The following graph details the number of performances of plays a Shakespearean acting company has performed over the past five years.

If the company has performed 147 times in the past five years, how many times have they performed Othello? Round to the nearest whole performance, if necessary.

A.51
B.28
C.19
D.7

Answer: \(2\dfrac13\ h\)

Step-by-step explanation:

Given: Speed = \(10\dfrac15\) mi/h  \(=\dfrac{21}{5}\)mi/h  

Distance need to be travel = \(1\dfrac45\) miles \(=\dfrac{9}{5}\) miles

\(speed=\dfrac{distance}{time}\\\\\Rightarrow\ time=\dfrac{distance}{speed}\)

\(\Rightarrow\ time =\dfrac{\dfrac{21}{5}}{\dfrac{9}{5}}\\\\\Rightarrow\ time =\dfrac{21}{9}\\\\\Rightarrow\ time =\dfrac{7}{3}\\\\\Rightarrow\ time =2\dfrac13\ h\)

Hence, time taken to travel = \(2\dfrac13\ h\)

In the direct synthesis method for controller design, the process dynamics are described by the transfer function \(G_p = \frac{5}{(s+2)(s+3)}\).

The transfer function \(G_p\) represents the relationship between the input and output of the process. In this case, the transfer function is a ratio of polynomials in the Laplace domain, where \(s\) is the complex frequency variable.

To design the controller using the direct synthesis method, the transfer function of the desired closed-loop system, denoted as \(G_c\), needs to be specified. The controller transfer function is then determined by the equation \(G_c = \frac{1}{G_p}\).

In this scenario, the transfer function of the process is given as \(G_p = \frac{5}{(s+2)(s+3)}\). To find the controller transfer function, we take the reciprocal of \(G_p\), yielding \(G_c = \frac{1}{G_p} = \frac{(s+2)(s+3)}{5}\).

The resulting controller transfer function \(G_c\) can be used in the direct synthesis method for controller design, where it is combined with the process transfer function \(G_p\) to form the closed-loop system.

It's important to note that this summary provides an overview of the direct synthesis method and the transfer functions involved. In practice, further steps and considerations are needed for a complete controller design.

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Answer:

(7-4)+17-14+2×5

3+17-14+2×5

3+17-14+10

3+27-14

30-14

16

Answer:

\(m<-\frac{185}{k};\quad \:k>0\)

Step-by-step explanation:

\(-mk-110>75\\\\\mathrm{Add\:}110\mathrm{\:to\:both\:sides}\\\\-mk-110+110>75+110\\\\Simplify\\\\-mk>185\\\\\mathrm{Multiply\:both\:sides\:by\:-1\:\left(reverse\:the\:inequality\right)}\\\\\left(-mk\right)\left(-1\right)<185\left(-1\right)\\\\Simplify\\\\mk<-185\\\\\mathrm{Divide\:both\:sides\:by\:}k;\quad \:k>0\\\\\frac{mk}{k}<\frac{-185}{k};\quad \:k>0\\\\Simplify\\\\m<-\frac{185}{k};\quad \:k>0\)

Answer:

15

Step-by-step explanation:

6.65:5=1.33

1.33х15=19.95$

we need to around the 19.95 and we get a 20$

have a nice day

The equation of the plane orthogonal to the line (x, y, z) = (9, 5, 7) + t(-2, -4, 4) and passing through the point (5, 7, 9) can be written as -2x - 4y + 4z = 36.

To find the equation of a plane orthogonal (perpendicular) to a line, we need a direction vector of the line and a point that lies on the plane. In this case, the given line has a direction vector of (-2, -4, 4) and passes through the point (9, 5, 7).

We can start by finding a normal vector to the plane by taking the cross product of the direction vector of the line and a vector formed by subtracting the given point (5, 7, 9) from any point on the line (9, 5, 7). The cross product of (-2, -4, 4) and (4, 2, 2) gives us a normal vector of (4, 0, 0).

