If the sun is 69° above the horizon, find the length of the shadow cast by a building 91 ft tall. Round your answer to the nearest tenth.

The value for a1 in geometric series 2, -6, 18, -54, ..... is a1 = 2, and the recursive formula is a(n) =a^(n-1)·(-3) for n≥2.

What is geometric series?

A geometric series is a collection of terms in mathematics that have an unlimited number and a fixed ratio between each term. A geometric series is typically expressed as a + ar + ar² + ar³ + ..., where r is the common ratio between neighbouring terms and a is the coefficient of each term.

The given geometric series is -

2, -6, 18, -54, ..... (1)

Let A(n) be the geometric series defined in (1).

Then the first term A(1) = 2

The second term A(2) = -6

We need to find the common ratio from one term to the next.

r =  common ratio  

The formula for r is -

r =  subsequent term / previous term = -6/2 = -3

The third term A(3) = 18

The r value for A(3) is -

r =  subsequent term / previous term = 18/-6 = -3

The fourth term A(4) = -54

The r value for A(4) is -

r =  subsequent term / previous term = -54/18 = -3

The formula for a(n) terms will be -

a(n) =a^(n-1)·(-3)

Therefore, the recursive formula is a(n) =a^(n-1)·(-3).

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To find the football field's area in square yards, we need to multiply the length by the width, both of which are given in different units of measurement (yards and feet).

Steps:

1. Convert the width of the field from feet to yards: 160 feet / 3 feet/yard = 53.33 yards

2. Multiply the length and width of the field to find its area: 100 yards * 53.33 yards = 5,333 square yards. Therefore, the area of the football field is 5333.33 square yards.

The room is square since the length and range of the room are the same. Hence, we can apply the area of the square formula to cipher the area of the given carpet demanded to cover the room. Hence, the answer is 16 square yards.

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The area of the field in square yards will be 16 sq. yards.

To calculate the size of a football field in square yards, multiply the length by the width, which are both given in separate units of measurement (yards and feet).

First, we'll convert the field's width from feet to square yards.

There are 3 feet in 1 yard,

So 160 feet is the same as 160 / 3 = 53.333 yards.

Then we'll multiply the length by the width: 100 * 53.333 = 5333.33 square yards.

Therefore, the area of the football field is 5333.33 square yards.

The room is square since its length and width are equal.

As a result, we can use the area of the square formula to calculate the area of the provided carpet required to cover the room.

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a) The table is given below..

b) x + y = 45

c) 5.20x + 9y = 291

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

Example:

2x + 3 = 8 is an equation.

We have,

Cost of small box x = $5.20

Cost of large box y = $9

Now,

Number of boxes sold in one hour = 45

Total amount earned = $291

We can make two equations.

x + y = 45

x = 45 - y

Substituting

5.20x + 9y = 291

5.20 (45 - y) + 9y = 291

234 - 5.20y + 9y = 291

234 + 3.8y = 291

3.8y = 291 - 234

3.8y = 57

y = 15

Now,

x = 45 - y

x = 45 - 15

x = 30

Table:

Categories     Value   Number     Amount

Small box       5.20         30          30 x 5.20 = 156

Large box        9              15          15 x 9 = 135

Thus,

The table is given above.

The equation is x + y = 45

The equation is 5.20x + 9y = 291

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Two compound propositions p and q are logically equivalent if p↔q is a tautology. Alternatively,  p and q are equivalent if and only if the columns in a truth table giving their truth values agree.

Two compound propositions p and q are logically equivalent if and only if p logically implies q and q logically implies p. In other words: two compound propositions are logically equivalent if and only if they have the same truth table.

let us consider,

       T be the truth and F be the false of a problem statement.

Then the compound propositions p and q are logically equivalent if :

                 P                           q               P→q

                  T                             T                  T

                  F                             F                   T

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The complete question is :

What is the correct way of determining of two compound propositions p and q are equivalent.

construct a truth table for p→q if the proposition is tautology.

Yes, you can distinguish the two components if you have two detectors. The detectors can measure different properties of the components, such as:

By using the two detectors and measuring different properties of the components, you can identify which components belong to which state. For example, a detector can measure the size of the components, and another detector can measure the density of the components. If the components from one state have a larger size or a higher density than the components from another state, then the detectors can distinguish between the two components.

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Check the picture below.

so following the inscribed quadrilateral conjecture, let's get those equations that add  up to 180°.

