1) The area of the shaded sector is 51.3 square feet. What is an estimate for the radius of the
circle? Round the answer to the nearest foot.
B
60°
D
120°
C

A sequence is an ordered list of elements or objects that follows a specific pattern or rule, where the order of the terms is important.

A sequence is an ordered list of numbers, symbols, or other mathematical objects. The order in which the elements appear is important and determines the identity of the sequence. For example, consider the following two sequences:

1, 3, 5, 7, 9

3, 5, 1, 7, 9

The first sequence consists of odd numbers in ascending order, while the second sequence consists of the same numbers but in a different order. These two sequences are different because the order of the terms is different.

Sequences can have different patterns or rules that determine the order of the terms. For example, the sequence of Fibonacci numbers, which is a famous sequence in mathematics, has the following pattern:

1, 1, 2, 3, 5, 8, 13, 21, 34, ...

Each term in the sequence (starting with the third term) is the sum of the two preceding terms.

This pattern continues indefinitely, creating a sequence that has a distinct pattern and order.

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What is the arrangement of objects in a definite order called?

Step-by-step explanation:

ASA stands for angle, side, angle

How is triangle ABC congruent to DEF

If any two angles and the side included between the angles of one triangle are equivalent to the corresponding two angles and side included between the angles of the second triangle, then the two triangles are said to be congruent by ASA rule.

In the diagram you shared, side BC is equivalent to line FD

Angle B = angle F

Angle C = Angle D

(Compare the markings on both triangles)

The relationship between triangle ABC and triangle DEF are congruent only by 2 angles and one side.

Answer:

The correct probability is 16/100, or 4/25.

There are 1,728 ways for the 12 students to sit in their assigned seats while maintaining the grouping by major.

There are four groups based on major: chemistry, business, political science, and journalism. We need to find the number of ways the 12 students can sit in their assigned seats while maintaining the grouping by major.

We can approach this problem by first considering the number of ways each group can be seated separately, and then multiply the results together to get the total number of arrangements.

For the chemistry group, there are 3 students who can be seated in any order.

For the business group, there are 2 students who can be seated in any order.

For the political science group, there are 3 students who can be seated in any order.

Finally, for the journalism group, there are 4 students who can be seated in any order.

Therefore, the total number of arrangements for the 12 students is:

3! * 2! * 3! * 4! = 6 * 2 * 6 * 24 = 1,728

Therefore, there are 1,728 ways for the 12 students to sit in their assigned seats while maintaining the grouping by major.

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The inequality equation that can be used to solve this problem is x + y ≤ 250 and y ≥ 4x

An equation is an expression that shows the relationship between numbers and variables using mathematical operators such as addition, subtraction, exponent, multiplication and division.

Let x denote the area (in square feet) used for flowers and y denote the area (in square feet) used for vegetables.

A gardener will use up to 250 square feet for planting flowers and vegetables, hence:

x + y ≤ 250    (1)

She wants the area used for vegetables to be at least four times the area used for flowers. Hence:

y ≥ 4x     (2)

Plotting both equations using geogebra, the solution is the darker region.

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Answer:

a₉ = - 24

Step-by-step explanation:

the nth term of an arithmetic sequence is

[tex]a_{n}[/tex] = a₁ + (n - 1)d

given a₁ = 8 and d = - 4 , then

a₉ = 8 + (8 × - 4) = 8 + (- 32) = 8 - 32 = - 24

Answer:

Tn = a + (n - 1)d

T9 = 8 + (9 - 1) × -4

T9 = (8 + 8) × -4

T9 = 16 × -4

T9 = -64

All the answers related to null hypothesis are explained below.

Null hypothesis is used to test if there is any statistical significance between the two groups being compared.

1. The null hypothesis is that there is no difference in the number of counseling sessions attended by men and women.

2a. For a two-tailed .05test, you would reject the null hypothesis if the absolute value of the t-statistic is greater than the critical value of 1.96.

2b. For a one-tailed .05test, you would reject the null hypothesis if the t-statistic is greater than the critical value of 1.645.

2c. For a two-tailed .01test, you would reject the null hypothesis if the absolute value of the t-statistic is greater than the critical value of 2.58.

2d. For a one-tailed .01test, you would reject the null hypothesis if the t-statistic is greater than the critical value of 2.33.

3. Rejecting the null hypothesis means that the data is statistically significant and you are confident that the difference in the number of counseling sessions attended by men and women is not due to chance.

4. For a two-tailed test, a Type I error occurs when the null hypothesis is rejected when it should not have been. For a one-tailed test, a Type I error occurs when the null hypothesis is rejected when the difference between the two groups is not greater than the critical value.

5. Conceptually, something is considered to be statistically significant when it is unlikely that the observed results were due to chance.

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The expression can be written as the sum of two terms as 74.5 + 0.5d

Mathematical expressions are combinations of numbers, variables, and operators (such as +, -, ×, ÷, =) that represent a mathematical relationship or computation.

To write the given expression as the sum of two terms simplify the expression by multiplying and adding or subtracting like terms.

Here we have

The expression 75 + 0.5(d - 1) represents the fine for an overdue library book, where d is the number of days overdue.

Simplify expression as shown below

=> 75 + 0.5(d - 1)

= 75 + 0.5d - 0.5

= 0.5d + 74.5  

Now the expression is in the form of the sum of two terms

Therefore

The expression can be written as the sum of two terms as 74.5 + 0.5d

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From the given information provided, the area of the square room with rectangular section is 72 square feet.

Let's assume that the rectangular section of the floor that is tiled has length "L" and width "W". Since the area of the rectangular section is 18 square feet, we have:

L × W = 18

Since the room is square, its length and width are equal, let's say it's "x". Then, the area of the room is x².

Since the rectangular section is a part of the room, we have:

L ≤ x and W ≤ x

Therefore, we can find the minimum possible value of x by assuming that L = W = √18 (the sides of the rectangle are equal, and equal to the square root of 18), which gives:

x = √18 + √18 = 2√18

So, the area of the room is:

x² = (2√18)² = 4(18) = 72 square feet

Question - A contractor tiles a rectangular section of floor in a square room. The tiles covers 18sq. feet. What is the area of room?

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The true statement about the function notation are:

The definition of the graph is given as

The distance vs time graph

This is represented by F = d(t)

The function notation would be determined to be true or false by observation

This is so because the graph is not drawn to scale

Using the above as a guide, we have the following:

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The surface area of the pyramid is 105.6 square feet.

To find the surface area of this pyramid, we need to calculate the area of all its faces and add them up.

Since all sides of our hexagon are equal, we can simplify this formula to:

Surface Area of Hexagon = 6 x (3√3 / 2) x (Side length)²

Total Surface Area = Surface Area of Base + Surface Area of Triangular Faces

Total Surface Area = 6 x (3√3 / 2) x (Side length)² + 6 x (Side length x 15) / 2

We can simplify this expression further by factoring out 6 x (Side length)² from both terms:

Total Surface Area = 6 x (Side length)² x [(3√3 / 2) + 15]

To find the surface area of a right hexagonal pyramid with equal-length sides and triangular faces of height 15 ft, we use the formula above:

Total Surface Area = 6 x (Side length)² x [(3√3 / 2) + 15]

When the value of side length is 1, then total surface area is

=> Total Surface Area = 6 x (1)² x [(3√3 / 2) + 15] = 105.6 square feet.

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Answer:

Any line with a slope of -2/3 that doesnt have an intercept of -3

Step-by-step explanation:

y = − 2/3x − 3 is written in slope-intercept form y = mx + b, where m is the slope, and b is the y intercept

What your looking for is a line with the same -2/3 slope

Important! If a line has the same slope AND intercept, then they are identical, not parallel

Using percentages we know that the population after 25 years would be 12.4 billion which is 12,40,00,00,000.

A % is a quantity or ratio that, in mathematics, represents a portion of one hundred.

A dimensionless relationship between two numbers can be represented in a variety of ways, such as through ratios, fractions, and decimals.

The symbol "%" is frequently written after the number to indicate percentages.

Now, we know that:

The population is 8 billion.

The increasing percentage is 2.2%.

