[tex]\Rightarrow[/tex]
Suppose first that [tex]H\subset G[/tex] is a normal subgroup. Then by definition we must have for all [tex]a\in H[/tex], [tex]xax^{-1} \in H[/tex] for every [tex]x\in G[/tex]. Let [tex]a\in G[/tex] and choose [tex](ab)\in aH[/tex] ([tex]b\in H[/tex]). By hypothesis we have [tex]aba^{-1} =abbb^{-1}a^{-1}=(ab)b(ab)^{-1} \in H[/tex], i.e. [tex]aba^{-1}=c[/tex] for some [tex]c\in H[/tex], thus [tex]ab=ca \in Ha[/tex]. So we have [tex]aH\subset Ha[/tex]. You can prove [tex]Ha\subset aH[/tex] in the same way.
[tex]\Leftarrow[/tex]
Suppose [tex]aH=Ha[/tex] for all [tex]a\in G[/tex]. Let [tex]h\in H[/tex], we have to prove [tex]aha^{-1} \in H[/tex] for every [tex]a\in G[/tex]. So, let [tex]a\in G[/tex]. We have that [tex]ha^{-1} =a^{-1}h'[/tex] for some [tex]h'\in H[/tex] (by the hypothesis). hence we have [tex]aha^{-1}=h' \in H[/tex]. Because [tex]a[/tex] was chosen arbitrarily we have the desired .
A 1L bag of Normal Saline must infuse over 6 hours using tubing calibrated to deliver 20gtts/mL. How many drops per minute should be infused?
Answer:
total drop per minute is 56
Step-by-step explanation:
Give data:
total capacity of bag 1 L = 1000 ml
Duration of infuse 6 hr
quantity at the time delivered is 20 gtts/ml
Drop per minute can be determined by using following relation
Drop per minute [tex]= \frac{1000 ml\times 20 gtts/ml}{6\times 60 min} = 55.55 gtt[/tex]
therefore total drop per minute is[tex] 55.55 \approx 56[/tex]
A study was done by a social media company to determine the rate at which users used its website. A graph of the data that was collected is shown
What can be interpreted from the range of this graph?
The range represents the 24-month time period of the study
The range represents the number of users each month for 24 months
The range represents the 20-month time period of the study
The range represents the number of users each month for 20 months
Answer:
The range represents the number of users each month for 24 months
Step-by-step explanation:
The range depends on the y axis. Looking at the y axis we see the number of users for each month. Looking at the x axis we see that it's 24 months not 20 months
From the graph, we can interpret the range represents the number of users each month for 24 months. Therefore, option B is the correct answer.
We need to find what can be interpreted from the range of the given graph.
What is the range?The range is the difference between the smallest and highest numbers in a list or set. To find the range, first put all the numbers in order. Then subtract (take away) the lowest number from the highest.
From the given graph, we can see the x-axis represents the number of months and the y-axis represents the number of users.
So, the range represents the number of users each month for 24 months
20-15.8=4.2
Therefore, option B is the correct answer.
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Gary buys a 31/2 pound bag of cat food every 3 weeks.Gary feeds his cat the same amount of food each day.Write a numeric expression and solve to determine the number of pounds of cat food his cat eats each year?(year=52weeks)
Answer:
[tex]52\times \frac{7}{6}[/tex]
[tex]60\frac{2}{3}\text{ pounds}[/tex]
Step-by-step explanation:
Given,
The total pounds eaten by cat in 3 weeks = [tex]3\frac{1}{2}[/tex]= [tex]\frac{7}{2}[/tex]
∵ Each day the pounds of eaten is same,
⇒ Total pounds eaten in each week = [tex]\frac{7}{6}[/tex]
∵ 1 year = 52 weeks,
So, the pounds eaten in 52 weeks or 1 year = 52 × pounds eaten in each week
= 52 × [tex]\frac{7}{6}[/tex]
Which is the required expression,
By solving it,
The number of pounds eaten by cat in a year
[tex]=\frac{364}{6}[/tex]
[tex]=60\frac{2}{3}[/tex]
You have a plate of 50 cookies. Ten have chocolate chips and 14 have pecans. On the cookies mentioned in the preceding sentence, 6 have both chocolate chips and pecans. You select a cookie at random. What is the probability that your cookie has chocolate chips or pecans
The probability of selecting a cookie with either chocolate chips or pecans from a plate of 50 cookies is 36%.
