The only difference for these devices in 3701 is that the jk-FF (or jk-latch) has an additional control input, which is the clock (CK). The CK input is used to enable and disable the device so that the inputs, j and k, do not always affect the output (Q) of the device.
The SR-FF (or SR-latch) has two inputs, S and R, which directly affect the output, Q. When S=1, the output is set to 1, and when R=1, the output is reset to 0.
On the other hand, the jk-FF (or jk-latch) has three inputs, J, K and CK. When CK is 0, the device is disabled and the outputs remain the same. When CK is 1, the J and K inputs can be used to either set (J=1, K=0) or reset (J=0, K=1) the output, Q.
In summary, the j and k in the jk-FF (or jk-latch) are similar to the s and r in the SR-FF (or SR-latch).
So, the only difference is the addition of a clock (CK) input in the jk-FF (or jk-latch). This clock (CK) input enables and disables the device, which allows the inputs, j and k, to affect the output (Q) of the device.
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Six small and four medium bottles of lotion give a combined total of 93 fluid ounces of lotion. Which of the following pieces of information could help you determine the number of fluid ounces of lotion in a small bottle and the number of fluid ounces in a medium bottle?
Please answer this question. Giving out BRAINLIEST.
The information that could be used to determine the number of fluid ounces of lotion in a small bottle and the number of fluid ounces in a medium bottle is given as follows:
b) The number of fluid ounces in 8 small and 4 medium bottles of lotion.
How to obtain the amounts?The amounts are obtained with a system of equations, for which the variables are given as follows:
Variable x: amount in a small bottle of lotion.Variable y: amount in a medium bottle of lotion.Six small and four medium bottles of lotion give a combined total of 93 fluid ounces of lotion, hence:
6x + 4y = 93.
With 8 small and 4 medium bottles, the equation is given as follows:
8x + 4y = t.
Hence we can subtract the first equation by the second to obtain the value of x, then we replace and obtain the value of y, meaning that the correct option is given by option b.
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One yoar consumars spent an avernge of $21 on a mead at a testurant. Assumo that the amount spent on a resturant meat is normally distributod and that the standard deviation is $4 . Complete parts (a) through (c) bolow a. What is the probability that a randomly selected person spent more than $24? P(X>$24)= (Round to four decimal places as needed.) b. What is the probability that a randomiy selected person spent between $10 and $19? P($10
a) The probability of finding a value greater than $24 is given by:P(X > $24) = P(Z > (24 - 21) / 4) = P(Z > 0.75)Using the standard normal distribution table, we can find that P(Z > 0.75) = 0.2266.Rounding this result to four decimal places, we have:P(X > $24) = 0.2266.
b) The probability of finding a value between $10 and $19 is given by:P($10 < X < $19) = P((10 - 21) / 4 < Z < (19 - 21) / 4) = P(-2.75 < Z < -0.5)Using the standard normal distribution table, we can find that P(-2.75 < Z < -0.5) = P(Z < -0.5) - P(Z < -2.75) = 0.3085 - 0.0030 = 0.3055.Rounding this result to four decimal places, we have:P($10 < X < $19) = 0.3055.
The probability that a randomly selected person spent more than $24One year consumers spend an average of $21 on a meal at a restaurant. The amount spent on a restaurant meat is normally distributed with a standard deviation of $4.The first step to solve this problem is to standardize the normal random variable using the z-score formula, which is:(1)z= (x-μ) / σwhere x is the random variable, μ is the mean, and σ is the standard deviation. The probability of finding a value greater than $24 is given by:P(X > $24) = P(Z > (24 - 21) / 4) = P(Z > 0.75)Using the standard normal distribution table, we can find that P(Z > 0.75) = 0.2266.Rounding this result to four decimal places, we have:P(X > $24) = 0.2266.
The probability that a randomly selected person spent between $10 and $19 The probability of finding a value between $10 and $19 is given by:P($10 < X < $19) = P((10 - 21) / 4 < Z < (19 - 21) / 4) = P(-2.75 < Z < -0.5)Using the standard normal distribution table, we can find that P(-2.75 < Z < -0.5) = P(Z < -0.5) - P(Z < -2.75) = 0.3085 - 0.0030 = 0.3055.Rounding this result to four decimal places, we have:P($10 < X < $19) = 0.3055.
The amount spent by the middle 50% of the customers The middle 50% of the customers is equivalent to the interval that goes from the 25th percentile to the 75th percentile. This interval is also known as the interquartile range (IQR).The 25th percentile can be found by using the standard normal distribution table, which gives us that:P(Z < -0.6745) = 0.25 Solving for Z, we have:Z = -0.6745 Using the z-score formula, we can find the corresponding value of X:$21 + (-0.6745)($4) = $17.30
Therefore, the lower limit of the IQR is $17.30.The 75th percentile can be found by using the standard normal distribution table, which gives us that:P(Z < 0.6745) = 0.75 Solving for Z, we have:Z = 0.6745Using the z-score formula, we can find the corresponding value of X:$21 + (0.6745)($4) = $24.70
Therefore, the upper limit of the IQR is $24.70.The amount spent by the middle 50% of the customers is between $17.30 and $24.70.
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A small hotel in a popular resort area has 20 rooms. The hotel manager estimates that 15% (1 −
???? = 0.15) of all confirmed reservations are "no-shows." Consequently, the hotel accepts
confirmed reservations for as many as 25 rooms (???? = 25). If more confirmed reservations arrive
than there are rooms, the overbooked guests are sent to another hotel and given a
complimentary dinner. If the hotel currently has 25 confirmed reservations, find
a. the probability that no customers will be sent to another hotel
b. the probability that exactly 2 guests will be sent to another hotel
c. the probability that 3 or more guests will be sent to another hotel.
Let ???? be number of customers who confirmed the reservations and showed up. Then ???? has a
binomial distribution with parameters ???? = 0.85 and ???? = 25. Recall the formula for P(???? = x).
For question (a). find P(???? ≤ 20). Why?
For question (b). find P(???? = 22). Why?
For question (c). find P(???? ≥ 23). Why?
In Excel, for binomial distribution with parameters of probability of success ???? and number of
trials ????, the formulas:
For PDF: P(???? = x) is binom.dist(x, n, ????, 0) and
For CDF: ????5(x) = P(???? ≤ x) is binom.dist(x, n, ????, 1).
Note that P(???? ≥ x) = 1− P(???? < x)
P(???? > x) = 1− P(???? ≤ x)
P(???? < x) = P(???? ≤ x −1) in discrete case
Problem 1:
a) The probability that no customers will be sent to another hotel is 0.039.
b) The probability that exactly 2 guests will be sent to another hotel is 0.228.
c) The probability that 3 or more guests will be sent to another hotel is 0.492.
Problem 2:
a) ( ≤ 20) - Probability of having 20 or fewer customers show up for the reservations.
b) ( = 22) - Probability of exactly 22 customers confirming and showing up for the reservations.
c) ( ≥ 23) - Probability of having 23 or more customers show up for the reservations.
Problem 1:
a. To find the probability that no customers will be sent to another hotel, we need to calculate the probability that all 25 confirmed reservations will show up. Since the hotel manager estimates that 15% of reservations are "no-shows",
Then the probability that a reservation will show up is 1 - 0.15 = 0.85. The probability that all 25 guests will show up is,
P(all 25 show up) = [tex](0.85)^{25}[/tex]
= 0.039
So the probability that no customers will be sent to another hotel is 0.039.
b. To find the probability that exactly 2 guests will be sent to another hotel, we have to use the binomial distribution.
The probability of a reservation being a no-show is 0.15, and the probability of a reservation showing up is 0.85. We have 25 confirmed reservations, so the probability of exactly 2 no-shows is,
P(exactly 2 no-shows) = (25 choose 2)[tex](0.15)^2 (0.85)^{23}[/tex]
= 0.228
So the probability that exactly 2 guests will be sent to another hotel is 0.228.
c. To find the probability that 3 or more guests will be sent to another hotel, we need to use the complement rule.
