The decimal form of 4/5 is 0.80, and it is equivalent to 80% as a percent.
To convert the fraction 4/5 into a decimal and a percent, we start by dividing the numerator (4) by the denominator (5). The result is 0.80 as a decimal.
In decimal form, 4/5 is written as 0.80. The "0" before the decimal point represents whole units, and the "80" after the decimal point represents hundredths.
To express this decimal as a percent, we multiply it by 100, as a percent is a representation of parts per hundred. So, 0.80 multiplied by 100 equals 80. Therefore, 4/5 is equivalent to 80% when expressed as a percentage.
In summary, 4/5 as a decimal is 0.80, which means it represents 80 hundredths, and as a percent, it is 80%, which signifies 80 parts per hundred. This conversion is particularly useful in various mathematical and real-world applications, such as calculating discounts, grades, proportions, and percentages in everyday life and business contexts.
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Answer Immeditely Please
Answer:
√429.
Step-by-step explanation:
Triangles BCD and ABC are similar, so corresponding sides are in the same ratio, so:
x/ AC = DC/x
x/39 = 11/x
x^2 = 11*39
x^2 = 429
x = √429
if two samples a and b had the same mean and standard deviation, but sample a had a larger sample size, which sample would have the wider 95% confidence interval?
As a result of being more dispersed, sample A has a broader 95% confidence interval.
Given that sample A had a higher standard deviation and that we are aware that when standard deviation rises, the margin of error likewise does, widening the confidence interval as a result.
The average squared departure of each observation from the mean is the standard deviation's square root. In other words, it tells you how much the data points deviate from the average value.
Standard deviation is often used as a tool in statistical analysis to help determine the reliability of data. For example, if you were measuring the heights of a group of people, a low standard deviation would suggest that the majority of the people are around the same height, while a high standard deviation would suggest that there is a wider range of heights in the group.
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Suppose you carry out a significance test of h0: μ = 8 versus ha: μ > 8 based on sample size n = 25 and obtain t = 2.15. find the p-value for this test. what conclusion can you draw at the 5% significance level? explain.
a the p-value is 0.02. we reject h0 at the 5% significance level because the p-value 0.02 is less than 0.05.
b the p-value is 0.02. we fail to reject h0 at the 5% significance level because the p-value 0.02 is less than 0.05.
c the p-value is 0.48. we reject h0 at the 5% significance level because the p-value 0.48 is greater than 0.05.
d the p-value is 0.48. we fail to reject h0 at the 5% significance level because the p-value 0.48 is greater than 0.05.
e the p-value is 0.52. we fail to reject h0 at the 5% significance level because the p-value 0.52 is greater than 0.05.
We can draw at the 5% significance level, the p-value is 0.02. we reject h0 at the 5% significance level because the p-value 0.02 is less than 0.05. The correct answer is a.
To find the p-value, we need to find the area to the right of t = 2.15 under the t-distribution curve with 24 degrees of freedom (df = n - 1 = 25 - 1 = 24). Using a t-table or a calculator, we find that the area to the right of t = 2.15 is approximately 0.02.
Since the p-value (0.02) is less than the significance level (0.05), we reject the null hypothesis H0: μ = 8 and conclude that there is sufficient evidence to support the alternative hypothesis Ha: μ > 8 at the 5% significance level. This means that we can say with 95% confidence that the true population mean is greater than 8.
Therefore the correct answer is a.
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For each of the following functions find f(- x) and - f * (x) , then determine whether it is even, odd or neither. Justify your answer. F(x)= x^3-7/x
The function is neither even nor odd.
To find f(-x), we substitute -x for x in the function f(x):
f(-x) = (-x)^3 - 7/(-x) = -x^3 - 7/x
To find -f(x), we multiply the function f(x) by -1:
-f(x) = -1 * (x^3 - 7/x) = -x^3 + 7/x
To determine if the function is even, odd or neither, we compare f(-x) and -f(x).
If f(-x) = f(x), the function is even.
If f(-x) = -f(x), the function is odd.
If neither of these is true, the function is neither even nor odd.
Comparing f(-x) and -f(x), we have:
f(-x) = -x^3 - 7/x
-f(x) = -x^3 + 7/x
Since f(-x) and -f(x) are not equal, and f(-x) is not the negative of -f(x), the function is neither even nor odd.
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A person was driving their car on an interstate highway
and a rock was kicked up and cracked their windshield
on the passenger side.
The driver wondered if the rock was equally likely to
strike any where on the windshield, what the probability
was that it would have cracked the windshield in his line
of site on the windshield. Determine this probability,
provided that the windshield is a rectangle with the
dimensions 28 inches by 54 inches and his line of site
through the windshield is a rectangle with the
dimensions 30 inches
by 24 inches.
a) 0. 373
b) 0. 139
c) 0. 423
d) 0. 476
There is about a 47.62% or 0.476 chance that the rock hit the windshield in the driver's line of sight. Option D.
To determine the probability that the rock hit the driver's line of sight on the windshield, we need to compare the area of the driver's line of sight rectangle to the total area of the windshield rectangle.
The area of the windshield rectangle is:
A1 = 28 in x 54 in = 1512 sq in
The area of the driver's line of sight rectangle is:
A2 = 30 in x 24 in = 720 sq in
Therefore, the probability that the rock hit the driver's line of sight on the windshield is:
[tex]P= \frac{A2}{A1}= \frac{720 \:sq in}{1512 \:sq in }[/tex] = 0.476 or 47.6%
So, there is about a 47.62% chance that the rock hit the windshield in the driver's line of sight.
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If you spin a spinner 75 times, how many multiples of 2?
If you spin a spinner 75 times, the number of multiples of 2 could be either 7 or 38.
Assuming the spinner has an equal chance of landing on any number from 1 to 6, we can find the probability of landing on a multiple of 2 (2, 4, or 6) by dividing the number of multiples of 2 by the total number of possible outcomes:
Number of multiples of 2 = 3
Total number of possible outcomes = 6
So the probability of landing on a multiple of 2 is:
P(multiple of 2) = 3/6 = 1/2
This means that out of 75 spins, we can expect to land on a multiple of 2 about half the time. To find the exact number, we multiply the probability by the number of spins:
Number of multiples of 2 = P(multiple of 2) x Number of spins
Number of multiples of 2 = (1/2) x 75 = 37.5
Since we can't have a fraction of a spin, we need to round to the nearest whole number. In this case, we can round up or down depending on how we interpret the question. I
f we want to know how many times we can expect to land on a multiple of 2 on average, we should round down to 37.
If we want to know the closest integer to the expected value, we should round up to 38.
So depending on the context of the question, the answer could be either 37 or 38.
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A shipping container is in the shape of a right rectangular prism with a length of 11. 5
feet, a width of 8. 5 feet, and a height of 7 feet. The container is completely filled with
contents that weigh, on average, 0. 32 pound per cubic foot. What is the weight of the
contents in the container, to the nearest pound?
The weight of the contents in the container is approximately 222 pounds when rounded to the nearest pound.
The weight of the contents in the container can be calculated using the formula:
Weight = Volume x Density
First, we need to find the volume of the container, which is simply the product of its length, width, and height:
Volume = 11.5 x 8.5 x 7 = 696.5 cubic feet
Next, we need to multiply the volume by the density of the contents:
Weight = 696.5 x 0.32 = 222.08 pounds
It's important to note that the weight may vary depending on the actual density of the contents. Additionally, it's also important to consider the weight of the container itself, which would add to the total weight of the shipment.
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The circumference (C) of a circle is 16 cm. Which formula can you use to find the diameter (d) if you know that C = π
d?
Answer:
c/π=d
explanation:
d × π = c
divide c to isolate d
Answer: I would multiply pie by a diameter until it equals 16.
(I know this probably isn’t the professional way but it should work.
Please help I need it ASAP, also needs to be rounded to the nearest 10th
Answer: AB = 16.4
Step-by-step explanation:
You can use tan x = opposite/adjacent
tan 38 = AB/21
21 tan 38 = AB
AB = 16.4
A museum sells stone souvenirs shaped like a cone with a diameter of 4.2 centimeters and a height of 9.5 centimeters. What is the volume of each souvenir? Round to the nearest tenth
PLEASE HURRY
the volume of each souvenir is 43. 85 cm³
How to determine the volumeThe formula for calculating the volume of a cone is represented as;
V = 1/3 πr²h
Given that;
V is the volumer is the radius of the coneh is the height of the coneThen,
r = diameter/2 = 4.2 /2 = 2.1 centimeters
Substitute the values, we have
Volume = 1/3 × 3.14 × 2.1² × 9.5
find the square, we have;
Volume = 1/3 × 3.14 × 4. 41 × 9.5
Multiply the values
Volume = 131. 5503/3
divide the values
Volume = 43. 85 cm³
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Someone help me please
The corresponding values for the triangle in the larger circle are;
1. Perimeter of Δ BSH = 71.4 cm
2. The measure of ∠SBH = 102°.
3. The area of Δ BSH = 41.54 cm²
4. The length of the circumference of circle B = 52.275 cm
How do you calculate the corresponding values for the triangle in the larger circle, like perimeter?1. The ratio of the perimeters of similar triangles is equal to the ratio of their corresponding sides. Since OB/OA = 4.25, we have:
Perimeter(Δ BSH) = Perimeter(Δ ARG) × 4.25
Perimeter(Δ BSH) = 16.8 cm × 4.25 = 71.4 cm
2. Since the triangles are similar, their corresponding angles are congruent. Therefore, ∠SBH = ∠RAG = 102°.
3. The ratio of the areas of similar triangles is equal to the square of the ratio of their corresponding sides. Since OB/OA = 4.25, we have:
Area(Δ BSH) = Area(Δ ARG) × (4.25)²
Area(Δ BSH) = 2.3 cm² × (4.25)² = 2.3 cm² × 18.0625 = 41.54 cm²
4. The ratio of the circumferences of similar circles is equal to the ratio of their radii or diameters. Since OB/OA = 4.25, we have:
Circumference(circle B) = Circumference(circle A) × 4.25
Circumference(circle B) = 12.3 cm × 4.25 = 52.275 cm
The above answers are in response to the following questions below;
Dante created the following measurements and calculations:
He then made the following measurements and calculations:
He calculated the ratio OB = 4.25.
OA
He measured the perimeter of Δ ARG, and found it to be 16.8 cm.
He measured ∠RAG = 102°.
He calculated the area of Δ ARG, and found it to be 2.3 cm2.
He calculated the circumference of circle A, and found it to be approximately 12.3 cm.
He would now like to calculate corresponding values for the triangle in the larger circle, and he needs your help.
Calculate the following, using your knowledge that all circles are similar, along with the data already collected by Noah..
5. Find the perimeter of Δ BSH.
6. Find the measure of ∠SBH.
7. Find the area of Δ BSH.
8. Find the length of the circumference of circle B.
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Emma is sick a lot and as a result has to go to the doctor regularly. Each time she goes there is a $20 copay that she uses her FSA to pay for. Last month she went to the doctor 9 times. She earns $20 an hour at her job. How many hours (round up) would she have to work to pay these bills without an FSA/HSA? (She pays 17 percent in taxes. )
She would have to work for 11 hours to pay these bills without her FSA/HSA.
Emma went to the doctor 9 times last month, which means she had to pay a total of 9 x $20 = $180 in copays.
Without her FSA/HSA, she would have to work to earn $180 after taxes. Since she pays 17 percent in taxes, the amount she would have to earn before taxes is $180 / (1 - 0.17) = $216.87.
To earn $216.87, she would have to work for $216.87 / $20 per hour = 10.84 hours.
Rounding up, she would have to work for 11 hours to pay these bills without her FSA/HSA.
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In ΔWXY, x = 4.7 cm, y = 7.9 cm and ∠W=162°. Find the area of ΔWXY, to the nearest 10th of a square centimeter.
The area of the triangle to the nearest tenth is 5.8cm²
What is area of a triangle?A triangle is a closed, 2-dimensional shape with 3 sides, 3 angles, and 3 vertices. A triangle is also a polygon. Examples of triangle include, isosceles, equilateral , scalene e.t.c
The area of a triangle is expressed as;
A = 1/2 b h for right angle triangle and A = absinC for others.
Here; x = 4.7, y = 7.9, W = 162
area = 1/2× 4.7 × 7.9 sin162
= 1/2 × 4.7 × 7.9 × 0.31
= 5.8 cm²( nearest tenth)
Therefore the area of the triangle is 5.8cm²
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Help with problem in photo
Check the picture below.
[tex](x)(18)=(x+1)(16)\implies 18x=16x+16\implies 2x=16 \\\\\\ x=\cfrac{16}{2}\implies x=8=RW[/tex]
Willow bought 3 m of denim fabric and 5m of cotton
fabric. The total bill, excluding tax, was $22. Jared
bought 6 m of denim fabric and 2 m of cotton fabric
at the same store for $28. How much does the denim
fabric cost? How much does the cotton fabric cost?
How do I start?
The denim fabric costs $4 per meter and the cotton fabric costs $3 per meter.
To find out the cost per meter of each type of fabric, we can set up a system of two equations. Let d be the cost per meter of denim fabric and c be the cost per meter of cotton fabric. Then, we have:
3d + 5c = 22 (equation 1)
6d + 2c = 28 (equation 2)
We can use equation 2 to solve for one of the variables in terms of the other. Solving for c, we get:
c = 14 - 3d (equation 3)
We can substitute equation 3 into equation 1 and solve for d:
3d + 5(14 - 3d) = 22
Simplifying this equation, we get:
4d = 3
Therefore, d = 0.75, which means the denim fabric costs $0.75 per meter.
We can then use equation 3 to find the cost per meter of cotton fabric:
c = 14 - 3(0.75) = 11.25/2 = $5.625
Therefore, the cotton fabric costs $5.625 per meter.
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A builder wishes to fence in 80000 m2 of land in a rectangular shape. for security reasons, the fence along the front part of the land will cost $60 per meter, while the fence for the other three sides will cost $20 per meter.
how much of each type of fence should the builder buy to minimize the cost of the fence?
determine the length of the fence along the front part of the land that will be cost $60 per meter.
(give your answer as a whole or exact number.)
To minimize the cost of the fence, the builder should use the expensive fence along the shorter side of the rectangular shape, as this will require less length of the expensive fence. Let's say the length of the rectangle is x meters and the width is y meters. Then the area of the rectangle is given by:
A = xy = 80000
And the perimeter of the rectangle is:
P = 2x + 2y
We are given that the cost of the fence along the front part of the land will cost $60 per meter, while the fence for the other three sides will cost $20 per meter. So the total cost of the fence is:
C = 60x + 20(2x + 2y)
Simplifying this expression, we get:
C = 100x + 40y
We can now use the area equation to eliminate one of the variables. Solving for y, we get:
y = 80000/x
Substituting this expression for y into the cost equation, we get:
C = 100x + 40(80000/x)
Simplifying this expression, we get:
C = 100x + 3200000/x
To minimize this function, we need to take its derivative and set it equal to zero:
dC/dx = 100 - 3200000/x^2 = 0
Solving for x, we get:
x = sqrt(32000) = 178.89
So the length of the rectangle should be approximately 178.89 meters, and the width should be:
y = 80000/178.89 = 446.68
Therefore, the amount of expensive fence needed is 178.89 meters, and the amount of cheap fence needed is:
2(178.89) + 2(446.68) - 178.89 = 893.36 meters
Finally, the length of the fence along the front part of the land that will be cost $60 per meter is simply the width of the rectangle, which is:
y = 446.68 meters (rounded to two decimal places)
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Martha went skiing in Arizona she got on the ski lift at the bottom of the mountain which is at 189 feet below sea level the ski lift took her up ascending 790 feet to the very top of the mountain then she skied down part of the mountain down descending 254 feet what elevation is she at now?
Answer:
Martha started at 189 feet below sea level. She went up 790 feet to the top of the mountain, so her elevation was 790-189 = 601 feet above sea level. She then went down 254 feet, so her elevation is now 601-254 = 347 feet above sea level.
Here is the calculation in equation form:
```
Elevation = (Starting elevation) + (Ascent) - (Descent)
```
```
Elevation = 189 feet + 790 feet - 254 feet
```
```
Elevation = 347 feet
```
Answer: Martha is 347 ft above sea level.
Step-by-step explanation:
At first, she is -189 feet below sea level. She went up by 790 feet, bringing her to 690 feet above sea level. She descended by 254 feet and ended up at 347 feet above sea level.
Isabella grows two types of pepper plants. The following dot plots show the numbers of peppers, rounded to the nearest
5
55, per plant for each type. Each dot represents a different plant. Compare the typical number of peppers per plant. In general, the
had more peppers, with
per plant
The possible values of x that satisfy the equation |x+5| = c are x = c - 5 and x = -c - 5.
what is algebra?
Algebra is a branch of mathematics that deals with mathematical operations and symbols used to represent numbers and quantities in equations and formulas.
Determine the equation of the circle graphed below.
Answer:
(x-4)^2+(y-1)^2=9
Step-by-step explanation:
diameter = 6
radius = diameter/2 = 3
center (h,k) = (4,1)
standard equation of a circle (x-h)^2 + (y-k)^2=r^2
(x-4)^2+(y-1)^2=9
A spinner is divided into 15 identical sectors and labeled 1 through 15.
how many spins are expected for a multiple of 4 to be spun 7 times?
select from the drop-down menu to correctly complete the sentence.
the spinner is expected to have to spin approximately times for a multiple of 4 to be spun 7 times.
Answer: 35
Step-by-step explanation: The other person is wrong
Hope this helped :)
which is the range of the relation in the table below?
The range of the relation is ( 0,2)
What is range of relation?The set which contains all the second elements, on the other hand, is known as the range of the relation.
For example, the two terms a and b have the following values
a: 1, 2 ,4, 8, 10
b: 1, 4 , 12, 14.
The range of relation between the two values is ( 1 ,4) because the two values are common to both term.
Similarly, looking at the term x and y , we can see that only 0 and 2 are common to both terms.
Therefore the range of relation is (0,2)
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The figure shows the graphs of the functions y=f(x) and y=g(x). If g(x)=kf(x), what is the value of k? Enter your answer in the box given.
The value of k is -2
Let a line passes through the point [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex]. Thus the equation of line can be given as,
[tex](y -y_1)=\frac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]......Eq.(1)
We have the information from the graph:
The graph of f(x) and g(x) are given in the problem.
The equation given is,
g(x) = k × f(x)
We have to find the value of k and also find the equation of f(x) and g(x).
The line y = f(x) lies on the points, (2,1) and (0,-3). Thus the equation of this line is,
Plug all the values in eq.(1)
[tex](y -(-3))=\frac{-3-1}{0-2}(x-0)[/tex]
[tex]y+3=\frac{-4}{-2}x[/tex]
y + 3 = 2x
y = 2x -3
So, it can be written as:
f(x) = 2x -3
The line y = f(x) lies on the points, (0,6) and (2,-2). Thus the equation of this line is,
[tex](y -6)=\frac{-2-6}{2-0}(x-0)[/tex]
[tex](y-6)=\frac{-8}{2}x[/tex]
(y- 6) = -4x
y = -4x + 6
It can be written as:
g(x) = -4x + 6
The equation given in the problem is:
g(x) = k × f(x)
Put all the values in above given equation:
-4x + 6 = k(2x - 3)
-2(2x - 3) = k × (2x - 3)
Compare the value of k :
k = -2
Hence, The value of k = -2
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For complete question, to see the attachment:
Find the value of y
Step-by-step explanation:
x is the radius.....y is the diameter ...which is two times 'x'
find 'x' via the Pythagorean theorem
x^2 = 3.6^2 + 4^2
x = 5.38
y = 2x = 10.76 units
Diego has a bag with the letters DOG inside. Diego picks 30 letters from the bag, replacing the letter he picks each time. Is it possible that Diego could draw D 19 times, O 10 times, and G 1 time? Why or why not?
Therefore, it is possible for Diego to draw D 19 times, O 10 times, and G 1 time when picking 30 letters from the bag with replacement, although it is highly unlikely.
What is probability?Probability is a measure of the likelihood or chance of an event occurring. It is expressed as a number between 0 and 1, with 0 indicating that the event is impossible, and 1 indicating that the event is certain to occur.
Here,
Yes, it is possible for Diego to draw D 19 times, O 10 times, and G 1 time when picking 30 letters from the bag with replacement.
The probability of drawing the letter D on one pick is 1/3, since there is 1 D out of 3 letters in the bag. Similarly, the probability of drawing the letter O on one pick is also 1/3, and the probability of drawing the letter G on one pick is 1/3.
Since Diego replaces each letter he picks, the probability of drawing D 19 times in a row is (1/3)¹⁹, the probability of drawing O 10 times in a row is (1/3)¹⁰, and the probability of drawing G 1 time is 1/3.
The probability of all these events happening in this order is the product of their individual probabilities, which is:
(1/3)¹⁹ * (1/3)¹⁰ * 1/3 = (1/3)³⁰
This probability is very small, but it is still greater than zero.
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1. Paula has x cups of food in a container to feed her dogs. She pours 1. 5 cups of food into their bowls. There is now 5. 25 cups left in the container. Which equation would be used to solve this problem?
a. 1. 5 - x = 5. 25
b. 5. 25 - x = 1. 25
c. X - 1. 5= 5. 25
d. X + 1. 5= 5. 25
2. A box of donuts cost $9. You want to send donuts to the local nursing home. Set up an equation to find how many boxes you can send if you have $72.
a. 72 = 9 + b
b. 72 = 9 - b
c. 72 = 9b
d. 72 = 9/b
3. Jordan is purchasing a board to build a bookcase. He wants to divide the board into 1. 75 foot sections and he needs 6 sections. Which equation can be used to solve this problem?
a. B/1. 75 = 6
b. 1. 75b = 6
c. B - 1. 75 = 6
d. B + 1. 75 = 6
The correct option for each individual question is c. X - 1. 5= 5. 25, c. 72 = 9b and B/1.75 = 6.
1. Total food = poured food + remaining food
Keep the values in formula
x = 1.5 + 5.25
Rearranging the equation
x - 1.5 = 5.25
Thus, correct option is c. X - 1. 5= 5. 25
2. Cost of one box × number of boxes = total cost
9 × number of boxes = 72
Let us represent the number of boxes as b. So,
9b = 72
Hence, correct option is c. 72 = 9b.
3. Length of each section × number of sections = total length of bookcase sections
Let us represent total length of bookcase sections as B
1.75 × 6 = B
Rearranging the equation
B/1.75 = 6
So, the correct option is a. B/1. 75 = 6.
Thus, correct option are c. X - 1. 5= 5. 25, c. 72 = 9b and B/1.75 = 6.
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Question 10 9 pts Let f(c) = x3 +62? 15x + 3. (a) Compute the first derivative of f f'(x) = (c) On what interval is f increasing? interval of increasing = (d) On what interval is f decreasing? interval of decreasing = **Show work, in detail, on the scrap paper to receive full credit. (b) Compute the second derivative of / L'(x) = (e) On what interval is concave downward? interval of downward concavity = () On what interval is concave upward? interval of upward concavity = **Show work, in detail, on the scrap paper to receive full credit.
(a) The first derivative of f is f'(x) = 3x² - 15.
(b) The second derivative of f is f''(x) = 6x.
(c) f is increasing on the interval (-∞, √5) and decreasing on the interval (√5, ∞).
(d) f is decreasing on the interval (-∞, √5) and increasing on the interval (√5, ∞).
(e) f is concave downward on the interval (-∞, 0) and concave upward on the interval (0, ∞).
(a) To find the first derivative of f, we differentiate each term of the function with respect to x using the power rule. Thus, f'(x) = 3x² - 15.
(b) To find the second derivative of f, we differentiate f'(x) with respect to x. Thus, f''(x) = 6x.
(c) To determine the intervals where f is increasing, we set f'(x) > 0 and solve for x. Thus, 3x² - 15 > 0, which simplifies to x² > 5. Therefore, x is in the interval (-∞, √5) or (√5, ∞). To determine which interval makes f increasing, we can test a point within each interval.
For example, when x = 0, f'(0) = -15, which is negative, so f is decreasing on (-∞, √5). When x = 10, f'(10) = 285, which is positive, so f is increasing on (√5, ∞). Thus, f is increasing on the interval (√5, ∞) and decreasing on the interval (-∞, √5).
(d) To determine the intervals where f is decreasing, we set f'(x) < 0 and solve for x. Thus, 3x² - 15 < 0, which simplifies to x² < 5. Therefore, x is in the interval (-∞, √5) or (√5, ∞). Again, we can test a point within each interval to determine which one makes f decreasing.
For example, when x = 0, f'(0) = -15, which is negative, so f is decreasing on (-∞, √5). When x = 10, f'(10) = 285, which is positive, so f is increasing on (√5, ∞). Thus, f is decreasing on the interval (-∞, √5) and increasing on the interval (√5, ∞).
