Answer:
a) P({a, b, {a, b}})=[tex] 2*2*2=8[/tex]
b) P({∅, a, {a}, {{a}}})=[tex] 2*2*2*2=16[/tex]
c) P(P(∅))=P(P{∅})=2
Step-by-step explanation:
Previous concepts
For this case we need to remember the concpts of subset and the power set.
A is a subset of B if every element of A is an eelement if B and we write [tex]A \subseteq B[/tex]
The power set of a set R is th set of all the possible subsets of R and we writ this as P(R)
Solution to the problem
Part a
P({a, b, {a, b}}) as we can see this set contains 3 elements a,b and {a,b}
And since the power set contains all the possible subsets of the elements. For this case for each element we have 3-1 = 2 options in order to combine, then the number of possible subsets would be equal to the product of possible options and we got:
P({a, b, {a, b}})=[tex] 2*2*2=8[/tex]
Part b
P({∅, a, {a}, {{a}}}) as we can see this set contains 4 elements ∅,a,{a} and {{a}}
And since the power set contains all the possible subsets of the elements. For this case for each element we have 3-1 = 2 options in order to combine, then the number of possible subsets would be equal to the product of possible options and we got:
P({∅, a, {a}, {{a}}})=[tex] 2*2*2*2=16[/tex]
Part c
P(P(∅)) for this case we need to remember that P(∅) have all the possible subsets empty, but the power set for the empty set is also empty.
P(∅)={∅}
And we see that this last one set have just one element.
For this special case we have again 2 options since we can have the element in the subset or the element that is not on the subset, so then we have this:
P(P(∅))=P(P{∅})=2
The number of elements of the set are 8, 16, and 2.
How to solve the elements?It should be noted that the objects in a set are known as the elements or members of the set.
The number of elements in the set will be calculated thus:
P({a, b, {a, b} = 2³ = 2 × 2 × 2 = 8
P({∅, a, {a}, {{a}}) = 2⁴ = 16
P(P(∅)) = 2¹ = 2
In conclusion, the correct options are 8, 16, and 2.
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match the equation with its graph 5x-4y=20
A) First Picture
B) Second Picture
C) Third Picture
D) Fourth Picture
I've attached the correct image to this answer, just in case they're scrambled.
To match the equation 5x-4y=20 with its graph, convert it to slope-intercept form to identify a positive slope of 5/4 and a y-intercept of -5. Look for a graph with these features in the provided pictures.
Explanation:To match the equation with its graph for 5x-4y=20, we first need to rewrite it in slope-intercept form, which is y=mx+b. By isolating y, we get 4y = 5x - 20, or y = (5/4)x - 5. This equation signifies a line with a slope (m) of 5/4, meaning for every increase of 4 units in x, y increases by 5 units. The y-intercept (b) is -5, indicating where the line crosses the y-axis. Now, looking at the provided pictures, we should find a graph with a positive slope of 5/4 and a y-intercept of -5.
The correct graph will rise more than it runs since the slope is greater than 1, and will cross the y-axis below the origin at -5. Without seeing the actual images, we are unable to definitively identify which picture corresponds to the given equation. Typically, you would examine each graph to see which one matches these characteristics.
Triangle PQR with vertices P(3, −6), Q(6, −9), and R(−15, 3) is dilated by a scale factor of 3 to obtain triangle P′Q′R′. Which statement best describes triangle P′Q′R′?A. It is similar to triangle PQR and has coordinates P′(1, −2), Q′(2, −3), and R′(−5, 1).B. It is congruent to triangle PQR and has coordinates P′(1, −2), Q′(2, −3), and R′(−5, 1).C. It is similar to triangle PQR and has coordinates P′(9, −18), Q′(18, −27), and R′(−45, 9).D. It is congruent to triangle PQR and has coordinates P′(9, −18), Q′(18, −27), and R′(−45, 9).
Answer:
Option C.
Step-by-step explanation:
The vertices of triangle PQR are P(3, −6), Q(6, −9), and R(−15, 3).
It is given that triangle PQR dilated by a scale factor of 3 to obtain triangle P′Q′R′.
We know that a figure and its image after dilation are similar. It means triangle PQR and triangle P′Q′R′
If a figure dilated by factor k about the origin then
[tex](x,y)\rightarrow (kx,ky)[/tex]
PQR dilated by a scale factor of 3, so
[tex](x,y)\rightarrow (3x,3y)[/tex]
Using this rule we get
[tex]P(3,-6)\rightarrow P'(3(3),3(-6))=P'(9,-18)[/tex]
[tex]Q(6,-9)\rightarrow Q'(3(6),3(-9))=Q'(18,-27)[/tex]
[tex]R(-15,3)\rightarrow R'(3(-15),3(3))=R'(-45,9)[/tex]
The vertices of image are P'(9,-18), Q'(18,-27) and R'(-45,9).
Therefore, the correct option is C.
