For which value of theta is tan theta equal to sin theta?

A. pi

B. pi/2

C. pi/4

D. pi/6

Answer:

4 1/4

Step-by-step explanation:

Answer:

To find if the difference is statistically significant, we'll find the p-value and compare it to the significance level. If it's smaller, then it's significant.

On a graphing calculator, I conducted a 2-Proportion Z-test. It resulted in zTest_2Prop 643,1046,804,1315,0: stat.results and the p-value is shown as around 0.869485.

Since 0.869 > 0.05, the difference in the sample proportions is not statistically significant.

The actual implications of giving a bone to a subject would depend on the specific context, such as the subject's identity (human or animal), the purpose of giving the bone, and the cultural or medical considerations involved.

Assuming that a randomly selected subject is given a bone, it seems that we need to consider the context and determine the implications or consequences of this action. Without further information, it is difficult to provide a specific explanation or analysis. However, we can discuss some general possibilities and considerations related to giving a bone to a subject.

1. Medical Treatment: Giving a bone could be related to medical treatment or procedures. For example, in orthopedic medicine, bones may be used for grafting or reconstructive surgeries to repair damaged or fractured bones.

2. Nutritional Benefits: Bones, such as beef or chicken bones, can be used to make broths or stocks that are rich in nutrients like collagen, calcium, and other minerals. These bone-based products are often consumed for their potential health benefits.

3. Animal Care: Giving a bone to an animal, particularly dogs, is a common practice. Bones can serve as a form of entertainment or enrichment for pets, satisfying their chewing instincts and providing dental benefits.

4. Symbolic Meaning: In certain cultures or traditions, bones can hold symbolic meanings. They may be used in rituals, ceremonies, or artistic expressions to represent various concepts, such as strength, mortality, or spirituality.It's important to note that the above interpretations are speculative and based on general assumptions. The actual implications of giving a bone to a subject would depend on the specific context, such as the subject's identity (human or animal), the purpose of giving the bone, and the cultural or medical considerations involved.

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Answer:

$21.90

Step-by-step explanation:

You start by doing 14.60*1.5 because for overtime work is says she is paid time and a half. When you do the equation, you get $21.90.

Hope this helps!

Answer:

0.609   (the last choice shown)

Step-by-step explanation:

60.9 / 100 = 0.609

Answer:

The awnser is 2

Step-by-step explanation:

Answer:

A. 6m - 3p - 16

Step-by-step explanation:

Answer:

x = 2 , y = 0 , z = 3

Step-by-step explanation:

Cramer's rule is a rule through which we can find the solution of linear equation.

we have the three linear equations as

x+2y+3z=11

2x+y+2z=10

3x+2y+z=9

AX=B  

A: coefficient matrix

X= unknown vectors(x,y,z)

D = values of the linear equation (11 , 10 , 9)

now we find the determinant of the given linear equation

determinant of the matrix will be

A = \(\left[\begin{array}{ccc}1&2&3\\2&1&2\\3&2&1\end{array}\right]\)  = 1(1-4) - 2(2-6) + 3(4 - 3)

                    = 1(-3) - 2(-4) + 3(1)

                    = -3+8+3 = 8

also D\(\neq 0\)

so the determinant is Non zero we can apply Cramer's rule

we will be replacing the first column of the coefficient matrix A with the values of D

by replacing the first column we will get the value of the variable 'x'

Dx =  \(\left[\begin{array}{ccc}11&2&3\\10&1&2\\9&2&1\end{array}\right]\)   = 11(1-4) -2(10-18) + 3(20-9) = -33+16+33 = 16

x = \(\frac{Dx}{D}\)  = \(\frac{16}{8}\) = 2

similarly

Dy = \(\left[\begin{array}{ccc}1&11&3\\2&10&2\\3&9&1\end{array}\right]\) = 1(10-18) -11(2-6) + 3(18 -30) = -8 +44 -36 = 0

y = \(\frac{Dy}{D}\) = 0

Dz= \(\left[\begin{array}{ccc}1&2&11\\2&1&10\\3&2&9\end{array}\right]\) = 1(9 - 20) -2(18 - 30) + 11(4 -3) = -11 +24 +11 = 24

z = \(\frac{Dz}{D}\) = \(\frac{24}{8} = 3\)

so we have the solution as

x = 2 , y = 0 , z = 3

Therefore the solution for the given linear equations is (2,0,3).

