Line segment wx is the radius of circle x, and line segment zy is the radius of circle y. Points w, x, c, y, and z are all on line segment wz. What is the area of circle c, which passes though points w and z?.

a)The gradient of AD will be 2.

b)The length of BD. will be 159 m.

Trigonometry is a branch of mathematics that deals with the relationship between the sides and angles of a right-angle triangle.

It is given that,  A is 106 m above the ground, C is vertically below A, the gradient of AB is 1 and CD is 53 m.

Suppose the length BC is x

Gradient of AB = 1

AB/BC=1

106/x=1

x=106

BC=106 m

CD = 53 m

The gradient of AD is,

m = BC/CD

m=106/53

m=2

b)

The length of BD is found as,

BD=BC+CD

BD=106+53

BD=159 m

Thus, the gradient of AD will be 2 and the length of BD. will be 159 m.

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the probability of drawing a green marble, putting it aside, and then drawing another green marble is 3/68

Total 17 marbles

4 - blue marbles

6 - green marbles

2 - red marbles

The rest - yellow marbles

Probability of drawing red first:

P(red) = number of red / total number = 2/17

Probability of drawing green second, without replacement:

P(green) = number of green / number left in the bag = 6/16 = 3/8

Probability of red and green in order:

P = P(red)*P(green) = 2/17*3/8 = 3/68

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The correct statement is: 'A standard normal distribution has a mean of 0 and a standard deviation of 1 '

The correct answer is an option (b)

In this question, we need to complete given statement.

We know that the normal distribution is a symmetrical and bell-shaped distribution.

In standard normal distribution the mean, median and mode are all equal. Also, it always has a mean of zero and a standard deviation of one.

So,  A standard normal distribution has a mean of 0 and a standard deviation of 1 .

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The probability that the 5th card was the third and last jack is 0.016%

Standard card deck only have 4 jack cards and 48 other cards is not a jack. So, to calculate the probability is simply by dividing the number of favorable outcomes by the possible outcomes.

It is very important to note, wherever the first and second jacks are located it will not affect the calculation for the third jack.

So, you can calculate with this formula,
P(5th card is third and last jack) = (48/52)×(47/51)×(4/50)×(3/49)×(2/48)×(46/47)×(45/46)×(44/45)

or this formula,

P(5th card is third and last jack) = (4/52)×(3/51)×(48/50)×(47/49)×(2/48)×(46/47)×(45/46)×(44/45)

After we simplified calculation, we get

= (4 × 3 × 2 × 44) ÷ (52 × 51 × 50 × 49)

= 0.00016 or 0.016%

Thus, the probability is 0.016% for the third and last jack on 5th card.

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The correct option representing Tracy's total investment is a. $4,940.00.

She bought 150 shared of Upton group that offers each share at the price of $18.96. So, the cost of 150 shares = 150 × 18.96

Performing multiplication on Right and Side of the equation

The cost of 150 shares from Upton group = $2844

The cost of 100 shares of WHI health = 100 × 20.96

Performing multiplication on Right and Side of the equation

The cost of 100 shares of WHI Health = $2096

The total investment will be sum of the cost of these shares.

Total investment = 2844 + 2096

Performing addition on Right Hand Side

Total investment = $4940

Hence, the total investment of Tracy is $4940.

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The complete question is -

Use the information in the table below to answer the following question.

Name of Fund

NAV

Offer Price

Upton Group

$18.47

$18.96

Green Energy

$17.29

$18.01

TJH Small-Cap

$18.43

$19.05

WHI Health

$20.96

NL

Tracy buys 150 shares of Upton Group and 100 shares of WHI Health. What is Tracy's total investment?

a.

$4,940.00

b.

$5,040.00

c.

$5,914.50

d.

$5,988.00

The relation in option (a) is Transitive , in option (b) is Reflexive and Transitive and option (c) is Symmetric .

In the question ,

it is given that ,

Option(a) ,  

R is a relation on set of all people where (a,b) is in R if a is taller than b .

Reflexive : NO , because "a" cannot be taller than "a" itself .

Symmetric : NO , because if "a" is taller than "b" , then "b" will be shorter than "a" .

Transitive : YES , because if "a" is taller than "b" and "b" is taller than "c" , then "a" is taller than "c" .

Option(b)

R is a relation on set of integers > 0 where (a,b) is in R if a divides b .

Reflexive : YES , because every number divides itself .

Symmetric : NO , because if "a" divided "b" , then "b" may not divide "a" .

Transitive : YES , because if "a" divided "b" and "b" divides "c" , then "a" must divide "c" .

Option(c)

R is a relation on set of all people where (a,b) is in R if a is married to b .

Reflexive : NO , because marriage is between two people , and "a" cannot marry "a" .

Symmetric : YES , because if "a" is married to "b" , then "b" is married to "a" .

Transitive : NO , because if "a" is married to "b" and "b" is married to "c" , then "a" is not married to  "c" .

Therefore , The relation in option (a) is Transitive , in option (b) is Reflexive and Transitive and option (c) is Symmetric .

The given question is incomplete , the complete question is

Write in the space provided the property or properties that each relation possesses (reflexive, symmetric, transitive).

(a) R is a relation on the set of all people, (a,b) is in R if a is taller than b .

(b) R is a relation on the set of integers > 0 , (a,b) is in R if a divides b .

(c) R is a relation on the set of all people , (a,b) is in R if a is married to b .

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Answer:

B

Step-by-step explanation:

B. a + (-7 + 7) = a +0

When you remove a from both sides, you're left with -7+7=0 which shows that the opposites of the numbers add up to 0.

It's always true that a reflection on the x-axis followed by a reflection on the y-axis leaves a point in its original location.

What is a coordinate axis?

A coordinate system in geometry is a system that uses one or more numbers, or coordinates, to determine the position of points or other geometric elements on a manifold such as Euclidean space.

When a reflection in the x-axis followed by a reflection in the y-axis leaves a point in its original location. Is it always true?

The answer is true.

Reason: For example, piece of graph paper into 4 pieces, draw this same thing on all four:  

In this condition reflection in the x-axis followed by a reflection in the y-axis leaves a point in its original location of different color is yes.

Hence, it's always true that a reflection on the x-axis followed by a reflection on the y-axis leaves a point in its original location.

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The speed of rocket when it is very far away from the the rocket is 9990 m/s.

In the given question, a rocket is launched straight up from the earth's surface at a speed of 15000 m/s.

v = 15000m/s = 1.5×10^{4} m/s

We have to find the speed of rocket when it is very far away from the the rocket.

As we know,

Mass of Earth(M) = 5.972×10^{24} kg

Radius of Earth(R) = 6.371×10^{6} m

The value of G = 6.67×10^{-11}

Applying law of conservation of energy,

-GMm/R + 1/2 mv^2 = 0+1/2 mV^2

Taking common m on both side, we get

-GM/R + v^2/2 = V^2/2

Substituting the value

-(6.67×10^{-11})(5.972×10^{24})/ 6.371×10^{6} + (1.5×10^{4})^2/2 = V^2/2

V^2/2 = -6.67×5.972×10^{-11+24}/ 6.371×10^{6} + 2.25×10^{8}/2

V^2/2 = -6.252×10^{13-6} + 1.125×10^{8}

V^2/2 = -6.252×10^{7} + 11.25×10^{7}

V^2/2 = 4.998×10^{7}

Multiply by 2 on both side we get

V^2 = 9.996×10^{7}

V^2 = 99.96×10^{6}

Taking square root on both side, we get

V = 9.99×10^{3}

V = 9990 m/s

Hence, the speed of rocket when it is very far away from the the rocket is 9990 m/s.

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We use ANOVA to test for differences between population means by examining the amount of variability between the samples relative to the amount of variability within the samples. Hence, it is TRUE

The statistical analysis tool known as analysis of variance (ANOVA) divides the observed aggregate variability present in a data set into two categories: systematic variables and random components. The random factors have no statistical impact on the presented data set, whereas the systematic factors do. The ANOVA test is used by analysts to ascertain how independent factors in a regression analysis affect the dependent variable.

ANOVA basically stands for analysis of the variance.

Hence, according to above statements, given fact is true.

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Answer:

6.39 m

Step-by-step explanation:

( for a right triangle such as this)

Sin (theta) = opp leg / hypotenuse = AB / x    

sin (54) = AB / 7.9

7.9 * sin 54 = AB = 6.39 m

The flux of the given function f = x³i + y³j + z³k is given by f',

f' = 3(x²i + y²j + z²k)

Given, f = x³i + y³j + z³k

we have to find the flux of the given function f = x³i + y³j + z³k

On partial differentiating the function, we get

f' = 3x²i + 3y²j + 3z²k

f' = 3(x²i + y²j + z²k)

So, the flux of the given function f = x³i + y³j + z³k is given by f',

f' = 3(x²i + y²j + z²k)

Hence, the flux of the given function f = x³i + y³j + z³k is given by f',

f' = 3(x²i + y²j + z²k)

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Using the definition of divisibility, 2p is the greatest common factor.

In the given question we have to factor out the greatest common factor. If the greatest common factor is 1, just retype the polynomial.

The given polynomial is 2p^3+6p.

Now taking 2p common from both terms

=2(p^2+3)

By the definition of divisibility, we get

2p | 2p^3 and 2p|6p, 2| 2p^3 and 2|6p also p|2p^3 and p|6p.

So, 2,p and 2p are common factors of 2p^3 and 6p.

Hence, 2p is the greatest common factor.

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The right answer is:

Factor out the greatest common factor. If the greatest common factor is 1, just retype the polynomial.

2p^3+6p

The graph of the solution set of the given inequality can be seen in the image at the end.

Here we have the following inequality:

-0.96 ≥ x*0.3

To solve this, we need to isolate the variable x in one of the sides of the inequality.

To do that, we need to divide both sides by 0.3

-0.96/0.3  ≥ x*0.3/0.3

-3.2 ≥ x

So our variable x is smaller than or equal to -3.2

Then the graph will be a closed circle at x = -3.2 and a line that extends to the left side.

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The equation given is linear, not proportional, and thus, there is no constant of proportionality.

Here we have the following linear equation:

y = 5*x - 1/3

The general linear equation is:

y = m*X + b

Where m is the slope and b is the y-intercept, so in this case we have:

slope = 5

y-intercept = -1/3

Partocularly, when the y-intercept is 0 we have a proportional relation:

y = m*x

And then m is called the "constant of proportionality"

In this case the y-intercept is not zero, thus, there is no constant of proportionality, just a slope.

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Answer:

The numbers are 10 and 21.

Step-by-step explanation:

x + y = 31

xy = 210

x = 31 - y

(31 - y)y = 210

31y - y² = 210

y² - 31y + 210 = 0

(y - 21)(y - 10) = 0

y - 21 = 0  or  y - 10 = 0

y = 21  or  y = 10

The two real numbers are 10 and 21.

Quadratic Equations are algebraic expressions of degree 2 in one variable and are of the form ax² + bx + c = 0.

In simpler terms, a quadratic equation is be defined as a polynomial equation of degree 2.

Given that, there are two real numbers with a sum of 31 and a product of 210.

We need to find their values using the concept of quadratic equation,

So, according to the question,

x + y = 31 (eq 1)

xy = 210 (eq 2)

x = 31 - y

(31 - y) y = 210

31y - y² = 210

y² - 31y + 210 = 0

(y - 21) (y - 10) = 0

y - 21 = 0 or y - 10 = 0

y = 21 or y = 10

Hence, the two real numbers are 10 and 21.

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The Fundamental Theorem of Algebra states that a polynomial of fifth degree will have five roots, which is the case with this particular polynomial.

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Answer:

12

Step-by-step explanation:

Use 5 for m

Use -3 for x

Use 7 for y

y =mx + b

7 = (5)(-3) + b

7 = -5 +b

12 = b

The length of RS in the diagram is 25 units.

Given:

TQ = 18 units

From the figure:

TQ = RT

2x + 10 = 18

2x = 18 - 10

2x = 8

divide by 2 on both sides

2x/2 = 8/2

x = 4 units

Both the triangles are congruent by right angled hypotenuse side criteria.

so RS = QS

= 9x - 11

= 9*4 - 11

= 25 units

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Full question:

What is the length of RS in the diagram TQ is 18 units in length?

Diagram is in the image uploaded.

Question:

Which expressions are equivalent to 78 • 7? Select all that apply. A. 73 • 73 B. 71879 C. (73)3 D. 74 + 75 E. 74 • 75

None of the expressions are equivalent to 78 • 7

What is an expression?

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a complete sentence. Any one of the following mathematical operations can be used. A sentence has the following structure: Number/variable, Math Operator, Number/Variable is an expression.

None because 78 * 7 = 546

None of the options equal to 546.

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Answer:

D. Add 8x to both sides of the inequality.

Step-by-step explanation:

The value of the double integral is  [tex]I = \int\limits^{\pi/2}_{\pi/4} \int\limits^{3/sin0}_{r=0} r^{2}cos0drd0[/tex].

Let z* be the common (finite) optimal value of P and D.

Given integral is

[tex]I = \int\limits^3_{y = 0} \int\limits^y_{x=0} {x} \, dxdy[/tex]

The region of integration lies between

y = 0, y = 3, x = 0 & x = y

Let x = rcosθ, y = rsinθ,

[tex]x^{2} +y^{2}= r^{2}[/tex]

At y = 3, rsinθ = 3

Thus r varies from 0 to 3/sinθ

θ varies from π/4 to π/2

Now, dxdy ----> rdrdθ

Therefore,

[tex]I = \int\limits^{\pi/2}_{\pi/4} \int\limits^{3/sin0}_{r=0} r^{2}cos0drd0[/tex]

Hence the answer is The value of the double integral is  [tex]I = \int\limits^{\pi/2}_{\pi/4} \int\limits^{3/sin0}_{r=0} r^{2}cos0drd0[/tex].

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The number of small cups is 10, and the number of large cups is 50.

What is a linear equation?

A linear equation is an equation in which each term has at max one degree. Linear equations in variables x and y can be written in the form y=mx+c.

Linear equation with two variables, when graphed on the cartesian plane with axes of those variables, give a straight line.

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p = the number of small cups sold,

q = the number of large cups sold,

Salma sold 60 cups then the equation becomes:

p + q = 60                     ---------------(1)

Salma sold 60 cups of lemonade total of 920 ounces then the equation becomes:

12p + 16q = 920            ---------------(2)

Multiplying the equation 1 by 12 then substracted from equation 2, we get:

12p + 16q = 920

12p + 12q = 720

4q = 200

q = 50

Substituting q = 50 into equation (1) we get,

p + 50 = 60

p = 10

Hence, the number of small cups is 10, and the number of large cups is 50.

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Answer:

3 cats are not brown.

Step-by-step explanation:

First, take the 2/3 and divide 2 by 3 on a calculator to get 0.66. Then, set up this equation on the calculator:

0.66 x 8 = 5.28. We will round this to 5 cats.

Now, we take the 5 cats and subtract it from the total of 8 cats:

8 - 5 = 3 cats.

3 cats are not brown.

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Option B is the correct answer, The set of correlations which correctly shows the highest to lowest degree of relation is -0.91, +0.83, +0.10, -0.03.

What is correlation?

In statistics, the correlation is a technique used to determine the relationship between the two variables. The correlation's range is from -1 to +1. There are three primary categories of correlation: no correlation, positive correlation, and negative correlation. When the correlation value is zero, there is no association; the correlation value that is closest to zero indicates the weakest degree of relationship.

We must select the set of correlations in the question that accurately displays the highest to the lowest degree of relation.

Option B is the best choice since we must take the absolute value into account in order to determine the relationship's degrees. Here, the absolute values drop from 0.91 to 0.03.

Option A is incorrect since the absolute values decline from 0.91 to 0.03 and then climb to 0.10 in this situation.

Because the absolute values are not listed in decreasing order, Option C is incorrect.

Because the absolute values in this situation are not ordered in decreasing order, Option D is also a incorrect choice.

Therefore, option B, is the correct option.

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Answer:

x = 23

Step-by-step explanation:

The sum of two interior angles is equal to an exterior angle that is supplementary to the third interior angle.

We can write the following equation based on this information to find the value of x:

2x + 3 + 51 = 100 add like terms

2x + 54 = 100 subtract 54 from both sides

2x = 46 divide both sides by 2

x = 23

The probability that a number selected at random from the set {2, 3, 7, 12, 15, 22, 72, 108} will be divisible by both 2 and 3 is 3/8.

Given set:

random from the set {2, 3, 7, 12, 15, 22, 72, 108}

From the set:

The number that are divisible by both 2 and 3 is:

12,72,108.

So number of favorable outcomes is = 3

Number of possible outcomes = 8

we know that

probability = favorable outcomes / possible outcomes

= 3/8

= 37.5%

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The minimum sample size needed is 93.

In order to obtain survey findings that accurately represent a population you are researching while maintaining your chosen sampling error and confidence, you must have a required sample size.

A political scientist polls 300 random selection Atlanta votes cast, asking each one who those who currently support in the city's mayoral race in 2020. While 184 people indicated they would vote for candidate b, 184 people said they would pick for option a, and 15 people stated they felt undecided or would vote for a different candidate.

The community proportion of all Atlanta electors who intend to vote for candidate a was calculated with a 95% confidence level in query 8 by the political researcher. Furthermore, the researcher wants to determine p with a 3% error margin.

n = 101

p = 0.5

e = 5%=0.05

z score at 95% = 1.96

[tex]z score = (observed value - mean of the sample) / standard deviation of the sample[/tex]

On auditing the value to the given equation:

n = 93

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5 less than N means we subtract 5 to the given variable N. So the expression will be N - 5.

Algebra shows the numbers by alphabets in a equation including mathematical operations. In algebra we used alphabet which shows a variable unknown quantity, unknown variables which helps in changing a mathematical statement into an equation.

In the given question a mathematical statement is given and we have to change the mathematical equation into an algebraic expression by using the information.

The statement 5 less than N means 5 is being subtracted from N. The mathematical expression for 5 less than N is equal to N - 5.

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The ratio of the area of the circle to the area of triangle is πr : h+r.

We know that rs = A

where r is the radius , s is the semi perimeter and A is the area.

We have that the ratio of the area of the circle to the area of the triangle is

πr²/rs = πr/s.

Now we will express s as h and r. Denote the points where the in-circle meets the triangle as X,Y,Z where O is the in-center and denote

AX = AY = z, BX = BZ = y, CY = CZ = x.

Since XOZB is a square

Therefore r = BX = BZ = y.

The perimeter can be expressed as 2(x + y + x), so the semi perimeter is

x + y + z.

The hypotenuse is AY + CY = z + x.

Thus we have s = x + y + z

                          = (z + x) + y

                        s = h + r

Therefore the ratio of the area of circle to the area of the triangle will become πr : h+r.

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