Suggest an alternative method we can use to determine the equivalence point if you could not use a colorimetric indicator.

In the congruent triangles; ΔABC and ΔBDE, ∠ABC  = ∠DBE by CPCT that is Corresponding parts of Congruent Triangle.

So,

ΔABC and ΔBDE, are congruent  triangles

Thus,

∠ABC  = ∠DBE (Corresponding parts of Congruent Triangle) CPCT.

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The domain of the function g(x) = √x - 4 as an inequality is x ≥ 0.

The domain of a function is simply the set of all possible inputs for the function.

Given the function in the question;

g(x) = √x - 4

Domain: ?

To determine the domain of the function, set the radicand in √x to greater than or equal to 0 and find where the expression is defined,

x ≥ 0

Hence, the domain is all values of x that makes the expression defined.

Interval notation: [0,∞)

Set-Builder notation or inequality : { x|x ≥ 0 }.

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The most likely to watch TV for 4 hours is distribution B. Therefore, option B is the correct answer.

In statistics, a simple random sample is a subset of individuals chosen from a larger set in which a subset of individuals are chosen randomly, all with the same probability. It is a process of selecting a sample in a random way.

Given that, average number of hours American adults watch TV is 4 hours.

In distribution A, B, C and D, the most likely to watch TV for 4 hours is distribution B and less likely to watch TV for 4 hours is distribution A.

Therefore, option B is the correct answer.

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Answer:#

Step-by-step explanation:

Answer: 5 is 1/4 meaning 25%

Step-by-step explanation:

I think this is what you meant to ask... HOPE THIS HELPS U

The area of a 40° sector of this circle is 4m², the correct option is D.

Suppose the circle has radius of 'r' units, then, its area is given as:

[tex]A = \pi \times r^2[/tex]

sq. units

Since radius of a circle is half of its diameter, so if diameter is of 'd' length, then r= d/2, thus, area can be rewritten as:

[tex]A = \pi \times r^2[/tex]

sq. units

Given;

A circle has an area of 36 m².

Now,

40° of circle= 360/40=9

Area of circel;

=36/9

=4

Therefore, the area of 40° of circle will be 4m^2

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Answer:

Step-by-step explanation:

Percentage of girls = 35%

Percentage of boys = 100 - 35 = 65%

There are 910 boys:

65% = 910

Find the number of students in the school:

1% = 910 ÷ 65 = 14

100% = 14 x 100 = 1400

Answer: There are 1400 students in the school

Answer: Let's call the speed of the plane in still air "p" and the speed of the wind "w".

When flying with the wind, the plane's speed is increased by the wind speed, so the equation is:

359 = p + w

When flying against the wind, the plane's speed is decreased by the wind speed, so the equation is:

337 = p - w

We can add these two equations to eliminate "p":

696 = 2p

So,

p = 348

Now that we know the speed of the plane in still air, we can use either equation to find the speed of the wind:

w = 359 - p = 359 - 348 = 11 km/h.

So, the speed of the plane in still air is 348 km/h and the speed of the wind is 11 km/h.

Step-by-step explanation:

The solution is, 128 students are in Miss Oliver’s class. 4 students are in each team.

The ratio is defined as the comparison of two quantities of the same units that indicates how much of one quantity is present in the other quantity.

here, we have,

given that,

Each team has the same number of students.

let , each team has x students.

The ratio of teams to players is 8 : 32.

again, let, no. of teams = 8y

no. of players = 32y

so, we get,

8y*x = 32y

so, x = 4

Hence, The solution is, 128 students are in Miss Oliver’s class. 4 students are in each team.

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The percent tip Ruby left was 27%.

What is percent?

A percentage is a quantity or ratio that is stated as a fraction of one hundred. The percent sign, "%," is frequently used to represent it.

Calculate the tip amount:

The total cost of the meal including the tip is $34.29, and the cost of the meal before the tip is $27. Therefore, the tip amount is:

Tip = Total cost - Cost of meal

Tip = $34.29 - $27

Tip = $7.29

Calculate the percent tip:

The percent tip is the tip amount divided by the cost of the meal, multiplied by 100 to express the result as a percentage:

Percent tip = (Tip / Cost of meal) x 100%

Percent tip = ($7.29 / $27) x 100%

Percent tip = 27%

Therefore, the percent tip Ruby left was 27%.

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Answer:

the correct responses are:

The graph will have a vertical asymptote at x = π/2.