The question asks about the probability of selecting a cookie with either chocolate chips or pecans from a plate of 50 cookies, with some overlapping flavors. Given the information:
Total cookies: 50
Chocolate chip cookies: 10
Pecan cookies: 14
Cookies with both flavors: 6
To calculate the probability of choosing a cookie with either chocolate chips or pecans (or both), we can use the formula:
P(C OR N) = P(C) + P(N) \'u2013 P(C AND N)
where:
P(C) is the probability of choosing a chocolate chip cookie,
P(N) is the probability of choosing a pecan cookie, and
P(C AND N) is the probability of choosing a cookie with both flavors.
Thus:
P(C) = 10/50 = 0.20,
P(N) = 14/50 = 0.28, and
P(C AND N) = 6/50 = 0.12.
Therefore:
P(C OR N) = 0.20 + 0.28 - 0.12 = 0.36 or 36%.
This is the probability that a randomly selected cookie from the plate will have either chocolate chips, pecans, or both.
Translate the following sentence into math symbols. Then solve the problem. Show your work and keep the equation balanced. 10 less than x is -45
Answer:
look at the step by step explanation
Step-by-step explanation:
10<x=45
i dunno if this is correct
The sweater department ran a sale last week and sold 95% of the sweaters that were on sale. 38 sweaters were sold. How many sweaters were on sale?
Answer: 40.
Step-by-step explanation:
Given : The sweater department ran a sale last week and sold 95% of the sweaters that were on sale.
95% can be written as 0.95 [ by dividing 100 ]
Also, the number of sweaters sold = 38
Let x be the number of sweaters were on sale.
Then , we have the following equation :_
[tex]0.95x=38\\\\\Rightarrow\ x=\dfrac{38}{0.95}=\dfrac{3800}{95}=40[/tex]
Hence, 40 sweaters were on sale.
Convert the following systems of equations to an augmented matrix and use Gauss-Jordan reduction to convert to an equilivalent matrix in reduced row echelon form. (Show the steps in the process of converting to G-J). You don't have to find the solution set X12x223 = 6 2a1 3 = 6 X1x23x3 = 6
Answer:
System of equations:
[tex]x_1+2x_2+2x_3=6\\2x_1+x_2+x_3=6\\x_1+x_2+3x_3=6[/tex]
Augmented matrix:
[tex]\left[\begin{array}{cccc}1&2&2&6\\2&1&1&6\\1&1&3&6\end{array}\right][/tex]
Reduced Row Echelon matrix:
[tex]\left[\begin{array}{cccc}1&2&2&6\\0&1&1&2\\0&0&1&1\end{array}\right][/tex]
Step-by-step explanation:
Convert the system into an augmented matrix:
[tex]\left[\begin{array}{cccc}1&2&2&6\\2&1&1&6\\1&1&3&6\end{array}\right][/tex]
For notation, R_n is the new nth row and r_n the unchanged one.
1. Operations:
[tex]R_2=-2r_1+r_2\\R_3=-r_1+r_3[/tex]
Resulting matrix:
[tex]\left[\begin{array}{cccc}1&2&2&6\\0&-3&-3&-6\\0&-1&1&0\end{array}\right][/tex]
2. Operations:
[tex]R_2=-\frac{1}{3}r_2[/tex]
Resulting matrix:
[tex]\left[\begin{array}{cccc}1&2&2&6\\0&1&1&2\\0&-1&1&0\end{array}\right][/tex]
3. Operations:
[tex]R_3=r_2+r_3[/tex]
Resulting matrix:
[tex]\left[\begin{array}{cccc}1&2&2&6\\0&1&1&2\\0&0&2&2\end{array}\right][/tex]
4. Operations:
[tex]R_3=\frac{1}{2}r_3[/tex]
Resulting matrix:
[tex]\left[\begin{array}{cccc}1&2&2&6\\0&1&1&2\\0&0&1&1\end{array}\right][/tex]
A survey was conducted from a random sample of 8225 Americans, and one variable that was recorded for each participant was their answer to the question, "How old are you?" The mean of this data was found to be 42, while the median was 37. What does this tell you about the shape of this distribution?
The shape of the distribution is positively skewed distribution as per the concept of mean and median.
In this case, the mean is 42 and the median is 37.
