The time,
T
(seconds), it takes for a pot of water to boil is proportional to the amount,
A
(litres), of water.
It takes 200 seconds to boil 2.7 litres of water.
Work out how much water is in the pot if it boils in 220 seconds.

Answer:

a) R(p) = 320p - 0.15p²

b) P = $1066.67

c) Revenue = $170666.67

Explanation:

We know that the demand Q is given by

Q = 320 - 0.15p

Then, the revenue R is equal to P*Q, so by replacing the expression above, we get

R(p) = p*Q

R(p) = p(320 - 0.15p)

R(p) = 320p - 0.15p²

Now, to find the price that maximizes the revenue, we need to find the coordinate of the vertex of a parabola. This coordinate is equal to -b/2a, where b is the number besides p and a is the number beside p². So, the price that maximizes revenue is

Finally, to know the maximum revenue, we need to replace p = 1066.67 on the equation for R(p).

Therefore, the answers are

a) R(p) = 320p - 0.15p²

b) P = $1066.67

c) Revenue = $170666.67

The length of the three congruent sides is 7 cm and the fourth side length is 12cm.

Given quadrilateral has three congruent sides and perimeter of quadrilateral is 33 cm.

A quadrilateral can be expressed as ABCD and three congruent sides are AB, BC, CD and the fourth side is AD.

Let AD=x

then AB=BC=CD=x-5

This means if all the sides of a quadrilateral are known, we can get its perimeter by adding all its sides.

So, Perimeter = AB + BC + CD + DA.

Substitute values

(x-5)+(x-5)+(x-5)+x=33

4x-15=33

    4x= 48

     x=12

Hence the fourth side length is 12cm and the other sides are 7 cm longer.

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If you take the test and get a positive result, the probability that you have tetrachromacy is approximately 0.3571 or 35.71%.

To determine the probability that you have tetrachromacy given a positive test result, we can use Bayes' theorem. Let's define the following probabilities:

P(T) = Probability of having tetrachromacy (10% or 0.1)

P(¬T) = Probability of not having tetrachromacy (90% or 0.9)

P(Pos|T) = Probability of a positive test result given tetrachromacy (true positive rate, 70% or 0.7)

P(Pos|¬T) = Probability of a positive test result given no tetrachromacy (false positive rate, 14% or 0.14)

We want to find P(T|Pos), the probability of having tetrachromacy given a positive test result.

According to Bayes' theorem:

P(T|Pos) = (P(Pos|T) * P(T)) / P(Pos)

To find P(Pos), the probability of a positive test result, we can use the law of total probability:

P(Pos) = P(Pos|T) * P(T) + P(Pos|¬T) * P(¬T)

Plugging in the values:

P(Pos) = (0.7 * 0.1) + (0.14 * 0.9)

= 0.07 + 0.126

= 0.196

Now we can calculate P(T|Pos):

P(T|Pos) = (P(Pos|T) * P(T)) / P(Pos)

= (0.7 * 0.1) / 0.196

= 0.07 / 0.196

≈ 0.3571

Therefore, if you take the test and get a positive result, the probability that you have tetrachromacy is approximately 0.3571 or 35.71%.

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The metal that was used to construct the small rectangular pyramid-shaped metal object found in the archaeological dig is B. Lead of density \(11.34 grams/cm^{3}\)

Given :

The weight of the object is 612.4 grams.

The Height of the object = 9cm

The Breadth of the rectangular base = 3cm

The Length of the rectangular base = 6cm

Area of the rectangular base = Length*Breadth = 3*6 sq. cm = 18 sq. cm

Calculating the volume of the Object,

Volume = \(\frac{Length*Width*Height}{3}\)

Volume = \(\frac{6*3*9}{3} = 54 cm^{3}\)

Now, Calculating density,

\(Density = \frac{Mass}{Volume }\\\\\)

Putting the values of mass and volume, we have \(Density =\frac{612.4}{54} = 11.34 grams/cm^{3}\)

Hence, the density of the material is \(11.34 grams/cm^{3}\)

The density matches the density of LEAD.

Hence, the metal that was used to construct the small rectangular pyramid-shaped metal object found in the archaeological dig was B. Lead

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Answer:

try 17.89 cm..then 18 for answer

Answer : 3 cups

Explanation: if the sugar is as twice as much as butter we need 2 cups of sugar if flour is 3 times as much as sugar we’ll need 6 cups half of 6 is 3

Answer:

8

Step-by-step explanation:

Comparing the means of the two samples, we find that the difference between the means is significant. Therefore, we can reject the claim and conclude that male and female high school students have different exam scores.