Firm 1 and Firm 2 will produce the same quantity and charge the same price in this scenario.

To determine the price, quantity, and profit for Firm 1 and Firm 2, we need to analyze the market equilibrium. In a competitive market, the price and quantity are determined by the intersection of the market demand and the total supply.

Market Demand:

The market demand is given by the equation P = 100 - Q, where P represents the price and Q represents the total quantity demanded in the market.

Total Cost:

Both firms have identical total cost functions, which are not explicitly provided in the question. However, we can assume that the total cost function for each firm is given by TC = C + MC * Q, where TC represents the total cost, C represents the fixed cost, MC represents the marginal cost, and Q represents the quantity produced by the firm.

Given that the marginal cost is MC = 4 + Q, we can rewrite the total cost function as TC = C + (4 + Q) * Q.

Market Equilibrium:

To find the market equilibrium, we set the market demand equal to the total supply. In this case, since Firm 1 can charge any price that Firm 2 charges, both firms will produce the same quantity and charge the same price.

Market Demand: P = 100 - Q

Total Supply: QS = Q1 + Q2 (quantity produced by Firm 1 and Firm 2)

Setting the market demand equal to the total supply, we have:

100 - Q = Q1 + Q2

Since Firm 1 and Firm 2 have identical total cost functions, they will split the market equilibrium quantity equally. Therefore, Q1 = Q2 = Q/2.

Substituting Q1 = Q2 = Q/2 into the equation 100 - Q = Q1 + Q2, we get:

100 - Q = Q/2 + Q/2

100 - Q = Q

Solving this equation, we find Q = 50. Thus, both Firm 1 and Firm 2 will produce 50 units of output.

Price Calculation:

To calculate the price, we substitute the quantity (Q = 50) into the market demand equation:

P = 100 - Q

P = 100 - 50

P = 50

Therefore, both Firm 1 and Firm 2 will charge a price of 50.

Profit Calculation:

To calculate the profit for each firm, we subtract the total cost from the total revenue. The total revenue for each firm is given by the product of the price (P = 50) and the quantity (Q = 50).

Total Revenue (TR) = P * Q = 50 * 50 = 2500

The total cost function for each firm is TC = C + (4 + Q) * Q. Since the fixed cost (C) is not provided, we cannot determine the profit explicitly. However, we can compare the profit of Firm 1 and Firm 2 if their total costs are the same.

Since both firms have identical total cost functions, they will have the same profit when their costs are the same. If their costs differ, then the firm with lower costs will have higher profits.

Overall, both Firm 1 and Firm 2 will produce 50 units of output, charge a price of 50, and their profits will depend on their total costs, which are not explicitly provided in the question.

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Answer:

Let x be number of people who took crayons

Now, A/c to question

x=45/9

Step-by-step explanation:

The correct statement in the following is b. The variance of a random walk process increases as a linear function of time. This is because of the fact that it keeps adding the variance of the next increments to the variability we have in getting to where we are now.

a. The infix expression "3 * (5 2 * (77 10) - 6)" converted to postfix notation is "3 5 2 77 10 * 6 - * *".b. Evaluating the postfix expression "3 5 2 77 10 * 6 - * *" gives the value of the original expression, which is 196,080.

a. To convert the given infix expression to postfix, we can use the following steps:

1. Initialize an empty stack and an empty output string.

2. Scan the infix expression from left to right.

3. If the scanned character is an operand (number), add it to the output string.

4. If the scanned character is an opening parenthesis, push it onto the stack.

5. If the scanned character is a closing parenthesis, pop operators from the stack and add them to the output string until an opening parenthesis is encountered. Discard both the opening and closing parentheses.

6. If the scanned character is an operator (+, -, *, /), then:

  a. While the stack is not empty and the precedence of the operator on the top of the stack is greater than or equal to the precedence of the current operator, pop the operator from the stack and add it to the output string.

  b. Push the current operator onto the stack.

7. After scanning the entire infix expression, pop any remaining operators from the stack and add them to the output string.

8. The output string will be the postfix expression.

Applying these steps to the given infix expression (3 * (5 + 2 * (77 - 10) - 6)), we can convert it to postfix as follows:

Postfix expression: 3 5 2 77 10 - * + 6 - *

b. To evaluate the postfix expression and find the value of the original expression, we can use a stack-based algorithm. Here's how:

1. Initialize an empty stack.

2. Scan the postfix expression from left to right.

3. If the scanned element is an operand (number), push it onto the stack.

4. If the scanned element is an operator, pop the top two elements from the stack.

5. Apply the operator to the popped operands and push the result back onto the stack.

6. Repeat steps 3-5 until the entire postfix expression is scanned.

7. The final value left on the stack will be the value of the original expression.

Applying these steps to the given postfix expression (3 5 2 77 10 - * + 6 - *), we can evaluate it as follows:

Pop 3: Stack = [3]

Pop 5: Stack = [3, 5]

Pop 2: Stack = [3, 5, 2]

Pop 77: Stack = [3, 5, 2, 77]

Pop 10: Stack = [3, 5, 2, 77, 10]

Calculate 77 - 10 = 67: Stack = [3, 5, 2, 67]

Calculate 2 * 67 = 134: Stack = [3, 5, 134]

Calculate 5 + 134 = 139: Stack = [3, 139]

Pop 6: Stack = [3, 139, 6]

Calculate 139 - 6 = 133: Stack = [3, 133]

Calculate 3 * 133 = 399: Stack = [399]

The value of the original expression is 399.

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Table A does not represent a function, only table B represents a function.

To determine if a table of values represents a function, we need to check if each input value (also known as the domain) corresponds to a unique output value (also known as the range). If each input value is paired with exactly one output value, then the table of values represents a function. If any input value is paired with more than one output value, then the table of values does not represent a function.

In table A, x-value 1 is paired with two different y-values, -1 and 1. Therefore, table A does not represent a function while table B represents a function.

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The value of TN for this problem is given as follows:

B. 30.

A chord of a circle is a straight line segment that connects two points on the circle, that is, it is a line segment whose endpoints are on the circumference of a circle.

When two chords intersect each other, then the products of the measures of the segments of the chords are equal.

Then the value of x is obtained as follows:

8(x + 20) = 12 x 20

x + 20 = 12 x 20/8

x + 20 = 30.

x = 10.

Then the length TN is given as follows:

TN = x + 20

TN = 10 + 20

TN = 30.

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Answer:

1ft 7.7in/1.64 ft

Step-by-step explanation:

50/2.54=19.69in

12in=1ft

so 1ft 7.7in

19.69/12=1.64

Approximately 95% of the data fall within 2 standard deviations of the mean. That is, 2 standard deviations below and 2 standard deviations above the mean as in the following picture:

The declaration made indicates that Mabel left a $15.80 gratuity.

Percent, which is a relative number used to denote hundredths of any amount. Since one percent is equal to one tenth of something, 100 percent stands for everything, and 200 percent refers to twice the amount specified. percentage.

To find the amount of the tip that Mabel left, we can multiply the bill amount by the tip percentage, which is 20% or 0.2 in decimal form.

The amount of the tip is:

Tip = Bill Amount x Tip Percentage

Tip = $79 x 0.2

Tip = $15.80

Therefore, the tip that Mabel left was $15.80.

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The  probability that the change in heart rate of a randomly selected subject is below 8.3 beats per minute is approximately 0.4641 or 0.46411. option C

We'll use the standard normal distribution to find this probability.

Step 1: Standardize the value of 8.3 using the formula:

z = (x - μ) / σ

z = (8.3 - 7.3) / 11.1

z ≈ 0.09009

Look up the cumulative probability corresponding to the standardized value z using a standard normal distribution table or calculator.

From the standard normal distribution table, the cumulative probability for z ≈ 0.09009 is approximately 0.4641 or 0.46411.

Therefore, the probability that the change in heart rate of a randomly selected subject is below 8.3 beats per minute is approximately 0.4641 or 0.46411.

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In Friedman's test for a randomized block design, the correct alternative hypothesis is a. ha: not all the sample means are equal

The Friedman's test is a non-parametric statistical test used in randomised block designs, where the same individuals are evaluated under various circumstances or at various times, to compare three or more similar groups or treatments. In Friedman's test, the alternative hypothesis (Ha) argues that certain sample means are not equal to all other sample means,

Whereas in the test, null hypothesis (H0) states that all sample means are equal. In other words, the alternative hypothesis takes into account the likelihood of such differences and Friedman's test is used to assess if there are any statistically significant variations in the mean rankings of the groups or treatments.

Complete Question:

In friedman's test for a randomized block design, what is the correct alternative hypothesis?

a. ha: not all the sample means are equal

b. ha: all the medians are equal

c. ha: not all the medians are equal

d. ha: all sample means are equal

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If a matrix is skew symmetric, then its diagonal must all be 0.

In a skew symmetric matrix, the transpose of the matrix is equal to the negative of the matrix itself, i.e., A^T = -A. Let's consider a generic skew symmetric matrix A. The transpose of A is obtained by interchanging its rows and columns. Now, when we equate the transpose of A with -A, we can compare the corresponding elements of both matrices.

The diagonal elements of A are the elements for which the row index is equal to the column index. Let's assume A has a non-zero diagonal element at position (i, i). In the transpose of A, this element will be at position (i, i) as well. However, in -A, the corresponding element will be at position (i, i) but with a negative sign. Since the transpose of A is equal to -A, we can conclude that the element at position (i, i) must be equal to its negative counterpart, i.e., -a = a, where a is a non-zero diagonal element.

The only way for -a to be equal to a is if a = 0. Therefore, if a matrix is skew symmetric, all its diagonal elements must be 0.

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Answer:

40%

Step-by-step explanation:

Original price = x

Sale = 20% off

20% / 100 = 0.2 to convert from a percent to a decimal

Sale = x - 20% of x = x - 0.2x = 0.8x

Sale price = y = 0.8x

Reduction of sale prices = 25% = 0.25

Reduction = y - 25% of y = y - 0.25y = 0.75y

End price in terms of original price (x):

0.75y = 0.75(0.8)x

          = 0.6x

End price = 0.6 or 60% of original price, coming out to a 100-60 = 40% overall percentage reduction

Considering that R and S are points on the number line If RS= 10 and R lies at 13 then s will lie at

A number line is a sequence of numbers arranged at a particular pattern in a straight line

Information gotten form the question have it that"

RS= 10

R lies at 13

In a number line if R lies in point 13 and RS = 10 then we solve as follows

R + | 10 |

13 + 10 = 23

13 - 10 = 3

Hence R lies at point 3 or 13

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Answer:

c

Step-by-step explanation:

Answer:

Step-by-step explanation:

Step-by-step explanation:

let's look at the full numbers under the square roots when bringing the external factors back in :

sqrt(9×9×2) - sqrt(3×3×7) + sqrt(8) - sqrt(28)

and let's present these numbers as the product of their basic prime factors

sqrt(3×3×3×3×2) - sqrt(3×3×7) + sqrt(2×2×2) - sqrt(2×2×7)

now we see that we have 2 pairs of square roots : 1 pair ends with a factor of 2, and one pair with a factor of 7.

let's combine these

sqrt (3×3×3×3×2) + sqrt(2×2×2) - sqrt(3×3×7) - sqrt (2×2×7)

and now we move the factors of 2 and 7 back out in front (of course, we need to apply the square root on these factors) :

9×sqrt(2) + 2×sqrt(2) - 3×sqrt(7) - 2×sqrt(7) =

= (9+2)×sqrt(2) - (3+2)×sqrt(7) = 11×sqrt(2) - 5×sqrt(7)

and that is the first answer option.

Answer:

Every integer is a rational number, since each integer n can be written in the form n/1. For example 5 = 5/1 and thus 5 is a rational number. However, numbers like 1/2, 45454737/2424242, and -3/7 are also rational, since they are fractions whose numerator and denominator are integers.

Answer:

Rational numbers like -5/3, 8/11, 2/5, etc. are not integers as they don't simplify to give us a whole number.

~Hope this helps! :)

The solution to the equation 91 = 29^x is approximately x ≈ 1.08.

To solve for x in equation 91 = 29^x, we need to isolate the variable x. Here's the step-by-step process:

Add 150 to both sides of the equation to get rid of the constant term:

91 + 150 = 29^x + 150

Simplify the equation:

241 = 29^x + 150

Subtract 150 from both sides:

241 - 150 = 29^x

Simplify further:

91 = 29^x

Now, we can solve for x by taking the logarithm of both sides of the equation with base 29. Using the logarithm property log_b(a^c) = c * log_b(a), we have:

log_29(91) = x

Using a calculator or logarithm table, we can find that log_29(91) ≈ 1.08.

Therefore, the solution to the equation 91 = 29^x is approximately x ≈ 1.08.

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Answer:

25.9422 rounded to the nearest hundredth is 25.94.

Answer:

Step-by-step explanation:

The length of arc FH is approximately 9.42 units when rounded to the nearest hundredth.

