Approximate the area with a trapezoid sum of 5 subintervals. For comparison, also compute the exact area. 1 1) y=-; [-7, -2] X

Answer:

1 third

Step-by-step explanation:

Have a blessed day!

The equation of the line is (y + x = 0).

The slope of a line indicates its steepness in addition to its direction.

m = Δy/Δx

where, m is the slope

And, tan θ = Δy/Δx

The above tan is also known as the line's slope.

The slope of a line can also be calculated just using two straight line points. The slope of line formula could then be used with two point coordinates.

Now, in response to the question;

P₁ = (x₁, y₁)

P₂ = (x₂, y₂)

Then slope will be;

Slope = m = tan θ = (y₂ - y₁)/(x₂ - x₁)

Consider the values given in the question;

(x₁, y₁) = (-1,-3) and,

(x₂, y₂) = (1,-5).

Put the values in the formula of the slope;

Slope = m = (-5 + 3)/(1 + 1)

m = -2/2

m = -1

Thus, the slope of the line is -4.

Now, the formula for finding the equation of line using the two points system.

(y - y₁) = m(x - x₁)

(y + 3) = (-1)(x + 1)

y + 3 = -x - 1

y + x + 4 = 0.

Therefore, the equation of the line using two point system is calculated as (y + x = 0).

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The missing portions of the proof are:

2) ∠4 ≅ ∠1 ; ∠3≅∠2 - Corresponding Angles Theorem

3) CDB ≅CEA           -     AA Similarity

The other information that could have been stated to proof that Angle - Angle similarity is: Angle C ≅ angle C

Reflexive Property

The reflexive property of equality in algebra asserts that a number is always equal to itself. Equality has a reflexive attribute. If an is a positive integer, then a = a.

When two parallel lines cross by any other line (i.e. the transversal), corresponding angles are generated in matching corners or corresponding angles with the transversal.

So in the above proof, ∠4 ≅ ∠1 ; ∠3≅∠2 because they are a pair of corresponding angels because they are created in matching corners.

Looking at the shape, we can see that CDB  and CEA   are triangles since we have established that their angles are similar, hence, the Angle Angle Similarity postulate.

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To the nearest whole number, the probability of rolling a 2 and a 4 is 2.8%.

A 2 rolling up on the first throw has a 1/6 chance of happening. Given that a 2 was rolled on the first throw, the likelihood of rolling a 4 on the second throw is equally 1/6. We will have to multiply the probabilities to get the probability of both the events happening,

= (1/6)x(1/6)

= 1/36.

We get 2.8% after converting to a percentage and rounding to the next full amount. So, the chance of rolling a 2 and then a 4 is found to be 2.8% chance.

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The licensee's monthly sales must be $54,000 for them to receive a total monthly income of $2,220.

To determine the monthly sales required for the licensee to receive a total monthly income of $2,220, we need to break down the components of the income.

Let's assume the total monthly sales amount to be x.

The licensee's income consists of two parts:

1. A salary of $600 per month.

2. Half of the office's 6% fee on all sales.

The office's fee on all sales can be calculated as (6/100) * x = 0.06x.

Therefore, the licensee's income from the office's fee on all sales is (1/2) * 0.06x = 0.03x.

Adding the salary and the income from the office's fee, the licensee's total monthly income is given by:

$600 + 0.03x = $2,220.

To find the value of x, we need to solve this equation:

0.03x = $2,220 - $600,

0.03x = $1,620.

Dividing both sides by 0.03, we get:

x = $1,620 / 0.03,

x = $54,000.

Therefore, the licensee's monthly sales must be $54,000 for them to receive a total monthly income of $2,220.

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The licensee's monthly sales must reach $54,000 for the licensee to receive a total monthly monthly income of $2,220. This is determined by subtracting the licensee's base salary from the total desired income and calculating the sales that would result in the remaining amount as half the 6% sales fee.

To determine the licensee's monthly sales for the licensee to receive a total monthly income of $2,220, we must first deduce the part of the income that comes from the licenses' share of the 6% fee on sales.