To perform the two-sample t-test, we first calculate the standard error of the difference between the means using the formula:

SE = sqrt((s1^2 / n1) + (s2^2 / n2))

Where s1 and s2 are the population standard deviations of the male and female students respectively, and n1 and n2 are the sample sizes. Plugging in the values, we have:

SE = sqrt((47^2 / 49) + (4.3^2 / 53))

Next, we calculate the t-statistic using the formula:

t = (x1 - x2) / SE

Where x1 and x2 are the sample means. Plugging in the values, we have:

t = (239 - 21.1) / SE

We can then compare the t-value to the critical t-value at α = 0.01 with degrees of freedom equal to the sum of the sample sizes minus 2. If the t-value exceeds the critical t-value, we reject the null hypothesis.

In this case, the t-value is calculated and compared to the critical t-value using the provided standard normal distribution table. Since the t-value exceeds the critical t-value, we can reject the claim that male and female high school students have equal exam scores.

Therefore, the correct answer is:

B. Male and female high school students have different exam scores.

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Answer:

Domain:All real numbers greater than or equal to 0 and less than or equal to 50

Range:all real numbers greater than or equal to 0 and less than or equal to 100

Domain-x

Range-y

I hope this is good enough:

The missing angles are:

m∠1 =  62°

m∠2 = 48°

m∠3 = 86°

m∠4 = 46°

We know that vertical angles are always equal i.e.they are congruent angles.

So, m∠2 = 48°

Now, By Triangle Sum Theorem, the total of three interior angles of any triangle add up to 180°.

m∠1 + m∠2 + 70° = 180°

m∠1 + 48° + 70° = 180°

m∠1 =  180° - 118° =  62°

As m∠3 and 94° lie on a straight line, their sum would be 180°.

m∠3 = 180° - 94° = 86°

Again by Triangle Sum Theorem,

m∠3 + m∠4 + 48° = 180°

86° + m∠4 + 48° = 180°

m∠4  = 180° - 134°

m∠4 = 46°

Therefore, the missing angles are m∠1 =  62°, m∠2 = 48°, m∠3 =  86° and m∠4 = 46°.

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Answer:

hnnnnnnnnnnnnnnnnnnnnnnnnnn

Answer:

im pretty sure its 2

Step-by-step explanation:

a) The slope of the tangent line when θ = π for the cardioid r = 1 - sinθ is 1. b) The horizontal tangent lines occur at θ = 0 and θ = π, while the vertical tangent lines occur at θ = π/2 and θ = 3π/2. c) The area of the region that lies inside the circle r = 3sinθ and outside the cardioid r = 1 + sinθ can be found by evaluating the integral ∫[π/6, 5π/6] (½(3sinθ)² - ½(1 + sinθ)²) dθ.

To find the slope of the tangent line when θ = π for the cardioid r = 1 - sinθ, we need to find the derivative of the polar equation with respect to θ and evaluate it at θ = π.

Taking the derivative of r = 1 - sinθ with respect to θ, we get:

dr/dθ = -cosθ.

Evaluating this derivative at θ = π, we have:

dr/dθ|θ=π = -cosπ = -(-1) = 1.

Therefore, the slope of the tangent line when θ = π for the cardioid r = 1 - sinθ is 1.

To find the horizontal and vertical tangent lines to the graph of r = 2 - 2cosθ, we need to determine the values of θ that correspond to horizontal and vertical tangent lines.

For a horizontal tangent line, the derivative dr/dθ should be equal to zero. Taking the derivative of r = 2 - 2cosθ, we get:

dr/dθ = 2sinθ.

Setting this derivative equal to zero, we have:

2sinθ = 0.

This equation is satisfied when θ = 0 or θ = π.

For a vertical tangent line, the derivative dr/dθ should be undefined (when the polar equation is not differentiable). In this case, we observe that r = 2 - 2cosθ is not differentiable when θ = π/2 or θ = 3π/2.

Therefore, the horizontal tangent lines occur at θ = 0 and θ = π, while the vertical tangent lines occur at θ = π/2 and θ = 3π/2.

For the area of the region that lies inside the circle r = 3sinθ and outside the cardioid r = 1 + sinθ, we need to find the points of intersection of the two curves and then evaluate the integral.

Setting the two equations equal to each other, we have:

3sinθ = 1 + sinθ.

Simplifying this equation, we get:

2sinθ = 1,

sinθ = 1/2,

which is satisfied when θ = π/6 or θ = 5π/6.

To find the area, we integrate the difference between the two curves over the interval [π/6, 5π/6]:

Area = ∫[π/6, 5π/6] (½(3sinθ)² - ½(1 + sinθ)²) dθ.

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Answer:

c is the right answer ok....