The graph will have a vertical asymptote at x = 3π/2.

The graph will have a vertical asymptote at x = 2π.

The graph will not go through the point (π/4, 1).

Step-by-step explanation:

The statements that are true about the graph of f(x) = cot(x) are:

The graph will have a vertical asymptote at x = π/2.

The graph will have a vertical asymptote at x = 3π/2.

The graph will have a vertical asymptote at x = 2π.

These are true because the cotangent function has vertical asymptotes at every odd multiple of π/2, which includes π/2, 3π/2, and 5π/2, and so on.

The statement that the graph will go through the point (π/4, 1) is false. The cotangent function does not pass through this point, although it does have a vertical asymptote at x = π/4.

Therefore, the correct responses are:

The graph will have a vertical asymptote at x = π/2.

The graph will have a vertical asymptote at x = 3π/2.

The graph will have a vertical asymptote at x = 2π.

The graph will not go through the point (π/4, 1).

Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation:

Expanding (x + y)^2, we get:

(x + y)^2 = x^2 + 2xy + y^2

We are given that xy/2 = 7, so 2xy = 14. We are also given that x^2 + y^2 = 28. Substituting these values, we get:

(x + y)^2 = x^2 + 2xy + y^2 = x^2 + y^2 + 2xy = 28 + 14 = 42

Therefore, (x + y)^2 = 42.

a) (i) Average velocity = -96.8 ft/s

   (ii) Average velocity = -95.2 ft/s

   (iii) Average velocity = -92.8 ft/s

b) The instantaneous velocity of the pebble after 3 seconds is approximately -96 ft/s.

What is average velocity?

The change in position or displacement (x) divided by the time intervals (t) in which the displacement happens yields the average velocity. Depending on the sign of the displacement, the average velocity can be positive or negative.

(a)

(i) The time period from t = 3 to t = 3.1 is 0.1 seconds. The average velocity of the pebble during this time period can be found by taking the difference in position (y) divided by the difference in time (t).

Average velocity = (y(3.1) - y(3)) / (3.1 - 3)

Substituting [tex]y = 225 - 16t^2[/tex], we get:

[tex]Average\ velocity = [(225 - 16(3.1)^2) - (225 - 16(3)^2)] / (0.1)[/tex]

Average velocity = -96.8 ft/s (rounded to one decimal place)

(ii) The time period from t = 3 to t = 3.05 is 0.05 seconds. The average velocity of the pebble during this time period can be found using the same formula as above:

[tex]Average\ velocity = (y(3.05) - y(3)) / (3.05 - 3)[/tex]

Substituting [tex]y = 225 - 16t^2[/tex], we get:

[tex]Average\ velocity = [(225 - 16(3.05)^2) - (225 - 16(3)^2)] / (0.05)[/tex]

Average velocity = -95.2 ft/s (rounded to one decimal place)

(iii) The time period from t = 3 to t = 3.01 is 0.01 seconds. The average velocity of the pebble during this time period can be found using the same formula as above:

Average velocity = (y(3.01) - y(3)) / (3.01 - 3)

Substituting [tex]y = 225 - 16t^2[/tex], we get:

[tex]Average \ velocity = [(225 - 16(3.01)^2) - (225 - 16(3)^2)] / (0.01)[/tex]

Average velocity = -92.8 ft/s (rounded to one decimal place)

(b)

The instantaneous velocity of the pebble at any given time t can be found by taking the derivative of the position function y(t) with respect to time:

[tex]\frac{dy}{dt} =-32t\\[/tex]

Substituting t = 3, we get:

[tex]\frac{dy}{dt} =-96ft/s\\[/tex]

Therefore, the instantaneous velocity of the pebble after 3 seconds is approximately -96 ft/s.

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Answer: A

hope this helped

a) To find the probability that at least one of the dice is a 5, we can count the number of outcomes where this is true and divide by the total number of outcomes. There are 11 outcomes where at least one die is a 5: (1,5), (2,5), (3,5), (4,5), (5,1), (5,2), (5,3), (5,4), (5,5), (5,6), (6,5). Therefore, the probability is:

P(at least one 5) = 11/36

b) To find the probability that the sum of the dice is equal to 7, we can count the number of outcomes where this is true and divide by the total number of outcomes. There are 6 outcomes where the sum is 7: (1,6), (2,5), (3,4), (4,3), (5,2), (6,1). Therefore, the probability is:

P(sum is 7) = 6/36 = 1/6

c) To find the probability that the sum of the dice is 11 or more, we can count the number of outcomes where this is true and divide by the total number of outcomes. There are 2 outcomes where the sum is 11 or more: (5,6), (6,5). Therefore, the probability is:

P(sum is 11 or more) = 2/36 = 1/18

d) To find the probability that both dice are less than 3, we can count the number of outcomes where this is true and divide by the total number of outcomes. There is only 1 outcome where both dice are less than 3: (1,1). Therefore, the probability is:

P(both less than 3) = 1/36

e) To find the probability that the red die is larger than the green die, we can count the number of outcomes where this is true and divide by the total number of outcomes. There are 15 outcomes where the red die is larger than the green die: (2,1), (3,1), (3,2), (4,1), (4,2), (4,3), (5,1), (5,2), (5,3), (5,4), (6,1), (6,2), (6,3), (6,4), (6,5). Therefore, the probability is:

P(red is larger) = 15/36 = 5/12

f) To find the probability that the sum of the dice is greater than 9, we can count the number of outcomes where this is true and divide by the total number of outcomes. There are 4 outcomes where the sum is greater than 9: (4,6), (5,5), (5,6), (6,4), (6,5), (6,6). Therefore, the probability is:

P(sum is greater than 9) = 6/36 = 1/6

g) To find the probability that the red die is 6, we can count the number of outcomes where this is true and divide by the total number of outcomes. There are 6 outcomes where the red die is 6: (6,1), (6,2), (6,3), (6,4), (6,5), (6,6). Therefore, the probability is:

P(red = 6) = 6/36 = 1/6

h) To find the probability that the largest number rolled is 5, we can count

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Given the planes [tex]4x-5y+z=4[/tex] and [tex]5x-4y+3z=-2[/tex], find the angle between them.

Using the formula,

[tex]\theta=cos^{-1} (\frac{A_{x}B_{x}+A_{y}B_{y}+A_{z}B_{z} }{\sqrt{A^2_{x}+A^2_{y}+A^2_{z}}\sqrt{B^2_{x}+B^2_{y}+B^2_{z}} } )[/tex]

Where vector, [tex]A= < 4,-5,1 >[/tex] and vector [tex]B= < 5,-4,3 >[/tex].

Plug these values into the formula above...

[tex]\Longrightarrow \theta=cos^{-1} (\frac{A_{x}B_{x}+A_{y}B_{y}+A_{z}B_{z} }{\sqrt{A^2_{x}+A^2_{y}+A^2_{z}}\sqrt{B^2_{x}+B^2_{y}+B^2_{z}} } )[/tex]

[tex]\Longrightarrow \theta=cos^{-1} (\frac{(4)(5)+(-5)(-4)+(1)(3) }{\sqrt{(4)^2+(-5)^2+(1)^2}\sqrt{(5)^2+(-4)^2+(3)^2} } )[/tex]

[tex]\Longrightarrow \theta=cos^{-1} (\frac{43 }{\sqrt{42}\sqrt{50} } )[/tex]

[tex]\Longrightarrow \theta=cos^{-1} (\frac{43 }{10\sqrt{21} } )[/tex]

[tex]\Longrightarrow \theta \approx 20.2\textdegree[/tex]

The correct symbol forms are:

a)  x ≥ 7 is equivalent to  p v q

b) 11 > x > 7 is equivalent to p ∧ r

c)  11 > x ≥ 7 is equivalent to  ( p v q) ∧ r

We have the following definitions:

p = "x > 7"

q = "x = 7"

r = "11 > x"

a) The statement "x ≥ 7" is true if x is greater than 7 or if x is equal to 7. In other words, "x > 7 or x = 7" must be true. Using the given definitions, we can see that this is equivalent to p v q.

b) 11 > x > 7.  The statement "7 < x < 11" means that x is greater than 7 and less than 11. In other words, both "x > 7" and "x < 11" must be true. hence, it can be expressed as the conjunction of "x > 7" and "x < 11," which is equivalent to p ∧ r.

c) 11 > x ≥ 7. Combining answer from part a and b, this is equivalent to:

  ( p v q) ∧ r

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The answer is C) 6 units of consumption goods.

What is Cost of producing?

