A train drove the distance of 440 feet in 20 seconds. Select ALL the unit rates that are equivalent to the speed of the model airplane. (Use page 26 unit of measure chart to help.)

Answer:he will need to mix 20 cups of water if he uses 5 cups grape concentrate.

Step-by-step explanation:

Henry mixes 1 cup grape concentrate with 4 cups water to make his favorite drink. It means that the number of cups of grape concentrate that henry requires to mix 1 cup of water would be

1/4

Therefore, the number of cups of water that he needs to mix if he uses 5 cups grape concentrate would be

5/(1/4) = 20 cups of water

Answer: C: Whole number skills

Step-by-step explanation: The question involves simple understanding of whole numbers from counting 1 to 10, and also addition of these whole numbers, which makes its a basic understanding of whole number skills

Answer:

The dimensions of the original garden is [tex]27\times25\ ft[/tex].

Step-by-step explanation:

Let the width of the rectangular garden be 'x'.

Now given:

A rectangular garden is 2 feet longer than it is wide.

so we can say that;

Length of the rectangle = [tex](x+2) \ ft[/tex]

Now to fence the garden we need to find the perimeter of the garden.

Now Perimeter of the garden is equal to twice the sum of the length times width.

framing in equation form we get;

Perimeter of the rectangle = [tex]2(x+x+2)=2(2x+2)=4x+4[/tex]

Now given:

If the width is doubled, 50 extra feet of fencing will be needed

It  means that Perimeter of the doubled width rectangle is equal to perimeter of original garden plus 50.

framing in equation form we get;

[tex]2(2x+x+2)=4x+4+50\\\\2(3x+2)=4x+50[/tex]

Now Applying distributive property we get;

[tex]2\times3x+2\times2=4x+54\\\\6x+4=4x+54[/tex]

Combining the like terms we get;

[tex]6x-4x=54-4\\\\2x=50[/tex]

Dividing both side by 2 we get;

[tex]\frac{2x}{2}=\frac{50}{2}\\\\x=25 \ ft[/tex]

Length of the rectangular garden = [tex]x+2=25+2=27\ ft[/tex]

Hence the dimensions of the original garden is [tex]27\times25\ ft[/tex].

Answer: D All of the above

Step-by-step explanation:

Addition,subtraction,multiplication and division are basic mathematical operations used in the determination and assumption of numbers.

Without them,there will be no theorems .

Answer:

[tex]cos^{-1}(\frac{\sqrt 5}{6})[/tex]

Step-by-step explanation:

We are given that

[tex]a=<-2,5,1>,b=<-5,2,-5>[/tex] and c=<-1,-5,4>

We have to find the angles between  a and b .

[tex]\mid a\mid=\sqrt{(-2)^2+(5)^2+(1)^2}=\sqrt{30}[/tex]

[tex]\mid b\mid=\sqrt{(-5)^2+(2)^2+(5)^2}=3\sqrt{6}[/tex]

[tex]a\cdot b=<-2,5,1>\cdot <-5,2,-5>=10+10-5=15[/tex]

Angle between two vectors a and b is given  by

[tex]cos\theta=\frac{a\cdot b}{\mid a\mid \mid b\mid }[/tex]

Using the formula

[tex]cos\theta=\frac{15}{\sqrt{30}\times 3\sqrt{6}}[/tex]

[tex]cos\theta=\frac{5}{6\sqrt{5}}[/tex]

[tex]cos\theta=\frac{5\times \sqrt 5}{6\times (\sqrt 5)^2}=\frac{\sqrt 5}{6}[/tex]

[tex]\theta=cos^{-1}(\frac{\sqrt 5}{6})[/tex]

Hence, the angle between a and b=[tex]cos^{-1}(\frac{\sqrt 5}{6})[/tex]

Answer:

b

Step-by-step explanation:

The graph of the given function will increase from left to right.

Graphs are a popular tool for visually illuminating data relationships. A graph serves the objective of presenting data that are either too many or complex to be fully expressed in the text while taking up less room.

Given, a function y = 3ˣ. graph of this function is attached below. as we can see in the attached graph that it will increase from left to right.

For x = -3

y = 3⁻³ = 1/27

For x = -2

y = 3⁻² = 1/9

for x = 2

y = 3² = 9

For x = 3

y = 3³ = 27

Therefore, The supplied function's graph will rise from left to right.

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Answer:

  4/2 = 2 > 1

Step-by-step explanation:

The quotient of any two integers of the same sign and the dividend having the larger magnitude will be greater than 1:

  -88/-11 = 8 > 1

  4/2 = 2 > 1

Hence the conjecture is false.

Answer:

Step-by-step explanation:

The x-intercepts are where y = 0.

  (x +1)^2/9 +(0 -2)^2/8 = 1

  (x +1)^2/9 +1/2 = 1 . . . . . simplify a bit

  (x +1)^2 = 9/2 . . . . . . . . .subtract 1/2, multiply by 9; next: square root, add -1

  x = -1 ±√4.5 . . . . . x-intercepts

__

The y-intercepts are where x=0.

  (0+1)^2/9 +(y-2)^2/8 = 1

  1/9 + (y -2)^2/8 = 1 . . . . . simplify a bit

  (y -2)^2 = 64/9 . . . . . . . . subtract 1/9, multiply by 8,

  y = 2 ±8/3 . . . . . . take the square root, add 2 . . . . y-intercepts

Step-by-step explanation:

Let L be the length and W be the width.

The length of a rectangle is 4 meters less than twice the width.

That is

            L = 2W - 4

The area of the rectangle is 240 square​ meters

That is

        L x W = 240

        (2W - 4) x W = 240

         2W² - 4W = 240

         W² - 2W - 120 = 0

          (W -12 ) (W+10) = 0

         W = 12 m or W = -10 m

So width of rectangle is 12 meter

Length = 2 x 12 - 4 = 20 m

Length is 12 meter and width is 20 meter.

The median is all of the above: the second quartile, the 50th percentile, and the observation with half of the data on either side. It represents the central point of a data set where 50% of the values are below and 50% are above it.

The question asks to identify what the median represents in statistical terms. The median is:

The correct answer is d. all of the above. The median or second quartile (Q₂) is the value that divides the ordered dataset in half. It is also known as the 50th percentile since it implies that 50% of the data lies below this point and 50% lies above it. For example, in a dataset 1, 1, 2, 2, 4, 6, 6.8, 7.2, 8, 8.3, 9, 10, 10, 11.5, the median is 7, meaning that half of the values are smaller than 7 and half of the values are larger than 7.

Answer:

Option | and Option || is True

Step-by-step explanation:

Given:

If the square root of [tex]p^{2}[/tex] is an integer greater than 1,

Lets p = 2, 3, 4, 5, 6, 7..........

Solution:

Now we check all option for [tex]p^{2}[/tex]

Option |.

[tex]p^{2}[/tex] has an odd number of positive factors.

Let [tex]p=2[/tex]

The positive factor of [tex]2^{2}=4=1,2,4[/tex]

Number of factor is 3

Let [tex]p=3[/tex]

The positive factor of [tex]3^{2}=9=1,3,9[/tex]

Number of factor is 3

So, [tex]p^{2}[/tex] has an odd number of positive factors.

Therefore, 1st option is true.

Option ||.

[tex]p^{2}[/tex] can be expressed as the product of an even number of positive prime factors

Let [tex]p=2[/tex]

The positive factor of [tex]2^{2}=4=1,2,4[/tex]

[tex]4=2\times 2[/tex]

Let [tex]p=3[/tex]

The positive factor of [tex]3^{2}=9=1,3,9[/tex]

[tex]9=3\times 3[/tex]

So, it is expressed as the product of an even number of positive prime factors,

Therefore, 2nd option is true.

Option |||.

p has an even number of positive factors

Let [tex]p=2[/tex]

Positive factor of [tex]2=1,2[/tex]

Number of factor is 2.

Let [tex]p=4[/tex]

Positive factor of [tex]4=1,2,4[/tex]

Number of factor is 3 that is odd

So, p has also odd number of positive factor.

Therefore, it is false.

Therefore, Option | and Option || is True.

Option ||| is false.

Answer:

c

Step-by-step explanation:

because 39.5 hours makes 8.18

Fortuna's gross pay is $323.11

A unit rate means a rate for one of something. We write this as a ratio with a denominator of one. For example, if you ran 70 yards in 10 seconds, you ran on average 7 yards in 1 second. Both of the ratios, 70 yards in 10 seconds and 7 yards in 1 second, are rates, but the 7 yards in 1 second is a unit rate.

Given that, Fortuna worked 39.5 hours this week at $8.18 an hour.

Since, she is being paid $8.18 for 1 hour, that mean her unit rate is $8.18

To find total rate we will multiply her unit rate with total hours she worked.

Therefore,

The total pay = 39.5 × 8.18 = $323.11

Hence, Fortuna's gross pay is $323.11

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Answer:

A

Step-by-step explanation:

The mean is a good measure of central tendency because it takes into account all of the data compared to other. One of the instance where the mean is not good measure is when there are outliers ( extreme values) in the data in this case the median is better. In the scenario in the question the data set is nearly symmetrical therefore the mean is best central tendency measure to use

Answer:

Option A - The mean is the best choice because the data is nearly symmetrical.

Step-by-step explanation:

Given : A mini-golf course is determining the par score for each of its holes. The dot plot shows the number of strokes required to place a ball in the ninth hole for a sample of 25 players.        

To find : Which measure of center is best to use to determine the expected number of strokes required for the ninth hole?    

Solution :

To determine the expected number of strokes required for the ninth hole the best measure of center is the mean of the data as the data is nearly symmetrical about the center point 4 and 5.

We can also find the mean of the data,

Mean is defined as  the sum of observation divided by number of observation.

i.e, Sum of observation is

Referring the dot plot of ninth hole strokes

Total number of observation n= 25

Therefore, Option A is correct.

The mean is the best choice because the data is nearly symmetrical.

Step-by-step explanation:

θ is in quadrant IV, so:

sin θ < 0

cos θ > 0

tan θ = sin θ / cos θ < 0

csc θ = 1 / sin θ < 0

sec θ = 1 / cos θ > 0

Without doing any calculations, we can see only the third option fits (in the second option, sin θ / cos θ = -9/18, not -18/9.  In the fourth option, csc θ and sec θ are switched).

Let's go ahead and calculate the values.  There are several ways to solve this.  One way is to use Pythagorean identities (ex., 1 + cot²θ = csc²θ).  Another way is to simply draw a triangle in the fourth quadrant.

cot θ = 1 / tan θ, and tan θ = opposite / adjacent.  So cot θ = adjacent / opposite.  If we draw a triangle with angle θ, where the adjacent side is 9 and the opposite side is -18, then we can use Pythagorean theorem to find the hypotenuse:

c² = a² + b²

c² = (9)² + (-18)²

c = √405

Therefore:

sin θ = -18 / √405

cos θ = 9 / √405

csc θ = √405 / 18

sec θ = √405 / 9

tan θ = -18/9

Answer:

Her friend gave Sheila a markdown of $15.

Step-by-step explanation:

Given;

Amount paid for 2 tickets = $90

Actual amount for each ticket = $52.50

we need to find the markdown value did her friend gave to Shelia.

Solution:

each ticket = $52.50

2 tickets = Cost of 2 tickets.

By using unitary method we get;

Cost of 2 tickets = [tex]52.50\times 2 =\$105.00[/tex]

Now To find the markdown we will subtract the Amount paid for 2 tickets from the actual Amount of 2 tickets.

framing in equation form we get;

Markdown [tex]105-90 =\$15[/tex]

Hence her friend gave sheila a markdown of $15.

Answer:

Step-by-step explanation:

[tex]g(x)=log_{2}( x+4) -1\\let g(x)=y\\y=log_{2}(x+4)-1 \\x+4=2^{y+1} \\when y=0\\x+4=2^1=2\\x=2-4=-2\\when x=0\\4=2^{y+1}=2^y*2^1=2*2^y\\2^y=\frac{4}{2}=2=2^1\\so~y=1\\x -intercept=-2\\y-intercept=1[/tex]4. it is a transformation of 4 units left and 1 unit down.

Answer:

Step-by-step explanation:

For the sum to be even, both dice can be odd, or both even. The probability of a dice being odd is 1/2 and the same is for it to be even. Since the result of the dices are independent, we have that

P(E) = (1/2)² + (1/2)² = 1/2

Out of the 36 possible outcomes for the dice (assuming that you can distinguish between first and second dice), there are 11 cases in which one dice is a 6 (if you fix 1 dice as 6, there are 6 possibilities for the other, but you are counting double 6 twice, so you substract one and you get 6+6-1 = 11). Since all configurations for the dices have equal probability, we get that

P(F) = 11/32

The probability for the second dice to be equal to the first one is 1/6 (it has to match the same number the first dice got). Hence

P(G) = 1/6

for EF, you need one six and the other dice even. For each dice fixed as 6 we have 3 possibilities for the other. Removing the repeated double six this gives us 5 possibilities out of 32 total ones, thus

P(EF) = 5/32

If one dice is 6 and both dices are equal, then we have double six, as a result there is only one combination possible out of 32, therefore

P(FG) = 1/32

If both dices are equal, in particular the sum will be even, this means that G= EG, and as a consecuence

P(EG) = P(G) = 1/6

The probabilities are P(E) = 1/2, P(F) = 11/36, P(G) = 1/6, P(EF) = 1/6, P(FG) = 1/12, and P(EG) = 1/4.

To find the probabilities, we need to use the concept of counting outcomes.

There are 36 equally likely outcomes when two dice are thrown. Out of these, 18 outcomes result in an even sum. So, P(E) = 18/36 = 1/2.

There are 11 outcomes where at least one die lands on 6 out of the 36 total outcomes. So, P(F) = 11/36.

There are 6 outcomes where both dice show the same number, out of the 36 possible outcomes. So, P(G) = 6/36 = 1/6.

There are 6 outcomes where at least one die shows 6 and the sum is even. So, P(EF) = 6/36 = 1/6.

There are 3 outcomes where both dice show 6 and at least one of them shows 6. So, P(FG) = 3/36 = 1/12.

Out of the 36 outcomes, 9 outcomes result in both dice being the same and the sum being even. So, P(EG) = 9/36 = 1/4.

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Answer:

C

Step-by-step explaination:

A statistic is a data obtained by sampling a population

A sample is a part of a population studied for the purpose of testing of an hypothesis

6076 is a statistical value because it represents a part (sample) of the whole population

The value of 23% is a statistic calculated from a sample of 6076 adults in public restrooms.

In this question, the value of 23% represents the proportion of adults in public restrooms who did not wash their hands before exiting. Since this value is calculated from a sample of 6076 adults, it is considered a statistic. A statistic is a number that represents a property of a sample. On the other hand, a parameter is a numerical characteristic of the entire population. In this case, if we had data for all adults in public restrooms, the proportion would be a parameter.

Degree: 5; leading coefficient: –16

Explanation:

Given polynomial function is [tex]f(x)=-16x^5-7x^4-6[/tex]

The degree of the polynomial is a highest value of the exponent in one variable in the given polynomial.

Here, highest value of the exponent = 5

So, degree of the polynomial = 5

Leading coefficient is the value before the highest degree of the variable in the polynomial.

Here, leading coefficient = –16

Hence, the answer is Degree: 5; leading coefficient: –16.

