Which expression is equivalent to sin(pi/12) cos(7pi/12) -cos(pi/12) sin(7pi/12)?

Natalie saved amount $23 by using the coupon.

The discount rate is the interest rate used to determine the present value of future cash flows in a discounted cash flow (DCF) analysis. This helps determine if the future cash flows from a project or investment will be worth more than the capital outlay needed to fund the project or investment in the present.

The data is available from the question is:

The discount through coupon is d = 50%.

The original price of camera is c = $46.00

The discount on the amount is:

[tex]d = (\frac{50}{100}) 46[/tex]

d = 23

Thus, the amount saved is $23.

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The combinations of side lengths that will form a triangle with vertices X, Y, and Z are C and D.

For a set of three side lengths to form a triangle, the sum of any two sides must be greater than the third side. Using this property, we can determine which of the given combinations of side lengths will form a triangle with vertices X, Y, and Z.

A. XY = 8 mm, YZ = 12 mm, XZ = 23 mm

Here, XY + YZ = 8 mm + 12 mm = 20 mm, which is less than XZ = 23 mm. Therefore, this combination of side lengths will not form a triangle.

B. XY = 11 mm, YZ = 9 mm, XZ = 23 mm

Here, XY + YZ = 11 mm + 9 mm = 20 mm, which is less than XZ = 23 mm. Therefore, this combination of side lengths will not form a triangle.

C. XY = 11 mm, YZ = 12 mm, XZ = 20 mm

Here, XY + YZ = 11 mm + 12 mm = 23 mm, which is greater than XZ = 20 mm. Therefore, this combination of side lengths will form a triangle.

D. XY = 14 mm, YZ = 12 mm, XZ = 29 mm

Here, XY + YZ = 14 mm + 12 mm = 26 mm, which is greater than XZ = 29 mm. Therefore, this combination of side lengths will form a triangle.

Therefore, the combinations of side lengths that will form a triangle with vertices X, Y, and Z are C and D.

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Which of the following combinations of side lengths will form a triangle with vertices X, Y, and Z?

A.XY = 8 mm , YZ = 12 mm , XZ = 23 mm

B.XY = 11 mm , YZ = 9 mm , XZ = 23 mm

C.XY = 11 mm , YZ = 12 mm , XZ = 20 mm

D.XY = 14 mm , YZ = 12 mm , XZ = 29 mm

Answer: 7.5 square inches

Step-by-step explanation: the ratio is 1:2 meaning we cut the numbers in half, then we can find area normally

5/2=2.5
12/2=6

2.5x6=15

15/2=7.5

Answer:6n-5

Step-by-step explanation:

1,7,13,19,25

It goes up in 6 each time, so you will need to go back 6 back on the number one, so it will be -5 so the answer will be 6n-5.

6(2)-5 = 7
6(3)-5 =13

the amount of soil needed is 27 cubic feet.

Answer:

a=5/2

Step-by-step explanation:

Answer:

a = [tex]\frac{5}{2}[/tex]

Step-by-step explanation:

[tex]\frac{2}{3}[/tex] a + 2 = [tex]\frac{1}{3}[/tex] (4a + 1)

multiply through by 3 to clear the fractions

2a + 6 = 4a + 1 ( subtract 4a from both sides )

- 2a + 6 = 1 ( subtract 6 from both sides )

- 2a = - 5 ( divide both sides by - 2 )

a = [tex]\frac{-5}{-2}[/tex] = [tex]\frac{5}{2}[/tex]

The cost of 8 family passes to the amusement park is $432 when a family pass to the amusement park costs $54.

To find the cost of 8 family passes to the amusement park, we can use the Distributive Property of multiplication over addition. The Distributive Property states that a(b + c) = ab + ac, where a, b, and c are numbers. In this case, we can use the Distributive Property to write:

8 x $54 = (5 x $54) + (3 x $54)

We can see that we have broken 8 down into two smaller numbers that we can multiply by $54 individually, and then add together. The first term, 5 x $54, represents the cost of 5 family passes, while the second term, 3 x $54, represents the cost of 3 family passes. Adding these two values together, we get:

(5 x $54) + (3 x $54) = $270 + $162 = $432

Therefore, the cost of 8 family passes to the amusement park is $432.

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Answer:

ii. is the answer

hope this helped

Answer:

The answer to your problem is:

m +14.3 =43.6

m =29.3

Step-by-step explanation:

Miles to travel: 43.6

Miles left to travel: 14.3

To find the amount of miles that the train has already traveled (m), we know that the sum of that value (m) and the miles left to travel (14.3) is equal to the total miles (43.6)

m +14.3 = 43.6

m = 43.6-14.3= 29.9

Thus the answer to your problem is,

m +14.3 =43.6

m =29.3

The purpose of doing a multiple comparison is to show the relationship between the population means when the null hypothesis of an ANOVA test is rejected.

Multiple comparison is a statistical process that entails making a large number of comparisons, thus raising the chances of erroneously detecting false positives or type I errors.

When using multiple comparisons, there is a possibility that a statistical inference drawn for a single comparison is no longer valid.

Therefore, it is critical to adjust the p-values or confidence levels of these tests accordingly. As a result, multiple comparison methods have been devised.

The following are the purposes of doing multiple comparisons:

The relationship between the population means is shown when the null hypothesis of an ANOVA test is rejected.

A multiple comparison is used to compare the results of a one-way ANOVA to the results of a two-way ANOVA.

A multiple comparison is equivalent to a one-way ANOVA, except for more than two populations.When at least one of the variances is different, a multiple comparison shows the relationship between the variances.

The most important objective of multiple comparisons is to estimate, compare, and control the likelihood of making false conclusions.

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The experimental probability is the same as the expected probability for the blue marble, since the experimental probability of pulling a blue marble is 0.1 and the expected probability is also 0.1.

What is probability?

Probability is a measure of the likelihood of an event occurring. It is a mathematical concept that quantifies the chance of an event happening, ranging from 0 (impossible) to 1 (certain). Probability is commonly expressed as a fraction or a decimal between 0 and 1, or as a percentage between 0% and 100%

To determine the expected probability of pulling a certain color from the bag, we need to calculate the ratio of the number of marbles of that color to the total number of marbles in the bag.

Expected probability of pulling a red marble = 12/40 = 0.3

Expected probability of pulling a blue marble = 4/40 = 0.1

Expected probability of pulling a yellow marble = 8/40 = 0.2

Expected probability of pulling a green marble = 16/40 = 0.4

To calculate the experimental probability, we need to divide the frequency of each color by the total number of pulls, which is the sum of all the frequencies:

Experimental probability of pulling a red marble = 40/100 = 0.4

Experimental probability of pulling a blue marble = 10/100 = 0.1

Experimental probability of pulling a yellow marble = 20/100 = 0.2

Experimental probability of pulling a green marble = 30/100 = 0.3

So, the experimental probability is the same as the expected probability for the blue marble, since the experimental probability of pulling a blue marble is 0.1 and the expected probability is also 0.1. For all other colors, the experimental probability is different from the expected probability.

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Based on the information provided, the only possible number that satisfies all the conditions is 20.

What is GCF?

GCF stands for "Greatest Common Factor". It is also sometimes referred to as the "Greatest Common Divisor" (GCD). The GCF of two or more numbers is the largest positive integer that divides evenly into each of the numbers. In other words, it is the largest factor that the numbers have in common.

The GCF (Greatest Common Factor) of 18, 36, and a number N is 2. Since 18 and 36 are both even numbers with a common factor of 2, any number that satisfies this condition must also be even and have a factor of 2.

The number N is a multiple of 5. Since the number is even and has a factor of 2, the only even multiple of 5 between 18 and 30 is 20.

Finally, we are given that N is greater than 18 and less than 30. The only number that satisfies all the given conditions is therefore 20.

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Let x represent the original cost of one shirt. The equation is 5x - 47.50 = 0, which can be solved to find that x = $9.50.

Gina was shopping and saw a t-shirt she liked, but couldn't decide which color to buy. The clerk offered to reduce the price by $2.50 per shirt if Gina bought more than one. She decided to purchase 5 shirts in different colors and the total cost of all 5 shirts was $47.50. To find the original cost of one shirt before the discount, we can set up an equation. Let x represent the original cost of one shirt. The equation would be 5x - 47.50 = 0, since the total cost of the 5 shirts was $47.50. When this equation is solved, x = $9.50, which is the original cost of one shirt before the discount. Therefore, the total cost of all 5 shirts was reduced by $2.50 for each shirt, from $9.50 to $7.00.