The overall cost incurred by a business to manufacture a product or provide services is referred to as the cost of production. Supplies and raw materials consumed during production, as well as labor costs, are often included in production costs.

The opportunity cost of producing 3 units of capital is 6 units of consumption goods, as we can see from the data in the production possibilities curve.

Moving from producing 4 units of capital to producing 3 units of capital involves giving up 3 units of consumption goods (from 7 to 4), and moving from producing 3 units of capital to producing 2 units of capital involves giving up another 3 units of consumption goods (from 4 to 1).

Therefore, the opportunity cost of producing 3 units of capital is 6 units of consumption goods.

So, the answer is C) 6 units of consumption goods.

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The statement "the text from andretti created an enforceable agreement between mario and andretti the moment it was sent" is generally true.

In contract law, an agreement is formed when there is an offer from one party and an acceptance of that offer by the other party. An acceptance is typically effective upon communication to the offeror.

In this case, Mario made an offer to sell his 2002 Ford F-150 for $10,000 through a text message. Andretti responded to the offer with a text message accepting it.

The general rule is that an acceptance is effective upon communication to the offeror. Therefore, Andretti's acceptance of the offer was effective as soon as he sent the text message. It doesn't matter if the message was not received by Mario until later due to connection problems.

As long as Andretti sent the acceptance text message, it created an enforceable agreement between the two parties, assuming that there were no other legal issues that might affect the validity of the agreement.

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The coordinates of the image of vertex G after a reflection across the line y = x will be (-5, 4). Then the correct option is C.

It is the image of the point which is located in the opposite direction of a given point.

The rule of the refection given will be given as,

Firstly, the rule for reflecting a point about the line y = x is;

While reflecting on the line y = x, we get the reflected points by swapping the coordinates.

The coordinates are given below.

E(3, -3), F(5, -3), H(2, -5), G(4, -5)

The coordinates of the image of vertex G after a reflection across the line y = x are given as,

G(4, -5) ⇒ G'(-5, 4)

The coordinates of the image of vertex G after a reflection across the line y = x will be (-5, 4). Then the correct option is C.

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The Interest (simple interest) will be less on Loan A.

What exactly is simple interest?

Simple Interest is a simple way for computing interest on a loan or principle amount. Simple interest is a concept that is employed in numerous industries, including banking, finance, and automobiles. When you make a loan payment, the monthly interest is deducted first, followed by the principle amount.

The simple interest formula is as follows:

SI=P*R*T/100

SI stands for simple interest.

P stands for principal.

R is the interest rate (in percentage)

T denotes the length of time (in years)

The following formula is used to compute the total amount:

Amount (A) = Principal (P) x Simple Interest (SI)

Now,

For A Principal=$10000, Time = 3 years, Rate=5%

then interest paid=10000*3*5/100

=300*5=$1500

For B  Principal=$10000, Time = 5 years, Rate=8%

Interest=10000*5*8/100

=500*8

=$4000

That means SI(B)>SI(A)

Hence,  

          The Interest will be less on Loan A.

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Answer:

x= 7 ;

y+x=18

y=18-x

y=18-7

y=11

Therefore, (18²)⁻³ can be written as 18² - 10^⁻³ using positive exponents only.

An equation is a mathematical statement that shows that two expressions are equal. Equations can be used to represent relationships between variables, or to solve problems. Equations use mathematical symbols, such as the equal sign (=), to show the equality between the two expressions. For example, the equation 2x + 3 = 7 represents the relationship between the variable x and the constants 2 and 3. The equation can be solved for x to find its value. In this case, solving for x would give us x = 2.

Using positive exponents only, we can write (182)⁻³ as follows:

(182) can be written as 10²

-3 can be written as 10⁰/ 10³

So, (18²)⁻³ can be written as:

18² - 10⁰ / 10³= 18² - 10⁻³

Therefore, (18²)⁻³ can be written as 18² - 10^⁻³ using positive exponents only.

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Given the ratio of Year 7 pupils to Year 8 pupils as 9:5 and the ratio of Year 8 pupils to Year 9 pupils as 1:11, the ratio of Year 7, Year 8, and Year 9 pupils together is 9:5:55.

The ratio refers to the relative size of values.

Ratios are fractional values, depicted as fractions, decimals, or percentages.  Ratios can also be denoted in ratio form (:).

Ratios are computed as the comparative values that each quantity has in relation to other quantities or values.

The ratio of Year 7 pupils to Year 8 pupils = 9:5

The ratio of Year 8 pupils to Year 9 pupils = 1: 11

The ratio of Year 7, Year 8, and Year 9 = 9:5:55 (11 x 5)

The sum of ratios = 69 (9 + 5 + 55)

Thus, the ratio of Year 7, Year 8, and Year 9 is 9:5:55.

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There are only Year 7 pupils, Year 8 pup,ils, and Year 9 pupils in a group The ratio of Year 7 to Year 8 is 9:5. The ratio of Year 8 to Year 9 is 1: 11.

Find the ratio Year 7: Year 8: Year 9. Give your ratio in its simplest form with integer parts.

Answer:

36.39 hope this helps

Step-by-step explanation:

Answer: 2027.34

Step-by-step explanation:

first you plug in 10 for x

after you squared and multiplied you add

then it should come out to be 2027.34

In linear equation, 2027 .34 millions of smartphone units will be shipped worldwide in 2019.

What in mathematics is a linear equation?

An algebraic equation with simply a constant and a first-order (linear) term, such as y=mx+b, where m is the slope and b is the y-intercept, is known as a linear equation.

                               Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.

S(x)=-5.11x^2+243.57x+102.64   ...............1

For smartphone skipped in 2019

  x = 2019 - 2009

     x = 10

putting x = 10 in (1)

     S( 10 ) = -5.11 (10)² + 243.57 * 10 + 102.64

                 = -511 + 2435.7 + 102.64

               = 2027 .34

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The complete question is -

The total number (in millions) of smartphone units shipped worldwide from 2009 to 2016 is given by S(x)=-5.11x^2+243.57x+102.64. where is the number of years after 2009. Assuming the trend continues, how many millions of smartphone units will be shipped worldwide in 2019? (Do not round your answer.)

(Source: Statista 2017)

The value of JL is 21

A line segment is defined as the part of a straight line that is bounded by two distinct end points.

It is known to contain all the points on the line that is between its endpoints.

From the information given, we have that the point K is found between J and L and the line segment, JL

Then, we have;

JK + KL = JL

substitute the values, we have;

x + 8 + 10 = 7x

collect the like terms

x - 7x = -10 - 8

subtract the like terms

-6x = -18

x = 3

So. JL = 7(3) = 21

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The rate of the current is 5/11 of the speed of the barge in still water.

Let's call the speed of the barge in still water "s" (in miles per hour) and the speed of the current "c" (also in miles per hour).

When the barge travels upstream (against the current), its effective speed is reduced by the speed of the current, so the speed of the barge relative to the riverbank is (s - c). On the return trip, the current is going in the same direction as the barge, so the effective speed of the barge relative to the riverbank is (s + c).

distance upstream = (s - c) x 8 miles

distance downstream = (s + c) x 3 miles

(s - c) x 8 = (s + c) x 3

8s - 8c = 3s + 3c

5s = 11c

c = 5s/11

Therefore, the rate of the current is 5/11 of the speed of the barge in still water.

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The given equation is exact. An equation is said to be exact if it can be written in the form

M(x,y)dx + N(x,y)dy = 0

where M and N are functions of x and y, and their partial derivatives with respect to y and x, respectively, are equal.

In this case, we have:

M(x,y) = 2y^3

N(x,y) = 3y^2x + 2xy^2

Taking the partial derivative of M with respect to y gives:

∂M/∂y = 6y^2

Taking the partial derivative of N with respect to x gives:

∂N/∂x = 3y^2

Since ∂M/∂y = ∂N/∂x, the equation is exact.

To solve the equation, we need to find a function F(x,y) such that ∂F/∂x = M and ∂F/∂y = N.

Integrating M with respect to x gives:

F(x,y) = y^2x^2 + g(y)

where g(y) is an arbitrary function of y.

Taking the partial derivative of F with respect to y and comparing it with N, we get:

∂F/∂y = 2xy + g'(y) = N

Comparing the coefficients of y and the constant terms, we get:

2x = 3y^2, g'(y) = 2y^2

Solving these equations gives:

x = (3/2)y^2 and g(y) = (2/3)y^3 + C

where C is an arbitrary constant.

Substituting these values in F(x,y), we get:

F(x,y) = (2/3)y^3 + y^2x^2 + C

Therefore, the general solution of the given equation is:

(2/3)y^3 + y^2x^2 = C

where C is an arbitrary constant.

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