The probability that the secretary will receive 6 calls next hour is approximately 0.090 or 9.0%.
The Poisson distribution is a probability distribution that describes the number of events occurring in a fixed time interval, given the average rate at which events occur and the independence of events. In this case, the average rate of calls is 3 calls per hour.
The probability of receiving exactly 6 calls next hour can be calculated using the Poisson probability formula:
[tex]P(X = 6) = (e^(-λ) * λ^6) / 6![/tex]
where λ is the average rate of calls, e is the base of the natural logarithm, and 6! is the factorial of 6.
Substituting the values, we get:
[tex]P(X = 6) = (e^(-3) * 3^6) / 6! ≈ 0.090[/tex]
Therefore, the probability that the secretary will receive 6 calls next hour is approximately 0.090 or 9.0%.l
Learn more about the probability
https://brainly.com/question/30034780
#SPJ4
The probability that the secretary will receive 6 calls next hour is approximately 0.0504, or 5.04%
To calculate the probability that the secretary will receive 6 calls next hour, given that the average is 3 calls per hour
and the Poisson distribution applies, follow these steps:
Identify the given information: λ (average calls per hour) = 3, k (number of calls to calculate the probability for) = 6.
Use the Poisson probability formula:
P(k) =[tex](e^{(-\lambda)} \times\lambda^k) / k!,[/tex]
where P(k) is the probability of k calls,
e is the base of the natural logarithm (approximately 2.71828),
λ is the average rate (3 calls per hour), and
k! is the factorial of k (6 in this case).
Calculate [tex]e^{(-\lambda)}: e^{(-3)} = 0.04979.[/tex]
Calculate [tex]\lambda^k: 3^6 = 729.[/tex]
Calculate k!: 6! = 6 × 5 × 4 × 3 × 2 × 1 = 720.
Substitute these values into the formula: P(6) = (0.04979 × 729) / 720 ≈ 0.0504.
for such more question on probability
https://brainly.com/question/13604758
#SPJ11
A textbook store sold a combined total of 300 physics and biology textbooks in a week. The number of physics textbooks sold was 72 more than the number of biology textbooks sold. How many textbooks of each type were sold?
Hence, 186 physics textbooks and 114 biology textbooks were sold as it states that 300 textbooks were sold in total.
what is equation ?The formulas 2x + 3 and 7, for instance, are identical when written as 2x + 3 = 7, where x has been the variable. The x-value that fulfils the equality can be found by solving this equation. In this instance, we can take 3 out of both sides to get 2x = 4, and thereafter divide each sides by 2 to get x = 2. To describe relationships amongst quantities and to solve issues, equations are used widely in mathematics as well as in chemistry, chemistry, economics, and other sciences. They are also utilised in daily life, such as in financial computations and the solution of time, distance, and speed-related issues.
given
Assume that x biology textbooks were sold in total.
The issue states that there were 72 more physics textbooks sold than there were biology textbooks. Hence, x + 72 is the total number of physics textbooks sold.
It states that 300 textbooks were sold in total. Thus, we can create the following equation:
[tex]x + (x + 72) = 300[/tex]
When we simplify and find x, we obtain:
[tex]2x + 72 = 300\\2x = 300 - 72[/tex]
2x = 228
x = 114
Hence, 114 biology textbooks were sold.
The quantity of sold physics textbooks is given by x + 72, or 114 + 72 = 186.
Hence, 186 physics textbooks and 114 biology textbooks were sold as it states that 300 textbooks were sold in total.
To know more about equation visit:
https://brainly.com/question/649785
#SPJ1
A teacher surveyed her class after they had taken a vocabulary test. Eighteen of the students claimed they had studied
at least one hour for the test. The remaining twelve students admitted that they had not studied for the test at all. The
test results (expressed as a percent) for the two groups are shown below.
Studied: 88, 100, 94, 79, 92, 100, 95, 83, 89, 99, 100, 91, 89, 95, 100, 93, 96, 84
Did Not Study: 82, 72, 45, 91, 58, 83, 65, 87, 90, 77, 73, 89
1. Calculate the range and Interquartile range for each set of data.
2. Using complete sentences, compare the data sets based on your results in part A.
NEED THIS ASAP PLEASE
The coordinates of P are (-3, 8) and the coordinates of Q are (9, -2).
Find the equation of the line parallel to PQ that passes through the point (6, -1).
The equation of the line parallel to PQ that passes through the point (6, -1) is y = (-5/6)x + 4.
What is the equation of the line parallel to PQ that passes through the point (6, -1)?The formula for equation of line is expressed as;
y = mx + b
Where m is slope and b is y-intercept.
Given that: the coordinates of P are (-3, 8) and the coordinates of Q are (9, -2).
We can find the slope of line PQ.
m = (y2 - y1) / (x2 - x1)
Where (x1, y1) and (x2, y2) are the coordinates of points P and Q, respectively.
m = (-2 - 8) / (9 - (-3))
m = -10 / 12
m = -5/6
Since we want the equation of a line parallel to PQ, it will have the same slope.
Hence, the equation of the line can be written as:
y - y1 = m(x - x1)
where (x1, y1) is the point (6, -1) and m is the slope we found earlier.
Plugging in the values, we get:
y - (-1) = (-5/6)(x - 6)
y + 1 = (-5/6)x + 5
y = (-5/6)x + 5 - 1
y = (-5/6)x + 4
Therefore, the equation of the parallel line to PQ is y = (-5/6)x + 4.
Learn more about equation of line here: brainly.com/question/2564656
#SPJ1
What is the value of x in the equation 2x + 3 = 11?
Answer: x=4
Step-by-step explanation:
Isolate x using opposite operations.
2x + 3 = 11
2x = 8
x = 4
Answer:
4
Step-by-step explanation:
subract 3 from 11
2x=8
divide by 2
x=4
Adding and subtracting decimals
1) 34.12 - 41.23 + 14.01
2) -34.12 + 41.23 - 14.01
Combine all positive numbers:
Combine all negative numbers:
Rewrite:
(look at the picture)
Answer:
1Step-by-step explanation:
NEED HELP FAST PLEASE HURRY INDEED OF HELP
Answer:
Step-by-step explanation:
Hopefully this is right.
Area = (pi)r²
Which is pi times the the radius squared
The radius is 2, so 2² is 4, So we multiply 3.14, which is pi, by 4.
Multiply 3.14 by 4, and the answer is 12.56, the question says round to the nearest tenth, so the final answer will be 12.6
My math teacher back in 7th grade gave us this sentence to help us memorize the equations.
Cherry Pie Delicious (C=(pi)d), Apple Pie Are Too (A=(pi)r²)
Do the same with the other two questions, and the answer for question two will be 3.14, rounded to the nearest tenth will be 3.1
Question three do the same as well, and the answer will be 660.185, rounded will be 660.2
Hope this helps!
exploratory data analysis 1. when considering the research question, identify the two variables predictor (explanatory) variable: response variable: 2. use minitab to first create a scatterplot. minitab> graph > scatterplot how would you characterize the association between these two variables? a. linear or nonlinear? b. negative, none, or positive?
Identify the predictor and response variables, then create a scatterplot in Minitab. Characterize the association between the variables as linear or nonlinear and negative, none, or positive.
In exploratory data analysis, the first step is to identify the research question and the two variables of interest. The predictor variable (also known as the explanatory variable or independent variable) is the one that is used to explain or predict the outcome of the response variable (also known as the dependent variable).
After identifying the two variables, one can use software such as Minitab to create a scatterplot of the data. The scatterplot helps to visualize the relationship between the two variables.
To characterize the association between the two variables, we would first determine if the relationship appears to be linear or nonlinear. If the relationship is roughly linear, we would then determine if it is negative (meaning that as one variable increases, the other tends to decrease), positive (meaning that as one variable increases, the other tends to increase), or none (meaning that there is no clear trend).
Learn more about linear or nonlinear.
https://brainly.com/question/31510530
#SPJ4
A sphere has a diameter of 28 millimeters.solve for cubic millimeters
The volume of the sphere with a diameter of 28 millimeters is 4398.23 cubic millimeters.
To find the volume of a sphere with a diameter of 28 millimeters, we can use the formula for the volume of a sphere, which is V = (4/3)πr³, where V is the volume, r is the radius, and π (pi) is a mathematical constant approximately equal to 3.14159.
Step 1: Calculate the radius.
Since the diameter is 28 millimeters, the radius is half of that, which is 14 millimeters (28/2).
Step 2: Use the volume formula.
V = (4/3)πr³
V = (4/3)π(14³)
Step 3: Calculate the volume.
V = (4/3)π(2744)
V ≈ 4398.23 cubic millimeters
So, the volume of the sphere with a diameter of 28 millimeters is approximately 4398.23 cubic millimeters.
Learn more about volume here,
https://brainly.com/question/218706
#SPJ1
How to calculate a derivative using implicit differentiation
To calculate a derivative using implicit differentiation, follow these steps:
1. Write down the equation:
2. Differentiate both sides with respect to x:
3. Solve for dy/dx or y':
4. Simplify the result:
Write down the equation:
Start by writing down the equation involving both variables x and y, where y is an implicit function of x.
Differentiate both sides with respect to x: Apply the chain rule, product rule, or quotient rule, as needed, while differentiating both sides of the equation with respect to x.
Remember that when differentiating any term involving y, you'll also need to multiply by the derivative of y with respect to x, denoted as dy/dx or y'.
Solve for dy/dx or y': After differentiating both sides, you will have an equation involving dy/dx or y'.
Solve for this term to find the derivative.
Simplify the result: Simplify your answer as much as possible, if needed.
Remember to use implicit differentiation when the equation is not easily solved for y in terms of x.
It's a powerful technique that helps find derivatives in situations where explicit differentiation isn't feasible.
For similar question on differentiation.
https://brainly.com/question/30567791
#SPJ11
Let an be the number of ways to climb n stairs Identify the recurrence relation for the number of ways to climb n stairs if the person climbing the stairs can take one stair or two stairs at a time. O an = an + 1 + an + 2 O an = an-1+an - 2 O an= an-1+ an-2
The total number of ways to climb n stairs is the sum of the number of ways to climb n-1 stairs and the number of ways to climb n-2 stairs.
What is recurrence relation?An equation that represents a sequence based on a rule is called a recurrence relation. Finding the following term (next term) based on the prior term (previous term) is made easier.
The recurrence relation for the number of ways to climb n stairs if the person climbing the stairs can take one stair or two stairs at a time is:
an = an-1 + an-2
This is because to climb n stairs, the person can either take one stair from n-1 stairs and climb the remaining n-1 stairs, or take two stairs from n-2 stairs and climb the remaining n-2 stairs.
Therefore, the total number of ways to climb n stairs is the sum of the number of ways to climb n-1 stairs and the number of ways to climb n-2 stairs.
Learn more about recurrence relation on:
https://brainly.com/question/31043337
#SPJ4
FIND ZC OF THIS CIRCLE
The value of ZC is 16 units for the given circle and its identities.
What is a tangent of a Circle?A straight line that touches the circle at a single point—the point of tangency—is the tangent of a circle. The digression is opposite to the span of the circle at the place of juncture, and it broadens outward from the circle in the two bearings.
In the circle two external secant segments are LE and ZE, according to the external secant theorem;
⇒ LE × DE = ZE × CE (Here, ZE = ZC + 2)
⇒ 9 × 4 = (ZC + 2) × 2
⇒ ZC + 2 = 18
⇒ ZC = 18 - 2
⇒ ZC = 16
Therefore, the value of ZC is 16 units.
To know more about Circle, visit:
https://brainly.com/question/8952990
#SPJ1
Deduce the 3-digit secret number.
[A cow means a number is correct in value but in the wrong
position. A bull indicates that a number is both correct in
value and in the correct position. I. E. 2 cows and 1 bull wou
indicate that all three numbers were correct but two were in
the wrong positions. ]
If "cow" means that number is correct in value but in the wrong position, then the three-digit secret number is 714.
A "cow" means a digit is "correct in value" but in the "wrong position".
A "bull" means a digit is both "correct in value" and in the "correct position".
⇒ For the first guess (751),
There is 1 cow and 1 bull, which means that one digit is "correct in value" and in the "correct position" (1 bull), and another digit is "correct in value" but in the "wrong position" (1 cow).
⇒ For the second-guess (574),
There is 1 cow and 1 bull, which indicates that "one-digit" is "correct in value" and in the "correct position", and "another-digit" is "correct in value" but in the "wrong-position".
⇒ For the third guess (317),
There is 1 cow and 1 bull, which means that "one digit" is "correct in value" and in the "correct position", and "another digit" is "correct in value" but in the "wrong position".
So, Based on these clues, we can say that the correct secret number has 1 cow and 1 bull.
This means that two digits in the secret number are correct in value, with one digit in the correct position (1 bull), and another digit in the wrong position (1 cow). So, the secret number is likely 714, because it satisfies these conditions.
Learn more about Secret Number here
https://brainly.com/question/2362401
#SPJ4
The given question is incomplete, the complete question is
Deduce the 3-digit secret number.
[A cow means a number is correct in value but in the wrong position. A bull indicates that a number is both correct in value and in the correct position. i.e. 2 cows and 1 bull would indicate that all three numbers were correct but two were in the wrong positions. ]
Guess Secret Number Cows Bulls
1st 751 1 1
2nd 574 1 1
3rd 317 1 1
dentify the values of `a`, `h`, and `k` in the given function.
`y=\frac{5}{x+6}-2`
The values of a, h, and k are 5, -6 and -2, respectively
Identifying the values in the function.In the given function:
y = 5/(x+6) - 2
The function is in the form of a rational function, f(x) = a/(x-h) + k, where a = 5, h = -6, and k = -2.
Therefore, the values of a, h, and k are:
a = 5 (the numerator of the fraction)h = -6 (the value subtracted from x in the denominator of the fraction)k = -2 (the constant term added or subtracted to the rational function)Read more about function at
https://brainly.com/question/28532394
#SPJ1
Find the area of the circle. Round your answer to the nearest hundredth. Use $3.14$ or $\frac{22}{7}$
for $\pi$ .
area: about
ft2
The area of the given circle is 1.76625 square feet.
How to find the area of the circle?Remember that the area of a circle of radius R is given by the formula:
A = pi*R²
Where pi = 3.14
Here we know the diameter (2 times the radius) of the circle, which is 1.5ft, then the radius is:
R = 1.5ft/2 = 0.75ft
Then the area of the circle is:
A = 3.14*(0.75ft)²
A = 1.76625 ft²
Learn more about area at:
https://brainly.com/question/24487155
#SPJ1
What happens when the function f(x) = 2 sin(2) is transformed by the rule g (w) = - f(x)?
• f(x) is stretched away from the x-axis by a factor of 2 and is reflected over the x-axis.
O f(x) is reflected over the y-axis.
O f(x) is reflected over the x-axis.
• f(x) is compressed toward the y-axis by a factor of 1/2 and is reflected over the y-axis
Answer:
• f(x) is stretched away from the x-axis by a factor of 2 and is reflected over the x-axis.
Step-by-step explanation:
The function f(x) = 2sin(2x) has an amplitude of 2 and a period of π/2. When we apply the rule g(w) = - f(x), we are reflecting the graph of f(x) over the x-axis and then taking its opposite. This means that the amplitude of g(w) will still be 2, but the graph will be reflected and stretched away from the x-axis by a factor of 2.
I hope it helps you
How many times can 3.6 go into 80
Answer:
22.2
Step-by-step explanation:
Answer:
3.6 can go into 80 22 times.
Step-by-step explanation:
Two lines intersect such that the measure of one of the angles formed by the lines
is five times the measure of another of the angles formed by the lines. What are
the measures of the angles formed by the lines?
The measure of the angles formed by the lines are 30°, 30°, 150° and 150° by definition of vertically opposite angles.
When two straight lines intersect each other at some angle, say line AB intersect line CD, then the opposite angles formed by the two lines are called vertically opposite angles. A pair of vertically opposite angles are equal to each other.
There are two pairs of opposite angles formed by intersection of two straight lines.
The total sum of all the angles formed by intersection of two straight lines is 360°.
Let angle X = x° and angle Y= y° be a pair of opposite angles.
Let the other pair of opposite angles be of angle M = m° and angle N = n°.
Thus, by definition of opposite angles and sum of all angles on intersection of two lines we get,
angle X + angle Y + angle M + angle N = 360°
⇒ x° + y° + m° + n° = 360°
⇒ x° + x° + m° + m° = 360°
⇒ 2( x° + m°) = 360°
⇒ x° + m° = 180° ___ (1)
Also, the measure of one of the angles is five times the measure of another of the angles formed by the lines.
This relation can be written as,
angle X = 5 times of angle M
⇒ x° = 5m° ___(2)
Since angle X and angle M are not a pair of opposite angles but are supplementary angles as observed in equation (1).
Putting equation (2) in equation (1) we get,
5m° + m° = 180°
⇒ 6m° = 180°
⇒ m° = 30°
Thus, x° = 5(30°) = 150°
Hence the angles are 30°, 30°, 150° and 150°.
To know more about measures of angles and vertically opposite angles here
https://brainly.com/question/29147905
#SPJ4
a) find the area above 66 for a n(60,10) distribution b) find the area below 48 for a n(60,10) distribution.
In normal distribution the area above 66 for a n(60, 10) is 0.726
What is normal distribution?
In probability theory and statistics, the Normal Distribution, which is also called the Gaussian Distribution, is the most significant continuous probability distribution. It is also called a bell curve. In this distribution a large number of random variables are either nearly or exactly represented. Moreover, it can be used to approximate other probability distributions,
From the given data n(60, 10) so mean = 60 and standard deviation= 10
Now x≥ 66
so the z-score will be (66-60)/10
= 6/10
= 0.6
Now P(z>0.6)= 1- P(z< 0.6)
= 0.726
So, in normal distribution the area above 66 for a n(60, 10) is 0.726.
To know more about normal distribution
https://brainly.com/question/23418254
#SPJ4
Kevin has a remote control car. Every 3/40 of a second, the remote control car travels 3/ 8 of a foot. How many feet per second does the remote control car travel?
The number of feet per second that the remote control car travels is: 5 ft/s
How to divide fractions?The formula to find the speed from distance and time is:
Speed = Distance/time
Now, we are given:
Time: t = 3/40 seconds
Distance = 3/8 ft
Thus:
Speed = (3/8)/(3/40)
Speed = (3/8) * (40/3)
Speed = 5 ft/s
Thus, that is the speed that the remote control car travels
Read more about fraction division at: https://brainly.com/question/1622425
#SPJ4
Which inequality represents the values of that ensure triangle ABC exists?
A
2x + 4
B
18
6x
O A. < x < 1/1
OB. -< < 1/1
O C.
1 < x < 5
OD. 2 < x < 6
C
The Inequality which ensure triangle exists is 22 > 4x > 7.
What is inequality ?Inequality is defined as the relation between two quantities with the sign of inequality that is >, <, ≤ , ≥ ."
Theorem used In ΔABC,
AB + BC >AC
AC+ BC >AB
AC + AB > BC
According to the question,
In triangle ABC.
AC = 18units
BC = 6x units,
AB = 2x + 4 units
.
Substitute the value in the inequality to ensure triangle exists we get 4x > 7 and 22 > 4x.
From (1) and (2) inequality of triangle we get 22 > 4x > 7.
Hence, Inequality which ensure triangle exists is 22 > 4x > 7.
Learn more about Inequalities on
https://brainly.com/question/11317965
#SPJ1
Which inequality represents the values of that ensure triangle exists? a triangle with these side lengths: AC = 18 units, BC = 6x units, and AB = 2x + 4 units
Find ß in degrees. B 12 7 [?]° Round to the nearest hundredth.
Answer:
Set your calculator to degree mode.
[tex] \tan( \beta ) = \frac{7}{12} [/tex]
[tex] \beta = {tan}^{ - 1} \frac{7}{12} = 30.26 \: degrees[/tex]
it is known that roughly 2/3 of all human beings have a dominant right foot or eye. is there also right-sided dominance in kissing behavior? an article reported that in a random sample of 127 kissing couples, both people in 79 of the couples tended to lean more to the right than to the left.
It is possible that there is right-sided dominance in kissing behavior, based on the reported study. The fact that in a random sample of 127 kissing couples, both people in 79 of the couples tended to lean more to the right than to the left suggests a pattern of right-sided dominance.
However, it is important to note that this study alone is not conclusive evidence of right-sided dominance in kissing behavior.
Further research would be needed to confirm whether there is a consistent pattern of right-sided dominance in kissing behavior across different populations and cultures. It is also possible that other factors, such as social or psychological factors, could influence the direction in which people lean during a kiss. Therefore, it is important to approach this topic with caution and not draw any firm conclusions based on a single study.
Learn more about right-sided dominance
https://brainly.com/question/10709533
#SPJ4
Question 4 of 10
Does this table represent a function? Why or why not?
X
2
3
4
5
5
y
1
4
4
2
5
OA. Yes, because there is the same number of x-values as y-values.
OB. Yes, because every x-value corresponds to exactly one y-value.
C. No, because one x-value corresponds to two different y-values.
OD. No, because two of the y-values are the same.
Does this table represent a function: C. No, because one x-value corresponds to two different y-values.
What is a function?In Mathematics and Geometry, a function can be defined as a mathematical equation which is typically used for defining and representing the relationship that exists between two or more variables such as an ordered pair.
This ultimately implies that, all functions are used in mathematics to uniquely map an input variable (domain or independent values) to an output variable (range or dependent values).
Based on the table shown above, we can reasonably infer and logically deduce that it does not represent a function because the input values (domain or independent values) are not uniquely mapped to the output values (range or dependent values);
3 → 4
4 → 4
Read more on function here: https://brainly.com/question/27862183
#SPJ1
Miriam was testing � 0 : � = 18 H 0 :μ=18H, start subscript, 0, end subscript, colon, mu, equals, 18 versus � a : � < 18 H a :μ<18H, start subscript, start text, a, end text, end subscript, colon, mu, is less than, 18 with a sample of 7 77 observations. Her test statistic was � = − 1.9 t=−1.9t, equals, minus, 1, point, 9. Assume that the conditions for inference were met.
The requreid Miriam's test does not provide significant evidence that the true population mean is less than 18.
Since the sample size is small (n = 7) and the population standard deviation is unknown, we should use a t-test for this hypothesis test.
The test statistic is calculated as follows:
t = (x - μ) / (s / √n)
Given that Miriam's test statistic is t = -1.9, we can estimate the p-value associated with this test statistic. This denotes the probability of observing a test statistic as extreme as -1.9 or more extreme, assuming the null hypothesis is true.
Using a t-distribution table with 6 degrees of freedom (n-1), we find that the p-value for a one-tailed test at the 5% significance level is approximately 0.051.
Since the p-value (0.051) is greater than the significance level (0.05), we fail to reject the null hypothesis. We do not have sufficient evidence to conclude that the population mean is less than 18 at a 5% level of significance.
Thus, Miriam's test does not provide significant evidence that the true population mean is less than 18.
Learn more about the hypothesis here:
https://brainly.com/question/29519577
#SPJ1
Show that 2 5/8÷ 1 1/6= 2 1/4
Answer: True
9/4 = 2 1/4
Step-by-step explanation:
:) See the images below to know more.
Draw triangle PQR where PQ has length 4 cm PR has length 3.5 cm and angle RPQ is 32° 
Write linear equation in slope intercept form:1/4x+y=-2/7
The given linear equation in slope intercept form is y = -1/4(x) - 2/7.
What is the slope-intercept form?In Mathematics and Geometry, the slope-intercept form of the equation of a straight line is given by this mathematical equation;
y = mx + c
Where:
m represents the slope or rate of change.x and y are the points.c represents the y-intercept or initial value.By making "y" the subject of formula, we have the following:
1/4x + y = -2/7
y = -1/4(x) - 2/7
By comparison, we have the following:
Slope, m = -1/4.
y-intercept, c = -2/7.
Read more on slope-intercept here: brainly.com/question/7889446
#SPJ1
Find the length of the third side. If necessary, round to the nearest tenth
Answer:
3.6
Step-by-step explanation:
a^3+b^2=c^2
3^2+2^2=c^2
9+4=c^2
13=c^2
square root to get c alone
3.6055512754639=c
rounded= 3.6
Answer: 3.6
Step-by-step explanation: pythagorean theorem
A^2 + B^2 = C^2
3^2=9
2^2=4
13
Square root of 13 rounded to nearest 10th
3.6
Raw answer: 3.60555127546
Which is the only congruence theorem that cannot be use to prove these triangles to be congruent?
A
SAS
B
AAS
C
SSS
D
ASA
The only congruence theorem that cannot be used to prove these triangles to be congruent is option B, AAS (Angle-Angle-Side).
The SAS (Side-Angle-Side), SSS (Side-Side-Side), and ASA (Angle-Side-Angle) congruence theorems all involve matching corresponding sides and angles of two triangles. However, AAS only matches two angles and a non-included side, which is not enough to guarantee congruence in all cases.
In fact, the AAS congruence theorem only works if the given non-included side is between the two given angles, forming a "triangle sandwich" with the two given angles as the bread and the non-included side as the filling.
If the non-included side is not between the two given angles, then it is possible to have two non-congruent triangles with the same angle measures, but different side lengths.
Therefore, the AAS congruence theorem cannot be used to prove all cases of triangle congruence, making it the only option that cannot be used to prove these triangles to be congruent
Learn more about AAS congruence theorem here:
https://brainly.com/question/30094772
#SPJ1
Mr. Johnson took the price of a watch that was listed at $60 and marked it up by 30%. After the mark up, What is the selling price of the watch?
Answer:
$78
Step-by-step explanation:
60+30% = 78
...................