Using the normal vector (4, 0, 0) and the coordinates of the point (5, 7, 9), we can write the equation of the plane in the form ax + by + cz = d. Plugging in the values, we get -2x - 4y + 4z = 36.

Therefore, the equation of the plane orthogonal to the given line and passing through the point (5, 7, 9) is -2x - 4y + 4z = 36.

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Answer:

180

Step-by-step explanation:

because im always right

Answer:

180 degrees

Step-by-step explanation:

All triangles have an interior angle sum of 180 degrees.

The area of the triangle is 10 square units

The area of a triangle with vertices (x₁, y₁), (x₂, y₂) and (x₃, y₃) is given by:

A =  (1/2) [x₁(y₂ – y₃) + x₂(y₃ – y₁ ) + x₃(y₁ – y₂)]

Where:

A: (x₁, y₁) = (2, 1)

B: (x₂, y₂) = (4, 7)

C: (x₃, y₃) = (6, 3)

A =  (1/2) [x₁ (y₂ – y₃) + x₂(y₃ – y₁ ) + x₃(y₁ – y₂)]

A =  (1/2) [2 (7 – 3) + 4(3 – 1) + 6(1 – 7)]

A =  (1/2) [8+ 8 - 36]

A = 1/2 * [-20]

A = 10  square units

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Answer:

(f-g)(x) = 5x+11

Step-by-step explanation:

Given

\(f(x) = x + 8\)

\(g(x) = -4x - 3\)

as

(f-g)(x) = f(x) - g(x)

          = (x+8) - (-4x-3)

          = x+8+4x+3

          = 5x+11

Thus,

(f-g)(x) = 5x+11

Answer: y=(-1/2)x-6.5

Step-by-step explanation:

y=2x-6

the perpendicular to this will have the opposite reciprocal slope.

The new equation will be

y=(-1/2)x-b

--------------------------

To find the y-intercept of the equation, we should substitute the point into the equation (5,4)

y=(-1/2)x-b

4=(-1/2)×5-b

4=-2.5-b

b=-6.5

------------------------------

so the equation will be y=(-1/2)x-6.5

For a hypothesis testing, \(H_0 : µ = µ_0\) ; \(H_1 : µ > µ_0.\) the calculated P-value for test statistic value are following a) 0.9906 ; b) 0.9370 ; c) 0.9773; d) 0.9678 ; e) 0.4404.

We are testing the null hypothesis versus alternative hypothesis. Both are defined as \(H_0 : µ = µ_0\)

\(H_1 : µ > µ_0.\).

We have to calculate the P-value for the following observed values test statistic one by one.

a)z = 2.35

The P -value is calculated for as follows P ( z > Zo) = 1 - P( z≤ z0)

= 1 - P( z≤ 2.35)

Now, using the normal distribution table, the value of P( z≤ 2.35) is equals to 0.009387. So, P( z> 2.35) = 1 - 0.009387

= 0.990613

b) z₀ = 1.53

The P-value is calculated for as follows P ( z > z₀) = 1 - P( z≤ z₀)

= 1 - P( z≤ 1.53)

Now, using the normal distribution table , the value of P( z≤ 1.53) is equals to 0.063008. So, P( z> 1.53) = 1 - 0.063008

=0.936992

c) z₀ = 2.00

The P-value is calculated for as follows, P ( z > z₀) = 1 - P( z≤ z₀)

= 1 - P( z≤ 2.00)

Now, using the normal distribution table , the value of P( z≤ 2.00) is equals to 0.02275. So, P( z> 2.00) = 1 - 0.02275

=0.97725

d) z₀ = 1.85

The P-value is calculated for as follows P ( z > z₀) = 1 - P( z≤ z₀)

= 1 - P( z≤ 1.85)

Now, using the normal distribution table , the value of P( z≤ 1.85 ) is equals to 0.032157. So, P( z> 1.85) = 1 - 0.032157

=0.967843

e) z₀ = -0. 15

The P-value is calculated for as follows P ( z > -z₀) = P( z ≤ z₀)

= P( z≤ 0.15 )

Now, using the normal distribution table , the value of P( z≤ 0.15) is equals to 0.440382. So, P( z > - 0.15) = 0.44038. Hence the required P-value is 0.44038.