Since the mean is greater than the median, it suggests that the distribution is positively skewed.
This means that there are some relatively high values (outliers or extreme values) that are pulling the mean towards the higher end of the data range, which results in the median being lower than the mean.
In other words, the tail of the distribution extends more to the right (higher values) than to the left.
In a positively skewed distribution:
The mean > Median
The tail is longer on the right side (positive side).
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Final answer:
The mean age being higher than the median age in an age distribution survey with 8225 Americans indicates a right-skewed distribution. The distribution has a longer tail on the right side due to outliers or a subgroup of older individuals.
Explanation:
In the survey with a sample of 8225 Americans, the given mean age is 42, and the median age is 37. The fact that the mean is higher than the median suggests that there are outliers or a group of people who are much older than the rest skewing the average upwards. This is an indication that the age distribution is right-skewed, meaning that there is a longer tail on the right side of the distribution curve.
Statisticians commonly use the mean and median to understand the shape of a distribution. In a perfectly symmetrical distribution, these two measures would be the same. However, when there is skewness, the mean is pulled towards the tail of the distribution more so than the median. Therefore, when the mean is greater than the median, the distribution is positively skewed; conversely, if the mean is less than the median, the distribution is negatively skewed.
Understanding the skewness is important as it affects the distribution's measures of central tendency, making the mean less representative of the majority of the data points in a skewed distribution.
TRUE OR FALSE. The carrying capacity of Earth can be determined accurately without any ambiguity.
Answer:
false
Step-by-step explanation:
Two percent of all seniors in a class of 50 have scored above 96% on an ext exam, which of the following is the number of seniors who scored above 96%? O 10
Answer:
The number of seniors who scored above 96% is 1.
Step-by-step explanation:
Consider the provided information.
Two percent of all seniors in a class of 50 have scored above 96% on an ext exam.
Now we need to find the number of seniors who scored above 96%
For this we need to find the two percent of 50.
2% of 50 can be calculated as:
[tex]\frac{2}{100}\times50[/tex]
[tex]\frac{100}{100}[/tex]
[tex]1[/tex]
Hence, the number of seniors who scored above 96% is 1.
A jar of marbles contains the following: two red marbles, three white marbles, five blue marbles, and seven green marbles.
What is the probability of selecting a red marble from a jar of marbles?
5/17
2/15
2/17
17/2
The probability of selecting a red marble from the jar of marbles is 2/17.
To calculate the probability of selecting a red marble from the jar, we need to determine the total number of marbles in the jar and the number of red marbles.
Total number of marbles = 2 (red) + 3 (white) + 5 (blue) + 7 (green) = 17
Number of red marbles = 2
Now, the probability of selecting a red marble is given by:
Probability = (Number of red marbles) / (Total number of marbles) = 2 / 17
So, the correct probability of selecting a red marble from the jar is 2/17.
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Final answer:
The probability of selecting a red marble from the jar is [tex]\frac{2}{17}[/tex] since there are 2 red marbles out of a total of 17 marbles.
Explanation:
The probability of selecting a red marble from a jar of marbles containing two red marbles, three white marbles, five blue marbles, and seven green marbles can be calculated by dividing the number of red marbles by the total number of marbles in the jar. First, we determine the total number of marbles: 2 (red) + 3 (white) + 5 (blue) + 7 (green) = 17 marbles. Next, we calculate the probability of selecting a red marble by dividing the number of red marbles (2) by the total (17).
Therefore, the probability of selecting a red marble is [tex]\frac{2}{17}[/tex].
Find the distance between the origin and the point R = (9,7,8). The distance is: Ensure that you use at least 4 decimal place accuracy or exact values
Answer:
The distance between the origin and the given point is 13.9283 units.
Step-by-step explanation:
The coordinates of origin are (0,0,0)
We are given a point R(9,7,80
The distance formula:
[tex]\sqrt{(y_1 -x_1)^2 + (y_2 -x_2)^2 + (y_3 -x_3)^2}[/tex], where [tex](x_1, x_2, x_3)[/tex] are coordinates of one point and [tex](y_1, y_2, y_3)[/tex] are coordinates of other point.
Putting the values as:
[tex]y_1 = 9, y_2 = 7, y_3 = 8\\x_1 =0, x_2 = 0, x_3 = 0[/tex]
We get d = [tex]\sqrt{81 + 64 + 49}[/tex]
d = [tex]\sqrt{194}[/tex]
d = 13.9283
Thus, the distance between the origin and the given point is 13.9283 units.
The demand equation for kitchen ovens is given by the equation
D(q) = –338q + 4,634
where D(q) is the price in dollars and q is the number of kitchen ovens demanded per week. The supply equation for kitchen ovens is
S(q) = 400q^2 + 20
where q is the quantity the supplier will make available per week in the market when the price is p dollars. Find the equilibrium point (q, p) rounded to the nearest hundredth.
Answer:
The equilibrium point is (3, 3620)
Step-by-step explanation:
We set the supply and the demand equation equal to each other and solve:
[tex]-338q+4634=400q^2+20\\400q^2+338q-4614=0[/tex]
We can solve by factoring:
[tex]2(q-3)(200q+769)=0[/tex]
Setting each factor equal to zero we get:
[tex]q=3\text{ or }q=\displaystyle-\frac{769}{200}[/tex]
Only a positive quantity makes sense, so q=3 is the equilibrium quantity.
To get the equilibrium price we just plug 3 in place of q in any of the functions. Let us use the demand function which is easier to handle:
[tex]D(3)=-338(3)+4634=3620[/tex]
Therefore the equilibrium price is p=3620
In ordered pair form the equilibrium point is (3, 3620)
I need help with how to "Create a column vector from 15 to -25 with a step size of 5"
Answer:
Your column vector is:
[tex]\left[\begin{array}{c}15&10&5&0&-5&-10&-15&-20&-25\end{array}\right][/tex]
Step-by-step explanation:
The first step to solve your problem is knowing what is a column vector:
A column vector is a matrix that only has one column, and multiple rows.
The problem wants the vector to range from 15 to -25.
It means that the biggest value in the vector is 15, and the smallest is -25. Since it is from 15 to -25, the first element of your column vector is 15, and the last element is -25.
With a step size of 5
At each element, you decrease 5. So you have: 15,10,..,-20,-25.
The vector is:
[tex]\left[\begin{array}{c}15&10&5&0&-5&-10&-15&-20&-25\end{array}\right][/tex]
Mr Cosgrove is comparing movie rentals deals. Netflix charge a flat rate of $8.50 Blockbuster charge $4.50 plus a $0.50 per movie after how many movie rental with the cost of two stores be the same
Answer:
8 rental movies will make the costs of the two stores be the same
Step-by-step explanation:
- Mr Cosgrove is comparing movie rentals deals
- Netflix charge a flat rate of $8.50
- Blockbuster charge $4.50 plus a $0.50 per movie
- We need to find how many movie rental make the costs of the two
stores will be the same
- Assume that the number of rental movies is m
∵ Blockbuster charge $4.50 plus a $0.50 per movie
∴ Blockbuster cost = 4.50 + 0.50 m
∵ The cost of Netflix = 8.50
- Equate the two costs to find the number of the rental movies
∵ 4.50 + 0.50 m = 8.50
- Subtract 4.50 from both sides
∴ 0.50 m = 4
- Divide both sides by 0.50
∴ m = 8 movies
8 rental movies will make the costs of the two stores be the same
What are the odds against choosing a white or red marble from a bag that contains two blue marbles, one green marble, seven white marbles, and four red marbles?
3:11
3:14
11:3
14:3
Answer:
11:3
Step-by-step explanation:
You add all the white and red marbels up which equals 11 and then add up all the marbles that are not white or red and count them up too in a seperate pile which should give you your answer of 11:3
A machine that cuts corks for wine bottles operates in such a way that the distribution of the diameter of the corks produced is well approximated by a normal distribution with mean 4 cm and standard deviation 0.2 cm. The specifications call for corks with diameters between 3.8 and 4.2 cm. A cork not meeting the specifications is considered defective. (A cork that is too small leaks and causes the wine to deteriorate; a cork that is too large doesn't fit in the bottle.) What proportion of corks produced by this machine are defective? (Round the answer to four decimal places.)
Answer: 0.3173
Step-by-step explanation:
Given : A machine that cuts corks for wine bottles operates in such a way that the distribution of the diameter of the corks produced is well approximated by a normal distribution with
[tex]\mu=4\ cm[/tex] and [tex]\sigma=0.2\ cm[/tex]
The specifications call for corks with diameters between 3.8 and 4.2 cm.
