Answer:
Step-by-step explanation:
Formula
(numerator * numerator ) divided by (denominator * denominator)
Numerator * numerator = 6*9 = 54
Denominator * denominator = 4 * 12 = 48
The answer is 54 / 48 = 9/8 = 1 1/8
Both numerator and denominator can be divided by 6
A sonographer is trying to determine the size of a gallstone. If
the stone is spherical and has a diameter of 12 millimeters, what
Is its volume?
Answer:
0.9 cubic centimeters
Step-by-step explanation:
Angle θ is in standard position and ( 4 , 4 ) is a point on the terminal side of θ. What is the exact value of sec θ sec 0 in simplest form with a rational denominator?
Answer:
\(\sqrt{2}\)
Step-by-step explanation:
Angle θ is in standard position and (4,4) is a point on the terminal side of θ.
\(\text{Opposite of }\theta =4 \\\text{Adjacent of }\theta =4 \\$Using Pythagoras Theorem\\Hypotenuse^2=$Opposite^2$+Adjacent^2\\$Hypotenuse^2=4^2+4^2\\$Hypotenuse^2$=32\\Hypotenuse=\sqrt{32}=4\sqrt{2}\)
Now, secant is the inverse of cosine.
Therefore:
\(\sec \theta =\dfrac{Hypotenuse}{Adjacent} \\\sec \theta =\dfrac{4\sqrt{2}}{4} \\\sec \theta =\sqrt{2}\)
(b) How many ways are there to distribute two balls into four boxes if each box must have at most one ball in it if (i) both the balls and boxes are labeled? (ii) the balls are labeled, but the boxes are unlabeled? (iii) the balls are unlabeled, but the boxes are labeled? (iv) both the balls and boxes are unlabeled?
(i) distributed in \(4 \times 3 = 12\) different ways. (ii)statistical distribution of the balls is done in one of three ways. \((1 + 2 = 3)\) . (iii) there are 6 ways to divide the balls. \((4 + 2 \times 1).\) (iv) to distribute the balls \((1+2+1)\).
What is the statistical distribution?(i) Both balls and boxes are labeled:
Since one box already contains a ball, there are four options for where to place the first ball, and only three options remain for the second ball. The two balls can be distributed in \(4 \times 3 = 12\) different ways.
(ii) Balls are labeled, but boxes are unlabeled:
There is just one method to arrange the balls if there is only one ball in each box. There are two ways to determine which box receives both balls if only one box possesses them. The statistical distribution of the balls is done in one of three ways.
(1 + 2 = 3).
(iii) Balls are unlabeled, but boxes are labeled:
There are four alternatives available to the box if they are both in the same box. If they are in different boxes, the first ball's box has two options, leaving the second ball with just one. Accordingly, there are 6 ways to divide the balls.
(4 + 2 * 1).
(iv) Both balls and boxes are unlabeled:
There is only one method to arrange the balls if there is one ball in each box. There are two methods to decide which box gets both balls if only one box has both balls.
There is just one method to arrange the balls if neither box incorporates a ball. There are therefore a total of 4 options to distribute the balls (1+2+1).
Therefore,(i) distributed in \(4 \times 3 = 12\) different ways. (ii)statistical distribution of the balls is done in one of three ways. \((1 + 2 = 3)\) . (iii) there are 6 ways to divide the balls. \((4 + 2 \times 1).\) (iv) to distribute the balls \((1+2+1)\).
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please help me solve this math problem, tryna graduate here
Answer:
141°
Step-by-step explanation:
Simplify the expression:
7(1 + 7x) =
Answer:
7 x 8x
Step-by-step explanation:
peter is baking cookies. The recipe calls for 3/4 cups of flour. He needs to triple the recipe. How many cups of flour will he need? need help please
Answer:
\(3 \times \frac{3}{4} = \frac{3}{1} \times \frac{3}{4} \)
\( \frac{3}{1} \times \frac{3}{4} = \: \: \frac{9}{4} \: or \: \: 2 \:\times \frac{1}{4} \)
Step-by-step explanation:
Originally he needs 3/4 cups
If he is tripling it, he need 3 times 3/4.
You can see above since every number has a 1 under them you can write 3 as 3/1 if it make it easier dor you to understand.
Then, you multiply numerators and denominators with each other. 3 times 3 will give you 9 and 1 times 4 will give you 4.
So you got 9/4 whixh can also write as 2(times)1/4
Hope this is helps. Let me know if you have any questions.
Describe and explain the difference between the mean, median, and mode.
Make up an example (not in the book or in your lectures) in which the median would be the preferred measure of central tendency.
Answer:
Mean, median and mode are measures of central tendency. The median is a better measure of central tendency when the given data contains outliers.
Step-by-step explanation:
Mean, median and mode are all measures of central tendency. These are statistical information that gives the middle or centre of a set of data. Since the values are central, they usually represent the entire distribution.
The mean is the obtained by dividing the sum of all the scores by the number of scores. The median is the middle value when numbers are arranged in increasing or decreasing order of magnitude. The mode is the most frequently occurring score in a distribution.
Let us see an example of the median as a measure of central tendency. Given the set of values; 4, 10, 12, and 26, the median is obtained from the average of the two middle numbers in the set of values which are 10 and 12 as seen from the set of values above. Hence the median of this set of values is 11.
The median can be a very good measure of central tendency, even better than the mean mostly in situations where there are outliers, or extreme values.
Solve the system of equations by graphing.
y = -2
y = -3
2
x + 4
The system of graphs is a very unique concept which helps to understand various concepts in a visual way.
How does this occur?
The two lines intersect at (-3, -4), which is the system of equations' solution.
Using the slope and y-intercept, graph an equation as follows:The equation y = mx + b's y-intercept can be found.Determine the y-intercept. The purpose will be (0, b).The slope=m of the equation y = mx + b can be found.Run from the slope while taking a single step using the rise.Your line should join those two spots.This is how the equation can be solved-
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andy’s saving account pays 0.3% more interest then marty’s. martys account earns 200 in interest. how much does interest does andy’s account earn?
1. 200.60
2. 203.00
3. 206.00
4. 230.00
200.60 interest does andy’s account earn.
Let x be the amount of interest earned by Andy's account.
According to the problem, Andy's account earns 0.3% more interest than Marty's account, which means that Andy's account earns the same amount plus an additional 0.3% of that amount. Mathematically, we can express this as:
x = 200 + 0.3% of 200
Simplifying the right-hand side of the equation, we get:
x = 200 + 0.003 × 200
x = 200.60
Therefore, the answer is option 1: 200.60.
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4x+5(7x-3)=9(x-5)
x????
Answer:
x=-1
Step-by-step explanation:
4x+35x-15=9x-45
39x-15=9x-45
39x-9x=-45+15
30=+-30
x=-1
Answer:
\( \sf \: x = - 1\)
Step-by-step explanation:
Given equation,
→ 4x + 5(7x - 3) = 9(x - 5)
Now the value of x will be,
→ 4x + 5(7x - 3) = 9(x - 5)
→ 4x + 35x - 15 = 9x - 45
→ 39x - 15 = 9x - 45
→ 39x - 9x = -45 + 15
→ 30x = -30
→ x = -30 ÷ 30
→ [ x = -1 ]
Hence, the value of x is -1.
PLEASE HELP!!!!
dan has two pairs of shoes four pairs of pants and six shirts. how many outfits could he make?
Answer:
2 Outfits
Step-by-step explanation:
\(Materials\ Dan\ has:\\*2\ pair\ of\ shoes\\\*4\ pairs\ of\ pants\\*6\ pair\ of\ shirts\\Knowing\ that\ 1\ outfit\ requires,\ 1\ pair\ of\ shoes, 1\ pair\ of\ pants,\\ 1/2\ pair\ of\ shirts(1\ shirt).\\Now,\\As\ Dan\ has\ 2\ pairs\ of\ shoes,\ he\ could\ make\ 2\ outfits\ with\ it.\\As\ Dan\ has\ 4\ pairs\ of\ pants,\ he\ could\ make\ 4\ outfits\ with\ it.\\As\ Dan\ has\ 6\ pairs\ of\ shirts,\ he\ could\ make\ 12\ outfits\ with\ it.\\\)
\(Hence,\\At\ the\ maximum\ he\ could\ make\ only\ 2\ complete\ outfits\ using\ all\ the\ materials\ he\ has.\)
2. Suppose the price of good x increased from 4 birr to 5 birr. Because of change price of good x, quantity demand of good y changed from 5,000 to 6,250. a. Find cross price elasticity of demand b. What types of goods (good x and good y) are?
