The expression that represents how much Jade will pay for a sweater that costs x dollars, not including tax, is 0.765x.
If a sweater normally costs x dollars, a sale reduces the price by 10%. Therefore, the sale price is (1-0.10)x or 0.9x dollars. Then, if Jade has a coupon to save 15%, the price will be further reduced by 15% of 0.9x dollars, which is 0.15(0.9x) or 0.135x dollars.
Therefore, the total price that Jade will pay for the sweater is the sale price minus the discount from the coupon, which is (0.9x - 0.135x) or 0.765x dollars. This can be simplified as 0.765 times the original cost of the sweater, or 76.5% of the original price.
Thus, the expression that represents how much Jade will pay for a sweater that costs x dollars, not including tax, is 0.765x.
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Complete question is:
A sweater normally cost x dollars. A sale reduces the price of the sweater by 10% . Jade also has a coupon to save 15%. Which expression represents how much Jade will pay for a sweater that costs x dollars, not including tax?
5 to the power of 2x=20
The approximate value of x in the equation 5 to the power of 2x=20 is 0.93
Calculating the value of xFrom the question, we have the following parameters that can be used in our computation:
5 to the power of 2x=20
As an expression, we have
5^(2x) = 20
Take the natural logarithm of both sides
so, we have the following representation
2x = ln(20)/ln(5)
Evaluate the quotients
This gives
2x = 1.86
So, we have
x = 0.93
Hence, the value of x is 0.93
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a couple decide they want to have 6 children. use binomial probability to find the probability of having the same number of boys and girls.
This means that there is a [tex]31.25%[/tex] chance of having the same number of boys and girls, or roughly [tex]0.3125.[/tex]
The binomial-probability formula can be used to determine the likelihood of having a specific number of boys and girls, assuming that the odds of having either a boy or a girl are equal, which is [tex]1/2:[/tex]
[tex]C(n,k) = P(X=k) * p^k * (1-p)^{n-k}[/tex]
Where:
k is the number of successes, which is the number of boys the couple wants to have and is also equal to the number of girls because they want an equal number of each; in this case,[tex]k = 6[/tex], where n is the number of tries, which is the number of children the couple expects to have. As a result,[tex]k = n/2 = 3[/tex] and p is the success-probability, which is equal to the likelihood of having a boy or girl, which is equals to [tex]1/2[/tex]. [tex]C(n,k) = n! / (k! * (n-k)!)[/tex], where! stands for the factorial function, is the number of combinations of n things taken k at a time.
[tex]0.3125.[/tex]
When these values are added to the formula:
[tex]P(X=3) = C(6,3) × (1/2)^3 * (1/2)^(6-3) \\= 20 * (1/2)^6\\= 0.3125[/tex]
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A jet airplane reaches 846. Km/h on a certain flight. What distance does it cover in 13.0 min? Set the math up. But don't do any of it. Just leave your answer as a math expression. Also, be sure your answer includes all the correct unit symbols.
Answer:
Distance = (846 km/h) × (13.0 min × (1 h / 60 min))-----------------
To find the distance you can use the formula:
Distance = Speed × TimeGiven:
Speed = 846 km/hTime = 13.0 minFirst, we need to convert the time from minutes to hours:
13.0 min × (1 h / 60 min)Now, set up the equation using the given values and units:
Distance = (846 km/h) × (13.0 min × (1 h / 60 min))the sum of a number and the cube of a second number is 864. find the number so that the product is a maximum. calculus
To find the number that maximizes the product, we need to use calculus. Let's start by setting up the problem. Let x be the first number and y be the second number. We know that: x + y^3 = 864. We want to find the maximum value of xy.
Now, substitute this expression for x into our product function:
P(y) = (864 - y^3) * y
To find the maximum, we need to take the derivative of P(y) with respect to y and set it equal to 0:
dP/dy = -3y^4 + 864y - y^3(dy/dy)
dP/dy = -3y^4 + 864y - y^3(1)
Now, set dP/dy = 0 and solve for y:
0 = -3y^4 + 864y - y^3
It's a challenging polynomial to solve, but we can use numerical methods or technology to find the critical points of y.
Once we have the value(s) of y, we can plug it back into the equation x = 864 - y^3 to find the corresponding value(s) of x.