Answer:

i got 8.33 so I would say about 9. Im not sure about inequality statements but I know that's about how many days since he makes 300 per day, and you divide that by 2500

Step-by-step explanation:

Answer:

The question is incomplete as there are given options ;

Q:

Determine if the statement is true or false , and justify your answer . Suppose A is a matrix with n rows and m columns . If n < m, then the columns of A span R True, since there are more columns than rows. O False, since there are not enough columns to span R". True, since every column of A must be a nonzero column, False, since every column of A may be a zero column, True, since every column of A must be a non zero column, False, since every column of A may be a zero column

Step-by-step explanation:

Considering a matrix A with n-rows and m-columns,

given that n is less than m i.e the rows is less than the columns

then the columns of A span Rn? TRUE OR FALSE?

the matrix is of nxm as n is less than m, hence from linear transformation, T will span : Rm towards Rn

the concept of ranking of a matrix is applied here as ranking entails the  number of linearly independent rows or columns vectors in a matrix, in this case

the order is n x m where n is less than m, as such the rank of the matrix is n

So, Rank of MATRIX A is n

To prove if the rows vectors are linearly independent or not since n is the rank of the matrix

In this case, m columns vector will be considered with respect to n which is the rank and which is also less than m from the conditions, as such there exist a linearly independent relationship between them which R may be spanned since we know that from ranking, reduction to echelon form comes into play by trying to reduce every element of the column A to zero.

from the foregoing, the last option is the correct answer ; False, since every column of A may be a zero column

The statement 'If n < m, then the columns of A span R^n' is false because it implies a guarantee without considering the linear independence of the columns, which is necessary for them to span the space.

Determining whether the statement 'If n < m, then the columns of A span Rn' is true or false involves understanding linear algebra concepts. For a matrix A with more columns than rows (m > n), it is possible that the columns of A could span Rn, since there are enough vectors to possibly cover the entire n-dimensional space. However, without more information about the vectors, such as whether they are linearly independent, we cannot definitively conclude that they span the space.

The statement assumes that because there are more columns than rows, the columns automatically span the space. This could be true if the columns are linearly independent and cover the space. However, it's possible for a matrix to have redundant vectors that do not contribute to spanning the space, even if m > n. Therefore, the statement as given is false because it suggests a guarantee without consideration of linear independence.

Answer:

c^3+15c^2+75c+125

Step-by-step explanation:

Answer: Yes.

The remaining 2/3 elephants left could be a mix of blue and green shared equally.

Step-by-step explanation:

Total number of elephants= 1200

Number of possible colours=3 (blue,green and pink)

Number of pink elephants =1/3 of 1200

Number of pink elephants =1/3×1200

Pink elephants are 400

The remaining fraction will b 1-1/3=2/3

Total number of elephants - number of pink elephants = remaining number of elephants => 1200-400=800

It is true that 400 elephants are definitely blue because the number of elephants remaining is twice 400

Given:

Total number of elephants = 1200

Colours available:

Blue

Pink

Pink & green

Pure Pink = 1/3 of 1200

= 1/3 × 1200

= 1200/3

Pure Pink = 400

Elephants remaining = Total number of elephants - Pure Pink

= 1200 - 400

= 800

Therefore, it is true that 400 elephants are definitely blue because the number of elephants remaining is twice 400

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Answer:

The value of the baseball increase $0.15

Step-by-step explanation:

we have

The expression above represent a linear equation in slope intercept form

where

The slope or unit rate is equal to

The y-intercept is equal to ----> original value of a baseball card

therefore

The value of the baseball increase $0.15 per year

Final answer:

The value of the baseball card is increasing by $0.15 per year. For the bat and ball problem, the ball costs $0.05 and the bat costs $1.05.

Explanation:

To find out how much the baseball card's value is increasing per year, we look at the formula given for the value of the baseball card: 0.15y + 0.35. In this formula, y represents the number of years since the card was released. The coefficient of y is 0.15, which indicates the yearly increase in the value of the card.

Therefore, the value of the baseball card is increasing by $0.15 per year.

Now let's look at the classic bat and ball problem. The total cost of the bat and the ball is $1.10, and the bat costs $1.00 more than the ball. If we denote the cost of the ball as x, then the cost of the bat is x + $1.00. Setting up the equation x + (x + $1.00) = $1.10, we combine like terms to get 2x + $1.00 = $1.10. Solving for x, we subtract $1.00 from both sides to get 2x = $0.10. Dividing both sides by 2 yields x = $0.05. So, the ball costs $0.05, and the bat costs $1.05.

Answer:a) P(8 of the players numbers are drawn)=1.3×10^-8

b) P(7 of the players number are drrawn)=3.33×10^-c) P(at least 6 of the players number were drawn)=1.84×10^-4

Step-by-step explanation:

Players has 8 combinations of numbers from 1-40. The outcome S contains all the combinations of 8 out of 40

a) P(8 of the players numbers are drawn)= 1/40/8= 1.3×10^-8

There are one in hundred million chances that the draw numbers are precisely the chosen ones.

b) Number of ways of drawing 78 selected numbers from 1-40=8×(40-7)

8×32

P(7 of the players number are drawn)=8×32/40 =3.33×10^-6.

There are approximately 300,000 chances that 7 of the players numbers are chosen

c) P(at least 6 players numbers are drawn)= 32/2×(8/6) ways to draw.

P(at least 6 players numbers are drawn)=P(all 8 chosen are drawn)+P(7 players numbers drawn)+P(6 chosen are drawn) = 1+ 8 x32/40/8 +[8\6 ×32/2]

P(at least 6 players numbers are drawn) = 1.84×10^-4.

There are approximately 5400chances that at least6 of the numbers drawn are chosen by the player.

The probability that a player has all 8 of the numbers selected by the lottery commission

To find the probability that a player has all 8 numbers selected by the lottery commission, we need to determine the favorable outcome and the total possible outcomes. The favorable outcome is 1 because the player needs to match all 8 numbers. The total possible outcomes can be calculated using the combination formula. There are 40 numbers to choose from and the player must choose 8, so the total possible combinations is C(40,8). Therefore, the probability of a player matching all 8 numbers is:

P(all 8 numbers matched) = 1 / C(40,8)

Answer:

A = 14.2/1.1 hours

B = 5.091 hours

Step-by-step explanation:

Formulate 2 simultaneous equations

5.7A + 6.8B = 111.40..........(1)

A +B =18...............................(2)

Multiply each item in (2) by 5.7 to get

5.7A + 5.7B = 97.2............(3)

subtract (1) - (3) on each side

5.7A -5.7A + 6.8B - 5.7B = 111.40 -97.2

1.1B = 14.2

B = 14.2 /1.1

to get A use equation (2)

A = 18 - B

A = 18 - 14.2/1.1 = 5.091

Answer:in the week , he worked 10 hours at Job A and 8 hours at job B

Step-by-step explanation:

Let x represent the number hours that Joe worked at job A in a week.

Let y represent the number of hours that Joe worked at job B in a week.

Working his way through school, Joe works two part-time jobs for a total of 18 hours a week. This means that

x + y = 18

Job A pays $5.70 per hour, and Job B pays $6.80 per hour. He made a total of $111.4 working at each job during the week. It means that

5.7x + 6.8y = 111.4 - - - - - - - - - -1

Substituting x = 18 - y into equation 1, it becomes

5.7(18 - y) + 6.8y = 111.4

102.6 - 5.7y + 6.8y = 111.4

- 5.7y + 6.8y = 111.4 - 102.6

1.1y = 8.8

y = 8

x = 18 - y = 18 - 8

x = 10

Answer:

for an infinite geometric series the formula for the sum of the infinite geometric series when the common ratio is less than one is given by

[tex]\frac{a_{1} }{1 - r}[/tex] = [tex]\frac{120}{1 - \frac{1}{6} } = \frac{120}{\frac{5}{6} } =[/tex] [tex]\frac{120 \times 6}{5}[/tex] = 144.

Step-by-step explanation:

i) from the given series we can see that the first term is [tex]a_{1 }[/tex] = 120.

ii) let the common ratio be r.

iii) the second term is 20 = 120 × r

   therefore r = 20 ÷ 120 = [tex]\dfrac{1}{6}[/tex]

iv) the third term is [tex]\frac{10}{3}[/tex] = 20 × r

    therefore r = [tex]\dfrac{10}{3}[/tex] ÷ 20 = [tex]\dfrac{1}{6}[/tex]

v) for an infinite geometric series the formula for the sum of the infinite geometric series when the common ratio is less than one is given by

[tex]\frac{a_{1} }{1 - r}[/tex] = [tex]\frac{120}{1 - \frac{1}{6} } = \frac{120}{\frac{5}{6} } =[/tex] [tex]\frac{120 \times 6}{5}[/tex] = 144.

Answer:

C. 144

Step-by-step explanation:

Answer:

The answer to your question is the first option

Step-by-step explanation:

Process

1.- Identify the y-intercepts of the lines

blue line   y-intercept = -1

brown line  y-intercept = -2

With this information, we can discard the last option because those lines don't have those y-intercepts.

2.- We observe in the graphs that the lines are increasing so the slopes are positive. From this information, we can discard the second option.

3.- Calculate the slopes of the lines of options 1 and 3

Blue line Points  (0, -1)   (1, 2)

            m = [tex]\frac{2 + 1}{1 - 0} = \frac{3}{1} = 3[/tex]

Brown line Points (0, -2) (1, 1)

            m = [tex]\frac{1 + 2}{1 - 0} = 3[/tex]

As the slopes are 3, we conclude that the answer is the first option.

Answer:  [tex]4\sqrt{2}+10[/tex]

=============================================

Let [tex]x = \sqrt{8}[/tex]

We can replace every square root of 8 with x, since we have that equation above. We end up with 3-x+7+3x. This simplifies to 2x+10 after combining like terms.

Now we can reintoduce the square root back in

[tex]2x+10 = 2\sqrt{8}+10[/tex]

The use of x is optional as you can combine like terms directly. However, it might help to make the temporary replacement.

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

Now simplify the square root

[tex]\sqrt{8} = \sqrt{4*2}[/tex]

[tex]\sqrt{8} = \sqrt{4}*\sqrt{2}[/tex]

[tex]\sqrt{8} = 2\sqrt{2}[/tex]

--------

Therefore,

[tex]2\sqrt{8}+10[/tex]

turns into

[tex]2*2\sqrt{2}+10[/tex]

[tex]4\sqrt{2}+10[/tex]

Answer:

10 + 4sqrt(2)

Step-by-step explanation:

3 - sqrt(8) + 7 + 3sqrt(8)

3 - 2sqrt(2) + 7 + 6sqrt(2)

10 + 4sqrt(2)

sqrt: square root

Answer:

Possible ways to paint the house is 108

Step-by-step explanation:

Total number of houses to be painted=4

Total number of colours to b used(red,blue,green and yellow)=4

Number of ways to paint the first house=4

Number of ways to paint the second house=3

Number of ways to paint the third house=3

Number of ways to paint the fourth house=3

Total number of ways to paint the 4 houses=4×3^3=108 ways.

Final answer:

There are 24 different ways to paint the houses so that no two adjacent houses are of the same color.

Explanation:

To solve this problem, we can use the concept of permutations. Since there are 4 houses and 4 colors to choose from, we can start by selecting a color for the first house. We have 4 options for the first house. Next, we need to choose a color for the second house, but we must ensure that it is different from the color chosen for the first house. We have 3 options for the second house. For the third house, we have 2 options, and for the fourth house, we have only 1 option.

Therefore, the total number of ways to paint the houses without any two adjacent houses being the same color is calculated as:

4 x 3 x 2 x 1 = 24