Directions Read the instructions for this self-checked activity. Type in your response to each question, and check your answers. At the end of the activity, write a brief evaluation of your work. Activity In this activity, you will apply the laws of sines and cosines to solve for the missing angles and side lengths in non-right triangles. Question 1 in triangle ABC, ZA = 35°,mZB = 60°, and the length of side AB is 6 cm. Find the length of side BC using the law of sines.

The z-score is a measure of how many standard deviations a data point is from the mean. It can be calculated using the formula
z = (x - μ) / σ,
where x is the data point, μ is the mean, and σ is the standard deviation.

a. The z-score for a backyard structure costing $2300 can be calculated as follows:

z = (2300 - 3100) / 1200 = -800 / 1200 = -0.67

b. The z-score for a backyard structure costing $4900 can be calculated as follows:

z = (4900 - 3100) / 1200 = 1800 / 1200 = 1.

c. The z-score in part (a) is -0.67, which means that the backyard structure costing $2300 is 0.67 standard deviations below the mean. The z-score in part (b) is 1.5, which means that the backyard structure costing $4900 is 1.5 standard deviations above the mean. Neither of these z-scores are extreme enough to be considered outliers, as they are both within 2 standard deviations of the mean.

d. The z-score for the backyard shed-office combination costing $13,000 can be calculated as follows:

z = (13000 - 3100) / 1200 = 9900 / 1200 = 8.25

This z-score is much larger than 2, which means that the structure costing $13,000 is more than 8 standard deviations above the mean. This is an extreme value and should be considered an outlier.

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The polynomial function \(\(f(x) = 2(x^2+3)(x+1)^2\)\) has zeros at -3 with multiplicity 1, and -1 with multiplicity 2. The graph of the function crosses the x-axis at -3 and -1.

To find the zeros and their multiplicities, we set \(\(f(x)\)\) equal to zero and solve for \(\(x\).\)

Setting \(\(f(x) = 0\),\) we have:

\(\[2(x^2+3)(x+1)^2 = 0\]\)

Since the product of two factors is zero, at least one of the factors must be zero. Thus, we solve for \(\(x\)\) in each factor separately:

1. \(\(x^2 + 3 = 0\):\)

  This equation does not have real solutions since the square of a real number is always non-negative. Therefore, this factor does not contribute any real zeros.

2. \(\(x + 1 = 0\):\)

  Solving for \(\(x\), we find \(x = -1\).\) This gives us a zero at -1 with multiplicity 1.

Since the factor \(\((x+1)^2\)\) is squared, the zero -1 has a multiplicity of 2.

Therefore, the zeros for the polynomial function are -3 with multiplicity 1 and -1 with multiplicity 2. The graph of the function crosses the x-axis at both zeros.

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Step-by-step explanation:

65/x ×100 = 20

6500/20 = x

x = 325 Answer .. option (B)

\( \bold{ \underline{ \purple{Question}}}\)

if 65 is 20% of X then x = ?

\( \bold{Given}\)

\(\bold {\underline{SOLUTION}}\)

65 / 20 = x

\( \displaystyle\frac{65}{20} \times 100\)

\( \displaystyle \: \frac{65}{2 \cancel0} \times 10 \cancel0\)

\( \displaystyle \frac{65 \times 10}{2} \)

\( \displaystyle \frac{650}{2} \)

\(\displaystyle \frac{ \cancel {650}}{ \cancel2} \)

x= 325 Answer

hence option B is correct.

if 65 is 20% of X then x = 325

To find the expected number of each animal type treated by the veterinarian, we will multiply the percentage distribution by the total number of animals treated in a month.

Total animals = 230

Dogs: 61% * 230 = 0.61 * 230 = 140.3 (approximately 140)
Cats: 22% * 230 = 0.22 * 230 = 50.6 (approximately 51)
Livestock: 8% * 230 = 0.08 * 230 = 18.4 (approximately 18)
Birds: 6% * 230 = 0.06 * 230 = 13.8 (approximately 14)
Other: 3% * 230 = 0.03 * 230 = 6.9 (approximately 7)

So, the expected number of each animal type treated is:
Dogs: 140
Cats: 51
Livestock: 18
Birds: 14
Other: 7

The correct answer is C) Animal type Dogs Cats Livestock Birds Other Expected 140 51 18 14 7

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The dilation scaling factor that would map ΔABC to ΔADE is \(k = \dfrac{5}{3}\)

A dilation transformation is one in which the size of the object enlarged or reduced by a scale factor.

