Answer:
The water level is dropping at a rate of 0.24 ft/s
Step-by-step explanation:
Here, we simply want to calculate the change in depth (height of the cone) , given the volume change
Mathematically, we have the volume of a cone as;
V = 1/3 * π * r^2 * h
we are given dv/dt as 12 ft^3/m
dv/dh = 1/3 * π * r^2
Substituting the value for the radius, we have
dv/dh = 1/3 * 22/7 * 4^2 = 50.29
dh/dt = dh/dv * dv/dt
dh/dv = 1/(dv/dh) = 1/50.29
Thus,
dh/dt = 1/50.29 * 12
dh/dt = 0.24 ft/s
Write a simplified expression that represents the perimeter of an irregular quadrilateral with some de lengths (2 1/4t - 5) (4t + 3) (1/2t - 1) (3t + 2)
Answer:
[tex]Perimeter = \frac{39t-4}{4}[/tex]
Step-by-step explanation:
Given
[tex]Lengths: (2\frac{1}{4}t - 5), (4t + 3), (1/2t - 1), (3t + 2)[/tex]
Required
Determine the perimeter
The perimeter is calculated as the sum of the lengths of the irregular shape.
i.e.
[tex]Perimeter = (2\frac{1}{4}t - 5) + (4t + 3) + (1/2t - 1) + (3t + 2)[/tex]
Remove brackets
[tex]Perimeter = 2\frac{1}{4}t - 5 + 4t + 3 + 1/2t - 1 + 3t + 2[/tex]
Collect Like Terms
[tex]Perimeter = 2\frac{1}{4}t +4t + 1/2t + 3t - 5 + 3 - 1 + 2[/tex]
[tex]Perimeter = 2\frac{1}{4}t +4t + 1/2t + 3t -1[/tex]
Convert mixed number to improper fraction.
[tex]Perimeter = \frac{9}{4}t +4t + 1/2t + 3t -1[/tex]
Take LCM
[tex]Perimeter = \frac{9t + 16t + 2t + 12t}{4} -1[/tex]
[tex]Perimeter = \frac{39t}{4} -1[/tex]
Take LCM
[tex]Perimeter = \frac{39t-4}{4}[/tex] --- The perimeter of the shape
We want to find the perimeter of the irregular quadrilateral given that we know its lengths. By direct computation, we will get:
P(t) = (39/4)*t - 1
Remember that for any figure, the perimeter is defined as the sum of the lengths of each side.
Here we have that the lengths of the four sides of the quadrilateral are:
(2 1/4t - 5)
(4t + 3)
(1/2t - 1)
(3t + 2)
So we must sum that, we will get:
P = (2 1/4t - 5) + (4t + 3) + (1/2t - 1) + (3t + 2)
Notice that in the first part we have a mixed number, we can rewrite it as:
2 + 1/4 = 8/4 + 1/4 = 9/4
Then the sum is:
P = ((9/4)t - 5) + (4t + 3) + (1/2t - 1) + (3t + 2)
Now we simplify this sum:
P = (9/4 + 4 + 1/2 + 3)*t + (-5 + 3 - 1 + 2)
P = (39/4)*t - 1
So the perimeter, as a function of t, is:
P(t) = (39/4)*t - 1
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plz help with this question i know you could do it please help
Answer:
The answer is 44.99
Step-by-step explanation:
divide 89.98/2= 44.99
can anyone help me??
Answer:
angle j = 98 degrees
angle c = 78 degrees
JK = 16
AD = 32
x=8
y=11
Step-by-step explanation:
Solve for a: (a+4)/3 - a/7 = (a+7)/5
Answer:
a= -7
Step-by-step explanation:
I hope this helps! :)
Does - 4y - 3 = (12y - 9)
- Sy have one solution, no solution, or infinitely many solutions?
Answer:
One answer: 3/8 or 0.375
Step-by-step explanation:
Answer:
exact form y
=3/8
decimal
y=0.375
Step-by-step explanation:
Find each angle measure in the triangle.