(e) To determine the intervals of concavity, we examine the sign of the second derivative of f. If f''(x) > 0, then f is concave upward, and if f''(x) < 0, then f is concave downward. If f''(x) = 0, then the concavity changes. Thus, we set f''(x) > 0 and f''(x) < 0 and solve for x. We get f''(x) > 0 when x > 0 and f''(x) < 0 when x < 0.
Therefore, f is concave upward on (0, ∞) and concave downward on (-∞, 0).
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A circle with center c(2, 4) has radius 13. a) verify that a(14,9) and b(7, 16) are points on this circle. b) if m is the midpoint of ab, show that cm is perpendicular to ab.
a) To verify that the points A(14, 9) and B(7, 16) are on the circle with center C(2, 4) and radius 13, we can use the distance formula:
Distance between point A and C:
d_AC = sqrt[(x_A - x_C)^2 + (y_A - y_C)^2]
= sqrt[(14 - 2)^2 + (9 - 4)^2]
= sqrt[144 + 25]
= sqrt(169)
= 13
Since the distance between point A and C is equal to the radius of the circle, point A is on the circle.
Distance between point B and C:
d_BC = sqrt[(x_B - x_C)^2 + (y_B - y_C)^2]
= sqrt[(7 - 2)^2 + (16 - 4)^2]
= sqrt[25 + 144]
= sqrt(169)
= 13
Since the distance between point B and C is equal to the radius of the circle, point B is also on the circle.
Therefore, points A and B are on the circle with center C(2, 4) and radius 13.
b) The midpoint of line segment AB can be found using the midpoint formula:
M = [(x_A + x_B)/2, (y_A + y_B)/2]
= [(14 + 7)/2, (9 + 16)/2]
= [10.5, 12.5]
The slope of line segment AB can be found using the slope formula:
m_AB = (y_B - y_A)/(x_B - x_A)
= (16 - 9)/(7 - 14)
= -7/-7
= 1
The slope of a line perpendicular to AB will be the negative reciprocal of m_AB:
m_CM = -1/m_AB
= -1/1
= -1
The equation of the line passing through points C(2, 4) and M(10.5, 12.5) can be found using the point-slope form:
y - y_C = m_CM(x - x_C)
y - 4 = -1(x - 2)
y = -x + 6
The slope of line CM is -1, which is the negative reciprocal of the slope of line AB. Therefore, line CM is perpendicular to line AB.
Hence, we have shown that line segment CM is perpendicular to line segment AB.
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What does 9x5 equal to
Answer:
Step-by-step explanation:
9 groups with 5 in each equals to
45
Answer: 9 x 5 = 45
Step-by-step explanation:
9
18
27
36
45
54
63
72
81
90
99
108
5 dived by 465 long divsion 6th grade
Answer: 5 divided by 465 is 0.010752688172
465 divided by 5 is 93
Step-by-step explanation:
Solve the following diamond problem by finding the answers that would go in box 1 and box 2
20x?
sot
box2
-9x
box 1 =
box 2 =
Answer:
Step-by-step explanation:
The missing numbers are: box 1 = -5x and box 2 = 4sot, A diamond problem is a type of math puzzle that involves finding two missing values in a diamond-shaped diagram.
The top and bottom numbers of the diamond represent a product, and the left and right sides represent two numbers that add up to a middle value. The goal is to find the two missing values that fit into the diamond.
To solve a diamond problem, we need to factor the product of the top and bottom numbers and look for two factors whose sum is equal to the middle value. This is because the product of two numbers can only be made up of factors that multiply together to form the product. Once we find the two factors, we can insert them into the left and right sides of the diamond.
In the given diamond problem, we have 20x? as the top and sot as the bottom. The product of these two numbers is 20x^2sot. To find the factors, we can list all the possible factor pairs of this product and check which of them adds up to -9x, which is the middle value in the diamond. We found that -5x and 4sot are the factors that add up to -9x.
Solving diamond problems can help improve factoring skills and problem-solving abilities. It requires logical thinking and an understanding of how factors and multiples work. Additionally, diamond problems can be used to introduce algebraic concepts to students in a visual and intuitive way, making them a useful tool for teaching math to learners of all ages.
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