Since the area of the figure changed by a factor of 25, a factor by which the dimensions of the pentagon were multiplied include the following: C. 5.
What is a scale factor?In Geometry and Mathematics, a scale factor simply refers to the ratio of two corresponding side lengths in two similar geometric figures such as pentagons, which can be used to either horizontally or vertically enlarge (increase) or reduce (decrease or compress) a function that represents their size.
In Geometry, the scale factor of the dimensions of a geometric figure can be calculated by using the following formula:
(Scale factor of dimensions)² = Scale factor of area
(Scale factor of dimensions)² = 25
Scale factor of dimensions = √25 = 5
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Answer:
c.5
Step-by-step explanation:
Please solve this problem
I need help with math
The sales data for January and February of a frozen yogurt shop are approximately normal. 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. 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. Which month had a higher z-score for sales on the 15th, and what is the value of that z-score
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.
3/4+1/2= 2. 5/6+1/2= 3. 3/6+1/2= 4.1/6+4/8= 5.7/8+1/4= 6.3/8+1/2=
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
What is 1/2 of 25? _______Explain.
Answer:
12.5
Step-by-step explanation:
0.5x25=12.5. FILLER
Which graph below has an vertical shift of 2
A) y=sin(x-2)
B) y=sin(x)+2
C) y=sin{ pie(x) }
D) y=2sin(x)
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.
Is the following number rational or irrational?
Pi/5
Choose 1 answer:
Rational
B
Irrational
An official for a national dog show studies the characteristics of one breed of dog, the Dandie Dinmont Terrier. Two common measurements are the height and weight of the dog, and the official would like to develop a model that would be helpful in predicting weight based on a given height. The official first makes a scatterplot that relates height and weight, then another that compares the logs of each measurement.
A graph titled Dandie Dinmont Terrier height versus weight has height (inches) on the x-axis, and weight (pounds) on the y-axis. The points curve up.
A graph titled Dandie Dinmont Terrier log height versus log weight has log (height) on the x-axis, and log (weight) on the y-axis. The points curve up.
Based on the graphs, which type of model is likely appropriate for predicting weight from height?
A linear model is appropriate because the graph of the transformed data is roughly linear.
A power model is appropriate because the scatterplot of height versus weight appears curved.
A power model could be appropriate because the scatterplot of log height versus log weight is roughly linear. The next step is to look at the residual plot.
An exponential model is appropriate because the scatterplot of log height versus log weight has a stronger linear relationship than the scatterplot of the non-transformed data.
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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Service calls arriving at an electric company follow a Poisson distribution with an average arrival rate of 5656 per hour. Find the average and standard deviation of the number of service calls in a 1515-minute period. Round your answer to three decimal places, if necessary.
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.
the total cost of. $220 meal with 25% tip.
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
11 divided by 3 2/3 with step by step explination
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
Need some help a little bit stuck
Answer:
SA = 240
Step-by-step explanation:
SA = (10*10) + (8*10) + (6*10)
SA = 240
The space shuttle travels at about 28,000 km per hour. Using that information, estimate how many hours it will take the shuttle to reach Saturn from Earth. (Assume both planets are aligned with the sun and are on the same side of the sun.)
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.
find the difference between 3/4 and 5/10
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.
Help please picture inserted
If one side of a regular decagon is 4 cm, how long is each of the other sides?
Answer:
4cm
Step-by-step explanation:
A decagon has 10 sides that are probably equal. one of the sides is 4cm.The remaining 9sides = 9×4 = 36cmeach sides are 4cm.Each of the other sides of the regular decagon is (√19/4) cm long, or approximately 1.861 cm to three decimal places.
What is the Pythagorean theorem?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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You pick a card at random.
6 7 8
What is P(odd)?
Write your answer as a fraction or whole number.
Answer:
1/3
Step-by-step explanation:
1/3
* Question Completion Status:
QUESTION 3
Find the measure of the unknown angle of the triangle.
18
122
What does n equal?
EASY
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
plsssssssssssssssss help
Answer:
x = 7
Step-by-step explanation:
Find the point on the graph that has the y-value of 8. Determine its x-value.
Can someone help me? A: How long did it take Diane to complete her route on Thursday if, on average, it took her 46 minutes?
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
What is Mean?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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What is the value of x in the equation 4(2x + 12) = 0? (1 point)
Question 18 options:
1)
−8
2)
−6
3)
6
4)
8
Answer:
4 (2x + 12) = 0
8x + 48 = 0
8x = - 48
x = -48/8
x = - 6 (option 2)
you earn $9.15 per hour painting a fence. It takes 6.75 hours to paint the fence. did you make enough money. how much money do you have left.
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.
The family is hiking in the mountains at a rate of 6 miles every 3 hours
How long would it take the family to hike 7.5 miles?
(Hint: You will have a decimal or fraction in your final answer!)
Answer:
Time = 3 hours & 45 minutesStep-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
The measure of an angle is 47º. What is the measure of its complementary angle?
Answer:
137 degrees since it says 47
Step-by-step explanation:
Factor by removing a common
1. 3a +9ab
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.
The length of a rectangle is 3 inches more than three times it's width. Write an equation relating the length, “, of the rectangle to its width, w.
Find the missing sides
Answer: x =1/2
y = [tex]\sqrt{3}[/tex]/2
Step-by-step explanation:
I really need help!
Mercury is 3.6 x 10^6 miles from the sun. Pluto is 3.6 x 10^9 miles from the sun. how many times farther from the sun is pluto than mercury? Answer written in scientific notation.
Thank you!
Answer:
[tex]3.6 * 10^{3} \\\\[/tex]
Step-by-step explanation:
Please Help! SCAMMERS WILL BE REPORTED. Use Gauss-Jordan elimination to solve the following linear system
-4x + 4y + 5z = 9
-2x + 2y + z = 3
-4x + 5y = 4
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!