of the tangent line is given by dy/dx evaluated at that point.

Setting 4 - 2x equal to the slope of a line passing through the origin, which is given by y/x, we have:

4 - 2x = y/x

Multiplying both sides by x, we get:

4x - 2x^2 = y

So, one equation of the tangent line passing through the origin is y = 4x - 2x^2.

4. To find the second equation, we can use the fact that the product of the slopes of two perpendicular lines is -1. The slope of the tangent line is 4 - 2x, so the slope of the second line is -1/(4 - 2x).

Setting -1/(4 - 2x) equal to the slope of a line passing through the origin, which is given by y/x, we have:

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

Cross-multiplying, we get:

-1x = y(4 - 2x)

-2x = 4y - 2xy

2xy - 4y = -2x

y(2x - 4) = -2x

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

y = -x / (x - 2)

So, the second equation of the tangent line passing through the origin is y = -x / (x - 2).

Therefore, the equations for two lines through the origin that are tangent to the curve x^2 - 4x + y + 3 = 0 are y = 4x - 2x^2 and y = -x / (x - 2).

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If the situation shows an average rate of change that is negative then it means that b. it means that the median age of a man at the time of his first marriage is decreasing.

A negative rate of change means that the variable being investigated is decreasing as time goes on.

As the variable in this case seems to be the median age of a man at the time of his first marriage, it means that this median age is decreasing as time goes on.

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Answer:

if you meant %, the answer is 2016

Step-by-step explanation:

1120 + 80% is 2016

Answer:

The pythagorean theorem would be the most helpful.

To solve this problem:

\(x^2 + 8^2 = 15^2\\x^2 + 64 = 225\\x^2 = 161\\x = \sqrt{161}\)

Answer:

Pythagorean Theorem

Step-by-step explanation:

You want to use Pythagorean Theorem on right degree triangles. Using the formula:

a^2 + b^2= c^2, where a and b are the legs while c is the hypontuse( the slanted side of the triangle and the longest.) let plug in the numbers.

8^2+ x^2=15^2; Subsitution

64+x^2=225: Equalvelent Equation

x^2= 161: Subtraction Poperty of Equality

sqr root of 161= 12.688 or 12.69 or 12.7

x=12.689 ( if rounded to nearest hundredth) or x=12.7 if rounded to nearest tenth.

\(\sqrt{161}\)

The correct answer is the numbers are statistics because the numbers were calculated from a sample of city University of New York students and are estimates.

The study of statistics focuses on gathering, organising, analysing, interpreting, and presenting data. It is customary to initiate with a statistical population or a statistical model to be researched when applying statistics to a scientific, industrial, or social problem.

Populations which can refer to a variety of groupings of individuals or things, such as "every individual living in a nation" or "each atom making up a crystal."

Every facet of data which includes the planning of data collecting in terms of the layout of surveys and experiments, is covered by statistics.

When census data cannot be gathered, statisticians devise specialised experiment designs and survey samples to get data. A representative sample ensures that generalisations and inferences from the sample to the entire population are reasonable.

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Step-by-step explanation:

x + 4/2 x = 3/4 + 2/8 x

3x    = 3/4 + 1/4 x

2  3/4 x = 3/ 4

x = 3/4 / ( 2 /3/4)  = .273      ( or  3/11)

Answer:

the answer is 15

Step-by-step explanation:

Answer:0

Step-by-step explanation:

Answer:

c

Step-by-step explanation:

It was great percentage of a successful out come to get what they wanted, with a unlimited opportunity.

Answer:

c

Step-by-step explanation:

c

The given decimal number rounded to the nearest tenth is 7996.34.

The given decimal number is 7996.33774627.

We need to find round 7996.33774627 to the nearest tenth.

To round a number to the nearest tenth, we need to look to the right of the tenth place, which is the hundredth place. If the digit in the hundredth place is 5 or greater than 5, we need to add one to the digit in the tenth place. If it is 4 or less than 4, the tenth place digit remains the same. All the digits to the right of the tenth place should be changed to 0. That means, while rounding off a number to the nearest tenth, we will stop the rounding at the tenth place.

