Answer: c) [tex]\dfrac{3}{2}[/tex] .
Step-by-step explanation:
Mean value theorem : If f(x) is defined and continuous on the interval [a,b] and differentiable on (a,b), then there is at least one number c in the interval (a,b) (that is a < c < b) such that
[tex]\begin{displaymath}f'(c) = \frac{f(b) - f(a)}{b-a} \cdot\end{displaymath}[/tex]
Given function : [tex]f(x) = x^2[/tex]
Interval : [0,3]
Then, by the mean value theorem, there is at least one number c in the interval (0,3) such that
[tex]f'(c)=\dfrac{f(3)-f(0)}{3-0}\\\\=\dfrac{3^2-0^2}{3}=\dfrac{9}{3}\\\\=3[/tex]
[tex]\Rightarrow\ f'(c)=3\ \ \ ...(i)[/tex]
Since [tex]f'(x)=2x[/tex]
then, at x=c, [tex]f'(c)=2c\ \ \ ...(ii)[/tex]
From (i) and (ii), we have
[tex]2c=3\\\\\Rightarrow\ c=\dfrac{3}{2}[/tex]
Hence, the correct option is c) [tex]\dfrac{3}{2}[/tex] .
What is the new cost if a $2.75 toy is marked up by 29%?
Answer:
$3.55
Step-by-step explanation:
You need to add 29% of $2.75 to $2.75.
That means the price will be 129% of $2.75.
129% of $2.75 =
= 1.29 * $2.75
= $3.55
What is the slope of the line that contains the points (9,-4) and (1, -5)
А 1/8
B. -1/8
C.-1
D. 1
Answer:
A. 1/8
Step-by-step explanation:
m = rise/run
m = (y2-y1)/(x2-x1)
m = (-5- - 4)/(1-9)
m = (-5+4)/(-8)
m = (-1)/(-8)
m = 1/8
Answer:
The answer is A.
Step-by-step explanation:
Given that the formula to find gradient, m, is :
[tex]m = \frac{y2 - y1}{x2 - x1} [/tex]
Then, you have to substitute the coordinates into the formula :
[tex]let \: (9, - 4) \: be \: (x1,y1) \\ let \: (1, - 5) \: be \: (x2,y2)[/tex]
[tex]m = \frac{ - 5 - ( - 4)}{1 - 9} [/tex]
[tex]m = \frac{ - 5 + 4}{ - 8} [/tex]
[tex]m = \frac{ - 1}{ - 8} [/tex]
[tex]m = \frac{1}{8} [/tex]
Identify this angle. /_AME
Answer:
The answer is option B.Angle AME is 180° hence a straight angle.
Hope this helps you.
Answer:
straight
Step-by-step explanation:
<AME is a straight angle because:
in a straight angle, there are two rays that connect to form a sort of line. Point M is the endpoint that connects them together.a straight angle can also be formed by adding two right angles, and you can see that <AMC and <EMC are right angles. a straight angle forms 180 degrees, which forms a straight line.I hope this helped you, and have a great rest of your day!
If the function m(x) has the point (5, 2) on its graph name a point that would be on the function m(5x). (10, 2) (5, 10) (25, 2) (1, 2)
Answer:
(1, 2)
Step-by-step explanation:
The function m(x) has the point (5, 2) on its graph is equivalent to say that m(x) evaluated at x = 5 gives 2 as result, that is, m(5) = 2.
f(kx) transforms point (x, y) into (x/k, y). Therefore: m(5x) transforms point (5, 2) into (5/5, 2) or (1, 2).
Trying to find the missing segment to the triangle in the attached image.
Answer:
25
Step-by-step explanation:
The Side Splitter Theorem says that if a line intersects two sides of a triangle and is parallel to the third side of the triangle, it divides those two sides proportionally. Therefore:
6/15 = 10/?
6*? = 10*15
? = 10*15/6
? = 25
How can this same solution be written using set builder notation? {x | x > }?
