Answers
Answer:
Third choice is the one you want
Step-by-step explanation:
First off, we need to remember that for a line to be perpendicular to another line, its slope is the opposite reciprocal to the other line. The slope of our line is -1/4, so the opposite reciprocal slope is +4/1 or just 4. Now we know that m = 4.
The point-slope form of a line is
[tex]y-y_{1}=m(x-x_{1})[/tex]
where m is the slope, y1 is the y coordinate of the point, and x1 is the x coordinate of the point. Filling in:
[tex]y-5=4(x-(-3))[/tex] which simplifies to
[tex]y-5=4(x+3)[/tex] which simplifies further to
[tex]y-5=4x+12[/tex]
Add 5 to both sides to get the equation into slope-intercept form:
y = 4x + 17
choice 3
Related Questions
Based on the information marked in the diagram, MNP and QRS must be congruent. True or False. ty for the help! <3
Answers
Answer:
True
Step-by-step explanation:
The hypotenuse angle theorem, also known as the HA theorem, states that "If the hypotenuse and an acute angle of one right triangle are congruent to the hypotenuse and an acute angle of another right triangle, then the two triangles are congruent."
In triangles MNP and QRS:
NP=RS (hypotenuses);∠P=∠S (acute angles).Then, triangles MNP and PRS are congruent by HA theorem.
True
Answer:
True (just did it on a pex)
Step-by-step explanation:
Chris put $1,500 in a savings account at an annual interest rate of 5%. If Chris does not deposit or withdraw any money, what is the amount of interest Chris will earn the first year her money is in the savings account?
Answers
[tex]\bf ~~~~~~ \textit{Simple Interest Earned} \\\\ I = Prt\qquad \begin{cases} I=\textit{interest earned}\\ P=\textit{original amount deposited}\dotfill & \$1500\\ r=rate\to 5\%\to \frac{5}{100}\dotfill &0.05\\ t=years\dotfill &1 \end{cases} \\\\\\ I=(1500)(0.05)(1)\implies I=75[/tex]
Chris will earn $75 in interest in the first year by depositing $1,500 into a savings account with an annual interest rate of 5%, calculated using the simple interest formula.
To calculate the amount of interest Chris will earn in the first year the money is in the savings account, we will use the formula for simple interest, which is Interest = Principal × Rate × Time. In this case, the principal amount is $1,500, the annual interest rate is 5% or 0.05 when expressed as a decimal, and the time is 1 year since we are looking for the interest for the first year only.
Therefore, the interest Chris will earn after one year is calculated as follows:
Interest = $1,500 × 0.05 × 1
Interest = $75
Thus, at the end of the first year, Chris will have earned $75 in interest.
Theo is practicing for a 5 kilometer race. He runs 5 kilometers every day and records his time. His normal time is 25 minutes 15 seconds. Esterday it took him only 23 minutes 49 seconds. How much faster was his time yesterday than his normal time? What are you asked to find? What information do you know? How will you solve the problem? Solve the problem
Answers
2 minutes 21 seconds
Write the equation of a piecewise function with a jump discontinuity at x =3. Then, determine which step of the 3-step test for continuity that the function
fails.
Answers
Answer:
Here's a possible example:
Step-by-step explanation:
[tex]f(x) =\begin{cases} x & \quad x < 3\\x+3 & \quad x \geq 3\\\end{cases}[/tex]
Each piece is linear, so the pieces are continuous by themselves.
We need consider only the point at which the pieces meet (x = 3).
[tex]\displaystyle \lim_{x \longrightarrow 3^{-}} f(x) = \lim_{x \longrightarrow 3^{-}} x = 3\\\\\displaystyle \lim_{x \longrightarrow 3^{+}} f(x) = \lim_{x \longrightarrow 3^{+}} x+3 = 6\\\\f(3) = x + 3 = 6\\\\\displaystyle \lim_{x \longrightarrow 3^{-}} f(x) \neq f(3)[/tex]
The left-hand limit does not equal ƒ(x), so there is a jump discontinuity at x =3.
Final answer:
A piecewise function with a jump discontinuity at x = 3 could be f(x) = 2x for x < 3 and f(x) = 2x + 1 for x ≥ 3. It fails the 3-step test for continuity at x = 3 in the second step, as the limits on either side of the point x = 3 do not match.
Explanation:
To write the equation of a piecewise function with a jump discontinuity at x = 3, we can define one function for values of x less than 3, and another for values of x equal to or greater than 3. For instance:
For x < 3: f(x) = 2xFor x ≥ 3: f(x) = 2x + 1Now, to determine where the piecewise function fails the 3-step test for continuity at x = 3, we assess the following criteria:
The function must be defined at x = 3. Our function is defined at x = 3, so it passes this step.The limit of f(x) as x approaches 3 must exist. Since the left-hand limit as x approaches 3 is 6 and the right-hand limit as x approaches 3 is 7, the limits do not match, and the limit does not exist. Therefore, the function fails the second step of the test for continuity.The limit of the function as x approaches the point must equal the function's value at that point. As the limit does not exist, this step is not applicable.Therefore, the function has a jump discontinuity at x = 3 because it fails the second step of the 3-step test for continuity, where the left and right-hand limits are not equal.
What is the domain and range for the following function and its inverse?
f(x) = x2 + 3
f(x)
domain:
f–1(x)
domain:
Answers
Answer:
Step-by-step explanation:
The domain of that function is all real numbers. The x values will drop into negative infinity and will grow to positive infinity.
The range is found from the vertex form of a parabola, which is
[tex]y=(x-h)^2+k[/tex]
where h indicates side to side movement of the vertex and k indicates up or down. Our function has a +3 at the end of it and is positive (so it opens upwards), so the range is y ≥ 3.
To find the inverse of that function, switch the x and y coordinates and solve for the new y. Let f(x) be y, then switch the x and y:
[tex]x=y^2+3[/tex]
Now solve for the new y:
y = ±[tex]\sqrt{x-3}[/tex]
To find the domain of a radical, set the radicand greater than or equal to 0 and solve for x (this is because the radicand cannot be a negative number or we are dealing with imaginary numbers and that's not what you want. BTW, a radicand is the term under the radical sign).
x - 3 ≥ 0 so x ≥ 3. The domain of the inverse is all real numbers greater than or equal to 3.
This is a sideways parabola (the inverse is), and it opens to the right starting at the x value of 3. It will grow into positive values of y to infinity and will drop into negative values of y into negative infinity.
Just a little trick here to remember, and it ALWAYS holds true: the domain of a function is the range of its inverse, and the range of a function is the domain of its inverse. Look to our solution for your problem here and you'll see that it is true.
HELP PLEASE ASAP - 40 POINTS
WILL AWARD BRAINLIEST
The lunch special at Mrs. Tucker’s Country Buffet has a choice of:
2 appetizers
5 main courses
5 desserts
3 drinks
How many lunch meals are possible?
Answers
Answer: 2
Step-by-step explanation:
The reason is for each meal to have one thing of food for every lunch special. So then you would go one by one, theres 2 appetizers so that means it'll only reach to 2 lunches. Then theres 5 main courses and you seperate those having 2 of the 5 with the appetizers. Onto the desserts, there are 5 desserts and 2 out of the 5 you put it together with the lunches that have a main course and appetizers. Next, there are 3 drinks and 2 of those 3 you would put it with the 2 meals that has an appetizer,main course,dessert, and now a drink. In the end, Its only possible that there are 2 lunch special being able to be made. With all the food
Answer: 150
Step-by-step explanation:
We know that a complete lunch meal consist of an appetizer , a main course , a dessert and a drink.
Given: The number of appetizers=2
The number of main courses=5
The number of desserts=5
The number of drinks=3
Therefore, the number of possible lunch meals will be :
[tex]2\times5\times5\times3=150[/tex]
Hence, there are 150 lunch meals are possible.
A small factory planned to produce a batch of men’s shirts in 8 days. But producing 10 more shirts per day than planned, they finished the task one day early. How many shirts per day was the factory planning to produce?
Answers
70 shirts per day
We simply need to find how many shirts would have been produced on the 8th day. This can be done by multiplying the number of extra shirts produced per day by the number of days extra shirts were produced. Since one day was skipped due to finishing early, there were 7 days of producing extra shirts.
7 times 10 equals 70. This means that 70 shirts would have been produced on the 8th day, which means the factory was planning on producing 70 shirts for every other day as well.
Help asap 15 points!
What is the approximate area of a sector given Θ≈212 with a radius of 45 m?
Question 1 options:
2613.59 m²
3744.45 m²
3371.26 m²
2928.36 m
What is the approximate area of a sector given Θ≈92 degrees with a diameter of 9m?
Question 2 options:
60 m²
65 m²
15.6 m²
16.2 m
Answers
Final answer:
The approximate area of a 212-degree sector with a 45m radius is 3371.26 m², and the approximate area of a 92-degree sector with a 9m diameter (4.5m radius) is 16.2 m².
Explanation:
To find the approximate area of a sector of a circle, we use the formula for the area of a circle, A = πr², and then adjust it for the sector by multiplying by the ratio of the central angle to 360 degrees. For Question 1, the central angle θ is approximately 212 degrees and the radius is 45 m. The formula for the sector area becomes A = (π × (45 m)² × (212/360)). A quick calculation gives us the following area:
For the first sector with a 212-degree angle and a radius of 45m:
A = 3.1415927 × (45 m)² × (212/360) = 3.1415927 × 2025 m² × 0.5889 ≈ 3371.26 m²
For Question 2, the central angle θ is approximately 92 degrees and the diameter is 9m, which makes the radius 4.5m. The formula for the sector area then becomes A = (π × (4.5 m)² × (92/360)). The calculation yields the following area:
A = 3.1415927 × (4.5 m)² × (92/360) = 3.1415927 × 20.25 m² × 0.2556 ≈ 16.2 m²
Please please help me
Answers
Yes.
The triangle inequality theorem states that a triangle is possible if the sum of two sides is larger than the 3rd side.
In this case, the sides are 4, 5 and 6.
4+5 is bigger than 6
4 + 6 is bigger than 5
5 + 6 is bigger than 4.
The sum of any 2 sides is always larger than the 3rd side, so this triangle is possible.
-------------------------------------------------------
Answer: Yes
Identify the angle measures of PQRS. I'm so confused, please help me! SHOW YOUR WORK!!
Answers
10y + 7 + 3(3y + 7) = 180
10y + 7 + 9y + 21 = 180
19y + 28 = 180
19y = 180 - 28
19y = 152
y = 152/19
y = 8
Plug back into Q and S.
Q = 10y + 7
Q = 10(8) + 7
Q = 80 + 7
Q = 87
S = 3(3y + 7)
S = 9y + 21
S = 9(8) + 21
S = 72 + 21
S = 93
Without solving for x to find the other angles, we can easily see that the answer is choice C.
Answer:
P = 61°
Q = 87°
R = 119°
S = 93°
Done!
Find the coordinates of the midpoint of the segment whose endpoints are given. W (-3, -7) and X (-8, -4) (-5/2, -11/2) (-11/2, -11/2) (-5/2, -3/2)
Answers
Answer:
[tex]\large\boxed{\left(-\dfrac{11}{2};\ -\dfrac{11}{2}\right)}[/tex]
Step-by-step explanation:
The formula of a midpoint of the segment"
[tex]\left(\dfrac{x_1+x_2}{2};\ \dfrac{y_1+y_2}{2}\right)[/tex]
We have the points W(-3, -7) and X(-8, -4).
Substitute:
[tex]x=\dfrac{-3+(-8)}{2}=\dfrac{-11}{2}\\\\y=\dfrac{-7+(-4)}{2}=\dfrac{-11}{2}[/tex]
The coordinates of the midpoint of a line segment with endpoints (-3, -7) and (-8, -4) are (-5.5, -5.5) using the midpoint formula.
Explanation:The subject of this question is Mathematics, specifically dealing with geometry. The student is asked to find the midpoint of a line segment whose endpoints are given. The coordinates of the endpoints of the line segment are W(-3, -7) and X(-8, -4).
The formula to calculate the coordinates of a midpoint in a Cartesian plane is M = [(x1 + x2)/2, (y1 + y2)/2], where M denotes the midpoint, (x1, y1) and (x2, y2) are the coordinates of the endpoints of the line segment.
Thus, the midpoint M of the line segment WX is calculated as follows: M = [(-3 -8)/2, (-7 -4)/2] = [-11/2, -11/2]. So, the coordinates of the midpoint of the line segment WX are (-5.5, -5.5).
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Select all that apply. A point is reflected over the y-axis and translated up 3 units. How will the coordinates change? The x-coordinate will decrease by 3. The x-coordinate's sign will change. The y-coordinate's sign will change. The y-coordinate will increase by 3.
Answers
Answer:
Step-by-step explanation:
If the point is translated across the y axis then the x coordinate will change sign.
If the point is translated upwards then the y coordinate will increase by 3
So the answers are B and D.
The formula for the nth term b of a geometric series is b=arn-1. Find n when b=1,024, a=16 and r=2.
Answers
[tex]\bf b=ar^{n-1}~~ \begin{cases} b=1024\\ a=16\\ r=2 \end{cases}\implies 1024=16(2^{n-1})~~ \begin{cases} 1024=&2^{10}\\ 16=&2^4 \end{cases} \\\\\\ 2^{10}=2^4(2^{n-1})\implies \cfrac{2^{10}}{2^4}=2^{n-1}\implies 2^{10}\cdot 2^{-4}=2^{n-1}\implies 2^{10-4}=2^{n-1} \\\\\\ 2^6=2^{n-1}\implies \stackrel{\textit{same base, the exponents must be the same}}{6=n-1\implies 7=n}[/tex]
The value of n when b = 1,024, a = 16, and r = 2 is 7.
The student is asking to solve for n in the formula of the nth term of a geometric series given the formula b = ar^(n-1) and the values of b, a, and r. To find the value of n, we can substitute the known values into the formula and solve for n.
b = 1,024
a = 16
r = 2
Using these values:
Substitute the known values into the formula: 1,024 = 16 imes 2^(n-1)
Divide both sides by 16: 64 = 2^(n-1)
Recognize that 64 is 2 to the power of 6: 2^6 = 2^(n-1)
Therefore, n - 1 = 6
Add 1 to both sides to find n: n = 7
The value of n when b = 1,024, a = 16, and r = 2 is 7.
Molly made 3600 \text{ mL}3600 mL3600, space, m, L of tea for a party, and she served the tea divided equally in 121212 cups.
How many liters of tea did Molly put in each cup?
111 liter =1000=1000equals, 1000 milliliters
Answers
Answer:
0.3
Step-by-step explanation:
the parent function of the logarithm is f(x) =log x. if g(x) = log(x-4)-3 write down the transformation
The x and y
Answers
Answer:
Step-by-step explanation:
The (x - 4) indicates side-to-side movement, and the -3 at the end indicates up and down movement. This log graph has moved 4 units to the right (x - (4)) and down 3 units (-3)
Final answer:
The transformation consists of a horizontal shift to the right by 4 units and a vertical shift downward by 3 units from the parent function f(x) = log x to g(x) = log(x - 4) - 3.
Explanation:
The transformation of the parent function f(x) = log x to g(x) = log(x - 4) - 3 involves a horizontal shift to the right by 4 units and a vertical shift downward by 3 units. This is because for the horizontal shift, the logarithmic function is now evaluating (x - 4) instead of x, indicating a move to the right on the x-axis by 4 units. Similarly, subtracting 3 from the whole function log(x - 4) indicates that every value of the function will be decreased by 3 units on the y-axis.
Someone please help??
Answers
Answer:
[tex]\sqrt[3]{-0.064}=-0.4[/tex]
Step-by-step explanation:
An on-line calculator can do this if your own doesn't.
For a cube root, you may have to use the exponentiation function with an exponent of 1/3. Usually, that fraction will need to be put in parentheses. (See the second attachment for the result from a TI-84 calculator.)
Let p= x^2-7.
which equation is equivalent to (x^2-7)-4x^2+28 in terms of p
PLZ HELP
Answers
Since p = x² - 7, you can substitute/plug in p for x² - 7
So:
(x² - 7)² - 4x² + 28 = 5
(p)² - 4x² + 28 = 5 You can factor out -4 from (-4x² + 28)
p² - 4(x² - 7) = 5 Plug in p
p² - 4p = 5 Subtract 5
p² - 4p - 5 = 0 Your answer is C
To find an equation equivalent to (x^2-7)-4x^2+28 in terms of p, substitute x^2-7 with p. The equation equivalent to (x^2-7)-4x^2+28 in terms of p is -4x^2+p+28.
Explanation:To find an equation equivalent to (x^2-7)-4x^2+28 in terms of p, we can substitute x^2-7 with p. So we have (p)-4x^2+28. Now, we combine like terms by adding the coefficients of p and -4x^2, which gives us -4x^2+p+28.
Find the simplified quotient. (2x^2 + 5x +3 / x^2 - 3x -4) / (4x^2 + 2x - 6 / x^2 - 8x + 16)
Answers
ANSWER
[tex]\frac{x - 4}{2x - 2} [/tex]
EXPLANATION
The given expression is;
[tex] \frac{2 {x}^{2} + 5x + 3}{ {x}^{2} - 3x - 4} \div \frac{4 {x}^{2} + 2x - 6}{ {x}^{2} - 8x + 16} [/tex]
We factor to obtain;
[tex] \frac{(x + 1)(2x + 3)}{(x - 4)(x + 1)} \div \frac{2(x - 1)(2x + 3)}{(x - 4)(x - 4)} [/tex]
Multiply by the reciprocal of the second fraction
[tex]\frac{(x + 1)(2x + 3)}{(x - 4)(x + 1)} \times \frac{(x - 4)(x - 4)}{2(x - 1)(2x + 3)} [/tex]
Cancel out common factors to get,
[tex]\frac{1}{1} \times \frac{(x - 4)}{2(x - 1)} [/tex]
[tex]\frac{x - 4}{2x - 2} [/tex]
Answer:
X-4/2x-2
Step-by-step explanation:
The amount of money an employee earns monthly before taxes, in dollars, after selling n products is $1,300 + $300n. Which statement is correct? A. For every product sold, the employee's earnings increase by $1,300. B. For every product sold, the employee's earnings increase by $1,000. C. For every product sold, the employee's earnings increase by $1,600. D. For every product sold, the employee's earnings increase by $300.
Answers
Answer:
The answer is D
Step-by-step explanation:
for every increase in the product sold, the earnings increase by 300 respectively
Which of the following statements describes one part of completing the square for x 2 + 4x = 32? Take the square root of 36 and add 2. Take the square root of 32 and subtract 2. Take the square root of 36 and subtract 2.
Answers
take the square root of 36 and subtract 2 because √36= 6-2=4x
Answer:
take the square root of 36 and subtract 2 because √36= 6-2=4x
Step-by-step explanation:
A water storage tank is in the shape of a hemisphere (half a sphere) If the radius is 15 ft, approximate the volume of the tank in cubic feet
Answers
7068.58 cubic feet is the volume
Scott takes gets a student loan to go to college after high school. If he pays $750 in interest at a rate of 3%, how much must the loan have been for originally?
Answers
Answer: 5,000
Step-by-step
Answer:
5,000
Step-by-step explanation:
just got my paper graded
The circumference (C) of a circle is 16cm. Which formula can you use to find the diameter (d) if you know that C= πd?
Answers
The formula is d=C/π.
The diameter is 2 times the radius
The formula for the circumference using the radius is 2πr.
in order to do this backwards, we would have to do 16÷2÷π, but we're not looking for the radius.
Therefore, we take out the ÷2 part, which would be 16÷π
16 is the circumference
16÷π=d
d=C÷π
Answer:
d = /π
Step-by-step explanation:
PLEASE HELP ASAP!!! CORRECT ANSWER ONLY PLEASE!!!
If the table is that of f(x), find a point that lies on the graph of f-1(x).
Answers
Answer: D) (-5, 1)
Step-by-step explanation:
Inverse is when the x's and y's are swapped.
f(x) has the coordinate (1, -5) --> the inverse of that is (-5, 1), which is option D.
Given ΔABC, m∠A = 50°, m∠B = 60°, and a = 7. Find c.
Answers
Answer:
D) 8.6
Step-by-step explanation:
The Law of Sines tells you ...
c/sin(C) = a/sin(A)
The sum of angles in a triangle tells you ...
C = 180° -A -B = 180° -50° -60° = 70°
Then ...
c = a·sin(C)/sin(A) = 7·sin(70°)/sin(50°) ≈ 8.6 . . . . . above equation multiplied by sin(C)
_____
There are apps available for phone or tablet for solving triangles. Many graphing calculators have functions that will do the same. Also, there are on-line triangle solvers that will give you the answer.
We include the working here because you're supposed to know how to work the problem. If all you want is the answer, that can be found faster a number of different ways.
alfred invest $60 a month in annuity that earns 4% ApR and is compounded monthly .what is the future value of alfreds accoint in five years
Answers
Answer:
Step-by-step explanation:
Answer:
$934.30
Step-by-step explanation:
We have been given that Alfred invest $60 a month in annuity that earns 4% APR and is compounded monthly. We are asked to find the future value of Alfred's account after 5 years.
[tex]FV=C_0\cdot (1+r)^n[/tex], where,
[tex]C_0=\text{Initial value}[/tex],
[tex]r=\text{APR in decimal form}[/tex],
[tex]n=\text{Number of times interest is compounded per year}[/tex].
[tex]r=4\%=\frac{4}{100}=0.04[/tex]
[tex]FV=\$60\cdot (1+0.04)^{12*5}[/tex]
[tex]FV=\$60\cdot (1.04)^{70}[/tex]
[tex]FV=\$60\cdot 15.57161835[/tex]
[tex]FV=\$934.2971[/tex]
[tex]FV\approx \$934.30[/tex]
Therefore, the future value of Alfred's account in 5 years would be $934.30.
Which product of prime polynomials is equivalent to 36x3 – 15x2 – 6x? x(3x – 2)(4x + 1) 3x(3x – 2)(4x + 1) 3(x2 + 1)(4x – 1) 3(x2 + 1)(4x + 1)
Answers
Answer:
3x (3x-2)(4x+1)
Step-by-step explanation:
36x^3 – 15x^2 – 6x
factor out the "3x"
3x (12x^2-5x-2)
3x(3x - 2) (4x + 1)
= 9x^2 - 6x (4x + 1)
= 36x^3 + 9x^2 + - 24x^2 - 6x
= 36x^3 - 15x^2 - 6x
hope this helps!
The product of prime polynomials is equivalent to Option (A) [tex]3x(3x - 2)(4x + 1)[/tex].
Concept of prime polynomial -In mathematics, an irreducible polynomial (or prime polynomial) is approximately a non-constant polynomial that cannot be factored into the product of two non-constant polynomials. The expression can be expressed in product of prime polynomial by converting it into the factored form.
How to solve the given polynomial expression into product of prime polynomials ?Given polynomial expression = [tex]36x^{3} - 15x^{2} - 6x[/tex]
Solving the polynomial expression in factored form -
⇒ [tex]3x(12x^{2} - 5x - 2)[/tex]
⇒ [tex]3x(12x^{2} - 8x + 3x - 2)[/tex]
⇒ [tex]3x[4x(3x - 2) + 1(3x - 2)][/tex]
⇒ [tex]3x(3x - 2)(4x + 1)[/tex]
Therefore the product of prime polynomial is [tex]3x(3x - 2)(4x + 1)[/tex]
To learn more about product of prime polynomial, refer -
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2. Find the area of the trapezoid. Leave your answer in the simplest radical form.
Answers
Answer:
170 ft²
Step-by-step explanation:
First let's calculate the height of this trapezoid. Call it 'h.' Look at the triangle on the right; the base is equal to (22 ft - 12 ft), or (10 ft). Using the tangent function, we can find h:
h
tan 45° = ---------- = 1 and so we know that h = 10 ft
10 ft
The formula for the area of a trapezoid is
A = (average length)*(width)
Here we have:
A = [ (12 ft + 22 ft) / 2 ] * 10 ft, or
A = (17 ft)*(10 ft) = 170 ft²
add 2/3 yards 4/9 yard and 23/36 yard and please show work
Answers
Answer:
7/4 yard
Step-by-step explanation:
36 is a suitable common denominator for expressing these fractions. All measures are in yards.
2/3 + 4/9 + 23/36 = (12·2)/(12·3) + (4·4)/(4·9) + 23/36
= 24/36 + 16/36 + 23/36
= 63/36 = (9·7)/(9·4)
= 7/4 = 1 3/4 . . . . . yards
A water sprinkler sends water out in a circular pattern. How many feet away from the sprinkler can it spread water if the area formed by the watering pattern is 1,661.06 square feet?
Answers
Check the picture below.
Answer:
The correct answer is 23
Step-by-step explanation: