simplify the expression. 18+12x.

Answer:

81/16

Step-by-step explanation:

The simplification of the provided exponential expression is 81/16 option (C) 81/16 is correct.

In mathematics, integer exponents are exponents that should be integers. It may be a positive or negative number. In this situation, the positive integer exponents determine the number of times the base number should be multiplied by itself.

The complete question is:

Evaluate this exponential expression:

[tex]\dfrac{27}{8}^ {\dfrac{4}{3}}[/tex]

We have an exponential expression:

[tex]= \dfrac{27}{8}^ {\dfrac{4}{3}}[/tex]

[tex]\rm =\dfrac{27^{\dfrac{4}{3}}}{8^{\dfrac{4}{3}}}[/tex]

[tex]=\dfrac{81}{8^{\dfrac{4}{3}}}[/tex]

= 81/16

Thus, the simplification of the provided exponential expression is 81/16 option (C) 81/16 is correct.

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Answer:

45 is 5 times as many as 9 and 9 times as many as 5 :)

Step-by-step explanation:

45 is 5 times as many as 9 and is 9 times as many as 5.

We have the following statement -

45 is x times as many as 9 and is y times as many as 5

We have to find x and y.

n will be equal to -

n = ab

According to the question -

45 is x times as many as 9 and is y times as many as 5. Using the method shown above we can write two equations -

45 = [tex]x[/tex] x 9     ---(1)

and

45 = y x 5     ---(2)

Now -

Solving both, we get -

x = 5 and y = 9

Hence, 45 is 5 times as many as 9 and is 9 times as many as 5.

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Answer:

there is equal probability for each outcome

Step-by-step explanation:

Let's say you are flipping a coin.

The possible outcomes are : Head and Tail

Probability(Head) = 1/2

Probability(Tail) = 1/2

In this case, there is equal theoretical probability of each outcome

Answer:

so Area of Outer part = 8x + 16 square inches

Step-by-step explanation:

2 squares.

inner square dimension is  x inches by x inches.

width of outer region= 2inches.

We want the area of the border around the inner square.

so

Area of border = B  =  Area of Large - Area of Inner

B = (x+4)^2  - x^2

B = x^2 + 8x + 16 -  x^2

B = 8x + 16  square inches

so Area of Outer part = 8x + 16 square inches

To find the area of the outer part of the rug, we need to follow these steps:

1. Calculate the area of the entire square rug including the inner square.
2. Calculate the area of the inner square.
3. Subtract the area of the inner square from the area of the entire rug to find the area of the outer part.

The side length of the inner square is x inches.

Since the width of the outer region is 2 inches on all sides, this width will be added to each side of the inner square twice (once for each side of the corner) when calculating the side length of the entire rug. Thus, the entire side length of the rug will be x + 2 + 2 inches, which simplifies to x + 4 inches.

Now let's perform the calculations step-wise:

Step 1: Calculate the area of the entire square rug.
The formula for the area of a square is side length squared (A = side^2), so the area of the entire rug is (x + 4)^2 square inches.
 
Step 2: Calculate the area of the inner square.
Using the same formula (A = side^2), the area of the inner square is x^2 square inches.

Step 3: Subtract the area of the inner square from the area of the entire rug.
Now we subtract the area of the inner square from the area of the entire rug to find the area of the outer region:  
Area of the outer part = Area of the entire rug - Area of the inner square
Area of the outer part = (x + 4)^2 - x^2

To make it clearer, let's expand (x + 4)^2 using the distributive property (FOIL: First, Outer, Inner, Last):

(x + 4)^2 = (x + 4)(x + 4)
         = x*x + 4*x + 4*x + 4*4
         = x^2 + 4x + 4x + 16
         = x^2 + 8x + 16

So the Area of the outer part is:

Area of the outer part = x^2 + 8x + 16 - x^2
Area of the outer part = 8x + 16 square inches

This is the area of the outer part of the rug.

Answer:

  0.4

Step-by-step explanation:

The conditions are mutually exclusive (X cannot be both 0 and 2), so the probability is the sum of the individual probabilities:

  P(x = 2 or 0) = P(x=2) +P(x=0)

  P(x = 2 or 0) = 0.1 +0.3

  P(x = 2 or 0) = 0.4

Answer:

speed of freight train = 40 MPH

speed of passenger train = 45MPH

Step-by-step explanation:

Let the speed of freight train be X miles per hour

speed of passenger train is 5 mph more than speed of freight train

Therefore speed of passenger train is  X + 5 mph

we will use the formula to calculate distance which is givn below

distance travelled by any object is = speed * time

______________________________________________

Time at which the distance between the train are calculated = 8 AM

for freight train

since it started at 2 AM morning and traveled until 8 AM

duration for which it traveled = 8 - 2 = 6 hours

distance traveled by freight train in those 6 hours  = speed of freight train * duration for which it travelled = X * 6 = 6X   ----equation A

______________________________________________

for passenger train

since it started at 00.00AM  morning and traveled until 8 AM

duration for which it traveled = 8 - 0 = 8 hours

distance traveled by passenger train in those 8 hours  = speed of passenger train * duration for which it travelled = X + 5 * 8

= 8X + 40  -------  equation B

_______________________________________________

Distance between passenger train and freight train at 8 AM = 120 miles

also distance can be calculated using distance calculated above in equation A and B

Distance between passenger train and freight train at 8 AM in terms if X = distance traveled by passenger train in  8 hours - distance travelled by freight train in  6 hours = 8X + 40 - 6X = 2X + 40

2X + 40 distance is equal to 120 miles as given in question

therefore

2X + 40 = 120

2X = 120 -40

X = 80/2 = 40

therefore speed of freight train = X = 40 MPH

speed of passenger train = X + 5 = 40 + 5 = 45MPH

Answer:

The correct answer for this is [tex](-4,6)[/tex].

Step-by-step explanation:

As it can be seen from the attached graph image:

Now, according to question, the translation is performed 6 points up i.e. towards positive y-axis and 4 points towards left i.e. towards negative x-axis.

And, as per rule, the co-ordinates are represented as [tex](x,y)[/tex] where [tex]x[/tex] is the x-co-ordinate and [tex]y[/tex] is y-co-ordinate.

So, the answer here is [tex](-4,6)[/tex].

Answer:

12 = 2.5h + 4

Step-by-step explanation:

Answer:

x=4

Step-by-step explanation:

The solution for the logarithmic equation is x = 4 and it is graphically shown in the figure.

Every logarithmic function is the inverse function of an exponential function, we can think of every output on a logarithmic graph as the input for the corresponding inverse exponential equation.

For the given situation,

The equation is

[tex]log_{2}x+log_{2}(x-2) =3[/tex]

⇒ [tex]log_{2} (x)(x-2)=3[/tex]

⇒ [tex]log_{2}(x^{2} -2x)=3[/tex]

we know that [tex]y=log_{b} x[/tex] can be written as [tex]x=b^{y}[/tex]

⇒ [tex]x^{2} -2x=2^{3}[/tex]

⇒ [tex]x^{2} -2x-8=0[/tex]

⇒ [tex](x-4)(x+2)[/tex]

⇒ [tex]x=4[/tex] or [tex]x=-2[/tex]

The solution for the logarithmic function is shown in the graph below.

Hence we can conclude that the solution for the logarithmic function is x = 4.

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The expressions 1.62 ÷ 0.8, 16.2 ÷ 8, and 0.0162 ÷ 0.008 all have the same value of 2.025, while 0.08 ÷ 0.08 has a different value of 1.

To solve this problem, calculate each of the expressions:

So, the first three expressions are the same because they all equal 2.025. However, the fourth expression is different because it equals 1. In the given question, they are not all equal. Thus, the values of three expressions could be 2.025, and the value of the fourth expression could be 1.

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Answer:Probability of the tie going well [tex]=\frac{2}{3}[/tex]

Step-by-step explanation:

Given

There are 27 ties in closet out of which 18 go well with coat

and remaining 9 does not go well with coat

Probability of the tie going well [tex]=\frac{\text{Choosing a go well tie}}{\text{choosing a tie out of 27 }}[/tex]

Probability of the tie going well [tex]=\frac{18}{27}=\frac{2}{3}[/tex]

Probability of the tie not going well [tex]=\frac{\text{Choosing a not go well tie}}{\text{choosing a tie out of 27 }}[/tex]

Probability of the tie not going well [tex]=\frac{9}{27}=\frac{1}{3}[/tex]

Odds in favor of the tie going well is [tex]=18:9=2:1[/tex]

Odds against of the tie going well is [tex]=9:18=1:2[/tex]

The probability of picking a tie that matches the sport coat is 2/3 or .67, with the odds being 2:1. The probability of choosing a tie that does not match the sport coat is 1/3 or .33, with the odds being 1:2.

The topic at hand is about probability and odds. Probability defines the likelihood that an event will occur out of all possible outcomes, while odds compare the likelihood of the event happening to it not happening.

In this situation, Casey has 27 ties in total. The probability of him picking a tie that goes well with the sport coat is the number of favorable outcomes – 18 ties – over the total number of outcomes – 27 ties. So, the probability would be 18/27 which simplifies to 2/3 or approximately .67.

The odds of this happening, on the other hand, are 18 to 9 or simplified to 2:1. This means that for every three ties he picks, two are likely to go well with the sport coat.

The probability of picking a tie that doesn't go well with the sportcoat is 9/27, which simplifies to 1/3 or approximately .33. The odds of this are 9 to 18, or simplified to 1:2. This means that for every three ties he picks, one is likely not to match the sport coat.

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Answer:

The mean of the number of restaurants that failed within a year is 28.38 and the standard deviation is 4.02.

Step-by-step explanation:

For each restaurant, there are only two possible outcomes. Either it fails during the first year, or it does not. The probability of a restaurant failling during the first year is independent of other restaurants. So we use the binomial probability distribution to solve this question.

Binomial probability distribution

Probability of exactly x sucesses on n repeated trials, with p probability.

The expected value of the binomial distribution is:

[tex]E(X) = np[/tex]

The standard deviation of the binomial distribution is:

[tex]\sqrt{V(X)} = \sqrt{np(1-p)}[/tex]

In the city where she lives, the probability that an independent restaurant will fail in the first year is 43 %.

This means that [tex]p = 0.43[/tex]

66 independent restaurants

This means that [tex]n = 66[/tex]

Mean:

[tex]E(X) = np = 66*0.43 = 28.38[/tex]

Standard deviation:

[tex]\sqrt{V(X)} = \sqrt{np(1-p)} = 4.02[/tex]

The mean of the number of restaurants that failed within a year is 28.38 and the standard deviation is 4.02.

Answer:

b

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

C cannot be folded upon any axis and lay upon itself.

Answer: Option D.

Step-by-step explanation:

this is a quadratic equation of the form:

y = ax^2 + bx + c

First, things you must see.

The graph opens up, so we must have thata a is greater than zero, so we can discard the first option.

Second, we can see that the vertex is located in x ≈ 70

The vertex of a quadratic equation is: x = -b/2a

so we have:

70 = -b/2a

let's try our options and see if we can discard other:

B:

-b/2a = 69.9/2 = 34.95

we can discard this option.

C:

-b/2a = 78/2 = 39 we can discard this option.

D:

-b/2a = 69.9/2*0.5 = 69.9

This is the only one that fits, so this is the correct option.

Answer:

Its D!!

Step-by-step explanation:

Since we already know that there is a 25% chance to guess the correct answer to a multiple choice question, all we have to do is multiply .25 and 68 to get the expected amount of answers a student can possibly guess. We multiply .25 since it is the decimal form of 25% and 68 is our total questions.

.25 x 68 = 17

Therefore, a student can expect to guess 17 answers correct on a test with 68 multiple choice questions.

Answer:

the answer is 17

Step-by-step explanation:

Hope this helps!

Answer:

  -1, +3

Step-by-step explanation:

The equation can be factored as ...

  2(x² -2x -3) = 0

  2(x -3)(x +1) = 0

The zeros are the values of x that make the factors zero:

  x = 3, x = -1

The zeros are -1 and 3.

Answer:

There was 3 stacks of 19 books.

Answer:

The area of trapezium is 87.5 cm square.

Step-by-step explanation:

Calculate are of trapezium by:

Base 1 (10cm)+ Base 2 (15cm) divided by 2 and times height (7cm)

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Answer:

14.46% probability that the instructor can finish grading in 4 and a half hours

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal probability distribution

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

For sums of n values from a distribution, the mean is [tex]n\mu[/tex] and the standard deviation is [tex]s = \sqrt{n}\sigma[/tex]

In this problem, we have that:

[tex]\mu = 6*50 = 300, s = \sqrt{50}*4 = 28.2843[/tex]

What is the probability that the instructor can finish grading in 4 and a half hours

Four and half hours is 4.5*60 = 270.

So this probability is the pvalue of Z when X = 270.

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{270 - 300}{28.2843}[/tex]

[tex]Z = -1.06[/tex]

[tex]Z = -1.06[/tex] has a pvalue of 0.1446

14.46% probability that the instructor can finish grading in 4 and a half hours

Answer:

Step-by-step explanation:

For mixture problems, it is convenient to define a variable to represent the amount of the greatest contributor. Let x represent the amount of 22% solution in the mix. Then 4.8-x is the amount of 10% solution.

The amount of alcohol in the mix is ...

  0.22x +0.10(4.8-x) = 0.12(4.8)

Eliminating parentheses, we have ...

  0.22x -0.10x +0.10(4.8) = 0.12(4.8)

Subtracting (0.10)(4.8) and combining x-terms gives ...

  0.12x = 0.02(4.8)

  x = (0.02/0.12)(4.8) = 0.8 . . . . . divide by the x-coefficient

The scientist needs 0.8 L of 22% solution and 4.0 L of 10% solution.