Answer:
C
Step-by-step explanation:
If point D is placed on AC, how will the measure of DAB relate to the measure of CAB?
Answer:angle DAB will be equal to angle CAB
Step-by-step explanation:
AC is a straight line and forms one of the sides of triangle ABC. If point D is placed on line AC, angle DAB would remain equal to angle CAB since they are on the same line the angle formed with line AB remains the same.
The measure of angle DAB will be congruent to angle CAB if AB and CD are parallel and right angles to AC and AD. The relationship changes as point D moves along AC, with angle DAB diminishing if DE remains parallel to AB.
Explanation:If point D is placed on AC, the measure of ∠DAB will relate to the measure of ∠CAB based on several geometric principles. If AB is parallel to CD and D moves along AC, with DE remaining constantly parallel to AB, the angle at D (∠DAB) will diminish as D moves away from A. If AB and CD maintain parallels and AC makes equal angles with them, then accordingly ∠DAB will also equal ∠CAB at the point where the two angles are bisected by AC.
Moreover, if AB and CD are right angles to AC and AD, as described by the circle theorem stating that angles inscribed in the same arc are congruent, then ∠DAB will be congruent to ∠CAB.
The table shows the ages and weights of babies at a hospital. A 2-row table with 10 columns. The first row is labeled age (weeks) with entries 1, 2, 3, 3, 4, 4, 6, 8, 9, 9. The second row is labeled weight (pounds) with entries 7.5, 7.25, 8.2, 7.95, 8.0, 9.75, 9.25, 8.9, 9.85, 10.0. What is the correlation between age and weight as shown in the table? none positive negative constant
Answer:
Option (b) is correct.
The correlation between age and weight shown in the table is positive.
Step-by-step explanation:
According to the given values, it is found that there is a positive correlation between age and weight.
What is a correlation coefficient?It is an index that measures correlation between two variables, assuming values between -1 and 1.If it is positive, the relation is positive, that is, they are direct proportional. If it is negative, they are inverse proportional.If the absolute value of the correlation coefficient is greater than 0.6, the relationship is strong.In this problem, when the age increases, so does the weight, hence they have positive correlation.
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The Norwood Tigers are having team shirts made. One option is to pay Harold's Tees a $41 setup fee and then buy the shirts for $10 each. Another option is to go to City Printing, paying $36 for a setup fee and an additional $15 per shirt. The team parent in charge of the project notices that, with a certain number of shirts, the two options have the same cost. What is the cost? How many shirts is that?
The cost will be the same when 1 shirt is ordered.
Explanation:Cost Comparison
Option 1: Cost = $41 (setup fee) + $10 (shirt price)
Option 2: Cost = $36 (setup fee) + $15 (shirt price)
Let's assume the number of shirts is 'x'.
Equating the costs of both options:
$41 + $10x = $36 + $15x
$5x = $5
x = 1
Therefore, the cost will be the same for 1 shirt.
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Consider that the length of rectangle A is 21 cm and its width is 7 cm. Which rectangle is similar to rectangle A?
Question is incomplete, complete question is given below.
Consider that the length of rectangle A is 21 cm and its width is 7 cm. Which rectangle is similar to rectangle A? A) A rectangle with a length of 9 cm and a width of 3 cm. B) A rectangle with a length of 20 cm and a width of 10 cm. C) A rectangle with a length of 18 cm and a width of 9 cm. D) A rectangle with a length of 27 cm and a width of 3 cm.
Answer:
A) A rectangle with a length of 9 cm and a width of 3 cm.
Step-by-step explanation:
Given,
Length = 21 cm Width = 7 cm
[tex]Ratio = \frac{Length}{Width}\\\\Ratio = \frac{21}{7}=3:1[/tex]
For the similarity of rectangle the ratio of length to width of any two rectangles should be equal.
So we have four options given;
A) A rectangle with a length of 9 cm and a width of 3 cm.
[tex]Ratio =\frac{9}{3}=3:1[/tex]
Here the ratio is equal as of rectangle A. So this rectangle is similar to rectangle A.
B) A rectangle with a length of 20 cm and a width of 10 cm.
[tex]Ratio =\frac{20}{10}=2:1[/tex]
Here the ratio is not equal as of rectangle A. So this rectangle is not similar to rectangle A.
C) A rectangle with a length of 18 cm and a width of 9 cm.
[tex]Ratio =\frac{18}{9}=2:1[/tex]
Here the ratio is not equal as of rectangle A. So this rectangle is not similar to rectangle A.
D) A rectangle with a length of 27 cm and a width of 3 cm.
[tex]Ratio =\frac{27}{3}=9:1[/tex]
Here the ratio is not equal as of rectangle A. So this rectangle is not similar to rectangle A.
Thus the correct option is A) A rectangle with a length of 9 cm and a width of 3 cm.