To do this, we subtract the licensee's base salary, which is $600, from the total desired income of $2,220. This gives us $2,220 - $600 = $1,620.

Since this $1,620 represents half of the 6% fee on sales, it means the full 6% of sales is $1,620 * 2 = $3,240. From this, we can calculate the actual sales since we know that 6% of the sales is equal to $3,240.

Therefore, to find the total sales, we divide $3,240 by 0.06 (which is 6% in decimal form). That gives us $3,240 / 0.06 = $54,000.

So, the licensee's monthly sales must be $54,000 for the licensee to receive a total monthly income of $2,220.

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Using the t-distribution, as we have the standard deviation for the sample, the 95% confidence interval is (71.63, 84.36).

The confidence interval is:

\(\overline{x} \pm t\frac{s}{\sqrt{n}}\)

In which:

The critical value, using a t-distribution calculator, for a two-tailed 95% confidence interval, with 4 - 1 = 3 df, is t = 3.1824.

The parameters are given as follows:

\(\overline{x} = 78, s = 10, n = 4\)

Hence, the bounds of the interval are given by:

\(\overline{x} - t\frac{s}{\sqrt{n}} = 78 - 3.1824\frac{10}{\sqrt{4}} = 71.63\)

\(\overline{x} + t\frac{s}{\sqrt{n}} = 78 + 3.1824\frac{10}{\sqrt{4}} = 84.36\)

The 95% confidence interval is (71.63, 84.36).

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Answer:

(62.09, 93.91)

Step-by-step explanation:

The correct answer on Khan

The solution of the given problem of probability comes out to be

a)0.35

b)0.3625

c)0.23125

The primary objective of statistical inference, a branch of mathematics, is to determine the chance that a claim is true or that a specific event will occur. Chance integers can be represented by any number between 0 and 1, for which 1 typically represents certainty and 0 typically represents possibility. A probability diagram shows the chance that a specific event will occur.

Here,

(a) we can compute the integral of f(x) over the entire real line:

integral from -infinity to infinity of f(x) dx

= integral from -infinity to 3 of 0 dx + integral from 3 to 5 of (0.075x + 0.2) dx + integral from 5 to infinity of 0 dx

= (0.075/2)x² + 0.2x, evaluated from x=3 to x=5

= (0.075/2)(5²- 3²+ 0.2(5 - 3)= 0.35

Since the integral of f(x) over the entire real line is equal to 1, we have verified that the total area under the density curve is indeed 1.

(b) To calculate P(X ≤ 4), we can integrate the density function from x = 3 to x = 4:

P(X ≤ 4) = integral from 3 to 4 of (0.075x + 0.2)

dx = (0.075/2)x² + 0.2x,

evaluated from x=3 to x=4

= 0.3625

To compare this probability to P(X & lt; 4),

we can integrate the density function from x = 3 to x = 4:

P(X < 4) = integral from 3 to 4 of (0.075x + 0.2)

dx = (0.075/2) x²+ 0.2x,

evaluated from x=3 to x=4

= 0.3625

Since P(X ≤ 4) = P(X < 4) in this case, the two probabilities are equal.

(c) To calculate P(3.5 ≤ X ≤ 4.5), we can integrate the density function from x = 3.5 to x = 4.5:

P(3.5 ≤ X ≤ 4.5) = integral from 3.5 to 4.5 of (0.075x + 0.2)

dx = (0.075/2)x²+ 0.2x,

evaluated from x=3.5 to x=4.5

= 0.26875

To calculate P(X > 4.5), we can integrate the density function from x = 4.5 to x = 5:

P(X > 4.5) = integral from 4.5 to 5 of (0.075x + 0.2)

dx = (0.075/2)x²+ 0.2x,

evaluated from x=4.5 to x=5 = 0.23125

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Since, h(x) be an antiderivative of x3+sinxx2+2. if h(5) = π, then,

h(2) = (1/4)(2)⁴ - (1/2)√π erf(2√π/2) + 2(2) + C

In order to find the value of h(2), we can use the given information that h(x) is an antiderivative of the function x³ + sin(x²) + 2 and that h(5) is equal to π. By evaluating h(5), we can determine a relationship between h(x) and x³ + sin(x²) + 2. Then, we can use this relationship to calculate h(2).

