All the dimensions of a pentagon were multiplied by the same factor, and the area of the figure changed by a factor of
25. By what factor were the dimensions of the pentagon multiplied?

a) 12.5
b) 625
c) 5
d) 50

Answer:

1/3

Step-by-step explanation:

1/3

Answer:

Step-by-step explanation:

Distance = 6 miles

Time = 3 hours

Speed = Distance ÷ Time

Speed = 6 ÷ 3

Speed = 2 miles/hour

....................................................

Speed = 2 miles/hour

Distance = 7.5 miles

Time = Distance ÷ Speed

Time = 7.5 ÷ 2

Time = 3.75 hours

3.75 hours = 3 hours & 45 minutes

Answer:

Step-by-step explanation:

Time taken to travel 6 miles = 3 hours

Time taken to travel 1 mile = 3 ÷ 6 = [tex]\frac{3}{6}=\frac{1}{2} hour[/tex] = 30 minutes

Time taken to travel 7.5 miles = 30 * 7.5 = 225 minutes = 3.45 hours

Answer:

[tex]3.6 * 10^{3} \\\\[/tex]

Step-by-step explanation:

Answer:

n=8/11

Step-by-step explanation:

Answer:

C) n=8/11

Step-by-step explanation:

3/4n=6/11

n=6/11÷3/4

invert and multiply

n=6/11x4/3

n=24/33

n=8/11

Answer:

This is possible and the answer is (-1,0,1)

Step-by-step explanation:

It’s difficult to write out matrices here.

I apologize!

Answer:

The answer would be 1/4. I explained below if you don't get how you get the answer. Good luck!

Step-by-step explanation:

1. Find the LCM of 4 and 10

4, 8, 12, 16, 20

10, 20

The LCM of 4 and 10 is 20.

2. Divide 4 and 10 by 20.

20 ÷ 4 = 5

20 ÷ 10 = 2

3. Multiply the numbers by the answer you got in step 2.

3 x 5 = 15

5 x 2 = 10

4. Put it together.(example:number you got in step 3/20)

15/20

10/20

5. Subtract

15/20 - 10/20 = 5/20

You get the answer of 5/20 or 1/4. I would write 1/4 though.

Answer:

137 degrees since it says 47

Step-by-step explanation:

Answer:

4cm

Step-by-step explanation:

Each of the other sides of the regular decagon is (√19/4) cm long, or approximately 1.861 cm to three decimal places.

Pythagorean theorem states that for a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

We can apply this theorem only in a right triangle.

Example:

The hypotenuse side of a triangle with the two sides as 4 cm and 3 cm.

Hypotenuse side = √(4² + 3²) = √(16 + 9) = √25 = 5 cm

We have,

A regular decagon is a polygon with ten sides of equal length and ten angles of equal measure.

To find the length of each of the other sides, we can use the fact that a regular decagon can be divided into ten congruent isosceles triangles.

The isosceles triangle can be split into two right triangles by drawing an altitude from the vertex opposite the base to the midpoint of the base.

Let's call the length of one of the equal sides of the isosceles triangle "s", and let's call the length of the altitude "h".

Then we can use the Pythagorean theorem to find the length of the other side:

s² = h² + (s/2)²

We can solve for "h" in terms of "s" as follows:

h² = s² - (s/2)²

h² = (4s²)/4 - s²/4

h² = (15s²)/16

h = (s√15)/4

Since the altitude divides the isosceles triangle into two congruent right triangles, each with a hypotenuse of "s",

We can use the Pythagorean theorem again to find the length of each of the other sides of the regular decagon:

s² = h² + (s/2)²

s² = [(s√15)/4]² + (s/2)²

s² = (15s²)/16 + (s²)/4

s² = (15s² + 4s²)/16

s^2 = (19s²)/16

s = √(19/16) s

s = (√19/4) cm

Therefore,

Each of the other sides of the regular decagon is (√19/4) cm long, or approximately 1.861 cm to three decimal places.

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Answer:

t = 42857.14 h

Step-by-step explanation:

Given that,

The speed of space shuttle, v = 28000 km/h

We know that, the distance between the Saturn and the Earth is 1,200,000,000 km.

Let t be the time.

As we know, speed = distance/time

So,

[tex]t=\dfrac{d}{v}\\\\t=\dfrac{1,200,000,000}{28000}\\\\t=42857.14\ h[/tex]

So, the required time is equal to 42857.14 hours.

Answer:

3a(1+3b)

Step-by-step explanation:

First step is to find the greatest common factor between these two terms, which is 3a. Next you'll need to divide the two terms by that factor, which would give you what would be in the parenthesis, placed the factor in front to signify the multiplication of those terms and voila, you got the fully factored form.

Answer:

The average number of service calls in a 15-minute period is of 14, with a standard deviation of 3.74.

Step-by-step explanation:

In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:

[tex]P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}[/tex]

In which

x is the number of sucesses

e = 2.71828 is the Euler number

[tex]\mu[/tex] is the mean in the given interval. The variance is the same as the mean.

Average rate of 56 calls per hour:

This means that [tex]\mu = 56n[/tex], in which n is the number of hours.

Find the average and standard deviation of the number of service calls in a 15-minute period.