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Answer:

35 to 23

Step-by-step explanation:

In both cases, the size and shape of the quadrilateral remain the same, only its position on the coordinate plane changes.

Quadrilateral ABCD on the coordinate plane can be transformed through rotations about the origin. A rotation of 90° counterclockwise about the origin will result in a new quadrilateral that is positioned to the left of the original quadrilateral.

This means that point A will move to point D, point D will move to point C, point C will move to point B, and point B will move to point A. The new quadrilateral will still be congruent to the original quadrilateral.

On the other hand, a rotation of 90° clockwise about the origin will result in a new quadrilateral that is positioned to the right of the original quadrilateral.

This means that point A will move to point B, point B will move to point C, point C will move to point D, and point D will move to point A. The new quadrilateral will also be congruent to the original quadrilateral.
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a) No, a single spray of 10 grams of butter would not be enough to entirely cover the area of 4 slices of toast at 2 meters. The area of 4 slices of toast is larger than the area of 1 slice of toast, meaning that it would require more butter than 10 grams to cover the entire area.

b) A single spray of 10 grams of butter would be enough to cover the area of 8 slices of toast at 3 meters.

c) These changes would affect the amount of butter on each piece of toast in that there would be more butter on each piece with a larger rack and further distance from the "butter gun".

d) At 5 meters from the gun, our up-and-coming chef would be able to spray 16 slices of toast with a single burst of 10 grams of butter. Each piece of toast would also have more butter than it would if it was sprayed at a closer distance.

e) To duplicate the original single-slice toast at 5 meters from the gun, the chef would need to reduce the amount of butter being sprayed. He could do this by simply reducing the distance between the gun and the toast rack.

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Complete question :

A harried chef can't keep up with his breakfast orders and decides to automate the process with a "butter gun." The gun provides a 10 gram burst of butter spray with each hit of the trigger. He starts with a rack that holds one piece of toast 1 meter away. The demand again exceeds supply and he realizes he can use the same gun to produce more toast by placing a larger rack at a greater distance. He finds that a four-slice rack works at a distance of 2 meters. Pleased with profits he carries the idea a step further and puts a holder 3 meters away, maintaining a 10 gram spray. See figure below.a) If 1 spray entirely covers the area of a single slice at 1 meter, can it entirely cover the area of 4 slices at 2 meters? Why or why not?b) How many slices can one spray cover with a 3 meter arragnement?c) How do these changes affect the amount of butter on each piece of toastd) Our up-and-coming chef moves the fun back to 5 meters. Predict how much toast he can spray and how much better each piece gets.e) Explain how he could duplicate the original single-slice toast at 5 meters from the gun.

If Sabia and Arlan bought 45 books for rs 30, then at the rate of rs 24, they can buy 34 books.

It is defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division. It has basic four operators that are +, -, ×, and ÷.

It is given that, Sabia and Arlan bought 45 books for rs 30, then at the rate of rs 24, how many books they can buy,

Rs 30 = 45 book

Rs 30 = 45

Rs 1 = 45 / 30

Rs 24 = 3/2 × 24

Rs 24 = 34 books

Thus, if Sabia and Arlan bought 45 books for rs 30, then at the rate of rs 24, they can buy 34 books.

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Answer:

B. 63

C. 41

Step-by-step explanation:

B step-by-step explanation:

first, multiply and evaluate.

27 + 36

then, just calculate.

27 + 36 = 63

C step-by-step explanation:

first, evaluate and divide.

9 x 5 - 2^2

then, multiply and evaluate.

45 - 4

finally, calculate that.

45 - 4 = 41

The model's fit to the data is weak, indicated by a correlation coefficient of -0.34. There is a weak negative relationship between the variables, with the model's predictions being imprecise and scattered around the line of fit.