Based on the cross-price elasticity of Demand, we can conclude that good X and good Y are substitutes.
Let's calculate the cross-price elasticity of demand using the given information:
a. Find the percentage change in quantity demanded of good Y:
Percentage Change in Quantity Demanded of Good Y = (New Quantity Demanded - Initial Quantity Demanded) / Initial Quantity Demanded * 100
Percentage Change in Quantity Demanded of Good Y = (6250 - 5000) / 5000 * 100 = 25%
b. Find the percentage change in the price of good X:
Percentage Change in Price of Good X = (New Price - Initial Price) / Initial Price * 100
Percentage Change in Price of Good X = (5 - 4) / 4 * 100 = 25%
Now, we can calculate the cross-price elasticity of demand:
Cross-Price Elasticity of Demand = Percentage Change in Quantity Demanded of Good Y / Percentage Change in Price of Good X
Cross-Price Elasticity of Demand = 25% / 25% = 1
b. Based on the calculated cross-price elasticity of demand, we can determine the types of goods:
If the cross-price elasticity of demand is positive (as in this case, where it is 1), it indicates that the two goods are substitutes. This means that when the price of good X increases, the quantity demanded of good Y also increases, suggesting that consumers view these goods as alternatives to each other.
Therefore, based on the cross-price elasticity of demand, we can conclude that good X and good Y are substitutes.
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Answer:
Step-by-step explanation:
very easy 5th grade math pls answer giving brainliest!!! look at photo
Answer:
Top box would be 10 x 2 x 3 which would be 60. Then for bottom box would be 3 x 4 x 5 which would be 60 so add them together and get 120
Step-by-step explanation:
Answer:
top box : v= 60 ( UNIT)
bottom box: v= 60 ( unit)
both boxes : v = 120 (unit)
Step-by-step explanation:
we know that the volume = lenth × height× width
so if we apply this rule , we find it
The graph below shows the solutions to which inequality?
A. x^2-3x+3 ≥0
B. x² + 3x-3 <0
C. x²-3x+3<0
D. x² + 3x-3>0
The inequality expression that corresponds to the solution of the inequality graph is x² + 3x - 3 < 0.
option B.
What is the solution of the inequality?The inequality expression that corresponds to the solution of the inequality graph is determined by simplifying the equations as follows;
The solution of the graph,
x > -4 and x < 1
The first equation with "≥" is ruled out because the graph doesn't have a thick dot.
Let's simplify the second expression;
x² + 3x - 3 < 0
solve using quadratic formula;
x > -3.79 or x < 0.79
The third expression is ruled out since its solution will be complex.
For the last expression;
x² + 3x - 3 > 0
x < -3.79 or x > 0.79
Thus, the correct inequality expression is x² + 3x - 3 < 0.
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help needed. due today TT
There is a linear relationship between the number of people in a group and the cost to enter a museum. The museum charges $20 for two people and $28 for three people.
Part C: Using your work from Part A, complete this prompt: How many people can enter the museum for $100?
Answer:
11 people could enter for $100
Step-by-step explanation:
According to the information given:
$28=3 people
$20=2 people
so it goes up by 8 dollars for every person added
20-8= 16, the original fee, meaning the sequence formula would be:
8n+8 (n being the number of people)
if 8n+8=100
8n=92
n=11.5 rounded down would be 11
WHOEVER GOT BEST RAP IS CROWNED
Answer:
Yeah uh
대취타 대취타 자 울려라 대취타
대취타 대취타 자 울려라 대취타
대취타 대취타 자 울려라 대취타
대취타 대취타 자 울려라 대취타
대취타 대취타 자 울려라 대취타
빛이나 빛이나 내 왕관이 빛이나
잊지마 잊지마 지난 날을 잊지마
We so fly, we so fly 전세기로 we so fly
Yeah umm 종놈 출신에 왕된 놈
미쳐버린 범 광해 flow
개천 출신에 용된 몸
그게 내가 곧 사는 법
미안 걱정은 말라고
나도 잃을건 많다고
과건 뒤주에 가두고
내걸 챙겨 다 잡수쥬
말이 안되지 yeah umm 내가 개라니 yeah
범으로 태어났지 적어도 너처럼 약하진 않지
좆밥들의 걍 재롱잔치
솔까 존나게 어이없지
싹다 죽여 난 예의 없이
새꺄 그래 너 예외없이
Flexing 난 없지
필요가 없지
Who's the king, who's the boss
다 알잖아 내 이름
입만 산 새끼들
당장 놈의 목을 쳐 ah!
대취타 대취타 자 울려라 대취타
대취타 대취타 자 울려라 대취타
대취타 대취타 자 울려라 대취타
대취타 대취타 자 울려라 대취타 (hey)
대취타 (yeah) 대취타 (yeah)
대취타 대취타 자 울려라 대취타
대취타 대취타 자 울려라 대취타
한탕해먹고 곧바로 난 전세기로 날아
나를 담기엔 이 나란 아직 여전히 작아 (yeh)
Woo 누가 시간은 금이래
내 시간은 더 비싼데 tick tock
선비새끼들 면상에다 침을 칵 뱉어
꺾인 적이 없는 매출출출출출출출
우리 방시혁 피디는 매일 춤춤춤춤춤춤춤
참 감사하네 (ey ey) 내가 천재임에
고작 그런 이유로 약을 빨다니 애잔하기 그지없네
재능이 없는거지 뭐
원하는 건 모두 가졌지 이제는 뭘 더 가져야만 만족이 될지
내가 원했던 것 옷옷 다음은 돈돈 다음은 goal goal 이 다음은 도대체 뭐지
그 다음은 그래 뭘까 심히 느껴지는 현타 위가 없는 현상
위만 보던 난 이제 걍 아래만 보다가 이대로 착지하고파
I'm a king, I'm a boss
새겨놓아 내 이름
입만 산 새끼들
당장 놈의 주리를 틀어
I'm a king I'm a boss
다 알잖아 내 이름
입만 산 새끼들
당장 놈의 목을 쳐 ah (ah)
대취타 대취타 자 울려라 대취타
대취타 대취타 자 울려라 대취타
대취타 대취타 자 울려라 대취타
대취타 대취타 자 울려라 대취타 (hey)
대취타 (yeah) 대취타 (yeah)
대취타 대취타 자 울려라 대취타
대취타 대취타 자 울려라 대취타
Step-by-step explanation:
Answer:
lol ghjghguf jx mc cjcuuuguifgkfy
5.3 MATHEMATICS HOLIDAY PACKAGE-TERM 2(2023) Instructions: Attempt ALL items 1. Your family has seven siblings; peter, John, Sarah, Joy, Ali, Mary and Ivan. There is an interval of 2 years between the ages of the children from Ivan to peter. Ivan is three years old. Task: Using an arrow diagram, explain the information about your family.
i 15 =
A -1
B 1
C -i
d i
Answer:
C. -i
Step-by-step explanation:
i^n is expondential. i^1 = i
i^2 = -1
i^3 = -i
i^4 = 1.
Answer:
it is i
Step-by-step explanation:
Which choice is equivalent to the expression below? √-12
A. 12i
B. -12i
C. -2√3
D. 2i √3
E. -2√3i
PLEASE DON’T GUESS
Answer:
D. 2i√3
Step-by-step explanation:
You have the expression √-12. You can divide the number in the radical sign into the numbers that make up the expression. After you do this, you will be able to take numbers out of the radical sign
√(-12)
√(-1 × 4 × 3)
√-1 = i
√4 = 2
√3 = √3
2i√3
The answer is D.
A triangle has side lengths of 8 cm, 15 cm, and 17 cm. Classify it as acute, obtuse, or right.
acute
obtuse
O
right
Answer:
\(15^{2}\) = 225
\(8^{2}\) = 64
\(17^{2}\) = 289
\(15^{2}\) + \(8^{2}\) + \(17^{2}\)
= 225 + 64 = 289
289 = 289
Hence its a right angled triangle
Hope it helps
Please mark me as the brainliest
Thank you
30 POINTS
Madison can make a keychain in 1 minute 35 seconds. At this rate how much time will it take her to make 8 keychains?