Let x be the random variable that represents the the diameter of the corks.
Using formula [tex]z=\dfrac{x-\mu}{\sigma}[/tex], the z-score corresponding to x= 3.8 will be :_
[tex]z=\dfrac{3.8-4}{0.2}=1[/tex]
z-score corresponding to x= 4.2 will be :_
[tex]z=\dfrac{4.2-4}{0.2}=1[/tex]
Now, by using the standard normal distribution table for z, we have
[tex]\text{P value}=P(-1<z<1)=2P(z<1)-1\\\\=2(0.8413447)-1\\\\=0.6826894\approx0.6827[/tex]
∴The proportion of corks produced by this machine are meeting the specifications=0.6827
∴The proportion of corks produced by this machine are defective = [tex]1-0.6827=0.3173[/tex]
The question asks about the proportion of defective corks produced by a machine. Given that the corks diameters' are normally distributed with a mean of 4cm and a standard deviation of 0.2cm, and the specifications are between 3.8cm and 4.2cm, about 68% of corks will meet the specification. This implies that about 32% will be defective.
Explanation:The subject of this question is statistics, specifically dealing with normal distribution, mean and standard deviation. To find the proportion of corks produced by the machine that are defective, we can use the properties of normal distribution where the diameters of the corks represent a normal distribution with µ (mean) = 4 cm and σ (standard deviation) = 0.2 cm.
As the corks' specification falls between 3.8 cm and 4.2 cm, these values are 1 standard deviation below and above the mean respectively. In normal distribution, the area (i.e., proportion) within one standard deviation is approximately 0.68 (or 68%). So, the proportion within the specification is 0.68.
To obtain the proportion of defective corks, you subtract the proportion within specification from 1 (the total proportion). Hence, the proportion of defective corks is 1 - 0.68 = 0.32 or 32%. This means that approximately 32% of the corks produced are outside the specification and are deemed defective.
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A local eat-in pizza restaurant wants to investigate the possibility of starting to deliver pizzas. The owner of the store has determined that home delivery will be successful only if the average time spent on a delivery does not exceed 25 minutes. The owner has randomly selected 21 customers and delivered pizzas to their homes in order to test whether the mean delivery time actually exceeds 25 minutes. Suppose the p-value for the test was found to be .0284. State the correct conclusion.
Question 22 options:
At ? = .025, we fail to reject H0.
At ? = .05, we fail to reject H0.
At ? = .03, we fail to reject H0.
At ? = .02, we reject H0.
Answer:
Claim : The average time spent on a delivery does not exceed 25 minutes.
n = 21
We are given that p-value for the test was found to be .0284.
Now we are supposed to state the conclusions
a) At α = .025, we fail to reject [tex]H_0[/tex].
p value = 0.0284
α = 0.025
P value > α
So, we accept the null hypothesis i.e. we fail to reject null hypothesis.
b)At α = .05, we fail to reject [tex]H_0[/tex].
p value = 0.0284
α = 0.025
P value < α
So, we reject the null hypothesis
c)At α =.03, we fail to reject [tex]H_0[/tex].
p value = 0.0284
α = 0.025
P value < α
So, we reject the null hypothesis
d)At α =.02, we reject [tex]H_0[/tex].
p value = 0.0284
α = 0.025
P value > α
So, we accept the null hypothesis i.e. we fail to reject null hypothesis.
We have seen combinatorial problems in a few places now, including India. Solve the following problem: You arrive at a restaurant and sit down with the menu. There are 3 appetizers, 3 salads, 5 entrees, and 4 desserts. How many meals (combinations of appetizer, salad, entrée and dessert) can you make? You may use any method you wish, but you must show how you arrived at the answer.
Answer:
You can make 180 meals.
Step-by-step explanation:
We can look at this problem the following way:
For each appetizers, we can choose 3 salads.
For each salad, we can choose 5 entrees. So we already have 3 salads, each with 5 possible entrees, so there are already 3*5 = 15 possibilities.
For each entree, we can choose 4 desserts. So for each of the 15 possibilites of salad and entrees, there are 4 desserts. So there are 15*4 = 60 possibilities.
There are also 3 appetizers possible for each of the 60 possibilities of salads, entrees and desserts. So there are 60*3 = 180 possibilities.
