Construct segment so that it is perpendicular to segment and segment so that it is perpendicular to segment .

Complete the proof.

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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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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Answer: a) To calculate the total rate of return if Josh invests the same amount in each company, we need to add up the individual rates of return from each company and divide by the number of companies.

The total rate of return for the four companies is: (7.62% + -4.17% + -0.83% + 3.70%) / 4 = 2.52%

So the total rate of return if Josh invests the same amount in each company is 2.52%.

b) To calculate the total rate of return if Josh invests three times as much in Stiller Co. as in the other companies, we need to multiply the rate of return for Stiller Co. by 3 and add it to the rates of return for the other companies.

The total rate of return for the four companies is: (-4.17% x 3) + 7.62% + -0.83% + 3.70% = -7.32%

So the total rate of return if Josh invests three times as much in Stiller Co. as in the other companies is -7.32%.

It's important to note that the answer may change if the investment amount on each company is different.

Step-by-step explanation:

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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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.

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:

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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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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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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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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Answer:

24.5 days i believe

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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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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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 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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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%

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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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:

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

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]

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 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:

2

Step-by-step explanation:

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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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 like terms are listed as follows:

-y, 7y and y/2.

Like terms are terms that share these two features:

If two terms are like terms, then they can be either added or subtracted.

Hence the first option is the only option in which all the three terms are like terms, as:

The remaining options have terms with different letters(second and third), or different exponents (fourth), hence they are not like terms.

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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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