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
Answer:
12 minutes 40 seconds
Step-by-step explanation:
One keychain, 1 minutes 35 second = 1*60 + 35 = 95 seconds
8 keychains, 95 * 8 = 760 seconds = 760/60 = 12.66667 minutes
= 12 minutes 0.66667*60 seconds
= 12 minutes 40 seconds
what is the value of 2/5 + 5/7
Answer:
2/5 + 5/7 = 39/35Step-by-step explanation:
I hope it helps ❤❤❤❤2 men can build a wall in 10 days. in how many days will 8 men build the wall?
Step-by-step explanation:
8 men can do 60 man days of work by dividing 60 man days by the 8 men, which gives us 60/8 = 7 1/2 da
Gina wants to go to the water park with her friends. They have a total of www dollars to buy 555 tickets. Each ticket costs 151515 dollars. Select the equation that matches this situation. Choose 1 answer: Choose 1 answer: (Choice A) 5 = 15 \times w5=15×w5, equals, 15, times, w A 5 = 15 \times w5=15×w5, equals, 15, times, w (Choice B) w = 15 +5w=15+5w, equals, 15, plus, 5 B w = 15 +5w=15+5w, equals, 15, plus, 5 (Choice C) w = 5 \times 15w=5×15w, equals, 5, times, 15 C w = 5 \times 15w=5×15
The equation which correctly represents the given situation as required to be determined is; Choice C; w = 5 × 15.
Which equation correctly matches the given situation?It follows from the task content that the equation which correctly represents the Given situation is to be determined.
Since the intention is to buy 5 tickets in which case; each ticket costs 15 dollars; we have that;
Since the total amount of dollars they have is w dollars; The equation which holds true for the situation is; w = 5 × 15.
Consequently, answer choice C; w = 5 × 15 is correct.
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please help me with this question
Answer:
see explanation
Step-by-step explanation:
the equation for direct variation is
y = kx ← k is the constant of variation
divide both sides by x , then
k = \(\frac{y}{x}\)
calculate k for each ordered pair from the table
k = \(\frac{2}{-4}\) = - \(\frac{1}{2}\)
k = \(\frac{1}{-2}\) = - \(\frac{1}{2}\)
k = \(\frac{-4}{8}\) = - \(\frac{1}{2}\)
since k is constant for all ordered pairs
then the table shows a direct variation with equation
y = - \(\frac{1}{2}\) x
---------------------------------------------------------------------------------
similarly for the second table
k = \(\frac{5}{2}\)
k = \(\frac{10}{4}\) = \(\frac{5}{2}\)
k = \(\frac{21}{6}\) = \(\frac{7}{2}\)
since k is not constant for all ordered pairs then NOT direct variation
Stephen is combining all juice shown to make fruit punch. Does the expression (64+28+76)/6 make sense’s
Yes, the expression (64+28+76)/6 makes sense as it represents the average quantity of juice per unit when combining all the shown juices.
To determine whether the expression (64+28+76)/6 makes sense, we need to evaluate the components of the expression and consider whether the mathematical operations are valid.
The expression (64+28+76)/6 represents the sum of three numbers (64, 28, and 76), divided by 6. Let's break it down step by step:
Addition: We have three numbers being added together: 64, 28, and 76. The sum of these numbers is 168 (64 + 28 + 76 = 168).
Division: The sum of the three numbers, 168, is then divided by 6. Division is a valid mathematical operation.
Now, let's analyze whether the expression makes sense in the context of Stephen combining all the juice to make fruit punch. The numbers 64, 28, and 76 may represent quantities of juice (in some units) that Stephen is combining. However, without further information or context, we cannot determine if the expression accurately represents the combination of these juices.
If the numbers 64, 28, and 76 represent quantities of juice in the same units (such as milliliters or liters), then the expression (64+28+76)/6 would represent the average quantity of juice per unit. The result, 168/6, would be 28. This would imply that each unit (e.g., glass or serving) of the fruit punch contains an average of 28 units of juice.
In summary, mathematically, the expression (64+28+76)/6 is valid. However, without additional context regarding the units or quantities being represented, it is not possible to determine whether the expression accurately describes the process of combining the juices to make fruit punch.
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If (Un+1)= √(Un +1)₁, U₁ = 1.prove that limit Un=1/2(1+√5)
n—> ∞
The limit of Un as n approaches infinity is equal to 1/2(1+√5), confirming the given statement.
To prove that the limit of Un as n approaches infinity is equal to 1/2(1+√5), we can use the concept of limits and apply algebraic manipulation.
