2.5% of what number is 14?

No, the network in (d) does not have a Hamiltonian cycle. A Hamiltonian cycle is a path in a graph that visits each vertex exactly once and returns to the original vertex.

Vertex is a point in geometry. It is a corner or a point where two or more lines, edges, or faces of a shape meet. In three-dimensional shapes, a vertex is a point where three or more edges meet. In two-dimensional shapes, a vertex is a point where two or more lines meet. A vertex is usually denoted by a capital letter such as A, B, and C. A vertex is also known as a corner point, node, or intersection. In graphs, a vertex is a point where two or more edges meet.

In the network in (d), there are four vertices (A, B, C, and D), and it is not possible to form a path that visits each vertex exactly once and returns to the original vertex. Therefore, this network does not have a Hamiltonian cycle.

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Answer (with explanation):

1. Given

2. UY ≅ WY

3. Definition of Midpoint

4(statement). ∠UYX ≅ ∠VYW

4(reason). Side-Angle-Side SAS

5. Vertical Angle Theorem

in most proofs, (almost ALL the proofs) the first reason is always given.

you need given before you do anything.

on 2., the reason is Definition of Midpoint so you can tell it's UY is congruent to WY (uses the theorem)

on 3., it's the other way around and similar to 2. so the answer is definitely Definition of a Midpoint

on 4. statement and reason, you're side UY, angle Y, and side YX to prove that side VY, angle Y, and side YW are congruent. so, use the ∠UYX ≅ ∠VYW with the SAS

and on 5., you use vertical angles to say that ∠UYX reflects to ∠VYW so they are the same (aka congruent)

Answer:

\(\large\begin{array}{|l|l|}\cline{1-2}\sf Statement&\sf Reason\\\cline{1-2}1.\;\textsf{$Y$ is the midpoint of $UW$ and $VX$}&1.\;\sf Given\\\cline{1-2}2.\;UY \cong WY & 2.\; \sf De\:\!finition\;of\;a\;midpoint\\\cline{1-2}3.\;VY \cong XY&3.\; \sf De\:\!finition\;of\;a\;midpoint\\\cline{1-2}4.\;\angle UYX \cong \angle VYW&4.\; \sf Vertical\;Angle\;Theorem\\\cline{1-2}5.\; \triangle UYX \cong \triangle VYW &5.\;\sf Side-Angle-Side\;(SAS)\\\cline{1-2}\end{array}\)

Step-by-step explanation:

Midpoint

The point that is halfway between the endpoints of the line segment.

Side-Angle-Side (SAS) Congruence Theorem

If two sides and the included angle in one triangle are congruent to two sides and the included angle in another triangle, the triangles are congruent.

Vertical Angles Theorem

When two straight lines intersect, the opposite vertical angles are congruent.

\(\large\begin{array}{|l|l|}\cline{1-2}\sf Statement&\sf Reason\\\cline{1-2}1.\;\textsf{$Y$ is the midpoint of $UW$ and $VX$}&1.\;\sf Given\\\cline{1-2}2.\;UY \cong WY & 2.\; \sf De\:\!finition\;of\;a\;midpoint\\\cline{1-2}3.\;VY \cong XY&3.\; \sf De\:\!finition\;of\;a\;midpoint\\\cline{1-2}4.\;\angle UYX \cong \angle VYW&4.\; \sf Vertical\;Angle\;Theorem\\\cline{1-2}5.\; \triangle UYX \cong \triangle VYW &5.\;\sf Side-Angle-Side\;(SAS)\\\cline{1-2}\end{array}\)

Work Shown:

LCM = (product of two numbers)/(HCF of the two numbers)

LCM = 1536/16

LCM = 96

The margin of error is defined as follows:

M = 1.9z/sqrt(n).

In which:

The bounds of the confidence interval are given as follows:

\(\overline{x} \pm z\frac{\sigma}{\sqrt{n}}\)

In which:

The margin of error is then given as follows:

\(M = z\frac{\sigma}{\sqrt{n}}\)

The problem is incomplete, hence the general procedure to obtain the sample size was presented.