The probability of 0, 1, or 2 guests being sent to another hotel is,
⇒ P(0 guests sent) + P(1 guest sent) + P(2 guests sent)
= [tex](0.85)^{25}[/tex]+ (25 choose 1)[tex](0.15)^1 (0.85)^{24}[/tex] + (25 choose 2)[tex](0.15)^2 (0.85)^{23}[/tex]
= 0.039 + 0.168 + 0.301
= 0.508
The probability of 3 or more guests being sent to another hotel is,
P(3 or more guests sent) = 1 - P(0, 1, or 2 guests sent)
= 1 - 0.508
= 0.492
So the probability that 3 or more guests will be sent to another hotel is 0.492.
Problem 2:
a) To find ( ≤ 20),
We have to add up the probabilities of all the possible values of from 0 to 20. This is because we want to find the probability that 20 or fewer customers confirmed and showed up for the reservations.
We can use the binomial probability formula to calculate each individual probability, or we can use a binomial cumulative distribution table to look up the probability directly.
The reason we want to find this probability is to determine the likelihood of having fewer than 20 customers show up, which could impact staffing and resource allocation for the event.
b) To find ( = 22),
Use the binomial probability formula to calculate the probability of exactly 22 customers confirming and showing up for the reservations. This is because we are interested in a specific outcome, and want to know the likelihood of that outcome occurring. Knowing this probability can help us plan for specific scenarios, such as having to accommodate 22 customers if they all show up.
c) To find ( ≥ 23),
We have to add up the probabilities of all the possible values of from 23 to 25. This is because we want to find the probability that 23 or more customers confirmed and showed up for the reservations.
We can use the binomial probability formula or a binomial cumulative distribution table to find this probability.
The reason we want to find this probability is to assess the risk of having too few resources available if more customers show up than expected, which could lead to a poor customer experience.
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Determine if 0. 68 is rational or irrational and give a reason for your answer
0.68 is a rational number because it can be expressed as a ratio of two integers (17/25).
0.68 is a rational number because it can be expressed as a ratio of two integers.
To see this, we can convert 0.68 to a fraction by placing the decimal value over a denominator of 1 followed by the number of decimal places (two in this case):
0.68 = 68/100
We can simplify this fraction by dividing both the numerator and denominator by their greatest common factor,
which is 4:
68/100 = 17/25
Thus, 0.68 can be expressed as the ratio of two integers (17 and 25) and is therefore a rational number.
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In 2016, the mean score on the AP Statistics exam was 2. 80, with a standard deviation of 1. 35. The mean score on the AP Calculus exam was a 2. 86, with a standard deviation of 1. 55. What is the combined mean and standard deviation for these exams?
Mean, 2. 83; standard deviation, 0. 2
Mean, 5. 66; standard deviation, 2. 9
Mean, 5. 66; standard deviation, 2. 055
Mean, 2. 83; standard deviation, 2. 9
Mean, 5. 66; standard deviation, 4. 225
the combined mean and standard deviation for these exams will be Mean, 5. 66; standard deviation, 2. 055.
Combined mean=5.66
Combined standard deviation = 2.06
Combined mean= (MXa+ n×Xb)/(m+n)
Combined mean =2.80+2.86=5.66
Combined mean= sqrt(1.55)^2+(1.35)^2)
Combined deviation = 2.06
The mean is the number you get by separating the amount of a bunch of values by the quantity of values in the set.
Conversely, the middle is the center number in a bunch of values when those values are organized from littlest to biggest.
The mode of a bunch of values is the most often rehashed esteem in the set.
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The crafts store charges 49 cents for each of the first five yards of fabric and 30 cents for each additional yard. If you have $10.50, what is the greatest number of yards you could purchase?
Answer:
buy a maximum of 31.83 yards of fabric
After heating up in a teapot, a cup of hot water is poured at a temperature of 207 F. The cup sits to cool in a room at a temperature of 71 F
The cup of water reaches the temperature of
182 F after 1.5 minutes. Using this information, find the value of k, to the nearest thousandth. Use the resulting equation to determine the Fahrenheit temperature of the cup of water, to the nearest degree, after 5 minutes.
The cup of water reaches a temperature of 173 F after 5 minutes.
What is temperature?Temperature is a measure of the average kinetic energy of particles in a system. It is an important physical quantity used to describe the state of a system, and is widely used in science, engineering, and everyday life. Temperature is a thermodynamic property of a system that indicates how much energy is available to do work. In everyday terms, temperature is a measure of how hot or cold something is.
k = -0.2416
The equation for the cooling rate of the cup of water is:
T(t) = 207 - 0.2416t
After 5 minutes, the temperature of the cup of water can be found by substituting t = 5 into the equation:
T(5) = 207 - 0.2416(5) = 173.08 F
Therefore, the cup of water reaches a temperature of 173 F after 5 minutes.
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1. Explain what Marc did in steps 4 and 5.
2. Why did he do this?
3. Create your own radical equation and explain how to solve it.
4. Is there an extraneous solution to your equation?
A radical equation is √(x + 2) = 4 - x and the extraneous solution is x = 7
Explaining step 4 and 5, and why it is doneFrom the question, we have the following parameters that can be used in our computation:
The solution to a radical equation
In step 4 and 5, we have
x = ∛5 * 5 * 5 * 5
x = 5∛5¬ * 5¬ * 5¬ * 5
The above steps are carried out because it would simplify the radical expression to its simplest form
The reason it is done is to have the value of x in its simplest form
Create a radical expression
Here's an example of a radical equation:
√(x + 2) = 4 - x
Square both sides
x + 2 = 16 - 8x + x^2
Evaluate the like terms
x^2 - 9x + 14 = 0
Factor the quadratic equation
(x - 2)(x - 7) = 0
Solve for x:
x = 2 or x = 7
Is there an extraneous solution to your equation?For x = 2:
√(2 + 2) = 4 - 2
√4 = 2
2 = 2
This is true, so x = 2 is a valid solution.
For x = 7:
√(7 + 2) = 4 - 7
√9 = -3
3 = -3
This is not true, so x = 7 is not a valid solution.
So, there is an extraneous solution
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A. Jace collected data on the distances electric vehicles can travel on one charge. He wants to show the average distance and the range an electric vehicle can travel on one charge.
Choose and make an appropriate display of the data
b. Jace wants to compare the range and shape of his electric-vehicle data to related data he collected on gas-powered vehicles. Choose and make appropriate data displays
A box-and-whisker plot is the appropriate data display for Jace's electric-vehicle data and gas-powered vehicle data, and it will give him a visual representation of the difference between the two datasets.
The appropriate data displays for Jace's electric-vehicle data and gas-powered vehicle data would be a box-and-whisker plot. This type of plot is a graphical representation of the five-number summary of a dataset. The five-number summary consists of the minimum, first quartile (Q1), median, third quartile (Q3), and maximum values. It can be calculated using the following formulas:
Minimum = smallest value
Q1 = 25th percentile (the value below which 25% of the data lies)
Median = 50th percentile (the value below which 50% of the data lies)
Q3 = 75th percentile (the value below which 75% of the data lies)
Maximum = largest value
Using these formulas, Jace can calculate the five-number summary for his electric-vehicle data and his gas-powered vehicle data. He can then use these values to create a box-and-whisker plot that compares the range and shape of each dataset. The box-and-whisker plot will give him a clear visual representation of the difference between the two datasets. By comparing the range and shape of the two datasets, Jace can get a better understanding of the difference between the electric-vehicle data and the gas-powered vehicle data. From there, he can draw conclusions about the differences between the two vehicle types.
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Ali takes a full-time position as a makeup artist in Atlanta. Her starting salary is $29,000. Her taxes are 28%. What is her net monthly income?
b. $3,840
c. $2,088
d. $1,740
The correct answer is (c) Ali has a monthly net income of $2,088 after paying 28% in taxes.
.
To calculate Ali's net monthly income, we first need to find out the amount of tax she pays, and then we can subtract it from her annual income to get her net annual income. We'll then divide it by 12 to get her monthly net income.
Calculations: Ali's tax rate is 28%. 28% of 29,000 is 8,12029,000 - 8,120 = 20,88020,880 / 12 = 1,740
Therefore, Ali's net monthly income is $1,740. The correct answer is option D, $1,740. ($29,000 salary x 28% taxes = $8,120 in taxes annually; $8,120 / 12 months = $677 in taxes per month; $29,000 - $677 = $2,088 net monthly income).
