The c has only one number is c = 81/4 that satisfy the conclusion of rolle's theorem.
The three hypotheses of Rolle's theorem are:
(a) f(x) is continuous on [a,b]
(b) f(x) is differentiable on (a,b)
(c) f(a) = f(b)
i) If you graph f(x), you can see that it is continuous that is no breaks on the interval [0,81]
ii) f(x) is differentiable on (0,81)
f '(x) = 1/(2√x) - 1/9 which exists on the open interval (0,81)
iii) f(0) = f(81) = √81 - 81/9 = 9-9 = 0
Rolle's Conclusion:
f'(c) = 0
f'(c) = 1/(2√c) -1/9 = 0
(9 - 2√c)/(18√c) = 0
√c = 9/2
c = 81/4
There is one number c = 81/4, which satisfies f '(c) = 0.
Therefore the c has only one number is c = 81/4 that satisfy the conclusion of rolle's theorem.
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Full question:
Verify that the function satisfies the three hypotheses of Rolle's Theorem on the given interval. Then find all numbers c that satisfy the conclusion of Rolle's Theorem. (Enter your answers as a comma-separated list.)
f(x) =x − 1/9 x, [0, 81].
In your own words, explain what is meant by prezygotic mechanisms of reproductive isolation. Use 1-3 sentences.
Using the theories of prezygotic, we got that in my words prezygotic mechanisms of Reproductive isolation is defined as the mechanism that keeps species from mating with others. Prezygotic isolation actually prevents the fertilization of eggs while the postzygotic isolation prevents the formation of fertile offspring.
Reproductive isolation keeps species from mating with others. Prezygotic mechanisms include the habitat isolation, mating seasons, "mechanical" isolation, gamete isolation and the behavioral isolation.
Hence, in my words, prezygotic mechanisms of reproductive isolation is defined as the mechanism that keeps species from mating with others. Prezygotic isolation actually prevents the fertilization of eggs while the postzygotic isolation prevents the formation of fertile offspring.
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The three-dimensional figure below is a cylinder with a hole in the shape of a rectangular prism going through the center of it. The radius is 10 yards. Find the volume of the solid in cubic yards, rounded to the nearest ten. Use 3.14 for pi.
The solid has an estimated volume of 1510.8 cubic yards
Volume of CylinderThe volume of a cylinder is the density of the cylinder which signifies the amount of material it can carry or how much amount of any material can be immersed in it. Cylinder’s volume is given by the formula, πr²h , where r is the radius of the circular base and h is the height of the cylinder.
The volume of the cylinder can be calculated as
v = πr²h
v = π* 10² * 5
v = 500π yd³
Let's calculate the volume of the rectangular figure
v = l * w * h
v = 3 * 4 * 5
v = 60 yd³
We should subtract the volume of the rectangular figure from the volume of cylinder to determine the volume of the solid.
V = 500π - 60
v = 1510.8 yd³
The volume of the solid is calculated as 1510.8 yd³
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Answer:
1,510
Step-by-step explanation:
three different methods for assembling a product were proposed by an industrial engineer. to investigate the number of units assembled correctly with each method, 30 employees were randomly selected and randomly assigned to the three proposed methods in such a way that each method was used by 10 workers. the number of units assembled correctly was recorded, and the analysis of variance procedure was applied to the resulting data set. the following results were obtained: sst
The p-value is found to be 0.0006 by using the f-ratio.
Given that ,
SST = 10, 800 , SSTR = 4560
Sum of Square error SSE = SST- SSTR = 10800- 4560
SSE = 6240
df for treatment K= 1, where K are the level of treatment and given that K=3.
df treatment = k-1 = 3 - 1 = 2.
df error = n-k = 30- 3=27.
df total = n- 1 = 30 - 1= 29 .
Mean Square for treatment = SSTR / If treatment
=4560/ 2 = 2280
MSTR = 2280
MSE = SSE/ df error = 6240/27 = 231.11
F-ratio = MSTR/ MSE = 2280 / 231.11
= 9.8654 -=9.87 ( rounded to 2 decimal )
F ratio = 9.87
By using F-table the value of P-value in
F = 9.87 , and df1 = 2, df2=27 , with Significance level =0.05 , then the value is
P-value = 0.0006 .
Therefore, The p-value is 0.0006
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7) What is the value of x?
21
42°
21
Drawing not to scale
The value of x in the given figure is x = 71° , the correct option is (c) .
In the question ,
a triangle ABC is given ,
the measure of angle A = 38°
we can see that length of the sides AB and AC is 21 , and we know when the length of two sides of the triangle is equal , it is called as isosceles triangle .
In isosceles triangle , the two angles corresponding to the two equal sides are equal , that means
angle B = angle C = x
In triangle ABC ,
By Angle Sum Property , we get
angle A + angle B + angle C = 180°
38 + x + x = 180
38 + 2x = 180
subtracting 38 from both the sides , we get
2x = 180 - 38
2x = 142
Dividing both sides by 2 , we get
x = 142/2
x = 71
Therefore , The value of x in the given figure is x = 71° .
The given question is incomplete , the complete question is
What is the value of x ,in the figure given below ? Drawing not to scale
(a) 21°
(b) 42°
(c) 71°
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Write an equation in slope-intercept form for the line that passes through the given point and is parallel to the graph of the equation.
(−4, 2); y=−1/2x+6
Answer:
y = mx + b
-2 = ½(-4) + 6
Step-by-step explanation:
formula ; y = mx + b
where y = y co-ordinate
m = slope
x = x co-ordinate
b = y intercept
Therefore; y = mx + b
-2 = ½(-4) + 6
What is the product of 1/23 and −3/12?
through: (-4, 1) and (1, -3) how do u write the point slope form of the equation of the line through the given points ?
Answer:
through: (-4, 1) and (1, -3) how do u write the point slope form of the equation of the line through the given points ?
Step-by-step explanation:
to find slope you do delta y over delta x meaning 3 - 1 over 1 - (-4) you get 2/5 that is slope then you do to find b you take one of the points and you plug in for y = mx + b doesn't matter which one so -3 = 2/5 (1) + b
-3 = 2/5 + b
subtract 2/5 from both sides you get
-17/5 = b
so the equation is
y = 2/5x - 17/5
Tom drove at a constant speed of 50 miles per hour for 2.5 hours.
Albert drove at a constant speed of 65 miles per hour for 2 hours.
Who drove farther? How many more total miles did he drive?
Use the equation d=r×t to solve.
Answer:
Albert drove further.
He drove 5 miles further.
Step-by-step explanation:
The formula d = r x t is used to determine distance.
D is distance. R is rate ( in this case miles per hour). T is time.
Tom: D= 50 x 2.5
50 multiplied by 2.5 hours = 125
Tom drove 125 miles.
Albert: D= 65 multiplied by 2 hours = 130
Albert drove 130 miles.
Which equation has the solution x = 9? Select each correct answer. Responses x3+7=8 x over 3 end fraction plus 7 equals 8 4 + 5x = 18 4 + 5, x, = 18 81x−3=6 81 over x end fraction minus 3 equals 6 24−2x=13 24 minus 2 x equals 13 2x−3=15 2 x minus 3 equals 15 3x + 2 = 25 3, x, + 2 = 25
The equation be which has the solution x = 9 are:
81/x - 3 = 62x - 3 = 15Which equation has the solution x = 9?x/3 + 7 = 8
substract 7 from both sides
x/3 = 8 - 7
x/3 = 1
cross product
x = 3
4 + 5x = 18
Subtract 4 from both sides
5x = 18 - 4
5x = 14
divide both sides by 5
x = 14/5
x = 2.8
81/x - 3 = 6
Add 3 to both sides
81/x = 6 + 3
81/x = 9
cross product
81 = 9x
divide both sides by 9
x = 81/9
x = 9
24 - 2x = 13
Subtract 24 from both sides
-2x = 13 - 24
-2x = -11
divide both sides by -2
x = -11/-2
x = 5.6
2x - 3 = 15
Add 3 to both sides
2x = 15 + 3
2x = 18
divide both sides by 2
x = 18/2
x = 9
3x + 2 = 25
Subtract 2 from both sides
3x = 25 - 2
3x = 23
divide both sides by 3
x = 23/3
x = 7.67
So therefore, the equations 81/x - 3 = 6, 2x - 3 = 15 has x = 9 as the solution.
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AB= 6 cm, AC = 12 cm
Calculate the length of CD.
Give your answer to 3 significant figures.
C
D
55°
12 cm
B 6 cm
A
The length of the side CD of the triangle is 12.686 cm up to 3 significant figures.
We know from the information that
AB = 6cm AC = 12cm
Now we have to calculate the length of DC
From given figure, we have,
In Δ ACB,
CA² = BA² + BC² (By using Pythagoras theorem)
12² = CB²+ 6²
CB² = 12² - 6²
CB² = 144 - 36
CB² = 108
∴ BC = √( 108) cm.
Now consider, in Δ CBD,
as, we know that from trigonometric ratios , sin x = opposite side / hypotenuse
sin 55° = BC / DC
0.81915 = √108 / DC
DC = 10.392 / 0.81915
⇒ DC = 12.68632...
∴ DC ≈ 12.686 cm
Therefore the length of the side DC is approximately 12.686 cm up to 3 significant figures.
Disclaimer: The missing image of the triangle is attached below.
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In a family of 48, 24 member like caava and 36 member like potatoe. 12 member like both caava and potatoe. How many member like caava?
Using the subtraction, the number of member who only like caava is 12.
In the given question we have to find how many member like caava.
Total member of family = 48
Member who like caava=24
Member who like potato=36
Member who like both caava and potato=12
In the given number of member who like caava having a member who also like potato and some are who only like caava.
So the number of member who only like caava = Total number of member who like caava−Total number of member who like both caava and potato
The number of member who only like caava =24−12
The number of member who only like caava =12
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Approximate negative thirteen plus square root of seventy to the nearest tenth.
−8.4
−4.6
4.6
8.4
The value of the expression -13+√70 to the nearest tenth is -4.6
What is Arithmetic operation?Arithmetic operations involves the study of numbers, operation of numbers that are useful in all the other branches of mathematics. It basically comprises operations such as Addition, Subtraction, Multiplication and Division.
The expression -13+√70 comprises of addition of -13 and √70
The value of √70 is 8.4(to the nearest tenth).
Therefore the value of -13+√70
=-13+8.4
= -4.6( nearest tenth)
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Describe the sequence of transformation that maps quadrilateral ABCD onto quadrilateral A'B'C'D'.
The sequence of transformation that maps quadrilateral ABCD onto quadrilateral A'B'C'D' is A'(3,-1) , B'(3,2), C'(4,3) and D'(4,0)
From the graph:
A(-4,5) , B(2,5) , C(4,3) ,D(-2,3)
transformations:
A'(-4+7,5-6)
= A'(3,-1)
B'(2+1,5-3)
= B'(3,2)
C'(4,3)
D'(-2+6,3-3)
= D'(4,0)
Therefore the sequence of transformation that maps quadrilateral ABCD onto quadrilateral A'B'C'D' is A'(3,-1) , B'(3,2), C'(4,3) and D'(4,0).
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Which of the following best describes the solution to the equation below?
9x + 5 = 9x + 5
Answer:
x is undefined
Step-by-step explanation:
The correlation coefficient between two quantitative variables is approximately 0. 2. What does the value of this correlation coefficient indicate about how well the model fits the data?.
As per the concept of correlation coefficient "tell us" that the model in question does not fit the data well, in whose case we need to find another that can do it.
Correlation coefficient:
Correlation coefficient refers the a statistical measure of the strength of a linear relationship between two variables. And its values can range from -1 to 1.
Given,
The correlation coefficient between two quantitative variables is approximately 0. 2.
Here we need to find the value of this correlation coefficient indicate about how well the model fits the data
While we looking into the given question, a correlation coefficient of 0.02 is near to zero. In this case, the correlation coefficient is "telling us" that the two variables do not follow the cases 1 and 2 above described. Instead, it follows the case 3.
Therefore, the model in question does not fit the data well, in whose case we need to find another that can do it.
Therefore, it is important to remember that the correlation coefficient does not tell us anything about that one variable causes the other variable, only behaviors as described above.
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f(x) = 1/3x + 1; h(x)= -f(x)
Answer:
h(x) = -1/3 x - 1
Step-by-step explanation:
Solution
h(x) = - f(x) This is a given
f(x) = (1/3) x + 1 Put h(x) on the left. Use a minus sign for f(x)
h(x) =-1((1/3)x + 1) Remove the outside brackets.
h(x) = -(1/3) x - 1
The outside brackets make 1/3 x and 1 = to a minus when a minus is put in front of f(x)
what are the solutions?
I need help, The problem is in the picture
Answer: i think its a=52
and b=8 srry if its wrong tell me and ill try to fix it thx:)
Step-by-step explanation:
Solve for x
5x+7>-13
Answer:
x > - 4
Step-by-step explanation:
5x + 7 > - 13 ( subtract 7 from both sides )
5x > - 20 ( divide both sides by 5 )
x > - 4
Estimate 76.94 - 44.478 by first rounding each number to the nearest whole number.
Estimating 76.94 - 44.478 by first rounding each number to the nearest whole number gives 33
How to estimate the subtraction problemRounding to the nearest whole numbers the figures are written s follows
rounding to the nearest whole is achieved by checking the number following the decimal.
If the number is up to 5 a number is added to the last number before the decimal as in here
76.94 = 77 (to the nearest whole number)
/when the number following the decimal is less than 5 is number is neglected as in here
44.478 = 44 (to the nearest whole number)
The subtraction is continued as follows
= 77 - 44
= 33
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Mario is setting up a new tent during a camping trip the tech game was 7 feet of rope the instructions are to use 34.5. Inches of rope to tie a tarp on top of the tack then the remaining rope should be cut into 8 1/4 in section 2 times the 10th two steaks in the ground Mario will use all the rope as instructed right and solve an equation to determine the number of 8 1/4 inch sections of Mario can come from the rope
If Mario will use all the rope as instructed right the number of 8 1/4 inch sections of Mario that can come from the rope is: 6.
How to find the inches?First step is to convert the 7 feet rope to inches
7 feet robes = 84 inches
Second step is to find the inches of rope left
Inches of rope left =84 inches - 34.5 inches
Inches of rope left = 49.5 inches
Now let find the number of 8 1/4 inch sections
Number of 8 1/4 inch sections =49.5 / 8.25
Number of 8 1/4 inch sections =6
Therefore 6 is the number of 8 1/4 inch sections .
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what is x if 4x+2=6 wwwwwwwwwwwwwwwwwwwwwwwww
Answer:
x=1
Step-by-step explanation:
in photo
The equation 5x + (–2y) = 8 relates the amount spent, y, to the number of picture frames purchased, x, after a discount for buying two or more frames is applied to the total cost of the frames. How much is the discount?
The equation for straight line can be used to plot it on the graph. The amount of discount is 4.
What is the equation for a straight line?A straight line can be written in the form of equation as, y = mx + c.
Two straight lines intersect each other only at one point.
When two straight lines are parallel to each other the angle between them is zero.
The given equation is as follows,
5x + (–2y) = 8
Here, x is the number of picture frames purchased after discount.
And, y is the total amount spent.
In order to find the discount, write the equation in terms of y as,
5x + (–2y) = 8
=> 2y = 5x - 8
=> y = 5 / 2 x - 4
The above equation can be plotted as a graph which is shown below,
It is found from the graph that slope is 5 / 2 which is the rate of per picture.
Since the frames are being purchased after the discount, from the above graph discount can be obtained as 4.
Hence, the discount on the picture frames is given by 4.
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In a concrete mixture, the ratio of cement to sand is 1 to 4. At this ratio, how many shovelfuls of cement would be needed to be mixed with 80 shovelfuls of sand?
Answer: 20 shovelfuls of cement would be needed to be mixed with 80 shovelfuls of sand.
Step-by-step explanation:
First, we'd find out 4 divided by 1. This would equal 4.
Because we knew the amount of sand we had, we'd divide instead.
80 divided by 4
(If we had known the amount of cement we had, we would multiply)
This equals 20. This is how we get our answer, 20 to 80
truck travelled from Town A to Town B. A van travelled from Town B to Town A at the same time . They met 10 km from the middle of the journey. Find the distance between Town A and Town B if the truck and the van travelled at 85 km / h and 60 km / h respectively .
Answer:
58 miles
Step-by-step explanation:
One truck second truck
rate 85 60
time t t
Distance d + 10 d -10
d + 10 = 85t d - 10 = 60t
d = 85= -10 d = 60t +10
Set the two equations equal to each other and solve
85t -10 = 60t + 10 Subtract 60t from each side
25t - 10 = 10 Add 10 to each side
25 t = 20 Divide both sides by 25
t = [tex]\frac{4}{5}[/tex]
Each were driving 4/5 of an hour. Plug into the one of the equaions
d + 10 = 85t
d + 10 = 85([tex]\frac{4}{5}[/tex])
d +10 = 68 Subtract 10 from both sides
d = 58
Answer:
Step-by-step explanation:
Givens
Truck = 85 km/hr
Van = 65 km/hr
t is the time they meet
Note
Truck A is travelling faster, so the place where they meet is closest to Town B.
Solution
Let the distance travelled by the truck be
d/2 + 10
Let the distance travelled by the van be
-d/2 + 10
Let t be the time they meet
85* (d/2 + 10) /t = -60*(d/2 + 10)/t multiply both sides by t
85*(d/2 + 10)*t/t = -60*(d/2 + 10)*t/t Combine
85*(d/2 + 10) = -60(d/2 + 10) Remove the brackets.
42.5 d + 850 = -30d - 600 Add 30 d to both sides
72.5d+ 850 = - 600 Subtract 850 from both sides.
72.5d = - 600 - 850 Combine
72.5d = -1450 Divide by 72.5
d = -1450 / 72.5
d = -20
The minus means that you are looking at it from the van's point of view.
work out 2 1/4 x 3 1/5 giving in its simplest form
Answer:
36/5
Step-by-step explanation:
32.55
Step-by-step explanation:
21/4×31/5
651/20
A line has a slope of 2 and passes through the point (1, 5). What
is its equation in slope-intercept form?
Answer:
Y= 2x+3
Step-by-step explanation:
Slope = (y-y1)/(x-x1)
2= (y-5)/(x-1)
Cross multiply
Y-5= 2x-2
Collect like terms
Y= 2x+3
5. Find TR if PR = 10m and QT=7 m
Explain correctly and will give brainlist
In triangle ABC, which side is the longest if these are the measures of the angles?
mzA= 60°, mzB = (3x - 2)°, mzC = (2x + 7)°
Applying the triangle sum theorem and the angle-side relationship, the longest side of triangle ABC is: side AC.
What is the Triangle Sum Theorem?The triangle sum theorem states that if we add all three interior angles of a triangle, the sum we get would be equal to 180 degrees.
What is the Angle-Side Relationship of a Triangle?The angle-side relationship of a triangle explains that the longest side of a triangle is always opposite to its largest angle, the medium side is opposite to the medium angle, and the shortest side is to the smallest angle of the triangle.
Given that triangle ABC has the following angle measures:
m∠A = 60°
m∠B = (3x - 2)°
m∠C = (2x + 7)°
Therefore:
m∠A + m∠B + m∠C = 180
Substitute:
60° + (3x - 2)° + (2x + 7)° = 180
60 + 3x - 2 + 2x + 7 = 180
Combine like terms:
65 + 5x = 180
5x = 180 - 65
5x = 115
x = 23
Find the measure of each of the angles by plugging in the value of x:
m∠B = (3x - 2)° = 3(23) - 2 = 67°
m∠C = (2x + 7)° = 2(23) + 7 = 53°
The largest angle is m∠B = 67°.
AC is opposite to angle B, therefore, AC is the longest side of the triangle.
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Your team win 16 medal at a competition. The medal are gold, ilver, and bronze in a ratio of 6 : 1 : 1. How many of each medal did your team win?