Log4 (x^2-49) -5log4 (x+7)=
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Related Questions
The temperature of a cup of coffee varies according to Newton's Law of Cooling: dT dt equals negative k times the quantity T minus A, where T is the temperature of the coffee, A is the room temperature, and k is a positive constant. If the coffee cools from 100°C to 90°C in 1 minute at a room temperature of 25°C, find the temperature, to the nearest degree Celsius of the coffee after 4 minutes.
74
67
60
42
Answers
Answer:
67.3°C
Step-by-step explanation:
A = 25, T(0) = 100, T(1) = 90, find T(4)
dT/dt = -k(T - A)
d(T - A)/dt = -k(T - A)
d(T - A)/(T - A) = -k dt
ln(T - A) = lnC - kt
[tex]T(t) -A=Ce^{-kt}\\T(t) = A + Ce^{-kt} = 25 + Ce^{-kt}\\T(0) = 25 + C = 100\\C=75[/tex]
[tex]T(t) = 25 + 75e^{-kt}\\T(1) = 25 + 75e^{-k} = 90\\75e^{-k} = 65\\e^{-k} = \frac{65}{75}, k = ln\frac{75}{65} = 0.1431\\T(t) = 25+75e^{-0.1431t}\\T(4) = 25+75e^{-0.1431\times4} = 67.3[/tex]
numbers that has 10 as a factor
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Answer:
1, 2, 5 & 10
Step-by-step explanation:
The table shows how many miles Sally drove, y, in x hours. What is the constant rate of change in the number of miles Sally drove?
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Answer:
(X)73.2miles=the change in the constant rate of miles.
the number of miles times 73.2 equals the constant change of miles.
what is 2+ 1,528
pls help!!!!!!
Answers
Answer:
1530 is the sum of 2+1528
Answer:
1,530
Step-by-step explanation:
Mrs. Kwan will teach 8 workshops next week. Each workshop is 2 hours long. Mrs. Kwan tries to tell a joke ever 1/3. How many times will she tell a joke by the end of the last workshop?
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Assuming you meant every 1/3 hour, she will tell 48 jokes
1/3 hr = 20 mins
16 hrs = 960 mins
960/20= 48 jokes
You could also take 16 hrs and the 3 from 1/3, 16*3=48
Much faster method i forgot until just now..
At the U.S. Open Tennis Championship a statistician keeps track of every serve that a player hits during the tournament. The statistician reported that the mean serve speed of a particular player was 100 miles per hourâ (mph) and the standard deviation of the serve speeds was 13 mph. If nothing is known about the shape of theâ distribution, give an interval that will contain the speeds of at least eight-ninths of theâ player's serves.
a. 74 mph to 126 mph
b. 61 mph to 139 mph
c. 48 mph to 152 mph
d. 139 mph to 178 mph
Answers
Answer:
b. 61 mph to 139 mph
Step-by-step explanation:
Chebyshev's theorem states that
For k> 1
1 - 1/k²
Where:
At least 75% or 3/4 of data falls within 2 standard deviations from the mean - between μ – 2σ and μ + 2σ.
At least 88.89% of 8/9 of data falls within 3 standard deviations from the mean - between μ - 3σ and μ + 3σ.
From the question, we are told to find an interval that will contain the speeds of at least eight-ninths of the player's serves.
Mean (μ)= 100mph
Standard deviation (σ) = 13mph
At least 88.89% of 8/9 of data falls within 3 standard deviations from the mean - between μ - 3σ and μ + 3σ.
Hence:
μ - 3σ
100 - 3(13)
= 100 - 39
= 61 mph
μ + 3σ
= 100 + 3(13)
= 100 + 39
= 139 mph
Therefore, the interval is between 61 mph to 139 mph. Option b is correct
Your neighbor leaves his yard, which is 120 ft from the bus stop. He begins to walk toward you at the bus stop and then passes you. He walks at
a speed of 4 ft/s. His distance d from you after t seconds is given by d = 120 - 4t). After how many seconds is your neighbor 30 ft from you?
A.-22.5 s and -37.5 s
B. 22.5 s and 37.5 s
C. 30 s
D. 15 s and 45 s
Answers
Answer:
ANSWER B
Step-by-step explanation:
d=(120-4t)
30=120-4t
4t=120-30=90
t=90/4=22.5 s
-30==120-4t
4t=120+30=150
t=150/4=37.5 s
A cabin on a ferris wheel has traveled one fourth of the circumference
of the wheel, a distance of 117.75 feet. What is the radius, in feet, of
the ferris wheel? Use 3.14 for pi
Answers
Solving for the circumference and using the formula for the circumference we got the radius as 74.95 feet
Mensuration of Flat ShapesGiven Data
1/4 of the circumference = 117.75 feet.
Let the circumference be x feet
1/4*x = 117.75
x/4 = 117.75
cross multiplying
x = 4*117.75
x = 471 feets
The expression for the circumference is given as
C = 2πr
471 = 2πr
Making r subject of formula we have
r = = 471/2*3.142
r = 471/6.284
r = 74.95 feet
Learn more about Circles here
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Please help me with my math
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cos (3x)
Which symbol can be used to correctly compare the two fractionsPlease help asap!!!
Use >, <, or =.
2/5 35/100
Answers
Answer:
The symbol we can be used is " > "
Step-by-step explanation:
To compare two fractions you must make their denominator equal
Example:
To compare the fractions [tex]\frac{3}{4}[/tex] and [tex]\frac{7}{50}[/tex] ,
You should make their denominators equal. Multiply 4 by 25 to get 100 and multiply 50 by 2 to get 100, So, [tex]\frac{3*25}{4*25}=\frac{75}{100}[/tex] and [tex]\frac{7*2}{50*2}=\frac{14}{100}[/tex]. Since 75 > 14, then [tex]\frac{75}{100}>\frac{14}{100}[/tex] ,Which means [tex]\frac{3}{4}>\frac{7}{50}[/tex]Let us solve the question
∵ The fractions are [tex]\frac{2}{5}[/tex] and [tex]\frac{35}{100}[/tex]
→ Change denominator 5 to 100 by multiplying it by 20
∵ [tex]\frac{2}{5} =\frac{2*20}{5*20}=\frac{40}{100}[/tex]
∵ 40 > 35
∴ [tex]\frac{40}{100}>\frac{35}{100}[/tex]
∴ [tex]\frac{2}{5}>\frac{35}{100}[/tex]
∴ The symbol we can be used is " > "
7th grade math help me please :).
Answers
Answer:
a
Step-by-step explanation:
divide each price by the number of juice packs they got, then subtract the smaller number from the larger one. you get 0.15
y = 5x+p point (-2, 1) p=?
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y = 5x + p
1 = 5(-2) + p
1 = -10 + p
11 = p
-
Consider f(x) = 7x3 - 15x2 - 19x +3. Find the solutions of each of the following equations!
(a) f(x) = 0
(b) f(x-1)= 0
(c) f(x + 2) = 0
(d) f(2x)= 0
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What is the domain of the function f(x)=−12x+15? PLEASE HELP!!!
x≤30x≤30
x≥0x≥0
x≥−2x≥−2
all real numbers
Answers
Answer:
Fourth option
Step-by-step explanation:
Given the following question:
[tex]f(x)=-12x+15[/tex]
The domain of a function is all possible x inputs for a function, on the contrary range of a function would be all possible y inputs for a function.
[tex]f(x)=-12x+15[/tex]
Since the function has all defined points, it basically means that the functions possible x inputs are "all real numbers" or the fourth option.
[tex]-\infty \: < x < \infty[/tex]
Hope this helps.
One basketball team played 30 games throughout their entire season. If this team won 80% of those games, how many games did they win? Enter a numerical answer only.
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Find the amount of tax owed: vacant land valued at $500,000.00; assessed at 18%; taxed at $6.50 per hundred dollars worth of property
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Answer:
7
Step-by-step explanation:
WHICH DOT PLOT BEST REPRESENT THESE DATA?
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What's the reciprocal 22/7
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Answer:
3 1/7 however, the reciprocal is 7/22, or, 7 1/3.
explanation:
Convert improper fraction to mixed number.
7 x 3 = 21
Add 1 to get 22.
Now, convert and reverse the order.
Therefore,
the answer is [tex]3\frac{1}{7} / 7\frac{1}{3}[/tex]
What is the equation of this line?
y=1/2x−3
y=−1/2x−3
y=−2x−3
y=2x−3
Answers
Answer:
y=1/2x-3
Step-by-step explanation:
starting at the origin, you go down 3 to reach the line/point, hence the -3. Then you go up 1 over the right 2 to get reach the point, hence the 1/2.
It would not be negative 1/2 because we didn't go down 1 to the right.
An electrician charges a $100 flat fee, plus $75 per hour to work on a house.
a. Complete the table that shows the cost of hiring the electrician for 3 hours.
Hours, t Cost (dollars)
1
2
3
b. An expression for the cost (in dollars) of hiring the electrician for t hours is
.
c. It costs $
to hire the electrician for 5 hours.
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Answer:
a. 1. 175
2. 250
3. 325
b. 75t + 100
c. 75(5)+100 = $475
Step-by-step explanation:
What is .64 2/3 in fraction form?
Answers
Answer:
32/75 in fraction form 0.426 in decimal
Step-by-step explanation:
0.64 2/3
convert tge decimal into a fraction = 64/100 reduce/simplify to 16/25
64 ÷ 4 = 16
___
100 ÷ 4 = 25
16/25 × 2/3 = 32/75
16 × 2 = 32
___
25 × 3 = 75
The simplified fraction form of .64 2/3 is 66/75. To convert the mixed number .64 2/3 to fraction form, we need to combine the whole number part and the fractional part.
The whole number part is 0.64, and the fractional part is 2/3.
To combine them, we multiply the whole number part by the denominator of the fraction and then add the numerator. Then, we put the result over the denominator.
Step 1: Convert the decimal to a fraction.
0.64 = 64/100
Step 2: Combine the whole number part and the fractional part.
0.64 2/3 = 64/100 + 2/3
Step 3: Find a common denominator (the least common multiple of 100 and 3 is 300).
0.64 2/3 = (64/100) + (200/300)
Step 4: Add the fractions.
0.64 2/3 = (64/100) + (200/300) = 264/300
Step 5: Simplify the fraction, if possible.
264/300 can be simplified by dividing both the numerator and denominator by their greatest common divisor (GCD), which is 4.
264 ÷ 4 = 66
300 ÷ 4 = 75
So, the simplified fraction form of .64 2/3 is 66/75.
To know more about fraction form:
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Rewrite each equation without absolute value for the given conditions. y = |x−3| + |x+2| − |x−5| if x>5
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Using the definition of the absolute value function, it is found that the equation is written as: y = x + 4
What is the definition of the absolute value function?It is the distance of a given point x to the origin(vertex of the function), hence the definition is as follows:
[tex]|x - a| = x - a, x \geq a[/tex]
[tex]|x - a| = -x + a, x < a[/tex]
Hence, considering that all expression are positive for x > 5, we have that:
|x - 3| = x - 3;|x + 2| = x + 2;|x - 5| = x - 5;Then, the expression is:
y = |x−3| + |x+2| − |x−5|
y = x - 3 + x + 2 - x + 5
y = x + 4
More can be learned about the absolute value function at https://brainly.com/question/24734454
Find the Slope for the line which passes through these two points (-1,5) and (-4,-4).
Answers
Answer: positive 3 is the final answer
Step-by-step explanation:
Answer:
9/3 or just 3
Step-by-step explanation:
First we need to recognize that points are given by numbers that represent the x and y coordinates (or locations) of the point. So in this problem, the first point (-1,5) has an x value of -1 and a y value of 5. Similarly the second point has an x value of -4, and a y value of -4.
Slope is defined as rise over run, or change in y (rise as it goes up or down) over the change in x (or run as it moves left or right).
Change in x and y can be found by subtracting the first number from the second number.
So to calculate this, set up your equation like this:
[tex]\frac{5-(-4)}{-1-(-4)}[/tex]
After performing the subtraction, you should get:
[tex]\frac{9}{3}[/tex]
This further simplifies to 3.
7/8 × 5/4 what is the answer please
Answers
Answer:
[tex]\frac{35}{32}[/tex]
Step-by-step explanation:
1. (7/8) * (5/4)
2. (7)(5)
(8)(4)
Bonus : 35/32 as a decimal is 1.09375
Awnser provided by Education Point
Explain how the shapes shown have been sorted. Two groups of shapes. In group A, one shape has four equal side lengths of three, and no right angles. The opposite sides are parallel. Two shapes have two pairs of opposite equal side lengths. One shape has side lengths of four and eight. The other side lengths are three and two. Opposite sides are parallel, and there are no right angles. In group B there are three four sided shapes. One has opposite equal side lengths of seven and four and four right angles. One shape has four equal side lengths of three and four right angles. One shape has one set of opposite parallel sides and one right angle. None of the side lengths in the last shape are equal.
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There are different kinds of shapes. The shapes have been sorted below:
The shape that has one shape has four equal side lengths of three, and no right angles is rhombus.The opposite sides are parallel is parallelogram .Two shapes have two pairs of opposite equal side lengths is a parallelogram.A shape that has side lengths of four and eight is quadrilateral and octagon.Opposite sides are parallel, and there are no right angles is a parallelogramHeptagon has opposite equal side lengths of seven Quadrilaterals and triangle shape has shape has four equal side lengths of three and four right angles.Trapezoids has one set of opposite parallel sides and the shape that has one right angle is right-angled triangles.None of the side lengths in the last shape are equal is scalene triangle. What do you understand by the term shapes?The term shape is a word that connote the form or dimensions of an object and also their outline.
It is made up of outer boundary and also outer surface. Most of everything in the world today do have shape.
Learn more about Angles from
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Answer:
rectangle
Step-by-step explanation:
trust
Which expression is equivalent to 5(h+9)?
45h
0 14h
5h+9
5h+45
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Step-by-step explanation:
5(h + 9) = 5×h + 5×9 = 5h + 45
Answer: 5h+9!
Step-by-step explanation: hope this helps!! -marina mae :)
tHanks again for the response.
Answers
Answer:
(-3,-2)
Step-by-step explanation:
Equations are
y=2x+4y=-x-5Solve both
2x+4=-x-53x=-9x=-3On solving
y=3-5=-2Graph is also attached if you need another way
Answer:
(-3, -2)
Step-by-step explanation:
When the two lines intersect, f(x) = h(x)
2x + 4 = -1x - 5
Rearranging like terms together
3x = -9
x = -3
Substituting back into h(x) for x = -3
y = h(3) = 2(-3) + 4 = -2
So the point is (-3, -2)
A group of students went on a field trip. There were 3 boys for every 4 girls in the group. If there were 20 girls, how many students in all went on the field trip?
Answers
Answer:
35 students
Step-by-step explanation:
So if every 3 boys there is 4 girls you can solve that there is 5 times the amount of girls to get to 20. So to solve for the boys you do the same.
3 x 5 = 15
That means there are 15 boys and 20 girls but we want to know the total so what you do is just add 15+20=35
So 35 total students.
Hope that helps and have a great day!
Write the ratio in simplest form.
14:28?
How do I do that?
Answers
Answer:
2/3 is simplest form
Step-by-step explanation:
you find the greatest common factor of both numbers, in this case it is 7. Then, you divide both numbers by the greatest common factor to get the simplest form.
hope this helps ☺
Answer:
2/3 is
Step-by-step explanation:
Help please!
Area of a triangle using trigonometry!
Answers
Answer: 120
Step-by-step explanation: u just multiply the 2 numbers together