The curve defined by the equation [tex]x^3 + 3xy + y^2[/tex]= 0 has two stationary points. At the point (4,5) on the curve defined parametrically by x = 2t and y =[tex]3t^2 - 4t +1[/tex], .The gradient of the curve at the point (4,5) is 4.
To find the stationary points of the curve[tex]x^3 + 3xy + y^2[/tex]= 0, we need to calculate the partial derivatives with respect to x and y and set them equal to zero. Taking the partial derivative with respect to x, we have[tex]3x^2 + 3y[/tex] = 0. Similarly, taking the partial derivative with respect to y, we have 3x + 2y = 0. Solving these two equations simultaneously, we can find the values of x and y that satisfy both equations, which correspond to the stationary points.
For the curve defined parametrically by x = 2t and y = [tex]3t^2 - 4t + 1,[/tex] we can find the gradient at the point (4,5) by evaluating the derivative of y with respect to x. We substitute the given values of x and y into the parametric equations and find the corresponding value of t. In this case, when x = 4, we have 4 = 2t, which gives us t = 2. Substituting t = 2 into the equation y = [tex]3t^2 - 4t + 1,[/tex] we get y =[tex]3(2)^2 - 4(2) + 1 = 9[/tex]. To find the gradient at the point (4,5), we take the derivative of y with respect to x, which gives dy/dx = (dy/dt)/(dx/dt) = (6t - 4)/(2) = (12 - 4)/2 = 4. Therefore, the gradient of the curve at the point (4,5) is 4.
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The G.M and H.M between two number are respectively 9 & 5.4. Find the numbers.
Answer:
The numbers are 3 and 27.
Step-by-step explanation:
The explanation is attached below.
plz help fast!!!!!!!!!!!!!!!!!!!!!
Answer:
D) 156/100 = n/70
Step-by-step explanation:
n = 156% of 70
% indicates a fraction over 100.
"of" indicates multiplication.
n = 156/100 • 70
Let's divide both sides by 70 to have one fraction one each side.
n/70 = 156/100
This is equal to D) [tex](\frac{156}{100}) = (\frac{n}{70})[/tex]
Simplify.
+6 - 4 =
please help ..........
Answer:
2
Step-by-step explanation:
it's literally 6-4 = 2
Answer: 2
Step-by-step explanation: +6 is simply 6 and 6-4 is 2.
Wiseman Video plans to make four annual deposits of $2,000 each to a special building fund. The fund’s assets will be invested in mortgage instruments expected to pay interest at 12% on the fund’s balance. (FV of $1, PV of $1, FVA of $1, PVA of $1, FVAD of $1 and PVAD of $1) (Use appropriate factor(s) from the tables provided.)
Using the appropriate annuity table, determine how much will be accumulated in the fund on December 31, 2019, under each of the following situations.
1. The first deposit is made on December 31, 2016, and interest is compounded annually.
Table or calculator function: FVA of $1
Payment: $2,000
n = 4
i = 12%
Fund balance 12/31/2019: $9,559
2. The first deposit is made on December 31, 2015, and interest is compounded annually.
Table or calculator function: FVAD of $1
Payment: $2,000
n = 4
i = 12%
Fund balance 12/31/2019: $10,706
3. The first deposit is made on December 31, 2015, and interest is compounded quarterly.
Using the FV of $1 chart, calculate the fund balance:
Deposit Date i = n = Deposit Fund Balance 12/31/2019
12/31/2015 3% 16 $2,000 $3,209
12/31/2016 3% 12 2,000 2,852
12/31/2017 3% 8 2,000 2,534
12/31/2018 3% 4 2,000 2,251
$10,846
4. The first deposit is made on December 31, 2015, interest is compounded annually, and interest earned is withdrawn at the end of each year.
Deposit Amount No. of Payments Interest left in Fund Fund Balance 12/31/2019
$2,000 $8,000
The fund balance at the end of 2019 will be $8,000.
The given problem has four different parts, where we are supposed to calculate the accumulation of funds at the end of 2019 in different scenarios.
Scenario 1In the first scenario, the first deposit is made on December 31, 2016, and interest is compounded annually.
Using the FVA of $1 table; Payment: $2,000n = 4i = 12%
Fund balance 12/31/2019: $9,559
Hence, the fund balance at the end of 2019 will be $9,559.Scenario 2In the second scenario, the first deposit is made on December 31, 2015, and interest is compounded annually.