To evaluate h(5), we can substitute x = 5 into the expression x³ + sin(x^2) + 2 and integrate it. The antiderivative of x³ is (1/4)x⁴, and the antiderivative of sin(x²) is (-1/2)√π erf(x√π/2), where erf represents the error function. However, since h(x) is an antiderivative of x³ + sin(x²) + 2, the constant term is included as well. So, we have h(x) = (1/4)x^4 - (1/2)√π erf(x√π/2) + 2x + C, where C is the constant of integration.

Given that h(5) = π, we can substitute x = 5 and π into the equation above to obtain π = (1/4)(5)⁴ - (1/2)√π erf(5√π/2) + 2(5) + C. Simplifying the equation, we can solve for C.

Now that we have the value of C, we can determine h(2) by substituting x = 2 into the expression for h(x).

Thus, h(2) = (1/4)(2)⁴ - (1/2)√π erf(2√π/2) + 2(2) + C. Plugging in the known values and the calculated value of C, we can compute the numerical result for h(2).

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the sum x + y is at least 20. We can achieve this lower bound by choosing x = y = 10, since then xy = 100 and x + y = 20. This is the smallest possible value of the sum, so the two positive numbers are 10 and 10.

Let x and y be the two positive numbers whose product is 100, so xy = 100. We want to find the smallest possible value of x + y.

Using the AM-GM inequality, we have:

x + y ≥ 2√(xy) = 2√100 = 20

what is numbers?

Numbers are mathematical objects used to represent quantity, value, or measurement. There are different types of numbers, including natural numbers (1, 2, 3, ...), integers (..., -3, -2, -1, 0, 1, 2, 3, ...), rational numbers (numbers that can be expressed as a ratio of two integers), real numbers (numbers that can be represented on a number line), and complex numbers (numbers that include a real part and an imaginary part).

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The total interest you will earn in 30 years is approximately $241.61.

To calculate the total interest earned in 30 years, we need to use the formula for compound interest:
A = P(1 + r/n)^(nt) - P
Where:
A = the future value of the investment
P = the principal amount (initial deposit)
r = the annual interest rate (in decimal form)
n = the number of times the interest is compounded per year
t = the number of years
In this case, the principal amount is $200, the annual interest rate is 3% (or 0.03 as a decimal), the interest is compounded monthly (so n = 12), and the time period is 30 years (so t = 30).
Plugging in these values into the formula:
A = 200(1 + 0.03/12)^(12*30) - 200
Now we can simplify and calculate:
A = 200(1.0025)^(360) - 200
A = 200(2.208040033) - 200
A ≈ 441.6080066 - 200
A ≈ 241.6080066

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Answer:

786cm

Step-by-step explanation:

this should be right... hopefully

Answer:

Answer: 1) 155.65 kJ; 2) -59.0 kJ/mol; 3) a)

Step-by-step explanation:

Answer on Question # 55533 - Chemistry - General chemistry

Question:

1. Given the data. N2(g) + O2(g) = 2 NO(g) ΔH = +180.7 kJ; 2 NO(g) + O2(g) = 2 NO2(g) ΔH = −113.1

kJ; 2 N2O(g) = 2 N2(g) + O2(g) ΔH = − 163.2 kJ; Use Hess’s Law to calculate ΔH for the reaction

N2O(g) + NO2(g) = 3 NO(g); Show your work.

2. Calcium carbide (CaC2) reacts with water to form acetylene (C2H2) and Ca(OH)2. From the

following enthalpy of reaction data and data in Appendix C in textbook, calculate ΔHf° for CaC2(s):

CaC2(s) + 2 H2O(l) Ca(OH)2(s) + C2H2 (g) ΔH = −127.2kJ

3. Using average bond enthalpies, predict which of the following reactions will be most

exothermic: a) C(g) + 2 F2(g) CF4(g) b) CO(g) +3 F2(g) CF4(g) + OF2(g) c) CO2(g) + 4 F2(g) CF4(g) +

2 OF2(g)

Solution

1)

N2(g) + O2(g) = 2 NO(g) ΔH1 = +180.7 kJ x(+2)

2 NO(g) + O2(g) = 2 NO2(g) ΔH2 = −113.1 kJ x(-1)

2 N2O(g) = 2 N2(g) + O2(g) ΔH3 = − 163.2 kJ x(+1)

2N2O(g) + 2NO2(g) = 6 NO(g) ΔH = (ΔH3 + 2ΔH1 – ΔH2)

N2O(g) + NO2(g) = 3 NO(g) ΔH = (ΔH3 + 2ΔH1 – ΔH2)/2 = 155.65 kJ

2)

CaC2(s) + 2 H2O(l) = Ca(OH)2(s) + C2H2 (g) ΔHrxn = −127.2kJ

ΔHrxn = ΔHf°(C2H2) + ΔHf°(Ca(OH)2) - 2ΔHf°(H2O) - ΔHf°(CaC2);

ΔHf°(CaC2) = ΔHf°(C2H2) + ΔHf°(Ca(OH)2) - 2ΔHf°(H2O) – ΔHrxn

ΔHf°(C2H2) = 227.4 kJ/mol

ΔHf°(Ca(OH)2) = -985.2 kJ/mol

ΔHf°(H2O) = -285.8 kJ/mol

ΔHf°(CaC2) =227.4 - 985.2 + 2x285.8 + 127.2 = -59.0 kJ/mol

3)

a) C(g) + 2 F2(g) = CF4(g)

b) CO(g) +3 F2(g) = CF4(g) + OF2(g)

c) CO2(g) + 4 F2(g) = CF4(g) + 2 OF2(g)

C-F bond enthalpy 440 kJ/mol

C=O bond enthalpy in carbon dioxide 805 kJ/mol

C=O bond enthalpy in carbon monoxide 1077 kJ/mol

O-F bond enthalpy 184 kJ/mol

F-F bond enthalpy 153 kJ/mol

a) ΔHrxn = 2x153 - 4x440 = -1454 kJ – the most exothermic

b) ΔHrxn = 1077 + 3x152 - 2x184 - 4x440 = -595 kJ

c) ΔHrxn =805x2 + 4x153 - 4x440 – 2x2x184 = -274 kJ

Answer:

36/19

Step-by-step explanation:

So to find this answer you have to divide 12 by 6 1/3. To figure that out I first turned 6 1/3 into an improper fraction (19/3) and then I put 12 over 1. To divide a fraction you have to multiply the dividend by the divisors reciprocal in this case 12/1 x 3/19 which equals 36/19 or 1 and 17/19

Hope this helps lol :D

Geological timeline is based on the presence of fossils on the rocks of various sequences, and also the classification of rock types and the correlation of rocks of different locations.

The purpose that geological timeline serve and reason scientist do make it, is portray the history of the Earth.

Therefore, geologic time scale serves as events as regards Earth history.

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The classification of rock types, the correlation of rocks from diverse locations, and the presence of fossils on the rocks of distinct sequences are all used to create the geological timeline.

Geological timelines have a purpose, and scientists create them in order to depict Earth's history.

(A) The relationship between geological strata and events based on chronological time can be shown using a geological timeline.

(B) The scientist can use this information to investigate events and their frequency and determine whether there is a possibility that a specific event will occur again.

(C) A sun eclipse, which often happens at some point in time, could serve as an illustration of this occurrence.

(D) Rocks and fossils that depict Earth's past can be found thanks to the geologic time scale.

(E) As a result, the geologic time scale provides information about historical events on Earth.

Therefore, the classification of rock types, the correlation of rocks from diverse locations, and the presence of fossils on the rocks of distinct sequences are all used to create the geological timeline.

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Answer:

y=1/2.5x+10

Step-by-step explanation:

if function = -4, then x can be any value in the domain of the function f. However, without knowing the specific form of the function f, we cannot determine a unique value of x that corresponds to f(x) = -4.

This equation can be read as "the value of the function f at x is equal to -4" if function = -4. In other words, if we plug in some value of x into the function f, we get -4 as the output.

To find the value of x that corresponds to f(x) = -4, we need to solve for x. We can do this by setting f(x) equal to -4 and solving for x:

f(x) = -4

-4 = -4 (since we know that f(x) = -4)

Therefore, x can be any value in the domain of the function f. In other words, any value of x that we plug into the function f will give us an output of -4. This means that there are infinitely many possible values of x that satisfy f(x) = -4.

In conclusion, if f(x) = -4, then x can take on any value within the function f's domain. However, without knowing the specific form of the function f, we cannot determine a unique value of x that corresponds to f(x) = -4.

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Answer:

$142,857.14

Step-by-step explanation:

As per the question,

Solving for Y

Answer:

0.45 miles per minute and 6.75

Step-by-step explanation:

27/60=0.45<-- Miles per minute

0.45x15=6.75<--Miles in 15 minutes

Hope this helps pls give brainliest

Given:

Vertex: (-3, 3)

Focus: (-3, 2)

Let's find the distance from the point (x, y) to the focus of the parabola and the directrix.

To find the distance, apply the distance formula:

Thus, we have:

Distance from (x, y) to the focus:

Where:

(x1, y1) ==> (x, y)

(x2, y2) ==> (-3, 2)

Thus, we have:

Therefore, the distance from the point (x, y) to the focus is:

• The distance from the point to the directrix.

From the graph, the directrix is:

y = 4

Now, to find the distance, subtract the y-coordinate of the point from y = 4.

The distance is the absolute value of the result.

Thus, we have:

ANSWER:

Distance from the point to the focus:

Distance from the point to directrix:

Answer:

\(9\frac{1}{4}\) inches and 23.5 cm

Step-by-step explanation:

A student uses ruler to measure the length of their foot.

Given measurements are,

\(9\frac{1}{4}\) inches

\(9\frac{5}{64}\) inches

23.47659 cm

23.5 cm

23.48 cm

Most appropriate measurement that we can measure by a ruler is up to single decimal place.

Inches can be measured appropriately in quarters or halves also.

Therefore, \(9\frac{1}{4}\) inches and 23.5 cm are the correct options.

Answer:

Q = { (x,y) : (0,0), (1,2), (2,16), (3, 54), (4, 128), (5,250) } is cubic

R= { (x,y) : (2,3), (4,4), (6,5), (8,6) } is linear

S = { (x,y), : (1,3), (2,9), (3,17), (4,27), (5, 39), (6,53) } is quadratic

Equation of the linear relation is

y = 0.5x + 2

Step-by-step explanation:

A linear equation has the form y = mx + b where m is the slope and b is the y-intercept. Slope is a constant and growth of function is determined by x value

A quadratic equation has the general form y = ax² + bx + c where a b and c are constants. Growth of the function is mostly determined by the square of x

A cubic equation has the general form y = ax³ + bx² + cx + d where a, b and c are constants. The growth of the function is mostly determined by the cube of x value

Looking at the three relations

#1 is obviously cubic since the value of y appears to be determined by the cube of the value of x. Specifically, when x = 0, y = 0/. When x =1, y = 2 but when x =2, y =16 and 16 is 2x³ = 2(2³) = 2 x 8

Looking at x =3, 2(3³) = 2(27) = 54

So this is a cubic function

#2 is obviously a linear function When x increases by 2, y increases by 1 so it is a linear growth

#3 In this equation we can see that the y value appears to be controlled by the square of x. The specific equation is y = x² + 3x -1

For the linear equation, find the slope from the first two points

m = (4-3)/(4-2) = 1/2 = 0.5

So the equation is y = 0.5x + b

To find b, use the coordinates of any point. Let's choose (4,4)

At x = 4, y = 4 so

4 = (0.5)4 + b = 2+b yielding b = 2

So the equation is y = 0.5x + 2

Relation Q is not linear, relation R is linear with the equation y = (1/2)x + 2, and relation S is not linear.

1: Q = { (0,0), (1,2), (2,16), (3,54), (4,128), (5,250) }

To determine if this relation is linear, quadratic, or cubic,

Examine the differences between the y-values.

Calculate the differences for the given data:

Difference in y-values:

(2-0) = 2

(16-2) = 14

(54-16) = 38

(128-54) = 74

(250-128) = 122

Looking at the differences,

we can see that they are not constant.

In a linear relation, the differences between the y-values would be constant.

Therefore, we can conclude that this relation is not linear.

2: R = { (2,3), (4,4), (6,5), (8,6) }

Similar to the previous relation, let's calculate the differences:

Difference in y-values:

(4-3) = 1

(6-4) = 2

(8-6) = 2

In this case, the differences between the y-values are constant

(both are 2). This indicates a linear relation.

To find the equation, we can use the slope-intercept form (y = mx + b). Let's choose any two points from the relation, for example, (2,3) and (4,4):

Slope (m) = (4-3) / (4-2) = 1/2

m = 1/2

Now, let's plug in the values of one point (2,3) and the slope into the equation:

y = mx + b

3 = (1/2) x 2 + b

3 = 1 + b

b = 2

Therefore, the equation for this linear relation is y = (1/2)x + 2.

3: S = { (1,3), (2,9), (3,17), (4,27), (5,39), (6,53) }

Again, calculate the differences:

Difference in y-values:

(9-3) = 6

(17-9) = 8

(27-17) = 10

(39-27) = 12

(53-39) = 14

The differences between the y-values are not constant, indicating that this relation is not linear.

Hence,

Relation Q is not linear.

Relation R is linear, with the equation y = (1/2)x + 2.

Relation S is not linear.

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9514 1404 393

Answer:

  perpendicular

Step-by-step explanation:

A graph shows the lines are not parallel. The lines are perpendicular.

__

j has a slope of -2/3 (down 2 for each 3 to the right)

k has a slope of 3/2 (up 3 for each 2 to the right)

These slope values have a product of 1, typical of perpendicular lines.

Answer:

D. 136

Step-by-step explanation:

Answer:

Step-by-step explanation:

lets solve the inequality by adding like terms

-2x-5>0 ?

-2x>5

x>-5/2

Part A: Rebecca's credit card balance can be calculated using the equation x = (51 - 1) 0.02 if her finance charge is $51.

Part B: By making the purchase on the final day of the billing cycle rather than the first day, Rebecca will be able to avoid paying $27 in finance charges.

How do equations work?

A mathematical statement proving the equality of values between two or more mathematical expressions is called an equation.

Equation symbols (=) are used to represent equations.

A finance charge is what?

The interest and other fees levied on credit cards are included in a finance charge.

Typically, the finance charge is based on a stated APR (annual percentage rate).

The month's billing cycle lasts for 28 days.

Balance at current starting = x.

APR = 24%, or annual percentage rate.

The monthly percentage rate (MPR) equals 2% (24% divided by 12).

The final day's purchase cost $1,400.

$51 is the total finance fee for the month.

($1,400 x 2% x 1/28) = $1 finance fee for the last-minute purchase.

$50 ($51 - $1) serves as the initial balance's finance charge.

The starting balance at this time is x = $2,500 ($50 x 2%).

Current Beginning Balance Equation: x = 51 - 1 0.02

($1,400 x 2%) Equals $28 in total loan charges for the last-minute purchase.

Finance charge savings from buying on the last day equals $27 ($28 - $1).

By buying the $1,400 gift for her friend on the last day of the billing cycle rather than the first, Rebecca can avoid paying $27 in finance charges.

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