Answer:
30, 60, 90
Step-by-step explanation:
since there are 6 x's in total, and there are a total of 180 degrees in any triangle, we do 180/6= 30
so now we know x=30, 2x=60, and 3x=90
PLSS HURRY!!!
The line f(x) = x is graphed in the xy-coordinate plane.
How does the graph of the function f(x) + 1 compare to the graph of f(x)?
Answer:
Please check the attached diagram.
Thus, we conclude that:
In the diagram,
The red line represents the parent function f(x) = xThe blue line represents the function f(x) = x+1The blue line indicates that the parent function has been shifted 1 unit upward.
Step-by-step explanation:
Let us recall some transformation knowledge.
We know that
if y = f(x), then y = f(x) + b simply means a transformation of (0, b).
In other words, if we add some constant let say 'b' in the output or y-value, the graph simply shifts upward by b units.
Given that
f(x) = x
so
f(x+1) = x+1 means the parent function f(x) = x has been shifted 1 unit upward.
Please check the attached diagram.
Thus, we conclude that:
In the diagram,
The red line represents the parent function f(x) = xThe blue line represents the function f(x) = x+1The blue line indicates that the parent function has been shifted 1 unit upward.
1. Which of the following is a solution to the
equation - 2/5x = 10?
a. X = -4
b. X = -25
c. X= 4
d. X = 25
I am beging pls pls pls pls pls pls pls pls pls pls HELP ME!!!!!!!!!!!!!!!!!!!!!!!!!!
1. [Image: Vertical number line ranging from negative 5 to 5.] On this number line, zero represents sea level. Plot the following points based on the description provided. • opposite of 4
2. [Image: Vertical number line ranging from negative 5 to 5.] On this number line, zero represents sea level. Plot the following points based on the description provided. • –2
Answer:
wouldnt opposite of 4 just be -4
and wouldnt -2 just be at -2?
Step-by-step explanation:
hope this helps <3
Answer:
1. Negative 4
2. Negative 2
Step-by-step explanation:
1. Opposite of positive 4 is negative 4.
Negative 4 will be below sea level, so on the number line it will be below the zero, on -4.
2. Negative 2
Negative 2 will be below sea level, so on the number line it will be below the zero, on -2.
I hope it makes sense.
The ____________particles of an atom which are called electrons.
Answer:
Atomic Particles
The nucleus (center) of the atom contains the protons (positively charged) and the neutrons (no charge). The outermost regions of the atom are called electron shells and contain the electrons (negatively charged).
Step-by-step explanation:
Tracee buys a shirt for $15 and a pair of Jeans for $32.50. If the sales tax is 8% what is the total price Tracee pays for the items?
Answer:
38.00
Step-by-step explanation:
A real estate agent needs to estimate the average value of a residential property of a given size in a certain area. The real estate agent believes that the standard deviation of the property values is
Answer:
Follows are the solution to this question:
Step-by-step explanation:
[tex]95 \% \[/tex] the confidence level for z:
[tex]\alpha = 1 - 95 \% \\\\[/tex]
[tex]= 1 - 0.95 \\\\ = 0.05[/tex]
[tex]\to \frac{\alpha}{2} = \frac{0.05}{2} = 0.025\\\\\\to Z \ \frac{\alpha}{2} = Z_{0.025} = 1.96[/tex]
Calculating the Margin of error:
[tex]E = Z\ \frac{\alpha}{2} \times ( \frac{\sigma}{\sqrt{n}})[/tex]
[tex]= 1.96 \times ( \frac{5000}{\sqrt{\sqrt{100}}})\\\\= 980[/tex]
The population means estimate a 95 % confidence interval is:
[tex]\to \bar{x} \frac{+}{-} E\\\\ = \$ 90000 \frac{+}{-} 980[/tex]
Help please on circle theorems
Answer:
n = 28
Step-by-step explanation:
The angle at the centre is twice the angle on the circle subtended on the same arc, then
35 + m = 0.5 × 98 = 49 ( subtract 35 from both sides )
m = 14
∠ n is at the centre subtended on the same arc as ∠ m , thus
n = 2m = 2 × 14 = 28
What is the solution set to log(x + 7) > log3x?