The price of a ceryain item js P dollars. The sales tax on the item is 7%. Which expressio.N represents the total cost if the itsm , in dollars, -aftee the tas has been applied
Answer:
The expression representing the Total Cost of the item is [tex]P + 0.07P[/tex].
Step-by-step explanation:
Given:
Price of Certain item = 'P' dollars
Sales tax =7%
We need to find the expression for Total Cost of the item when tax is applied.
we will first find the Amount deducted in tax;
Amount deducted in Tax is equal to Percentage of sales tax multiplied by Price of Certain item and then divide by 100
Framing in equation form we get;
Amount Deducted in Tax = [tex]\frac{7}{100}\times P = 0.07P[/tex]
Now Total Cost of the item is equal to sum of Price of Certain item and Amount deducted in tax.
Expressing in expression form we get;
Total Cost of item = [tex]P + 0.07P[/tex]
Hence The expression representing the Total Cost of the item is [tex]P + 0.07P[/tex].
Eugene had 3 pies. He gave 1 4/5 to his friend. And kept the rest for himself. Who had more pie? How much more?
Answer:
Eugene friend will have more pie than Eugene.
Eugene friend has [tex]\frac{3}{5}[/tex] more pie than Eugene.
Step-by-step explanation:
Given:
Amount of pie Eugene has = 3
Amount of Pie given to friend = [tex]1\frac{4}{5}[/tex]
[tex]1\frac{4}{5}[/tex] can be Rewritten as [tex]\frac{9}{5}[/tex]
We need to find who has pie and how much more.
We will first find the amount of pie Eugene is left with.
The amount of pie Eugene is left with is equal to Amount of pie Eugene had minus Amount of pie given to friend.
Framing the equation we get;
The amount of pie Eugene is left = [tex]3-\frac{9}{5}[/tex]
We will take LCM to solve the same.
The amount of pie Eugene is left = [tex]3-\frac{9}{5} = \frac{3\times5}{5}-\frac{9}{5} =\frac{15}{5}-\frac{9}{5} = \frac{15-9}{5} =\frac{6}{5}[/tex]
Now [tex]\frac{9}{5} = 1.8[/tex] and [tex]\frac{6}{5} = 1.2[/tex]
Hence [tex]\frac{9}{5}[/tex] is greater than [tex]\frac{6}{5}[/tex]
Hence Eugene friend will have more pie than Eugene.
Now we will find amount more pie Eugene friend has.
Amount More Eugene friend has can be calculate by Subtracting Amount of of Eugene has with Amount of pie his friend has.
Amount More Eugene friend has =[tex]\frac{9}{5} - \frac{6}{5} =\frac{9-6}{5}= \frac{3}{5}[/tex]
Hence Eugene friend has [tex]\frac{3}{5}[/tex] more pie than Eugene.
Tran has a credit card with a spending limit of $2000 and an APR (annual percentage rate) of 12%. During the first month, Tran charged $450 and paid $150 of that in his billing cycle. Which expression will find the amount of interest Tran will be charged after the first month?
Step-by-step explanation:
Given data:
Tran has a credit card with a spending limit of $2000 and an APR (annual percentage rate) of 12%.
During the first month, Tran charged $450 and paid $150 of that in his billing cycle.
The expression which will find the amount of interest Tran will be charged after the first month is (0.012)(300)
Here 0.01 because it is 1 month tax.
300 is remaining amount as Tran used $450 but paid $150.
Answer:
its 0.01 [300]
Step-by-step explanation:
(1.005)[tex]x^{2} 400[/tex]
Jose has 5/6 hour to spend on his homework. He wants to spend 1/3 of his time on math homework, 15 minutes of his time on reading homework, and then the remaining time on science homework. How much time in minutes, does Jose have to spend on his science homework?
Jose will spend 18 minutes on his science homework.
Step-by-step explanation:
Given,
Time Jose have to spend on homework = 5/6 hour
We know that 1 hour = 60 minutes
Therefore;
[tex]\frac{5}{6}\ hour = \frac{5}{6}*60\ minutes\\\\\frac{5}{6}\ hour = 50\ minutes[/tex]
Time Jose have to spend on homework = 50 minutes
Time spent on math home work = [tex]\frac{1}{3}\ of\ his\ time[/tex]
Time spent on math home work = [tex]\frac{1}{3}*50=16.66\ minutes[/tex]
Rounding off to nearest whole minute;
Time spent on math homework = 17 minutes
Time spent on reading homework = 15 minutes
Total time spent = Mathematics + Reading + Science
50 = 17+15+Science
50 = 32 + Science
Science = 50-32 = 18 minutes
Jose will spend 18 minutes on his science homework.
Keywords: addition, fraction
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There are 225 students at March Middle School. On Friday, 135 students wore spirit shirts. What percent of the students did NOT wear spirit shirts on Friday?
Answer:
40%
Step-by-step explanation:
135 of 225 is equal to 60%. Therefore, the remaining percent, which should equal to 100, did not wear spirit shirts. 100 - 60 = 40. Therefore, 40% of students did not wear spirit shirts on Friday.
The percentage of students who did NOT wear spirit shirts on Friday is 40%
Explanation:To find the percentage of students who did NOT wear spirit shirts on Friday, we subtract the number of students who wore spirit shirts from the total number of students and divide by the total number of students.
Then, multiply by 100 to get the percentage.
Number of students who did NOT wear spirit shirts = Total number of students - Number of students who wore spirit shirts = 225 - 135 = 90.
Percentage of students who did NOT wear spirit shirts = (90 / 225) x 100 = 40%
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How many three-digit positive integers exist, all of whose digits are 2's and/or 5's?
Answer:
8
Step-by-step explanation:
There are two choices for each digit, and 3 digits, so 2^3 = 8 possible numbers. Here's a list:
222, 225, 252, 255
522, 525, 552, 555
Answer:
8
Step-by-step explanation:
The first digit has two possibilities; it can either be a 2 or a 5.
The second digit has two possibilities; it can either be a 2 or a 5.
The third digit has two possibilities; it can either be a 2 or a 5.
2 x 2 x 2 = 8 integers.
(Here are the numbers listed out):
222
225
252
255
522
525
552
555
Six hundred chances are sold at $3 apiece for a raffle. There is a grand prize of $700, two second prizes of $200, and five third prizes of $50. First calculate the expected value of the lottery. Determine whether the lottery is a fair game. If the game is not fair, determine a price for playing the game that would make it fair.
Answer:
Expected net gain is -$0.75. Not a fair game. Appropriate price is $2.25.
Step-by-step explanation:
There is 1 in 600 chance to win the grand price (1/600)
There are 2 in 600 chance to win the 2nd price (2/600 = 1/300)
There are 5 in 600 chance to win the 3rd price (5/600 = 1/120)
We can use these probability to calculate the expected gain from this game
[tex]E_g = 700\frac{1}{600} + 200*\frac{1}{300} + 50*\frac{1}{120} = \$2.25[/tex]
Since the cost to play is $3, the expected net gain from this game is
$2.25 - $3 = -$0.75
So this game is not fair as the player is losing money. The appropriate price should instead be $2.25
The expected value of $1.91 is less than the cost of $3 per ticket, indicating it is not a fair game. To make it fair, the price per ticket should be set at $1.91.
Calculate the total amount collected from selling all tickets: 600 tickets × $3 = $1800.Calculate the expected value by taking into account the probabilities of winning and the respective prizes: ($700 × 1/600) + ($200 × 2/600) + ($50 × 5/600) = $1.91.Determining Fairness:
The expected value of $1.91 is less than the cost of $3 per ticket, indicating it is not a fair game. To make it fair, the price per ticket should be set at $1.91.
Need some help with these problems!
Answer:
h=12, w=24, t=8
Step-by-step explanation:
System of Linear Equations
We have 3 unknown variables and 3 conditions between them. They form a set of 3 equations with 3 variables.
We have the following data, being
w = price of a sweatshirt
t = price of a T-shirt
h = price of a pair of shorts
19.
The first condition states the price of a sweatshirt is twice the price of a pair of shorts. We can write it as
[tex]\displaystyle w=2h[/tex]
The second condition states the price of a T-shirt is $4 less than the price of a pair of shorts. We can write it as
[tex]\displaystyle t=h-4[/tex]
The final condition states Brad purchased 3 sweatshirts, 2 pairs of shorts, and 5 T-shirts for $136, thus
[tex]\displaystyle 3w+2h+5t=136[/tex]
This is the system of equations we need to solve for w,t,h
20.
To solve the system, we replace w in terms of h and t in terms of h. Those relations have been already written, so
[tex]\displaystyle 3(2h)+2h+5(h-4)=136[/tex]
Operating
[tex]\displaystyle 6h+2h+5h-20=136[/tex]
[tex]\displaystyle 13h=156[/tex]
Solving for h
[tex]\displaystyle h=12[/tex]
The other two variables are
[tex]\displaystyle w=2h=24[/tex]
[tex]\displaystyle t=12-4=8[/tex]
Baby Kana's parents measure her height every month. H(t)H(t)H, left parenthesis, t, right parenthesis models Kana's height (in centimeters) when she was ttt months old. What does the statement H(160)=150H(160)=150H, left parenthesis, 160, right parenthesis, equals, 150 mean?
Answer:
H(160)=150 means that Kana's height is 150 cm when she is 160 months old
Step-by-step explanation:
According to the model described in the question:
H(t)=X where
X is the measure of Kana's height in centimeterst is Kana's lifetime in months when Kana's parents measure her height.Thus H(160)=150 states
150 as Kana's heights as centimeters160 as Kana's lifetime in months when her height was measured as 150 cmAnswer:
When Kana was 160 months old, her height was equal to 150 centimeters.
Step-by-step explanation:
The length, L, of a rectangle is decreasing at the rate of 2cm/sec, while the width, W, is increasing at the rate of 2 cm/sec.When L = 12 cm and W = 5 cm, find the rates of change of :______________
A) The area
B) The Perimeter
C) The lengths of the diagonals of the rectangle
Answer:
A) 14 cm² per sec
B) 0 cm per sec
C) -28 cm per sec
Step-by-step explanation:
We know that,
If l = length of a rectangle and w = width of the rectangle
A) Area of a rectangle,
[tex]A=l\times w[/tex]
Differentiating with respect to t ( time )
[tex]\frac{dA}{dt}=l\frac{dw}{dt}+w\frac{dl}{dt}[/tex]
We have,
[tex]l=12\text{ cm}, w=5\text{ cm}, \frac{dw}{dt}=2\text{ cm per sec}, \frac{dl}{dt}=-2\text{ cm per sec}[/tex]
[tex]\frac{dA}{dt}=12\times 2+5\times -2[/tex]
[tex]\frac{dA}{dt}=24-10[/tex]
[tex]\frac{dA}{dt}=14\text{ square cm per sec}[/tex]
B) Perimeter of the rectangle,
[tex]P=2(l+w)[/tex]
Differentiating with respect to t ( time ),
[tex]\frac{dP}{dt}=2(\frac{dl}{dt}+\frac{dw}{dt})=2(-2+2)=0[/tex]
C) Length of the diagonal,
[tex]D=\sqrt{l^2+w^2}[/tex]
[tex]D^2 = l^2 + w^2[/tex]
Differentiating with respect to t ( time ),
[tex]2D\frac{dD}{dt}=2l\frac{dl}{dt}+2w\frac{dw}{dt}[/tex]
Since, if l = 12 cm, w = 5 cm,
[tex]D=\sqrt{12^2+5^2}=\sqrt{144+25}=\sqrt{169}=13\text{ cm}[/tex]
[tex]\implies 2\times 13 \frac{dD}{dt}=2(12)(-2)+2(5)(2)[/tex]
[tex]26\frac{dD}{dt}=-48+20=-28\text{ cm per sec}[/tex]
Using implicit differentiation, it is found that:
a) The rate of change of the area of the rectangle is: 14 cm²/sec.
b) The rate of change of the perimeter of the rectangle is: 0 cm/sec.
c) The rate of change of the lengths of the diagonal of the rectangle is: [tex]\mathbf{-\frac{14}{13}}[/tex] cm/sec.
Item a:
The area of a rectangle of length l and width w is given by:
[tex]A = lw[/tex]
Applying implicit differentiation, the rate of change is of:
[tex]\frac{dA}{dt} = w\frac{dl}{dt} + l\frac{dw}{dt}[/tex]
For this problem, the values are:
[tex]w = 5, \frac{dl}{dt} = -2, l = 12, \frac{dw}{dt} = 2[/tex]
Then:
[tex]\frac{dA}{dt} = 5(-2) + 12(2)[/tex]
[tex]\frac{dA}{dt} = 14[/tex]
The rate of change of the area is of 14 cm²/sec.
Item b:
The perimeter is given by:
[tex]P = 2l + 2w[/tex]
Applying implicit differentiation, the rate of change is of:
[tex]\frac{dP}{dt} = 2\frac{dl}{dt} + 2\frac{dw}{dt}[/tex]
Then
[tex]\frac{dP}{dt} = 2(-2) + 2(2) = 0[/tex]
The rate of change of the perimeter is of 0 cm/sec.
Item c:
The diagonal is the hypotenuse of a right triangle in which the sides are the length and the width, then, applying the Pythagorean Theorem:
[tex]d^2 = l^2 + w^2[/tex]
The value of the diagonal is:
[tex]d^2 = 5^2 + 12^2[/tex]
[tex]d^2 = 169[/tex]
[tex]d = \sqrt{169}[/tex]
[tex]d = 13[/tex]
The rate of change is:
[tex]2d\frac{dd}{dt} = 2l\frac{dl}{dt} + 2w\frac{dw}{dt}[/tex]
Then
[tex]26\frac{dd}{dt} = -48 + 20[/tex]
[tex]26\frac{dd}{dt} = -28[/tex]
[tex]\frac{dd}{dt} = -\frac{14}{13}[/tex]
The rate of change of the lengths of the diagonals of the rectangle is of [tex]\mathbf{-\frac{14}{13}}[/tex] cm/sec.
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When solving for an unknown variable that has a number preceding it, you will divide both sides of the equation by this number, which is known as the ______________.
Answer: Coefficient
Step-by-step explanation:
When solving for an unknown variable that has a number preceding it, you will divide both sides of the equation by this number, which is known as the coefficient.
A coefficient is a number preceding any variable in a function for example, given the function 4x, the variable is 'x' and the number preceding it is 4. This number preceding the variable is what we call 'coefficient' of the variable 'x'
Property A initially sold for $412,500. The property sold a second time 12 months later for $430,500. What was A's monthly rate of change? (Round the final calculation to four decimal places.)
i got 1.0436 on my calculation hope this helps...
A croissant shop has plain croissants, cherry croissants, chocolate croissants, almond croissants, apple croissants, and broccoli croissants. How many ways are there to choose
a)a dozen croissants?
b)three dozen croissants?
c)two dozen croissants with at least two of each kind?
d)two dozen croissants with no more than two broccoli croissants?
e)two dozen croissants with at least five chocolate croissants and at least three almond croissants?
f)two dozen croissants with at least one plain croissant, at least two cherry croissants, at least three chocolate croissants, at least one almond croissant, at least two apple croissants, and no more than three broccoli croissants?
Answer:
A. 6 188
B. 749 398
C. 6 188
D. 52 975
E. 20 349
F. 11 316
Explanation:
(a) The shop has 6 types of croissants of which a dozen(12) has to be selected
Therefore n=6, r=12
Repetition of croissants is permitted
And C(n+r-1, r)
C(6+12-1, 12) = C(17, 12) = 17!÷ 12!(17-12)! = 17!÷12! 5! =6 188
(b) The shop has 6 types of croissants of which three dozen(36) has to be selected
Therefore n=6, r=36
Repetition of croissants is permitted
And C(n+r-1, r)
C(6+36-1, 12) = C(41, 36) = 41!÷ 36!(41-36)! = 41!÷36! 5! = 749 398
(c) The shop has 6 types of croissants of which two dozen(24) has to be selected
Let us first select 2 of each kind which 12 croissants in total. Then we still need to select the remaining 12 croissants
Therefore n=6, r=12
Repetition of croissants is permitted
And C(n+r-1, r)
C(6+12-1, 12) = C(17, 12) = 17!÷ 12!(17-12)! = 17!÷12! 5! =6 188
(d) The shop has 5 types of croissants of which two dozen(24) has to be selected
Therefore n=5, r=24
Repetition of croissants is permitted
And C(n+r-1, r)
C(5+24-1, 24) = C(28, 24) = 28!÷ 24!(28-24)! = 28!÷24! 4! = 20 475
This problem involves calculating the number of combinations with repetition where the order of choosing croissants does not matter and requires applying the combinatorics formula for such scenarios.
Explanation:The question asked is concerning the number of ways to choose different quantities of croissants from a croissant shop that has six different types. This is a classic example of a combinatorics problem which falls under the category of counting the number of combinations with repetition.
The counting principle states that if there are 'n' ways to do one thing, and 'm' ways to do another, then there are n * m ways to do both. However, when choosing with repetition where the order does not matter, we use the formula for combinations with repetition: (n + r - 1)! / r!(n - 1)!, where 'n' is the number of types and 'r' is the number of items to be chosen.
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Answer:
The product of 'x' and 'y' is [tex]\boxed 8[/tex].
Step-by-step explanation:
Given:
[tex]\log_{5\sqrt5}125=x\\\\\log_{2\sqrt2}64=y[/tex]
We need to determine the product of 'x' and 'y'.
Using the following logarithmic property:
[tex]\log_ab=\frac{\log b}{\log a}[/tex]
Here, [tex]a=5\sqrt5\ and\ 2\sqrt2[/tex]
[tex]b=125\ and\ 64[/tex]
So, [tex]log_{5\sqrt5}125=\frac{\log 125}{\log 5\sqrt{5}}\\\\log_{5\sqrt5}125=\frac{\log 5^3}{\log 5\times5^{1/2}}.......[\sqrt5=5^{1/2}][/tex]
[tex]log_{2\sqrt2}64=\frac{\log 64}{\log 2\sqrt{2}}\\\\log_{2\sqrt2}64=\frac{\log 2^6}{\log 2\times2^{1/2}}.......[\sqrt2=2^{1/2}][/tex]
Now, we use another property of log and exponents.
[tex]\log a^m=m\log a\\a^m\times a^n=a^{m+n}[/tex]
[tex]log_{5\sqrt5}125=\frac{3\log 5}{\log 5^{1+{1/2}}}=\frac{3\log 5}{\log 5^{\frac{3}{2}}}=\frac{3\log 5}{\frac{3}{2}\log 5}=2\\\\\\\\log_{2\sqrt2}64=\frac{6\log 2}{\log 2^{1+{1/2}}}=\frac{6\log 2}{\log 2^{\frac{3}{2}}}=\frac{6\log 2}{\frac{3}{2}\log 2}=\frac{12}{3}=4[/tex]
So, [tex]x=2\ and\ y=4[/tex]
The product of 'x' and 'y' = [tex]2\times 4=8[/tex]
Therefore, the product of 'x' and 'y' is 8.
question 1. Enter the ratio equivalent to sin(B)
question 2. Consider this a right triangle. enter the measure of angle CAB to the nearest hundredth degree.
question 3. Suppose angle A is an angle such that angle cosA < sinA. select ALL angle measures that are possible values for angle A. 25, 35, 45, 55, 66, 75.
Answer:
The three questions about the given triangle has been answered below.
Step-by-step explanation:
We are given a right angled triangle whose sides are of length 20, 21 and 29.
(1) sin(B) = [tex]\frac{side opposite to B}{hypotenuse}[/tex]
= [tex]\frac{21}{29}[/tex]
= 0.72
(2) sin(A) = [tex]\frac{20}{29}[/tex]
sin(A) = 0.689
∠CAB = [tex]sin^{-1}(0.689)[/tex]
∠CAB = 43.551°
(3) We suppose that cosA < sinA and we haveto find which all angles will satisfy this condition.For this the angle A should be greater than 45°.
From the given options the angles that satisfy this are 55 , 66 and 75.
45 is not included as then sinA = cosA and that condition is not there.
We can use sine and cosine trigonometric ratios to calculate the ratio and measures of angles.
A: The ratio equivalent to sin(B) is [tex]\dfrac{21}{29}[/tex]
B: The measure of angle ∠CAB is [tex]43.6^\circ[/tex]
C: The possible measures of angle A can be: 55, 66 or 75
Given that:AB = 29 unitsBC = 20 unitsCA = 21 unitsUsing definitions of specific trigonometric ratios:A: The ratio equivalent to sin(B) is:
[tex]sin(B) = \dfrac{CA}{AB} = \dfrac{21}{29}\\[/tex]
B: The measure of angle ∠CAB is calculated as:
[tex]sin(A) = \dfrac{CB}{BA} = \dfrac{20}{29} = 0.69\\\\A = arcsin(0.69) = 43.6^{\circ}\\\\\angle CAB = 43.6^{\circ}[/tex]
C: When sin A > cos A, the measures of angle A from 25,35,45,55,66,75 are:
55, 65 and 75:
The reason for the angles possible are 55, 66 ,75 is that:
[tex]\theta \leq 45\\sin(\theta) \leq cos(\theta)[/tex]
Thus, we have:
A: The ratio equivalent to sin(B) is [tex]\dfrac{21}{29}[/tex]
B: The measure of angle ∠CAB is [tex]43.6^\circ[/tex]
C: The possible measures of angle A can be: 55, 66 or 75
Learn more about trigonometric ratios here:
https://brainly.com/question/95152
There are 2 numbers and the sum of those numbers are 40 and the difference of those numbers is 10 what are the numbers that equal the sum and difference
Answer:
15 and 25
Step-by-step explanation:
15+25=40
10+20=30+5+5=10+30=40
Answer:one number is 15 and the other number is 25
Step-by-step explanation:
Let x represent one of the numbers.
Let y represent the other number.
There are 2 numbers and the sum of those numbers are 40. This means that
x + y = 40 - - - - - - - -1
The difference of those numbers is 10. This means that
x - y = 10 - - - - - - - - -2
We would eliminate x by subtracting equation 2 from equation 1, it becomes
2y = 50
y = 50/2 = 25
Substituting y = 25 into equation 1, it becomes
x + 25 = 40 - 25 = 15
The function f is f of x= √4-x
What is the xcoordinate of the point on the functions graph that is closest to the origin?
Answer:
0.5
Step-by-step explanation:
We assume your function is
[tex]f(x)=\sqrt{4-x}[/tex]
The distance formula can be used to find the distance from the point on the curve (x, f(x)) to the origin:
d^2 = (x)^2 + (f(x))^2 = x^2 + (4 -x)
Written in vertex form, this is ...
d^2 = (x -1/2) + 3.75
This has a minimum at x=1/2, so that is the x-coordinate of the point closest to the origin.
In the function f(x) = √(4-x), the x-coordinate of the point on the graph that is closest to the origin is x=0 because the function exists in the first quadrant, meaning the shortest distance to the origin is along the y-axis.
Explanation:The function described is f(x) = √(4-x). We're looking for the x-coordinate of the point on the graph of this function that is closest to the origin. The distance from any point (x, y) to the origin (0, 0) is given by D=√(x²+y²). For this function, y=f(x) = √(4-x), so the distance can be written as D=√(x²+(4-x)²). To find the minimum distance, we take the derivative of this distance function with respect to x, set it equal to zero and solve for x. However, because this function lives in the first quadrant (y is always equal to or greater than 0), the shortest distance to the origin would be along the y-axis. Thus, the solution is x=0, and that is the x-coordinate of the point on the function's graph that is closest to the origin.
Learn more about Minimum Distance here:https://brainly.com/question/31871004
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A property's taxes are $9,540 and are paid for in arrears. The property was sold and closing took place on March 7. The seller was responsible for the day of closing. Using the 360 day method, how will taxes be prorated?
1 - Credit the buyer $1,776 and debit the seller $1,776.
2 - Credit the seller $186 and debit the buyer $186.
3 - Credit the buyer $1,590 and debit the seller $1,590.
4 - Credit the buyer $1,675.50 and debit the seller $1,675.50.
Answer:
Credit the buyer $1,776 and debit the seller $1,776.
Step-by-step explanation:
In accounting books the buyer will be credit from $1,776 and seller will be debit from $1,776.
Answer:
1) Credit the buyer $1,776 and debit the seller $1,776.
Step-by-step explanation:
For this, we are to simply understand and follow the calculation of proration. Proration is the allocation or dividing of certain money items at the closing.
The buyer pays:
Total taxes = $ 9540
Total Time Span before closing took place = 2 months and 7 days
Per month charge = [tex]\frac{9540}{12}[/tex] = $795 per month
Charges per day = [tex]\frac{795}{30}[/tex] =$ 26.5 per day
2 months charge = 795 x 2 = $1590
Charges for 7 days = 7 x 26.5 = $185.5
Total Charges = 1590 + 185.5 = $ 1775.5 ≈ $1776 (Rounding off)
As the property's taxes were paid for by the buyer and the seller was responsible for the day of closing, and buyer paid for the arrears too of the previous 2 months and 7 days, the buyer gets a credit and seller gets a debit. The seller owes the buyer $1776.
Hence,
The buyer gets a credit of $1,776 and Seller gets a debit of $1,776
The number of representatives is 160 less than five times the number of senators. There are a total of 560 members. Find the number of senators and the number of representatives
Answer:
The number of Senators are 120 and number of Representatives are 440.
Step-by-step explanation:
Given,
Total number of members = 560
Solution,
Let the number of Senators be 'x'.
Since, the number of representatives is 160 less than five times the number of senators.
Framing the above sentence in equation form,we get the number of Representative.
So, number of Representative = [tex]5x-160[/tex]
Now, Total number of members is the sum of total number of Senators and total number of representative.
Total number of members = Total number of Senators + Total number of representative
On substituting the values, we get;
[tex]x+5x-160=560\\\\6x=560+160\\\\6x=720\\\\x=\frac{720}{6}\\\\x=120[/tex]
Total number of Senators = 120
So, number of Representative = [tex]5\times120-160=600-160=440[/tex]
Thus the number of Senators are 120 and number of Representatives are 440.
A researcher measures the time (in seconds) it takes a sample of five participants to complete a memory task. It took four of the participants 7, 8, 8, and 9 seconds. If M = 9, then what must be the fifth time recorded?
Using the mean formula and the data given, the fifth participant’s time to complete the memory task must be 13 seconds to result in a mean (M) of 9 seconds for all five participants.
To find the fifth time recorded when four participants took 7, 8, 8, and 9 seconds to complete a memory task and the mean (M) time is 9 seconds, we need to use the formula for the mean of a sample which is the sum of all values divided by the number of values.
Here's the equation based on the data provided:
(7 + 8 + 8 + 9 + x) / 5 = 9
First, calculate the sum of the times we know:
7 + 8 + 8 + 9 = 32 seconds
Now, insert this sum into the equation and solve for x, where x represents the fifth time:
(32 + x) / 5 = 9
32 + x = 45
x = 45 - 32
x = 13 seconds
The fifth participant must have taken 13 seconds to complete the memory task to have a mean time of 9 seconds.
7a-3=3-2a(If there is no solution, type in "no solution") a= Answer
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Suppose the expression a(b)n models the approximate number of people who visited an aquarium each day since an aquarium opened, where a is the initial number of people who visited, b is the rate of increase in the number of people who visited each day, and n is the number of days since the aquarium opened.
If the expression below models the number of visitors of a particular aquarium, what is the correct interpretation of the second factor?
54(1.3)^7
A.
There were 9.1 times as many people who visited the aquarium on the 7th day as on the first day.
B.
There were 1.3 times as many people who visited the aquarium on the 7th day as on the first day.
C.
There were 6.27 times as many people who visited the aquarium on the 7th day as on the first day.
D.
There were 10.2 times as many people who visited the aquarium on the 7th day as on the first day.
Answer:
C. There were 6,27 times as many people who visited the aquarium on the seventh day as on the first day.
Explanation:
[tex]\displaystyle 1,3^7 = 6,2748517 ≈ 6,27[/tex]
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A price fixed above equilibrium that change the incentives that both buyers and sellers face is called price
Answer:
floor
Step-by-step explanation:
price floor is a situation when the price changed is greater or leave than the equilibrium price determined by the force of demand and supply. For a price floor to be effective, the minimum price has to be higher than the equilibrium price. It must be set above the equilibrium price. The opposite of price floor is price ceiling.