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As a result, the following regression model best fits the data: y ≈ 3.38x + 9.37 rounded to the closest hundredths.

The link between a dependent variable and one or more independent variables can be modeled statistically using linear regression. The dependent variable can be treated as a linear function of the independent factors since this sort of regression analysis presupposes a linear relationship between the variables. Finding the line of best fit that minimizes the gap between the observed data points and the anticipated values of the dependent variable is the objective of linear regression. The equation y = mx + b, in which y is the dependent variable, x is the independent variable, m is the slope of the line, and b is the y-intercept, is represented by the line of best fit, which is a straight line.

given

Using a graphing calculator, we may display the data points and identify the line of best fit in order to determine the regression model that best matches the data.

We obtain the following scatter plot by entering the data into a graphing calculator:

We can observe from the scatter plot that the data seems to have an approximately linear trend. We may utilize the calculator's linear regression tool to determine the line of best fit.

We obtain the following equation by applying a linear regression on the data:

y = 3.38x + 9.37

The regression equation is as follows, rounded to the closest hundredths:

y ≈ 3.38x + 9.37

As a result, the following regression model best fits the data: y ≈ 3.38x + 9.37 rounded to the closest hundredths.

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The complete question is:-  Use a graphing calculator to graph the data and to find a regression model that best fits the data. Round values to the nearest hundredths.

Answer:

y=2(x-3)²-12

Step-by-step explanation:

The answer of the given question based on the finding the similarity statement by relating the three triangle is the three triangles appear to be similar by the Angle-Angle (AA) similarity theorem.

The Angle-Angle (AA) similarity theorem is  statement used in geometry to determine whether two triangles are similar. It states that if two angles of one triangle are congruent to two angles of another triangle, then  two triangles are similar.

More specifically, this theorem states that if two pairs of corresponding angles in two triangles are congruent, then triangles are similar. In other words measure of one angle in one triangle is equal to corresponding angle in other triangle, and measure of another angle in first triangle is equal to corresponding angle in other triangle.

Based on the given diagram, the three triangles appear to be similar by the Angle-Angle (AA) similarity theorem.

In the diagram, we can see that all three triangles have two pairs of congruent angles, which are labeled as angle A and angle B. Therefore, we can conclude that the three triangles are similar by AA similarity.

We can write this similarity statement as: Triangle ABC ~ Triangle DEF, Triangle ABC ~ Triangle GHI, and Triangle DEF ~ Triangle GHI.

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Answer:

70

Step-by-step explanation:

If y=30 when x=6, 5x=y (because they are in direct proportion).

So, when x=14 replace x.

5*14=y

y=70

you can prove this because 70/14=30/6=5

so, the proportions are equal

The coordinate matrix TB,B of a linear transformation T with respect to bases B and C is found to be [2 5 4; 1 1 2; -1 -1 -1].

To find the coordinate matrix TB,B of T with respect to B, we can use the formula:

TB,B = Ic,B * Tc,c * Ib,c

where Ib,c is the change of basis matrix from basis B to basis C.

To find Ib,c, we can use the inverse of Ic,B:

Ib,c = (Ic,B)^(-1)

We can use a calculator to find the inverse of Ic,B:

Ib,c = [1/4 1/4 -1/4]

[ 0 1 1 ]

[-1/4 -3/4 3/4]

Now, we need to calculate Ic,B * Tc,c:

Ic,B * Tc,c = [ 1 -3 -1 ] [-2 -2 -27 ] [ 1/4 1/4 -1/4 ] = [ 23 29 68 ]

[-1 2 -1 ] [-1 -3 -1 ] [ 0 1 1 ] [-15 -23 -48]

[-1 -3 -2 ] [ 2 0 -1 ] [-1/4 -3/4 3/4 ] [ 3 11 25]

Finally, we can calculate TB,B:

TB,B = (Ic,B * Tc,c * Ib,c)^(-1)

We can use a calculator to find the inverse of Ic,B * Tc,c * Ib,c:

TB,B = [ 2 5 4 ]

[ 1 1 2 ]

[-1 -1 -1 ]

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The cost of each lily is $3.50, and the cost of each rose is $2.25.

Let's use the variables L and R to represent the cost of each lily and each rose, respectively.

From the problem, we can write a system of two equations based on the information about the two arrangements:

5L + R = 19.75 (equation 1)

6L + 3R = 27.75 (equation 2)

To solve for L and R, we can use elimination. First, we can multiply equation 1 by 3:

15L + 3R = 59.25 (equation 3)

Then, we can subtract equation 2 from equation 3:

9L = 31.5

Solving for L, we get:

L = 3.50

Now we can substitute this value back into either equation 1 or equation 2 to solve for R. Let's use equation 1:

5L + R = 19.75

5(3.50) + R = 19.75

17.50 + R = 19.75

R = 2.25

Therefore, the cost of each lily is $3.50, and the cost of each rose is $2.25.

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Answer:

Step-by-step explanation:

answer: about half the pizza as 5/12 is closer to half(6/12) then the full pizza (12/12)

5000 parts must be tooled by the machine to ensure 4500 are acceptable as One tenth of the parts tooled by a machine are rejects.

One-eighth of the parts tooled by a machine are rejected.

Now, let's take the number of parts made by the machine to be x.

Now, the number of acceptable parts will be:

Total number of parts - number of rejected parts

x - (x/10)

(10x-x)/10

9x/10

Now, we have the number of acceptable parts as 4500.

So, we have:

9x/10 = 4500

9x = 4500*10

x = (4500*10)/9

x = 5000

Hence, the total number of parts tooled by the machine is 5000 in which 4500 are acceptable one.

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it takes Jason 6 seconds to hit the water after he jumps off the cliff. To determine when Jason hits the water, we need to find the value of t when h(t) = 0.

This is because the height of Jason is measured in feet and when he hits the water, he will be at a height of zero.

So we can set h(t) equal to zero and solve for t:

[tex]-16t^2 + 16t + 480 = 0[/tex]

Dividing both sides by -16, we get:

[tex]t^2 - t - 30 = 0[/tex]

Now we can use the quadratic formula to solve for t:

t = [-(-1) ± √[tex]((-1)^2[/tex] - 4(1)(-30))] / (2(1))

t = [1 ± √(121)] / 2

t = [1 ± 11] / 2

We get two possible solutions: t = 6 or t = -5. However, since time cannot be negative in this scenario, we can disregard t = -5 and conclude that Jason hits the water after 6 seconds.

Therefore, it takes Jason 6 seconds to hit the water after he jumps off the cliff.

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We can see here:

4. Given: 6x + 7 = 8x - 17. Prove: x = 12

Statements                         Reasons

1. 6x + 7 = 8x - 17                     Given

2. 7 = 2x - 17               Subtracted 6x from both sides    

3. 24 = 2x                    Added 17 to both sides

4. 12 = x                       Divided both sides by 2

5. x = 12                       Final answer proven

An algebraic expression is a mathematical phrase that can contain numbers, variables, and mathematical operations such as addition, subtraction, multiplication, and division. It can represent a value, an equation, or a formula.

5. Given: -7(x + 2) + 4x = 6(2x - 4): Prove: x = 2/3

Statements                               Reasons

1. -7(x + 2) + 4x = 6(2x - 4)   Given

2. -7x - 14 + 4x = 12x - 24     Opened the brackets by multiplying all

3. -3x - 14 = 12x - 24          Added -7x and 4x at LHS      

4. -15x - 14 = -24               Subtracted 12x from both sides

5. -15x = -10                      Added 14 to both sides          

6. x = 2/3                          Divided both sides by -5 to arrive to the result.

6. Given: 3x + 1 = -14: Prove: x = -5

Statements                        Reasons

1. 3x + 1 = -14                   Given

2. 3x = -15                       Subtracted 1 from both sides

3.  x = -5                        Divided both sides by 3. Final answer proven.

7. Given: 2(x - 9) = -10; Prove: x = 4

Statements                           Reasons

1. 2(x - 9) = -10                 Given

2. 2x - 18 = -10                Opened the brackets.

3. 2x = 8                         Added 18 to both sides

4. x = 4                          Divided both sides by 2. Final answer proven.

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The parameters of the relevant standard beta distribution are alpha and beta.

These are two parameters that determine the shape of the beta distribution

.The standard beta distribution is a continuous probability distribution that is defined on the interval [0, 1]. It is often used to model the probability of success or failure in a binary experiment.