Finally, determine whether the critical points result in a maximum by checking the second derivative or analyzing the function's behavior around the critical points. The pair of numbers (x, y) will yield the maximum product.
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an urn contains 13 white balls and 7 green balls. a sample of seven is selected at random. what is the probability that the sample contains at least one green ball?huffled standard 52-card deck of cards. what is the probability that the hand contains 4 jacks?
the probability of the sample containing at least one green ball when selecting 7 balls randomly is approximately 0.9779 or 97.79%.
To find the probability that the sample contains at least one green ball, it's easier to calculate the probability of the complementary event (not getting any green balls) and then subtract that from 1. The complementary event would be selecting all 7 balls as white balls.
1. Total balls in the urn = 13 white balls + 7 green balls = 20 balls
2. Calculate the probability of selecting 7 white balls:
- Number of ways to choose 7 white balls out of 13 = C(13,7) = 1716
- Number of ways to choose 7 balls out of 20 = C(20,7) = 77520
- Probability of selecting 7 white balls = 1716 / 77520 = 0.0221267
3. Calculate the probability of getting at least one green ball:
- Probability of at least one green ball = 1 - Probability of 7 white balls
- Probability of at least one green ball = 1 - 0.0221267 = 0.9778733
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z varies with y and inversely with x when z=6, x=4, and y=3
If z varies with y and inversely with and z = 6 when x = 4 and y = 3, then the value of Proportionality Constant is given by 8.
Proportion is a relation between two mathematical variables. If two variables vary directly that states if one increases another will also decrease and same for decrease.
If two variables are in inverse relation that states that if one variable increases then another decreases and if one variable decreases then another increases.
Given that, z varies with y and inversely with x. So,
z = k*(y/x), where k is the proportionality constant.
Given that, z = 6 when x = 4 and y = 3. So,
6 = k*(3/4)
k = (6*4)/3
k = 2*4
k = 8
Hence the value of Proportionality Constant is 8.
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The question is incomplete. The complete question will be -
"z varies with y and inversely with x when z=6, x=4, and y=3. Find the value of Proportionality Constant."
Jeremiah is working on a model bridge. He needs to create triangular components, and he plans to use toothpicks. He finds three toothpicks of lengths 4 in., 5 in., and 1 in. Will he be able to create the triangular component with these toothpicks without modifying any of the lengths?
• Yes, according to the Triangle Inequality TheoremYes, according to the Triangle Sum Theorem
No, according to the Triangle Inequality Theorem
• No, according to the Triangle Sum Theorem
No, according to the triangle inequality theorem he will not be able to create the triangular component. That is option C
What is triangular inequality theorem?The triangular inequality theorem states that the sum of any two sides of a triangle is greater than the length of the third side.
That is;
a+b > c
a+ c > b
b+c > a
The lengths given include the following;
a = 4 in
b = 5 in
c = 1 in
Using the theorem;
a+b = 4+5 = 9 > 1
a+c = 4+1 = 5 = 5
b+c = 5+1 = 6> 4
Therefore he won't be able to create a triangular component using the three lengths of the tooth pick because is goes against the triangle inequality theorem rule.
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Answer:
Step-by-step explanation:
the answer is A
i took the text
A 8-kg block is set moving with an initial speed of 6 m/s on a rough horizontal surface. If the force of friction is 12 n, approximately how far does the block travel before it stops?.
The block will cover the distance 12m before it stops.
Newton's second law of motion:According to Newton's second law of motion, the acceleration a
of a body of mass m is determined by the net force [tex]F_n_e_t[/tex] acting on it:
[tex]F_n_e_t[/tex] = ma.
The mass of a block, m = 8 kg
The initial speed of the block on rough horizontal surface , u = 6 m/s
The force of friction, F = 12N
We know that, the Newton's 2nd law: [tex]F_n_e_t[/tex] = ma.
Therefore, its final velocity is zero, v = 0
Since the only force that is acting on the body along the horizontal direction is the kinetic frictional force
[tex]F_n_e_t[/tex] = ma. ([tex]F_n_e_t[/tex] is acting in opposite direction to that of object motion)
a = [tex]\frac{f_n_e_t}{m}[/tex] = [tex]\frac{-12}{8} = -1.5m/s^2[/tex]
Negative sign shows that it is in the opposite direction to that of initial velocity.
By using the third kinematic equation, we get:
[tex]v^2=u^2+2as\\\\= > s = \frac{0-6^2}{2(-1.5)}\\ \\s = \frac{36}{3} = 12m[/tex]
Therefore, the block will cover the distance 12m before it stops.
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On Thursday night Antonio watched a movie that was 1 hour and 43 minutes long. If the movie ended at the time shown on the clock below, what time did Antonio start watching the movie? Be sure to include a.m. or p.m. in your answer.
Antonio started watching the movie at 5:17pm
At what time did Antonio start the movie?If the movie ended at 7:00pm, and we know that the movie was 1 hour and 43 minutes long, we can then subtract 1 hour and 43 minutes from 7:00pm to find out what time Antonio started the movie.
To subtract 1 hour and 43 minutes from 7:00pm:
We will first convert 7:00pm to 24-hour format which is 19:00.We can subtract 1 hour and 43 minutes which gives us:= 19:00 - 1:43
= 17:17
As a 24-hour mode, when we convert 17:17 to 12 hours, this gives us 5:17pm.
Note: The movie ended at 7:00pm
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An SRS of 20 orangutans is selected, and 65 cc of blood is to be drawn from each orangutan using a 100 cc syringe. In the sample, the mean volume is 64 cc and the standard deviation is 12 cc. Assume that in the population of all such procedures, the amount of blood drawn follows a Normal distribution with mean ?.
Reference: Ref 17-1
We are interested in a 95% confidence interval for the population mean volume. The margin of error associated with the confidence interval is
Answer
A. 4.64.
B. 2.68.
C. 6.84.
D. 5.62.
The margin of error associated with the 95% confidence interval for the population mean volume is: D. 5.62.
To calculate the 95% confidence interval for the population mean volume, we can use the formula:
CI = x ± (t * (s/√n))
Where CI represents the confidence interval, x is the sample mean, t is the t-score associated with the desired confidence level (95%), s is the sample standard deviation, and n is the sample size.
In this case, x = 64 cc, s = 12 cc, and n = 20 orangutans. We need to find the t-score for a 95% confidence interval with 19 degrees of freedom (n-1). Using a t-table, we find that the t-score is approximately 2.093.
Now we can calculate the margin of error:
Margin of Error = t * (s/√n) = 2.093 * (12/√20) ≈ 5.62
Therefore, the margin of error associated with the 95% confidence interval for the population mean volume is: D. 5.62.
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-17>6x+7
Solve the inequality for x
Answer:
x < -4
Step-by-step explanation:
-17>6x + 7
Switch it to: 6x + 7 <-17
6x + 7 < -17
Now, Subtract the opposite of 7 by both sides.
6x = -24
Divide both sides by 6
Answer : x < -4
consider the function arctan(x^2) write a partial sum for the power series which represents this function consisting of the first four non zero terms
The partial sum for the power series of arctan[tex](x^2)[/tex] consisting of the first four non-zero terms can be written as: arctan[tex](x^2) ≈ x^2 - (1/3)x^6 + (1/5)x^10 - (1/7)x^14[/tex]
The power series representation of the function f(x) = arctan[tex](x^2)[/tex] is given by:
[tex]f(x) = ∑n=0^∞ (-1)^n x^(2n+1) / (2n+1)[/tex]
To find the partial sum consisting of the first four non-zero terms, we can simply substitute n = 0, 1, 2, and 3 into the above expression, and add up the resulting terms:
[tex]f(x) ≈ x - x^3/3 + x^5/5 - x^7/7[/tex]
This is the desired partial sum for the power series representation of arctan[tex](x^2)[/tex], consisting of the first four non-zero terms. Note that as we add more terms to this sum, we get a better and better approximation to the function f(x) over a wider range of x values.
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if a>0 and b>0 then 3(a^0b^2)=
The expression can be simplified to get:
[tex]3*(a^0*b^2) = 3b^2[/tex]
How to simplify the given expression?Remember that for any real:
x > 0
We have that the power when the exponent is zero, is equal to one.
