Answer:
1). Options (B) and (E)
2). First train is going faster than the second train.
Step-by-step explanation:
1). Rate of 2 gallons of vinegar = $3
Therefore, per gallon rate of vinegar = \(\frac{3}{2}\) = $1.5
In $3 quantity of vinegar chef will get = 2 gallons
Therefore, quantity of vinegar chef will get in $1 = \(\frac{2}{3}\) gallons
Option (A).
Price of 4 gallons = 4 × $1.5 = $6.00
False.
Option (B)
Price of 1 gallon = $1.50
True
Option (C)
Price of 30 gallons = 30 ×$1.5 = $45
False.
Option (D)
In $2 number of gallons of vinegar chef will get = \(\frac{2}{3}\times 2=\frac{4}{3}\) gallons
False
Option (E)
Number of gallons of vinegar chef gets in $1 = \(\frac{2}{3}\)
True
Therefore, Options (B) and (E) are the correct.
2). Speed = \(\frac{\text{Distance}}{\text{Time}}\)
For first train,
Speed = \(\frac{30}{\frac{1}{3}}\)
= 90 miles per hour
For second train,
Speed = \(\frac{20}{\frac{1}{2}}\)
= 40 miles per hour
Since, 90 miles per hour > 40 miles per hour
First train is going faster than the second train.
using the clausius‐clapeyron equation determine what variables related to the measured values would be graphed on the x and y axes, along with what m and b would represent.
In the Clausius-Clapeyron equation, the variables related to the measured values that would typically be graphed on the x and y axes depend on the specific application.
Generally, the natural logarithm of the vapor pressure (ln P) is plotted on the y-axis, while the reciprocal of the absolute temperature (1/T) is plotted on the x-axis. The slope (m) and y-intercept (b) of the resulting linear graph have specific interpretations in the context of the equation.
The Clausius-Clapeyron equation relates the vapor pressure of a substance to its temperature. It is expressed as ln(P) = -ΔHvap/R * (1/T) + C, where P is the vapor pressure, ΔHvap is the enthalpy of vaporization, R is the gas constant, T is the temperature, and C is a constant. When graphing this equation, we often plot ln(P) on the y-axis and 1/T on the x-axis.
The graph obtained from plotting these variables follows a linear relationship. The slope of the resulting line, denoted as m, is equal to -ΔHvap/R. This slope provides valuable information about the enthalpy of vaporization, which is a measure of the energy required to convert a substance from its liquid phase to its gas phase. The y-intercept, denoted as b, represents the constant C in the equation, which accounts for any initial conditions or deviations from the ideal gas behavior.
By plotting ln(P) against 1/T, we can determine the slope and y-intercept of the linear graph. These parameters have specific physical interpretations and can provide insights into the thermodynamic properties of the substance under investigation. Analyzing the slope and y-intercept values can help in quantifying the enthalpy of vaporization and understanding the behavior of the substance as its temperature changes.
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CHALLENGE ACTIVITY 2.3.2: Excel: Linear Regression
Three main implications for linear regression analysis are as follows:
(1) determining the strength of the predictor, (2) foreseeing an impact, and (3) trend forecasting.
Linear regression:
A fundamental and popular technique for predictive analysis is linear regression. Regression's overarching objective is to look at two things:
Accurately can a group of predictor variables forecast an outcome (dependent) variable.
Factors in particular, and how do they affect the outcome variable, are strongly predictive of both.
There are three main functions for regression analysis:
Assessing predictor power, foreseeing an outcome, and trend forecasting.
The regression equation's simplest version, y = c + b*x, has one dependent and one independent variable.
where,
y is the estimated score for the dependent variable, c is a constant, b is the regression coefficient, and x is the estimated score for the independent variable.
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which two parts of the vehicle are most important in preventing traction loss
The tires and the traction control system work in tandem to ensure maximum traction and stability, minimizing the risk of traction loss and improving overall vehicle control and safety.
The two most important parts of a vehicle in preventing traction loss are the tires and the traction control system.
Tires: Tires are the primary point of contact between the vehicle and the road surface. The quality and condition of the tires greatly influence traction. Tires with good tread depth and appropriate tread pattern are essential for maintaining grip on the road. Tread depth helps to channel water, snow, or debris away from the tire, preventing hydroplaning or loss of traction. Additionally, tire pressure should be properly maintained to ensure even contact with the road. Choosing tires suitable for the specific driving conditions, such as all-season, winter, or performance tires, is crucial for optimal traction and handling.
Traction Control System: The traction control system is a vehicle safety feature that helps prevent the wheels from slipping or spinning on low-traction surfaces. It uses various sensors to monitor the speed and rotation of the wheels. If the system detects a loss of traction, it will automatically reduce engine power and apply braking force to the wheels that are slipping. By modulating power delivery and braking, the traction control system helps maintain traction and prevent wheel spin, especially in challenging conditions like slippery roads or during quick acceleration.
The tires and the traction control system work in tandem to ensure maximum traction and stability, minimizing the risk of traction loss and improving overall vehicle control and safety.
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HOW MANY ZEROS WILL BE IN THE PRODUCT OF 5 TIMES 10EXPONT OF 5 EXPLAIN HOW YOU KNOW
Answer:
50 Zeros
Step-by-step explanation:
Since 10 is the exponent number and 5 is the base, then 5 would be written out 10 times but since you multiply that by 5, it's 50 zeros in total
Answer:
5 zeros because 5 × 10 is 50 if you multiply 5 by 10 5 times then there are 5 zeros.
Step-by-step explanation:
AC is a diameter of OE, the area of the
circle is 289 units2, and AB = 16 units.
Find BC and mBC.
B
A
C
E. plssss hurry !!
The measure of arc BC is 720 times the measure of angle BAC.
Given that AC is the diameter of the circle and AB is a chord with a length of 16 units, we need to find BC (the length of the other chord) and mBC (the measure of angle BAC).
To find BC, we can use the property of chords in a circle. If two chords intersect within a circle, the products of their segments are equal. In this case, since AB = BC = 16 units, the product of their segments will be:
AB * BC = AC * CE
16 * BC = 2 * r * CE (AC is the diameter, so its length is twice the radius)
Since the area of the circle is given as 289 square units, we can find the radius (r) using the formula for the area of a circle:
Area = π * r^2
289 = π * r^2
r^2 = 289 / π
r = √(289 / π)
Now, we can substitute the known values into the equation for the product of the segments:
16 * BC = 2 * √(289 / π) * CEBC = (√(289 / π) * CE) / 8
To find mBC, we can use the properties of angles in a circle. The angle subtended by an arc at the center of a circle is double the angle subtended by the same arc at any point on the circumference. Since AC is a diameter, angle BAC is a right angle. Therefore, mBC will be half the measure of the arc BC.
mBC = 0.5 * m(arc BC)
To find the measure of the arc BC, we need to find its length. The length of an arc is determined by the ratio of the arc angle to the total angle of the circle (360 degrees). Since mBC is half the arc angle, we can write:
arc BC = (mBC / 0.5) * 360
arc BC = 720 * mBC
Therefore, the length of the arc BC equals 720 times the length of the angle BAC.
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What’s 10-8+434+87+64
-24 = -3w +21 what is w?
Answer:
w=15
Step-by-step explanation:
PLEASE help I’ll mark you as the Brainiest please!!!!
Answer:
c
Step-by-step explanation:
As a shareholder of common shares in a public company, what are the benefits available
to you?
you have ownership of a portion of the company and receive coupon payments from the issuer
you may receive dividends from the company, if the company pays them, and you have
ownership of a portion of a company, and you vote on members of the board of directors
you can select members of the management team (e.g., the chief executive officer (ceo)) and
vote for members of the board of directors
you must receive dividends from the company (all companies must pay them) and you can select
members of the management team (e.g., the chief executive officer (ceo) and chief marketing
officer (cmo))
As a shareholder of common shares in a public company, there are various benefits available to you. Firstly, you have ownership of a portion of the company, which can give you a say in the company's decision-making processes.
Additionally, you may receive coupon payments from the issuer, which is the company that has issued the shares. You may also receive dividends from the company, if the company pays them out. Dividends are a portion of the company's profits that are distributed to shareholders.
Another benefit is that you have the right to vote on members of the board of directors, who oversee the company's management and make important decisions. As a shareholder, you can also select members of the management team, such as the CEO or CMO, by voting for them. It's important to note that not all companies pay dividends, and there may be restrictions on voting rights depending on the type of shares you hold.
Overall, owning common shares in a public company can provide potential financial benefits and a say in the company's direction.
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the clock on the wall at the aops office has an hour hand that's 4 cm long and a minute hand that's 8 cm long. at exactly 2:00, at what rate, in centimeters per minute, is the distance between the tips of the two hands changing?
At exactly 2:00, the distance between the tips of the two hands is changing at the rate of 4 cm/min.Therefore, at exactly 2:00, the distance between the tips of the two hands is changing at the rate of \(2\sqrt{13}\) cm/min.
What is meant by "at exactly 2:00"?The phrase "at exactly 2:00" means that at 2:00:00, the hour hand and the minute hand overlap. Both hands are together pointing upwards in the vertical direction. At this moment, the angle between the minute hand and the hour hand is 0 degrees.How do we determine the rate of change of the distance between the tips of the two hands?We start by calculating the angle between the two hands. The angle is given by:
θ(t) = 30h - 11/2m
where h is the number of hours past midnight and m is the number of minutes past the most recent hour. At exactly 2:00, h = 2 and m = 0. Thus:
θ(t) = 30(2) - 11/2(0) = 60 degrees
Next, we use the formula for the distance between two points (the tips of the two hands). Let the hour hand be at the point (0,0) and let the minute hand be at the point (x,y).
The distance between the two points is given by:
\(d(t) = \sqrt{(x^2 + y^2)}\)
To find x and y, we use the formulas:
x(t) = r cos θ(t)y(t) = r sin θ(t)
where r is the length of each hand. At exactly 2:00:
\(r = 4 cmx(t) = 4 cos 60 = 2 my(t) = 4 sin 60 = 2\sqrt{(3) m}\)
Therefore: \(d(t) = \sqrt{(x^2 + y^2)} = \sqrt{(2 m)^2 + (2sqrt(3) m)^2)} = 2\sqrt{(13) m}\)
Finally, we differentiate with respect to time t to find the rate of change of \(d(t):d'(t) = 2\sqrt{13}\) cm/min
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what is a type ii error? rejecting a false null hypothesis accepting a false alternate hypothesis rejecting a false alternate hypothesis failing to reject a false null hypothesis
A type II error is a statistical term used to describe the failure to reject a false null hypothesis. It occurs when the null hypothesis is actually false but is not rejected because the statistical test failed to find significant evidence against it.
In other words, it happens when an alternative hypothesis is true, but we fail to reject the null hypothesis.
Types of errors in hypothesis testing
There are two types of errors in hypothesis testing:
Type I error: Rejecting a true null hypothesis
Type II error: Failing to reject a false null hypothesis.Type I error occurs when a true null hypothesis is rejected while Type II error occurs when a false null hypothesis is not rejected. These types of errors are inversely related, meaning that a decrease in one type of error causes an increase in the other.
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A classroom can accommodate less than 24 students.
Which of the following inequalities represents the number of students the classroom can
accommodate?
A.
O
19
30 31
20
21
22
23
24
25 26 27 28 29
B.
O
29
30
31
28
24
25
23
26
27
19 20 21 22
O
C.
25 26
27
28 29 30 31
24
22
23
21
19
20
O
D.
28
25
27
29 30 31
28
19 20 21 22 23 24
The inequalities represents the number of students the classroom can
accommodate is Number line C.
What is Inequality?Mathematical expressions with inequalities are those in which the two sides are not equal. Contrary to equations, we compare two values in inequality. Less than (or less than or equal to), greater than (or greater than or equal to), or not equal to signs are used in place of the equal sign.
We have,
A classroom can accommodate less than 24 students.
For less than we use the inequality as '<'.
let the x be the number of students than the condition is
x < 24.
Now, For '<' inequality the arrow should head towards left side of 24 which means for x= 23, 22, 21, .....
Thus, the number line for the situation is C.
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Find the lateral surface area.
Answer:
Step-by-step explanation:
What is the quotient of 2.262 and 0.13? Select one: A. 11.5 B. 12.3 C. 15.9 D. 17.4
Which expression is equivalent to 6(x – 4)Zoe, Latoya, Christina, and Rhoda each used a different method to verify that Negative 2 (3 x minus 12) = negative 6 x + 24
Answer:
Rhoda
Step-by-step explanation:
sub same values of x into both expressions. The expressions are equivalent if the values of the expressions are equal
VSpeeding A trucker handed in a ticket at a toll booth showing that in 2 h she had covered 159 mi on a toll road with speed limit 65 mph. The trucker was cited for speeding. Why
Answer:
The trucker was cited for speeding because his speed was above that of the speed limit of the toll road by 14.5mph
Step-by-step explanation:
Step 1
We calculate the speed of the trucker
Speed = Distance(miles)/Time(hours)
Distance = 159 miles
Time = 2 hours
Speed = 159 miles/2 hours
Speed = 79.5 miles per hour = 79.5 mph
From the question, we are told that: that toll road has a speed limit of 65mph
Step 2
We calculate the difference
= 79.5 mph - 65 mph
= 14.5 mph
Hence, the trucker was cited for speeding because his speed was above that of the speed limit of the toll road by 14.5mph
Gatorade comes in two different sizes A 16 ounce costs $2.10 and a 20nounce bottle costs $3.15 which is a better deal to explain your thinking.
How much do you save per ounce by buying the better one?
Based on the cost of each bottle, the better deal is the 16 ounce size and the amount saved per ounce is $0.03
The first step is to find the cost per ounce of each bottle.
For the 16 ounce bottle:
= 2.10 / 16
= $0.13 per ounce
For the 20 ounce bottle:
= 3.15 / 20
= $0.16
The 16 ounce size is therefore better and the amount saved per ounce is:
= 0.16 - 0.13
= $0.03
In conclusion, the 16 ounce is better as it saves $0.03 per ounce.
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Take some time but answer correctly
Answer:
c) 2⁻⁹
Step-by-step explanation:
1) use negative power rule: \(x^{-a} =\frac{1}{x^{a} }\)
1/2⁹
2) simplify ₂⁹ to 512
1/512 ( same as (8) ⁻3
Answer:
c
Step-by-step explanation:
Using the rule of exponents
\((a^m)^{n}\) = \(a^{mn}\)
note that 8 = 2³ , then
\((8)^{-3}\)
= \((2^3)^{-3}\)
= \(2^{3(-3)}\)
= \(2^{-9}\) → c
Find the approximate perimeter of AABC plotted
below.
A(2,7)
C(6,7)
B(-4,-3)
Answer:
29.8 units
Step-by-step explanation:
Answer:
29.8
Step-by-step explanation:
Find the largest possible area for a rectangle with base on the x-axis and upper vertices on the curve.
A rectangle with its base on the x-axis and its vertices on the curve
y =4 - x² can have a maximum area of 32/3√3.
The formula for calculating a rectangle's area is A=length*breadth
The base's length is x.
y represents the curve's vertices (width).
Given that a rectangle's area increases as its base moves along the x-axis, our base will be 2x.
The rectangle's surface area will change to:
A = 2x ( 4 - x²)
When the area is at its largest, da / dx should be maximum.
A = 8x - 2x³
da/dx = 8 - 6x²
8 - 6x² = 0
6x² = 8
x² = 8/6
x = √4/3
=2/√3
We shall substitute 2/√3 into the region in order to obtain the maximum area.
A= 8x - 2x³
= 8*2/√3 - 2*(2/√3)³
=32/3√3
Therefore, the largest area a rectangle with a base on the x-axis and vertices on the curve y = 4 - x² can have is 32/3√3.
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hardest question
X+X*94%=1164
X=?
Answer:
x = 600 and 1.94!=0
Step-by-step explanation:
Answer:
X = 600
Step-by-step explanation:
This is the answer because:
1) All you have to do is just isolate the variable by dividing each side by factors that don't contain the variable.
Hope this helps! :D
in a sample of 1,600 registered voters, 912 or 57% approve of the way the president is doing his job. the 57% approval is an example of
By understanding the definition of the statistics method, it can be concluded that 57% is an example of the result of inference statistics.
In statistics, the population is defined as the entire research subject, while the sample is a representative or part of the population, which has the same characteristics that can describe and represent the entire population.
There are two methods used to perform data analysis:
a. Descriptive statistics: an analytical method used to describe the characteristics of data. The end result of this method is in the form of tables, charts, graphs, etc.
b. Inference statistics: an analytical method used to draw conclusions about a population based on a sample. The end result of this method is in the form of a possibility or probability and is expressed in percent units.
If we look at the given problem, it is stated that "in a sample of 1,600 registered voters, 912 or 57% approve of the way the president is doing his job"
By understanding the definition of descriptive and inference statistics, it can be concluded that 57% is an example of the result of Inference statistics.
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A candy bar cost the store $0.79. The store wants a 65% mark up. What would the price of the candy bar be to have a 65% mark up?
Answer:
1.30$
Step-by-step explanation:
The price of the candy bar to have a 65% mark up is $1.3035.
What is Markup Percentage?Markdown percentage is defined as the increase in the price which is calculated as a percent of the selling price.
Given that,
Markup percentage = 65% = 65/100 = 0.65
Let x be the price of the candy bar be to have a 65% mark up.
(x - 0.79) / 0.79 = 0.65
x - 0.79 = 0.5135
Adding 0.79 to both sides,
x = 1.3035
Hence the price of the candy bar would need to be $1.3035.
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Charles buys 20 packs of pens.
There are 15 pens in each pack.
Each pack costs £2.50.
Charles sells each pen for 65p but he only manages to sell į of the pens.
How much profit did he make?
Answer:
their will be at least $159
y=[(C1)+(C2)x]exp(Ax) is the general solution of the second order linear differential equation: (y'') + (-4y') + ( 4y) = 0. Determine A.
When y [(C1)+(C2)x]exp(Ax) is the general solution of the second order linear differential equation: (y'') + (-4y') + ( 4y) = 0 then the values of A that satisfy the given differential equation are A = ±2.
To determine the value of A in the second-order linear differential equation (y'') + (-4y') + (4y) = 0, we can use the general solution y = (C1) + (C2)\(x^Ae^{Ax}\), where C1 and C2 are constants.
By comparing the general solution with the given differential equation, we can identify the value of A.
The given differential equation is (y'') + (-4y') + (4y) = 0.
We can substitute the general solution y = (C1) + (C2)\(x^Ae^{Ax}\) into the differential equation to find the value of A.
First, let's calculate the first and second derivatives of y:
y' = C2(\(Ax^{A-1}e^{Ax}\)) + C1\(e^{Ax}\)
y'' = C2(A(A-1)\(x^{A-2}e^{Ax}\)) + C2(\(A^2x^{A-1}e^{Ax}\)) + C1(\(Ae^{Ax}\))
Now, substitute these derivatives into the differential equation:
C2(A(A-1)\(x^{A-2}e^{Ax}\)) + C2(\(A^2x^{A-1}e^{Ax}\)) + C1(\(Ae^{Ax}\)) + (-4)(C2(\(Ax^{A-1}e^{Ax}\)) + C1\(e^{Ax}\)) + 4(C1) + 4(C2)\(x^Ae^{Ax}\) = 0
Simplifying the equation and collecting like terms:
C2[\((A^2 - 4) x^{A-1} + A x^{A-1}\)]\(e^{Ax}\) + (C1A - 4C2A)\(e^{Ax}\) + (4C1 + 4C2)\(x^Ae^{Ax}\) + 4C1 = 0
For this equation to hold true for all x, the coefficient of each term must be zero.
Therefore, we can equate each coefficient to zero and solve for A.
Let's equate the coefficients:
For the term involving \(x^{A-1}e^{Ax}\):
C2[\((A^2 - 4) x^{A-1} + A x^{A-1}\)] = 0
For the term involving x\(e^(Ax)\):
(4C1 + 4C2)\(x^A\) = 0
For the constant term:
4C1 = 0
From the first equation, we have two possibilities:
(\(A^2\) - 4) = 0, which leads to A = ±2.
A = 0, which results in the trivial solution y = C1.
From the second equation, we have two possibilities:
\(x^A\) = 0, which implies A < 0 (not valid for our general solution).
4C1 + 4C2 = 0, which means C1 = -C2.
Now, let's consider the value of A = ±2.
For A = 2:
The general solution becomes y = (C1 + C2\(x^2\))\(e^{2x}\).
For A = -2:
The general solution becomes y = (C1 + C2\(x^{-2}\))\(e^{-2x}\).
So, the values of A that satisfy the given differential equation are A = ±2.
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A nationwide poll of 2.525 adults estimated with a 95% confidence that the proportion of Americans that support health care reform is 0.78 ± 0.0162. A member of Congress thinks that 95% confidence isn't enough. He wants to be 99% confident. How would the margin of error of a 99% confidence interval based on the same sample compare with the 95% interval?
a) It would be smaller, because it omits only 1% of the possible samples instead of 5% percent.
b) It would be the same, because the sample is the same.
c) It would be larger, because higher confidence requires a larger margin of error.
d) Can't tell, because the margin of error varies from sample to sample.
e) Can't tell, because it depends on the size of the population.
c) It would be larger, because higher confidence requires a larger margin of error.
When increasing the confidence level from 95% to 99%, the margin of error of the confidence interval tends to increase. This is because a higher confidence level means we want to be more certain or have a higher level of confidence in capturing the true population parameter.
To achieve a higher confidence level, we need to widen the interval to account for more potential variability in the population. As a result, the margin of error increases, reflecting the increased uncertainty and the need for a larger range of values to capture the true population parameter with higher confidence.
Therefore, the margin of error of a 99% confidence interval, based on the same sample, would be larger compared to the 95% interval.
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Which type of factoring is required to change x2 - 16 into factored form?
a.)Greatest Common Factor
b.) Difference of Squares
c.) Trinomial Factoring
suppose that you ask a random friend of yours appropriate questions to get answers that represent the variables above. they are 19 years old, 173 cm tall, and has an annual salary of $27.3 k. what would be their predicted success factor based upon your data and model? show work to justify your answer.
The predicted success factor for your friend based on the given data and model is 301.71.
To predict the success factor of your friend based on the given data and model, we can use the following equation:
Success Factor = BT0 + BT1 × Age + BT2 × Height + BT3 × Annual Salary
Substituting the values for age, height, and annual salary, we get:
Success Factor = -30.2 + 19.3 * 19 + -0.2 × 173 + 1.7 × 27.3
Success Factor = -30.2 + 365.7 + -34.6 + 46.61
Success Factor = 301.71
To predict the success factor of your friend based on the given data and model, we need to plug in their values for age, height, and annual salary into the equation for the model:
Y = BTX
Where Y is the success factor, BT is the vector of coefficients for the model, and X is the vector of values for age, height, and annual salary.
Substituting in the values for BT and X, we have:
Y = (-30.2, 19.3, -0.2) × (19, 173, 27.3)
Performing the matrix multiplication, we get:
Y = (-30.2 × 19) + (19.3 × 173) + (-0.2 × 27.3)
Y = -576.8 + 3335.9 - 5.46
Y = 2553.5
Therefore, the predicted success factor for your friend based on the given data and model is 2553.5.
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Which of the following is the correct sequence of project phases? O A. Concept - Planning - Definition O B. Definition - Planning - Performance O C. Postcompletion - Performance - Planning OD. Performance - Concept - Planning
The correct sequence of project phases is Definition - Planning - Performance. The correct answer is B.
This is the typical order of project phases in a traditional project management approach. It starts with the definition phase, where the project's goals, the scope, and the requirements are established.
Then comes the planning phase, where the project plan is developed, including the allocation of resources, scheduling, and budgeting.
Finally, the performance phase begins, during which the project activities are executed, monitored, and controlled to ensure the successful project completion.
Therefore the sequence of project phase is Definition - Planning - Performance The correct answer is B.
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suppose a normal distribution has a mean of 79 and a standard deviation of 7 what is p if x is greater than or equal to 93
Given a population X with normal distribution with mean μ=79 and standard deviation σ=7
You have to calculate the probability of X greater than or equal to 93, symbolically:
\(P(X\ge93)\)To calculate this probability you have to "transform" this value to the standard normal distribution. You have to use the standard normal or Z distribution because it is tabulated, i.e. its values and accumulated probabilities are known.
To translate a value of any normal distribution to a value of the standard normal distribution you have to subtract the mean and divide by the standard deviation.
The standard normal distribution is defined as:
\(Z=\frac{X-\mu}{\sigma}distN(0,1)\)Calculate the Z value
\(Z=\frac{93-79}{7}=2.00\)So the probability you have to calculate is
\(P(X\ge93)=P(Z\ge2.00)\)Now the tables of the standard normal distribution indicate the accumulated probabilities, to determine the probability above a determined value, you have to subtract the probability accumulated until that value to the total probability.
Remember that for any distribution of probability, the total probability is always 1. So under The normal distribution or the standard normal distribution, the total area of under the curve is 1
\(P(Z\ge2.00)=1-P(Z<2.00)\)In the Z table (right entry) look for the corresponding value of the probability
\(P(Z<2.00)=0.977\)So
\(1-P(Z<2.00)=1-0.977=0.023\)The probability of X is greater than or equal to 93 is 0.023
\(P(X\ge93)=0.023\)