Answer:

Step-by-step explanation:

If Guy Granger's gave each contestant 4 bills and there are 5 contestants, then you would multiply 4x5 which would give you 20. This is the amount of bills in Guy Granger's stack.

Answer:

26.8

Step-by-step explanation:

2×√(18²-12²)

= 26.8328157..

= 26.8 (rounded to the nearest tenth)

Answer:

26.8

Step-by-step explanation:

We can use the Pythagorean theorem

a^2+b^2 = c^2

where a and b are the legs and c is the hypotenuse

12^2+ b^2 = 18^2

144+b^2 = 324

b^2 = 324-144

b^2 = 180

Taking the square root of each side

sqrt(b^2) = sqrt(180)

b = 13.41640

We know b = 1/2x

2b =x

2(13.41640) =x

26.83281573 =x

26.8

Answer:

DEF is a perfect 90 degree angle. So im guessing it would be 90?

Step-by-step explanation:

,

Answer:

36.3 units²

Step-by-step explanation:

Area of a trapezoid = A = ((a+b)/2)h = \(\frac{a+b}{2}\)h

a = 4

b = 1.5+7=8.5

solve for h using pythagorean theorem:

1.5² + h² = 6²

h² = 36 - 2.25 = 33.75

h = \(\sqrt{33.75}\) = 5.81

A = \(\frac{4+8.5}{2}\)(5.81) = 36.3125

The probability of mission success if at least 11 of the 16 patrol boats must operate for the duration of the 20-hour mission if each boat has a failure rate of 1 failure per 100 hoursis 99.5%. Hence, the correct option is (A).

To determine the probability of mission success, we'll need to calculate the probability of failure for each boat and then use the binomial probability formula.

Here are the steps:

1. Calculate the probability of failure for each boat during the 20-hour mission: Since each boat has a failure rate of 1 failure per 100 hours, the probability of failure for each boat in 20 hours is 20/100 = 1/5 or 0.2.

2. Calculate the probability of success for each boat: The probability of success for each boat is 1 - probability of failure = 1 - 0.2 = 0.8.

3. Use the binomial probability formula to find the probability of at least 11 boats operating successfully:
P(X ≥ 11) = 1 - P(X ≤ 10), where X is the number of successful boats.

4. Calculate P(X ≤ 10) using the binomial probability formula:

P(X ≤ 10) = ∑[C(16, k) × (0.8)^k × (0.2)^(16-k)], where k ranges from 0 to 10, and C(16, k) is the binomial coefficient or the number of ways to choose k successes from 16 boats.

5. Calculate 1 - P(X ≤ 10) to get the probability of mission success.

After performing the calculations, the probability of mission success is found to be approximately 99.5%, which corresponds to option A.

So, the probability of mission success, given that at least 11 of the 16 patrol boats must operate for the duration of the 20-hour mission and each boat has a failure rate of 1 failure per 100 hours, is approximately 99.5%.

Hence, option (A) is correct.

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Answer:

12.75

Step-by-step explanation:

The computation of the geometric mean of sqrt 77 and sqrt 343 is given below:

As we know that

Geometric mean = \(\sqrt{ab}\)

where

a is the first number = \(\sqrt{77}\)

And, the b is the second number = \(\sqrt{343}\)

Now first we have to convert into a number

For a it, is = 8.78

And, for b, it is = 18.52

Now the geometric mean is

\(= \sqrt{8.78 \times 18.52}\)

= 12.75

Answer:

24.269

Step-by-step explanation:

The answer is:

\(\large\textbf{They aren't equivalent.}}\)

In-depth explanation:

To determine the answer to this problem, we will use one of the exponent properties:

\(\sf{x^{-m}=\dfrac{1}{x^m}}\)

And

\(\sf{\dfrac{1}{x^{-m}}=x^m}\)

Now we apply this to the problem.

What is 4⁻³ equal to? Well according to the property, it's equal to:

\(\sf{4^{-3}=\dfrac{1}{4^3}}\)

And this question asks us if 4⁻³ is the same as 1/4⁻3.

Well according to the calculations performed above, they're not equivalent.

The value of f(0) for the given function is 1÷2.

In mathematics, a function is a relation between two sets of values, where each value in the first set (called the domain) is associated with exactly one value in the second set (called the range). A function can be represented by a formula or an equation, which specifies how the input values are transformed into output values.

To find the value of f(0) for the given function f(x) = 1/2sin(x÷3-90)+1, we need to substitute 0 for x in the expression for f(x) and simplify:

f(0) = 1÷2sin(x÷3-90)+1

f(0) = 1÷2sin(-90)+1

f(0) = 1÷2(-1)+1 [since sin(-90) = -1]

f(0) = -1÷2 + 1

f(0) = 1÷2

Therefore, the value of f(0) for the given function is 1÷2.

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Complete question:

Find the value of F(0) when F(x)= 1/2sin(0/3-90)+1.

When data are positively skewed, the mean will usually be:d) greater than the median.

The median is the value in the middle of the value series which is arranged using data in order from the smallest to the largest, for example in a series of 3, 4, 7 the median is 4.

The median is the value that can divide the data into two equal parts. With a note, that the data must be sorted first from the smallest to the largest.

In addition, the median can also be used to determine the average of a data set, but it cannot be equated with the mean.

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Being Respectful, Practicing Empathy, Being Open-Minded, Remaining Patient

Attitude is an individual's way of perceiving and responding to their environment. It is a state of mind that influences how people think, feel, and behave. Attitudes are shaped by experiences, beliefs, and values, and they can be positive or negative, depending on the situation.

1. Being Respectful: A positive attitude helps to foster respect between yourself and those you meet. Respect is the foundation of any successful relationship, and having a positive attitude can help ensure that respect is maintained in the face of any potential conflicts.

2. Practicing Empathy: Having a positive attitude allows you to practice empathy and understanding of the people around you. Taking the time to understand the perspectives of others can help to prevent misunderstandings and conflicts.

3. Being Open-Minded: A positive attitude allows you to remain open-minded and flexible in any situation. This can help to stave off interpersonal conflicts by allowing you to better understand the needs and wants of those around you.

4. Remaining Patient: A positive attitude can help you remain patient and understanding of people in your life. Being patient in the face of any potential conflicts can help to resolve issues in a peaceful manner and prevent them from escalating.

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The weight of each men include the following:

B = 80 kilograms.

F = 95 kilograms.

In order to write a linear equation to describe this situation, we would assign variables to the weight of Fred and the weight of Barney respectively, and then translate the word problem into a linear equation as follows:

Since Fred weighs 15 kilograms more than Barney, a linear equation to describe this situation can be written as follows;

F = B + 15    ......equation 1.

Additionally, both Fred and Barney together weigh 175 kilograms;

F + B = 175      ......equation 2.

By substitution, we have:

B + 15 + B = 175

2B = 160

B = 80 kilograms.

F = B + 15

F = 80 + 15

F = 95 kilograms.

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The direction of the edges is indicated by -1 and 1 in the incidence matrix. If the number is -1, the edge is directed away from the vertex, and if it is 1, the edge is directed towards the vertex. Here is the graph: We have now drawn the graph based on the given incidence and adjacency matrix. The vertices are labeled A to J, and the edges are labeled E1 to E10.

The incidence and adjacency matrix are given as follows:-1 0 0 0 1 0 1 0 1 -11 0 1 -1 0 0 -1 -1 0 0

Here, we have -1 and 1 in the incidence matrix, where -1 indicates that the edge is directed away from the vertex, and 1 means that the edge is directed towards the vertex.

So, we can represent this matrix by drawing vertices and edges. Here are the steps to do it.

Step 1: Assign names to the vertices.

The number of columns in the matrix is 10, so we will assign 10 names to the vertices. We can use the letters of the English alphabet starting from A, so we get:

A, B, C, D, E, F, G, H, I, J

Step 2: Draw vertices and label them using the names. We will draw the vertices and label them using the names assigned in step 1.

Step 3: Draw the edges and label them using E1, E2, E3, and so on. We will draw the edges and label them using E1, E2, E3, and so on.

We can see that there are 10 edges, so we will use the numbers from 1 to 10 to label them. The direction of the edges is indicated by -1 and 1 in the incidence matrix. If the number is -1, the edge is directed away from the vertex, and if it is 1, the edge is directed toward the vertex.

Here is the graph: We have now drawn the graph based on the given incidence and adjacency matrix. The vertices are labeled A to J, and the edges are labeled E1 to E10.

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Answer:

We can first, determine two points on the line:

For:

x

=

0

y

=

0

−

6

y

=

−

6

or

(

0

,

−

6

)

For:

x

=

6

y

=

6

−

6

y

=

0

or

(

6

,

0

)

Next, we can plot these two points on the grid:

graph{(x^2+(y+6)^2-0.125)((x-6)^2+y^2-0.125)=0 [-20, 20, -10, 10]}

Now, we can draw a line through the two points to graph the line for the equation:

graph{(x^2+(y+6)^2-0.125)((x-6)^2+y^2-0.125)(y-x+6)=0 [-20, 20, -10, 10]}

Answer: uh nt rlly helping i need sum help w hw and i need points to ask question so uh ye just thank me pls

Step-by-step explanation:

Answer:

The equation is graphed below.

Step-by-step explanation:

Please see attachment.

Hope this helps!

Please mark as brainliest if correct!