[tex]x^0 = 1[/tex]
Here we know that:
a > 0, b > 0.
And we have the expression:
[tex]3*(a^0*b^2)[/tex]
The first power can be removed, because that is equal to 1, then we can simplify our expression to get.
[tex]3*(a^0*b^2) = 3b^2[/tex]
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what is true about quantitative versus qualitative research? multiple choice all of the statements about quantitative versus qualitative research are true. none of the statements about quantitative versus qualitative research are true. quantitative research is more subjective than qualitative research quantitative research is richer than qualitative research quantitative research is more time-consuming than qualitative research
None of the statements about quantitative versus qualitative research are true.
This is because the comparison between quantitative and qualitative research is not a matter of one being objectively better or more subjective, richer, or more time-consuming than the other. They are different approaches to research, each with its strengths and limitations, and the choice between them depends on the research question, the nature of the data, and the research design.
Quantitative research is characterized by the collection of numerical data that can be analyzed using statistical methods to identify patterns, relationships, and trends. This approach is used when the research question requires an objective measurement of variables that can be quantified and compared across groups. For example, a quantitative study may examine the relationship between height and weight in a population, using statistical techniques to identify the strength of the relationship and its significance.
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Assume a company has 7 departments and they want to assign unique 3-letter codes to each department. The first two characters of the code must be capital letters (A through Z) and the last character must be a digit ( 0 through 9 ). Therefore, a department code can be any string of the form: Letter-Letter-Digit. (i) How many different department codes are possible?
(ii) How many department codes are possible if no letter appears more than once? (iii) How many department codes are possible if no letter or digit appears more than once?
(i) To find the number of different department codes possible, we need to determine the number of choices available for each character in the code.
The first two characters can be any of the 26 capital letters of the alphabet, so there are 26 choices for each of these characters. The third character must be a digit, so there are 10 choices for this character. Therefore, the total number of different department codes possible is: 26 x 26 x 10 = 6,760.
(ii) If no letter appears more than once, then we have to choose three distinct letters for the code. There are 26 choices for the first letter, 25 choices for the second letter (since we've already used one letter), and 24 choices for the third letter (since we've already used two letters).
The third character must be a digit, so there are 10 choices for this character. Therefore, the total number of different department codes possible is: 26 x 25 x 24 x 10 = 15,600.
(iii) If no letter or digit appears more than once, then we have to choose three distinct characters (either letters or digits) for the code. There are 26 choices for the first character (since it can be any letter), 25 choices for the second character (since it can be any letter except the one we chose for the first character or any digit),
and 10 choices for the third character (since it can be any digit except the one we chose for the second character). Therefore, the total number of different department codes possible is:
26 x 25 x 10 = 6,500
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If a bat catches a total of 560 bugs in 7 nights, and each night the bat catches the same number of bugs, how many bugs did the bat catch on the fifth night?
Answer:
400
Step-by-step explanation:
get the number of bugs caught in night and multiply it by five
Select the correct answer. Which value of x from the set {4, 5, 6, 7}, makes this equation true? 4(8 − x) = 8 A. 4 B. 5 C. 6 D. 7
Answer: c. 6
Step-by-step explanation:
Option-C is correct that is 6 number from the set {4 , 5, 6, 7} makes the equation 4(8 - x) = 8 true.
Given that,
We have to find which value of the x from the set {4 , 5, 6, 7} makes the equation 4(8 - x) = 8 true.
We know that,
What is a set?A group of well defined objects is referred to as a set. Only on the basis of simplicity are the objects of a set considered to be distinct.
A family or collection of sets are common names for a group of sets.
So,
The set has 4 numbers by substituting the numbers we get to know if the equation is true or false.
Take the equation,
4(8 - x) = 8
If x = 4,
4(8 - 4) = 8
4 × 4 = 8
16 ≠ 8
Now, If x = 5,
4(8 - 5) = 8
4 × 3 = 8
12 ≠ 8
Now, If x = 6,
4(8 - 6) = 8
4 × 2 = 8
8 = 8
And, If x = 7,
4(8 - 7) = 8
4 × 1 = 8
4 ≠ 8
Therefore, Option-C is correct that is number 6.
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what is the probability that maximum speed differs from the mean value by at most 2.5 standard deviations?