A relationship coefficient of - 0.34 shows a frail negative connection between's the factors in the information. This intends that as one variable expands, the other variable will, in general, diminish, however, the relationship isn't a serious area of strength for exceptionally.

The line of fit for the information recommends that there is a general pattern or example, however, it doesn't fit the information focuses intently. The scatterplot of the information would show focuses spread around the line, for certain focuses straying a considerable amount from it.

The model's capacity to foresee the specific upsides of the reliant variable in light of the free variable(s) is restricted. In outline, the attack of the model to the information isn't an area of strength for extremely, there is a frail negative connection between the factors.

The model's forecasts may not be profoundly precise, and there may be different elements or factors not caught by the model that impact the information.

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Answer:

21°

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Equality Properties

Geometry

Step-by-step explanation:

Step 1: Set Up Equation

(x + 7)° = (5x - 49)°

Step 2: Solve for x

Step 3: Find angle measure

R is not reflexive. To show this, we need to find an integer a such that a is not related to itself under R. Let a = 1, then 3a - 5a = -2, which is not even. Therefore, 1R1 is not true, and R is not reflexive.

R is not symmetric. To show this, we need to find integers a and b such that aRb but bRa is not true. Let a = 1 and b = 2, then 3a - 5b = -13, which is odd. Therefore, 1R2 is false. However, 3b - 5a = 1, which is also odd, so 2Ra is false. Therefore, R is not symmetric.

R is anti-symmetric. To show this, we need to show that if aRb and bRa, then a = b. Suppose 3a - 5b and 3b - 5a are both even. Then we can write 3a - 5b = 2k and 3b - 5a = 2m for some integers k and m. Adding these equations gives 2a - 2b = 2(k + m), or a - b = k + m, which is even. Therefore, aRb and bRa implies that a = b, and R is anti-symmetric.

R is transitive. To show this, suppose aRb and bRc, then 3a - 5b and 3b - 5c are both even. We can write 3a - 5b = 2k and 3b - 5c = 2m for some integers k and m. Substituting the first equation into the second gives 3a - 5c = 3b - 5b - 5c = -2b - 5c + 10b = 8b - 5c = 2(4b - 5c/2) = 2n for some integer n. Therefore, aRc, and R is transitive.

R is not an equivalence relation because it is not reflexive and not symmetric. However, R is a partial order because it is anti-symmetric and transitive.

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Answer:

A, C, and E I believe.

Step-by-step explanation:

The probability of rolling a 9 or higher on the 3rd roll is 4/27, or approximately 14.8%.

Probability is a branch of mathematics that deals with determining the likelihood or chance of an event occurring. It is often expressed as a fraction or a percentage.

Conditional probability is the probability of an event happening given that another event has already happened.

The probability of not rolling a 9 or higher on the first roll is 8/12 or 2/3, as there are 8 numbers on the cube that are less than 9.

The same is true for the second roll, so the probability of not rolling a 9 or higher on the first two rolls is (2/3) * (2/3) = 4/9.

The probability of rolling a 9 or higher on the third roll is 4/12 or 1/3, as there are 4 numbers on the cube that are 9 or higher.

So, the probability of rolling a 9 or higher on the third roll given that the previous two rolls did not result in a 9 or higher is

=> (4/9) * (1/3) = 4/27

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Since 80 out of 100 free throws were successful, the standard deviation of the success rate would be 8, and the standard deviation of a binomial distribution is the square root of (p*q)/n, where p is the probability of success, q is the probability of failure (1-p), and n is the total number of trials.

Standard deviation is calculated as follows:

p*q/n = 0.8*0.2/100 = 0.0016 = 0.04 = 8

Since 80% of 100 equals 80 successful free throws, the standard deviation of the successes from 100 free throws would be 8. The dispersion in a set of data is measured by standard deviation. A binomial distribution's standard deviation is equal to the square root of (p*q)/n, where p is the success probability, q is the failure probability (1-p), and n is the number of trials. Since the success rate in this instance is 80%, p = 0.8, q = 0.2, and n = 100. The standard deviation is then equal to the square root of (p*q/n): (0.8*0.2/100) = (0.0016) = (0.04), which equals 8. Therefore, the standard deviation of the successes from 100 free throws for a basketball player who makes 80% of them would be 8.

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Answer:

Step-by-step explanation:

The 3rd root of 64, or 64 radical 3, or the cube root of 64 is written as 3√64=4.

For the given equation which shows the relation of temperature in Celsius and Fahrenheit, the correct option is Option D.

What is meant by temperature?

Indicating the direction in which heat energy will naturally flow from a hotter body (one with a higher temperature) to a colder body(one at a lower temperature), the temperature is a measure of hotness or coldness defined in terms of any of several arbitrary scales.

The given equation is:

\(C = \frac{5}{9} (F- 32)\)

where C = temperature in Celsius

          F = temperature in Fahrenheit

The above equation can be rewritten as:

C = 5/9F - 160/9

Now, this is an equation of a straight line with a formula,

y = mx + c

Comparing,

m = 5/9 which is the slope of the equation.

This means that for a temperature increase of 1 degree Fahrenheit, the equivalent increase in temperature in Celsius is 5/9.

So the option I is true.

Similarly, an increase in 1 degree Celsius of temperature is equivalent to 9/5 = 1.8 degree increase in Fahrenheit.

So option II is true.

Option III is not true as is discussed above.

Therefore for the given equation of temperature, the correct option is Option D.

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Answer:

D

Step-by-step explanation:

I have nothing else to say- lol

Answer:

f(3) = 9

Step-by-step explanation:

In the given figure,

when x=3,

f(x)=9

substituting x=3 in f(x),

=> f(3)=9

\(8^{3} \cdot 8^{-7} =8^{-4}=\boxed{\frac{1}{8^4}}\)

Answer: I think it's D.

Step-by-step explanation:

I'm on the same thing and my best answer is Both functions are increasing, but function g increases at a faster average rate.

Both functions are increasing, but function g increases at a faster average rate.

x         f(x)

-2        -46

-1         -22

0         -10

1           -4

2          -1

If the slope of a function is continuously increasing or constant in an interval, the function is known as an increasing function.

Let us assume \(f(x)=ab^x+c\)

at x=0, f(0)=-10

So, \(-10=a+c\)

Similarly, by satisfying the above table in the f(x)

\(f(x)=-\frac{33}{5} (\frac{1}{11} )^x-\frac{17}{5}\)

\(f'(x) > 0\)

So we can say that f(x) is an increasing function.

\(g(x)=-18(\frac{1}{3} )^x+2\)

\(g'(x)=-18(\frac{1}{3} )^xln(\frac{1}{3} )\)

\(ln\frac{1}{3} < 0\)

So, \(g'(x) > 0\)

So, g(x) is an increasing function.

For any x∈f(x) and  x∈g(x) \(g'(x) > f'(x)\)

So, g increases at a faster average rate

Thus,  Both functions are increasing, but function g increases at a faster average rate.

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The probability that their first child will have kidney disease is 1/8.

What is probability?

The proportion of favorable cases to all possible cases is used to determine how likely an event is to occur.

Here, we have

Both parents must be heterozygous to have a 1/4 chance of having an

affected child. Parent 2 is heterozygous (her father was homozygous recessive, but she has unaffected).

For the child to have the disease, both Parent 1 and Parent 2 would need to be heterozygous

There is a 50% chance of this for Parent 1 and a 100% chance of this for Parent 2 and then, there is a 25% chance that their first child will be affected:

50%× 100% × 25% = 12.5%

1/2 × 1/4 = 1/8

Hence, the probability that their first child will have kidney disease is 1/8.

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Answer:

The answer is D or 36

Step-by-step explanation:

Divide the cups by servings

9/.25=36