Using the FVAD of $1 table;Payment: $2,000n = 4i = 12%
Fund balance 12/31/2019: $10,706 Therefore, the fund balance at the end of 2019 will be $10,706.Scenario 3In the third scenario, the first deposit is made on December 31, 2015, and interest is compounded quarterly. Using the FV of the $1 chart, we get the following calculation:
Deposit Date i = n = Deposit Fund Balance 12/31/2015 3% 16 $2,000 $3,20912/31/2016 3% 12 $2,000 $2,85212/31/2017 3% 8 $2,000 $2,53412/31/2018 3% 4 $2,000 $2,251
The interest rate is 3%, and the payment is $2,000. Hence, the fund balance at the end of 2019 will be $10,846.Scenario 4In the fourth scenario, the first deposit is made on December 31, 2015, interest is compounded annually, and interest earned is withdrawn at the end of each year.
Deposit Amount No. of Payments Interest left in Fund Fund Balance 12/31/2019$2,000 $8,000 Hence, the fund balance at the end of 2019 will be $8,000.
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I NEEED HELP match the equation with the term it belongs to. 3.14 *r *r. 2* 3.14 *r
Answer:
3.14 * r * r = area of circle, 2 * 3.14 * r = circumference
Step-by-step explanation:
Remember these formulas, very important.
3. This spinner is divided into eight equal-sized sections. Each section is labeled with a number
Jake spins the arrow on the spinner once.
Drag and drop the events into the correct order from least likely to most likely.
Answer:
Least Likely: Arrow lands on a section labeled with an odd number.
_____: Arrow lands on a section labeled with the number 1.
Most Likely: Arrow lands on a section labeled with a number less than 4.
Step-by-step explanation:
The spinner:
There are 8 sections, 4 labeled with the number 1, 2 labeled with the number 3, 1 labeled with the number 3, and 1 labeled with the number 4.
Probabilities of the spinner:
Probability of landing on 1: 4/8 - 50%Probability of landing on 2: 1/8 - 12.5%Probability of landing on 3: 2/8 - 25%Probability of landing on 4: 1/8 - 12.5%The options:
A - Arrow lands on a section labeled with an odd number.
B - Arrow lands on a section labeled with the number 1.
C - Arrow lands on a section labeled with a number less than 4.
The least likely possibility out of the options would be B because, while a 50% chance sounds like a lot, it is the least of the three options.The mid possibility out of the options would be A. The odd numbers labeled on the spinner make up 75% of the whole. (1s and 3s - 50% + 25%)The most likely possibility out of the options is C because it accounts for every section except for the single section labeled with the number 4. (100% - 12.5%, 87.5%)write both an explicit equation and recursive equation for the sequence 64,8,1,0,0.125..
HURRY PLEASE!!
Answer:
a(n) = n/8
Step-by-step explanation:
64/8 = 8, 8/8 = 1, 1/8 = 0.125.…
Explicit Equation: a(n) = n/8
Recursive Equation: a(1) = 64; a(n) = n/8
i dont know if this is correct or not but here you go!
how to read a q q q q q q q q q q q q q q q q q
Your read from left to right. Read intensively if you want to practice the fundamentals and learn vocabulary. Intensive reading is focused more on individual details of what you’re reading.
hope this helped <3
Answer:
This is how to read a
Pronounce it with your mouth open as in "ah" then smile with an "ee" sound. Say "Ay" and that's how you say A or "Ah"
How to read Q? Just pronounce it as "Kyuu" or when reading it say "Ck" with a sharper sound.
Hope this helped!
Which expression is equivalent to 36 + 24?
Answer:
60
Step-by-step explanation:
What does 1/3 represent for the picture below?
Answer:
c the ratio of the measure of arc QR and the circle
Step-by-step explanation:
i just took the quiz
hope this helps (:
This trapezoid is made up of two right triangles and one rectangle.
Drag numbers to show the area of each triangle and the area of the rectangle. Then drag a number to show the total area of the trapezoid.
30 PIONT IF YOU ANSWER
9514 1404 393
Answer:
each triangle: 29.75 in²rectangle: 374 in²total area: 433.5 in²Step-by-step explanation:
The base of each triangle is half the difference between the bases of the trapezoid:
(29 in -22 in)/2 = 7 in/2 = 3.5 in
The area of the triangle is given by the formula ...
A = 1/2bh
A = 1/2(3.5 in)(17 in) = 29.75 in² . . . triangle area
__
The area of the central rectangle is the product of its base and height.
A = bh = (22 in)(17 in) = 374 in² . . . rectangle area
__
The total area of the trapezoid is the sum of the areas of the two triangles and the area of the rectangle.
total area = 2(29.75 in²) + 374 in² = 433.5 in² . . . total trapezoid area
Write 0.4% in simplest form
Answer:
if simplest form by you mean fraction then the answer is 2/5
hope this is the answer you are looking for
Step-by-step explanation:
please answer this i will mark brainliest
Answer:
The median is 2
Step-by-step explanation:
Arrange your numbers in numerical order.
0011112233445
Count how many numbers you have.
If you have an odd number, divide by 2 and round up to get the position of the median number.
If you have an even number, divide by 2. Go to the number in that position and average it with the number in the next higher position to get the median.
PLEASE MARK ME BRAINLIEST
You are a civil engineer designing a bridge. The walkway needs to be made of wooden planks. You are able to use either Sitka spruce planks (which weigh 3 pounds each), basswood planks (which weigh 4 pounds each), or a combination of both. The total weight of the planks must be between 600 and 900 pounds in order to meet safety code. If Sitka spruce planks cost $3.25 each and basswood planks cost $3.75 each, how many of each plank should you use to minimize cost while still meeting building code?
The optimal solution to minimize cost while meeting the building code is to use 0 Sitka spruce planks and 150 basswood planks.
How to Minimize Cost Using Function Equations?To minimize the cost while meeting the building code, let's assume we use x Sitka spruce planks and y basswood planks.
We want to minimize the cost, so our objective function is the cost of the planks. The cost is given by:
Cost = 3.25x + 3.75y
We also have the constraint that the total weight of the planks must be between 600 and 900 pounds:
3x + 4y ≥ 600
3x + 4y ≤ 900
To solve this optimization problem, we can use linear programming. We'll use the Simplex method to find the optimal solution.
Let's rewrite the constraints in standard form:
-3x - 4y ≤ -600
3x + 4y ≤ 900
Now we have the following system of equations:
-3x - 4y ≤ -600
3x + 4y ≤ 900
The feasible region is a quadrilateral with vertices at (0, 150), (0, 225), (300, 150), and (225, 0).
To minimize the cost, we need to find the corner point of the feasible region that lies on the cost line, which is given by 3.25x + 3.75y.
Let's evaluate the cost at each corner point:
Cost at (0, 150) = 3.25(0) + 3.75(150) = 562.50
Cost at (0, 225) = 3.25(0) + 3.75(225) = 843.75
Cost at (300, 150) = 3.25(300) + 3.75(150) = 1500.00
Cost at (225, 0) = 3.25(225) + 3.75(0) = 731.25
From the evaluations, we can see that the minimum cost is achieved at (0, 150), which means we should use 0 Sitka spruce planks and 150 basswood planks.
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38 − 7x = −2(x − 29)
Answer:
x = -4Step-by-step explanation:
38 − 7x = −2(x − 29)
=> 38 - 7x = -2x + 58
=> 38 - 58 = 7x - 2x
=> -20 = 5x
[tex] = > x = \frac{ - 20}{5} [/tex]
=> x = -4 (Ans)
A standard test of intelligence is scaled so that the mean IQ is 100, and the standard deviation is 15. If there are 40,00 people in a certain town , what is the percentage of people who have an IQ between 70 and 130 ?
a. 47.5%
b. 95%
c. 68 %
d. 99.7
The correct option to the sentence "The percentage of people who have an IQ between 70 and 130 ?" is:
b. 95%.
To solve for the percentage of people who have an IQ between 70 and 130, we will have to use the standard deviation and the mean IQ.
It is given that: Mean = 100, Standard deviation = 15
Now we will use these values to find the percentage of people who have an IQ between 70 and 130.
The first step to this process is to standardize the IQ scores by converting them to Z-scores.
The formula for Z-score is:
Z = (X - µ) / σ, where X represents the IQ score, µ represents the mean IQ, and σ represents the standard deviation.
IQ score of 70:
Z = (70 - 100) / 15
Z = -2
IQ score of 130:
Z = (130 - 100) / 15
Z = 2
Now that we have the Z-scores for IQ scores of 70 and 130, we can find the percentage of people who have an IQ between these two scores. We will use the Z-table to do this. The Z-table provides the area under the standard normal distribution curve for a given Z-score.
From the Z-table, we can find that the area under the curve between Z = -2 and Z = 2 is approximately 0.9545. This means that approximately 95.45% of people have an IQ between 70 and 130.
