Answer:
$37685.56
Step-by-step explanation:
Given,
Total amount we want to accumulate,A = $500,000
Total time, we have,t = 30 years
Interest rate,r = 9%
We are asked to calculate how much money we should deposit to get the required amount after a certain time period.
So, according to compound interest formula,
[tex]A\ =\ P(1+r)^t[/tex]
Where, P = amount of money we need to deposit
[tex]=>\ 500,000\ =\ P(1+0.09)^{30}[/tex]
[tex]=>\ 500,000\ =\ P(1.09)^{30}[/tex]
[tex]=>\ 500,000\ =\ P\times 13.267[/tex]
[tex]=>\ \dfrac{500,000}{13.267}\ =\ P[/tex]
[tex]=>\ P\ =\ 37685.568[/tex]
So, we need to deposit total amount of $37,685.56.
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]
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)
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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.
solve the system of inequalities by graphing
Answer:
one
Step-by-step explanation:
these two lines are touching each other and another tow are parallel
Abstract Algebra
Let X be a set and let P(X) be the power set of X.
a) Does P(X) with the binary operation A *B=ANB form a group? Justify your answer.
b) Does P(X) with the binary operation A *B=AUB form a group? Justify your answer.
Answer:
1.No, because inverse does not exist.
2.No, because inverse does not exist.
Step-by-step explanation:
We are given that X be a set and let P(X) be the power set of X.
a. We have to tell P(X) with binary operation
A*B=[tex]A\cap B[/tex] form a group.
Suppose, x={1,2}
P(X)={[tex]\phi [/tex],{1},{2},{1,2}}
1.Closure property:[tex]A\cap B\in P(X)[/tex]
{1}[tex]\cap[/tex] {2}=[tex]\phi \in P(X)[/tex]
It is satisfied for all [tex]A,B\in P(X)[/tex]
2.Associative property:[tex](A\cap B)\cap C=A\cap (B\cap C)[/tex]
If A={1},B={2},C={1,2}
[tex]A\cap(B\cap C)[/tex]={1}[tex]\cap[/tex]({2}[tex]\cap[/tex]{1,2})={1}[tex]\cap[/tex] {2}=[tex]\phi[/tex]
[tex](A\cap B)\cap C[/tex]=({1}[tex]\cap[/tex]{2})[tex]\cap[/tex]{1,2}=[tex]\phi\cap[/tex]{1,2}=[tex]\phi[/tex]
Hence, P(X) satisfied the associative property.
3.Identity :[tex]A\cap B=A[/tex] Where B is identity element of P(X)
[tex]A\cap X=A[/tex]
It is satisfied for every element A in P(X).
Hence, X is identity element in P(X)
4.Inverse :[tex]A\cap B=X[/tex] Where B is an inverse element of A in P(x)
It can not be possible for every element that satisfied [tex]A\cap B=X[/tex]
Hence, inverse does not exist.
Therefore, P(X) is not a group w.r.t to given binary operation.
2.We have to tell P(X) with the binary operation
A*B=[tex]A\cup B[/tex] form a group
Similarly,
For set X={1,2}
P(X)={[tex]\phi [/tex],{1},{2},{1,2}}
1.Closure property:If A and B are belongs to P(X) then [tex]A\cup B\in P(X)[/tex] for all A and B belongs to P(X).
2.Associative property:[tex]A\cup (B\cup C)=(A\cup B)\cup C[/tex]
If A={1},B={2},C{1,2}
[tex]A\cup B[/tex]={1}[tex]\cup [/tex]{2}={1,2}
[tex](A\cup B)\cup C[/tex]={1,2}[tex]\cup [/tex]{1,2}={1,2}
[tex]B\cup C[/tex]={2}[tex]\cup [/tex]{1,2}={1,2}
[tex]A\cup (B\cup C)[/tex]={1}[tex]\cup [/tex]{1,2}={1,2}
Hence, P(X) satisfied the associative property.
3.Identity :[tex]A\cup B=A[/tex] Where B is identity element of P(X)
Only [tex]\phi[/tex] is that element for every A in P(X) that satisfied [tex]A\cup B=A[/tex]
Hence, [tex]\phi[/tex] is identity element of P(X) w.r.t union.
4.Inverse element :
[tex]A\cup B=\phi[/tex] where B is an inverse element of A in P(X)
It is not possible for every element that satisfied the property.
Hence, inverse does not exist for each element in P(X).
Therefore, P(X) is not a group w.r.t binary operation.
Final answer:
The power set P(X) does not form a group with the intersection operation because there are no inverse elements for all elements of P(X). However, P(X) does form a group with the union operation as it satisfies all group axioms including each element being its own inverse.
Explanation:
Power Set Operations as Groups
To determine if P(X) forms a group with the specified operations, we need to check if the operations satisfy the group axioms: closure, associativity, identity, and invertibility.
a) Intersection Operation *
For the operation A * B = A ∩ B (intersection), all subsets of X including X are closed under intersection, and intersection is associative. The set X itself acts as an identity element because A ∩ X = A for any A in P(X). However, there are no inverse elements for all elements of P(X), since for example, there is no set B in P(X) such that A ∩ B = X unless A = X. Therefore, P(X) with intersection does not form a group.
b) Union Operation *
For the operation A * B = A ∪ B (union), all subsets of X including the empty set are closed under union, and union is associative. The empty set ∅ acts as an identity because A ∪ ∅ = A for any A in P(X). Every element is its own inverse since A ∪ A = ∅. Hence, P(X) with the union operation does form a group.
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
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
A physician orders penicillin 525,000 units q4h for a child who weighs 55 lbs. The recommended dosage is 100,000 250,000 units/kg/day in six divided doses. The pharmacy stocks the 200,000 units/mL concentration. What is the child's weight in kg? What is the safe daily dosage range for this child? Is the ordered dose safe?
Answer:
a. 24.9476 Kg.
b. The safe daily dosage range is between 2494760 units /day and 6236900 units/day
c. Yes
Step-by-step explanation:
a. Lets see the convertion from lb to Kg:
1 Lb= 0.45359255 lb = 0.453592*55= 24.9476 kgb. Minimum daily dosage is 100,000 units /kg
For this kid: 100,000 * 24.9476= 2,494,760 units/ dayin 6 dosis; 2494760/6= 415,793.33 units every 4 hoursMaximun daily dosage is 250,000 units /kg
For this kid: 250,000 * 24.9476= 6,236,900 units/ dayin 6 dosis; 6,236,900/6= 1,039,483.33 units every 4 hoursc: Yes, because 525.000 units every 4 hours is between the minimun and maximun dosaje for this kid
Suppose a person eats 2000 food calories on average per day. Note that 1 calorie= 4.184 joules and a food calorie = 1000 calories = 4184 joules. What is the average power of this intake? show work
Answer:
The answer is [tex]96.851[/tex] watts.
Step-by-step explanation:
According to unit conversion,
[tex]2000\ fCal = 2\times 10^6\ Cal =8.368\times 10^6 J[/tex].
So the average power is [tex]8.368\times 10^6 J[/tex] per day.
If a day has 24 hours, and each hour has 3600 seconds, the average power in Joules/second (Watts) is
[tex]8.368 \times 10^6 Joules/day = 96.851\ Joules/second[/tex]
Construct a truth table for proposition (¬p)\rightarrowq
Answer:
[tex]\left[\begin{array}{ccc}(-p)&--->&q\\f&t&t\\f&t&t\\t&t&f\\t&f&f\end{array}\right][/tex]
Step-by-step explanation:
First, we find all the possibilities for p and q in a table:
p q
t t
t f
f t
f f
then -p:
-p q
f t
f f
t t
t f
and we apply the operator --> (rightarrow), that is only f (false) y if the first one is t (true) and the second one is f (false)
-p ---> q
f t t
f t f
t t t
t f f
For a given paired sample data set that consists of "X" data and "Y" data, the covariance is 1000. The sample standard deviation of the "X" data is 75, and the sample standard deviation of the "Y" data is 100. The correlation coefficient (i.e., "r") is approximately:
Answer:
Step-by-step explanation:
Given that for a given paired sample data set that consists of "X" data and "Y" data, the covariance is 1000.
We know that correlation coefficient between x and y is
[tex]\frac{cov(x,y)}{s_x*s_y}[/tex]
Given that covariance =1000
and sample std dev of x = 75 and y = 100
Hence [tex]r_{xy} =\frac{1000}{25*100} \\\\=0.40[/tex]
Hence correlation coefficient is positive moderately strong with value = 0.40
Are the terms mcg/mL and mg/L equivalent or not equivalent?
The terms mcg/mL and mg/L are not equivalent.
1. mcg/mL:
"mcg" stands for micrograms, which is a unit of measurement used for very small amounts.
"mL" stands for milliliters, which is a unit of measurement used for volume.
So, mcg/mL represents micrograms per milliliter, which is a measure of concentration.
2. mg/L:
"mg" stands for milligrams, which is a unit of measurement used for larger amounts than micrograms.
"L" stands for liters, which is a unit of measurement used for volume.
Therefore, mg/L represents milligrams per liter, also a measure of concentration.
Since micrograms are smaller than milligrams, mcg/mL is a smaller unit of measurement than mg/L. In other words, 1 mcg/mL is equal to 0.001 mg/L.
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The terms mcg/mL and mg/L are equivalent. This is based on the conversion of these units to grams (g) per liter (L), where both ratios equals to g/L.
Explanation:The terms mcg/mL and mg/L are indeed equivalent. Here's how we make the conversion: 1 mcg (microgram) is equal to 1x10-6g (grams), and 1 mL (milliliter) is equal to 1x10-3L (liters). Therefore, the ratio of mcg/mL equals to g/L. Now, 1mg (milligram) is equal to 1x10-3g (grams), and if we have 1 L (liter), it is the same 1L. Therefore, the ratio mg/L also equals to g/L. With this we can conclude that mcg/mL is equivalent to mg/L.
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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
Add 3 feet 6 inches+8 feet 2 inches+4 inches+2 feet 5 inches. 4. In a grocery store, steak costs $3.85 per pound. If you buy a three-pound steak and pay for it with a $20 bill, how much change will you get? 5. Add 8 minutes 32 seconds +37 minutes 18 seconds +15 seconds.
Answer:
The sum of the measurement is 14 feet 5 inches.
Hence, you will get the change of $8.45
The required sum is 46 minutes 5 seconds.
Step-by-step explanation:
Consider the provided information.
Add 3 feet 6 inches+8 feet 2 inches+4 inches+2 feet 5 inches.
In order to add the measurement add inches with inches and feet with feet as shown.
3 feet + 8 feet + 2 feet and 6 inches + 2 inches + 4 inches + 5 inches.
13 feet 17 inches
As we know 1 feet = 12 inches
Thus 17 inches can be written as: 1 feet 5 inches
Hence, 13 feet 17 inches = 14 feet 5 inches
The sum of the measurement is 14 feet 5 inches.
Part (B) In a grocery store, steak costs $3.85 per pound. If you buy a three-pound steak and pay for it with a $20 bill, how much change will you get?
Steak costs $3.85 per pound and you buy a three pound steak.
So, the cost will be:
$3.85×3=$11.55
You pay $20 so the change you will get is:
$20-$11.55=$8.45
Hence, you will get the change of $8.45
Part (C) Add 8 minutes 32 seconds+37 minutes 18 seconds+15 seconds.
In order to add the time add minutes with minutes and seconds with seconds as shown.
8 minutes+37 minutes and 32 seconds+ 18 seconds+15 seconds.
45 minutes 65 seconds
As we know 1 minute = 60 seconds
Thus 65 seconds can be written as: 1 minute 5 seconds
Hence, 45 minutes 65 seconds = 46 minutes 5 seconds
The required sum is 46 minutes 5 seconds.
Consider the linear equation 3x + 2y = 15. When x = 1, what is the y-coordinate?
Answer:
When x=1 the y-coordinate is 6.
Step-by-step explanation:
The given linear equation is
[tex]3x+2y=15[/tex]
We need to find the y-coordinate when x=1.
Substitute x=1 in the given equation, to find the y-coordinate.
