A, B and C are points on the circumference of a circle.
XY is a tangent to the circle at the point A.
Angle BAY = 72° and angle ABC = 54°.
Prove that triangle ABC is an isosceles
triangle.
You must give a reason for any statement
that you make or any calculation that you
carry out.

Answer:

x = 135

Step-by-step explanation:

You need to find the supplementary angle of x.

To find x, use the supplementary angle theorem. (The angles "lie" on a straight line, so they add up to 180°, or a straight line.)

45+x = 180

x = 135

1/2 ef sinG is the expression that correctly represents the area of triangle EFG. Select option d.

Given: the triangle EFG as shown in the image

The formula for the Area of triangle is:

A = 1/2 × base(b) × height(h)  

Area of EFG = 1/2 × f × h

Using trigonometric ratio:

sin G = h/e     (opp. / hyp.)

h = e sin G

put h = g sin E into the Area of EFG:

Area of EFG = 1/2 × f × e sin G = 1/2 ef sin G

Therefore, the expression correctly represents the area of EFG is 1/2 ef sinG

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The number of toy cars are in 1,000 boxes is 25000 and the place value of 25 increases by 4 places to the left.

It should be noted that place value is used to know the value of the numbers that are given in a data.

In this case, toy company puts 25 toy cars in each box, the number of toy cars that are in 1,000 boxes will be:

= 25 × 1000

= 25000

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This is completely Randomized experiment design .

Randomized block design is an experiment design in which the experimental units are categorized into groups, which are called blocks.

In the given question, we see that Estelle's cornfield is divided into 666 regions. She is curious about whether a new pesticide is effective because she uses pesticides and assigns each of the 666 regions at random.Now, the experiment units, i.e., 666, are not split into groups before random assignment. The entire region is randomly assigned to a pesticide. A randomised block design assigns some of each block to different treatment and control groups.

So , this is a completely randomized block design.

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The ladder Brian borrowed for painting should go 19.08 feet up the house if Brian sets the base 6 feet from the house

information given in the question

hypotenuse = 20-foot ladder

adjacent = 6 feet from the house

opposite =  how far up the house = ?

The problem is solved using the Pythagoras theorem is applicable to right angle triangle.  the formula of the theorem is

hypotenuse² = opposite² + adjacent²

plugging the values as in the problem

let x be the required distance

20² = 6² + x²

400 = 36 + x²

400 - 36 = x²

x² = 364

x = √364

x = 19.08

The ladder Brain borrowed will go 19 feet high

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The number 74.9963 would round down to 70

Rounding some number to a specific value is making its value simpler (therefore losing accuracy), mostly done for better readability or accessibility.

Rounding to some place keeps it accurate on the left side of that place but rounded or sort of like trimmed from the right in terms of exact digits.

We need to round  74.9963 to the nearest 10

We can see that the 74.9963 is below 75 so it goes down, and it rounds down to 74.9963 instead of, 74.9 then that would round up to the decimal is higher than 70.

The answer would be 70

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Total cost of cement that Marcus has to pay is $6.5.

What is volume?

Volume could be a measure of occupied three-dimensional area. it's usually quantified numerically using SI derived units or by numerous imperial or North American country customary units.

Main body:

According to question:

Length of concrete patio = 15 ft

Width of patio = 9 ft

Height of patio = 3 inches

So first we need to convert inches into ft.

we know that ,

12 inches = 1 ft.

3 inches = (1/12)*3

3 inches = 1/4 ft

Volume of concrete patio = l*b*h

volume = 15*9*1/4

            = 33.75 cubic ft.

Now we need to convert feet into yard as cost is given in cubic yard

1 cubic foot  =  0.03704 cubic yards

33.75 cubic foot = 0.03704 * 33.75

                           = 1.2501 cubic yards

So cost of cement = total volume * cost of cement sack

               cost = 1.25 * 5.2

cost = $6.5

Hence the total cost to Marcus is $6.5

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The chance that the call arrived when the switchboard was not completely busy is 0.75.