Corrected Question
The solution to an inequality is represented by the number line. How can this same solution be written using set-builder notation? {x | x > }
Answer:
[tex]\{x | x >3 \}[/tex]
Step-by-step explanation:
Given an inequality whose solution is represented by the number line attached below.
We observe the following from the number line
There is an open circle at 3, therefore the solution set does not include 3. (We make use of > or < in cases like that)
The arrow is pointed towards the right. All points to the right of 3 are greater than 3, therefore:
The solution in the number line can be written using set-builder notation as:
[tex]\{x | x >3 \}[/tex]
The table represents a linear function. What is the slope of the function?
Answer:
The slope of a linear function. The steepness of a hill is called a slope. The same goes for the steepness of a line. The slope is defined as the ratio of the vertical change between two points, the rise, to the horizontal change between the same two points, the run
Step-by-step explanation:
:)
THINKING
4. Given is the Linear and Quadratic System g(x) = 3x2 + 8x + k and f(x) = 2x – 1.
Determine k such that g(x) = 3x2 + 8x + k intersects f(x) = 2x – 1 at one point.
Answer:
k = 2
Step-by-step explanation:
Given the equations:
g(x) = 3x² + 8x + k
f(x) = 2x - 1
At the intersection point:
g(x) = f(x)
3x² + 8x + k = 2x - 1
3x² + 6x + (k+1) = 0
If there is only one intersection point, the discriminant must be equal to zero:
b² - 4(a)(c) = 0
6² - 4(3)(k+1) = 0
36 - 12(k+1) = 0
36 - 12k - 12 = 0
24 = 12k
24/12 = k
2 = k
plz help, I need it asap
Answer:
see below
Step-by-step explanation:
15+2x> 31
Subtract 15 from each side
2x > 16
Divide by 2
2x/2 > 16/2
x > 8
There is an open circle at 8
The line goes to the right
rationalise the denominator and simplify 15÷
[tex] \sqrt{3} [/tex]
Answer:
[tex]5\sqrt{3}[/tex]
Step-by-step explanation:
=> [tex]\frac{15}{\sqrt{3} }[/tex]
Multiplying and dividing by [tex]\sqrt{3}[/tex]
=> [tex]\frac{15}{\sqrt{3} } *\frac{\sqrt{3} }{\sqrt{3} }[/tex]
=> [tex]\frac{15\sqrt{3} }{(\sqrt{3})^2 }[/tex]
=> [tex]\frac{15\sqrt{3} }{3}[/tex]
=> [tex]5\sqrt{3}[/tex] (A Rationalized denominator!)
Answer:
5√3
Step-by-step explanation:
To rationalize the denominator, all you have to do is multiply both the numerator and the denominator by whatever is in the denominator, if it is only a single term in the denominator. This means you multiply [tex]\frac{15}{\sqrt{3} }[/tex] [tex]* \frac{\sqrt{3}}{\sqrt{3}}[/tex] . Since √3 divided by itself is 1, this doesn't change the value of the expression. Now multiplying this we get (15√3)/3. Now we can divide 15√3 by 3 to get 5√3, which is the final answer.
I will give you all ⭐⭐⭐⭐⭐ Try to zoom in or flip your phone to see better.
Answer:
The correct option is:
x+y = 2
Step-by-step explanation:
Street 1 is given.
If Street 2 is parallel to Street 1, then they will have the same slope.
Find slope of Street 1:
Take any 2 points on Street 1. Consider (-2,3) and (1,0)
Slope is given by:
m = (y₂ - y₁) / (x₂ - x₁)
m = 0-3 / 1-(-2)
m = -3/3
m = -1
For Street 2:
y = mx + c
y = -1x +c
As it passes through (-2,4), substitute the point in the above equation:
4 = -1(-2) + c
c = 2
So substitute m = -1 and c =2 into general form of equation:
y = mx + c
y = -x + 2
or
x+y = 2
⚠ PLEASE HELP ⚠ Calculate the product. (1- 1/4) * (1- 1/9) * (1- 1/16) *...* (1- 1/225) will award BRAINLIEST.
Answer:
5/8
Step-by-step explanation:
The value of the expression is 8/15
What is expression?An expression in maths is a sentence with a minimum of two numbers or variables and at least one maths operation.
Given an expression, (1- 1/4) * (1- 1/9) * (1- 1/16) *...* (1- 1/225)
The expression is in the form of (1- 1/4) * (1- 1/9) * (1- 1/16) *...* (1- 1/n²)
We know, (1- 1/4) * (1- 1/9) * (1- 1/16) *...* (1- 1/n²) = (n+1)/2n
Here, n = 15.
So, (1- 1/4) * (1- 1/9) * (1- 1/16) *...* (1- 1/225) = (15+1)/(2.15) = 16/30
= 8/15
Hence, The value of the expression is 8/15
For more references on expressions, click;
https://brainly.com/question/14083225
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Express as a product: 1+2cosα
Answer:
Step-by-step explanation:
1+2 cos α
[tex]=1+2(2 cos^{2} \frac{\alpha }{2} -1)\\=1+4 ~cos^2\frac{\alpha }{2} -2\\=4 ~cos^2\frac{\alpha }{2} -1\\=(2cos \frac{\alpha }{2} +1)(2 cos \frac{\alpha }{2} -1)[/tex]
Identify the surface area of the composite figure in terms of π.
Answer:
78π m²
Step-by-step explanation:
The lateral area of the cylinder is ...
LA = 2πrh
LA = 2π(3 m)(8 m) = 48π m²
The lateral area of one cone is ...
LA = πrh . . . . where h is the slant height
LA = π(3 m)(5 m) = 15π m²
Then the total surface area of the figure is the area of the two cones plus that of the cylinder:
S = 2(cone area) + cylinder area
S = 2(15π m²) +(48π m²)
S = 78π m²
Simplify the expression –3(x + 3)² – 3 + 3x. What is the simplified expression in standard form?
Answer:
-3x^2-15x-30
Step-by-step explanation:
Follow order of operations
Answer:
-3x^2 -15x -30
Step-by-step explanation:
First you would square the parenthesis, and get x^2 +6x+9 inside the parenthesis, then you would multiply it by the -3 and get -3x^2 -18x-27-3+3x then you combine like terms to get the answer.
Find the missing length indicated
Answer:
x = 25.
Step-by-step explanation:
Since the side of the triangle that is labeled as 60 units bisects the right angle of the largest triangle, we can say that the smallest triangle, medium triangle, and largest triangle are all similar.
Since the smaller length of the middle triangle corresponds to x, and the longer length of the middle triangle (144) corresponds to the longer length of the smaller triangle (60), we can set up a proportion!
[tex]\frac{x}{60} =\frac{60}{144}[/tex]
144 * x = 60 * 60
144x = 3600
2x = 50
x = 25
Hope this helps!
You are taking 1500 US dollars on a trip. After checking the exchange rate, you figure out the exchange rate is 1 US dollar to 0.74 euros. Task: write an equation to convert US dollars to euros. Will mark most brainiest if you answer!
Answer:
y= 0.74x
0.74 (1500) = 1,110 euros
Step-by-step explanation:
Hi, to answer this question we have to write an equation with the information given:
Since: 1 US dollar = 0.74 Euros
To convert x US dollars to Euros we have to multiply it by 0.74:
y= 0.74x
Where:
y = value in EUROS
x = value in US dollars
For 1500:
y = 0.74 (1500) = 1,110 euros
Feel free to ask for more if needed or if you did not understand something.
4x⁶-12x³+9 factorizar las expresiones
Answer:
(2x³ - 3)²
Step-by-step explanation:
4x⁶ - 12x³ + 9
2²x⁶ - 12x³ + 9
2²x²ˣ3 - 2 * 2x³ * 3 + 3²
2² * (x³)² - 2 * 2x³ * 3 + 3²
(2x³)² - 2 * 2x³ * 3 + 3²
(2x³ - 3)²
Hope this helped! :)
Given the figure below, find the values of x and z.
Answer:
X= 6°z= 112°Solution,
Finding the value of X,
[tex]11x + 2 = 68[/tex]
( being vertically opposite angles)
[tex]11x = 68 - 2 \\ 11x = 66 \\ x = \frac{66}{11} \\ x = 6[/tex]
Value of X is 6
Now, finding the value of z
[tex]z + 68 = 180[/tex]
(sum of angle in linear pair)
[tex]z = 180 - 68 \\ z = 112[/tex]
Value of z is 112.
Hope this helps....
Good luck on your assignment...
Here is a circle touching a square.
The area of the square is 36 cm2
Work out the area of the circle.
Give your answer in terms of pie .
Answer: 9πcm²
Step-by-step explanation: area of the square= 36cm²
Therefore, the area of one side= √area = √36 = 6cms
Since the circle is touching the sides of the square, the side of the square = the diameter of the circle
Therefore the radius of the circle= side/2 = 3cm
The formula for the ares of the circle is πr²
π*3*3 = 9πcm²
Interpret the standard deviation of a set of data
Question
A food processing plant fills snack-sized bags of crackers. The mean number of crackers in each bag is 22 and the
standard deviation is 2. The factory supervisor selects one bag that contains 24 crackers.
Which of the following statements is true?
Select the correct answer below
des
The number of crackers in the supervisor's bag is 2 standard deviations to the right of the mean
ery
The number of crackers in the supervisor's bag is 2 standard deviations to the left of the mean.
The number of crackers in the supervisor's bag is i standard deviation to the right of the mean.
upport
Top
The number of crackers in the supervisor's bag is i standard deviation to the left of the mean
O
Previous
Show
Answer:
C. The number of crackers in the supervisor's bag is 1 standard deviation to the right of the mean.
Step-by-step explanation:
Data
the mean number of crackers in each bag is 22 the standard deviation is 2mean + standard deviation = 22 + 2 = 24, that is, 1 standard deviation to the right of the mean (the addition is to the right, the subtraction to the left).
The numbers 1 through 10 are put in one bag, and the numbers 5 through 14 are put in another bag. When you pick one number from each bag, what is the probability you get the same number? please answer as an unsimplified fraction.
Answer:
36/100
Step-by-step explanation:
this is because you find the overlapping ranges of each bag which is 5 - 10 on the first bag and 5 - 10 on the second bag. both bags have 10 total numbers, so 6/10 * 6/10 because there are six numbers on each bag and 10 overall choices, so we multiply these two because its an and statement which gives us 36/100.
The probability that we get the same number is 9/25.
What is probability?It is simply likeliness of happening an event. The probability of an event lies between 0 to 1.
How to find the probability?Numbers in first bag=10
Numbers in second bag=10
Common numbers=5,6,7,8,9,10
Total common numbers=6
So the probability that we get the same numbers will be
= 6/10* 6/10
=36/100
=18/50
=9/25
Hence the probability that we will get the same numbers is 9/25.
Learn more about probability at https://brainly.com/question/24756209
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10 ft
8 ft
D
Hint: Circumference
of a circle: C = rid
Find the perimeter of this figure to the
nearest hundredth. Use 3.14 to
approximate n.
P = [?] ft
Notice that only half of the circle is included in the figure!