Net income refers to the amount of money that a company or an individual has earned after deducting all the expenses and taxes from their gross income. In the context of a company, net income is also called profit, and it is an important measure of a company's financial performance.
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A home has a replacement value of $324,000. What is the amount of the insurance if the
coverage is:
a. 100% of the replacement value?
b. 90% of the replacement value?
c. 80% of the replacement value?
Answer:
a) $324,000
b) $291,600
c) $259,200
Step-by-step explanation:
The percentage of the replacement value represents how much of the house will be insured.
a) 100% of 324000 = 1.00 * 324000 = $324,000
b) 90% of 324000 = 0.9 * 324000 = $291,600
c) 80% of 324000 = 0.8 * 324000 = $259,200
what is 12/37 divided by 5/18
Answer: [tex]\frac{216}{185} \;\approx 1.1676[/tex]
Given:
[tex]\displaystyle \frac{\frac{12}{37}}{ \frac{5}{18} }[/tex]
Use the method of "keep, change, flip:"
* keep the first fraction, change to multiplication, flip the second
[tex]\displaystyle \frac{12}{37}* \frac{18}{5}[/tex]
Multiply across and divide:
[tex]\displaystyle \frac{216}{185} \;\approx 1.1676[/tex]
A 2-column table with 6 rows. The first column is labeled x with entries negative 3, negative 2, negative 1, 0, 1, 2. The second column is labeled f of x with entries negative 16, negative 1, 2, negative 1, negative 4, negative 1.
Analyze the table of values for the continuous function, f(x), to complete the statements.
A local maximum occurs over the interval
A local minimum occurs over the interval
________
We can say that after answering the offered question Therefore, the equation constant of proportionality in this scenario is 11.25.
What is equation?An equation is a mathematical statement that proves the equality of two expressions connected by an equal sign '='. For instance, 2x – 5 = 13. Expressions include 2x-5 and 13. '=' is the character that links the two expressions. A mathematical formula that has two algebraic expressions on either side of an equal sign (=) is known as an equation. It depicts the equivalency relationship between the left and right formulas. L.H.S. = R.H.S. (left side = right side) in any formula.
In this case, we may use the following formula to calculate the proportionality constant:
proportionality constant = output/input
where the output is John's pay and the input is the number of hours he worked.
As a result, the proportionality constant is:
Paycheck/hours worked = proportionality constant
proportionality constant = 450/40
proportionality constant = 11.25
As a result, the proportionality constant in this scenario is 11.25.
In this case, we may use the following formula to calculate the proportionality constant:
proportionality constant = output/input
where the output is John's pay and the input is the number of hours he worked.
As a result, the proportionality constant is:
Paycheck/hours worked = proportionality constant
proportionality constant = 450/40
proportionality constant = 11.25
Therefore, the constant of proportionality in this scenario is 11.25.
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please help me What is the circumference of a circular swimming pool with a diameter of 6 ½ feet? 0 20 -/-/ 099/ 0 6 1/1 0 71/1/2 .ft. (use 22/7 for pi)
The circumference of the circular swimming pool is approximately 245.04 inches.
What connection exists between a circle's diameter and circumference?The circumference of a circle is the distance around it, whereas the diameter is the distance across the circle that passes through its centre. The circumference is equal to (pi) times the diameter, according to the connection between the diameter and circumference. No of the size or proportions of the circle, this connection is true for all circles.
The circumference of the circle is given as:
C = 2πr
We know that, D = 2r = 6 1/2 feet.
6 ½ feet = 6.5 × 12 inches = 78 inches
Substituting the values we have:
C = π × 78 inches = 245.04 inches
Hence, the circumference of the circular swimming pool is approximately 245.04 inches.
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Linda read 1/3 of her book on Friday. She reads 2/6 of the book on Saturday. On Sunday she reads the remaining 2/12 of the book. How much of the book did she read
As per the concept of unitary method, Linda read 5/6 of the book.
In this problem, the quantity we are dealing with is the book that Linda is reading. Let's call the total number of units in the book "x". Since Linda read 1/3 of the book on Friday, we can say that she read (1/3)x units of the book on Friday. Similarly, she read (2/6)x units of the book on Saturday, and (2/12)x units of the book on Sunday.
Now, we need to add up all of these quantities to find the total number of units of the book that Linda read. But before we do that, we need to make sure that all of the fractions have the same denominator. The smallest common multiple of 3, 6, and 12 is 12. So, we will convert all of the fractions to twelfths.
(1/3)x = (4/12)x
(2/6)x = (4/12)x
(2/12)x = (2/12)x
Now, we can add up all of these quantities:
(4/12)x + (4/12)x + (2/12)x = (10/12)x
So, Linda read (10/12)x units of the book in total. But we can simplify this fraction by dividing both the numerator and the denominator by their greatest common factor, which is 2:
(10/12)x = (5/6)x
Therefore, the resulting value of x is 5/6
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a standard number cube has six sides labeled 1 through 6. think about rolling a number cube one time.is it more likely that the cube will show a multiple of 2 or a multiple of 3?
Answer:
Multiple of 2
Step-by-step explanation:
There are six possible outcomes when rolling a standard number cube labeled 1 through 6. Out of these six possible outcomes, there are three outcomes that are multiples of 2 (2, 4, and 6) and two outcomes that are multiples of 3 (3 and 6).
Therefore, it is more likely that the cube will show a multiple of 2 than a multiple of 3. The probability of rolling a multiple of 2 is 3/6 or 1/2, while the probability of rolling a multiple of 3 is 2/6 or 1/3.
A person makes $1800 per month, but 1/3 of that amount goes to her rent. What two numbers can you multiply to find out how much she has after playing her rent?
The two numbers that are multiplied to find out the amount she has after playing her rent is: 2/3 and 1800.
Explain about the fraction of number?Part of an entire unit is represented by a fraction. A fraction's numerator is the number at the top, and its denominator is the number at the bottom. Hence, the numerator of the fraction 3/5 is 3 and the denominator is 5.Total income of person: $1800 per month.
Rent amount = 1/3 * income
Remaining amount : 1 - 1/3 = 2/3 of income
So,
Remaining amount = 2/3*1800
Remaining amount = 1200
Thus, the two numbers that are multiplied to find out the amount she has after playing her rent is: 2/3 and 1800.
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Calculate the Total amount that Theo has to pay back if she takes the loan
If Theo takes the loan R9000 that is payable over 48 months monthly installment =R 318,92, the total amount that Theo has to pay back for the loan is R15,307.16.
To calculate the total amount that Theo has to pay back if she takes a loan of R9000 payable over 48 months with a monthly installment of R318.92, we need to multiply the monthly installment by the number of months and add any applicable fees or interest charges.
First, let's calculate the total amount that Theo will pay for the loan over the 48-month period:
Total amount = Monthly installment x Number of months
Total amount = R318.92 x 48
Total amount = R15,307.16
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Complete question is:
Calculate the total amount that Theo has to payback if she takes the loan R9000 that is payable over 48 months monthly installment =R 318,92
A manager must choose five employees from a pool of 17 people to
take a survey. How many different ways can the CEO choose these
people?
There are 6,188 different ways the CEO can choose five employees from a pool of 17 people to take a survey.
To determine how many ways the CEO can select five employees from a pool of 17 people to take a survey, you can use the combination formula. The combination formula is nCr = n!/r!(n-r)! where n is the total number of items to choose from, and r is the number of items to choose.
In this case, n = 17 and r = 5.Using the combination formula: n Cr = 17C5= 17!/5!(17-5)!= 6188 There are 6,188 different ways the CEO can choose five employees from a pool of 17 people to take a survey.
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Please Help!! A Ferris wheel ride varies sinusoidally. When loading, people are 4 feet above the ground. The radius of the Ferris wheel is 60 feet. The ride takes 4 minutes to complete one revolution. if a person starts the ride 10 feet off the ground, give the cosine function of the ride.
f(x)=Acos(Bx-C)+D
I have found:
A=60
Period=4
B=π/2
I cannot find C and D.
Step-by-step explanation:
To find C and D, we can use the given information about the initial position of the person on the ride.
When the person starts the ride, they are 10 feet off the ground. This means that the cosine function has a vertical shift of 10 units, so we have:
f(x) = Acos(Bx - C) + D = 60cos(π/2x - C) + D
At the start of the ride, when x = 0, f(x) = 10. Substituting these values, we get:
10 = 60cos(-C) + D
Simplifying, we get:
D = 10 - 60cos(-C)
We can also use the fact that the minimum height of the ride is 4 feet above the ground. This means that the cosine function has a vertical shift of 4 units, so we have:
f(x) = Acos(Bx - C) + D = 60cos(π/2x - C) + D
At the lowest point of the ride, when x = 1/4, f(x) = 4. Substituting these values, we get:
4 = 60cos(π/8 - C) + D
Substituting D = 10 - 60cos(-C) from the first equation, we get:
4 = 60cos(π/8 - C) + 10 - 60cos(-C)
Simplifying, we get:
cos(-C) = (4 - 10 - 60cos(π/8 - C))/(-60)
cos(-C) = (3cos(π/8 - C) - 1)/2
Using the identity cos(-x) = cos(x), we can rewrite this as:
cos(C) = (3cos(π/8 - C) - 1)/2
Solving for C numerically, we get:
C ≈ 0.438
Substituting this value of C and D = 10 - 60cos(-C) into the equation for f(x), we get:
f(x) = 60cos(π/2x - 0.438) + 10 + 60cos(0.438)
Five friends each bought a shirt and a pair of shoes. The table shows the cost of the tems. The expression 5(x+24) shows the total amount of money they spent. Expand the expression using the Distributive Property
Answer:
5x+120
Step-by-step explanation:
5(x) + 5(24)
5x+120
Which is the solution set of the compound inequality 3.5x-10>-3 and 8x-9 <39?
-2
-2
2
2
Answer:
OPTION C: 2 < x < 6
Step-by-step explanation:
3.5x - 10 > -3
Adding 10 to both sides:
3.5x > 7
Dividing by 3.5:
x > 2
8x - 9 < 39
Adding 9 to both sides:
8x < 48
Dividing by 8:
x < 6
Therefore, the solution set of the compound inequality is:
2 < x < 6
At Cheapmore supermarket, 1 litre of fruit juice cost R25 and 1,5 litres cost R34. Which juice is cheaper. Show your calculations.
NEED QUICK! WILL GIVE BRAINLIEST!!!
Find [g•f](x) for f(x) = 2x+5 and g(x) = x² - 3.
Show all work.
Answer: To find the composition g∘f, we first need to find g(f(x)), which means we need to substitute f(x) into g(x) everywhere we see x. So we have:
g(f(x)) = g(2x+5) = (2x+5)^2 - 3
Expanding the square, we get:
g(f(x)) = (4x^2 + 20x + 25) - 3
Simplifying, we get:
g(f(x)) = 4x^2 + 20x + 22
Therefore, the composition g∘f is equal to 4x^2 + 20x + 22.
Step-by-step explanation:
PLEASE SHOW WORK!!!!!!!!!
By making linear equation for the given statement, The salesman sold 40 suits in that week.
What is a linear equation, exactly?
A linear equation is a mathematical equation in which the variables (usually represented by x and y) are raised to the first power and are related to each other by a straight line. In other words, a linear equation represents a straight line on a graph. The general form of a linear equation is y = mx + b, where m is the slope of the line and b is the y-intercept (the point at which the line crosses the y-axis).
Now,
Let "x" the number of suits the salesman sells in that week.
We know that he sells discounted shirts with 10% of the suits sold, so he sells 0.1x discounted shirts.
The regular price of a suit is $200, so the total revenue from selling x suits is 200x.
The discounted price of a shirt is $20, so the revenue from selling 0.1x discounted shirts is 20(0.1x) = 2x.
Now we can set up an equation based on the total revenue:
200x + 2x = 8080
Simplifying this equation, we get:
202x = 8080
Dividing both sides by 202, we get:
x = 40
Therefore,
the salesman sold 40 suits in that week.
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Which situation can be represented by 11+ 6.5p ≤ 89?
A Napoleon is buying shirts online for $11 each. The cost to mail all the shirts is $6.50. He wants to spend at
least $89. What is p, the number of shirts Napoleon can buy?
Napoleon is buying shirts online for $11 each. The cost to mail all the shirts is $6.50. He wants to spend at
most $89. What is p, the number of shirts Napoleon can buy?
Napoleon is buying shirts online for $6.50 each. The cost to mail all the shirts is $11. He wants to spend at
least $89. What is p, the number of shirts Napoleon can buy?
Napoleon is buying shirts online for $6.50 each. The cost to mail all the shirts is $11. He wants to spend at
most $89. What is p, the number of shirts Napoleon can buy?
The answer of the given question based on the inequality equation the answer is given below,
What is Equation?An equation is mathematical statement that asserts equality of two expressions. It typically includes of variables, constants, and mathematical operations like addition, subtraction, multiplication, and division
The situation that can be represented by 11+ 6.5p ≤ 89 is:
a) Napoleon is the buying shirts online for $11 each. The cost to mail all the shirts is $6.50. He wants to spend at most $89. What is p,
To solve for p, we can follow these steps:
11 + 6.5p ≤ 89 (subtract 11 from both sides)
6.5p ≤ 78 (divide both sides by 6.5)
p ≤ 12
Therefore, Napoleon can buy at most 12 shirts if he wants to spend at most $89.
b) None of the given situations can be represented by the inequality 11 + 6.5p ≤ 89 when p represents the number of shirts Napoleon can buy. This is because the inequality implies that the total cost of buying p shirts at $11 each and mailing them for $6.50 is no more than $89, which is not consistent with the given information about the cost of the shirts and mailing.
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Identify the radii of the given circle check all that apply
The radii of circle are AB, AC and AE.
The radius of a circle is the distance from the center of the circle to any point on its circumference. To find the radius of a circle, you can use the formula:
radius = diameter / 2
where the diameter is the distance across the circle, passing through its center.
Here, in this figure we need to identify the radii. It means we need to find those lines which starts from centre and touches it's circumference.
Let us first see the option AB, it follows the condition passes through centre and touches the circumference. So, it is radius of circle.
Now, let's look at CE in figure, it passes through centre and touch the two ends of circumference. So, it is diameter not radius.
Now, AC satisfies the condition of radius. So, AC is radius.
FD touches the two ends of circle at circumference not passes through centre. So, it is chord not radius.
AE starts from centre and it's other end touches the circumference of circle. So, it is radius.
So, the radii of circle in given figure are : AB, AC and AE.
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Find the value of the variable 7x + 19
Answer:
Step-by-step explanation:
7x+19=0
7x=-19
x=-19/7 ---> This is your final answer!
Plug in the x we found to see if the expression is correct:
7(-19/7)+19=0
-19+19=0
So our x value is correct!
Basketball
30%
(A)
(B)
(C)
(D)
Tennis
36⁰
300
360
720
900
Cricket
35%
If 180 students played football, how many
students are in the group?
Football
Proportionately, if 32% represent students who played football, and the total number of them is 180, the total students in the group is 563.
What is proportion?Proportion is the ratio of two quantities equated to each other.
Proportion is a fractional value and we represent proportional values as between zero and one.
Basketball Tennis Cricket Football
Percentage 30% 3% 35% 32% (100 - 30 - 3 - 35)
The number of
students 169 17 197 180 (32% of 563)
The number of students who played football = 180
Proportionately, if 32% = 180, 100% representing the total number of students in the group = 563 (180/0.32).
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Please help given mts & sqp find sp
The value of length SP for the two given similar triangles is 11.
What is similar triangle?
Similar triangles are triangles that have the same shape but are different in size. In other words, their corresponding angles are equal, and their corresponding sides are proportional.
This means that if you were to take one of the similar triangles and enlarge or shrink it, while keeping the angles the same, it would still be a similar triangle.
The value of length SP is calculated by applying the following method;
|SP| = |ST|
3x + 2 = 5x - 4
3x - 5x = -4 - 2
-2x = - 6
x = 3
Length SP = 3x + 2
= 3(3) + 2
= 11
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