James sends text messages from his cell phone. the chart below shows how many messages he sent each day what is the median of this set of data?
The chart says Monday 20 Tuesday 25 Wednesday 36 and Thursday 29
Answer:
The median of this set of data is 30.5 .
Step-by-step explanation:
The chart below shows how many messages he sent each day
Monday 20
Tuesday 25
Wednesday 36
Thursday 29
Now we are supposed to find the median
n = 4 (even)
[tex]Median = \frac{\frac{n}{2}th +(\frac{n}{2} +1)th}{2}[/tex]
[tex]Median = \frac{\frac{4}{2}th +(\frac{4}{2} +1)th}{2}[/tex]
[tex]Median = \frac{2nd +3rd}{2}[/tex]
[tex]Median = \frac{25+36}{2}[/tex]
[tex]Median = 30.5[/tex]
Hence The median of this set of data is 30.5 .
Answer:
27
Step-by-step explanation:
25 + 29 = 54 / 2 = 27
have fun with your answer
An article reports "attendance increased 5% this year, to 4948." What was the attendance before the increase? (Round your answer to the nearest whole number.)
Answer: The attendance before the increase was 4712.
Step-by-step explanation:
Let the attendance before the increase be 'x'.
Rate of increment = 5%
so, Attendance after increment becomes
[tex]\dfrac{100+5}{100}\times x = 4948\\\\\dfrac{105}{100}\times x=4948\\\\1.05\times x=4948\\\\x=\dfrac{4948}{1.05}\\\\x=4712.38\\\\x=4712[/tex]
Hence, the attendance before the increase was 4712.
Final answer:
To find the original attendance, an equation was formulated where the original attendance (x) increased by 5% equals 4,948. By solving for x, the original attendance before the increase was determined to be approximately 4,712 when rounded to the nearest whole number.
Explanation:
The question asks to find the original attendance before a 5% increase that resulted in a final attendance of 4,948. To calculate the initial attendance, you can set up an equation where the original attendance (which we will call 'x') plus 5% of the original attendance equals the final attendance (4,948).
This can be expressed algebraically as:
x + 0.05x = 4948
Solving for x gives you:
1.05x = 4948
x = 4948 / 1.05
x = 4,712 (rounded to the nearest whole number)
Therefore, the attendance before the increase was approximately 4,712.
Callie's Gym is a complete fitness center. Owner Callie Ducain employs various fitness trainers who are expected to staff the front desk and to teach fitness classes. While on the front desk, trainers answer the phone, handle walk-ins and show them around the gym, answer member questions about the weight machines, and do light cleaning (wiping down the equipment, vacuuming the floor). The trainers also teach fitness classes (e.g., pilates, spinning, body pump) according to their own interest and training level. The cost of the fitness trainers is $600 per month and $30 per class taught. Last month, 100 classes were taught and five trainers were employed.
Required:
(1) Develop a cost equation for total cost of labor.
(2) What was total variable labor cost last month?
(3) What was total labor cost last month?
(4) What was the unit cost of labor (per class) for last month?
(5) What if Callie increased the number of classes offered by 50 percent?
Answer:
a)Total Labor Cost = $600x + $30y.
b) Total variable cost = $3000.
c) Total labor cost last month = $6000.
d) Unit cost of labor per class = $60.
e) Total variable labor cost = $30 * 150 = $4500, Total Labor Cost = $3000 + $4500 = $7500, and Unit cost of labor per class = $7500/150 = $50.
Step-by-step explanation:
a) It is given that the labor cost includes two components: cost of trainers, which is actually their salaries, and cost of a fitness class taught. Fitness trainer costs $600 and one fitness class costs $30. Assuming there are x number of trainers and y number of classes, therefore the model can be expressed as:
Total Labor Cost = Fitness Trainer Cost * number of trainers + Fitness Class Cost * number of classes.
Total Labor Cost = $600x + $30y.
b) The total variable labor cost will be the cost spent on the number of classes. Since number of classes are 100 and the cost of one class is $30, therefore:
Total variable cost = cost of one class * number of classes.
Total variable cost = $30 * 100.
Total variable cost = $3000.
c) Furthermore, last month, x = 5 and y = 100. Plug these values in the total labor cost equation:
Total labor cost last month = $600(5) + $30(100).
Total labor cost last month = $3000 + $3000.
Total labor cost last month = $6000.
d) The total labor cost is $600. Number of classes are 100. Therefore:
Unit cost of labor per class = Total Labor Cost/Number of classes.
Unit cost of labor per class = $6000/100.
Unit cost of labor per class = $60.
e) If the number of classes are increases by 50%, this means that the number of classes will be 150 instead of 100. Therefore:
Total variable labor cost = $30 * 150 = $4500.
Total Labor Cost = $3000 + $4500 = $7500.
Unit cost of labor per class = $7500/150 = $50!!!
Which of the following statements is NOT true about triangles?
A. The sum of interior angles in any triangle is always equal to 180 degrees
B. The square of the hypotenuse of a right-angle triangle equals the sum of the squares of the other two sides
C. The ratio of a side of a plane triangle to the sine of the opposite angle is the same for all three sides
D. The ratio of a sine of an angle of a plane triangle to the opposite side is the same for all three angles
E. None of the above
Answer:
For the given question the correct answer is option 'C'.
Step-by-step explanation:
For a plane triangle we have:
1) Sum of the all the interior angles is 180 degrees. Hence option 'A' is correct.
2) For a right angled triangle from Pythagoras theorem we know that [tex]H^2=a^2+b^2[/tex]
where,
H is the hypotenuse of the triangle
a,b are the sides of the right angled triangle
hence the option 'B' is also correct
3) For any triangle ABC we know that
[tex]\frac{sin(A)}{BC}=\frac{sin(B)}{AC}=\frac{sin(C)}{AB}=constant[/tex]
hence option 'D' is also correct.
Thus only incorrect answer among the given option is 'C'.
A survey was conducted among 78 patients admitted to a hospital cardiac unit during a two-week period. The data of the survey are shown below. Let B equals the set of patients with high blood pressure. Let C equals the set of patients with high cholesterol levels. Let S equals the set of patients who smoke cigarettes.n(B) equals 36 n(B intersect S) equals 10 n(C) equals 34 n(B intersect C) equals 12 n(S) equals 30 n(B intersect C intersectS) equals 5 n[(B intersect C) union (B intersect S) union (C intersect S)] equals 21
Sets and set operations are ways of organizing, classifying and obtaining information about objects according to the characteristics they possess, as objects generally have several characteristics, the same object can belong to several sets, an example is the subjects of a school , where students (objects) are classified according to the subject they study (set).
The intersection of sets is a new set consisting of those objects that simultaneously possess the characteristics of each intersected set, the intersection of two subjects will be those students who have both subjects enrolled.
The union of sets is a new set consisting of all the objects belonging to the united sets, the union of two subjects will be all students of both courses.
In this case there are three sets B, C and S of which we are given the following information:
Answer
n(BꓵSꓵC)=5
n(BꓵS)=10 – 5 = 5
n(BꓵC)=12 – 5 = 7
n[(BꓵC)ꓴ(BꓵS)ꓴ(CꓵS)]=21 – 5 – 5 – 7 = 4
n(B)=36 – 5 – 5 – 7 = 19
n(S)=30 – 5 – 5 – 4 = 16
n(C)=34 – 5 – 7 – 4 = 18
If a is an integer, prove that (14a + 3, 21a + 4) = 1.
Answer:
(14a+3, 21+4) = 1
Step-by-step explanation:
We are going to use the Euclidean Algorithm to prove that these two integers have a gcd of 1.
gcd (14a + 3, 21a + 4) = gcd (14a+3, 7a + 1) = gcd (1, 7a+1) = 1
Therefore,
(14a + 3, 21a + 4) = 1
what‘s -x if x is -4? is it 4 or -4?
Answer:
If x = -4, then -x = 4.
Step-by-step explanation:
The procedure for answering this question is straightforward, you just have to substitute the value of x, when you write -x:
If x = -4, then -x = -(-4) = 4 (remember the law of signs)
Therefore: -x = 4.
It actually holds for any real number.
A bird flies from its nest (528 1/5) to the bottom of the canyon (-89 3/5). How far did the bird fly?
same as before here, the bird is up above and from there goes down, so we sum up both amounts.