Answer:

83.56/p

Step-by-step explanation:

Let the weight of the players = p

Let the weight of the reserve players = r

Since there 9 players, there weight = 9p

And since there 3 reserve players, there weight = 3r

(9p + 3r) / 12 = 188

9p + 3r = 12 * 188

9p + 3r = 2256

Solve for r

r = 2256 / 27p

r = 83.56/p

Answer:

1.5 hours per lawn

Step-by-step explanation:

Take the hours and divide by the number of lawns

9 hours / 6 lawns

1.5 hours per lawn

Answer:

See Explanation

Step-by-step explanation:

A prime number is a number that has only two factors, by 1 and itself.

A composite number on the other hand are numbers which have more than two factors.

To determine the number of prime cards needed to build each composite number, we first express the number as a product of its prime factors.

These are:

4=2X2

6=2X3

8=2X2X2

9=3X3

10=2X5

12=2X2X3

14=2X7

15=3X5

16=2X2X2X2

18=2X3X3

20=2X2X5

21=3X7

22=2X11

24=2X2X2X3

26=2X13

27=3X3X3

28=2X2X7

30=2X3X5

32=2X2X2X2X2

33=3X11

34=2X17

35=5X7

36=2X2X3X3

38=2X19

39=3X13

40=2X2X2X5

42=2X3X7

44=2X2X11

45=3X3X5

46=2X2X13

48=2X2X2X2X3

49=7X7

50=2X5X5

Therefore for each of the numbers, those are the prime number cards to be used.

Take for example, the number 50, the prime numbers that will be used to build 50 are the prime factors of 50.

50=2 X 5 X 5

Therefore, its prime factors are 2 and 5.

We will use the following prime number cards:

Answer:

x^2-x-12

Step-by-step explanation:

I used the box method its easier than foil method if that helps in the future

Answer:

7th Month

Step-by-step explanation:

The number of hectares of Lucia's land grows arithmetically by 5 hectares each month.

Whereas, the number of hectares of Maria's land grows geometrically with a common ratio of 1.4 every month.

Writing this as sequence expressions:

For Lucia,

First term, a=11 hectares

Common difference, d=5

Therefore:

[tex]T(n)=a+(n-1)d[/tex]

[tex]11+5(n-1)=11+5n-5\\=6+5n[/tex]

For Maria,

First term, a=6 hectares

Commons ratio=1.4

[tex]T(n)=ar^{n-1}\\=6*1.4^{n-1}[/tex]

Next, we compute and compare the results for values of n of these two equations:

[tex]Lucia, T(n)=6+5n[/tex]

[tex]Maria,T(n)=6*1.4^{n-1}[/tex]

[tex]Lucia, T(1)=6+5=11[/tex]

[tex]Maria,T(1)=6*1.4^{1-1}=6[/tex]

[tex]Lucia, T(2)=6+5(2)=16[/tex]

[tex]Maria,T(2)=6*1.4^{2-1}=8.4[/tex]

[tex]Lucia, T(3)=6+5(3)=21[/tex]

[tex]Maria,T(3)=6*1.4^{3-1}=11.76[/tex]

[tex]Lucia, T(4)=6+5(4)=26[/tex]

[tex]Maria,T(4)=6*1.4^{4-1}=16.56[/tex]

[tex]Lucia, T(5)=6+5(5)=31[/tex]

[tex]Maria,T(5)=6*1.4^{5-1}=23.05[/tex]

[tex]Lucia, T(6)=6+5(6)=36[/tex]

[tex]Maria,T(6)=6*1.4^{6-1}=32.27[/tex]

[tex]Lucia, T(7)=6+5(7)=41[/tex]

[tex]Maria,T(7)=6*1.4^{7-1}=45.18[/tex]

Therefore, in the seventh month, Maria's land will exceed that of Lucia.

The fish tank, when filled halfway with a height of water at 5 inches, contains 1920 cubic inches of water based on its dimensions of 24 inches by 16 inches by 5 inches.

To calculate the volume of water in the fish tank when it is filled halfway, we need to use the tank's dimensions and consider only half the height, as it is filled to that level. The tank measures 24 inches long, 16 inches deep (width), and 10 inches tall. Since it is filled halfway, the water level is at 5 inches high.

Volume of the tank is calculated by the formula for the volume of a rectangular prism: Volume = Length × Width × Height. So we calculate half the volume: Volume = 24 inches × 16 inches × 5 inches. The calculations would be: 24 × 16 × 5 = 1920 cubic inches.

Therefore, the fish tank has 1920 cubic inches of water when filled halfway.

Answer:

x = -6

Step-by-step explanation:

−5x = 30

Divide each side by -5

-5x/-5 = 30/-5

x = -6

Answer:

x=-6

Step-by-step explanation:

−5x = 30

divide both sides by -5 to isolate x

x=-6

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