15 minute is one fourth of a hour, which means that [tex]n = \frac{1}{4}[/tex]. So

[tex]\mu = 56n = \frac{56}{4} = 14[/tex]

The variance is also 14, which means that the standard deviation is [tex]\sqrt{14} = 3.74[/tex]

The average number of service calls in a 15-minute period is of 14, with a standard deviation of 3.74.

Answer:

12.5

Step-by-step explanation:

0.5x25=12.5. FILLER

Answer:

b. y=sin(x)+2

Step-by-step explanation:

A vertical shift moves the graph up and down on the y axis. In order to move the graph up 2 units, 2 must be added to the entirety of sin(x). Vertical shifts always appear last in the equation and are always added or subtracted.

Answer:

1.) [tex]\frac{5}{4\\}[/tex]

2.) [tex]\frac{4}{3}[/tex]

3.) 1

4.) [tex]\frac{2}{3}[/tex]

5.) [tex]\frac{9}{8}[/tex]

6.) [tex]\frac{7}{8}[/tex]

Step-by-step explanation:

The 2 steps for all of these is to get common denominators and then add and simplify.

1.) 3/4 + 1/2 (common denominator) 3/4 + 2/4 = 5/4

2.) 5/6 + 1/2 (common denominator) 5/6 + 3/6 = 4/3

3.) 3/6 + 1/2 (common denominator) 3/6 + 3/6 = 6/6 (simplify) = 1

4.) 1/6 + 4/8 (common denominator) 8/48 + 24/48 =  32/48 (simplify) = 2/3

5.) 7/8 + 1/4 (common denominator) 7/8 + 2/8 = 9/8

6.) 3/8 + 1/2 (common denominator) 3/8 + 4/8 = 7/8

Answer: x =1/2

y = [tex]\sqrt{3}[/tex]/2

Step-by-step explanation:

Answer:

SA = 240

Step-by-step explanation:

SA = (10*10) + (8*10) + (6*10)

SA = 240

Answer:

275

Step-by-step explanation:

Answer:

Total Cost = $275

Step-by-step explanation:

25% = 0.25

Multiply $220 by 0.25 to get 25% of $220.

0.25 × $220 = $55

Now add $220 and $55 to get the total cost.

$220 + $55 = $275

Answer:

x = 7

Step-by-step explanation:

Find the point on the graph that has the y-value of 8. Determine its x-value.

Answer: B.) 43

I just did it on usatestprep and I got 43

Step-by-step explanation:

The solution is Option B.

The time it took for Diane to complete her route on Thursday is given by the equation T = 43 minutes

The mean value in a set of numbers is the middle value, calculated by dividing the total of all the values by the number of values.

Mean = Sum of Values / Number of Values

Given data ,

Let the mean of the data be represented as M = 46 minutes

The time it took for Diane to complete her route on Thursday be T

Now , the total time for all the 7 days be represented as S

And , the value of S is

S = 58 + 39 + 42 + 46 + T + 49 + 45

S = 279 + T

Substituting the values in the equation , we get

Mean = Sum of Values / Number of Values

46 = ( 279 + T ) / 7

Multiply by 7 on both sides of the equation , we get

322 = 279 + T

Subtracting 279 on both sides of the equation , we get

T = 322 - 279

T = 43 minutes

Hence , the value of T is 43 minutes

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Answer:

3

Step-by-step explanation:

11/1 divided by 11/3

keep change flip to get:

11/1 x 3/11

and multiply to get:

33/11

Simplify to get:

3/1 or 3

Answer:

3

Step-by-step explanation:

step one is to make the fraction into a unbalanced fraction

step two is to make it a proper fraction by switching the values (I am talking about 2 2/3s so you know)

Then remove the greatest common factor, so 11, and only three remains

Based on the graphs provided its is seen that, a power model could be appropriate because the scatter plot of log height versus log weight is roughly linear. Therefore, option C is the correct answer.

Scatter plots are used to observe and plot relationships between two numeric variables graphically with the help of dots. The dots in a scatter plot shows the values of individual data points.

Based on the graphs provided its is seen that, a power model could be appropriate because the scatter plot of log height versus log weight is roughly linear. The next step is to look at the residual plot.

Therefore, option C is the correct answer.

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Answer:

January had a higher z-score for sales on the 15th, and the value of that z-score was of 0.5.

Step-by-step explanation:

z-score:

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score 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 p-value, we get the probability that the value of the measure is greater than X.

January:

The mean daily sales for January was $300 with a standard deviation of $20. On the 15th of January, the shop sold $310 of yogurt. This means, respectively, that [tex]\mu = 300, \sigma = 20, X = 310[/tex]. So

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

[tex]Z = \frac{310 - 300}{20}[/tex]

[tex]Z = 0.5[/tex]

February:

The mean daily sales for February was $320 with a standard deviation of $50. On the 15th of February, the shop sold $340 of yogurt. This means, respectively, that [tex]\mu = 320, \sigma = 50, X = 340[/tex]. So

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

[tex]Z = \frac{340 - 320}{50}[/tex]

[tex]Z = 0.4[/tex]

January had a higher z-score for sales on the 15th, and the value of that z-score was of 0.5.

Answer:

$61.76

Step-by-step explanation:

So I can't answer how much do you have left or did you make enough money, but I can calculate the money you made. Since it's $9.15 per hour and you worked 6.75, you simply multiply the numbers together. The money you made was $61.76.

Answer:

4 (2x + 12) = 0

8x + 48 = 0

8x = - 48

x = -48/8

x = - 6 (option 2)