[tex]\bf \stackrel{mixed}{528\frac{1}{5}}\implies \cfrac{528\cdot 5+1}{5}\implies \stackrel{improper}{\cfrac{2641}{5}}~\hfill \stackrel{mixed}{89\frac{3}{5}}\implies \cfrac{89\cdot 5+3}{5}\implies \stackrel{improper}{\cfrac{448}{5}} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{2641}{5}+\cfrac{448}{5}\implies \stackrel{\textit{using an LCD of 5}}{\cfrac{(1)2641+(1)448}{5}}\implies \cfrac{3089}{5}\implies 617\frac{4}{5}[/tex]
Answer:
[tex]617\frac{4}{5}[/tex]
Step-by-step explanation:
We have been given that a bird flies from its nest [tex]528\frac{1}{5}[/tex] to the bottom of the canyon [tex]-89\frac{3}{5}[/tex].
First of all, we will convert both mixed fractions into improper fraction.
[tex]528\frac{1}{5}\Rightarrow \frac{2640+1}{5}=\frac{2641}{5}[/tex]
[tex]89\frac{3}{5}\Rightarrow \frac{445+3}{5}=\frac{448}{5}[/tex]
To solve our given problem, we will find difference of both elevations as:
[tex]\frac{2641}{5}-(-\frac{448}{5})[/tex]
[tex]\frac{2641}{5}+\frac{448}{5}[/tex]
[tex]\frac{2641+448}{5}[/tex]
[tex]\frac{3089}{5}[/tex]
[tex]617\frac{4}{5}[/tex]
Therefore, the bird flown [tex]617\frac{4}{5}[/tex] units.
Juliana wants to write the number twenty thousand, one hundred ninety in expanded notation. Which the following would complete the expression? Select all that apply.
(2x?)+(1x100)+(9x10)
A. 1,000
B. 10^4
C. 100,000
D. 10^3
E. 10,000
Answer: B
Step-by-step explanation:
twenty thousand is 20,000
10^4 is 10,000
2x10,000 = 20,000
The completed expression would be (2×10,000) + (1×100) + (9×10) which is the correct option (B) 10^4
What is Number Line?In math, a number line can be defined as a straight line with numbers arranged at equal segments or intervals throughout. A number line is typically shown horizontally and can be extended indefinitely in any direction.
The numbers on the number line increase as one moves from left to right and decrease on moving from right to left.
Juliana wants to write the numbers twenty thousand, and one hundred ninety in expanded notation.
Given the expression as (2×?)+(1×100)+(9×10)
Here (2×10,000) + (1×100) + (9×10)
Since twenty thousand is 20,000
⇒ 10⁴ is 10,000
⇒ 2×10,000
⇒ 20,000
Hence, the completed expression would be (2×10,000) + (1×100) + (9×10)
Learn more about the number line here:
brainly.com/question/17617832
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Two resistors have the values as given, R1 = 110Ω, and R2 = 560Ω. Find the equivalent resistance when the two resistors are in series and when the two resistors are in parallel.
Answer: SERIES = 670 Ω
PARALLEL = 91.94 Ω
Step-by-step explanation:
Hi, resistors in series obey the following equation :
R1+ R2 = RT
RT is the equivalent resistance. We have the value of both resistances, so we apply the ecuation:
R1 = 110Ω, and R2 = 560Ω
110Ω+ 560Ω = 670 Ω
When resistors are in parallel, resistors obey the following equation:
1/R1 + 1/R2= 1/RT
so, in our case:
1/ 110Ω +1/560Ω = 1/rt
0.01087Ω = 1/RT
RT= 1/0.01087 Ω= 91.94 Ω
The revenue from manufacturing and selling x units of toaster ovens is given by:
R(x) = –.03x^2 + 200x – 82,000
How much revenue should the company expect from selling 3,000 toaster ovens?
Answer:
$248,000.
Step-by-step explanation:
We have been given that the revenue from manufacturing and selling x units of toaster ovens is given by [tex]R(x)=-0.3x^2+200x-82,000[/tex].
To find the amount of revenue earned from selling 3,000 toaster, we will substitute [tex]x=3,000[/tex] in the given formula as:
[tex]R(3,000)=-0.03(3,000)^2+200(3,000)-82,000[/tex]
[tex]R(3,000)=-0.03*9,000000+600,000-82,000[/tex]
[tex]R(3,000)=-270,000+518,000[/tex]
[tex]R(3,000)=248,000[/tex]
Therefore, the company should expect revenue of $248,000 from selling 3,000 toaster ovens.