Possible parts of the question obtained from a similar question, found online are;

Triangle ΔABC is similar to triangle ΔADE

ΔABC ~ ΔADE

The triangle ΔABC is inscribed in the triangle ΔADE, such that the vertex B is located on the side AD and the vertex C is located on the side AE

The similar relationship between the two triangles indicates that the ratio of the corresponding sides on each triangles have the same values, therefore;

\(\dfrac{AD}{AE}\) = The ratio of the corresponding sides on the triangle ΔABC

\(\dfrac{AD}{AE} = \dfrac{12+8}{18+12} = \dfrac{2}{3} = \dfrac{12}{18} = \dfrac{AB}{AC}\)

Therefore, the corresponding side to AD is AB, and the corresponding side to AE is AC

The scale factor, k, that maps ΔABC to ΔADE, produce the length of AD from AB, or AE from AC as follows;

AD = k × AB

20 = k × 12

Therefore; \(k = \dfrac{20}{12} = \dfrac{5}{3}\)

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Answer:

There were 46 customers who ate at the restaurant.

Step-by-step explanation:

First we need to subtract the total by how much the ban was paid to perform.

$142 - $50 = $92

$92 ÷ 46 = $2

Answer: The interest customer earn in 20 years will be, $ 660

Step-by-step explanation :

Given:

Principle = $3000

Interest rate = 1.1 %

Time = 20 years

Now we have to determine the simple interest.

Formula used :

where,

P = principle

R = interest rate

T = time

S.I = simple interest

Now put all the given values in the above formula, we get:

Thus, the interest customer earn in 20 years will be, $ 660

Hoped this help :) I’m also a fan of flimflam

Answer:

op 2

Step-by-step explanation:

the Answer is b

hope this helps

The given function is

f(x) = - 2|x+5| + 2

The x intercept is the value of x when f(x) = 0

Substituting f(x) = 0 into the function, we have

0 = - 2|x+5| + 2

Subtract 2 from both sides

0 - 2 = - 2|x+5| + 2 - 2

- 2 = - 2|x+5|

Divide both sides by - 2. It becomes

- 2/- 2 = - 2|x+5|/- 2

1 = |x+5|

x + 5 = 1 or x + 5 = - 1

x = 1 - 5 or x = - 1 - 5

x = - 4 or x = - 6

x intercepts are x = - 6, x = - 4

Writing the x intercepts as points, they are

(- 6, 0) and (- 4, 0)

The y intercept is the value of f(x) when x = 0

substituting x = 0 into the function, we have

f(0) = - 2|0+5| + 2

f(0) = - 2|5| + 2 = - 2(5) + 2 = - 10 + 2

f(0) = - 8

y intercept = (0, - 8)

Answer:

Step-by-step explanation: 3√2

Answer:

52% Copper, 28% Zinc, 20% Nickel

Step-by-step explanation:

Copper is 13 out of 13+7+5 = 25

13/25 = 52%

Zinc is 7 out of 25 so 28%

Nickel is 5/25 = 20%

Answer:

31.2

Step-by-step explanation:

it's just basic division

Answer:

I'm not sure if it's .45 or just 45 so I'll do both

0.45 x 120 = 54

45 X 120 = 5400

I don't think a person would weigh 5400kg

Answer:

$45.65

Step-by-step explanation:

$48.92 - $3.27 = $45.65

Convenience purchase: Coca-Cola. Shopping purchase: Apple iPhone. Specialty purchase: Rolex. These brand name products correspond to their respective purchase types based on convenience, shopping involvement, and specialty appeal in the consumer marketplace.

Convenience purchases refer to low-involvement purchases made by consumers for everyday items that are readily available and require minimal effort to obtain. These purchases are typically driven by convenience and habit rather than extensive consideration or brand loyalty.

Shopping purchases involve higher involvement and more deliberate decision-making. Consumers invest time and effort in comparing options, seeking the best value or quality, and may consider multiple brands before making a purchase. These purchases often involve durable goods or products that require more consideration.

Specialty purchases are distinct and unique purchases that cater to specific interests, preferences, or hobbies. These purchases are driven by passion, expertise, and a desire for premium or specialized products. Consumers are often willing to invest more in these purchases due to their unique features, quality, or exclusivity.

Three specific brand name products in the consumer marketplace that correspond to these types of purchases are

Convenience Purchase: Coca-Cola (Soft Drink)

Coca-Cola is a widely recognized brand in the beverage industry. It is readily available in various sizes and formats, making it a convenient choice for consumers seeking a refreshing drink on the go.

With its widespread availability and strong brand presence, consumers often make convenience purchases of Coca-Cola without much thought or consideration.

Shopping Purchase: Apple iPhone (Smartphone)

The Apple iPhone is a popular choice for consumers when it comes to shopping purchases. People invest time researching and comparing features, pricing, and user reviews before making a decision.

The shopping process involves considering various smartphone brands and models to ensure they select a product that meets their specific needs and preferences.

Specialty Purchase: Rolex (Luxury Watches)

Rolex is a well-known brand in the luxury watch industry and represents specialty purchases. These watches are associated with high-quality craftsmanship, precision, and exclusivity.

Consumers who are passionate about luxury watches and seek a premium product often consider Rolex due to its reputation, heritage, and unique features. The decision to purchase a Rolex involves a significant investment and is driven by the desire for a prestigious timepiece.

These examples illustrate how different types of purchases align with specific brand name products in the consumer marketplace, ranging from convenience-driven choices to more involved shopping decisions and specialty purchases driven by passion and exclusivity.

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Both options a. A = 129.9° and b. A = 53.1° are correct.

To find the possible values for angle A in triangle ABC, we can use the Law of Sines, which states that in any triangle, the ratio of the length of a side to the sine of its opposite angle is constant.

Using the Law of Sines, we have sin(A)/a = sin(B)/b. Plugging in the given values, we get sin(A)/36 = sin(51°)/35.

To find the two possible values for angle A, we can solve the equation sin(A)/36 = sin(51°)/35. Taking the arcsine of both sides, we have A = arcsin((sin(51°)/35)*36).

Calculating this expression, we find two possible values for angle A:

A ≈ 53.1° (rounded to the nearest tenth)

A ≈ 129.9° (rounded to the nearest tenth)

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Answer:

35997

Step-by-step explanation:

The two numbers are 6 and 2.

Let's assume the first number is x and the second number is y.

From the first statement, we can write the equation x = y + 4.

From the second statement, we can write the equation 2x = 4y + 2.

Now, we can substitute x in terms of y from the first equation into the second equation:

2(y + 4) = 4y + 2

Simplifying this equation, we get:

2y + 8 = 4y + 2

2y = 6

y = 3

Substituting y = 3 in the first equation, we get:

x = y + 4 = 3 + 4 = 7

Therefore, 6 and 2 are the two numbers,


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Answer:

t = 13

Step-by-step explanation:

Solve for t

\(-6(t-12)=-6\)

Simplify

\(-6(t+-12)=-6\)

Distribute -6

\(-6t+72=-6\)

Subtract 72 on both sides

\(-6t=-78\)

Divide by -6

\(t=13\)

For a given sample proportion of 0.5, the sample size that will produce the widest confidence interval is the largest option given, which in this case is 80.

The sample size that will produce the widest 95% confidence interval, given a sample proportion of 0.5, is option b, 80. This is because the width of the confidence interval is directly proportional to the sample size, meaning that as the sample size increases, the confidence interval becomes narrower.

Additionally, the width of the confidence interval is inversely proportional to the square root of the sample size. Therefore, for a given sample proportion of 0.5, the sample size that will produce the widest confidence interval is the largest option given, which in this case is 80.

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After answering the provided question, we can state that Therefore, the equation solution for k is k = tm.

In mathematics, an equation is a proclamation stating the equality or two manifestations. An equation is made up of two sides that are separated by an analytical solution (=). For example, the argument "2x + 3 = 9" asserts that the statement "2x + 3" equals the value "9". The goal of equation solving is to determine the value or beliefs of the variable(s) that will allow the equation to be true. Equations can be simple or complex, normal or nonlinear, and include one or more factors. In the eqn "x2 + 2x - 3 = 0," for example, the variable x is raised to the powercell. Lines are utilized by numerous fields of mathematics, which include algebra, calculus, or geometry.

To solve for k in the equation r=tmr/k,

\(k * r = tmr\\k = tmr/r\\k = tm\)

Therefore, the solution for k is k = tm.

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Step-by-step explanation:

Given that,

12 over 30 and 18 over 45

We need to tell whether the ratios are Proportional or Not Proportional.

\(\dfrac{12}{30}=\dfrac{2}{5}\)

And

\(\dfrac{18}{45}=\dfrac{2}{5}\)

The ratio for both fraction is same i.e. 2/5 Hence, each ratios are Proportional.

The expression of the perimeter of the right triangle is 12a³

Perimeter is the distance around the edge of a shape. Learn how to find the perimeter by adding up the side lengths of various shapes.

Therefore , if the three sides of a triangle is represented by a, b,c then the perimeter = a+b+c.

The hypotenuse of the triangle =

√(3a³)² + 4a³)²

= √ 9a⁶+16a⁶

= √ 25a⁶

= 5 a³

therefore the perimeter of the triangle =

5a³ + 3a³ + 4a³

= 12a³

therefore the perimeter of the triangle is 12a³

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Calculate the square root in both sides of the calculation:

Distribute the square roots

Simplify the square roots.

Then:

The mode is the most appropriate measure of center to represent the data in the graph because it reflects the most common value(s) observed in the dataset. In this case, the mode is 3.

The most appropriate measure of center to represent the data in the given line plot is the mode.

The mode is the value or values that occur most frequently in a dataset. In this case, we can observe the frequencies of the data points on the line plot:

There is one dot above 2, 4, 8, and 9.

There are two dots above 6 and 7.

There are three dots above 3.

Based on this information, the mode(s) of the dataset would be the values that have the highest frequency. In this case, the mode is 3 because it appears most frequently with a frequency of three. The other data points have frequencies of one or two.

The mode is particularly appropriate in this scenario because it represents the most common or frequently occurring value(s) in the dataset. It is useful for identifying the central tendency when the data is discrete and there are distinct peaks or clusters.

While the median and mean are also measures of center, they may not be the most appropriate in this case. The median represents the middle value and is useful when the data is ordered. However, the given line plot does not provide an ordered arrangement of the data points. The mean, on the other hand, can be affected by outliers and extreme values, which may not accurately represent the central tendency of the dataset in this scenario.

Therefore, the mode is the most appropriate measure of center to represent the data in the graph because it reflects the most common value(s) observed in the dataset. In this case, the mode is 3.

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Answer:

x≥7 or x≤−14

Step-by-step explanation:

Let's solve your inequality step-by-step.

|2x+7|≥21

Solve Absolute Value.

|2x+7|≥21

We know either2x+7≥21or2x+7≤−21

2x+7≥21(Possibility 1)

2x+7−7≥21−7(Subtract 7 from both sides)

2x≥14

2x

2

≥

14

2

(Divide both sides by 2)

x≥7

2x+7≤−21(Possibility 2)

2x+7−7≤−21−7(Subtract 7 from both sides)

2x≤−28

2x

2

≤

−28

2

(Divide both sides by 2)

x≤−14

Answer:

x≥7 or x≤−14

Answer:

the answer I believe is true because f or r at least equals 1. so 1 times 12 is 12 + 71 is greater than or equal too 21. (12+71=83)

Step-by-step explanation:

The required answer is  sec θ = -√2.

Explanation:-

Part 1: Given cosine of theta is equal to radical 3 over 2 on the domain [0,[infinity]).

To determine three possible angles θ,  the cosine inverse function which is a cos and since cosine function is positive in the first and second quadrant. Therefore  conclude that, cosine function of θ = radical 3 over 2 implies that θ could be 30 degrees or 330 degrees or 390 degrees. So, θ = {30, 330, 390}.Part 2:To convert 495° to radians, multiply by π/180°.495° * π/180° = 11π/4To find sec θ, we use the reciprocal of the cosine function which is sec.

Therefore, sec θ = 1/cos θ.To find cos 11π/4,  the reference angle, which is 3π/4. Cosine is negative in the third quadrant so the final result is sec θ = -√2.

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Answer:

0.47

Step-by-step explanation:

47% = to 0.47