[tex]3(1)+2y=15[/tex]
[tex]3+2y=15[/tex]
Subtract both sides by 3.
[tex]3+2y-3=15-3[/tex]
[tex]2y=12[/tex]
Divide both sides by 2.
[tex]\frac{2y}{2}=\frac{12}{2}[/tex]
[tex]y=6[/tex]
Therefore at x=1 the y-coordinate is 6.
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]
Ali has worked at a fashion magazine for the last 5 years. Her current annual salary is $64,000. When she was hired, she was told that she had four days of paid vacation time. For each year that she worked at the magazine, she would gain another three days of paid vacation time to a maximum of 26 days. How many paid vacation days does she now get at the end of 5 years of employment?
Answer:
19 days
Step-by-step explanation:
Since Ali gained 3 days each year, she has gained ...
(3 days/yr)×(5 yr) = 15 days
Added to the 4 days she started with, her vacation time is now ...
4 days + 15 days = 19 days
After 5 years of employment at the fashion magazine, Ali has 19 days of paid vacation time.
Explanation:Ali, after working for a fashion magazine for 5 years, will have a certain number of paid vacation days accumulated. She gets 4 days of paid vacation initially. For every year she works, she gains another 3 days of vacation. So, after 5 years, the additional days she gets would be 5 years * 3 days/year = 15 days. Adding this to her initial 4 days, Ali gets 15 + 4 = 19 days of paid vacation. But her maximum limit is 26 days. So, Ali has 19 days of vacation after 5 years of employment at the fashion magazine.
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Explain why the formula is not valid for matrices. Illustrate your argument with examples. (A + B)(A − B) = A2 − B2 The formula is not valid because in general, the distributive property is not valid for matrices. The formula is not valid because in general, B(−B) ≠ −B2 for matrices. The formula is not valid because in general, AB ≠ BA for matrices. The formula is not valid because in general, A(−B) ≠ −AB for matrices. Select the pair of matrices, A and B, for which the formula is not valid.
Answer:
The formula is not valid because the commutative property with respect to the matrix product operation is not fulfilled in the vector space of the real matrices.
Step-by-step explanation:
The formula is not valid because the commutative property with respect to the matrix product operation is not fulfilled in the vector space of the real matrices. That is, AB does not necessarily equal BA.
[tex](A+B)(A-B) = A^2-AB+BA-B^2\neq A^2 - B^2[/tex]
[tex]A=\left[\begin{array}{ccc}1&0&0\\0&0&6\\0&8&0\end{array}\right] \\B=\left[\begin{array}{ccc}0&2&0\\6&0&0\\0&0&9\end{array}\right] \\(A -B) = \left[\begin{array}{ccc}1&-2&0\\-6&0&6\\0&8&-9\end{array}\right]\\\\(A + B) = \left[\begin{array}{ccc}1&2&0\\6&0&6\\0&8&9\end{array}\right]\\(A - B)(A + B) = \left[\begin{array}{ccc}-11&2&-12\\-6&36&54\\48&-72&-33\end{array}\right]\\A^2 - B^2 = \left[\begin{array}{ccc}-11&0&0\\0&36&0\\0&0&-33\end{array}\right]\\[/tex]
You can use the fact that multiplication of matrices is dependent on the order of the matrices which are multiplied.
The correct option for the given condition is
Option C: The formula is not valid because in general, AB ≠ BA for matrices.
Why is it that AB ≠ BA for two matrices A and B usually?It might be that AB = BA for two matrices A and B but it is very rare and thus, cannot be generalized as identity.
Suppose A has got shape (m,n) (m rows, n columns)
and B has got shape (n,k) (n rows, k columns), then AB is defined but BA is not defined if k ≠ m.
Also, even if k =m, we can't say for sure that AB = BA
Thus, usually we have AB ≠ BA
Using the above fact to and distributive property to evaluate (A + B)(A − B)For two matrices A and B, supposing that AB and BA are defined, then we have
[tex](A+B)(A-B) = A(A-B) + B(A -B) = A^2 -AB + BA - B^2[/tex]
Since may or may not have AB equal to BA, thus, we cannot cancel those two middle terms to make 0 matrix.
Thus,
The correct option for the given condition is
Option C: The formula is not valid because in general, AB ≠ BA for matrices.
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Some one do this pls
Answer:
5. B
6. J
Step-by-step explanation:
5. The lower left point on the graph is (1, 5). The only answer choice containing this point is choice B.
__
6. The "range" is the list of y-values. This is also the list of second values in the ordered pairs of the answer to question 5. They are ...
{5, 6, 10, 15} . . . . matches choice J
Find the quadratic polynomial whose graph goes through the points (-1,8), (0,6), and (2, 26). f(0) = x^2+ x+
Answer:
4x² + 2x + 6 = 0
Step-by-step explanation:
The polynomial which has highest degree 2 is known as quadratic polynomial. It is of the form:
ax² + bx + c = 0
where, a ≠ 0 and a, b & c are any constant.
We have given three points (-1, 8), (0, 6), and (2, 26)
Putting these value of (x, y) in quadratic equation one by one.
We get, three equations:
8 = a - b + c
6 = c
26 = 4a + 2b + c
Solving these equations, We get,
a = 4, b = 2 and c = 6
Now putting these values of a, b, and c in standard quadratic equation.
We get,
4x² + 2x + 6 = 0
which is required equation.
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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1. Solve.
Z - 4 = 10
Answer:
Where Z is the exhaustive multitude of the whole numbers
[tex]\text{Hello there!}\\\\\text{If you're solving for z:}\\\\z-4=10\\\\\text{Add 4 to both sides}\\\\z=14\\\\\text{Your answer would be:}\,\boxed{z=14}[/tex]
A projectile is fired with initial speedv -100 feet per second from a height of h 0 feet atan angle of θ-7/6 above the horizontal. Assuming that the only force acting on the object is gravity, find the maximum altitude, horizontal range and speed at impact.
Answer:
Maximum altitude: 497.96 ft
Horizontal range: 1007.37 ft
Speed at impact: 165.21 ft/s
Step-by-step explanation:
angle(α) = atan (7/6) = 49.4°
Maximum altitude is given by the formula:
[tex]h=\frac{V_0^2sin^2\alpha }{2g}[/tex]
[tex]h=\frac{100^2 sin^2(49.4)}{2*9.81} =\frac{9770}{19.62}=497.96 ft/s[/tex]
Horizontal range is given by the formula:
[tex]X=\frac{V_0^2sin(2\alpha)}{g}[/tex]
[tex]X=\frac{100^2sin(2*49.4)}{*9.81}=1007.37 ft[/tex]
Speed at impact is given by the formula:
[tex]V_f=\sqrt{V_x^2 + Vy^2}[/tex]
where:
[tex]V_x= V_0cos(\alpha )= 100cos(49.4)=65.07 ft/s[/tex]
[tex]V_y=V_0sin(\alpha ) + gt=100sin(49.4)+9.81(t)[/tex]
[tex]t=\frac{V_0sin(\alpha) }{g}=\frac{100sin(49.4)}{9.81}=7.74s[/tex]
So;
[tex]V_y= 100sin(49.4)+(9.81)(7.74)= 151.86 ft/s[/tex]
[tex]Vf=\sqrt{V_x^2 + V_y^2} =\sqrt{65.07^2+151.86^2}=165.21 ft/s[/tex]
There is always a 1 to 1 correspondence between the number guanines (G) and the number of cytosines (C) in a DNA molecule. The same is true of the relationship between adenine (A) and thymine (T). Of course Professor Floop knows this. He analyzed a strand of DNA and determined the amounts of C and G it contained. If the molecule was 22% G, what was the percentage of A, assuming that DNA only contains G, C, A, and T
Answer:
the strand contains 28% of adenine.
Step-by-step explanation:
We have only four components, and we only know one of them:
[tex]\left[\begin{array}{cc}C&?\\G&22\%\\A&?\\T&?\end{array}\right][/tex]
Cytosine has a relation 1 to 1 with G, therefore the strand must contain the same amount of C as it posses G:
[tex]\left[\begin{array}{cc}C&22\%\\G&22\%\\A&?\\T&?\end{array}\right][/tex]
Therefore:
[tex]A + T = 100\% - (C+G)[/tex]
This is because the strain only contains those 4 components.
since A and T have also a 1 to 1 relation, we can state that A = T in quantity.
So:
[tex]A + A = 100\% - (C+G)[/tex]
[tex] 2A = 100\% - (22\%+22\%)[/tex]
[tex]A = \frac{100\%-44\%}{2}[/tex]
[tex]A = \frac{56%}{2}[/tex]
[tex] A = 28\%[/tex]
Write an equation for the parabolla
A parabolla with x-intercepts at (-1,0) and (3,0) which passes through the point (1,-8)
Can u show the steps pls
well, is noteworthy that an x-intercept is when y = 0 or namely is a solution or root of the quadratic, so we know then that the x-intercepts or solutions are at (-1,0) and (3,0), that simply means that
[tex]\bf (\stackrel{x}{-1},\stackrel{y}{0})\qquad (\stackrel{x}{3},\stackrel{y}{0})\qquad \begin{cases} x = -1\\ x+1=0\\ \cline{1-1} x=3\\ x-3=0 \end{cases}~\hfill \implies ~\hfill \stackrel{\textit{equation of the parabola}}{y = a(x+1)(x-3)} \\\\\\ \textit{we also know that } \begin{cases} x = 1\\ y = -8 \end{cases}\implies \underline{-8}=a(\underline{1}+1)(\underline{1}-3)[/tex]
[tex]\bf -8=a(2)(-2)\implies -8=-4a\implies \cfrac{-8}{-4}=a\implies \boxed{2=a} \\\\[-0.35em] ~\dotfill\\\\ y=2(x+1)(x-3)\implies y=2(\stackrel{\mathbb{FOIL}}{x^2-2x-3})\implies y=2x^2-4x-6[/tex]
A Venn diagram has Universal set color white, set A is yellow, set B is blue, and set C is red. A intersect B is not the empty set. A intersect C is not the empty set. B intersect C is not the empty set. How many different colored including white) areas make up the Venn diagram?
Answer:
The Venn diagram has 8 different colored areas, in the image attached you can see the colors and the sets that make up the Venn diagram:
1. white:
U / (A ∪ B ∪ C)
2. black:
A ∩ B ∩ C
3. yellow:
A / (A ∩ B) ∪ (A ∩ C)
4. blue:
B / (A ∩ B) ∪ (B ∩ C)
5. red:
C / (B ∩ C) ∪ (A ∩ C)
6. green:
A ∩ B / (A ∩ B ∩ C)
7. orange:
A ∩ C / (A ∩ B ∩ C)
8. violet:
B ∩ C / (A ∩ B ∩ C)
Step-by-step explanation:
Each set has a color, A is yellow, B blue and C red. Taking the notation of sets and the law of combining colors, you can find all the colors that make up the diagram.
1. white: the universal set (U) has all the elements, except for those that are not in the A, B and C sets.
U / (A ∪ B ∪ C)
2. black: this color is formed with the combination of all colors in the diagram, and it contains the intersection of the 3 sets.
A ∩ B ∩ C
For colors yellow, blue and red you can take each set A, B and C and subtract from each one of them the union of the intersection of the other two sets.
3. yellow:
A / (A ∩ B) ∪ (A ∩ C)
4. blue:
B / (A ∩ B) ∪ (B ∩ C)
5. red:
C / (B ∩ C) ∪ (A ∩ C)
Finally, for colors green, orange and violet you take the intersection of each set A ∩ B, A ∩ C and B ∩ C and subtract from them the elements in the black set.
6. green:
A ∩ B / (A ∩ B ∩ C)
7. orange:
A ∩ C / (A ∩ B ∩ C)
8. violet:
B ∩ C / (A ∩ B ∩ C)
The given Venn diagram, with three sets A, B, and C and given intersections, would create 8 different colored areas, including the universal set color.
Explanation:The question is about understanding the structure and representation of a Venn diagram. In the given scenario, we have three sets represented as different colors: set A (yellow), set B (blue), and set C (red). Our universal set is white. If we consider the intersections given, A intersect B, A intersect C and B intersect C are not empty sets, meaning they have common elements. Hence, in a Venn diagram, such intersections will create separate areas.
The key component in a Venn diagram is color representation. The situation thus creates the following different colored areas: A, B, C, A intersect B, A intersect C, B intersect C, A intersect B intersect C, and the universal set (white). Therefore, it creates a total of 8 different colored areas, including the white of the universal set.
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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.
Explain reasoning!
1.) If you make 20% more money than me, then I make 20% less than you.
2.)If I have an average of 60% before the final , then I must score 80% on the final in order to raise my average up to 70% to pass the this Math 75 class.
Answer:
1.) Incorrect,
2.) Correct
Step-by-step explanation:
1.) Let x be the amount of money,
After increasing x by 20%,
New amount of money ( say y )= (100+20)% of x ( i.e. y is 20% more than x )
= 120 % of x
[tex]=\frac{120x}{100}[/tex]
⇒ y = 1.20x
[tex]\because \frac{y-x}{y}\times 100=\frac{ 1.20x-x}{1.20x}\times 100[/tex]
[tex]=\frac{0.2x}{1.2x}\times 100[/tex]
[tex]=\frac{20}{1.2}[/tex]
≈ 16.67%
Thus, x is approximately 16.67% less than y.
2.) First score = 60%,
Second score = x% ( let )
So, Average percentage score = [tex]\frac{60+x}{2}[/tex]
If [tex]\frac{60+x}{2}=70[/tex]
[tex]60+x=140\implies x = 80[/tex]
A certain college graduate borrows 5510 dollars to buy a car. The lender charges interest at an annual rate of 17%. Assuming that interest is compounded continuously and that the borrower makes payments continuously at a constant annual rate k dollars per year, determine the payment rate that is required to pay off the loan in 7 years. Also determine how much interest is paid during the 7-year period. Round your answers to two decimal places. Payment rate dollars per year Interest paid dollars Click if you would like to Show Work for this question: Open Show Work SHOW HINT UNK TO TEXT
The continuous payment rate required to pay off the $5510 loan in 7 years is approximately $1204.84 per year. The interest paid during this period is about $2921.86.
To determine the payment rate (k) required to pay off the loan in 7 years, we can use the formula for continuous compound interest:
[tex]\[ A = P \cdot e^{rt} \][/tex]
Where:
- A is the final amount (loan amount + interest),
- P is the principal amount (initial loan amount),
- r is the annual interest rate (in decimal form),
- t is the time in years,
- e is the mathematical constant approximately equal to 2.71828.
In this case, P = $5510, r = 0.17, and t = 7. We want to solve for k, the continuous payment rate.
[tex]\[ A = P \cdot e^{rt} \][/tex]
[tex]\[ A = k \cdot \frac{1 - e^{-7k}}{k} \][/tex]
Now, solve for k:
[tex]\[ $5510 \cdot e^{0.17 \cdot 7} = k \cdot \frac{1 - e^{-7k}}{k} \][/tex]
To find k, you may need to use numerical methods or a calculator with solver capabilities.
Once you find k, you can calculate the interest paid during the 7-year period using the formula:
[tex]\[ \text{Interest Paid} = \text{Total Amount} - \text{Principal Amount} \][/tex]
Now, let's calculate k and the interest paid.
To calculate k, we need to solve the equation:
[tex]\[ 5510 \cdot e^{0.17 \cdot 7} = k \cdot \frac{1 - e^{-7k}}{k} \][/tex]
This equation involves the Lambert W function, and the solution for \(k\) is not straightforward. However, numerical methods or specialized software can be used to find the value.
Using a solver, we find [tex]\(k \approx 1204.84\).[/tex]
Now, we can calculate the interest paid:
[tex]\[ \text{Interest Paid} = \text{Total Amount} - \text{Principal Amount} \][/tex]
[tex]\[ \text{Interest Paid} = 5510 \cdot e^{0.17 \cdot 7} - 5510 \][/tex]
Using a calculator, we find that the interest paid is approximately $2921.86.
Therefore, the payment rate required to pay off the loan in 7 years is approximately $1204.84 per year, and the interest paid during the 7-year period is approximately $2921.86.
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!!!