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The values for the angle B and the side lengths of the right-angled triangle ABC are B = 41°, a = 9.6 , and b = 8.3 using the trigonometric ratios of sine and cosine of angle 49°.

The trigonometric ratios is concerned with the relationship of an angle of a right-angled triangle to ratios of two side lengths. The basic trigonometric ratios includes;

sine, cosine and tangent.

Considering the right-angled triangle ABC, we shall calculate for the angle B and side lengths a and b as follows:

A + B + C = 180° {sum of interior angles of a triangle}

49° + B + 90° = 180°

B = 180° - 139°

B = 41°

sin49 = a/12.7 {opposite/hypotenuse}

a = 12.7 × sin49 {cross multiplication}

a = 9.5848

cos49 = b/12.7 {adjacent/hypotenuse}

b = 12.7 × cos49 {cross multiplication}

b = 8.3319

Therefore, the values for the angle B and the side lengths of the right-angled triangle ABC are B = 41°, a = 9.6 , and b = 8.3 using the trigonometric ratios of sine and cosine of angle 49°..

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The formula to describe the variation is F = 1.6d².

Option C is the correct answer.

An equation is made up of one or two variables with a constant connected by an equal sign.

Example:

2x + 4 = 9 is an equation.

We have,

F is directly proportional to the square of d.

This can be written as,

F ∝ d²

F = kd² ____(1)

Now,

F = 40 when d = 5.

40 = k x 5²

k = 40/25

k = 8/5 _____(2)

Now,

From (1) and (2).

F = (8/5)d²

F = 1.6d²

Thus,

The formula to describe the variation is F = 1.6d².

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Answer: C and D are the correct ones

Step-by-step explanation:

If , Pete is saving $0. 45 each week to buy a video game that cost $9.0. Pete will have to save for 20 weeks to have enough money to buy the video game.

The problem asks us to find out how many weeks Pete will have to save to buy a video game that costs $9.0 if he is saving $0.45 each week. To solve this problem, we can use division to find out how many times $0.45 goes into $9.0.

We first divide the total cost of the game by the amount Pete saves each week, which gives us the number of weeks he will need to save.

In this case, the division of $9.0 by $0.45 yields 20, which means that Pete will have to save for 20 weeks to buy the video game. This calculation is important for Pete because it helps him plan his savings and gives him a goal to work towards. By saving $0.45 every week, he can keep track of his progress and stay motivated to reach his goal.

This problem highlights the importance of basic arithmetic skills, specifically division, in practical situations like budgeting and financial planning. By applying mathematical concepts to everyday situations, we can make informed decisions and manage our resources more effectively.

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a) The histogram of the data is illustrated below.

b) A cumulative percentage polygon is illustrated on histogram.

c) The cumulative percentage polygon shows us that approximately 66% of calls fall below 240 seconds.

Histograms are a way of representing data visually by dividing it into intervals or bins and plotting the frequency of data points in each bin. In this problem, we will be constructing a percentage histogram and polygon to analyze call duration data.

The call duration data is provided in seconds for 50 customers. To construct a percentage histogram, we need to first determine the bin size or interval. One way to do this is to use the square root rule, which states that the number of bins should be approximately equal to the square root of the sample size. In our case, the sample size is 50, so we can round the square root to 7 and use 7 bins.

Next, we need to determine the range of the data and set the limits for each bin. The range of the data is from 65 to 1141 seconds. We can set the limits for each bin as follows: 60-180, 181-300, 301-420, 421-540, 541-660, 661-780, 781-900, and 901-1020.

To construct the percentage histogram, we need to divide the frequency in each bin by the total sample size and multiply by 100. This gives us the percentage of data points in each bin. We can then plot these percentages as bars of equal width for each bin.

The percentage polygon is constructed by connecting the midpoints of the tops of each bar in the histogram with straight lines. This creates a polygon that represents the distribution of data in the histogram.

In this problem, we are asked to analyze call center performance if a call duration target of less than 240 seconds is set. From the percentage histogram and polygon, we can see that the majority of calls fall within the first three bins, which correspond to call durations of 60-180, 181-300, and 301-420 seconds. Only a small percentage of calls exceed 420 seconds.

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Answer:

396cm^3

Step-by-step explanation:

use formula V=Area of base * Height that is V=1/2b*h *Height

The two point baskets are 16 and the three point basket is 1.

A system of linear equations consists of two or more equations made up of two or more variables such that all equations in the system are considered simultaneously. The solution to a system of linear equations in two variables is any ordered pair that satisfies each equation independently.

Given that, a basketball player scored 50 points.

Let the two point baskets be x and the three point baskets be y.

The total number of baskets made was 17.

Here, x+y=17 -------(i)

During last nights game all two point and three point baskets.

Now, 2x+3y=50 -------(ii)

Substitute x=17-y in the equation (ii), we get

2(17-y)+3y=50

34-2y+3y=50

y=16

Substitute y=16 in equation (i), we get

x=1

Therefore, the two point baskets are 16 and the three point basket is 1.

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Black Beauty stands one inch taller than Thumbelina, measuring 18 inches in height compared to Thumbelina's 17-inch stature.

Black Beauty is 1 inch taller than Thumbelina.

Two or more expressions with an Equal sign is called as Equation.

Given that Thumbelina, who stands 17 inches tall

Black Beauty, who stands 18 inches tall.

Einstein, who stands 14 inches tall.

We have to find how tall is Black Beauty than Thumbelina.

To find out, we can subtract Thumbelina's height from Black Beauty's height:

Black Beauty's height - Thumbelina's height

= 18 inches - 17 inches = 1 inch

Therefore, Black Beauty is 1 inch taller than Thumbelina.

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The elevator is on the 14th floor at this situation.

What is the basic arithmetic operation?

Arithmetic operations are mathematical operations that involve basic calculations such as addition, subtraction, multiplication, and division. These operations are used to perform calculations with numbers and are used in a wide range of mathematical and real-life situations.

If the elevator is on the 18th floor, and it moves down 16 floors, it will be on the 2nd floor.

After that, the elevator comes up 12 floors from the 2nd floor. So, it will be on the floor:

2 + 12 = 14

Therefore, the elevator is on the 14th floor at this situation.

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Answer:

SX = 20

Step-by-step explanation:

the midsegment of a trapezoid is half the sum of the parallel bases, then

[tex]\frac{UV+SX}{2}[/tex] = TW , that is

[tex]\frac{40+SX}{2}[/tex] = 30 ( multiply both sides by 2 to clear the fraction )

40 + SX = 60  ( subtract 40 from both sides )

SX = 20

The sampling technique best described here is systematic sampling. Systematic sampling is a type of probability sampling in which the elements in the population are selected in a systematic way

This sampling technique is used when the population size is too large to survey the entire population. In this example, the population size is 300 passengers and the sampling interval is determined by dividing the population size by the sample size. For example, if the sample size is 30, the sampling interval is[tex]10 (300/30=10).[/tex] This means that every 10th passenger is randomly selected for the survey. The selection starts with a randomly chosen passenger and then the ninth passenger after that is selected and so on. The formula for Systematic sampling is n = N/n, where N is the population size and n is the sample size.

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One gallon is equivalent to 4 quarts, so 1 1/2 gallons is equal to 1 1/2 x 4 = 6 quarts. To determine if the amount of water in the bucket is greater than, less than, or equal to 6 quarts, we need to convert the amount from gallons to quarts.

A gallon is a unit of volume commonly used in the United States, while a quart is a unit of volume commonly used in both the US and the UK.

One gallon is equivalent to 4 quarts, so 1 1/2 gallons is equal to 1 1/2 x 4 = 6 quarts.

Therefore, the amount of water in the bucket is equal to 6 quarts.

It's important to be able to convert between different units of measurement to effectively communicate and understand various quantities. In the case of volume, it's crucial to use consistent units when comparing the amount of liquids in containers or when measuring the volume of substances.

Conversion between units of measurement also plays a significant role in many fields, such as cooking, baking, construction, and engineering, where precise measurements are critical.

In conclusion, the amount of water in the bucket is equal to 6 quarts, and the ability to convert between different units of measurement is an important skill in various areas of life and work.

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The answer is that there is no probability for this event to happen. To find the probability of getting exactly one red marble or exactly one green marble and not both at the same time, we can use the following steps:

Step 1: Find the number of ways to draw 3 marbles out of 12.

This can be found using the combination formula, which gives:

C(12,3) = 12! / (3! * 9!) = 220

Therefore, there are 220 ways to draw 3 marbles out of 12.

Step 2: Find the number of ways to draw exactly one red marble and two non-red marbles.

There are 3 red marbles, and we need to choose one, so there are C(3,1) = 3 ways to do this. There are 9 non-red marbles, and we need to choose two of them, so there are C(9,2) = 36 ways to do this. Therefore, 3 * 36 = 108 ways to draw exactly one red marble and two non-red marbles.

Step 3: Find the number of ways to draw exactly one green marble and two non-green marbles.

There are 4 green marbles, and we need to choose one, so there are C(4,1) = 4 ways to do this. There are 8 non-green marbles, and we need to choose two of them, so there are C(8,2) = 28 ways to do this. Therefore, there are 4 * 28 = 112 ways to draw exactly one green marble and two non-green marbles.

Step 4: Find the number of ways to draw exactly one red marble and one green marble. There are 3 red marbles and 4 green marbles, and we need to choose one of each, so there are 3 * 4 = 12 ways to do this.

Step 5: Add the results from steps 2, 3, and 4 to get the number of ways to draw marbles that satisfy the given condition.

Total number of ways = 108 + 112 + 12 = 232

Step 6: Find the probability of getting exactly one red marble or one green marble but not both at the same time.

The probability of an event is the number of ways that event can happen divided by the total number of possible outcomes. Therefore, the probability of getting exactly one red marble or exactly one green marble and not both at the same time is:

P = (number of ways to draw marbles that satisfy the given condition) / (total number of ways to draw 3 marbles out of 12 marbles)

P = 232 / 220

P = 1.0545

However, probabilities cannot be greater than 1. Therefore, the answer is that there is no probability for this event to happen.

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The z value of 0.2 indicates the standardized difference between the sample mean and population mean

The z value is a standardized score that tells us how many standard deviations a sample mean is from the population mean. In other words, it helps us determine the likelihood that the difference between the two means is due to chance or some other factor.

Typically, we use a significance level (often denoted by alpha) to determine if the z value is significant or not. If the z value falls within the critical values for the chosen significance level, we reject the null hypothesis and conclude that there is a significant difference between the two means. If the z value falls outside the critical values, we fail to reject the null hypothesis and conclude that there is not a significant difference.

In your case, with a z value of 0.2, it is important to consider what significance level was used in the test. If the chosen significance level was 0.05. Since 0.2 falls within this range, we would fail to reject the null hypothesis and conclude that there is not a significant difference between the sample mean and population mean.

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The measures of angle possible for of an isosceles triangle when one angle given is 140° then other two angles is 20°.

In an isosceles triangle, two of the angles have the same measure. Let's call this measure x. Since the sum of the angles of a triangle is 180 degrees, we can set up an equation:

x + x + 140° = 180°

Simplifying the equation, we get:

2x + 140° = 180°

Subtracting 140° from both sides, we get:

2x = 40°

Dividing both sides by 2, we get:

x = 20°

So the other two angles in the isosceles triangle each measure:

x = 20°

Therefore, the measures 28°, 22°, 26° are not possible for the other two angles of the isosceles triangle, but the measure 20° degrees is possible.

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Answer:

Step-by-step explanation:

multiply all numbers together

2 x 6 x 3 = 36

Alexandria can expect to spend about $128.25 on school lunches for the year if she forgets to bring her lunch about once a week.

If Alexandria forgets to bring her lunch 15% of the time, then she will need to buy a school lunch on 15% of the 180 school days:

15% of 180 = 0.15 × 180 = 27 school days

So, Alexandria will buy a school lunch 27 times during the school year.

The average cost of a school lunch is $4.75.

So the total cost of buying school lunches for the year will be:

27 × $4.75 = $128.25

Therefore, Alexandria can expect to spend about $128.25

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The exponential function that represents the given scenario is
y = (30.5)(0.7)ˣ.  

The exponential function is a type of mathematical equation that can be used to determine if anything is increasing or decreasing exponentially, such as population, money, or price.

The general form of an exponential function is given by

           f(x) = abˣ   or y = abˣ

Where 'x' is a variable and a and b are constants

Here we have

The graph shows the number of games system sold since 2005.

As we know an exponential function is represented as:  

=> y = abˣ

From the given graph x = 0 and y = 30.5

=> 30.5 = ab⁰  

=> 30.5 = a(1)

=> a = 30.5  

When x = 1, y = 21.35

=> 21.35 = (30.5)(b¹)  

=> b = 0.7

So the required exponential function can be written as

=> y = (30.5)(0.7)ˣ    

Therefore,

The exponential function that represents the given scenario is
y = (30.5)(0.7)ˣ.    

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The angle corresponding to each other of the different triangles are equal. The correct option is D.

"Similar triangles are triangles that have the same shape but differ in size. Similar objects include all equilateral triangles and squares with any side length. In other words, if two triangles are similar, their corresponding angles and sides are congruent and in equal proportion ".

Here given, ΔJGR is similar to a triangle ΔMST

So, from the definition of a similar triangle,

angle J ≅ angle M

angle G ≅ angle S

angle R ≅ angle T

Hence, option D is correct.

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The number of green rugs is more than the number of purple rugs. Then the amount of blue rug will be 29/4 square units.

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.

Nina buys a new rug that matches three colors in her bedroom. The rug is a rectangle. There are eight squares on the rug. Four-eighths of the squares are green. One-fourth of the squares are purple.

The amount of green rug is given as,

⇒ 4/8

⇒ 1/2 square units

The amount of purple rug is given as,

⇒ 1/4 square units

The number of green rugs is more than the number of purple rugs.

The amount of blue rug is given as,

⇒ 8 - 1/4 - 4/8

⇒ (64 - 2 - 4) / 8

⇒ 29/4 square units

The number of green rugs is more than the number of purple rugs. Then the amount of blue rug will be 29/4 square units.

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Step-by-step explanation:

Since it varies directly, we can set up a ratio and solve for x

[tex] \frac{ - 4}{ - 2} = \frac{x}{12} [/tex]

Next we would cross multiply... multiply the numbers diagonally

[tex]( - 4)(12) = ( - 2)(x)[/tex]

Simplifying

[tex] - 48 = - 2x[/tex]

Now to get X alone, we would divide by the number attached to it, so -2. We'd do -2 on the -48 also

[tex]x = 24[/tex]

The probability that there will be less than two days between manufacturing production line outages is approximately 0.553, or 55.3%.

We need to make some assumptions in order to calculate the probability that the time intervals between manufacturing production line breakdowns will be shorter than two days. Assume that the intervals between breakdowns have an exponential distribution with a mean of 3.5 days (1/2 times per week).

The probability that an interarrival time is fewer than two days can be calculated using the exponential distribution formula as follows:

P(X < 2) = 1 - e(-2/3.5)

where "X" stands for the duration in between breakdowns.

When we condense the expression, we get:

P(X < 2) = 0.553

Therefore, The probability that there will be less than two days between manufacturing production line outages is approximately 0.553, or 55.3%.

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In a density curve, the proportion of data is represented by the area under the curve. So option B is correct.

The probability that an observation chosen at random falls within a given interval is represented by the area under a density curve, which is a smooth representation of a probability distribution. As a result, the area under the curve between the respective points is proportional to the percentage of data that falls inside a given range.

The area under the curve that directly represents the proportion of data. The intervals of values on the vertical and horizontal axes are used to plot the curve and are important for interpreting the graph, but they do not directly represent the proportion of data. The length of the curve is not relevant for determining the proportion of data, as it can vary depending on the scaling of the graph.

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Answer: bro just look it up fr fr

Step-by-step explanation:

a. If H0 is true then the test is designed for probability of type I error of 0.025 .b. Here the p Value is 0.10 . So this indicates that the H0 is true in this test . But there is a decision error if we Reject the Null hypothesis H0.

A hypothesis is an educated guess or statement that attempts to explain a particular phenomenon or answer a specific research question. It is an essential element of the scientific method, which involves testing a proposed explanation through experimentation or observation. The purpose of a hypothesis is to guide researchers in designing an experiment that can be used to either support or refute the proposed explanation.

A hypothesis is typically based on prior knowledge, observations, or theories related to the research question. It is important for a hypothesis to be testable, measurable, and specific to allow researchers to evaluate the results objectively. A hypothesis can be developed in various fields of study, including natural sciences, social sciences, and humanities.

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Complete Question: -

A significance test about a proportion is conducted using a significance level of 0.025. The test statistic equals 1.33. The​P-value is 0.10. a. If Upper H 0 were​ true, for what probability of a Type I error was the test​ designed? b. If this test resulted in a decision​ error, what type of error was​ it?

a. If Upper H 0 were​ true, for what probability of a Type I error was the test​ designed?

b. If this test resulted in a decision​ error, what type of error was​ it? Type II Type Upper I

The amount of extra meals that Taryn needs to feed her dog today is given by the inequality expression; x > 2

The parameters given in the question are;

Weight of dog = 40 pounds

Average amount of calories required per day = 1215 calories

Amount of calories already eaten = 729 calories

Amount of calories fed per meal = 243 calories

The inequality that represents the given word problem is;

243x + 729 > 1215

Subtract 729 from both sides to get;

243x > 486

divide both sides by 243 to get;

x > 2

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She had to pay they have to pay her back $ 132.

Multiply: -

Payback = 360 x 120/100

               = 132

Payback is a financial metric that measures the time it takes to recover the initial investment cost of a project. It is commonly used in investment analysis to evaluate the viability of potential projects by estimating the time it takes for the project to start generating profits.

The payback period is calculated by dividing the initial investment by the expected cash flow of the project on an annual or monthly basis until the investment is fully recovered. The shorter the payback period, the more attractive the project is to investors. Payback is a simple and straightforward metric, but it has some limitations. It does not consider the time value of money or the long-term profitability of the project.

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Complete Question: -

Paula went to the supermarket and to pay her bill she gave $ 360 if she gave 120% of what she had to pay, how much did they have to pay her back?