[tex](2y+74)+(7x+1)=180\implies 2y+7x+75=180\implies \underline{2y+7x=105} \\\\[-0.35em] ~\dotfill\\\\ (2y+100)+(6x-10)=180\implies 2y+6x+90=180\implies \underline{2y+6x=90} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{using the 1st equation}}{2y+7x=105}\implies 2y=105-7x \\\\\\ \stackrel{\textit{using the 2nd equation}}{2y+6x=90}\implies 2y=90-6x\implies \stackrel{\textit{substituting from above}}{105-7x=90-6x} \\\\\\ 105=90+x\implies \boxed{15=x}[/tex]

[tex]\stackrel{\textit{since we know that}}{2y+7x=105}\implies 2y+7(15)=105\implies 2y+105=105 \\\\\\ 2y=0\implies y=\cfrac{0}{2}\implies \boxed{y=0}[/tex]

The mistake Derek did was d = 8.

The correct step is d = 9.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

Example:

2x + 4 = 55 is an equation.

We have,

8d = 72

Step 1:

Divide both sides with 8.

8d/8 = 72/8

[ 8 x 9 = 72 ]

So,

d = (8 x 9)/ 8

d = 9

Thus,

Derek's mistake is d = 8.

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If he continued at the same rate, he would travel  370 miles in 10 hours.

A proportion is described as an equation having two ratios that are set equal to each other.

It is the mathematical comparison of numbers or variables.

In mathematics, the different types of fractions are;

From the information given, we have that;

sauv drove 296 miles in 8 hours

Then,

If 296 miles  = 8 hours

x miles = 10 hours

cross multiply

8x = 2960

Make 'x' the subject of formula

x = 370 miles

Hence, the value is 370 miles

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Answer:

2

Step-by-step explanation:

The number of arrivals who came in each day while this particular widget shop was open. Therefore, statement 2 is correct.

The process by which a sample of observations is selected from a population to assume the population is known as random sampling. This process ensures that the results we get from your sample should be close to what we would have gotten if we measured the complete population. So that all the units in the population have an equal chance of being chosen using the simplest random sample.

In the given scenario, the number of arrivals each day for the widget store should have equal chance. To be specific, we should only take into account the number of visitors on the days when the store is open.

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The probability that a student rides a bike to school, given that the student's school has a crossing guard is given by 0.25.

For two events A and B, we have:

Probability that event A or B occurs = Probability that event A occurs + Probability that event B occurs - Probability that both the event A and B occur simultaneously.

We know that;

For two events A and B:

The chain rule states that the probability that A and B both occur is given by:

⇒ P (A∩B) = P (A) P (B|A) = P (B) P (A|B)

You can remember this fact by using a trick that when A is on left, it is behind B in next term P(A) P(B|A)

And when B is on left, then it is behind A in next term P(B)P(A|B)

P(A|B) = Probability that A will happen given B has already happened.

P(B|A) = Probability that B will happen given A has already happened.

Using those above stated rules, we have

Let the event A be that a student rides bike to school.

Let the event B be that the student's school has a crossing guard

Then we are given that:

P(A) = P{rides bike to school}) = 0.14

P(B) = P{has crossing guard}) = 0.48

P{rides bike and crossing guard}) = 0.12

We have to find P(a student rides a bike to school, given that the student's school has a crossing guard) = P(A | B)

From the chain rule of probability, we have;

⇒ P (A ∩ B) = P (B) P (A |B)

⇒ 0.12 = 0.48 × P (A|B)

⇒ P (A|B) = 0.12 / 0.48

⇒ P (A|B) = 0.25

Thus, The probability that a student rides a bike to school, given that the student's school has a crossing guard is given by 0.25.

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The numbers in order from smallest to in largest are 65.6, 66.6. and 67.6 respectively

Algebraic expression are expressions comprising of terms, variables, coefficients, constants and factors.

These algebraic expressions are also composed of arithmetic operation, such as;

From the information given as;

x+1 + 2x + 4 + 2x + 6 = 334

collect like terms

x + 2x + 2x = 334 - 11

add or subtract like terms

5x = 323

Make 'x' the subject of formula

x = 64. 6

The numbers are;

x + 1 = 65.6

x+ 2 = 66. 6

x + 3 = 67. 6

Hence, the numbers are 65.6, 66.6. and 67.6

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The exponential function [tex]Y=21{(1.44)}^x[/tex] represents growth when x ∈ N.

The formula for exponential growth is [tex]y = y_0.e^{(kt)}.[/tex]

The formula for exponential decay is [tex]y = y_0.e^{(-kt)}.[/tex].

Given, An exponential function [tex]Y=21{(1.44)}^x[/tex].

Now, This function can represent growth or decay depending upon the values of 'x'.

If x ∈ N, Then this exponential function [tex]Y=21{(1.44)}^x[/tex] represents growth.

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The number of days a software engineer can go without wearing the same combination of three items will be 36.

A permutation is an act of correctly arranging things or pieces. Combinations are a method of taking stuff or pieces from an assortment of items or sets in which the order of the items is irrelevant.

A software engineer owns 3 pairs of pants, 4 shirts, and 3 pairs of shoes. Then the number of different ways is given as,

⇒ ³C₁ × ⁴C₁ × ³C₁

⇒ 3 x 4 x 3

⇒ 36

The number of days a software engineer can go without wearing the same combination of three items will be 36.

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Note that:

There are three separate planes and three different lines in the diagram. Line X crosses two of the planes, whereas Line Z intersects just one of the planes, and Line Y has points on all three planes.

Line y has points A and B in each of the three planes.

A plane is a flat surface that can be sliced across by a straight line connecting any two locations on the plane.

As a result of the diagram, we may deduce that

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The set of items that are part of both sets F and G is indicated by the symbol F G. It is the group of equilateral triangles that are also isosceles triangles, to put it another way.

Due to its three congruent sides, every equilateral triangle is an isosceles triangle. F G = F hence equals "equilateral triangles." By eliminating the unnecessary component, we can make F G simpler.

Consequently, F G = "equilateral triangles"

When seen collectively, a set is a group of items. The elements or members of the set are the things that make it up. Any mathematical object, such as integers, functions, or other sets, may be one of the elements of a set.

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When a fifth degree polynomial with a root of multiplicity 3 at x = 2, and a root of multiplicity to at x = -3. The polynomial can be written in the form

Each zero's multiplicity is the quantity that indicates how frequently its corresponding factor appears. In other words, the powers are the multiplicities.

The polynomial is expressed as  y = (x - 2) ^a (x - b)^c

for x = 2, x - 2, and the multiplicity is 3 hence

(x - 2)³

for x = -3, x + 3 and the multiplicity is will be 2 hence

(x + 3)²

Because of this we can say that

a = 3, b = -3 and c = 2

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The correct orientation and location of triangle DEF is option B (as shown in the attachment to this answer).

Rotation is one of the types of solid transformation which involves turning a given object about a reference point or line at a certain required measure of angle. Other types of transformation are: dilation, translation and reflection.

Dilation: This is a process in which the dimensions of an object is either increased or decreased to produce its image.

Translation: This is a procedure that requires moving a given object a number of units in a specified direction.

Reflection: This requires flipping an object over a line to produce an image.

In the question, after rotating triangle ABC 90^o clockwise; the correct orientation and location of triangle DEF is option B.

A sketch of this is attached to this answer for clarity.

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A boy walked 7km on a bearing of 60°. Represented this information on a diagram given below.

A bearing in mathematics is the angle, measured in degrees and anticlockwise from north. Typically, bearings are given as a three-figure bearing. For instance, 30° clockwise from north is typically expressed as 0°.

"Pieces that aid objects' rotation" are bearings. They support the rotating shaft that moves the machinery. Cars, planes, power generators, and other devices all use bearings.

To lessen friction between two spinning or sliding surfaces, a bearing is a mechanical component.

There are many different types of bearings, including ball and roller bearings, linear bearings, and mounted versions that may use either, and they are used for rotating or linear shaft applications. Bearings are mechanical assemblies that include rolling elements and typically inner and outer races.

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The Length of RS = 7 units.

The set of points that lie on a straight line is known as Collinear points. In other words, two or more points that lie on the same straight line are said to be Collinear points.  

Here we have

RS = x + 5, ST = 14x − 15, and RT = 20  

When R, S, and T are considered as 3 collinear points

=> RT = RS + ST

From the given data,

=> 20 = x + 5 + 14x − 15  

=> 15x − 10 = 20

=> 15x = 30

=> x = 2

Length of RS = x + 5 = 2 + 5 = 7

Therefore,

The Length of RS = 7 units

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Answer:

4 × 5p = 20p

(Multiply the terms; don't have to be like terms)

Reason:

I'm assuming the x refers to multiplication. If so, then 4 x 5 = 4 times 5 = 20. The p doesn't change.

A real world example would be that 5p represents a box with 5 pens inside it. Then imagine 4 such boxes to get 4 x 5 = 20 pens total.

Answer: We can use the distributive property to write an expression that shows how many bracelets were in each box.

Let b be the total number of bracelets that Sidney made.

The number of bracelets in each box can be represented as:

b/4

This expression means that Sidney divided the total number of bracelets she made, represented by b, by 4, the number of gift boxes.

So, the total number of bracelets in each box is b/4 bracelets.

Step-by-step explanation:

We come to the conclusion that if the scale factor from S to M is 3/2, the scale factor from M to S must be 2/4.

Assume we have a figure S. If we apply a stretch of scale factor K to our figure S, we may say that all of figure S's dimensions have been multiplied by K.

Following the stretch, we will have a bar of length M, such that:

M = S*K

If the scale factor is 3/2, the following scenario arises:

M = (3/2)*S

In the relationship mentioned above, S can be separated out as follows:

(2/3)*M = S

We now have an equation (similar to the first one).

As of right now, the scaling factor from M to S is 2/3, according to an equation (like the first one).

After that, we draw the conclusion that if the scale factor from S to M is 3/2, the scale factor from M to S must be 2/4.

The complete question is,

Scale factor is 3/2 for the range of S to M. How many are there in the scale from M to S?

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The number of people in the town in the next four years is 7610.

We know that the population growth rate can be obtained when we apply the exponential growth formula. In this case we would have;

P= Poe^rt

P = Population at time t

Po = Initial population

r = Population growth rate

t = time taken

3(4709) =4709e^9r

3 = e^9r

ln3 = 9r

r = ln3/9

r = 0.12 or 12%

In the next four years;

P =4709e^4 * 0.12

P = 7610

The population can be obtained as 7610.

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Answer:

see below

Step-by-step explanation:

7300 investment

annual rate 6.6% compounded monthly = 6.6/12 months = 0.55% per month

t years = t*12 months

so function is = 7300 * (1+6.6%/12)^12t

APY = (1+0.55%)^12 - 1 = 1.068-1 = 0.068 = 6.8%

The completed proof for the two triangles is as follows -

ST bisects ∠UTV - Given

∠UTS ≅ ∠VTS - Angle Bisection Theorem

∠TUS and ∠TVS are right angles - Given

∠TUS ≅ ∠TVS - All right angles are congruent

ST ≅ ST - Reflexive property of congruence

ΔUTS ≅ ΔVTS - Angle Angle Side (AAS) Theorem

SU ≅ SV - CPCTC Rule

SU = SV - Congruence Theorem

What are triangles?

Triangles are a particular sort of polygon in geometry that have three sides and three vertices. Three straight sides make up the two-dimensional figure shown here. An example of a 3-sided polygon is a triangle. The total of a triangle's three angles equals 180 degrees. One plane completely encloses the triangle.

Two right angle triangles ΔSUT and ΔSVT are given with line segment ST being the common.

It is given that line segment ST bisects ∠UTV as ST is the common line between the two triangles.

∠UTS ≅ ∠VTS as it is bisected by the line segment ST and it follows the rule of angle bisection theorem.

∠TUS and ∠TVS similar as they both are right-angles which is denoted by the small square symbol in the diagram.

∠TUS ≅ ∠TVS as they both are right-angles and all the right angles are equal and congruent having a measure of 90°.

ST ≅ ST since it is mid line segment of both the triangles and it follows the rule of reflexive property of congruency.

ΔUTS ≅ ΔVTS as they satisfy the AAS theorem, where two angles of a triangle and side between them are equal. Here, ∠UTS ≅ ∠VTS, ∠UTS ≅ ∠VTS and ST ≅ ST.

SU ≅ SV as corresponding parts of the congruent triangles are congruent. So, the CPCTC rule is applied.

SU = SV as they are part of the congruent triangles, so the line segments must be equal.

Therefore, ΔUTS is equal and congruent to ΔVTS.

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Answer:     Hope this helps sorry for answering late ^ ^

Step-by-step explanation: i got it right

Answer:

Step-by-step Explaination:

Area of base section of prism = area of square

Area of square = a²

side = 14 unit

=> (14)²

=> 196 unit square

The value of the standardized test statistic is D. 1.77.

A standardized test statistic is a measure of the difference between a sample statistic and the population parameter it estimates, expressed in units of the standard deviation.

The value of the standardized test statistic can be calculated using the formula:

(x - μ) / (s / √n)

where x is the sample mean, μ is the population mean, s is the population standard deviation, and n is the sample size.

Given the information provided in the question, the standardized test statistic is:

(20.3 - 20) / (1.2 / √50) = 1.7678

Rounding to two decimal places, the answer is D. 1.77.

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Researchers might study the role of predators in natural selection by testing the hypothesis that animals with camouflage colorings have a greater chance of survival when they are exposed to predators.

They can do this by setting up an experiment in which they expose animals with different colorings, including camouflage, to predators and then measure the survival rate of the different colorings. This would test if animals with camouflage colorings have a higher chance of survival when they are exposed to predators.

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