Total amount of water after 18 minutes is 1365 Liters.
Given that
1) Owners of a recreation area are filling a small pond with water.
2) They are adding water at a rate of 35 liters per minute.
3) There are 700 liters in the pond to start.
4) Let W represent the total amount of water in the pond (in liters),
5) let T represent the total number of minutes that water has been added.
Now we have originally 700 litres i.e. when time =0 W =300
Next is rate of change of water per minutes = Positive 35
Thus the linear relationship between w and T has slope as 35 and y intercept as 300
Hence equation is
y = m x + c
W = 35T + 700
When T=19 minutes
W = 35(19) + 700
W = 1365 litres
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The equation relating W to T is W = 400 + 34T and total amount of water after 18 minutes is 1012 liters.
Equation will be formed by adding the amount of water already present with product of rate of water adding and amount of time in minutes. Representing this as equation -
W = 400 + 34T
Keep the value of T in the equation to find the total amount of water after 18 minutes.
W = 400 + 34×18
Performing multiplication on Right Hand Side of the equation
W = 400 + 612
Performing addition on Right Hand Side of the equation
W = 1012 liters
Therefore, the equation is W = 400 + 34T and amount of water is 1012 liters.
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Find
d93 /dx93 *(cos x)
by taking the first few derivatives and observing the pattern that occurs.
d93 /dx93 *(cos x) = - sin x
Now,
d/dx (cos x ) = -Sin x
d2/dx2 (cos x) = - cos x
d3/dx3 (cos x) = sin x
d4/dx4 (cos x) = cos x
d5/dx5 (cos x) = - sin x
d6/dx6 (cos x) = -cos x
The same pattern will repeat for every 6th derivative so ,
Now,
93 = (4 x 23) + 1
Therefore,
d93 /dx93 *(cos x) = - sin x
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A circle has a diameter of 24 centimeters. Central angle FOG is drawn, determining an arc FG. The radian measure of angle FOG is 3/4 What is the length of arc FG in centimeters?16 cm9 cm32 cm18 cm
Answer:
9 cm
Explanation:
We are given the following information:
Diameter = 24 cm
Angle FOG = 3/4 rad
The formula for calculating arc length is written below:
[tex]\begin{gathered} L=\theta\times r \\ where\colon \\ \theta=central\text{ angle of }arc,\text{ in }rad \\ r=radius \\ r=\frac{\text{Diameter}}{2}=\frac{24}{2}=12cm \\ \theta=\frac{3}{4}rad \\ \text{Substitute these into the formula, we have:} \\ L=\frac{3}{4}\times12 \\ L=\frac{3\times12}{4} \\ L=9cm \\ \\ \therefore L=9cm \end{gathered}[/tex]Therefore, the arc length is 9 cm
Describe the shape, orientation, and vertex of
each parabola relative to the graph of y=x².
Sketch each graph.
a) y=-0.5x² + 2
c) y = -0.1x² - 6
e) y=-3x²-5
g)y=8x²+4
b) y = 2x²
d)y=x²+4
f) y=0,1x² +2
h) y=-0.7x²-3
The parabola y = - 0.5x² + 2 opens downwards and the vertex is at (0,2) .
A parabola is a mirror-symmetric planar curve with a rough U-shape. It can be defined by many seemingly unrelated mathematical descriptions that all relate to the same curves.
One way to interpret a parabola is with a line and a point (the focus) (the directrix). The directrix is less significant. The parabola lies between the directrix or the focus and the endpoints in this plane that are uniformly spaced apart.
a) y=-0.5x² + 2 vertex is at (0,2)
c) y = -0.1x² - 6 vertex at (0,6)
d)y=x²+4 vertex at (0,-4)
e) y=-3x²-5 vertex at (0,5)
g)y=8x²+4 vertex at (0,-4)
h) y=-0.7x²-3 vertex at (0,3)
A parabola can also be thought of as a conic section formed by joining a right circular conical area with a plane perpendicular to another axis.
The graph of the parabola is attached below.
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2(y−1)+6y = −10 please help fastest answer gets 37 points
Point P(-3, 4) is a point on the terminal side of 0 in standard form. Find the exact value ofsine, cosine, and tangent for 0.
Solution
Step 1
The terminal side, containing point (-3, 4) is located in Quadrant 2.
sine is positive
cosine and tangent are both negative.
Step 2
Draw a diagram to illustrate the information
Step 3
[tex]\begin{gathered} Find\text{ d using the Pythagoras theorem} \\ d^2\text{ = 3}^2+\text{ 4}^2 \\ d^2\text{ = 9 + 16} \\ d^2\text{ = 25} \\ d\text{ = }\sqrt{25} \\ \text{d = 5} \end{gathered}[/tex]Step 4:
[tex]\begin{gathered} sine\text{ = }\frac{Opposite}{Hypotenuse} \\ Sin\theta\text{ = }\frac{4}{5} \end{gathered}[/tex][tex]\begin{gathered} Cosine\text{ = }\frac{Adjacent}{Hypotenuse}\text{ = }\frac{x}{d} \\ Cos\theta\text{ = }\frac{-3}{5} \end{gathered}[/tex][tex]\begin{gathered} tangent\text{ = }\frac{Opposite}{Adjacent}\text{ = }\frac{y}{x} \\ tan\theta\text{ = }\frac{-4}{3} \end{gathered}[/tex]Final answer
[tex]\begin{gathered} sin\theta\text{ = }\frac{4}{5} \\ cos\theta\text{ = }\frac{-3}{5} \\ tan\theta=\frac{-4}{3} \end{gathered}[/tex]Assume the annual day care cost per child is normally distributed with a mean of $8000 and a standard deviation of $1500. In a random sample of 300 familles, how many pay morethan $6440 annually for day care per child?Of the 300 families, approximately pay more than 56440 annually for day care per child(Round to the nearest whole number as needed.)
Let's begin by listing out the information given to us:
Mean = $8,000, SD = $1,500
In a sample of 300, how many pay more than $6440?
In the diagram below, the circle has a radius of 25 inches. the area of the unshaded is 500pi in^2Determine and state the degree measure of angle Q, the central angle of the shaded sect
1) In this question, we are going to make use of the formula for the area of that sector, to find the central angle.
2) So, let's write it out an expression involving the area of a circle, the unshaded area, and the shaded one and then plug into that the given data:
[tex]\begin{gathered} A=\frac{\alpha}{360^{\circ}}\times\pi r^2 \\ A_{Unshaded}+A_{shaded}=A_{Circle} \\ 500\pi+\frac{\alpha}{360}\times\pi r^2=\pi r^2 \\ \\ 500\pi+\frac{α}{360}\pi25^2=25^2\pi \\ \\ 500\pi+\frac{125\piα}{72}=625\pi \\ \\ 500\pi +\frac{125\pi α}{72}-500\pi =625\pi -500\pi \\ \\ \frac{125\pi α}{72}=125\pi \\ \\ \frac{72\times \:125\pi α}{72}=72\times \:125\pi \\ \\ \frac{125\pi α}{125\pi }=\frac{9000\pi }{125\pi } \\ \\ α=72^{\circ} \\ \\ \end{gathered}[/tex]Thus, the centra angle of that shaded area is 72º
4. A student asks, “If the average income of 10 people is $10,000 and one person gets a raise of $10,000, is the median or the mean changed and, if so, by how much?
Since we don't know the specific income of each person in the sample, we don't know for sure if the median will change. Nevertheless, the mean will surely raise.
Since the current average income is $10,000, if one of them gets a raise of $10,000, then the sum of all incomes would be $100,000+$10,000=$110,000. And the new average income will be:
[tex]\frac{110,000}{10}=11,000[/tex]Then, the mean increases by $1,000, and we can't say anything about the median.
12+212+25,432*5,000+
Answer:
127160224
or use a calculator
Solve for brainliest and 20 points
Answer:
x = 50
Step-by-step explanation:
50 x 3 - 15 = 135
an octagon has 8 sides & 8 angles. 135 x 8 = 1,080 which is the amount of degrees an octagon equals.
Answer:
50
Step-by-step explanation:
Total angles in an octagon is 1080
Because there are 8 sides you must divide 1080/8 to find the angle of one side ... 1080/8 = 135
3x-15=135
1) 135+15 = 150
2)150/3=50
Hope this helps, have a great day!
For what values of m does the graph of y = 3x² + 7x + m have two x-intercepts?
0 m> 25
O
Om<25
3
49
Om 12
49
m> 12
The graph of y = 3x² + 7x + m will have two x-intercepts if m < 49/12.
The given function is,
y = 3x² + 7x + m
Having two x-intercepts means that the value of y should be 0.
So, we can write,
3x² + 7x + m = 0
Now, this has become a quadratic equation and it will have two zeroes according to the question,
As we know, the condition of quadratic to have two different values of x is,
0 < √(b²-4ac)
Where,
a = 3
b = 7
c =m
Putting all the values,
√(7²-4(3)(m)) > 0
Squaring both sides,
7²-4(3)(m) > 0
49-12m > 0
49/12 > m.
So, the graph will have two intercepts if m < 49/12.
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Brittany has 34,011 in a savings account that earns 6% annually. the interest is not compounded. How much interest will she earn in 4 years? use the formula I = PRT, where I is the interest earned, p is the principal, r as the interest rate expressed as a decimal, and T is the time in years.
Notice that we are dealing with simple interest, and therefore given by the formula:
I = P * R * T
where P = $34,011
R = 6% in "decimal" form (0.06)
T = 4 (for 4 years)
Then, we have:
I = 34011 * 0.06 * 4 = $8162.64
This is the interest Brittany earned in 4 years.
How many solutions does this system of equations have?
y = x2 + x + 3
y = -2x - 5
Answer: (x, y) = (-8/5, -9/5)
Consider the rectangle with width 20 in and length 26 in, write a ratio of the width to length
The ratio of the width of the rectangle to the length of the rectangle is 10/13
We are provided with the rectangle. The dimensions of the rectangle are mentioned below;
Width of rectangle = 20
Length of rectangle = 26
We were asked to calculate the ratio of width of the rectangle to the length of the rectangle. So, to calculate the ratio of width of the rectangle to the length of the rectangle we need to divide the width of rectangle to the length of the rectangle as mentioned below;
( Width of rectangle/Length of rectangle ) = 20 / 26
( Width of rectangle/Length of rectangle ) = 10/13
So, we can finally conclude that the ratio of width of the rectangle to the length of the rectangle is 10/13 .
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need help with these parts. both parts use the same table
Given:
[tex]f(x)=h(2x)[/tex]And the values in the table.
Required:
The equation of a normal line to f at x=3.
Explanation:
The equation of the line that passes through from point (x,y) and has slope m
is given by the formula
[tex]y-y_1=m(x-x_1)[/tex]From the table at x=3, f(x)=h(2x)
that is f(3)= h(6)=9
And the slope from the table at x=3 is 1/2.
Now the equation of the line is:
[tex]\begin{gathered} y-9=\frac{1}{2}(x-3) \\ 2(y-9)=(x-3) \\ 2y-18=x-3 \\ x-2y=-15 \end{gathered}[/tex]Final answer:
Thus the equation of the normal line is
[tex]x-2y+15=0[/tex]What value of x makes this equation true?x+7------7A. 6B. 8C. 35 D. 42
We have
[tex]\begin{gathered} \frac{x+7}{7}=6 \\ x+7=6\times7 \\ x+7=42 \\ x=42-7 \\ x=35 \end{gathered}[/tex]Option C
How long do people typically spend traveling to work? The answer may depend on where they live. Here are the travel times in minutes of 20 randomly chosen workers in New York state
Based on the information given, the standard deviation for the observation is: 23.802698 or approximately 24.
The standard deviation in statistics is a measure of the degree of variation or dispersion in a set of values. A low standard deviation implies that the values are close to the set's mean, whereas a high standard deviation shows that the values are spread out over a larger range.
The formula for Standard deviation is given as:
σ[tex]= \sqrt{\frac{1}{N-1} \sum_{i=1}^N (x_i - \overline{x})^2} .[/tex]
Where
σ = population standard deviation
[tex]\bar x[/tex] = mean
x = each value of the population
n = number of observation
Note that mean ([tex]\bar x[/tex]) = [tex]\( \frac{1}{n} \sum_{i=i}^{n} x_{i} \),[/tex]
[tex]\bar x[/tex] = (5+10+10+10+10+12+15+20+20+25+30+30+40+40+60+60+65+70+70+70)/20
= 33.6
Hence the standard deviation for travel times for these 20 New York workers is:
Standard Deviation = [tex]\sqrt{\frac{\sum(x_{1} - {\bar x})^{2} }{n-1} }[/tex]
= √ [(5-33.6)²+ (10 - 33.6)² + .... + (70 - 33.6)²]/(20-1)]
Standard Deviation = √(10764.8)/(20-1)
SD = √(10764.8/19)
SD = √566.56842
SD = 23.802698
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Full Question:
How long do people spend traveling to work? The answer may depend on where they live here are the travel times in minutes for 20 workers in New York chosen at random by the census bureau:
5 10 10 10 10 12 15 20 20 25 30 30 40 40 60 60 65 70 70 70
What is the standard deviation for travel time for these 20 New York state workers?
what is the slope of the line that passes through the points (-7,-8) and (-5,-6)? Write your answer in simplest form.
Answer:
m=1
Step-by-step explanation:
Which expression is equivalent to (sin 2θ)(sec2θ)? 2sin θ sin θ tan θ 2tan θ
Answer:
Explanation:
Here, we want to get the expression that is equivalent to the given expression
We have this as follows:
[tex]\begin{gathered} \text{ sec 2}\theta=\text{ }\frac{\sec^2\theta}{2-\sec^2\theta} \\ \\ \sin 2\theta\text{ = 2sin}\theta\cos \theta \end{gathered}[/tex]Now, we can rewrite the overall expression as:
[tex]undefined[/tex]Arc Length S. Central Angle 0 82 miles. 135°Find the radius and radians r of a circle with an arc length s and a central angle 0.
Central angle of 135 degrees = 135 (Pi/180) = (3/4)Pi = 2.356 radians
First answer:
Central angle = 2.356 radians
Arc lenght = 2 Pi r (angle/360), in this case:
82 = 2 Pi r (135/360) = 2 Pi r (3/8) = (3/4) Pi r
82 = (3/4) Pi r
r = 82/(3/4)Pi = 82/2.35619449
r = 34.80188089
Second answer:
Radius = 34.8 miles
please help me solve. I have the answer in yellow, but it's not correct.
Remember that
27=(3)(3)(3)=3^3
so
[tex]\sqrt[]{3\cdot}\sqrt[\square]{27}=\sqrt[]{3\cdot}\sqrt[\square]{3^3}=\sqrt[]{3^4}=3^2=9[/tex]answer is 9
so
9 NA
blank 1 ------> 9
blank 2 ------> NA
Which equation has a constant of proportionality equal to 1? Choose 1 answer: A y 10 1 11 B y 7 8 3 y = 15 D y = 2
we know that
A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form y=kx
where
k is the constan of proportionality
therefore
in this problem
the answer is the option Dy=x
because, the value of k =1
Find the critical numbers of the function. (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.)
h(x) = x−1⁄3 (x − 12)
The critical value of the given function is = -11/2
The x values for which f'(x) = 0 are the crucial values of a function f(x).
The function in this quandary is:
h(x) = x−1⁄3 (x − 12)
The derivative is discovered using the quotient rule as follows:
[tex]h(x) = \frac{x - 1}{3(x - 12)} \\\\h'(x) = \frac{ (x-1) (3x - 36)' - (x - 1)'(3x - 36)}{(3x - 36)^{2} }\\\\h'(x) = \frac{ (x-1) (3) - (-1)(3x - 36)}{(3x - 36)^{2} }\\\\On equating it to 0\\\\\frac{ (x-1) (3) + 1(3x - 36)}{(3x - 36)^{2} } = 0\\\\3x - 3 + 3x + 36 = 0\\\\6x + 33 = 0\\\\x = \frac{-11}{2}[/tex]
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(2tanθ-3cosθ) Expand
Evaluate the expression below using the properties of operations. -36 ÷ 1/4 • (-1/8) • (-3) ÷ 6
Answer:
-9
Step-by-step explanation:
We are working with multiplications and divisions, which have no precedence over each other. So we can do the operations in order. It is important to remind that in these operations, if two numbers have different signals, the result of the operation is negative, otherwise, positive.
-36 ÷ 1/4
Different signals, so the result will be negative
[tex]\frac{-36}{\frac{1}{4}}=-36\ast\frac{4}{1}=-36\ast4=-144[/tex]-36 ÷ 1/4 • (-1/8) = -144 * (-1/8)
Same signal, so positive
[tex]-144\ast(-\frac{1}{8})=\frac{144}{8}=18[/tex]-36 ÷ 1/4 • (-1/8) • (-3) = 18 * (-3) = -54
-36 ÷ 1/4 • (-1/8) • (-3) ÷ 6 = -54 ÷ 6 = -9
- The Freedom Tower in New York City is 1776 feet
tall. The equation f(t) = -16t² + 1776 models the
height f(t) (in feet) of an object t seconds after it is
dropped from the top of the tower.
a. After how many seconds will the object hit the
ground? Round your answer to the nearest
hundredth of a second.
b. What is the height of the object 3 seconds after
it has been dropped from the top of the tower?
A golf ball is hit from the ground, and its height
can be modeled by the equation h(t) ==16t² + 128t,
where h(t) represents the height (in feet) of the ball
t seconds after contact. What will the maximum
height of the ball be?
WILL GIVE BRAINLIEST PLSSS
Part a: time when object hit the ground is 10.5 sec.
Part b: The height of the object 3 seconds is 1632 ft.
What is termed as the equation of motion?A mathematical formula which describes this same position, velocity, as well as acceleration of a body in relation to a specific frame of reference is known as an equation of motion. The equation of motion is second law, that also states that the force that acts on an object is equivalent to the mass m of a body multiplied by the acceleration an of its center of mass.For the given question;
The equation that models the height f(t) (in feet) of an object t seconds after it is when dropped from the top of the tower is,
f(t) = -16t² + 1776
Part a: time when object hit the ground.
When the object hit the ground, height will be zero.
Put f(t) = 0.
0 = -16t² + 1776
-16t² = -1776
t² = 111
t = 10.5 sec.
The, time after which the object will hit the ground is 10.5 sec.
Part b: The height of the object 3 seconds;
Put t = 3 in the equation.
f(3) = -16(3)² + 1776
f(3) = 1632 ft
The height of the object after 3 sec will be 1632 ft.
Thus, the values for the object hitting the ground are found.
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a=460 rounded to the nearest 10 b=11.9 rounded to 1 dp find the minimum (to 2 dp) of a / b
The minimum result (to 2 dp) of a / b is 38.66
What is rounding decimals?The term "rounding decimals" refers to the accurate rounding of decimal figures. When rounding a decimal number, certain principles must be followed. Simply put, if the last digit is less than 5, round down the previous digit. However, if it is 5 or greater, round the previous digit up.Given:
a=460 rounded to the nearest 10
b=11.9
Now, substitute the values of a and b in a/b,
a/b = 460/11.9
Multiply the same integer(10) by both the numerator and denominator,
a/b = 4600/119
Round the number obtained
a/b ≅ 38.66
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11. Algebra The total cost of the Fatigato
family's two cars was $71,482. The cost of
one car was $38,295. Write an equation
using a variable to represent the cost of
the family's other car.
Answer:
$33,187
Step-by-step explanation:
Our total is 71,482 so let's set our equation to 71482=_________
Now we have $38,295 for one car, and we will subtract it from the total to find the other car, as there are 2 cars.
Equation:
71482-38295=x OR 71482=38295+x
X is the cost of the second car.
If one of the flights is randomly selected find the probability that the flight silicon Rosa United Airlines flight given that it was on time.
Total of flights on time: 22 + 53 = 75
probability that the flight selected was silicon Rosa United Airlines:
53/75 = 0.71 = 71%
Assume that different groups of couples use a particular method of gender selection and each couple gives birth to one baby. This method is designed to increase the likelihood that
each baby will be a girl, but assume that the method has no effect, so the probability of a girl is 0.5. Assume that the groups consist of 18 couples.
Find the expected number of girls in groups of 18 births
Answer:
since the method is deemed to have no effect
which means probability of having a girl child is same as having a boy child which is 0.5
Total births = 18
Therefore, expected number of girls in groups should be equal to = 0.5 × 18 = 9
I hope this is helpful