Answer: (-∞, 3.5)
Step-by-step explanation:
Here we can use the relation:
Exp( Log(X)) = X
Now, we start with the equation:
log(x + 7) > log(3x)
Now we can apply the exponential function to both sides of the inequality to get:
Exp(log(x + 7)) > Exp(log(3x))
x + 7 > 3x
7 > 3x - x
7 > 2x
7/2 > x
3.5 > x
Then the solutions will be all the values of x smaller than 3.5, this set can be written as:
(-∞, 3.5)
Answer:
(0,3)
Step-by-step explanation:
used an online calculator
Which are the intercepts of the equation y+2=4(x+1) ?
Answer:
x-intercept is ([tex]- \frac{1}{2}, 0[/tex]) and y-intercept is ([tex]0, 2[/tex])
Step-by-step explanation:
How do we find the y-intercept of a function?We solve the equation when x=0. Let's try that with [tex]y+2=4(x+1)[/tex]
First, let's simplify it so that it resembles [tex]y=mx+b[/tex] more noticeably
[tex]y = 4x + 4 - 2 \\y = 4x + 2[/tex]
Now let's plug in 0 for x to find the y-intercept:
[tex]y = 4\cdot 0 + 2\\y = 2[/tex]
How do we find the x-intercept of a function?We solve the equation when y=0. Let's try this from the simplified equation we got ([tex]y = 4x + 2[/tex])
[tex]0 = 4x + 2\\-2 = 4x\\\frac{-2}{4} = x\\x = - \frac{1}{2}[/tex]
We must remind ourselves that all y-intercepts have an x that is equal to 0 and that all x-intercepts have a y equal to 0.
That means that our x-intercept will be ([tex]- \frac{1}{2}, 0[/tex]) and our y-intercept will be ([tex]0, 2[/tex])
This corresponds to the 3rd option counting from the left.
Good luck!
2. Rohit has notes of denominations 1000, 500 & 20. He has 40 notes of Rs.20 and 20
notes of Rs.1000. He made a payment of Rs.29300. How many notes of Rs.500 did he have?
a) 12
b) 14
c) 18
d) 17
Answer:
17
Step-by-step explanation:
To find how many notes of Rs. 500 he has, we need to find out the total value of all the Rs. 500 notes.
Total value of Rs. 20 notes = 20 × 40
= 800
Total value of Rs. 1000 notes = 1000 × 20
= 20 000
Total value of Rs. 500 notes = 29 300 - 800 - 20 000
= 8500
No. of Rs. 500 notes = 8500 ÷ 500
= 17
Rohit has total 17 notes of Rs.500
What is Unitary method?" Unitary method is the process of finding value of one unit using which we can find the value of other units."
According to the question,
Number of Rs.20 notes = 40
Total amount of Rs.20 = 20 × 40
= Rs.800
Number of Rs.1000 notes = 20
Total amount of Rs.1000 = 20 × 1000
= Rs.20,000
Total amount of Rs.20 and Rs.1000 notes = 20,000 +800
= Rs.20,800
Made a payment of Rs.29,300
Left amount of Rs.500 notes = 29,300 -20,800
= Rs.8500
Number of Rs.500 notes = 8500 ÷ 500
= 17 notes of Rs.500
Hence, Rohit has total 17 notes of Rs.500.
Learn more about unitary method here
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) Emma already owns 8 hair bands, and additional hair bands are priced at 3 for a dollar.
How much money does Emma need to spend on new hair bands in order to own a total of
47 hair bands?
Answer:$15.66
Step-by-step explanation:
Your cellphone bill in august was $61.43,which was $21.75more than your bill in July.Your cell phone bill in July was $13.62 less than your bill in June.what was your cell phone bill in June?
