a tree is a connected and acyclic graph. how many edges must be included in any tree with 100 vertices?

Answer:

225

Step-by-step explanation:

if you convirt them all to fractions and make it 5/1*10/1*36/1=225

The value of measure of x in the triangle is,

⇒ x = 4√3 units

We have to given that,

A triangle is shown in image.

Now, WE can formulate by trigonometry formula we get;

⇒ tan 30° = Opposite / Base

⇒ tan 30° = 4 / x

⇒ 1/√3 = 4/x

⇒ x = 4√3 units

Thus, The value of measure of x in the triangle is,

⇒ x = 4√3 units

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Answer:

B : Theoretical Probability

Explanation:

In probabilitty, experimental probability are based on "what has happened".

• Each of the outcomes are not equally as likely to occur.

Experimental probabilities are derived from the results of experiments or repeated trials.

On the other hand, when all the outcomes are equally as likely to occur, the probability is said to be of the theoretical type.

It is theoretical probability that answers the question on "what could happen".

The correct option is B.

The solution to find the five number summary shown below.

When conducting descriptive analyses or conducting an initial analysis of a sizable data set, a five-number summary is particularly helpful. The maximum and minimum values in the data set, the lower and upper quartiles, and the median make up a summary's five values.

To find a five number summary we have follow:

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Answer:

b is the correct answer

hope it helps you and remember me

Answer:

60+96

156

Step-by-step explanation:

Answer:

They will be 10 miles apart on the 4th hour

Step-by-step explanation:

4hr=60 (15miles)

4hr=48 (12miles)

60

-48

12 more than 10 hours apart

The monthly PMI Payment for Christina's loan is $37.50.The correct answer is option B.

To determine Christina's monthly PMI (Private Mortgage Insurance) payment, we need to find the corresponding interest rate for her loan-to-value (LTV) ratio. The LTV ratio is calculated by dividing the loan amount by the property value.

The loan amount can be calculated by subtracting the down payment from the property value:

Loan amount = Property value - Down payment

           = $170,000 - $20,000

           = $150,000

Now we can calculate the LTV ratio:

LTV ratio = Loan amount / Property value * 100

         = $150,000 / $170,000 * 100

         = 88.24%

Since Christina is obtaining a 30-year mortgage, we need to look at the interest rates for LTV ratios between 85.01% and 90%. According to the table, the interest rate for this range is 0.30%.

To calculate the PMI payment, we multiply the loan amount by the PMI rate and divide it by 12 months:

PMI payment = (Loan amount * PMI rate) / 12

           = ($150,000 * 0.30%) / 12

           = $450 / 12

           = $37.50

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The Probable question may be:
Christina is buying a $170,000 home with a 30-year mortgage. She makes a $20,000 down payment.

Use the table to find her monthly PMI payment

Base to loan% = 95.01% to 97%,90.01% to 95%,85.01% to 90%,80.01% to 85%.

30-year fixed-rate loan = 0.55%,0.41%,0.30%,0.19%

15-year fixed-rate loan = 0.37%,0.28%,0.19%,0.17%.

A. $51.25

B. $37.50

C. $23.75

D. $42.50

Answer:

\( \frac{19 + 6 \sqrt{3} }{2} \)

Step-by-step explanation:

\(2a - \frac{1}{ \sqrt{a} } + \frac{1}{a} \: \: \: when \: \: a = 4 + 2 \sqrt{3} \)

\(2 \times (4 + 2 \sqrt{3} ) - \frac{1}{ \sqrt{4 + 2 \sqrt{3} } } + \frac{1}{4 + 2 \sqrt{3} } \)

Expand the brackets (multiply every term inside the bracket by the term on the outside) and make the denominator the same (4 + 2√3):

\( \frac{(8 + 4\sqrt{3} )\times(4 + 2 \sqrt{3} ) }{4 + 2 \sqrt{3} } - \frac{ \sqrt{4 + 2 \sqrt{3} } }{4 + 2 \sqrt{3} } + \frac{1}{4 + 2 \sqrt{3} } \)

\( \frac{32 + 16 \sqrt{3} + 16 \sqrt{3} + 24 - \sqrt{4 + 2 \sqrt{3} } + 1}{4 + 2 \sqrt{3} } \)

Collect like-terms:

\( \frac{57+ 32 \sqrt{3} - \sqrt{4 + 2 \sqrt{3} } }{4 + 2 \sqrt{3} } \)

\( \frac{57 + 32 \sqrt{3} - \sqrt{( {1 + \sqrt{3}) }^{2} } }{4 + 2 \sqrt{3} } \)

\( \frac{57 + 32 \sqrt{3} - (1 + \sqrt{3} )}{4 + 2 \sqrt{3} } \)

Eliminate the parentheses:

\( \frac{57 + 32 \sqrt{3} - 1 - \sqrt{3} }{4 + 2 \sqrt{3} } \)

Collect like terms:

\( \frac{56 + 31 \sqrt{3} }{4 + 2 \sqrt{3} } \)

\( \frac{56 + 31 \sqrt{3} }{4 + 2 \sqrt{3} } \times \frac{4 - 2 \sqrt{3} }{4 - 2 \sqrt{3} } = \frac{224 - 112 \sqrt{3} + 124 \sqrt{3} - 186}{16 - 4 \times 3} = \frac{38 + 12 \sqrt{3} }{4} \)

\( \frac{2(19 + 6 \sqrt{3}) }{4} = \frac{19 + 6 \sqrt{3} }{2} \)

Answer:

9x2 and 9x2

Step-by-step explanation:

Answer:

Bottom right

Step-by-step explanation:

Answer: bottom right!!

Step-by-step explanation

your answer would be -239.45.

356.54

-595.99

-------------

-239.45

Answer:

X=2

Step-by-step explanation:

x

=

−

2

Explanation:

Collect terms in x on the left side of the equation and numeric values on the right side.

add 3x to both sides.

5

x

+

3

x

+

12

=

−

3

x

+

3

x

−

4

⇒

8

x

+

12

=

−

4

subtract 12 from both sides.

8

x

+

12

−

12

=

−

4

−

12

⇒

8

x

=

−

16

To solve for x, divide both sides by 8

8

x

8

=

−

16

8

⇒

x

=

−

2

As a check

Substitute this value into the equation and if the left side is equal to the right side for this value then it is the solution.

left side  

=

(

5

×

−

2

)

+

12

=

−

10

+

12

=

2

right side  

=

−

(

3

×

−

2

)

−

4

=

=

6

−

4

=

2

⇒

x

=

−

2

is the solution

Answer:

b Beacuse you can't times 3 by twelve but you can multiple 3times7+1 to get 19

5 years longer then Bill, 2x5=10.

10+2=12.

12-5=7

Hoang has be there for 12 years. Bill has for 7 years.

Answer:

x=31

Step-by-step explanation:

we need to isolate x so we put 48 t the other side to make -x=17-48

we do 17-48 =-31 so -x=-31

x=31

The answers to all parts shown below.

1. The actual dimension of bathroom

Length = 1 inch

Width = 1 3/4 inch

2.  The actual dimension of bedroom 3

Length = 2 1/4 inch

Width = 2 inch

3.  The actual dimension of entire house

Length = 4 inch

Width = 6 inch

4. The actual area of Kitchen

= 9/4 x 7/4

= 63/16 square inch

5. The scale drawing will be = 10/4 = 5/2 inch

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The correct answer is A) The recipe will need 16 cups of sauce and three and a half teaspoons of oregano for 8 servings.

To determine the amount of sauce and oregano needed to make 8 servings, we can use the ratio of sauce to oregano from the table.

According to the table, for 3 servings, 6 cups of sauce are used along with 1 & 1/2 teaspoons of oregano. We need to find the ratio of sauce to oregano to scale it up for 8 servings.

Ratio of sauce to oregano:

6 cups of sauce / 1 & 1/2 teaspoons of oregano = 6/1.5 = 4 cups of sauce per teaspoon of oregano

Now, for 8 servings, we need to multiply the ratio by the number of teaspoons of oregano required:

8 servings * 1 teaspoon of oregano = 8 teaspoons of oregano

Therefore, for 8 servings, we would need:

8 teaspoons of oregano * 4 cups of sauce per teaspoon of oregano = 32 cups of sauce

Therefore, the correct answer is A) The recipe will need 16 cups of sauce and three and a half teaspoons of oregano for 8 servings.

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Answer:

To evaluate an algebraic expression means to find the value of the expression when the variable is replaced by a given number. To evaluate an expression, we substitute the given number for the variable in the expression and then simplify the expression using the order of operations

Answer:

To evaluate an algebraic expression means to find the value of the expression when the variable is replaced by a given number. To evaluate an expression, we substitute the given number for the variable in the expression and then simplify the expression using the order of operations

Step-by-step explanation: Hope it Helpss :D

Answer: X= -4

Step-by-step explanation:

A. The solution of  linear equation is (x, y) = (-3, 8).

B. The solution is (x, y) = (3/4, -1).

C. The solution is (x, y) = (-31/8, 3/8).

D. The solution is (x, y) = (55/7, -117/14).

A. 3x - y = -11 --- (1)

-x + y = 5 --- (2)

From equation (2), we can write y = x + 5, and substitute it in equation (1):

3x - (x + 5) = -11

2x = -6

x = -3

Substituting x in equation (2):

-y = -8

y = 8

Therefore, the solution of the system is (x, y) = (-3, 8).

To check the solution, we substitute the values of x and y in the original equations:

3(-3) - 8 = -11 (True)

-(-3) + 8 = 5 (True)

So, the solution is correct.

B. -2y + 3 = 4x + 2 --- (1)

6x + 4y = 1 --- (2)

From equation (1), we can write 4x + 2 = -2y + 3, and substitute it in equation (2):

6x + 4y = 1

6x - 4y = 8 (rearranging)

12x = 9

x = 3/4

Substituting x in equation (1):

-2y + 3 = 4(3/4) + 2

-2y + 3 = 5

-2y = 2

y = -1

Therefore, the solution of the system is (x, y) = (3/4, -1).

To check the solution, we substitute the values of x and y in the original equations:

-2(-1) + 3 = 4(3/4) + 2 (True)

6(3/4) + 4(-1) = 1 (True)

So, the solution is correct.

C. 32y - x = -25 --- (1)

5x = 100 + x - 8y --- (2)

From equation (2), we can write 4x = 100 - 8y, and substitute it in equation (1):

32y - x = -25

32y - (100 - 8y) = -25

40y = 75

y = 3/8

Substituting y in equation (1):

32(3/8) - x = -25

x = -31/8.

Therefore, the solution of the system is (x, y) = (-31/8, 3/8).

To check the solution, we substitute the values of x and y in the original equations:

32(3/8) - (-31/8) = -25 (True)

5(-31/8) = 100 + (-31/8) - 8(3/8) (True)

So, the solution is correct.

D. To solve the system of equations:

2y + 3x = 6 --- (1)

4x + 5y + 20 = 0 --- (2)

We can rearrange equation (2) to isolate one of the variables:

4x + 5y = -20 (subtracting 20 from both sides)

5y = -4x - 20 (subtracting 4x from both sides)

y = (-4/5)x - 4 (dividing both sides by 5)

Substituting this value of y in equation (1):

2((-4/5)x - 4) + 3x = 6

(-8/5)x - 8 + 3x = 6

(-8/5)x + 3x = 14

(-8/5 + 3)x = 14

(-8/5 + 15/5)x = 14

(7/5)x = 14

x = 10

Substituting this value of x in the equation for y:

y = (-4/5)(10) - 4

y = -12.

Therefore, the solution of the system is (x, y) = (10, -12).

To check the solution, we substitute the values of x and y in the original equations:

2(-12) + 3(10) = 6 (True)

4(10) + 5(-12) + 20 = 0 (True)

So, the solution is correct.

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a) To find the average life of the ten batteries, we need to calculate the mean, which is the sum of all the values divided by the number of values.Sum of all values = 10.8 + 10.6 + 11.4 + 8.9 + 10.1 + 10.6 + 9.9 + 12.6 + 10.5 + 11.9 = 106.2

Number of values = 10

Average life = Sum of all values / Number of values = 106.3 / 10 ≈ 10.63

Therefore, the average life of the ten batteries, rounded to the nearest tenth of an hour, is approximately 10.6 hours.

b) Comparing the two advertisements:

i) The first advertisement claims that Atlas batteries are guaranteed to last 10 hours. This means that all Atlas batteries are expected to last at least 10 hours. However, based on the data provided, we can see that the average life of the batteries is approximately 10.6 hours, which is higher than the guaranteed 10-hour minimum

ii) The second advertisement claims that Atlas batteries have an average life of over 10 hours. This statement aligns with the data we have, as the average life of the batteries is indeed over 10 hours.

Based on the information provided, the second advertisement claiming that Atlas batteries have an average life of over 10 hours is more accurate, as the average life calculated from the given data is 10.6 hours.

In summary, the average life of the ten batteries is approximately 10.6 hours, and the second advertisement stating an average life of over 10 hours is more accurate based on the data provided.

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\( \{ \: \alpha \: , \: \beta , \: a, \: b \}\)

\( \sf \longrightarrow \: No. \: of \: \: subsets = {2}^{n} \)

where, n denotes to number of elements in set .

Since, given set contains 4 elements .

Thus , 2⁴ {2 raise to power 4} .

\( \sf \longrightarrow \: No. \: of \: \: subsets = {2}^{4} \)

\( \sf \longrightarrow \: No. \: of \: \: subsets = 2 \times 2 \times 2 \times 2\)

\( \sf \longrightarrow \: No. \: of \: \: subsets = 4 \times 4\)

\( \sf \longrightarrow \: No. \: of \: \: subsets = 16\)

Therefore, Required subsets are 16.

They are , Namely;

\( \sf \longrightarrow \: subsets \: = \phi \: \{ \alpha \} \{ \beta \} \{ a\} \{ b\} \: \{ \alpha \beta \} \{ \alpha a\} \{ \alpha b\} \{ \beta a\} \{ \beta b\} \: .....\)

_____________________________

If n is the number of elements in the set then,

No. of subsets possible for this subset is 2^n that's the (2 raise to the power n).

Let's take another example, {1,2}

Here, n = 2

subsets =2^2 =4

Subsets = ϕ, {1}, {2},{1,2}

Note :- every set is a subset of itself i.e. {1,2} and ϕ is a subset of every set

Answer:

facts

Step-by-step explanation:

Answer:

\(y= 9/4x+5\)

Step-by-step explanation:

I'll go over #7 and you should be able to do the rest.

Slope intercept form general equation is:

y = mx + b

I bolded the value you need to change/find.

m is the slope

b is the y-intercept

You can calculate m using:

\(m=\frac{y_2-y_1}{x_2-x_1}\)

you're given (-4,-4) and (0,5) so y₂=5, y₁=-4, x₂=0, x₁=-4

\(m=\frac{5-(-4)}{0-(-4)}=9/4\)

Plug your value into the point-slope formula.

\(y = m(x-x_1)+y_1\)

\(y = (9/4)(x-(-4))+(-4)\)   simplify it

\(y= 9/4x+5\)  the simplified form is the slope-intercept formula

The traveler must walk 17 blocks to reach the State Building.

The traveler needs to walk 8 blocks from the intersection of Orovada Street and Washington Avenue to the State Building.

She also knows that the intersection of Orovada Street and Washington Avenue is 5 blocks from the intersection of Wyoming Street and Washington Avenue, so she needs to walk 5 blocks from the intersection of Wyoming Street and Washington Avenue to the intersection of Orovada Street and Washington Avenue.

Also, the traveler had to walk 4 blocks to get from the intersection of Wyoming Street and Green Avenue to the intersection of Orovada Street and Green Avenue.

Therefore, the traveler must walk 8 + 5 + 4 = 17 blocks to reach the State Building.

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76.89 sjsbs austere. Sisson whenever. Ebenezer oe eie h rur fuf 8r r earned e 3epoe9 r rur 8e e aonwowne e7 rjr or

Answer:

The numbers are 19 and 5

Step-by-step explanation:

Given

Let the numbers be \(x\ and\ y.\)

So:

\(x = 9 + 2y\) --- First statement

\(x*y = 95\) --- second statement

Required

Find x and y

Substitute \(x = 9 + 2y\) in \(x*y = 95\)

\((9 + 2y) * y = 95\)

\(9y + 2y^2 = 95\)

Rewrite as:

\(2y^2 + 9y - 95 = 0\)

Expand

\(2y^2 -10y +19y- 95 = 0\)

Factorize

\(2y(y -5) +19(y- 5) = 0\)

\((2y +19)(y- 5) = 0\)

Solve for y

\(2y + 19 =0\) or \(y - 5 = 0\)

\(2y = -19\) or \(y = 5\)

\(y = -\frac{19}{2}\) or \(y=5\)

Since the numbers are positive, we take only:

\(y=5\)

Substitute \(y=5\) in \(x = 9 + 2y\)

\(x = 9 + 2 * 5\)

\(x = 9 + 10\)

\(x = 19\)

The numbers are 19 and 5

Answer:

333234

Step-by-step explanation:

333234$ for the next 4 years and the ecvation is 69$+-2$

The value of d in the image that shows the two parallel lines that are crossed by the transversal is determined as: 125°.

In geometry, a transversal is a line that intersects two or more other lines at distinct points. When a transversal intersects a pair of parallel lines, it creates various angles and relationships between those angles.

The image attached below shows the two parallel lines which are crossed by the transversal, where angle d and 125° are vertical angles.

Since they are vertical angles, they will be equal or congruent to each other. Therefore, the value of d = 125°

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