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Answer:

D=42

B and C =138

:)))))))))

Answer:

24*10^3=24000

Step-by-step explanation:

Answer:

the answer is 24000 grams

Step-by-step explanation:

hope this helped

Answer:  \(\frac{dy}{dx}\) = \(\frac{ 7 - sin y }{ -6 y^{2} + x cos y }\)

Step-by-step explanation:

Given data,

                       x sin y - 2y^3 - 5 = 7x

Differentiate with each term with respect to the independent variable,

            \(\frac{d}{dx}\) (x sin y) - \(\frac{d}{dx}\) (2y^3) - \(\frac{d}{dx}\) (5) = \(\frac{d}{dx}\) (7x)  

Apply to the product rule,

         sin y * \(\frac{d}{dx}\) (x) + x * \(\frac{d}{dx}\) (sin y) - \(\frac{d}{dx}\) (2 \(y^{3}\)) - \(\frac{d}{dx}\) (5) = \(\frac{d}{dx}\) (7x)

Apply the chain rule,

sin y * \(\frac{d}{dx}\) (x) + x* \(\frac{d}{dy}\) (sin y) * \(\frac{dy}{dx}\) - \(\frac{d}{dy}\) (2 \(y^{3}\))* \(\frac{dy}{dx}\) - \(\frac{d}{dx}\) (5) = \(\frac{d}{dx}\) (7x)

Take out the coefficients,

sin y * \(\frac{d}{dx}\) (x) + x * \(\frac{d}{dy}\) (sin y) * \(\frac{dy}{dx}\) -2 \(\frac{d}{dy}\) (\(y^{3}\)) *  \(\frac{dy}{dx}\) - \(\frac{d}{dx}\) (5) = 7 * \(\frac{d}{dx}\) (x)

Differentiate the constants and power functions,

 sin y + x * \(\frac{d}{dy}\) (sin y) * \(\frac{dy}{dx}\) - 2 * 3 * \(y^{2}\) * \(\frac{dy}{dx}\) = 7    

Differentiate sin (x),

  sin y + cos y * \(\frac{dy}{dx}\) - 2 * 3 * \(y^{2}\) * \(\frac{dy}{dx}\) = 7

Isolate,

             \(\frac{dy}{dx}\) = [ 7-sin y ] / (-6 \(y^{2}\) + x cos y )

Therefore,

              \(\frac{dy}{dx}\) = \(\frac{ 7 - sin y }{ -6 y^{2} + x cos y }\)

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Answer:

Two independent sample t test

Step-by-step explanation:

The research described describes the statistics of two different samples which are also independent,

Sample 1 :

Sample size, n1 = 16

Mean, xbar = 4.75

Standard deviation s2 = 2.8

Sample 1 :

Sample size, n1 = 15

Mean, xbar = 3.93

Standard deviation s2 = 2.4

The hypothesis :

H0 : μ1 = μ2

H1 : μ1 ≠ μ2

The t statistic :

(xbar1 - xbar 2) ÷ sqrt[(s1²/n1 + s2²/n2)

From on the test statistic, obtain the p value and compare with Given α - value to make and conclude in a decision.

Answer:

hope this helps ✌

MULTIPLY THE FIRST EQUATION BY -2 & ADD THEM.

-4X+8Y=-14

4X-2Y=9

6Y=-5

Y=-5/6 ANSWER.

4X-2*-5/6=9

4X+10/6=9

Step-by-step explanation:

Lets start with the given system of linear equations

2%2Ax-4%2Ay=7

4%2Ax-2%2Ay=9

In order to solve for one variable, we must eliminate the other variable. So if we wanted to solve for y, we would have to eliminate x (or vice versa).

So lets eliminate x. In order to do that, we need to have both x coefficients that are equal but have opposite signs (for instance 2 and -2 are equal but have opposite signs). This way they will add to zero.

So to make the x coefficients equal but opposite, we need to multiply both x coefficients by some number to get them to an equal number. So if we wanted to get 2 and 4 to some equal number, we could try to get them to the LCM.

Since the LCM of 2 and 4 is 4, we need to multiply both sides of the top equation by 2 and multiply both sides of the bottom equation by -1 like this:

2%2A%282%2Ax-4%2Ay%29=%287%29%2A2 Multiply the top equation (both sides) by 2

-1%2A%284%2Ax-2%2Ay%29=%289%29%2A-1 Multiply the bottom equation (both sides) by -1

So after multiplying we get this:

4%2Ax-8%2Ay=14

-4%2Ax%2B2%2Ay=-9

Notice how 4 and -4 add to zero (ie 4%2B-4=0)

Now add the equations together. In order to add 2 equations, group like terms and combine them

%284%2Ax-4%2Ax%29-8%2Ay%2B2%2Ay%29=14-9

%284-4%29%2Ax-8%2B2%29y=14-9

cross%284%2B-4%29%2Ax%2B%28-8%2B2%29%2Ay=14-9 Notice the x coefficients add to zero and cancel out. This means we've eliminated x altogether.

So after adding and canceling out the x terms we're left with:

-6%2Ay=5

y=5%2F-6 Divide both sides by -6 to solve for y

y=-5%2F6 Reduce

Now plug this answer into the top equation 2%2Ax-4%2Ay=7 to solve for x

2%2Ax-4%28-5%2F6%29=7 Plug in y=-5%2F6

2%2Ax%2B20%2F6=7 Multiply

2%2Ax%2B10%2F3=7 Reduce

2%2Ax=7-10%2F3 Subtract 10%2F3 from both sides

2%2Ax=21%2F3-10%2F3 Make 7 into a fraction with a denominator of 3

2%2Ax=11%2F3 Combine the terms on the right side

cross%28%281%2F2%29%282%29%29%2Ax=%2811%2F3%29%281%2F2%29 Multiply both sides by 1%2F2. This will cancel out 2 on the left side.

x=11%2F6 Multiply the terms on the right side

So our answer is

x=11%2F6, y=-5%2F6

which also looks like

(11%2F6, -5%2F6)

Notice if we graph the equations (if you need help with graphing, check out this solver)

2%2Ax-4%2Ay=7

4%2Ax-2%2Ay=9

we get

graph of 2%2Ax-4%2Ay=7 (red) 4%2Ax-2%2Ay=9 (green) (hint: you may have to solve for y to graph these) and the intersection of the lines (blue circle).

and we can see that the two equations intersect at (11%2F6,-5%2F6). This verifies our answer.You really don't want to solve this system by 'addition.' What you want is to solve it by elimination, using addition as one of the steps of the process.

The idea of solving by elimination is to multiply (if necessary) one of the equations by some constant so that one of the variables will have a coefficient that is the additive inverse of the coefficient on the same variable in the other equation.

In this example, multiply the first equation by -2, resulting in a coefficient on the x term of -4. -4 is the additive inverse of the 4 coefficient on x in the second equation.

-4x+%2B+8y+=+-14

4x-2y=9

Now you can add the two equations, term-by-term. That is, you add the x terms to the x terms, the y terms to the y terms, and the constants to the constants, resulting in one equation with a zero coefficient on one of the variables, in this case, x.

The sum equation is:

0x%2B6y=-5

Divide by 6:

y=-%285%2F6%29

Now that you have a value for y, you can either substitute that value into either one of the original equations and solve for x, or you could take the original two equations, multiply one of them by an appropriate constant to eliminate the y variable so that you can solve for x. Either way works. Watch carefully:

4x-2%28-5%2F6%29=9

4x%2B5%2F3=9

4x=%2827%2F3%29-%285%2F3%29

4x=22%2F3

x=11%2F6

Answer:

4s-300= Jessica's current salary

Answer:

x=24 or 25

Step-by-step explanation:

90% is x=24

89.999999 repeat% is x =25

Answer:

A and D

Step-by-step explanation:

The graph of the function "g", which is defined for all "real-numbers" is shown below.

The function "g" which is defined for all "real-numbers" is represented as :

g(x) = {2 if x<0,

         {-1 if x=0

         {-3 if x>0

this function means that, for every input-value, which is less than 0, the output will be always 2,

For the input-value "0", the output-value will be = -1;

For all the input-value which are greater than "1", the out will be always "-3",

So, from the above information, the graph is plotted below,

The red-line represents "2 if x<0", the green line represents "-3 if x>0".

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Answer:

3 trips

Step-by-step explanation:

I think it is three trips because 3 out of the 5 train tracks from city x were found in city y, therefore only 3 train tracks will be found in city z so there are 3 trips

A table that best represent the equation include the following: H. table H.

In order to determine the table that best represent the equation, we would have to substitute each of the values of x (x-values) into the linear function and then evaluate as follows;

When the value of x = 1 in table F, the linear function is given by;

y = x - 12

y = 1 - 12

y = -11 (False).

When the value of x = 0 in table G, the linear function is given by;

y = x - 12

y = 0 - 12

y = -12 (True).

When the value of x = 2 in table G, the linear function is given by;

y = x - 12

y = 2 - 12

y = -10 (False).

When the value of x = 0 in table H, the linear function is given by;

y = x - 12

y = 2 - 12

y = -10 (True).

When the value of x = 4 in table H, the linear function is given by;

y = x - 12

y = 4 - 12

y = -8 (True).

When the value of x = 6 in table H, the linear function is given by;

y = x - 12

y = 6 - 12

y = -6 (True).

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

Answer:

80 feet

Step-by-step explanation:

6 cm = 15 feet

1 cm = 5/2 feet

32 cm = 90 feet

The actual perimeter of the room is 90 feet.

A scale factor is defined as the ratio between the scale of a given original object and a new object,

We have,

The scale drawing of a rectangular room measures 10 cm long by 6 cm wide.

The actual width of the room is 15 feet.

This means,

6cm = 15 feet

1 cm = 15/6 feet

1 cm = 5/2 feet

Now,

The perimeter of the rectangular room.

= 2(10 + 6)

= 2 x 16

= 32 cm

1 cm = 5/2 feet

So,

32 cm = 32 x 5/2 feet

32 cm = 16 x 5 feet

32 cm = 90 feet

Thus,

The actual perimeter of the room is 90 feet.

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Answer:

Step-by-step explanation:

We can use the formula for the future value of an annuity to determine how much Marcia needs to invest today to meet her retirement goal of $90,000. The formula for the future value of an annuity is:

FV = PMT x [(1 + r/n)^(n*t) - 1] / (r/n)

where:

FV = future value of the annuity

PMT = payment (or deposit) made at the end of each compounding period

r = annual interest rate

n = number of compounding periods per year

t = number of years

In this case, we want to solve for the PMT (the amount Marcia needs to invest today). We know that:

Marcia wants to retire in 15 years (when she is 65), so t = 15

The interest rate is 10% per year, compounded semiannually, so r = 0.10/2 = 0.05 and n = 2

Marcia wants to have $90,000 in her retirement account

Substituting these values into the formula, we get:

$90,000 = PMT x [(1 + 0.05/2)^(2*15) - 1] / (0.05/2)

Simplifying the formula, we get:

PMT = $90,000 / [(1.025)^30 - 1] / 0.025

PMT = $90,000 / 19.7588

PMT = $4,553.39 (rounded to the nearest cent)

Therefore, Marcia needs to invest $4,553.39 today in order to meet her retirement goal of $90,000, assuming an interest rate of 10% per year, compounded semiannually.

Answer:

.25

Step-by-step explanation:

Answer:

27 23/25

Step-by-step explanation:

Given

To find the value of x/3.

Explanation:

It is given that,

That implies,

Hence, x/3 = y/2.

Looks like the given limit is

\(\displaystyle \lim_{n\to\infty} \left(\frac n{3n-1}\right)^{n-1}\)

With some simple algebra, we can rewrite

\(\dfrac n{3n-1} = \dfrac13 \cdot \dfrac n{n-9} = \dfrac13 \cdot \dfrac{(n-9)+9}{n-9} = \dfrac13 \cdot \left(1 + \dfrac9{n-9}\right)\)

then distribute the limit over the product,

\(\displaystyle \lim_{n\to\infty} \left(\frac n{3n-1}\right)^{n-1} = \lim_{n\to\infty}\left(\dfrac13\right)^{n-1} \cdot \lim_{n\to\infty}\left(1+\dfrac9{n-9}\right)^{n-1}\)

The first limit is 0, since 1/3ⁿ is a positive, decreasing sequence. But before claiming the overall limit is also 0, we need to show that the second limit is also finite.

For the second limit, recall the definition of the constant, e :

\(\displaystyle e = \lim_{n\to\infty} \left(1+\frac1n\right)^n\)

To make our limit resemble this one more closely, make a substitution; replace 9/(n - 9) with 1/m, so that

\(\dfrac{9}{n-9} = \dfrac1m \implies 9m = n-9 \implies 9m+8 = n-1\)

From the relation 9m = n - 9, we see that m also approaches infinity as n approaches infinity. So, the second limit is rewritten as

\(\displaystyle\lim_{n\to\infty}\left(1+\dfrac9{n-9}\right)^{n-1} = \lim_{m\to\infty}\left(1+\dfrac1m\right)^{9m+8}\)

Now we apply some more properties of multiplication and limits:

\(\displaystyle \lim_{m\to\infty}\left(1+\dfrac1m\right)^{9m+8} = \lim_{m\to\infty}\left(1+\dfrac1m\right)^{9m} \cdot \lim_{m\to\infty}\left(1+\dfrac1m\right)^8 \\\\ = \lim_{m\to\infty}\left(\left(1+\dfrac1m\right)^m\right)^9 \cdot \left(\lim_{m\to\infty}\left(1+\dfrac1m\right)\right)^8 \\\\ = \left(\lim_{m\to\infty}\left(1+\dfrac1m\right)^m\right)^9 \cdot \left(\lim_{m\to\infty}\left(1+\dfrac1m\right)\right)^8 \\\\ = e^9 \cdot 1^8 = e^9\)

So, the overall limit is indeed 0:

\(\displaystyle \lim_{n\to\infty} \left(\frac n{3n-1}\right)^{n-1} = \underbrace{\lim_{n\to\infty}\left(\dfrac13\right)^{n-1}}_0 \cdot \underbrace{\lim_{n\to\infty}\left(1+\dfrac9{n-9}\right)^{n-1}}_{e^9} = \boxed{0}\)

Answer:

24 square yards

Step-by-step explanation:

Find the diagram attached.

The area of the diagram = Area of rectangle + Area of triangle

Area of rectangle = 3 * 4

Area of rectangle = 12 square yards

Area of triangle = 1/2 * base * height

Area of triangle = 1/2 * 6 * 4

Area of triangle = 12 square yards

Area of the diagram = 12 + 12

Area of diagram =  24 square yards

Hence 24 square yards of carpeting is needed

Answer:

500 and 4.3

Step-by-step explanation:

A decigram is one-tenth of a gram and a kilometer is one-thousandth of a meter. Using this information, we must multiply the given amounts by the values.

5000 × 0.1 = 500

4300 × 0.001 = 4.3

Thus, the answers [in order] are 500 and 4.3

Hope this helps and feel free to ask any questions.

Answer: 9 nickles and 16 dimes

Step-by-step explanation: if she has 9 nickles that is equal to 45 cents plus the 16 dimes which equals to 1 dollar 60 cents plus the 45 cents for the nickles in total that equals to 2.05 dollars.

The number of dimes and nickels will be 16 and 9, respectively.

The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.

Michaela has $2.05 in dimes and nickels in her change purse. She has seven more dimes than nickels.

Let 'x' be the number of dimes and 'y' be the number of nickels. Then the equations are given as,

0.10x + 0.05y = 2.05    ....1

x = y + 7                        ....2

From equations 1 and 2, then we have

0.10(y + 7) + 0.05y = 2.05

0.10y + 0.7 + 0.05y = 2.05

0.15y = 1.35

y = 9

Then the value of the variable 'x' is given as,

x = 9 + 7

x = 16

The number of dimes and nickels will be 16 and 9, respectively.

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Answer:

If we are given diameter and we need to find radius then,

Radius(r) = Diameter(d) ÷ 2

⇒ r = d÷2

So here d = 41

So r = d÷2

⇒ r = 41 ÷ 2

⇒ r = 20.5

The function of the object height is an illustration of a projectile motion

The object will never hit the ground

The function is given as:

h=16t^2+80t+96.

When the object hits the ground, h = 0

So, we have:

16t^2+80t+96 = 0

Divide through by 16

t^2+5t+6 = 0

Expand

t^2 + 3t + 2t + 6 = 0

Factorize

t(t + 3) + 2(t + 3) = 0

Factor out t + 3

(t + 2)(t + 3) = 0

Solve for t

t = -2 or t = -3

The time (t) cannot be negative.

Hence, the object will never hit the ground

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Answer:

6

Step-by-step explanation:

did this question in savvas