Answer:
53.3
Step-by-step explanation:
Please help. Will give brainliest. Please answer in SIMPLE terms. The book has the answer and solution but it just doesn’t make sense.
Answer:
250 cm²
Step-by-step explanation:
1 cm : 2 km
1 cm² : 4 km²
1 000 km² ÷ 4 km² = 250 cm²
62 is 90.5% of what number?
Answer:
62 is 90.5% of what number? 68.51 (I think)
When computing the control limits for the p-chart, what value is used when the population proportion of defective items is not known
Answer:
sample proportion of defective items
Step-by-step explanation:
The p-chart is a type of chart in which the sample is taken periodically from the production process, so as to determine if the population proportion of defective items in the sample falls within the control limits on the chart.
For a P-chart, as the sample size gets larger it turns more into a normal distribution making it possible to approximate the distribution of the proportion defective.
Given f(x)=20x+11, find f(4)
Answer:
91
Step-by-step explanation:
Substitute 4 in place of x
f(4)=20*4+11
f(4)=80+11
f(4)=91
Complete the equivalent ratio = 9/4 = 81/?
Answer:
81/36
Step-by-step explanation:
81/9 is 9
9 times 4 is 36
Answer:
Hi there the answer is 81/36. Hope this helps! c:
Step-by-step explanation:
First, figure out what ratio was used to make 9, 81.
You can recall that 9 x 9 = 81.
Therefore you must multiply the bottom of the fraction by 9 as well in order to create the correct ratio.
Thus, 4 x 9 = 36.
A pet store has three fish tanks, each holding a different volume of water and a different number of fish. Tank A has 5 fishes with a volume of 40 liters. Tank B has 12 fishes with a volume of 100 liters. Tank C has 23 fishes with a volume of 180,000 milliliters. Which tank has the greatest volume per fish?
Answer:
Tank B
Step-by-step explanation:
A pet store has three fish tanks, each holding a different volume of water and a different number of fish.
a) Tank A has 5 fishes with a volume of 40 liters.
Volume per fish = 40 liters/5 fishes
= 8 liters/fish
b) Tank B has 12 fishes with a volume of 100 liters.
Volume per fish = 100 liters/12 fishes
= 8.33 liters/ fish
c) Tank C has 23 fishes with a volume of 180,000 milliliters.
Convert 180,000 milliliters to liters
1 milliliter = 0.001 liter
180,000 milliliters = x
x = 180,000ml × 0.001 l
x = 180 liters
Volume per fish = 180 liters/23 fishes
= 7.8260869565 volume per fish
Approximately = 7.83 liters/fish
Which tank has the greatest volume per fish?
The tank that had the greatest volume per fish is Tank B at 8.33 liters/ fish
help me plzzzz :)) tyy if you do
A population of bacteria doubles every 15 hours. Initially, the population of bacteria is 40. What is this population of the bacteria after 40 hours?
Willy rents a bike for 7 days. The charge is $15 plus the $0.08 per mile. He wants to spend exactly $35. How many miles can he ride the bike? *
Answer:
Willy can ride the bike for 250 miles.
Step-by-step explanation:
$35 - $15 = $20
$0.08 × 12.5 = $1
$1 per 12.5 miles
$20 × 12.5 = 250
which of the following statements best describes the graph of x + y =2?
A) it is a line which intersects the y-axis at (2,2).
B) it is aligned joining the points whose x- and Y- coordinates add up to 2.
C) it is a line which intersects the x-axis at (2,2).
D) it is a line joining the points whose x- and Y- coordinates add up to 4.
Step-by-step explanation:
so x+y=2
a line would have to go 0,2 2,0
so the answer would be D
Lines A, B, and C show proportional relationships. Which line has a constant of proportionality between y and x of 2/3?
Answer:
Line C
Step-by-step explanation:
slope
Answer:line c
Step-by-step explanation:
What is the LCM of 6, 10, and 15?
50
Answer:
okay
Step-by-step explanation:
Answer:
1
Step-by-step explanation: