As d2y/dx2 is positive, the rate of change of gradient is positive, that means (2,-10) is a minimum point.
As stated in the video, the rate of change of dy/dx is the second derivative ( d2y/dx2 )
Thus, at a stationary point (dy/dx = 0), when d2y/dx2 < 0 meaning the rate of change of the gradient is negative the point is a maximum point. We can see that in the image below.
And at minimum points the rate of change of gradient is positive. Thus d2y/dx2 > 0 at minimum points.
A curve has equation y=x3 -12x +6 Find the coordinates of each stationary point, and the nature of these points (minimum or maximum).
Find when dy/dx = 0
dy/dx=3x2 -12
3x2 – 12 = 0
x2 =4
x = 2 or x=-2
when x = 2 y=-10 when x= -2 y=22
Thus, coordinates of stationary points are (2,-10) and (-2,22)
Now in order to find whether they are maximum or minimum points, we have to calculate d2y/dx2
d2y/dx2 = 6x
when x=2 d2y/dx2 = 12
As d2y/dx2 is positive, the rate of change of gradient is positive, that means (2,-10) is a minimum point.
when x= -2 d2y/dx2 = -12
As d2y/dx2 is negative, the rate of change of the gradient is negative, which means that (-2,22) is a maximum point
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2. Fill in the blanks to factor the trinomial 3x² + 13x - 10 by grouping.
3x² + 13x - 10 = 3x² -
=
3x²-x+.
_X+X-10
(3x - 2) +(3x - 2)
+
)(3x - 2)
Answer:
-2 and 15x and 5x and 5Step-by-step explanation:
You want the steps involved in factoring 3x² +13x -10 by grouping.
FactorsTo fill in the blanks, you need to know the product of the first and last coefficients, and the factor pairs of that product that have a sum equal to the middle coefficient.
3(-10) = -30 = (-1)(30) = (-2)(15) = (-3)(10) = (-5)(6)
The sums of these factor pairs are 29, 13, 7, 1. The sum of interest is ...
-2 + 15 = 13
These are the values that go in the first pair of blanks.
= 3x² -2 x + 15 x -10
Factors of pairsWe want to identify the common factor for each pair of terms:
= x (3x -2) + 5 (3x -2)
Factored trinomialFinally, the common factor (3x -2) is removed and we have ...
= ( x + 5 )(3x -2)
justin purchased a lawn sprinkler costing 9.23. If Justin recived 9.07 in change, how much money did he give the cashier
Answer: $18.30
Step-by-step explanation:
The sprinkler cost 9.23, and the change is 9.07, so adding both of them equal $18.30
Answer 18.3
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You have two instruments with which to measure the height of a tower. If the true height is 100 meters, measurements with the first instrument vary with mean 100 meters and standard deviation 1. 2 meters. Measurements with the second instrument vary with mean 100 meters and standard deviation 0. 85 meter. You make one measurement with each instrument. Your results are X1 for the first and X2 for the second, and are independent. A) To combine two measurements, you might average them, Y=(X1+X2)/2. What are the mean and standard deviation of Y? b) It makes sense to give more weight to the less variable measurement because it is more likely to be close to the truth. Statistical Theory says that to make the standard deviation as small as possible you should weight X2 is very close to half the variance of X1, so X2 should get twice the weight of X1. That is, use W=1/3X1 + 2/3X2 What are the mean and standard deviation of W?
(a) The mean of Y is 100 meters, and the standard deviation of W is approximately 0.7348 meters.
(b) The mean of W is 100 meters, and the standard deviation of W is approximately 0.6935 meters.
a) To find the mean and standard deviation of Y, where Y = (X₁ + X₂) / 2, we use the properties of the mean and variance of a sum of independent random variables.
Mean of Y:
The mean of Y is simply the average of the means of X₁ and X₂, as the measurements are independent and have the same true height of 100 meters.
Mean(Y) = (Mean(X₁) + Mean(X₂)) / 2 = (100 + 100) / 2 = 100 meters
The standard deviation of Y:
When adding or subtracting independent random variables, the variances add up. Since the measurements are independent, we can use the formula:
Var(Y) = Var((X₁ + X₂) / 2) = (Var(X₁) + Var(X₂)) / 4
Now, calculate the variance of Y:
Var(Y) = (1.2² + 0.85²) / 4 ≈ 0.54
Standard deviation(Y) = √Var(Y)
≈ √0.54
≈ 0.7348 feet
b) Now, let's find the mean and standard deviation of W, where W = (1/3)X₁ + (2/3)X₂.
Mean of W:
Mean(W) = (1/3) * Mean(X₁) + (2/3) * Mean(X₂)
= (1/3) * 100 + (2/3) * 100
= 100 meters
The standard deviation of W:
To calculate the standard deviation of W, we need to find the variance of W and then take its square root.
Var(W) = (1/3)² * Var(X₁) + (2/3)² * Var(X₂)
= (1/9) * 1.2² + (4/9) * 0.85²
Now, calculate the variance of W:
Var(W) = 0.0181 + 0.1956 =0.481
Standard deviation(W) = √Var(W)
≈ √0.481
≈ 0.6935 meters
So, the mean of W is 100 meters, and the standard deviation of W is approximately 0.6935 meters.
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What is the correct prime factorization of 24? 2 ∙ 2 ∙ 6 2 ∙ 3 ∙ 3 2 ∙ 2 ∙ 3 ∙ 3 2 ∙ 2 ∙ 2 ∙ 3
Answer:
2x2x2x3
Step-by-step explanation:
(a) Write 7.97 x 10 ^-6 as an ordinary number.
Answer:
0.00000797
Step-by-step explanation:
Write an equation of the line that passes through the point (1, 4) and has a slope of -2
WIth point- intercept form
The equation of the line that passes through the point (1, 4) and has a slope of -2 is y = -2x + 6
What is slope-intercept form of a line?
The equation of the line in slope-intercept form is given by:
y = mx + c
Here,
(x, y) = Every point on the line
m = Slope of the line
c = y-intercept of the line
According to the given question:
The given line has slope m = -2 and point (1, 4) passes through the line.
By slope-intercept form general equation of line is y = mx + b where b is
y-intercept.
Substituting values of m and point (1, 4) in this equation to get value of b
y = mx + b
4 = -2(1) + b
b = 6
Hence equation of the line is y = -2x + 6
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What will the dividend income be on W number of shares of XYZ stock if XYZ distributes a $Y per share dividend?
Answer:
In general, the dividend income on W number of shares of XYZ stock will be W * Y dollars if XYZ distributes a $Y per share dividend.
Step-by-step explanation:
The dividend income on W number of shares of XYZ stock will be W * Y dollars if XYZ distributes a $Y per share dividend. This is because the dividend income is calculated by multiplying the number of shares that an investor owns by the amount of the dividend per share.
For example, if an investor owns W = 100 shares of XYZ stock and XYZ distributes a $Y = 5 per share dividend, then the investor's dividend income will be 100 * 5 = 500 dollars.
In general, the dividend income on W number of shares of XYZ stock will be W * Y dollars if XYZ distributes a $Y per share dividend.
Select the correct answer. about 1,500,000 bacteria are found in 1 milliliter of water of coastal ocean. how many bacteria will be there in 100 milliliters of water? a. 1.5 × 104 b. 1.5 × 105 c. 1.5 × 106 d. 1.5 × 107 e. 1.5 × 108
The amount of bacteria that will be there in 100 milliliters of water will be: 1.5 × 10⁸.
What is standard notation?A standard notation is a method of writing a given number, equation, or expression in a specific format that adheres to certain rules. 4.5 billion years, for example, is written as 4,500,000,000 years.
The main reason for converting numbers to scientific notation is to make calculations involving unusually large or small numbers easier.
Even though zeros are no longer always seemed to set the decimal point, all digits in a scientific notation number are significant.
Here, it is given that,
The number of bacteria found in 1 milliliter of water = 1,500,000.
So,
The number of bacteria in 100 milliliters of water = 1,500,000 x 100
The number of bacteria in 100 milliliters of water = 15,00,00,000
The number of bacteria in 100 milliliters of water = 1.5 × 10⁸.
Correct option: e
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What is the answer i need answers now I'm am going to fail
pls explain to
Answer:
Step-by-step explanation:
It is not a prime factorization because the term 8 is common multiplied by 2 and the line has 2 elevated to 3 that itselt is 8.
A prime factorization should be stay equal without any commom multiples.
The number of students in attendance since 2000 at Lamar Community College can be represented by the equation below, where x equals the time in years after 2000. S(x) = (x - 50)² + 19 The college creates a graph to better view the decreases and increases in attendance. Which of the following describes the end behavior of their graph? O A. As x approaches positive infinity, S(x) remains constant. OB. As x approaches positive infinity, S(x) approaches positive infinity. OC. As x approaches positive infinity, S(x) approaches zero. OD. As x approaches positive infinity, S(x) approaches negative infinity.
As domain x approaches positive infinity, S(x) approaches positive infinity. Option B is correct.
What is a graph?The graph is a demonstration of curves that gives the relationship between the x and y-axis.
Given expression for the attendance of the student is,
S(x) = (x - 50)² + 19
The end behavior of their graph is given as after x = 50 the graph starts heigh increasing gradient and it keeps increasing, till x = infinity, as shown in the graph.
Thus, the curve of the given equation S(x) will increase from x = 50 to x = ∞ .
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............. i need help past due
The unit rate in acres of land planned by the workers per day is found is 16/35 acres.
What is meant by rate of doing work?Power refers to the rate of work completion. It is a measure of how much energy is used up each unit of time. The joule per second (J/s) is the unit of power in the SI system.Force applied across a distance is called work. Examples such work include dragging down a confined helium balloon, driving a vehicle up a steep hill, and lifting an article against the gravitational attraction of the Earth. Energy manifests mechanically as work.For the mentioned question-
Total acres of land planted = 2/5 acres.
Total time taken = 7/8 days.
Thus, unit rate in acres per day = Total acres of land planted / Total time taken
unit rate in acres per day = (2/5) / (7/8)
unit rate in acres per day = (2*8)/(5*7)
unit rate in acres per day = 16/35
Thus, unit rate in acres of land planned by the workers per day is found is 16/35 acres.
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In \triangle EFG,△EFG, \angle E \cong \angle G,∠E≅∠G, GE = 17GE=17 and FG = 10FG=10. Find the length of EF. EF
In the triangle EFG, ∠E≅∠G, GE = 17 units and FG = 10 units, then the length of the side EF is 10 units
The given triangle EFG
The length of the side GE = 17 units
The length of the side FG = 10 units
The measure of angle E is equal to the measure of angle G
The equation will be
∠E≅∠G
Therefore the triangle is Isosceles triangle
The length of the side FG will be equal to the length of the side FE
The length of the side EF = The length of the side FG = 10 units
Therefore, the length of the side EF is 10 units
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There is a dramatic change in desert temperatures from day to night because:
A: of the lack of nitrogen in the soil.
B: of the lack of water.
C: sand is such a poor insulator.
D: of the lack of vegetation
There is a dramatic change in desert temperatures from day to night because B. of the lack of water.
Why is there a change in temperature?It should be noted that because the air in the desert is so dry, heat escapes quickly at night, the temperature can vary dramatically from day to night. The temperature during the day averages 38°C, while at night it can drop to -4°C in some deserts. The temperature varies greatly depending on where you are in the desert.
During the day, the sand's radiation from the sun's energy superheats the air, causing temperatures to rise. And, because the desert air is so dry, heat escapes quickly at night, according to NASA. The desert biomes are the driest of all biomes.
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what is (-4x² + 3x + 3)(x² - 2x + 2) as a polynomial
The given expression is in the form of the polynomial as -4x⁴+11x³-5x²+6 and the degree of the polynomial is 4.
What is a polynomial?Polynomial is the combination of variables and constants systematically with "n" number of power in ascending or descending order.
[tex]\rm a_1x+a_2x^2+a_3x^3+a_4x^4..........a_nx^n[/tex]
It is given that the polynomial expression is, (-4x² + 3x + 3)(x² - 2x + 2)
We have to simplify the expression by multiplying the expression as,
=-4x²(x² - 2x + 2)+3x(x² - 2x + 2)+3(x² - 2x + 2)
=-4x⁴+8x³-8x²+3x³-6x²+6x+3x²-6x+6
= -4x⁴+11x³-5x²+6
Thus, the given expression is in the form of the polynomial as -4x⁴+11x³-5x²+6 and the degree of the polynomial is 4.
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how would your conclusion change if your sample mean had been 1.355 mg/l? what point does this make about statistical significance?
A small change in x can change the conclusion of our test.
Given :
how would your conclusion change if your sample mean had been 1.355 mg/l.
t - test :
A t-test is a statistical test that compares the means of two samples. It is used in hypothesis testing, with a null hypothesis that the difference in group means is zero and an alternate hypothesis that the difference in group means is different from zero.
if x = 1.355
t = 1.355 - 1.3 / 0.18 / [tex]\sqrt{30}[/tex]
= 0.055 / 0.18 / [tex]\sqrt{30}[/tex]
= 0.055 * [tex]\sqrt{30}[/tex] / 0.18
= 1.67
df = n - 1
= 30 - 1
= 29
P - value from t table :
p = 0.525
fail to reject [tex]H_0[/tex]
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Full question :
The Environmental Protection Agency has determined that safe drinking water should contain no more than 1.3 mg/liter of copper. You are testing water from a new source, and take 30 water samples. The mean copper content in your samples is 1.36 mg/l and the standard deviation is 0.18 mg/l. There do not appear to be any outliers in your data .
how would your conclusion change if your sample mean had been 1.355 mg/l? what point does this make about statistical significance?
Damian was out at a restaurant for dinner when the bill came. His dinner came to $26. He wanted to leave a 31% tip. How much was his meal plus the tip, before tax, in dollars and cents?
Answer:
34 dollars and 6 cents
Step-by-step explanation:
1 percent = 0.26
0.26 x 31 = 8.06
26 + 8.06 = 34 dollars and 6 cents
I believe it is 34.06
which statement about the graph of y=3x+5 is correct?
The correct statement regarding the linear function y = 3x + 5 is given as follows:
The line passes through the ordered pair (0,5) and has a slope of 3.
What are the slope and the intercept of the linear function?The slope-intercept definition of a linear function is presented as follows:
y = mx + b.
The slope and the intercept are given as follows:
m is the slope, representing the rate of change of the linear function.The intercept is of b, representing the numeric value of the function when the input is of zero, hence the line passes through the ordered pair (0,b).In this problem, the function is defined as follows:
y = 3x + 5.
Hence the coefficients have the values given as follows:
m = 3, b = 5.
Missing InformationThe statements are given by the image shown at the end of the answer.
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Three friends, Jessa, Tyree, and Ben, are collecting canned food for a culinary skills class. Their canned food collection goal is represented by the expression 9x2 − 3xy + 5. The friends have already collected the following number of cans:
Jessa: 5xy + 2
Tyree: 6x2 − 5
Ben: x2
Part A: Write an expression to represent the amount of canned food collected so far by the three friends. Show all your work. (5 points)
Part B: Write an expression that represents the number of cans the friends still need to collect to meet their goal. Show all your work. (5 points)
Answer:
Part A
7x² + 5xy – 3
Part B
2x² – 8xy + 8
Step-by-step explanation:
Part A
the canned food collected so far is the sum of the canned food the three friends have by combining the expression
5xy + 2 + 6x² – 5 + x²
= 6x² + x² + 5xy + 2 – 5
= 7x² + 5xy – 3
Part B
The total of cans the friend need to collect to meet their goal is the canned food collected so far minus their targeted goal
= 9x² – 3xy + 5 – (7x² + 5xy – 3)
= 9x² – 3xy + 5 – 7x² – 5xy + 3
= 9x² – 7x² – 3xy – 5xy + 5 + 3
= 2x² – 8xy + 8
i hope this helps
Reflect TIY across y=x to map onto DOG.
(PLEASE HELP!)
The coordinates will be after applying the transformation, I(-5,0) --I'(0, -5), Y(0, 2) - -> Y'(2, 0) and T(4, 4) --> T'(4, 4).
What is geometric transformation?It is defined as the change in coordinates and the shape of the geometrical body. It is also referred to as a two-dimensional transformation. In the geometric transformation, changes in the geometry can be possible by rotation, translation, reflection, and glide translation.
It is given that:
The graph is shown in the picture.
From the picture the coordinates are:
I(-5,0), Y(0, 2), and T(4, 4)
The transformation rule:
(x, y) --> (y, x)
I(-5,0) --I'(0, -5)
Y(0, 2) - -> Y'(2, 0) and
T(4, 4) --> T'(4, 4)
Thus, the coordinates will be after applying the transformation, I(-5,0) --I'(0, -5), Y(0, 2) - -> Y'(2, 0) and T(4, 4) --> T'(4, 4).
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The graph shows the results of a survey that asked people to choose their favorite
dinner foods. One of the persons surveyed is chosen at random.
What is the probability that she chose Potatoes?
Answer:
7.5%
Step-by-step explanation:
a probability is always
desired cases / totally possible cases
the totally possible cases is everybody in the survey :
24+18+14+10+8+6 = 80
the desired cases are everybody having potatoes a favorite food : 6
the probability the picked person prefers potatoes is
6/80 = 3/40 = 0.075 = 7.5%
Determine if the triangles are similar by Angle-Angle similarity
The triangles are similar by Angle-Angle similarity since they are congruent.
What is Angle-Angle Similarity?According to the Angle-Angle Similarity Theorem, if two angles in one triangle are equal to two angles in another triangle, the triangles are similar. The triangles are similar if two pairs of corresponding angles in a pair of triangles are congruent. We know this because if two angle pairs are equal, then the third pair must be equal as well.
Two triangles with two angles, starting with Triangle 1, one measuring 47 degrees and the other measuring 53 degrees, are congruent to two angles in Triangle 2. Following the AA similarity theorem, it is assumed that Triangle 1 is similar to Triangle 2.
In this case, angle MNP = angle QPL (corresponding angles, //lines) (A)
angle QLP is common angle (A)
By AA, the 2 triangles are similar.
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In this diagram, the area of the large square is equal to the combined areas of the tilted square and the four right triangles.
(the picture)
When written as an equation, this relationship can be simplified algebraically, as shown in these 4 steps.
Step 1: (a + b) (a + b) = c2+ 2ab
Step 2: a2 + 2ab + b2 = c2 + 2ab
Step 3: a2 + 2ab ─ 2ab + b2 = c2 + 2ab ─ 2ab
Step 4:
What equation fits in the box in Step 4 to complete the proof
(part B)
Builders use the equation from Part A to determine the number, height, and depth of stairs necessary to extend from the first floor to the second floor of a building.
Given that the ceiling is 12 feet high, stairs are 8 inches high and the stairwell is 16 feet long, describe in detail how a builder could use the equation to determine the number, height, and depth of the stairs.
Answer:
Step-by-step explanation:
There were 234 roses growing in the back garden. If 50% of the roses were red. How many were not red?
Answer:117
Step-by-step explanation:
I’m good at math
Answer:
117 Roses
Step-by-step explanation:
234 *0.5 = 117
the graph shoes the value a stock( to the nearest dollar) over an 8-hour period. FInd the average rate of change in the stock from hour 3 to hour 7. Round to the nearest cent if necessary.
The average rate of change in the stock from hour 1 to hour 6 is -$0.20/hr.
What is average rate of change in stock?
By subtracting the price of a security at time B from the price of the same security at time A and dividing the result by the price at time A, the price rate of change can be calculated. The indicator is a technical analysis tool that measures unbounded velocity versus a zero-level middle.We need to find the average rate of change of stock from 1 hour to 6 hours.
The value of stock was $11 in hour 1 and $10 in hour 6.
Average rate of change = Δy/ Δx
= $10 - $11 / 6-1
= - $1/5
= -$0.20 /hr
Hence, the average rate of change in the stock from hour 1 to hour 6 is -$0.20/hr.
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Jane had 5 1/6 pecan pies. Marge had 4 3/6 pecan pies. How much pie do they had all together?
Answer:
9 4/6
Step-by-step explanation:
5 + 4 = 9
1/6 + 3/6 = 4/6
9 4/6
Hope this helps! :)
3. The coordinate (4, 3) is the solution to which system of equations?
The coordinate (4, 3) is the solution of the following system of equations:
y = 1/2x + 1 and y = -x + 7
y = x - 1 and y = 1/4x + 2
The solution implies that the coordinate is the: point of intersection.
What is the Solution to a System of Equations?The solution to a system of equations are the coordinate of the point where the two lines that represent the equations of the system intersect each other. The coordinate of x and the coordinate of y, when plugged into any of the equations would be true.
The graph of the system of equations, y = x - 1 and y = 1/4x + 2 shows that both equations intersect at the point with the coordinate (4, 3) [see the graph in figure 1].
Also, the graph in figure two shows that y = 1/2x + 1 and y = -x + 7 also intersect at (4, 3).
Therefore, we can state that, the system of equations with (4, 3) as the solution are:
y = 1/2x + 1 and y = -x + 7
y = x - 1 and y = 1/4x + 2
The solution means point of intersection.
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Solve 3+8X+6 = 5(X+2) + 3X-1
Answer: x= (−∞,∞)
Step-by-step explanation:
3+8x+6 = 5(x+2) + 3x-1
9+ 8x = 5x +10 + 3x -1
9 + 8x = 8x +9
Subtract nine on both sides
8x= 8x
x = Any number!
$35.82 total. He gives the cashier $50. How much change should Rishank receive?
Answer: $14.18
Step-by-step explanation:
Because total change is the amount the cashier is giving back to us,
we can do
$ amount given - $ price of order = $ total change
So:
50 - 35.82 = $14.18
The cashier will give us $14.18 back in change.
The number of beads in a jar is 50 to the nearest ten.
(a) What is the minimum possible number of beads in the jar?
(b) What is the maximum possible number of beads in the iar?
Answer:
a) 45
b) 54
Step-by-step explanation:
a) To be able to round up to the nearest 10, the number in the "ones column" needs to be 5 at the minimum.
You could argue it could be a decimal point however, you shouldn't really have a decimal of a bead ( it's possible but it over complicates the answer ) and, it's to the nearest 10, not nearest one decimal point for example.
Therefore, the min is 45 beads
b) ( The above poster was correct oops, I made a silly mistake )
The max is 54 beads as if anything in the ones column is under 4, you can't round up to the nearest 10. Hence it remains as 50 when rounding
Therefore, the max is 54 beads
The volume of a cylinder having height one and half of the radius is 12,936 m3 what minimum square cm of paper is needed to cover the curved surface area of the cylinder? The answer should be 1848m2. please solve my question.
Answer:
Lateral Surface Area = 1848 m^2 (does not include the top and bottom)
Step-by-step explanation:
Vol Cylinder = pi*r^2 *h
h = (3/2)r
Vol = pi*r^2((3/2)r) [We are told that the volume is 12,936 m^3]
pi*r^2((3/2)r) = 12,936 m^3
pi*(3/2)*(r^3) = 12,936 m^3
pi*r^3 = (12,936 m^3)*(2/3)
pi*r^3 = 8,624 m
r^3 = (8,624 m)/(3.14)
r^3 = 2745.1
r = 14.0 m
Lateral Surface = 2*(pi)*r*h [Lateral is just the curved portion of the right cylinder.
Lateral Surface Area = 2*(3.14)*(14.0)(21.0)
Lateral Surface Area = 1848 m^2