Now, the decimal number 7996.33774627 rounded to the nearest tenth.

In the decimal number 7996.33774627, the digit in the hundredth place is 7 which is greater than 5.

So, the decimal number is rounded to 7996.34.

Therefore, the given decimal number rounded to the nearest tenth is 7996.34.

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Answer:

1 5/8 is equal to 13/8

Step-by-step explanation:

An economist's use of experiments and real-world data to test a theory is an example of empirical research, which involves gathering data through observation and experimentation to support or refute a hypothesis.

Empirical research is a cornerstone of the scientific method and is used in a wide range of disciplines to explore, understand, and predict natural and social phenomena. In the case of an economist, this might involve conducting a controlled experiment in a laboratory setting or analyzing data from real-world economic transactions to test a hypothesis or theory.

The use of empirical research in economics is important because it provides a way to test and refine economic theories and models, as well as to gain insight into complex economic phenomena. By combining theoretical models with real-world data, economists can develop more accurate and nuanced understandings of economic systems and make informed predictions about future trends. This, in turn, can inform policy decisions and help guide the development of effective economic strategies.

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When two variables are correlated, it means that there is a statistical relationship between them. However, correlation does not necessarily imply causation.

In other words, just because two variables are correlated does not mean that one variable causes the other. There may be other factors or variables that contribute to the relationship between the two variables. To establish causation, a researcher would need to conduct further studies to rule out any confounding variables and establish a clear temporal sequence between the variables. Therefore, researchers cannot be completely sure that one variable causes the other simply based on correlation.                                                                                                                                                            A variable is a quantity that may change within the context of a mathematical problem or experiment. Typically, we use a single letter to represent a variable. The letters x, y, and z are common generic symbols used for variables.

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The volume of the prism shown is equal to 145.89 cubic inches.

In Mathematics and Geometry, the volume of a triangular prism can be determined or calculated by using the following formula:

Volume of triangular prism, V = 1/2 × b × h.

Where:

By substituting the given dimensions (side lengths) into the formula for the volume of a triangular prism, we have;

Volume of triangular prism, V =  1/2 × 5.27 × 8.13 × 6.81

Volume of triangular prism, V = 291.775131/2

Volume of triangular prism, V = 145.89 cubic inches.

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The volume of the prism is 145.89 cubic inches.

To find the volume of a prism, multiply the area of the base by the height of the prism.

We know the formula for the volume of a triangular prism is:

\(V = \frac{1}{2}\times b \times h\)

Where:

b represent the base area of a triangular prism.

h represent the height of a triangular prism.

Therefore, we can calculate the volume of the prism by cubing the length of one of its sides:

\(V = \frac{1}{2}\times 5.27\times 8.13 \times 6.81\)

\(V= \frac{291.775131}{2}\)

\(V = 145.89\) cubic inches.

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If a storage facility charges $1 per cubic yard and the storage space is 32 ft. The storage charge is $1999.97.

What is mathematical conversions?

Mathematical conversions refer to the process of changing one unit of measurement to another unit of measurement that is equivalent in value.

First, we need to convert the dimensions from feet to yards, since the rate is given per cubic yard.

32 feet = 10.6667 yards (dividing by 3)

160 feet = 53.3333 yards (dividing by 3)

10 feet = 3.3333 yards (dividing by 3)

Next, we can calculate the volume of the storage space in cubic yards by multiplying the three dimensions:

Volume = 10.6667 yards x 53.3333 yards x 3.3333 yards

Volume = 1999.97 cubic yards (rounded to two decimal places)

Finally, we can calculate the storage charge by multiplying the volume by the rate:

Charge = 1999.97 cubic yards x $1/cubic yard

Charge = $1999.97

Therefore, the storage charge is $1999.97.

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