To find the length of arc FH in circle G, we need to use the formula:

Arc Length = (Central Angle / 360°) \(\times\) Circumference

First, let's calculate the central angle m/FGH in degrees:

m/FGH = 60°

Next, we need to find the circumference of the circle. We know that the radius of the circle is equal to half the length of FG:

Radius = FG/2 = 18/2 = 9 units

Circumference = 2 \(\times\) π \(\times\) Radius = 2 \(\times\) π \(\times\) 9

Now, let's substitute the values into the formula to calculate the arc length:

Arc Length = (60/360) \(\\\times\) (2 \(\times\) π \(\times\) 9)

Simplifying this expression:

Arc Length = (1/6) \(\times\) (18π) = 3π units

To round the answer to the nearest hundredth, we can substitute the value of π as approximately 3.14:

Arc Length ≈ 3 \(\times\) 3.14 ≈ 9.42 units

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a.) Suppose you have 500 feet of fencing to enclose a rectangular plot of land that borders on a river. If you do not fence the side along the river, then the length of the plot would be equal to that of the river. Suppose the length of the rectangular plot is x and the width is y.

So, the fencing required would be 2x + y = 500. y = 500 − 2x. The area of the rectangular plot would be xy.

Substitute y = 500 − 2x into the equation for the area.

A = x(500 − 2x) = 500x − 2x²

Now, differentiate the above equation with respect to x.

A = 500x − 2x²

dA/dx = 500 − 4x

Set dA/dx = 0 to get the value of x.500 − 4x = 0or, 500 = 4x

So, x = 125

Substitute x = 125 into y = 500 − 2x to get the value of y.y = 500 − 2x = 250 ft

The maximum area is A = xy = 125 × 250 = 31,250 sq. ft.

b.) Let the length and width of the rectangular playground be L and W respectively. Then, the perimeter of the playground is L + 3W. Given that 900 feet of fencing is used, we have:

L + 3W = 900 => L = 900 − 3W

Area = A = LW = (900 − 3W)W = 900W − 3W²

dA/dW = 900 − 6W = 0W = 150

Substitute the value of W into L = 900 − 3W to get:

L = 900 − 3(150) = 450 feet

So, the dimensions of the playground that will maximize the enclosed area are L = 450 feet, W = 150 feet. The maximum area is A = LW = 450 × 150 = 67,500 square feet.c.)

Let x be the number of $1 increments. Then the rental rate would be $25 + x and the number of cars rented would be 62 − 2x. Hence, the revenue would be (25 + x)(62 − 2x) = 1550 − 38x − 2x²

Differentiating with respect to x, we get dR/dx = −38 − 4x = 0or, x = −9.5. This value of x is not meaningful as rental rates cannot be negative. Thus, the rental amount that will maximize the agency's daily revenue is $25. The maximum daily revenue is R = (25)(62) = $1550.

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According to the information we can conclude that the maximum area for the plot is 15,625 square feet (part a). Additionally, the maximum area for the playground is 50,625 square feet (part b). Finally the maximum daily revenue is $975 (part c).

To find the dimensions that maximize the area, we can use the formula for the area of a rectangle:

We are given that the total length of fencing available is 500 feet, and since we are not fencing the side along the river, the perimeter of the rectangle is

Solving for L, we have

Substituting this into the area formula, we get

To find the maximum area, we can take the derivative of A with respect to w, set it equal to zero, and solve for w. The resulting width is 125 feet, and the length is also 125 feet. The maximum area is found by substituting these values into the area formula, giving us

Similar to the previous problem, we can use the formula for the area of a rectangle to solve this. Let the width of the playground be w, and the length be L. We have

As we are dividing the playground into two parts with a fence parallel to its width. Solving for L, we get

Substituting this into the area formula, we have

To find the maximum area, we can take the derivative of A with respect to w, set it equal to zero, and solve for w. The resulting width is 225 feet, and the length is also 225 feet. The maximum area is found by substituting these values into the area formula, giving us

Let x be the rental rate in dollars. The number of cars rented can be expressed as

Since for each $1 increase in rate, two fewer cars are rented. The daily revenue is given by the product of the rental rate and the number of cars rented:

To find the rental amount that maximizes revenue, we can take the derivative of R with respect to x, set it equal to zero, and solve for x. The resulting rental rate is $22. Substituting this into the revenue formula, we find the maximum daily revenue to be

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