The answer is that the probability that the maximum speed differs from the mean value by at most 2.5 standard deviations can be calculated using the normal distribution.
We first need to calculate the mean value and standard deviation of the speed data. Then, we can use the formula for the normal distribution to find the probability that the maximum speed falls within a certain range from the mean value.
Specifically, we can use the formula:
P(mean - 2.5SD < max speed < mean + 2.5SD) = P(z < 2.5) - P(z < -2.5)
where z is the z-score of the maximum speed, calculated as (max speed - mean)/SD.
We can find the probabilities P(z < 2.5) and P(z < -2.5) using a standard normal distribution table or calculator.
In general, if the maximum speed is normally distributed and the mean and standard deviation are known, we can use this formula to calculate the probability that the maximum speed falls within a certain range from the mean value.
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consider the postfix expression: a-b c*(d*e-f)/(g h*k). the equivalent postfix (reverse polish notation) expression is: group of answer choices
The equivalent postfix (reverse Polish notation) expression for the infix expression "A-B+C*(DE-F)/(G+HK)" is option B: AB-CDEF-+GHK*+/.
The equivalent postfix (reverse Polish notation) expression for the given infix expression "A-B+C*(DE-F)/(G+HK)" is
AB-CDEF-+GHK*+/
Therefore, the correct answer is B), expression can be obtained by following the order of operations for postfix notation start from the left and push operands onto a stack until an operator is encountered. When an operator is encountered, pop the top two operands, perform the operation, and push the result back onto the stack.
Repeat until the end of the expression is reached, and the final result is the top value on the stack.
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--The given question is incomplete, the complete question is given
" Consider the postfix expression: A-B+C*(D*E-F)/(G+H*K). The equivalent postfix (reverse Polish notation) expression is:
A.
AB-C+DE*F-GH+K**/
B.
AB-CDE*F-*+GHK*+/
C.
ABC+-E*F-*+GHK*+/
D.
None of these"--
What is the probability of selecting a heart replacing then selecting a star?
The probability of selecting a heart and then a star with replacement is approximately 0.1875 or 18.75%.
Assuming that a standard deck of 52 playing cards is used, with 13 cards of each suit (including hearts) and 4 suits in total, the probability of selecting a heart on the first draw and then selecting a star (presumably meaning a card from a different suit) on the second draw with replacement is
P (heart than star)
= P (heart) × P (star)
= 13/52 × 39/52
= 507/2704
= 0.1875
where P (heart) is 13/52 is the probability of selecting a heart on the first draw (since there are 13 hearts in the deck), and P (star) is the probability of selecting a card that is not a heart on the second draw (since there are 39 non-heart cards left in the deck after the heart is replaced).
Therefore, the probability of selecting a heart and then a star with replacement is approximately 0.1875 or 18.75%.
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-- The given question is incomplete, the complete question
"What is the probability of selecting a heart and then a star with replacement?" --
Use the integral test to determine whether the series is convergent or divergent.
We need to find the function f(n) whose terms are the same as the series in question. We can then integrate this function from n=1 to infinity and determine if the integral is convergent or divergent. If it is convergent, then the series is convergent. If it is divergent, then the series is also divergent.
To determine whether a series is convergent or divergent using the integral test, we need to first check if the series satisfies three conditions:
1) The terms of the series are positive.
2) The terms of the series are decreasing.
3) The series has an infinite number of terms.
Assuming these conditions are satisfied, we can use the integral test which states that if the integral of the function f(x) from n=1 to infinity is convergent, then the series with terms a_n = f(n) is also convergent. Conversely, if the integral is divergent, then the series is also divergent.
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a die is rolled twice. what is the probability that the number in the second roll will be higher than that in the first?
The probability of rolling a higher number on the second roll is 15/36 or approximately 0.42.
When rolling a die, each roll has an equal chance of landing on any of the six possible outcomes. Therefore, the probability of rolling any specific number on the first roll is 1/6, and the probability of rolling a number higher than the first on the second roll is also 1/6.
To find the probability of both events happening, we can use the multiplication rule of probability, which states that the probability of two independent events occurring together is equal to the product of their individual probabilities.