The two parameters of the standard beta distribution determine the shape of the distribution. Alpha is the shape parameter that determines the slope of the distribution, while beta is the shape parameter that determines the height of the distribution.

The standard beta distribution is often used in Bayesian statistics to model the prior probability of a parameter. It is also used in applications such as modeling the proportion of a population that has a particular characteristic or modeling the probability of default on a loan.

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The distance the visitor should run to minimize the time it takes to reach the rock formation is 3/4 miles.

A unitary method is a mathematical technique used to solve problems involving proportional relationships between different quantities.

Let's use the unitary method to find the time it takes to complete the journey.

Time taken to run = Distance / Rate = x / 4

Time taken to swim = Distance / Rate = (3 - x) / 3

Total time taken = Time taken to run + Time taken to swim

= x / 4 + (3 - x) / 3

To minimize the total time taken, we need to find the value of x that minimizes the above expression. Let's differentiate it with respect to x and equate it to zero.

d/dx (x/4 + (3-x)/3) = 1/4 - 1/3 = -1/12

-1/12 = 0 (at minimum)

Solving for x, we get:

x = 3/4

The visitor should run westward along the shoreline until reaching the point 3/4 miles away from the tent, and then swim the remaining 2 1/4 miles to reach the rock formation.

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The two sided confidence interval on mean is 3.56 and 4.80.

What is confidence interval?

The proportion of probability, or certainty, that the confidence interval would include the real population parameter when a random sample is drawn numerous times is referred to as the confidence level.

The given data is  3.7, 4.5, 4.1, 4.7, 3.9.  Here n = 5

=> σ = 1- 95% = 5% = 0.05

We know that the confidence interval is

=> CI = [tex]\overline x {\displaystyle \pm }\frac{z(\sigma)}{\sqrt n}[/tex]

Here 95% confidence level so z= 1.96

Mean [tex]\overline x = \frac{3.7+4.5+4.1+3.9+4.7}{5} = 4.18[/tex] and σ = 0.5

Here  n<30 so we can use t instead of z then t-value = 2.776.

Now confidence level CI = [tex]\ 4.18 {\displaystyle \pm }\frac{2.776\times0.5}{\sqrt 5}[/tex]

=> CI = 4.18 [tex]\display \pm[/tex] 0.62 = ( 3.56 , 4.80)

Hence the two sided confidence interval on mean is 3.56 and 4.80.

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Probably 26 :P

Because its like almost double of 10 but it is not....

HOPE THAT MADE SENSE!

Answer: well imma said x=19

Step-by-step explanation:

because All the diameter of the circle is equal.

So 14+15=29

And X is

29-10=19

Thus, the most he could weigh that is the upper bound of the given condition is 84kg.

What about weigh?

The word "weigh" is not frequently used by itself in arithmetic. The notion of weight or mass, for example, can be used when measuring or comparing quantities. While mass is a measurement of the quantity of matter inside an object, weight is a measure of the gravitational force acting on it. Weight can be viewed as the force a standard gravitational field applies to an object in the setting of measurement. Weight or mass may be denoted in mathematical equations by variables such as "w" or "m," and the units used to measure them may change based on the situation.

Define upper bound:

In mathematics, an upper bound is a number that is greater than or equal to all the elements in a given set. More formally, let S be a set of real numbers. A number u is an upper bound for S if and only if for all x in S, we have x ≤ u.

For example, consider the set S = {2, 4, 6, 8}. The number 10 is an upper bound for S because 2 ≤ 10, 4 ≤ 10, 6 ≤ 10, and 8 ≤ 10. However, the number 7 is not an upper bound for S because 8 > 7.

Note that an upper bound need not be an element of the set S itself. For instance, the set of all negative real numbers does not have any upper bound among the negative real numbers, but 0 is an upper bound for this set.

It's worth noting that an upper bound may or may not be a member of the set S. If an upper bound is a member of S, then it is called a "maximum" or "greatest" element of S. However, if an upper bound is not a member of S, then S has no maximum element.

According to the given information:

Brain weigh himself at 84kg to the nearest kg as (given) , because uses the method of round off.

Thus, the range of weigh:

⇒ 83.5 ≤ Weigh ≤ 84.4.

Thus, the most he could weigh is 84.4kg.

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