Write an explicit formula for a_na n ​ , the n^{\text{th}}n th term of the sequence 3, -15, 75, ...3,−15,75,....

Solution of given inequality is x < -12.

Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values.

Given inequality

- (1/2)x > 6
Multiplying with 2 on both sides

- (2/2)x > 6×2

- x > 12

Multiplying with -1 on both sides

x < -12

Hence, x < -12 is the solution of given inequality.

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Answer:

SSS

Step-by-step explanation:

Since [tex]\overline{AD} \cong \overline{AD}[/tex] by the reflexive property, there are three pairs of congruent sides.

Answer:

280

Step-by-step explanation:

Give me a moment, I am still gathering my explanation

Answer:

Step-by-step explanation:

.....-_-.....-__-....-___-_--____--_--_____--_--______________--_________________-u streched ma face dude.

As a result, no particular postulate can be used to demonstrate their congruence due to a lack of adequate data. So "None" is the correct response.

If two figures share the same form, congruent corresponding angles (which means the angles in the same locations of each shape are the same), and identical scale factors, they are said to be "similar figures." Equal scale factors signify a matched ratio between the lengths of their respective sides.

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Answer: None

Step-by-step explanation: I Just did it

The value of x is 7, therefore AC = 23 and BD = 23, which means diagonals AC = BD.

What is linear equations in two variables?

A linear equation in two variables is an equation that can be written in the form ax + by = c, where a, b, and c are constants, and x and y are variables. The graph of a linear equation in two variables is a straight line in the Cartesian coordinate system.

In a trapezium, the diagonals divide the trapezium into four triangles. The diagonals of a trapezium are also equal to the sum of the two parallel sides.

Let the two parallel sides of the trapezium be a and b. Then, we have:

8x - 33 = a + b ...(1)

37 - 2x = a + b ...(2)

We can solve for x by setting (1) and (2) equal to each other:

8x - 33 = 37 - 2x

10x = 70

x = 7

8(7) - 33 = 23

37 - 2(7)  = 23

Therefore, the value of x is 7.

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Answer:

To find the number of courts with doubles matches, we need to determine the total number of players playing doubles. If each court with a doubles match has 4 players, then the total number of players playing doubles would be 4 times the number of courts playing doubles.

Since there are 28 players in total, and each court with a singles match has 2 players, the number of players playing singles would be 28 - 4x, where x is the number of courts playing doubles.

Since each court with a singles match has 2 players, the number of courts playing singles would be 28/2 = 14.

So, 28 - 4x = 14, and solving for x, we get x = 7.

Therefore, there are 7 courts with doubles matches and 14 courts with singles matches.

Answer:

[tex]\sqrt{106}[/tex]

Step-by-step explanation:

Using the distance formula,

[tex]LM=\sqrt{(7-(-2))^2+(-1-4)^2}=\sqrt{106}[/tex]

Type I error would be weather remains dry, but school is needlessly canceled. Type II error would be don't cancel school, but the snow storm hits. The correct option is B.

In hypothesis testing, the null hypothesis is the default assumption that is being tested. In this case, the null hypothesis is that the weather will remain dry. The school superintendent must decide whether to reject or accept this null hypothesis based on the evidence available.

There are two types of errors that can occur in hypothesis testing: Type I and Type II errors.

Type I error occurs when the null hypothesis is rejected, even though it is actually true. In other words, the school superintendent decides to cancel school due to a snowstorm, but the weather remains dry. This can result in unnecessary school closures, which can disrupt students, teachers, and parents' schedules.

Type II error occurs when the null hypothesis is accepted, even though it is actually false. In other words, the school superintendent decides not to cancel school because of the assumption that the weather will remain dry, but a snowstorm hits. This can put students, teachers, and parents in danger as they try to commute to school in hazardous conditions.

The consequences of a Type I error and a Type II error can be significant in this scenario. The school superintendent must weigh the potential risks of making each type of error to make the best decision for the safety and well-being of the school community.

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Complete question is:

A school superintendent must make a decision whether or not to cancel school because of a threatening snow storm. What would the results be of Type I and Type II errors for the null hypothesis: The weather will remain dry?

A. Type I error: don't cancel school, but the snow storm hits.

Type II error: weather remains dry, but school is needlessly canceled.

B. Type I error: weather remains dry, but school is needlessly canceled.

Type II error: don't cancel school, but the snow storm hits.

C. Type I error: cancel school, and the storm hits.

Type II error: don't cancel school, and weather remains dry.

D. Type I error: don't cancel school, and snow storm hits.

Type II error: don't cancel school, and weather remains dry.

E. Type I error: don't cancel school, but the snow storm hits.

Type II error: cancel school, and the storm hits.

Histogram 1 is positively skewed, and Histogram 2 is symmetric, which is a true statement about the distributions represented by the histograms.

An illustrated display of data points arranged into user-specified ranges is called a histogram. By taking several data points and organising them into logical ranges or bins, the histogram, which resembles a bar graph in appearance, condenses a data series into an easily understood graphic.

Among graphing tools, the histogram is widely used. It is utilised to encapsulate discrete or continuous data that is measured on an interval scale. It is frequently employed as a convenient way to highlight the key characteristics of the data distribution.

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Answer:

C) Histogram 1 is negatively skewed, and Histogram 2 is positively skewed.

Step-by-step explanation:

When most of the data on a histogram is gathered to the right, then the distribution is negatively skewed. If most of the data is gathered to the left, then the distribution is positively skewed.

Assuming you are going off of these Histograms:

C is the correct answer.

Answer:

arc FA = 150°

Step-by-step explanation:

the central angle of a circle is equal to the measure of the arc that subtends it.

given BF is the diameter of the circle , then

∠ FCA + ∠ ACB = 180°

∠ FCA + 30° = 180° ( subtract 30° from both sides )

∠ FCA = 150°

then

arc FA = ∠ FCA = 150°

It would be expected to be correct approximately 14.82 times over the next 38 years, based on the 39% accuracy of Groundhog Day predictions.

The expected value, also known as the mathematical expectation, is a key concept in probability theory and statistics.

Here,
Groundhog Day predictions have a 39% accuracy, so on average, 39% of the predictions made on Groundhog Day are correct.

To find the expected number of correct predictions over the next 38 years, we can multiply the accuracy of the predictions (39%) by the number of predictions made (38),

39% * 38 = 14.82

So, we would expect to be correct approximately 14.82 times over the next 38 years, based on the 39% accuracy of Groundhog Day predictions.

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Answer:

4) 7 SqrRt( 5 )

5) 2 SqrRt( 10 )

6) 8 SqrRt( 6 )

The value of x is approximately 0.8 cm when rounded to the nearest tenth.

A triangle is a two-dimensional geometric shape that has three sides and three angles. It is the simplest polygon and is a fundamental building block in many areas of mathematics and science.

The three sides of a triangle can have different lengths and can be of different types, such as equilateral, isosceles, or scalene. An equilateral triangle has three sides of equal length, while an isosceles triangle has two sides of equal length and a third side of a different length. A scalene triangle has all three sides of different lengths.

In a right triangle, the sine of an angle is defined as the ratio of the length of the side opposite the angle to the length of the hypotenuse. Thus, we have:

sin(IHJ) = IJ/IH

Taking the sine of both sides and substituting the given values, we get:

sin(23°) = x/2

Multiplying both sides by 2, we have:

x = 2*sin(23°)

Using a calculator, we get:

x ≈ 0.83

Therefore, the value of x is approximately 0.8 cm when rounded to the nearest tenth.

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Applying the Two Tangents Exterior Angle Theorem, the value of x is: 12.

m(BD) = 120°

If you draw two tangents from a point outside a circle, the size of the angle they form is equal to half of the difference between the sizes of the two arcs they intercept inside the circle, based on the Two Tangents Exterior Angle Theorem.

Therefore, we have:

6x - 12 = 1/2[(-12 + 21x) - (12x - 24)] (according to the Two Tangents Exterior Angle Theorem)

Solve for x:

6x - 12 = 1/2[(-12 + 21x - 12x + 24)

2(6x - 12) = -12 + 21x - 12x + 24

12x - 24 = 9x + 12

12x - 9x = 24 + 12

3x = 36

x = 36/3

x = 12

m(BD) = 12x - 24 = 12(12) - 24

m(BD) = 120°

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We can say with 95% confidence that the true proportion of applicants accepted by Bridgeton University lies between 0.354 and 0.430.

What is confidence interval?

A confidence interval is a range of values that is likely to contain the true value of a population parameter with a certain degree of confidence. It is an interval estimate computed from a sample of data and is used to describe the uncertainty or variability associated with a sample estimate of a population parameter.

To calculate the confidence interval, we need to first find the point estimate of the proportion of applicants accepted by Bridgeton University:

Point estimate = number of applicants accepted / total number of applicants = 392 / 1000 = 0.392

The standard error of the proportion can be calculated as:

SE = sqrt(p*(1-p)/n), where p is the point estimate and n is the sample size.

SE = sqrt(0.392*(1-0.392)/1000) = 0.0194

To find the 95% confidence interval, we can use the formula:

CI = point estimate +/- z*SE, where z is the z-score for a 95% confidence level (1.96).

CI = 0.392 +/- 1.96*0.0194

CI = (0.354, 0.430)

Therefore, we can say with 95% confidence that the true proportion of applicants accepted by Bridgeton University lies between 0.354 and 0.430.

To evaluate whether Bridgeton's claim seems accurate, we can compare the confidence interval with the claimed acceptance rate of 42%. We can see that the claimed acceptance rate of 42% does not fall within the confidence interval, which suggests that the claim may not be accurate. However, it is important to note that this sample may not be representative of the entire population of applicants to Bridgeton University, and further investigation may be needed to confirm the accuracy of the claim.

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The equation of the total cost is C = 3 + 5x and the amount earned after 5 hours is $28.

A mathematical definition of an equation is a claim that two expressions are equal when they are joined by the equals sign ("="). For illustration, 2x - 5 = 13.

Two expressions are combined in an equation using an equal symbol ("="). The "left-hand side" and "right-hand side" of the equation are the two expressions on either side of the equals sign. Typically, we consider an equation's right side to be zero.

Let us suppose the number of hours = x.

The cost of additional hour is $5.

The cost of x hours is 5x.

Given that, Nicole charges a flat fee of $3, plus $5 per hour.

C = 3 + 5x

If she baby sits for 5 hours, that is x = 5, then:

C = 3 + 5(5)

C = 3 + 25

C = $28

Hence, the equation of the total cost is C = 3 + 5x and the amount earned after 5 hours is $28.

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The barn with shadow height, 70 feet, having the the height which is equals to the 30 feet, that is barn is 30 feet tall.

The height of farmer Cole = 6 feet

The height of shadow of farmer Cole = 14 feet

The height of shadow of barn = 70 feet

Let the height of barn be ' x feet '. We have to determine the value of x. Now, we the above figure, AB and CD represents height of barn and Cole respectively. Similarly BE and CE represent the shadow height of barn and Cole respectively.

Let angle BAE made here be equals to θ. Also angle BAE = angle CDE = θ. Now, consider right angled triangle, CDE with sides. Using triganomertric functions, tanθ = height/base

=> tanθ = CE/CD = 14/6

simplify, tanθ = 7/3 --(1)

Also, consider right angled triangle ABE,

tanθ = height/base = BE/AB

=> tanθ = 70 / x

=> x tanθ = 70

from equation (1), x (7/3) = 70

=> 7x/3 = 70

=> 7x = 210

=> x = 210/7

=> x = 30

Hence, required value of x is 30 feet.

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Step-by-step explanation:

50

because 50*(30/100)=1500/100

then it gives 15

so the 30 percent of a number is 15 that number is 50.

The requried, 30 percent of 50 is 15, as of the given condition.

The percentage is the ratio of the composition of matter to the overall composition of matter multiplied by 100.

We can use algebra to solve the problem.

Let's call the number we're looking for "x". Then we can translate the problem statement into an equation:

30% of x is 15:

0.3x = 15

To solve for x, we can divide both sides of the equation by 0.3:

x = 15 ÷ 0.3

x = 50

Therefore, 30 percent of 50 is 15.

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Answer:

18.84

Step-by-step explanation:

With a plane containing 40 lines, no 2 of which are parallel , here are 43 points where exactly 2 lines intersect.

In a plane that contains 40 lines, we are asked to find the number of points where exactly 2 lines intersect. Let's call this number "x".

Since every line intersects exactly 2 points, the total number of line intersections is equal to 2x. In other words, if we add up the number of intersections at each point, the total number should equal 2x.

The problem states that there are 3 points where exactly 3 lines intersect, 4 points where exactly 4 lines intersect, 5 points where exactly 5 lines intersect, and 6 points where exactly 6 lines intersect. At the same time, it states that there are no points where more than 6 lines intersect.

To calculate the total number of intersections, we need to multiply the number of lines that intersect at each point by the number of points, and then add them up. In mathematical terms:

2x = 3 * 3 + 4 * 4 + 5 * 5 + 6 * 6

Expanding the right side of the equation:

2x = 9 + 16 + 25 + 36

= 86

Dividing both sides of the equation by 2:

x = 43

So there are 43 points where exactly 2 lines intersect.

This is because at each point where exactly 2 lines intersect, the number of intersections is equal to the number of lines. In total, these 43 points account for 86 line intersections, which is half of the total number of line intersections in the plane.

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The fraction that is the ratio of the shaded area of the circle to the area between the two squares is (π−2)/2.

A fraction is a mathematical expression that represents a part or a proportion of a whole.

Let us assume that the radius of the circle is 'r' units. Therefore, the diameter of the circle is 2r units. The diagonal of the inner square is equal to the diameter of the circle, which is 2r units. Hence, the side of the inner square is r√2 units.

Now, let's consider the area of the circle. The formula for the area of a circle is

=>  A=πr².

Therefore, the area of the circle is πr².

The area between the two squares is the difference between the area of the outer square and the area of the inner square. The area of the outer square is

=> (2r)²=4r²,

and the area of the inner square is

=> (r√2)²=2r².

Hence, the area between the two squares is

=> 4r²−2r²=2r².

The shaded area of the circle is the area inside the circle but outside the inner square. We can find this area by subtracting the area of the inner square from the area of the circle. Therefore, the shaded area of the circle is

=> πr²−2r²=(π−2)r².

Now, let's find the ratio of the shaded area of the circle to the area between the two squares. We can express this ratio as a fraction. Thus,

ratio = (π - 2)r² / 2r

We can simplify this fraction by canceling out the common factor r^2 in both the numerator and denominator. Thus,

ratio = (π - 2) / 2

This fraction is closest to the ratio of the shaded area of the circle to the area between the two squares.

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The profit that they will make if they have 24 dogs for adoption is given as follows:

$160.

The profit is obtained with the subtraction of the revenue by the costs.

The revenue and the costs for this problem are obtained as follows:

Hence the profit made is obtained as follows:

Profit = 45 x 24 - 920

Profit = $160.

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The conclusion is that there is sufficient evidence at the 0.01 level to support the mayor's claim that under 51% of the residents favor construction of the bridge.

The mayor rejects the null hypothesis at the 0.01 level, which means that the results from the hypothesis test show that the actual proportion of residents who favor construction is less than 51%. The alternative hypothesis would be that the true proportion is less than 51%. After gathering information from 380 voters, the results of the hypothesis test were used to make a decision on whether to reject or fail to reject the null hypothesis.

If the hypothesis test showed that the null hypothesis could be rejected at the 0.01 level, it means that there was sufficient evidence to support the mayor's claim that less than 51% of the residents favor the bridge construction. However, it's important to note that hypothesis testing is not a perfect method and other factors such as sample size and sampling method should also be considered when interpreting the results.

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The probability of selecting a student who is wearing a yellow shirt is 36 %

The total number of students is 45 students and out of these, 3 / 7 are wearing blue shirts while 2 / 9 are wearing red shirts.

This means that the number of students wearing yellow is:

= 45 - ( 45 x 3 / 7 ) - ( 45 x 2 / 9 )

= 45 - 19 - 10

= 16 students

The probability of selecting a student who is wearing yellow is :

= 16 / 45

= 36 %

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The full question is:

A class has 45 students of the students are wearing 3/7 blue shirts, of

them are 2/9  wearing red shirts, and the rest are wearing yellow shirts.

What is the probability of selecting a student who is wearing a yellow

shirt?

8-3√11 is the expression which is equivalent to √11+√64-2√44.

The combination of variables, numbers and operators is called as expression.

The given expression is √11+√64-2√44

Square root of 11 plus square root of sixty four minus two square root of forty four.

Let us find the equivalent expression of √11+√64-2√44

The expressions in which the expressions look different but have save same value are Equivalent

√11+√64-2√44

√11+8-2√4×11

√11+8-4√11

Combine like terms

8-3√11

Hence, 8-3√11 is the expression which is equivalent to √11+√64-2√44.

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Which expression is equivalent to √11+√64-2√44

A. 8-4√44

B. 5√3-4√11

C. 8-3√11

With dilation at center (0,0) and a scale factor of 5, the coordinates as we can see from given graph are Q(-3,4), R(-2,-1), T(3,1), W(3,5).

What exactly is dilation?

Dilation is the process of modifying the size of an item or form by reducing or expanding its dimensions according to specific scaling variables. A circle of radius 10 unit, for example, is reduced to a circle with radius 5 unit. This approach is utilised in photography, arts and crafts, and the creation of logos, among other things. There are four primary types of transformations in geometry. They are as follows:

Dilation Properties

Some characteristics of forms that stay constant during dilation changes are:

Now,

As we can see from properties that the image does not change in dilation it stays same and angles are also same.

So, we can see coordinates from the given graph

hence,

         the coordinates as we can see from given graph are Q(-3,4), R(-2,-1), T(3,1), W(3,5).

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Step-by-step explanation:

Let the distance between them be y

sin20° =

=> 0.342 =           [  sin20° = 0.342]

=> y =  33/ 0.342

=> y = 96.5 ft

So, the distance between them is 96.5 ft

Answer:

B

Step-by-step explanation:

We start by trying out option A

2(1) + 3(3) = 9

1 + 5(3) = 15

9 and 15 are not equal to one another.

This means it has to be the other option, B.

the answer is 40780

I would show you my calculations  but I don't know how to add pictures to your answer .sorry

I hope that helped