So, the probability of rolling a number on the first roll and then rolling a higher number on the second roll is:
P = (1/6) x (1/6)
However, since the question doesn't specify a particular number for the first roll, we need to consider all the possible outcomes for the first roll. These outcomes are mutually exclusive and have an equal chance of happening, so we can add their probabilities to find the overall probability of rolling a higher number on the second roll:
P = (1/6) x (5/6) + (1/6) x (4/6) + (1/6) x (3/6) + (1/6) x (2/6) + (1/6) x (1/6) + (1/6) x 0
Simplifying this expression, we get:
P = 15/36
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Use the information given in the table on the right to complete each of the following statements. Brenda is 50 inches tall. Her z-score is .
The z-score of Brenda for the mean of 49 inches and standard deviation 2 inches is equal to 0.5.
Mean is equal to 49 inches
Standard deviation is equal to 2 inches
Brenda is 50 inches tall.
To find Brenda's z-score,
Calculate the number of standard deviations that her height is away from the mean height for 7-year-olds.
z-score = (Brenda's height - Mean height) / Standard deviation
Substituting the given values, we get,
⇒ z-score = (50 - 49) / 2
⇒ z-score = 0.5
Statement 1,
Brenda's height is 0.5 standard deviations above the mean height for 7-year-olds.
Statement 2,
Approximately 68.27% of 7-year-olds are shorter than Brenda.
Using a standard normal distribution table to find the percentage of the area under the curve to the left of z = 0.5.
Therefore, Brenda's z-score for the given mean and standard deviation is equal to 0.5.
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The above question is incomplete, the complete question is:
Use the information given in the table on the right to complete each of the following statements. Brenda is 50 inches tall. Her z-score is
Find individual value in normal distribution
Age Mean Standard deviation
7years 49 inches 2 inches
the following code segment is intended to set max equal to the maximum value among the integer variables x, y, and z. the code segment does not work as intended in all cases.
we do not have the code segment, we cannot identify which of the cases above will cause the code segment to not work as intended.
What is a conditional statement?
A conditional statement is a type of structure to express the relationship between two dependent variables. Its structure is as follows:
The code segment in question uses variables and conditional statements to determine the maximum value among three integer variables x, y, and z. However, there are cases where this code segment may not work as intended.
To determine which initial values for x, y, and z will cause this issue, we need to look at the code segment itself.
The code segment likely involves setting a variable called "max" to the value of one of the three variables (x, y, or z), and then using conditional statements to check if the other variables are larger than the current value of "max".
If they are, the value of "max" is updated to that variable.
To determine which initial values will cause issues, we need to consider cases where the conditional statements will not work as intended.
For example, if all three variables have the same value, the code segment may not correctly identify the maximum value.
Similarly, if two variables have the same value, but that value is smaller than the third variable, the code segment may not correctly identify the maximum value.
Based on the answer choices provided, it appears that the code segment may not work as intended for the initial values x = 1, y = 3, z = 2.
In this case, the initial value of "max" would be set to 1, and the conditional statements would not update the value of "max" to the correct maximum value of 3.
In conclusion, the code segment may not work as intended in cases where there are ties or when the initial values are not in order. It is important to test the code segment with different initial values to ensure that it works correctly in all cases.
The code segment in question is intended to set the variable "max" equal to the maximum value among the integer variables x, y, and z.
To demonstrate that the code segment does not work as intended in all cases, we need to evaluate each of the given initial values for x, y, and z.
1. x = 1, y = 2, z = 3: In this case, the maximum value is 3, which corresponds to the variable z.
2. x = 1, y = 3, z = 2: In this case, the maximum value is 3, which corresponds to the variable y.
3. x = 2, y = 3, z = 1: In this case, the maximum value is 3, which corresponds to the variable y.
4. x = 3, y = 2, z = 1: In this case, the maximum value is 3, which corresponds to the variable x.
Since we do not have the code segment, we cannot identify which of the cases above will cause the code segment to not work as intended.
However, you can test each case by implementing the code segment, assigning the initial values to the variables x, y, and z, and then checking if the variable "max" is set to the correct maximum value.
If any of the cases result in an incorrect "max" value, it means that the code segment does not work as intended for that particular set of initial values.
Hence, we do not have the code segment, we cannot identify which of the cases above will cause the code segment to not work as intended.