Probability is a branch of mathematics that studies the likelihood of a random event occurring.

It is given that the switchboard is fully busy for the first 15 seconds, that means it is not busy for the next 15 seconds to 60 seconds

Therefore the probability that calls arrived when the switchboard was not fully busy is

P(15< x < 60) = ∫_15^60▒f(x)dx

= ∫_15^60▒〖1/60 dx〗

=1/60 ∫_15^60▒〖1.dx〗

= 1/60 [ x ]6015

= (60 – 15)/60

= 45/60

= ¾

= 0.75

Therefore the probability that the call arrived when the switchboard was not fully busy is 0.75

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The redwood that the carpenter needs is 5 [tex]\frac{5}{6}[/tex] feet.

From the information, the carpenter uses 8 [tex]\frac{1}{2}[/tex] ft of cedar for every 13 [tex]\frac{2}{3}[/tex] ft of redwood for a construction project.

Let the redwood needed be illustrated as x.

It's important to note that 4 [tex]\frac{1}{4}[/tex] is half of 8 [tex]\frac{1}{2}[/tex]. Therefore, we will divide the redwoods given earlier by 2. This will be:

= 13 [tex]\frac{2}{3}[/tex] ÷ 2.

= 41 / 3 × 1/2

= 41 / 6.

= 6 [tex]\frac{5}{6}[/tex] ft

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The value of the cards in Bentley's original hand given the value of the cards currently, is 25.

The value of the cards that are currently in Bentley's hands are worth $75. This amount is triple the value in this original hands.

Given that the value of cards now is triple the value in Bentley's original hands, the value in Bentley's original hands can be found by performing a division of 3 on the current hand:

= Current value / 3

= 75 / 3

= $25

In conclusion, the value of the cards in the original hand was $25.

Full question is:

The cards in Bentley's hand have a value of $75 after the value of the cards in his original hand tripled. What was the value of the cards in his original hand?

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The quotient of the polynomial is 4x - 9 and the remainder is 20

The resultant of the division is called the quotient while the Remainder is the number that is left after division.

In long division, the terms on top of the division symbol are called the quotient while that at the bottom is called the remainder.

When a division has no remainder it means that the polynomial is divisible by the divisor.

The body of the calculation is found in the attached file below.

In conclusion, the Quotient and remainder are 4x - 9 and 20 respectively.

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The probability that a worker selected at random makes between $350 and $400 = 0.34134

What is a z score formula?

The standard score represents how far a raw score deviates from or exceeds the mean of the phenomenon being observed or measured. Positive standard scores are assigned to raw scores that are greater than the mean, while negative standard scores are assigned to raw scores that are less than the mean.

By using the z score formula:

z = (x - μ) / σ

Where,

x = raw score

μ = mean

σ = Standard deviation

We are told in the question to find the probability that a worker selected at random makes between $350 and $400

Consider, x1 = 350 and x2= 400 with the mean μ = 400 and standard deviation σ = $50.

z1 = (x1 - μ) / σ = (350-400) / 50 = -1

z2 = (x2 - μ) / σ = (400 - 400) / 50 = (0/50) = 0

From tables, P(z <= -1) = 0.15866

P(z <= 0) = 0.5

Then, the probability would give us, P(-1 ≤ z ≤ 0) =0.5 - 0.15866 = 0.34134

Hence, The probability that a worker selected at random makes between $350 and $400 = 0.34134

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[tex]~~~~~~~~~~~~\textit{distance between 2 points} \\\\ (\stackrel{x_1}{-16}~,~\stackrel{y_1}{11})\qquad (\stackrel{x_2}{16}~,~\stackrel{y_2}{4})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ d=\sqrt{(~~16 - (-16)~~)^2 + (~~4 - 11~~)^2} \implies d=\sqrt{(16 +16)^2 + (4 -11)^2} \\\\\\ d=\sqrt{( 32 )^2 + ( -7 )^2} \implies d=\sqrt{ 1024 + 49 } \implies d=\sqrt{ 1073 }\implies d\approx 32.76[/tex]

The value of expression n + p - 2q when n = p = q is 0

In this question, we have been given an expression n+p-2q

We need to find the value of given expression when n=p=q

Consider given expression,

n + p - 2q

Substitute n = p

= p + p - 2q

= 2p - 2q

Now we substitute p = q in above expression,

= 2q - 2q

= 0

Therefore, the value of expression n + p - 2q when n = p = q is 0

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Answer:

Step-by-step explanation:

Thevalueof theAC segmentknown asthe AB and BC segmentsis:

AC = 12x + 2y + 18

What is a segment?

It is the distance or vector obtained from the sum of the differences of the coordinates of the ends of that segment.

AB = B - A

What are mathematical operations?

They are those such as addition, subtraction, multiplication and division, being the most basic and also have the roots, exponents, among others ...

Thesumis addition to one number to another.

Subtraction is subtractingone number from another.

Multiplicationis adding the same number as many times as the multiplier indicates.

Divisionis the decomposition or separation of one number from another.

What is the value of AC?

Assume that AC is the length of the segment containing AB and BC.

AC = AB + BC

Being;

AB= 8x + 2y

BC = 4x + 18

Replace

AC = 8x +2y + 4x + 18

AC = 12x + 2y + 18

Answer:

f(g(x))= log4(2(8x^6))

or log4(16x^6)

Step-by-step explanation:

Mr. Fitzpatrick bought 9 adult tickets and 13 children's tickets.

It is given that Mr. Fitzpatrick bought 22 tickets

The tickets collectively cost him $265

The student tickets cost $10 while adult tickets cost $15

Let the no. of adult tickets sold be x

Let the no. of children's tickets sold be y

Therefore we get the equations

x + y = 22                      [1]

15x + 10y = 265                      [2]

or, 5x + 10x + 10y = 265

or, 5x + 10(x + y) = 265

from equation [1] we get

5x + 220 = 265

or, 5x = 265 - 220

or, 5x = 45

or, x = 9

Therefore,

y = 22 - 9

= 13

Therefore he bought 9 adult tickets and 13 children tickets.

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The flight of plane from Montego bay to freeport is 894 miles.

To solve this we use Pythagoras theorem.

What is Pythagoras theorem?

The hypotenuse side of a right-angled triangle's square is equal to the sum of its other two sides, according to Pythagoras' Theorem.

Main Body:

Formula for Pythagoras theorem = [tex]P^{2} +B^{2}[/tex]= [tex]H^{2}[/tex]

here H = 1200

B= 800

P =?

solving this equation

1200² = 800²+P²

P²= 800000

P=[tex]\sqrt{800000}[/tex]

P ≈ 894 miles

Hence the distance of flight from Montego Bay to Freeport is 894 miles.

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Using the concepts of weighting, we got that demographic groups helps in fixing  difference between the levels of different people if there are many or too few people in the sample from that group, compared to the population as a whole.

Demographic segmentation examples actually explain how researchers divide a market into the smaller groups according to age, gender, family income, race and ethnicity, qualification, marital status, nature of the  employment, etc.  

It is an extremely tedious task to the accommodate customers belonging to different demographics and develop the exhaustive marketing plan. Demographic examples ease creating the strategy for a marketer. Thus, they are one of  most commonly implemented marketing segmentation methods compared to the other techniques such as geographic segmentation, behavioral segmentation, or the psychographic segmentation.

Hence, certain demographic groups might end up being under or over-represented means that  there are too many or too few people in the sample from that group, compared to the population as a whole, in that case weighting can therefore potentially helps in fixing the difference in the levels of different people.

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Answer:

-40

Step-by-step explanation:

The Concept here is Complex Numbers

where [tex]\sqrt{-1}=i \ and \ i^{2} = -1[/tex]

Then [tex]\sqrt{-4}=\sqrt{4i^{2} } =\sqrt{(2i)^{2} } =2i[/tex]

Also [tex]\sqrt{-25}=\sqrt{25i^{2} } =\sqrt{(5i)^{2} } =5i[/tex]

Then [tex](\sqrt{-4} )(4\sqrt{-25} )=(2i)(4*5i)=40i^{2} =40*-1=-40[/tex]

Glad to Help:)

The length of the X using law of cosine is 34.30yd.

What is cosine?

In a right angled triangle, the cosine of an angle is:

The length of the adjacent side divided by the length of the hypotenuse.

The abbreviation is cos

cos(θ) = adjacent / hypotenuse

Consider that;

[tex]X = \sqrt{a^2+b^2-2abcosX}[/tex] (using law of cosine)

[tex]X = \sqrt{21^2+18^2-2\times 21\times 18\times cos(123 ^\circ)}[/tex]

[tex]X = \sqrt{441+324-756\times (-0.5446)}[/tex]

X = 34.30 yd

If A, B, and C are the measures of the angles of an oblique triangle, and a, b, and c are the lengths of the sides opposite the corresponding angles, then the square of a side of the triangle is equal to the sum of the squares of the other two sides minus twice the product of the two sides and the cosine of the included angle.

[tex]c^2 = a^2+ b^2- 2abcos C[/tex]

We have to the value of X which is present on the side c,

so, from the above formula we modified for the X,

and the formula become,

[tex]X = \sqrt{a^2+b^2-2abcosX}[/tex](using law of cosine)

rest of the solutions are only calculation which is elaborated  above which provide us the value of  X = 34.30 yd.

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Answer:

the additive inverse of 16 5/7 IS 26/7

We get the values when x is -8 y is 62, when y is -73 x is 7 and when x is 3 y is -37 for the linear equation y=-9x-10.

Given that,

The linear equation is y=-9x-10.

We have to fill the table given in the question.

First,

Taking x value is -8

We get y value as,

y=-9(-8)-10      (multiply -9 and -8)

y=72-10           (Subtracting 72 and 10)

y=62

When x is -8 y is 62.

Taking y value is -73

We get x value as,

-73=-9x-10

-73+10=-9x

-63=-9x

63=9x

x=63/9

x=7

When y is -73 x is 7.

Taking x value is 3.

We get y value as,

y=-9(3)-10

y=-27-10

y=-37

When x is 3 y is -37.

Therefore, We get the values when x is -8 y is 62, when y is -73 x is 7 and when x is 3 y is -37 for the linear equation y=-9x-10.

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Paul gained a total of 14 yards from both the catches during his football game.

Given,

Paul had two catches during his football game.

Paul lost 12 yards on his first catch.

Paul gained 26 yards on his second catch.

We have to find the total yards Paul gain from both the catches;

Here,

Total gained yards by Paul = Gained yards by Paul - Lost yards by Paul

Total gained yards by Paul = 26 - 12

Total gained yards by Paul = 14 yards

That is,

Paul gained a total of 14 yards from both the catches during his football game.

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The probability that a household in Maryland has an annual income of 100000 or more is 0.2373

Given Data;

Maryland had the greatest mean yearly household income of any state, according to Money magazine (time website). Consider a normal distribution with a mean of 75847 and a standard deviation of 33800 for the annual household income in Maryland.

Population Mean (μ) = 75847

Population Standard Deviation (σ) = 33800

'X' follows a normal distribution with a population mean and population standard deviation.

Here,

X ~ N ( μ = 75847 ,σ = 33800 )

Z =(X - μ)/σ

To get the probability that a household in Maryland has an annual income of 100000 or more.

Now, we have to compute P (X > 100000)

P (X > 100000) = 1 - P( (X-μ)/σ < (100000-75847)/33800 )

                         = 1 - p(z < 0.715 )

                         = 1 - 0.7627

                         = 0.2373

The required probability is 0.2373

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