Therefore, the correct option is: b. 95%.
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Use Strong Induction to prove that: If p + 1/p E N, then Pn+1/Pn EN for all nEN.
We prove with the help of Strong Induction.
Let P(n) be the statement that Pn+1/Pn E N.
In order to prove this statement, we will utilize strong induction.So we are given that p + 1/p E N. We will show that P(n) is true for all n >= 1.
Let's consider the base case
P(1):P2/P1 = (p + 1/p)^2 - 2 = (p^2 + 2 + 1/p^2) - 2p/p = (p^2 + 1/p^2) - (2p - 2/p)
Since p + 1/p E N, both p and 1/p must be integers.
Hence, p^2 and 1/p^2 are also integers. This implies that (p^2 + 1/p^2) is an integer.
It only remains to show that (2p - 2/p) is an integer. This is equivalent to showing that 2p^2 - 2 E 0 mod p. But this is clearly true, since 2p^2 - 2 = 2(p^2 - 1) and p^2 - 1 is divisible by p.
Let's assume that P(k) is true for all k such that 1 <= k <= n. We need to prove that P(n+1) is true as well.
Now we need to prove that P(n+1) is true. In other words, we need to show that P(n+2)/P(n+1) E N, assuming that P(n+1)/P(n) E N and P(n)/P(n-1) E N.
Using the definition of P(n), we have:P(n+1)/P(n) E N and P(n)/P(n-1) E N imply that P(n+1) = aP(n) and P(n) = bP(n-1) for some integers a and b. Then:P(n+2)/P(n+1) = (P(n+2)/P(n+1)) * (P(n)/P(n)) = (P(n+2)P(n))/(P(n+1)P(n)) = (aP(n+1)P(n))/(bP(n)P(n+1)) = a/bIf we can show that a/b E N, then P(n+2)/P(n+1) E N, and P(n+1) satisfies the inductive hypothesis.
But this follows from the fact that a and b are integers and the product of two integers is always an integer.
Hence, P(n+1) is true for all n >= 1, by strong induction.Therefore, by strong induction, we have proved that if p + 1/p E N, then Pn+1/Pn EN for all nEN.
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Solve each inequality.
2s+5> 49
_
Answer: S > 22
Step-by-step explanation:
Answer:
s = 23 and above
Step-by-step explanation:
2s + 5 > 49
-5 -5
2s > 44
44/2
= 22
However, the answer for s is not 22
Since it has this sign > not ≥ then that means s = 23 and above
Check:
2(23) + 5 > 49
46 + 5 > 49
51 > 49
a man sold an article at a gain of 5 percent if it had sold for rs 16.30 less he would have suffered a loss of 5 percent find the cost price?
Answer:
Step-by-step explanation:
let CP of the article = x
at 5% gain, SP of article = x + (5/100)x = 1.05x
at 5% loss, SP of article = x - (5/100)x = 0.95x
given that 1.05x - 0.95x = 16.5
⇒ 0.1x = 16.5
⇒ x = 16.5/0.1
⇒ x = Rs. 165.
The cost price of the article is Rs. 165.
A regular heptagon is shown below. What is the value of x?
Answer:
108+x=180
X=180-108
X=72
The value of the exterior angle (x) in a regular heptagon is approximately 51.43 degrees.
Given is a regular heptagon with one of the exterior angle be x we need to find the value of x
To find the value of the exterior angle of a regular heptagon, we can use the formula:
Exterior Angle = 360 degrees / Number of Sides
In this case, the heptagon has seven sides, so we can substitute the values into the formula:
Exterior Angle = 360 degrees / 7
Exterior Angle ≈ 51.43 degrees
Therefore, the value of the exterior angle (x) in a regular heptagon is approximately 51.43 degrees.
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HELPPP PLSSS Choose the most appropriate translation of the English sentence.
The radius of a balloon (which depends on the amount of air inside) is 3
inches.
Answer:
A radius(radius) = 3The radius of a balloon (which depends on the amount of air inside) is 3
inches
If a researcher wants to determine if there is a linear relationship between the number of hours a person goes without sleep and the number of mistakes he makes on a simple test. The following data is recorded.
n = 4, Σx = 20, Σy = 25, Σxy = 144 & Σx² = 120.
Find the equation of the regression line:
y = a + bx. y = (a = ____) + (b = _____)x.
b = [n(Σxy) - (Σx)(Σy)] / [n(Σx²) - (Σx)²] = ____
a = [(Σy)(Σx²) - (Σx)(Σxy)] / [n(Σx²) - (Σx)²] = _____
The equation of the regression line is: y = 1.5 + 0.95x
How to find the equation of the regression lineTo find the equation of the regression line, we can use the formulas:
b = [n(Σxy) - (Σx)(Σy)] / [n(Σx²) - (Σx)²]
a = [(Σy)(Σx²) - (Σx)(Σxy)] / [n(Σx²) - (Σx)²]
Given the following data:
n = 4
Σx = 20
Σy = 25
Σxy = 144
Σx² = 120
Let's calculate the values step by step:
b = [4(144) - (20)(25)] / [4(120) - (20)²]
= (576 - 500) / (480 - 400)
= 76 / 80
= 0.95
a = [(25)(120) - (20)(144)] / [4(120) - (20)²]
= (3000 - 2880) / (480 - 400)
= 120 / 80
= 1.5
Therefore, the equation of the regression line is:
y = 1.5 + 0.95x
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Let be an equivalence relation on a set S, and let a, b e S. Show that two equivalence classes under ~ are either equal or disjoint, i.e. either [a] = [b] or [a] n [b] = 0.
Given, an equivalence relation ~ on a set S. Let a and b be two elements in the set S. Assuming that [a] and [b] are two equivalence classes under the equivalence relation ~. Now we need to prove that either [a] = [b] or [a] ∩ [b] = ∅ (disjoint).
Proof:If [a] and [b] are not equal, then there must be some element c in the intersection of the equivalence classes [a] and [b]. i.e, c belongs to [a] and c belongs to [b].Thus, [a] ∩ [b] is not empty.
Let x be an element in [a], then x~a, and a~c (since c belongs to [a]) and hence x~c. So, x belongs to [c] which implies that [a] is a subset of [c].Now, let y be an element in [b], then y~b, and b~c (since c belongs to [b]) and hence y~c. So, y belongs to [c] which implies that [b] is a subset of [c].Thus, both [a] and [b] are subsets of [c].
Therefore, if [a] and [b] are not equal, then [a] and [b] are both subsets of [c] and hence the intersection of [a] and [b] is not empty. Thus, [a] and [b] are not disjoint. Hence, the proof by contradiction.
Conversely, if [a] and [b] are disjoint, then [a] ∩ [b] = ∅. And thus, [a] is not equal to [b].Therefore, two equivalence classes under the equivalence relation ~ are either equal or disjoint.
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Let p(x)=x+3x²-4x-12 a) Find the x-intercepts of the graph of p(x) c) Sketch a graph of p(x) b) Find the y-intercept of the graph of p(x)
a) The x-intercepts of p(x) are x = 3 and x = -4/3. b) The y-intercept of p(x) is y = -12.
a) To find the x-intercepts, we set p(x) = 0 and solve for x:
x + 3x² - 4x - 12 = 0
Simplifying the equation, we get:
3x² - 3x - 12 = 0
Factoring, we have:
(x - 3)(3x + 4) = 0
Setting each factor equal to zero, we find the x-intercepts:
x = 3 and x = -4/3
b) The y-intercept is the value of p(0), so we substitute x = 0 into the equation:
p(0) = 0 + 3(0)² - 4(0) - 12 = -12
Therefore, the y-intercept is -12.
c) To sketch the graph, we plot the x-intercepts (x = 3 and x = -4/3) and the y-intercept (y = -12) on a coordinate plane.
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I have an hour to do this please help
Answer:
6
Step-by-step explanation:
27/9 =3
now 18/3
=6
Last year, a marketing research company estimated Amazon Prime members spent $1,825 on Amazon.com. The company believes that due to the pandemic. Amazon Prime members have spent more on average at Amazon.com compared to last year. They take a sample of 150 Amazon Prime members to test their belief. These sample members spent an average of $1,950. Assume the population standard deviation is $600.
Specify the hypotheses.
Null hypothesis (H0): µ ≤ 1825, the alternative hypothesis is µ > 1825.
The hypotheses are given below:
Null hypothesis (H0): µ ≤ 1825
Alternative hypothesis (Ha): µ > 1825 where µ represents the population mean amount spent by Amazon Prime members on Amazon.com.
As given in the question, the company believes that due to the pandemic, Amazon Prime members have spent more on average at Amazon.com compared to last year.
Therefore, the alternative hypothesis is µ > 1825.
The null hypothesis is that there is no significant difference or increases in the mean amount spent on Amazon.com by Amazon Prime members last year and this year or that the mean amount spent this year is less than or equal to that of last year, which is µ ≤ 1825.
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The blood results for a particular sample unknown test from ten finalists of a medical study were recorded for further analysis. Find the following quantities below.
Blood test results: {580, 610, 530, 530, 440, 670, 480, 540, 590, 490 }
(Use only 2 decimal places. Ex. if answer is 34.568, just write 34.56. If the answer is 321 just leave as 321, do not add any decimals)
a) Mean _______
(b) Median______
(c) Mode________
(d) Range________
(e) Variance ________
(f) Standard deviation_______
(g) IQR ______
(h) Upper fence ________
Answer:
(a) Mean = 541.00
(b) Median = 535.00
(c) Mode: 530
(d) Range = 230
(e) Variance = 5340.40
(f) Standard deviation = 73.10
(g) IQR = 100
(h) Upper fence = 740.00
Step-by-step explanation:
Find the measurements of DBC
Answer:
72 degrees
Step-by-step explanation:
To determine the value of DBC, we first have to determine the value of q
Angle on a straight line = 180 degrees
7q - 46 + 3q + 6 = 180
10q - 40 = 180
collect like terms
10q = 180 + 40
10q = 220
q = 22
Substitute for q in angle dbc
3(22) + 6 = 72 degrees
 PLSSS HELP IMMEDIATELY!!!!! i’ll give brainiest, i’m not giving brainiest if u leave a link tho. (pls check whole picture!!) answer choices: (4,6) (0,1) (0,0) (5,4)
Answer:
(0, 1)
Step-by-step explanation:
All other choices do not match the two possible vertices of the square.
Find the probability using the normal distribution: P(0 P(0
The probabilities are:
P(0 < z < 1.96) = 0.4750
P(-1.23 < z < 0) = 0.3907
P(z > 0.82) = 0.2061
P(z < -1.77) = 0.0384
P(-0.20 < z < 1.56) = 0.5199
P(1.12 < z < 1.43) =0.0550
P(z > -1.43) = 0.9236
To locate the chances of the usage of the same old ordinary distribution, we will use a well-known normal desk or a calculator. Here are the calculations for the given possibilities:
P(0 < z < 1.96):
Using the standard everyday desk, the place to the left of one.Ninety-six is 0.9750, and the vicinity to the left of zero is 0.5000. Therefore, the chance between zero and 1.96 is:
P(0 < z < 1.96) = 0.9750 - 0.5000 = 0.4750
P(-1.23 < z < 0):
Using the usual ordinary table, the vicinity to the left of -1.23 is 0.1093, and the area to the left of zero is zero.5000. Therefore, the possibility between -1.23 and 0 is:
P(-1.23 < z < 0) = 0.5000 - 0.1093 = 0.3907
P(z > 0.82):
Using the standard everyday table, the region to the left of zero.82 is zero.7939. Therefore, the possibility of z being extra than 0.82 is:
P(z > 0.82) = 1 - 0.7939 = 0.2061
P(z < -1.77):
Using the same old regular desk, the vicinity to the left of -1.Seventy-seven is zero.0384. Therefore, the chance of z being much less than -1.77 is:
P(z < -1.77) = 0.0384
P(-zero.20 < z < 1.56):
Using the standard ordinary desk, the area to the left of -0.20 is 0.4207, and the area to the left of 1.56 is 0.9406. Therefore, the opportunity between -0.20 and 1. Fifty-six is:
P(-0.20 < z < 1.56) = 0.9406 - 0.4207 = 0.5199
P(1.12 < z < 1.43):
Using the standard regular desk, the place to the left of 1.12 is 0.8686, and the location to the left of one. Forty-three is zero.9236. Therefore, the opportunity between 1.12 and 1. Forty-three is:
P(1.12 < z < 1.43) = 0.9236 - 0.8686 = 0.0550
P(z > -1.43):
Using the same old normal desk, the location to the left of -1.43 is zero.0764. Therefore, the possibility of z being greater than -1. Forty-three is:
P(z > -1.43) = 1 - 0.0764 = 0.9236
Please word that the chances are rounded to 4 decimal locations for clarity.
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The correct question is:
"Find the probability using the standard normal distribution. P(0 < z <1.96), P(-1.23 < z < 0), P(z > 0.82), P(z < -1.77), P(-0.20 < z < 1.56), P(1.12 < z < 1.43), P(z > -1.43)"