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Magan invested $790 in an account paying an interest rate of 83% compounded
quarterly. Angel invested $790 in an account paying an interest rate of 8%
compounded continuously. After 7 years, how much more money would Magan have
in his account than Angel, to the nearest dollar?
Answer:3
Step-by-step explanation:
1437.9874-1444.882=3.1054
Sketch a curve y = f(x) that satisfies: f(0) = 3, and dy/dx =-2. What is f(x)?
The curve f(x) is f(x) = -2x + 3.
Given that dy/dx = -2, we can integrate both sides with respect to x to obtain:
dy/dx = -2
dy = -2 dx
Integrating both sides, we get:
y = -2x + C
where C is the constant of integration. To find the value of C, we use the initial condition f(0) = 3:
y = -2x + C
f(0) = 3
-2(0) + C = 3
C = 3
Thus, the equation of the curve is:
y = -2x + 3
Therefore f(x) is -2x + 3
We can sketch the curve by plotting a few points. For example, when x = 0, y = 3 (as required by the initial condition). When x = 1, y = 1. When x = -1, y = 5. We can also note that the slope of the curve is always -2, meaning that the curve is a straight line with a negative slope.
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The Blackburn family has a square field where they keep their cattle. The area of the field is 40,000 ft square, and Mr. Blackburn wants to put a fence diagonally through the field. What should the length of the fence be?
If "square-field" area is 40000 ft square, and Mr. Blackburn is planning to put a fence diagonally in field, then the length of fence should be 282.84 ft.
The area of the Blackburn's square-field is = 40000 ft²,
First, we equate this with area formula,
On Equating ,
We get,
⇒ (side)² = 40000,
⇒ side = 200,
substituting the "side-length" of the field as 200 ft, in the diagonal of a square formula,
we get,
⇒ Length of field's diagonal is = (side)√2,
⇒ Length of field's diagonal is = (200)√2,
⇒ Length of field's diagonal is ≈ 282.84 ft.
Therefore, the length of field's fence is 282.84 ft.
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what is the price of 700g at £2 a kg
Answer:
£1.4
Step-by-step explanation:
700g = 0.7kg
0.7 x 2 = 1.4
you are contracted to build a children's pool at the new public pool facility. the pool must be built on a fenced off 17 by 26 feet rectangular plot. the pool must be a 77 sq ft rectangle. furthermore, the facility manager wants the border fence to be the same distance, x, from all sides of the pool, except they want to put a lifeguard chair at one end of the length, so the fence should be twice as far away on that side. what are the dimensions of the pool?
The pool dimensions are approximately 12.22 by 21.22 feet.
To start, we know that the pool must be a 77 sq ft rectangle, so we can use the formula for the area of a rectangle (length x width = area) to solve for the dimensions.
77 = length x width
Next, we know that the fenced off plot is a 17 by 26 feet rectangle. We can use this information to set up an equation for the distance between the pool and the fence:
17 - 2x = length
26 - 2x = width
We also know that the fence should be twice as far away on the end where the lifeguard chair will be located, so we can set up another equation:
17 - 4x = length (on the side with the lifeguard chair)
Now we can substitute the expressions for length and width into the formula for the area of a rectangle:
77 = (17 - 2x)(26 - 2x)
Expanding the expression on the right side, we get:
77 = 442 - 86x + 4x^2
Rearranging and simplifying, we get a quadratic equation:
4x^2 - 86x + 365 = 0
Using the quadratic formula, we can solve for x:
x = (86 +/- sqrt(86^2 - 4(4)(365))) / (2(4))
x = (86 +/- sqrt(55284)) / 8
x = (86 +/- 234.85) / 8
x = 36.86 or 2.39
We can ignore the negative value, so x = 2.39 feet.
Now we can use the equations for length and width to solve for the dimensions of the pool:
length = 17 - 2x = 17 - 2(2.39) = 12.22 feet
width = 26 - 2x (except on the side with the lifeguard chair, where it is 4x) = 26 - 2(2.39) = 21.22 feet
So the pool dimensions are approximately 12.22 by 21.22 feet.
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Which best approximates the solution of 16 to the power of 2x = 125
Answer:
869
Step-by-step explanation: