Answer:
C. m = 1440d
Step-by-step explanation:
You want to know the equation that represents the relationship between days (d) and minutes (m) given the table of values (d, m) = (4, 5760), (7, 10080), or (11, 15840).
Proportional relationshipOn the off chance you don't already know that the number of days must be multiplied by minutes per day to find the number of minutes (m = 1440d), you can always try the table values in the response choices to see what works:
A. 5760 = 4/1440 . . . . . . nope
B. 5760 = 4 + 1440 . . . . . nope
C. 5760 = 1440·4 . . . . . . . yep
D. 4 = 1440·5760 . . . . . . . nope
The equation that works is m = 1440d.
__
Additional comment
Fractions work the same way with units that they do with numbers. Common factors in numerator and denominator cancel.
[tex]\dfrac{2}{3}\times 3=2\\\\\dfrac{\text{minutes}}{\text{day}}\times \text{days}=\text{minutes}[/tex]
QUICK, ANSWER THIS QUESTION FOR 30 POINTS!!!!
I will mark you brainiest!
What is the area of a rectangle with a length of 3 cm and a width of 4.5 cm?
A) 1.5 cm2
B) 6.75 cm2
C) 7 cm2
D) 13.5 cm2
Answer:
A equals 13.5 centimeters
help im doing the math diagnostic
Answer: -5 1/4
Step-by-step explanation:
After answering the final question incorrectly, Sandra's score will be -5 1/4 in fraction form, and -5.25 in decimal form. This is because every time Sandra gets a question wrong her grade goes down by -3/4 points. And -4 1/2 minus -3/4 is -5 1/4. I hope this helped. If not, let me know and I can try to reword it.
Answer: b
Step-by-step explanation:
Write an equation for a rational function with the given characteristics.
Vertical Asymptotes at x= -2 and x=4, x-intercepts at (-4,0) and (2,0), horizontal asymptote at y= -3.
Enclose numerators and denominators in parentheses. For example (a-b)/(1+n).
Include a multiplication sign between symbols. For example, a*x.
F(x) =
An equation for a rational function with the given characteristics is found as: f(X) = a(x+4)(x) / (x+2)(x-4).
Explain about the rational function?Any function that can be expressed as a polynomial divided by such a polynomial is said to be rational. The domain of either a rational function is just the set of all numbers besides the zeros of the denominator since polynomials are specified everywhere.As x = -2 and X = 4 have vertical asymptotes, the denominator will contain the equations (x+2) and (x-4)
The terms (x+4) and 1 will be in the numerator since the x intercepts are (-4,0) , respectively (x-0).
Our current formula is f(X) = a(x+4)(x) / (x+2)(x-4)
We examine the horizontal asymptote to determine the value of A.
The limit of a function as x -> infinity would be - 3 since the horizontal asymptote reflects what the function looks like as x approaches infinity.
Thus, an equation for a rational function with the given characteristics is found as: f(X) = a(x+4)(x) / (x+2)(x-4)
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Suppose you send about 12 text messages a day and your older sister sends more text messages than you do . together you send a total of about 26 messages per day. about how many text messages does she send a day ? Write an equation and solve for the unknown value
Let x be the number of text messages that your older sister sends per day. Then we can write an equation based on the given information:
x + 12 = 26
We can solve for x by subtracting 12 from both sides of the equation:
x = 26 - 12
x = 14
Therefore, your older sister sends about 14 text messages per day.
The following chart shows the number of rows in an auditorium and the total number of seats. Find an equation that defines the number of seats with respect to the number of rows
Answer:
Step-by-step explanation:
[tex]S=40R+20[/tex]
A one-topping pizza costs $12.99. This is $6.50 less than the cost of a specialty pizza. Explain how to write a subtraction equation that could be used to find the cost c of a specialty pizza.
Answer:
The cost of a specialty pizza is $19.49.
Step-by-step explanation:
To write a subtraction equation that could be used to find the cost c of a specialty pizza, we need to set up an equation that represents the relationship between the cost of a one-topping pizza and the cost of a specialty pizza.
The problem states that a one-topping pizza costs $6.50 less than a specialty pizza. Therefore, we can subtract $6.50 from the cost of a specialty pizza to get the cost of a one-topping pizza:
Cost of specialty pizza - $6.50 = Cost of one-topping pizza
We can rearrange this equation to solve for the cost of the specialty pizza:
Cost of specialty pizza = Cost of one-topping pizza + $6.50
Now, we can substitute the given value for the cost of a one-topping pizza:
Cost of specialty pizza = $12.99 + $6.50
Simplifying the expression, we get:
Cost of specialty pizza = $19.49
Therefore, the cost c of a specialty pizza is $19.49.
Hope this helps! I'm sorry if it doesn't. If you need more help, ask me! :]
HELP
Recipe:
Cinnamom Rolls
makes 12 rolls
1/4 -ounce package active dry yeasy
1 cupt warm water
3 tablespoons molasses
1/3 cup powedered milk
1 egg yolk,beaten
1 egg white, beaten
3 1/2 cups bread flour, divided
6 tablespoons butter, melted and divided
1 teaspoon salt
1/2 cup whole wheat flour
1/3 cup raisins
1 large egg, beaten
1/4 cup water
You will use the recipe above to answer the following questions:
Respond to the questions about the second recipe:
This recipe makes 12 rolls, but you need to make 30 rolls. What number will you need to multiply the amount of each ingredient by to adjust the recipe? How did you determine this number?
How many ounces of yeast will you need to make 30 rolls?
How many cups of powdered milk will you need to make 30 rolls?
How many tablespoons of butter will you need to make 30 rolls?
How many more cups of bread flour than whole wheat flour will you need to make 30 rolls?
Notice that the original recipe calls for
1
4
cup of water. If you put in
3
8
cup of water, by how much have you
To adjust the recipe to make 30 rolls instead of 12, we need to multiply the amount of each ingredient by a factor of 30/12 = 2.5.
What is factor?A factor is a number or expression that divides another number or expression evenly without a remainder.
According to question:To adjust the recipe to make 30 rolls instead of 12, we need to multiply the amount of each ingredient by a factor of 30/12 = 2.5.
To determine this factor, we divide the desired number of rolls (30) by the original number of rolls (12):
2.5 = 30/12
To find the amounts of each ingredient needed to make 30 rolls, we multiply the original amounts by 2.5:
Yeast: 1/4 oz x 2.5 = 0.625 oz (or about 0.63 oz)
Warm water: 1 cup x 2.5 = 2.5 cups
Molasses: 3 tbsp x 2.5 = 7.5 tbsp (or about 1/2 cup + 1 tbsp)
Powdered milk: 1/3 cup x 2.5 = 0.83 cups (or about 3/4 cup + 1 tbsp)
Egg yolk: 1 beaten yolk x 2.5 = 2.5 beaten yolks (or about 2 yolks)
Egg white: 1 beaten white x 2.5 = 2.5 beaten whites (or about 2 whites)
Bread flour: 3 1/2 cups x 2.5 = 8.75 cups (or about 8 3/4 cups)
Butter: 6 tbsp x 2.5 = 15 tbsp (or about 1 cup - 1 tbsp)
Salt: 1 tsp x 2.5 = 2.5 tsp (or about 2 1/2 tsp)
Whole wheat flour: 1/2 cup x 2.5 = 1.25 cups (or about 1 1/4 cups)
Raisins: 1/3 cup x 2.5 = 0.83 cups (or about 3/4 cup + 1 tbsp)
To make 30 rolls, you will need 0.625 oz (or about 0.63 oz) of yeast.
To make 30 rolls, you will need 0.83 cups (or about 3/4 cup + 1 tbsp) of powdered milk.
To make 30 rolls, you will need 15 tbsp (or about 1 cup - 1 tbsp) of butter.
To make 30 rolls, you will need 8.75 cups (or about 8 3/4 cups) of bread flour, which is 8.75 - 1.25 = 7.5 cups more than the 1.25 cups of whole wheat flour needed.
If you put in 3/8 cup of water instead of the 1/4 cup called for in the original recipe, you have added an extra 3/8 - 1/4 = 1/8 cup of water, or 2 tablespoons of water.
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Maurice can weed the garden in 45 minutes. Olinda can weed the garden in 50 minutes, how long would it take them to weed the garden if they work together
Tt would take Maurice and Olinda approximately 47.37 minutes
What is work done?
Work done in physics is the dot product of force and displacement. When a force applied on an object results in a displacement, it is said to be work is done on the object.
Let's denote the time it takes both Maurice and Olinda working together to weed the garden as t.
We can use the formula: 1 / t = 1 / a + 1 / b
Plugging in the given values, we get: 1 / t = 1 / 45 + 1 / 50
1 / t = (50 + 45) / (50 * 45) = 95 / 2250
Then, we can invert both sides of the equation to get: t / 1 = 2250 / 95
Simplifying the right-hand side by dividing both the numerator and the denominator by 5, we get:
t = 2250 / 95 = 47.37 minutes (rounded to two decimal places)
Therefore, it would take Maurice and Olinda approximately 47.37 minutes to weed the garden if they work together.
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You and your four friends buy tickets to a baseball game. The total cost is $70. Write and solve an equation to find the total cost of each ticket.
Answer: 14 dollars.
Step-by-step explanation:
You (1) + your four friends (4) is 5.
5 times a number is 70.
5x=70
70/5=14
x=14
Use the given information to find the unknown value.
2. y varies
1. y varies directly as the square root
inversely with the cube of x.
of x. When x = 16, then y = 4. Find y
y = 1. Find y when x = 1.
when x = 36.
When x = 3, then
3. The distances that an object falls varies directly with the
square of the time, t, of the fall. If an object falls 16 feet in one
second, how long for it to fall 144 feet?
4. The rate of vibration of a string under constant tension varies
inversely with the length of the string. If a string is 24 inches long
and vibrates 128 times per second, what is the length of a string
that vibrates 64 times per second?
Applying the definition of variation, we have:
1. When x = 36, y = 6.
2. When x = 1, y = 27.
3. It takes 3 seconds for the object to fall 144 feet.
4. Length of a string that vibrates 64 times per second is 48 inches.
What is an Inverse Variation?Inverse variation is a type of relationship between two variables in which one variable increases while the other decreases, or vice versa, in a way that the product of the two variables remains constant.
In other words, if we have two variables x and y that are inversely proportional, we can write:
x × y = k, where k is a constant.
1. We are given that y varies directly as the square root of x. This means that we can write:
y = k√x
where k is a constant of proportionality. To find the value of k, we can use the given information that when x = 16, y = 4:
4 = k√16
4 = 4k
k = 1
Now we can use this value of k to find y when x = 36:
y = 1√36
y = 6
Therefore, when x = 36, y = 6.
2. We are given that y varies inversely with the cube of x. This means that we can write:
y = k/x³
where k is a constant of proportionality. To find the value of k, we can use the given information that when x = 3, y = 1:
1 = k/3³
1 = k/27
k = 27
Now we can use this value of k to find y when x = 1:
y = 27/1³
y = 27
Therefore, when x = 1, y = 27.
3. We are given that the distance that an object falls varies directly with the square of the time, t, of the fall. This means that we can write:
d = kt²
where d is the distance, k is a constant of proportionality, and t is the time. To find the value of k, we can use the given information that when t = 1, d = 16:
16 = k(1)²
16 = k
k = 16
Now we can use this value of k to find the time it takes for the object to fall 144 feet:
144 = 16t²
9 = t²
t = 3
Therefore, it takes 3 seconds for the object to fall 144 feet.
4. We are given that the rate of vibration of a string under constant tension varies inversely with the length of the string. This means that we can write:
r = k/L
where r is the rate of vibration, L is the length of the string, and k is a constant of proportionality.
To find the value of k, we can use the given information that when L = 24 inches, r = 128 vibrations per second:
128 = k/24
k = 3072
Now we can use this value of k to find the length of a string that vibrates 64 times per second:
64 = 3072/L
L = 48 inches
Therefore, the length of a string that vibrates 64 times per second is 48 inches.
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Help me! I need help with my homework !
Answer:
Rounding to the nearest hundredth, the area of the shaded region is approximately 167.91 square yards.
Step-by-step explanation:
To find the area of the shaded region between two circles with the same center, we need to subtract the area of the smaller circle from the area of the larger circle.
The area of the larger circle is:
A_outer = πr_outer^2
= π(11.9 yd)^2
≈ 445.03 yd^2
The area of the smaller circle is:
A_inner = πr_inner^2
= π(9.4 yd)^2
≈ 277.12 yd^2
Therefore, the area of the shaded region is:
A_shaded = A_outer - A_inner
≈ 445.03 yd^2 - 277.12 yd^2
≈ 167.91 yd^2
Hope this helps! Sorry if it doesn't. If you need more help, ask me! :]
For what values of x does the graph of f(x) have a horizontal tangent? (Enter your answers as a comma-separated list.)
f(x) = x³ + 7x² + x + 1
X=
The point in which f(x) have a horizontal tangent are (-7 + √46)/3, (-7 - √46)/3
What values of x does f(x) have a horizontal tangentTo find the values of x where the graph of f(x) has a horizontal tangent, we need to find where the derivative of f(x) is equal to zero (since the derivative gives the slope of the tangent line).
First, we find the derivative of f(x):
f'(x) = 3x² + 14x + 1
Next, we set f'(x) equal to zero and solve for x:
3x² + 14x + 1 = 0
Using the quadratic formula, we get:
x = (-14 ± √(14² - 431)) / (2*3)
x = (-14 ± √(184)) / 6
x = (-14 ± 2√46) / 6
Simplifying:
x = (-7 ± √46) / 3
Therefore, the values of x where the graph of f(x) has a horizontal tangent are (-7 + √46)/3 and (-7 - √46)/3.
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Which of the following is the equation in slope-intercept form for the line that passes through the points (-4, 1) and (-3, 0)?
Answer:
y= -x - 3 is correct
Step-by-step explanation:
What is the total interest on a 4-year term loan of
$1,700 with a simple annual interest rate of 8%?
A. $544
B. $554
C. $564
D. $574
Answer:
a
Step-by-step explanation:
The formula to calculate simple interest is:
I = P * r * t
Where:
I = Interest
P = Principal amount
r = Rate of interest
t = Time period
Given:
Principal amount (P) = $1,700
Rate of interest (r) = 8% per annum
Time period (t) = 4 years
Using the formula of simple interest:
I = P * r * t
I = 1,700 * 0.08 * 4
I = $544
Therefore, the total interest on a 4-year term loan of $1,700 with a simple annual interest rate of 8% is $544.
Answer: A. $544
Identify the value for the variable.
What is the value of x in this simplified expression?
7-9-7-3-7x
x=
What is the value of y in this simplified expression?
114
= 11
118
y=
Answer: x=7 y=5
Step-by-step explanation:
I believe this is the answer to the question
LOTS OF POINTS HELP ASAP!
The time between the injections that is injected again when the dosage reaches 9 is solved to be 1.8 to the nearest tenth
How to find the time between the injectionsThe information given by the problem include the expression
D(h) = 20e^(-0.45h)
The expression is an exponential function that shows the relationship between time and the dosage in milligrams
given that D = 9 we find h
D(h) = 20e^(-0.45h)
9 = 20e^(-0.45h)
9/20 = e^(-0.45h)
take ㏑ of both sides
㏑(9/20) = -0.45h
isolating h by dividing by -0.45
h = ㏑(9/20) / -0.45
h = 1.774
h = 1.8 to the nearest tenth
This shows that the time is 1.8 hours
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A rectangle has an area of 60 square inches and the length is 4 inches more than the width. Find the length and width of the rectangle
Answer:
w = 6in, l = 10in
Step-by-step explanation:
Area of a rectangle is [tex]A=l*w[/tex]
and [tex]l = 4 + w[/tex]
We can solve for length and width by substituting these values for the equation.
[tex]60in^2=(4+w)*w[/tex]
[tex]60in^2=4w+w^2[/tex]
[tex]0 = w^2 + 4w + 60in^2[/tex]
factor out the equation.
[tex]0= (w+10)(w-6)[/tex]
therefore w = 6in (tossing out the negative solution)
which means
[tex]l = 4 + w[/tex]
[tex]l = 6in + 4[/tex]
l = [tex]10in[/tex]
Hope this helps!
Brainliest is much appreciated!
help me please this hard
Answer: -1/2
Step-by-step explanation:
To find the slope: rise/run
starting from the point (0,2), you go up 1 to reach the line
Therefore 1 is your rise.
Then go right 2 units and you hit the line again.
Therefore the slope is 1/2.
But the linear line is going downwards, so it is a negative slope
Therefore your final answer is:
-1/2
Can you please answer this question for me please and thank you 1/3+a=4/5
Okay so you want to make all of the fractions have a common denominator. Think of the lowest number that 3 and 5 go into, the answer you should get is 15. So 15 is the common denominator.
Now we're going to make 1/3 have a denominator of 15. 1/3 of 15 would be 5. You get that by figuring out what you have to multiply 3 by to get 15 which is 5. Then you multiply 5 and 1 and you get 5. The answer you will get will be 5/15 which is equal to 1/3.
Next we're going to make 4/5 have a denominator of 15. 4/5 of 15 would be 12/15. You can get this by figuring out what you have to multiply 5 by to get 15 which is 3. Then you take 3 and multiply it by 4 to get that 12 in 12/15. The answer 12/15 is equal to 4/5 of 15.
So now you have 5/15 + a = 12/15.
The denominator of the fraction that "a" will be is 15 because that is what we made the common denominator.
So what we have is 5/15 + x/15 = 12/15.
Think of what you have to add to 5 to get 12. (The answer is 7)
So a is equal to 7/15
Your final answer should be 5/15 + 7/15 = 12/15
Let U={2,3,4,5,6,7,8,9,10,11), A = {3,5,7,9,11}and B = {7,8,9,10,11}. Use this information to answer the following questions
A-B
(A-B)^c
U-(A-B)^c
(AUB)^c
(A^cUB^c)^c
Using set theory, the element in each of the set are, A - B = {3, 5}, (A - B)^c = {2, 4, 6, 7, 8, 9, 10, 11}, U - (A - B)^c = {3, 5}, (A \cup B)^c = {2, 4, 6} and (A^c U B^c)^c = {7, 9, 11}.
What is the element in each set?The given sets are:
U = {2,3,4,5,6,7,8,9,10,11}
A = {3,5,7,9,11}
B = {7,8,9,10,11}
We can use these sets to find the following:
1. A - B: The elements in set A that are not in set B are {3, 5}.
2. (A - B)^c: The complement of set A - B in U contains all the elements in U that are not in A - B. These elements are {2, 4, 6, 7, 8, 9, 10, 11}.
3. U - (A - B)^c: This set contains all the elements in U that are not in the complement of A - B. These elements are {3, 5}.
4. (A U B)^c: This set contains all the elements in U that are not in the union of sets A and B. The union of A and B is {3, 5, 7, 8, 9, 10, 11}, so the complement is {2, 4, 6}.
5. (A^c U B^c)^c: This set contains all the elements in U that are in neither the complement of set A nor the complement of set B. The complement of set A is {2, 4, 6, 8, 10} and the complement of set B is {2, 3, 4, 5, 6}. The union of these two sets is {2, 3, 4, 5, 6, 8, 10}, so the complement of this set in U is {7, 9, 11}.
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Solve y=2x+1 and 2x-y=3 using the substitucion méthod
Answer:
No solution
Step-by-step explanation:
y = 2x + 1 _____(equ 1)
2x - y = 3 _____(equ 2)
from equ 1
y = 2x + 1
2x + 1 = y
2x = y - 1
x = (y - 1)/2
substitute x = (y - 1)/2 into equ 2
2x - y = 3
2((y-1)/2) - y = 3
(2y - 2)/2 - y = 3
y - 1 - y = 3
y - y = 3 + 1
0 = 4
Hello and best regards sanungapatricio1985
This equation has no solution, since -1 cannot be equal to 3. Therefore, the system has no solution.
Step-by-step explanation:We have the following equations:
⇒ y = 2x + 1
⇒ 2x - y = 3
What is the substitution method?The substitution method is a common method for solving systems of linear equations. It consists of isolating one of the variables from one of the equations and substituting the expression obtained in the other equation to eliminate that variable and obtain an equation with a single variable, which can be solved to find the value of that variable. Then, the found solution can be substituted into any of the original equations to find the value of the other variable.
From the first equation we have a good substitution candidate:
⇒ y = 2x + 1
Now we have to plug y = 2x + 1 found from the first equation, into the second equation 2x - y = 3, to find that:
⇒ 2x - y = 3
⇒ 2x - (2x + 1) = 3
⇒ 2x - 2x - 1 = 3
Based on the previous results, the system has no solution.
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PLS HELP DUE TOMORROW!!
Answer:
Step-by-step explanation:
[tex]V=\pi r^2 h[/tex]
Substitute [tex]h=l,r=2,V=150,[/tex] we get
[tex]150=\pi \times 2^2 \times l[/tex]
[tex]150=4\pi l[/tex]
[tex]l=\frac{150}{4\pi}=11.94cm[/tex]
PLS 100PTS
WILL MARK AS BRAINLIEST
a ladder 20m long, leaning against a vertical wall makes an angle of 40⁰ with the horizontal ground. with the aid of a sketch diagram, determine the distance of the foot of the ladder from the wall (write your answer to 2 decimal places)
To determine the distance of the foot of the ladder from the wall, we can use trigonometry. Let's call the distance we want to find "x".
First, let's draw a diagram:
|\
| \
20 | \ x
| \
|____\
40°
In this diagram, the ladder is the hypotenuse of a right triangle, and the distance we want to find ("x") is one of the legs. The other leg is the height of the ladder on the wall, which we don't need to know in order to solve the problem.
We can use the trigonometric function for the sine of an angle to relate the angle of elevation to the distance "x" and the length of the ladder:
sin(40°) = x / 20
To solve for "x", we can multiply both sides by 20:
20 sin(40°) = x
Using a calculator, we can evaluate the sine of 40 degrees to get:
20 sin(40°) ≈ 12.85
So the distance of the foot of the ladder from the wall is approximately 12.85 meters, rounded to two decimal places.
Pls Help me with this problem, I will give brainliest to whoever answers this correctly. Answer is not x=0.1
Answer: the equation have two solutions: 0.25 and 0.75
[tex]x=\frac{1}{4}[/tex] or [tex]x=\frac{3}{4}[/tex]
Step-by-step explanation:
Notice the terms [tex]x+x^2+x^3+x^4+...+x^n[/tex] is just a geometric series (since -1<x<1)
A geometric series is given by the form
[tex]1+x+x^2+x^3+x^4+...+x^n = \frac{1}{1-x}[/tex]
This is
[tex]x+x^2+x^3+x^4+...+x^n = \frac{1}{1-x} -1[/tex]
plugging in in the equation
[tex]-1+\frac{1}{x} +\frac{1}{1-x} -1=\frac{10}{3}[/tex]
grouping terms
[tex]\frac{1}{x} +\frac{1}{1-x} =\frac{16}{3}[/tex]
groupings the fractions
[tex]\frac{1-x+x}{(x)(1-x)}=\frac{1}{(x)(1-x)} =\frac{16}{3}[/tex]
this leads to an simplified quadratic equation since X cannot be zero (notice the initial 1/x term)
[tex]3=16(x^2-x)[/tex]
the solution for this quadratic equation is just
[tex]x=\frac{1}{4}[/tex] or [tex]x=\frac{3}{4}[/tex]
Answer:
1/4 or 3/4
Step-by-step explanation:
You want the value of x in the infinite sum ...
-1 +1/x +x +x² +x³ +... = 10/3
for |x| < 1.
Geometric seriesAfter the 2nd term, this looks like a geometric series with a common ratio of x. If we define the series sum as ...
S = 1/x +1 +x +x² +x³ +...
we see that the equation of interest is ...
S -2 = 10/3
SumThe series sum is that of a geometric series with first term 1/x and common ratio x:
S = (1/x)(1/(1 -x)) = 1/(x(1-x))
Substituting for S in the above, we have the equation ...
1/(x(1-x)) -2 = 10/3
SolutionThis resolves to a quadratic that will have 2 real roots:
1/(x(1 -x)) = 16/3 . . . . add 2
x(1 -x) = 3/16 . . . . . . . invert both sides
x² -x +3/16 = 0 . . . . . . subtract the left side expression
(x -3/4)(x -1/4) = 0 . . . . . factor
Solutions are the values of x that make these factors zero:
x = 1/4 or x = 3/4
A well that pumps at a constant rate of 78,000 ft³/d has achieved equilibrium so that there is no change in the drawdown with time. The well taps an unconfined aquifer that consists of sand overlying impermeable bedrock at an elevation of 260 ft ASL. An observation well 125 ft away has a head of 277 ft ASL; another observation well 385 ft away has a head of 291 ft ASL. Compute the value of hydraulic conductivity using the Thiem equation.
Therefore, the value of hydraulic conductivity using the Thiem equation is approximately 10.67 ft/day.
What is equation?An equation is a mathematical statement that indicates that two expressions are equal. It typically consists of variables, constants, and mathematical operations such as addition, subtraction, multiplication, and division. The expressions on both sides of the equation are separated by an equal sign "=" which means that the two expressions have the same value. Equations are used to model relationships between variables, solve problems, and make predictions in various fields of science, engineering, economics, and mathematics. They are an essential tool in algebra, calculus, and other branches of mathematics.
Here,
To compute the value of hydraulic conductivity using the Thiem equation, we need to substitute the given values into the equation:
K = (Q / π) * ((h2 - h1) / log(r2/r1))
where:
Q = pumping rate = 78,000 ft³/d
h1 = head at the pumping well = 260 ft ASL
h2 = head at the observation well 385 ft away = 291 ft ASL
r1 = distance from the pumping well to the observation well 125 ft away = 125 ft
r2 = distance from the pumping well to the observation well 385 ft away = 385 ft
Substituting the values, we get:
K = (78,000 / π) * ((291 - 260) / log(385/125))
K = 10.67 ft/day
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Which of the following is the number 316.72 written in scientific notation?
A.
B. 3.1672 × 10²
C.
3.1672 x 10-2
D.
3.1672 x 103
3.1672 10
E. 3.1672 × 10-³
We can rewrite 3.1672 × 10¹² as 3.1672 × 10² The correct option is A
How to write a number in scientific notation ?First we first express it as a number between 1 and 10 multiplied by a power of 10. In this case, 316.72 can be expressed as:
3.1672 × 10¹² (since we move the decimal point 2 places to the right to get to 31672)
However, in scientific notation, the exponent should represent the number of places the decimal point is moved. Since we moved the decimal point to the right, the exponent should be negative.
Therefore, we can rewrite 3.1672 × 10¹² as:
3.1672 × 10²
So, the answer is (A).
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If 3000 dollars is invested in a bank account at an interest rate of 4 per cent per year,
Find the amount in the bank after 6 years if interest is compounded annually:
Find the amount in the bank after 6 years if interest is compounded quarterly:
Find the amount in the bank after 6 years if interest is compounded monthly:
Finally, find the amount in the bank after 6 years if interest is compounded continuously:
[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$3000\\ r=rate\to 4\%\to \frac{4}{100}\dotfill &0.04\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{\underline{annually}, thus once} \end{array}\dotfill &1\\ t=years\dotfill &6 \end{cases} \\\\\\ A = 3000\left(1+\frac{0.04}{1}\right)^{1\cdot 6} \implies A \approx 3795.96 \\\\[-0.35em] ~\dotfill[/tex]
[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$3000\\ r=rate\to 4\%\to \frac{4}{100}\dotfill &0.04\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{\underline{quarterly}, thus four} \end{array}\dotfill &4\\ t=years\dotfill &6 \end{cases} \\\\\\ A = 3000\left(1+\frac{0.04}{4}\right)^{4\cdot 6} \implies A \approx 3809.20 \\\\[-0.35em] ~\dotfill[/tex][tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$3000\\ r=rate\to 4\%\to \frac{4}{100}\dotfill &0.04\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{\underline{monthly}, thus twelve} \end{array}\dotfill &12\\ t=years\dotfill &6 \end{cases} \\\\\\ A = 3000\left(1+\frac{0.04}{12}\right)^{12\cdot 6} \implies A \approx 3812.23 \\\\[-0.35em] ~\dotfill[/tex]
[tex]~~~~~~ \textit{Continuously Compounding Interest Earned Amount} \\\\ A=Pe^{rt}\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill & \$3000\\ r=rate\to 4\%\to \frac{4}{100}\dotfill &0.04\\ t=years\dotfill &6 \end{cases} \\\\\\ A = 3000e^{0.04\cdot 6} \implies A \approx 3813.75[/tex]
i-ready an 80-ounce bottle of apple juice contains 32 ounces of water what percent of the bottle of apple juice is wayer
The percent of the bottle of apple juice is 40%.
What is a percentage, and how is it different from a fraction or a decimal?An element of a whole number is a fraction. There are many different kinds of fractions. Three-quarters, for instance, is a fraction.
A decimal point separates a fractional component from an integral component to form a decimal. In the decimal 2.5, for instance, the fractional portion comes after the decimal point and is followed by the integer 2, which is put before it.
Per cent simply means one in a hundred. Hence, it is a number with a fractional representation that has a denominator of 100. As a result, fractions of a whole number are also described using percentages.
Given that, 80-ounce bottle of apple juice contains 32 ounces of water.
Thus,
% of water = (32 / 80) * 100 = 40%
Hence, the percent of the bottle of apple juice is 40%.
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pelase help quick 25 points it 6th grade math
The median shows that the average number of students per middle school classroom in both districts is 24, while the mean shows that the average number of students per middle school classroom in one district is 24 and the other is 25.
What is median?Median is the middle value of a set of data. It is the value that divides the data set into two equal halves. It is an important measure of central tendency and is used to compare sets of data.
The difference between the mean number of students per middle school classroom in each school district is 2 students. The difference between the median number of students per middle school classroom in each school district is 0 students.
Based on the number of students shown for each school district, the median would provide the most accurate picture of the number of students in a middle school classroom, as there are some extreme values that would affect the mean but not the median.
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