Enter
Answer:
The perimeter of given figure = 56.56 ft
Step-by-step explanation:
Step(i):-
From diagram
The length of the rectangle = 10 ft
The width of the rectangle = 8 ft
Perimeter of the rectangle
= 2 ( l+w)
= 2 ( 10 + 8)
= 2 × 18
= 36
Step(ii):-
The semi circle is included in the given diagram
Now we will find the perimeter of semicircle
We know that
perimeter of the circle
p = 2πr + d
perimeter of the semicircle
[tex]P = \frac{1}{2} 2\pi r + d[/tex]
P = πr + 2 r (∵ d = 2 r)
Step(iii):-
From diagram the diameter of semicircle is equal to the width of the rectangle
d = 8
d = 2 r = 8
The radius of the circle 'r' = 4
perimeter of the semicircle
P = πr + 2 r
P = 3.14 ( 4) + 8
P= 20.56
Conclusion:-
The perimeter of given figure
= perimeter of rectangle + perimeter of semicircle
= 36 + 20.56
=56.56 ft
Match the graph to one of the exponential functions
Answer:
shoulf be the first one: f(x) (½)^x-3
Suppose you have a block of gold with a mass of 100 g. The density of gold is 19.3 g/cm3. What's the volume of your block of gold? Question 8 options: A) 0.193 g/cm3 B) 193 cm3 C) 1,930 cm3 D) 5.18 cm3
The sets D and J are given below.
D= {4,7,8)
J={-1,1,5,7,8)
Find the intersection of D and J.
Find the union of D and J.
WILL GIVE BRAINIEST TO THE FIRST ANSWER
Answer:x − 3 y = − 36
Step-by-step explanation:
Answer: The initial form is called slope intercept form// and the equation in standard form is 3y=37
Step-by-step explanation:
standard form = ax+by=c so you basically just have to take that and put it into the formula
Hope this helps
The first jumbo jet was the Boeing 747, which is 70.5 meters long. The wingspan of the 747 is 60 meters. A model 747 has a wingspan of 80 centimeters. What should the length of the model be? tell your work.
Answer: The correct answer is 94 cm.
Step-by-step explanation:
wingspan length
60 meters 70.5 m
----------------- = ----------------
80 cm x
Cross multiply
(60 m)x = (70.5 m)(80 cm)
Solve for x by dividing both sides of equation by 60 m:
x = (70.5 m)(80 cm) / (60 m) = 94 cm
The length of the model is 94 cm.
Answer:
94 cm
Step-by-step explanation:
Write and solve an equation of ratios:
70.5 m 60 m
----------- = -----------
L 80 cm
Cross multiplying, we get:
(70.5 m)(80 cm) = (60 m)L
(70.5 m)(80 cm)
Then the model length, L, should be L = -------------------------
60 m
or
L = 94 cm
50 points Please help Use the following random list of 100 numbers and the assignations 0-4 to represent girls and 5-9 to represent boys to answer the question below. 3199 9288 1023 1130 0809 1770 6231 7538 8927 4761 7258 7111 0209 0916 1450 9848 4654 7579 6150 3093 9608 0061 4014 9501 0382 3052 2385 9074 1664 6551 6577 1811 3454 5870 1277 5056 1063 5697 9141 4120 9181 1343 0168 3693 0463 4842 1704 3774 4908 4161 6404 9675 2518 3988 4268 6083 0636 9634 5295 5656 1918 3133 6831 8393 6363 2452 1531 1638 1317 2279 9395 0702 2091 5269 0422 0275 3373 1424 1958 0356 5163 0743 6658 6257 2772 0570 4522 2665 0890 3560 5549 2238 2172 9715 9741 4975 6617 9034 4441 8220 Based on the results of the simulation, what is the experimental probability that a group will include only boys? Based on the results of the simulation, what is the experimental probability that a group will not contain four boys? Based on the results of the simulation, if 224 groups are formed, about how many of them would you expect to contain all girls? Round your answer to the nearest number of groups.
Answer:
For the first question, there is a 39% chance for only boys and a 61% chance for only girls. For the second one it is, about 136 groups.
Step-by-step explanation:
100: 224 = 61:x → 61/100 = x/224
100x = 13664
x = 136.64 → 136 groups (You can't round up if you don't have enough people)
Hope this helped!
Answer: 39% chance for only boys and a 61% chance for only girls. For the second one it is, about 136 groups.
Step-by-step explanation:
:) The other answer is correct too! But just for clarification! :)
Write the expression that is represented by the phrase. The product of a number plus 7 and 3.