Then, the population after 25 years would be:

= 8000000000/100 * 2.2

= 17,60,00,000

Now, after 25 years:

= 17,60,00,000 * 25

= 4,40,00,00,000

Total population after 25 years:

4,40,00,00,000 + 8000000000 = 12,40,00,00,000

Therefore, using percentages we know that the population after 25 years would be 12.4 billion which is 12,40,00,00,000.

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The null hypothesis is that the mean weight of women is 145 lbs.The P-value is 0.0145. At a 0.05 significance level, the null hypothesis can be rejected. This suggests that the mean weight of women is not 145 lbs.

The null hypothesis is that the mean weight of women is 145 lbs. To test the hypothesis, we need to calculate the P-value. The mean of the sample of 40 weights is 153.2 lbs, with a standard deviation of 30.86 lb. The P-value is calculated using a z-score formula which is (153.2-145)/(30.86/sqrt(40)) = 0.0145. Since the P-value is less than 0.05, this suggests that the mean weight of women is not 145 lbs. Therefore, at a 0.05 significance level, the null hypothesis can be rejected.

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The experimental likelihood of rolling a number greater than 1 is 66.67%, which, according to the calculations above, is close to the theoretical probability of 83.33%.

Calculating the likelihood that an event will occur or a statement will be true is the subject of probability theory, a branch of mathematics. A risk is a number between 0 and 1, where 1 denotes certainty and a probability of about 0 denotes the likelihood that an event will occur. The likelihood that an event will take place is mathematically expressed as probability. Probabilities can also be expressed as percentages ranging from 0% to 100% or as integers between 0 and 1. the proportion of equally plausible possibilities that actually happen in relation to all other outcomes when a specific event occurs.

The bar graph displays how many times a number cube was rolled along with the outcome. The graph shows that the number cube was rolled 300 times in total, yielding the number larger than 1 200 times.

Experimental probability is calculated as follows: 200/300 = 0.6667, or 66.67%, where experimental probability = (number of times greater than 1)/(total number of rolls)

Theoretical probability is calculated as follows: 5/6 = 0.8333 or 83.33% (number of possibilities greater than 1) / (total number of possible outcomes).

The experimental likelihood of rolling a number greater than 1 is 66.67%, which, according to the calculations above, is close to the theoretical probability of 83.33%.

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The height of ladder is approximately 26.9 feet tall.

In order to get the length of the hypotenuse, divide the non-hypotenuse side that is close to the angle by cos(). If you prefer, you can multiply this length by tan() to obtain the length of the side that is perpendicular to the angle.

Let's tackle this issue using the Pythagorean theorem.

According to the Pythagorean theorem, the sum of the squares of the leg lengths in a right triangle equals

The length of the slide is the other leg, the distance from the ladder's bottom to its base is one leg, and the ladder itself is the hypotenuse.

b² = 18² + 20²

b² = 324 + 400

b² = 724

b = √(724)

b ≈ 26.9

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Answer:

£5329.51

Step-by-step explanation:

Knowing that £6502 is the price with 22% profit, we can understand that £6502 is 122% of the original price meaning that the individual would have had to multiply their original value by 1.22 to get £6502!

To find our answer we, therefore, have to do the inverse...

Turning the value into money we round to 2d.p leaving our answer as...

Hope this helps, have a lovely day! :)

We οbtain JN  44.3 by rοunding tο the nearest tenth, Length οf side JN is rοughly  44.3 units lοng as a result. Therefοre 44.3 is the right respοnse.

The sides οf a triangle are straight lines that are jοined by the three vertices οf the triangle. In οther wοrds, we can say that the sides οf a triangle are line segments that meet each οther at the vertices οf the triangle.

The sides οf a right-angled triangle can be fοund οut by using variοus methοds like the Pythagοras theοrem οr by using the perimeter οf the triangle. In case sοme οf the angles and οther side lengths are given, we can use the law οf cοsines οr the law οf sines tο find the lengths οf the sides οf a triangle.

Law of sines

sin(∠A)/a = sin(∠B)/b = sin(∠C)/c

Therefore,

39/sin(53°) = JN/sin(65°)

JN = (39×sin(65°))/sin(53°)

JN = 44.3

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Answer:

17,20,23...

Step-by-step explanation:

you just have to add 3 that's how the pattern works.

x + 3x + 2x = 180°

Being straight angle...

6x = 180°

[tex]x = \frac{180}{6} \\ [/tex]

x = 30°

Answer:

If m = -7 and n = 4, then we can substitute these values into the expression:

5m + 9n = 5(-7) + 9(4)

= -35 + 36

= 1

Therefore, 5m + 9n simplifies to 1 when m = -7 and n = 4.

Step-by-step explanation:

Answer: Diego's playlist has 36 songs in rock genre, 9 songs in Country genre, 27 songs in hip hop genre and 24 songs in electronica genre.

Based on the number of songs Diego has and the proportion of the genres, Diego's song classification is:

The number of songs from a particular genre is:

[tex]= \text{Total number of songs}\times\text{Percentage of genre}[/tex]

Rock:

[tex]= 40\% \times 90[/tex]

[tex]\bold{= 36 \ songs}[/tex]

Country:

[tex]= 10\% \times 90[/tex]

[tex]\bold{= 9 \ songs}[/tex]

Hip hop:

[tex]= 30\% \times 90[/tex]

[tex]\bold{= 27 \ songs}[/tex]

Electronica:

[tex]= (100\% - 40\% - 10\% - 30\%) \times 90[/tex]

[tex]\bold{= 18 \ songs}[/tex]

In conclusion, there are various genres on Diego's phone.

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Complete Question:

Diego has 90 songs on his playlist. How many songs are there for hip-hop?

40% rock

10% country

30% hip-hop

The rest is electronica

Answer:

ANswer ig

Step-by-step explanation:

1/12+1/3=1/12+[4]/12=5/12

6\12. 1\2

I have to add mor but that is all so I’m writing this

Answer:

d=50.3

Step-by-step explanation:

cos(29)/1=44/d

cos29d/cos29=44/cos29

d=50.31

d=50.3

The values of g(x) for the given values of x are g(0) = 4, g(-7) = 3, g(-4) = 0

Functions can be used to model a wide range of real-world phenomena, such as physical laws, economic relationships, or biological processes. They are a fundamental concept in mathematics and play a central role in many fields, including engineering, physics, computer science, and statistics.

Functions can be represented graphically, algebraically, or numerically, and can be manipulated and analyzed using a variety of mathematical tools and techniques. By understanding how functions work and how to use them, people can solve problems, make predictions, and gain insights into a wide range of mathematical and real-world phenomena.

To evaluate the piecewise function at each value of the independent variable, we need to substitute the given value of x into the appropriate expression for g(x):

a. To find g(0), we use the first expression since 0 is greater than or equal to -4:

g(0) = 0 + 4

g(0) = 4

b. To find g(-7), we use the second expression since -7 is less than -4:

g(-7) = -(-7 + 4)

g(-7) = -(-3)

g(-7) = 3

c. To find g(-4), we need to consider both expressions since -4 is exactly equal to -4:

g(-4) = -(-4 + 4) (using the second expression)

g(-4) = 0 (simplifying)

or

g(-4) = -4 + 4 (using the first expression)

g(-4) = 0 (simplifying)

So, g(-4) is equal to 0 using both expressions.

Therefore, the values of g(x) for the given values of x are:

g(0) = 4

g(-7) = 3

g(-4) = 0

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The ratio of x:y is -9:5 or 3:-2.

The given equation is 2x-3y=0 and x+5y=0.

Since x is greater than 0 and y is greater than 0, we can solve the equations for x and y

2x = 3y

x = 3/2y

and

x = -5y

Substituting x = 3/2y in the second equation,

-5y = 3/2y

-10y = 3

y = -3/10

Substiuting y = -3/10 in the first equation,

2x = 3(-3/10)

x = -9/5

Therefore, the ratio of x:y is -9:5. In the simplest form, the ratio can be written as -9:5 or 3:-2.

2x - 3y = 0

x + 5y = 0

2x = 3y

x = 3/2y

-5y = 3/2y

-10y = 3

y = -3/10

2x = 3(-3/10)

x = -9/5

Therefore, x:y = -9:5 or 3:-2

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The value of line segment AC is 8√2

Pythagoras theorem states that, in a right triangle, the square of the hypotenuse is equal to the sum of the square of the other two sides.

If the other two sides of the right triangle are a and b and the hypotenuse is c, then mathematically l, Pythagoras theorem can be written as:

c² = a²+b²

If CD = 4 and AD = 12, then AC will be

12² = (AC)² +4²

(AC)² = 12² - 4²

(AC)² = 144-16

(AC)² = 128

AC = √128

AC = 8√2

therefore the value of the line segment AC is 8√2

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a. The population in this question is all the Cheapo Coffee stores around the country.

b. The sample in this question is the 17 coffee shops that were visited and their daily sales data was recorded.

In statistics, a population is the entire group of individuals, items, or events that we are interested in studying. In this case, the population is all the Cheapo Coffee stores across the country, and we are interested in studying the number of cups of coffee sold per day at these stores.

However, it is often impractical or impossible to study the entire population, so we select a subset of the population, which is called a sample.

The sample is a representative subset of the population that we study to draw conclusions about the population as a whole. In this case, the sample consists of 17 Cheapo Coffee stores that were randomly selected from four major cities in the US, and the number of cups of coffee sold per day was recorded for each store.

We can use the data from the sample to estimate the average number of cups of coffee sold per day at all Cheapo Coffee stores across the country, which is the parameter of interest in this study.

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The scale factor given in the map to measure the distance is 1 unit = 557 miles.

What is scale factor?

The scale factor of a shape refers to the amount by which it is increased or shrunk. It is applied when a 2D shape, such as a circle, triangle, square, or rectangle, needs to be made larger.

The map is given for United States of America.

The map shows different states with their locations.

The maps say that 1 unit measures 557 miles.

The scale factor is the means to measure the distance on the map.

The scale factor mentioned in the map is 1 unit.

The value of 1 unit is given as  557 miles.

Therefore, the scale factor is 1 unit = 557 miles.

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Therefore, the shopkeeper made a profit of Rs. 30,000 and the profit percentage is 6.25%.

Percent is a way of expressing a fraction or a proportion as a quantity out of 100. The term "percent" means "per hundred". So, when we say that something is 50 percent, we mean that it is 50 out of 100 or 50/100, which can also be simplified to 1/2. The symbol used to represent percent is "%". For example, if a store is offering a discount of 20%, it means that the customer can buy the item for 20% less than the original price, or in other words, the customer will pay only 80% of the original price. Percentages are used in many different areas of life, such as finance, mathematics, science, and statistics. They are used to represent proportions, changes, growth rates, and many other types of data.

Here,

The total cost of 300 bicycles is:

Cost of 1 bicycle = Rs. 1500

Cost of 300 bicycles = 1500 x 300 = Rs. 4,50,000

Transportation cost per bicycle is Rs. 75, so the total transportation cost for 300 bicycles is:

Transportation cost of 1 bicycle = Rs. 75

Transportation cost of 300 bicycles = 75 x 300 = Rs. 22,500

The total cost of purchasing 300 bicycles including transportation cost is:

Total cost = Cost of bicycles + Transportation cost

Total cost = Rs. 4,50,000 + Rs. 22,500 = Rs. 4,72,500

The shopkeeper spent Rs. 7500 on advertising.

So, the total cost of the shopkeeper is:

Total cost = Cost of bicycles + Transportation cost + Advertising cost

Total cost = Rs. 4,72,500 + Rs. 7500 = Rs. 4,80,000

The selling price of 1 bicycle is Rs. 1700, so the selling price of 300 bicycles is:

Selling price of 1 bicycle = Rs. 1700

Selling price of 300 bicycles = 1700 x 300 = Rs. 5,10,000

The profit or loss is calculated by subtracting the total cost from the total selling price:

Profit/Loss = Selling price - Total cost

Profit/Loss = Rs. 5,10,000 - Rs. 4,80,000 = Rs. 30,000

Since the shopkeeper made a profit of Rs. 30,000, we can calculate the profit percentage as follows:

Profit percentage = (Profit / Total cost) x 100

Profit percentage = (30,000 / 4,80,000) x 100

Profit percentage = 6.25%

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