First, let's assume that the limit of Un as n approaches infinity is L. Mathematically, we can write:
lim (n→∞) Un = L
Since the given recurrence relation states that Un+1 = √(Un + 1)₁, we can substitute n+1 for n in the recurrence relation:
lim (n→∞) Un+1 = √(lim (n→∞) Un + 1)₁
Since the limit of Un as n approaches infinity is L, we can rewrite the equation as:
L = √(L + 1)₁
To solve for L, we can square both sides:
L^2 = L + 1
Rearranging the equation, we have:
L^2 - L - 1 = 0
This is a quadratic equation. By solving it using the quadratic formula, we find two possible values for L:
L = [1 ± √(1 + 4)] / 2
Simplifying the expression, we get:
L = [1 ± √5] / 2
The positive value, L = (1 + √5) / 2, corresponds to the golden ratio, which is approximately 1.618. The negative value can be ignored as the limit of Un cannot be negative.
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Three numbers are in the ratio of 1:2:4. If 3 is added to the first and 8 is subtracted from the third, the new numbers will be the first and third terms of an A.P., whose second term is the second number. Find the original numbers.
9514 1404 393
Answer:
5, 10, 20
Step-by-step explanation:
Suppose the three numbers are x, 2x, and 4x. Then they have the required ratios. After the transformation, we have ...
((x+3) +(4x -8))/2 = 2x . . . . . 2nd term is average of 1st and 3rd
5x -5 = 4x ⇒ x = 5
The original numbers are 5, 10, 20.
_____
After the adjustment, the arithmetic sequence is 8, 10, 12.
It is common knowledge that a fair penny will land heads up 50% of the time and tails up 50% of the time. It is very unlikely for a penny to land on its edge when flipped, so a probability of 0 is assigned to this outcome. A curious student suspects that 5 pennies glued together will land on their edge 50% of the time. To investigate this claim, the student securely glues together 5 pennies and flips the penny stack 100 times. Of the 100 flips, the penny stack lands on its edge 46 times. The student would like to know if the data provide convincing evidence that the true proportion of flips for which the penny stack will land on its edge differs from 0.5. The student tests the hypotheses H0: p = 0.50 versus Ha: p ≠ 0.50, where p = the true proportion of all flips for which the penny stack will land on its edge. The conditions for inference are met. The standardized test statistic is z = –0.80 and the P-value is 0.2119. What conclusion should the student make using the α = 0.10 significance level?
A) Because the test statistic is less than α = 0.10, there is convincing evidence that the true proportion of flips for which the penny stack will land on its edge differs from 0.5.
B) Because the P-value is greater than α = 0.10, there is convincing evidence that the true proportion of flips for which the penny stack will land on its edge differs from 0.5.
C) Because the P-value is greater than α = 0.10, there is not convincing evidence that the true proportion of flips for which the penny stack will land on its edge differs from 0.5.
D) Because the test statistic is less than α = 0.10, there is not convincing evidence that the true proportion of flips for which the penny stack will land on its edge differs from 0.5.
The correct answer is:
C) Because the P-value is greater than α = 0.10, there is not convincing evidence that the true proportion of flips for which the penny stack will land on its edge differs from 0.5.
The student set up a hypothesis test to investigate whether there is evidence that the true proportion of flips for which the penny stack will land on its edge differs from 0.5. The null hypothesis is that the proportion is 0.5, and the alternative hypothesis is that it differs from 0.5.
The student obtained a standardized test statistic of z = -0.80 and a P-value of 0.2119.
To make a conclusion, the student needs to compare the P-value to the significance level α.
The significance level is given as 0.10, which means that the student is willing to accept a 10% chance of making a Type I error (rejecting the null hypothesis when it is actually true).
Since the P-value of 0.2119 is greater than α = 0.10, there is not convincing evidence to reject the null hypothesis. Therefore, the student cannot conclude that the true proportion of flips for which the penny stack will land on its edge differs from 0.5.
Learn more about Null Hypothesis here:
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A researcher wants to collect data on how many hours bears sleep during the year. The researcher decides to put an electronic device on all bears that live less than one-half mile from the research station. Are the conclusions drawn from this sample likely to be true for all bears?
Yes
No
Answer:
yes
Step-by-step explanation: