Answer:
[tex]ln(8y^{6})[/tex]
Step-by-step explanation:
3ln(2)+6ln(y)
= [tex]ln(2^{3} )+ln(y^{6})[/tex]
= [tex]ln(8 )+ln(y^{6})[/tex]
= [tex]ln(8*y^{6})[/tex]
= [tex]ln(8y^{6})[/tex].
David gained 16 pounds over the winter. he went on a diet and lost 25 pounds. then he regained 4 pounds and weighed 177 pounds. how much did he weigh originally?
David's original weight was 182 pounds, as we determined by retracing his weight changes in reverse order.
Explanation:To find out how much David originally weighed, we need to work backwards from his ending weight, taking his weight changes into account. Currently David weighs 177 pounds. However, before gaining the last 4 pounds, he would have weighed 177 - 4 = 173 pounds.
Going back further, before losing 25 pounds, he would have weighed 173 + 25 = 198 pounds. Finally, before David gained 16 pounds over the winter, his original weight would have been 198 - 16 = 182 pounds.
So, David's original weight was 182 pounds.
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If you run a 10 kilometer race in 43 minutes 30 seconds, what is your average time per mile? what is your average speed in miles per hour?
Chris's uncle has a model car. the model is 6 inches long and 3 inches wide. the actual car is 75 inches long. what is the car's actual width, if we assume the model's proportions are accurate? if necessary, round to the nearest tenth of an inch.
I believe the right answer would be 37.5
What is the coefficient of x7 in the expansion of (1 + x)11?
Final answer:
Using the binomial theorem, the coefficient of x⁷ in the expansion of (1 + x)¹¹ is found by calculating '11 choose 7', which is 330.
Explanation:
The coefficient of x⁷ in the expansion of (1 + x)¹¹ can be found using the binomial theorem. To find the coefficient of x⁷, we look for the term that comes from choosing x seven times in the expansion. This corresponds to the 8th term, because the terms are indexed from 0, where the binomial coefficient is found by calculating "11 choose 7" or C(11, 7).
To calculate "11 choose 7", use the formula:
C(n, k) = n! / [k!(n-k)!], which gives us:
C(11, 7) = 11! / [7!(11-7)!] = 11! / (7!4!) = (11×10×9×8) / (4×3×2×1) = 330
Therefore, the coefficient of x⁷ in the expansion of (1 + x)¹¹ is 330.
Select all that justify the following statement.10 + x • 12 = 12x + 10
10 + x*12 = 12x+10
since the left side can be re-written as 12x+10 this does equal the right side
so any real number ( any value of x ) will work
Hour hand of a watch rotates 30 degrees every hour, how many rotations makes in 6 days
is 2xy = -8 a function
The equation 2xy = -8 is a rectangular hyperbola which is an example of the function.
What is a function?A function is an assertion, concept, or principle that establishes an association between two variables. Functions may be found throughout mathematics and are essential for the development of significant links.
When the transverse and conjugate axes of a hyperbola are both the same length, the diagnosis and appropriate are said to be rectangular.
The equation is given below.
2xy = -8
Separate the variable 'y', then we have
2xy = -8
xy = -4
y = -4/x
The equation 2xy = -8 is a rectangular hyperbola which is an example of the function.
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What is the simplified form of the expression? -(4)^-2
Answer:
The given expression [tex]-\left(4\right)^{-2}[/tex] becomes [tex]-\frac{1}{16}[/tex]
Step-by-step explanation:
Given : Expression [tex]-\left(4\right)^{-2}[/tex]
We have to write the simplified form of the given expression [tex]-\left(4\right)^{-2}[/tex]
Consider the given expression [tex]-\left(4\right)^{-2}[/tex]
Apply exponent rule , [tex]\:a^{-b}=\frac{1}{a^b}[/tex]
[tex]4^{-2}=\quad \frac{1}{4^2}[/tex]
[tex]\frac{1}{4^2} =\frac{1}{16}[/tex]
Thus, The given expression [tex]-\left(4\right)^{-2}[/tex] becomes [tex]-\frac{1}{16}[/tex]
if a job pays $45,000 per year, you live in a state where your total tax burden is 22%, and you receive a weekly paycheck, what is your take-home pay from each paycheck?
Answer:
$190.38 per week
Step-by-step explanation:
45,000 x .22 (the tax) is 9,900
9,900 / 52 (weeks in a year) is 190.384
Rounded, your answer is $190.38 per week
A ship leaves port at 1:00 p.m. and travels s35°e at the rate of 26 mi/hr. another ship leaves the same port at 1:30 p.m. and travels s20°w at 20 mi/hr. approximately how far apart are the ships at 3:00 p.m.?
Given the parent functions f(x) = 3x + 2 and g(x) = 5x − 10, what is g(x) − f(x)?
g(x) − f(x) = 5x − 8 − 3x
g(x) − f(x) = 5x − 12 − 3x<--------------------
g(x) − f(x) = 3x − 8 − 5x
g(x) − f(x) = 3x + 12 − 5x
Points earned on this question: 2
Answer:
Option B. g(x) - f(x) = 5x - 3x - 12
Step-by-step explanation:
In this question the given functions are
f(x) = 3x + 2
g(x) = 5x - 10
Now we have to calculate the value of g(x) - f(x)
g(x) - f(x) = (5x - 10) - (3x +2)
= 5x - 10 - 3x - 2
= (5x - 3x) - (10 + 2)
= 5x - 3x - 12
Option B. (5x - 3x - 12) is the answer.
Two pounds is equivalent to approximately how many kilograms
Which equation has the steepest graph
Answer:
b
Step-by-step explanation:
A coach needs both small and large cones to set up an obstacle course. The coach knows that there are fewer than 30 cones in the storage room. The coach needs at least a dozen large cones.
Let x represent the number of small cones and y represent the number of large cones.
Which inequalities model the situation? Select each correct answer.
x+y≤30
x>0
x+y<30
y≥12
y>12
Answer: The correct options are,
x+y < 30
y ≥ 12
Step-by-step explanation:
Here, x represent the number of small cones and y represent the number of large cones.
∵ Large cones are at least 12,
⇒ y ≥ 12,
Now, total cones = x + y
∵ There are fewer than 30 cones,
I.e. x + y < 30,
Now, number of cones can not be negative,
⇒ x, y ≥ 0
If y=x+2 were changed to y=x-1 how would the graph of the new function compare with the first one
Answer: C shifted down :)
Answer:
it would be shifted down
solve the system
x+3y=5
x+4y=6
A) (2,1)
B) (1,5)
C) (8,-1)
D (11,-2)
Answer:
A(2,1)
Step-by-step explanation:
We are given that system of equation
[tex]x+3y=5[/tex]
[tex]x+4y=6[/tex]
We have to solve the system
Subtract equation first from equation second
Then, we get
[tex]y=1[/tex]
Substitute the value of y in equation I
Then, we get
[tex]x+3(1)=5[/tex]
[tex]x=5-3=2[/tex]
Hence, the option A is true.
Answer:A(2,1)
A gardener charges an initial fee of $37.50 plus a rate of $44.90 per hour. Write a function that shows the total fees for H hours of work
In the above figure, ∠AOB = 80°. What does ∠ACB equal?
A. 80°
B. 10°
C. 160°
D. 40°
ACB would be half of AOB
80/2 = 40
answer is D 40 degrees
Patricia donated 1 pint of blood to the blood bank.The lab assistant divided patricia's blood equally into 3 bags.How much blood was in each bag?
Each bag contained [tex]\(\frac{1}{3}\)[/tex] pint of blood.
To solve the problem, we need to divide the total amount of blood donated by Patricia equally into 3 bags. Patricia donated 1 pint of blood.
Since there are 3 bags, we divide 1 pint by 3 to find out how much blood is in each bag. The division is straightforward:
[tex]\[ \frac{1 \text{ pint}}{3 \text{ bags}} = \frac{1}{3} \text{ pint per bag} \][/tex]
Therefore, each bag contains [tex]\(\frac{1}{3}\)[/tex] pint of blood. This is the simplest form of the fraction, and there is no need to convert it to a different unit or simplify it further. The answer is [tex]\(\frac{1}{3}\)[/tex] pint per bag.
A fisherman separated 1/10 of his catch into 2 equal bins.What fraction is the entire catch was in each bin?A. 20/1 B. 5/1 C. 1/20 D. 1/5 Plz help me plz i need help with this right now.
Each face of a pyramid is an isosceles triangle with a 82° vertex angle. What are the measures of the base angles? PLZ help
WILL GIVE BRAINLIEST
The value of the base angle will be 49 degrees.
What is an angle?The angle is defined as the span between two intersecting lines or surfaces at or close to the point where they meet.
A vertex is an angle that is connected to a vertex of an n-dimensional polytope in geometry. It refers to the angle created by two lines colliding in two dimensions.
Given that each face of a pyramid is an isosceles triangle with an 82° vertex angle.
The base angle will be calculated by using the formula below:-
Base angles = (180°-vertex)/2=(180-82)/2
Base angles = 98/2=49°
Base angles = 49°
Therefore, the value of the base angle will be 49 degrees.
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Solve for the width in the formula for the area of a rectangle.
formulas
1. w = A - L
2. w = AL
3. w = L/A
4. w = A/L
Use the rewritten formula to find the width of a rectangle with an area of 42 square inches and a length of 16.8 inches.
1. 2.5 inches
2. 4.2 inches
3. 12.6 inches
4. 25.2 inches
W=A/L................
2.5 inches...........
Use multiplying by 1 to find an expression equivalent to 18/19 with a denominator of 76b.
Tyrell does sit-ups every day. On Monday, he did 4 sit-ups. On Tuesday, he did 8 sit-ups, and on Wednesday, he did 12 sit-ups. Based on the pattern, make a conjecture about the number of sit-ups he will do on Friday.
Answer: 20 sit ups.
Step-by-step explanation: if tyrell does situps everyday on monday he does 4 sit ups and tuesday 8 situps wendsday 12 situps thursday 16 situps friday 20 situps all u do to solve is add 4 every day.
your welcome.
The area of a rectangle is 44 ft2 , and the length of the rectangle is 3 ft less than twice the width. find the dimensions of the rectangle.
Final answer:
To find the dimensions of a rectangle where the length is 3 ft less than twice the width and the area is 44 ft², we use the relationship between the width and length to set up a quadratic equation. After solving for the width, we use that width to find the length and confirm that the area is correct.
Explanation:
To find the dimensions of the rectangle with an area of 44 ft2, we need to set up an equation based on the given relationships. Let's denote the width of the rectangle as w and the length as l. According to the problem, the length is three feet less than twice the width, so we have l = 2w - 3. The area of the rectangle is the product of its width and length, so the equation to calculate the area is w × l = 44. Substituting the expression for l into this equation yields w × (2w - 3) = 44.
Solving this quadratic equation, we distribute the width and get 2w2 - 3w = 44. By moving all terms to one side, we have 2w2 - 3w - 44 = 0. Factoring the quadratic equation or using the quadratic formula will result in two values for w, where one will be the width and the corresponding l will be the length when plugged into l = 2w - 3.
Let's find the dimensions:
Width: wLength: 2w - 3Once the values are calculated, we can confirm that the width and length provide an area of 44 ft2.
Therefore, the width of the rectangle is w= 5.5 feet.
Now, we can find the length (l):
l=2w−3=2(5.5)−3=11−3=8
So, the length of the rectangle is l=8 feet.
Which situation CANNOT be represented by this equation? -13x+15=9
A-The water level in a tank measures 1515 inches and is decreasing every 1313 of a minute. At what rate, xx, does the water level need to decrease per minute to reach a depth of 99 feet?
B-The water level in a tank measures 99 inches and is rising 1313 of an inch every minute. How many minutes, xx, will it take for the water level to measure 1515 inches deep?
C-The water level in a tank measures 1515 inches and is decreasing 1313 of an inch every minute. How many minutes, xx, will it take for the water level to measure 99 inches deep?
THE ANSWER IS: PLEASE MARK AS BRAINLIST
The water level in a tank measures 9 inches and is rising 13 of an inch every minute.
How many minutes, x, will it take for the water level to measure 15 inches deep?
Identify an equation in slope-intercept form for the line parallel to y = 5x + 2 that passes through (–6, –1).
A. y = 5x + 29
B. y = –5x – 11
C. y= 1/5 x+1/6
D. y = 5x – 29
The equation of line which is parallel to y = 5x + 2 and passing through (-6, -1) is y = 5x + 29. Then the correct option is A.
What is a linear equation?A relationship between two or more parameters that, when shown on a graph, produces a linear model. The degree of the variable will be one.
The linear equation is given as,
y = mx + c
Where m is the slope of the line and c is the y-intercept of the line.
Identify an equation in slope-intercept form for the line parallel to y = 5x + 2 that passes through (–6, –1).
The slope of the parallel lines is the same.
Then the equation will be
y = 5x + c
And the line is passing through (-6, -1), then the value of c will be
-1 = 5(-6) + c
c = 30 - 1
c = 29
Then the equation of line which is parallel to y = 5x + 2 and passing through (-6, -1) is y = 5x + 29.
Then the correct option is A.
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Formulate the recursive formula for the following geometric sequence.
{-16, 4, -1, ...}
Answer: divide by -4
Step-by-step explanation:
The length of a rectangle is 2 in. more than twice its width. if the perimeter of the rectangle is 28 in., find the dimensions of the rectangle.
In how many different ways can a panel of 12 jurors and 2 alternates be chosen from a group of 17 prospective jurors?
Final answer:
To find the different ways of choosing a panel of 12 jurors and 2 alternates from 17 prospective jurors, calculate the combinations separately (C(17, 12) for jurors and C(5, 2) for alternates) and multiply them, yielding a total of 61,880 different ways.
Explanation:
The question asks in how many different ways a panel of 12 jurors and 2 alternates can be chosen from a group of 17 prospective jurors. To solve this, we use the concept of combinations in mathematics. Since the order in which we select the jurors and alternates does not matter, we are dealing with combinations, not permutations.
First, we choose the 12 jurors from the 17, which is the combination of 17 taken 12 at a time. This can be calculated using the formula for combinations:
C(n, k) = n! / (k! * (n - k)!),
where 'n' is the total number of items, 'k' is the number of items to choose from, and '!' denotes factorial.
For the 12 jurors, we compute C(17, 12) which equals 17! / (12! * (17 - 12)!) = 17! / (12! * 5!) = 6188.
Next, we need to choose 2 alternates from the remaining 5 jurors. The calculation is C(5, 2) which equals 5! / (2! * (5 - 2)!) = 5! / (2! * 3!) = 10.
Since choosing jurors and alternates are independent events, we multiply the two combinations to get the total number of different ways to choose the panel:
6188 (ways to choose jurors) * 10 (ways to choose alternates) = 61,880 different ways.