Taking the square root of a number means finding a number that when you square it, it equals the number in the square root.
√4 = 2 because 2² = 4
³√4 is already simplified.
Best of Luck!
If a taxi charges $0.68 per mile and $4 how far can you ride for $10? (round to 1 decimal
A ranch experienced growth of its gopher population at a 1.5% annual rate, compounded continuously. At the end of a 3 year period, the population had reached a size of 78 gophers. How many gophers were on the ranch at the beginning of the 3 years according to the exponential growth function? Round your answer up to the nearest whole number, and do not include units.
Answer:
75 gophers (about)
Step-by-step explanation:
We will use continuous compounding interest formula:
[tex]P(t)=P_0e^{rt}[/tex]
Where
P(t) is final value (at time t)
P_0 is initial value
r is the compounding rate
t is the time period
Given:
P(t) = 78
r is 1.5% or 1.5/100 = 0.015
t is 3
We solve for P_0, what we want, using algebra as shown below:
[tex]P(t)=P_0e^{rt}\\78=P_0e^{(0.015)(3)}\\78=P_0e^{0.045}\\\frac{78}{P_0}=e^{0.045}\\\frac{78}{P_0}=1.0460\\P_0=74.57[/tex]
So, the initial population was 75 gophers.
The 75 gophers were on the ranch at the beginning of the 3 years according to the exponential growth function.
To solve this problem, we can use the following exponential growth function:
P(t) = P_0 * e^(rt)
where:
P(t) is the population at time t
P_0 is the initial population
r is the annual growth rate
t is the time in years
We know that the population after 3 years is 78 gophers, and the annual growth rate is 1.5%. We want to find the initial population, P_0.
So, we can plug in the following values into the exponential growth function:
P(3) = 78 = P_0 * e^(0.015 * 3)
Dividing both sides by e^(0.015 * 3), we get:
P_0 = 78 / e^(0.015 * 3)
Using a calculator, we can evaluate P_0 to be approximately 75.0.
Rounding up to the nearest whole number, we get an initial population of 75 gophers.
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What is the value of x to the nearest whole number?
Answer:
65
Step-by-step explanation:
Use the formula: a²+b²=c²
63²=3969
16²=256
Add them = 4225 = c²
[tex]\sqrt{4225} = \sqrt{c^2}[/tex]
65 = c (or x in this case)
Answer:
17.96
Step-by-step explanation:
To find the hypotenuse we are will have to use Sine, since we are only given the degree and opposite leg. [tex]sin(degree)=\frac{Opposite}{Hypotenuse}[/tex]
[tex]sin(63)=\frac{16}{x}[/tex]
Let's cancel the x on the right side by multiplying both sides by x
sin(63)x = 16
Divide both sides by sin(63) [Or 0.866, depending on the type of calculator you have]
sin(63)x ÷ sin(63) = 16 ÷ sin(63)
x = 17.9572198
2. Below is a list of grades on
a math test. What is the
range of the scores?
Answer:
31
Step-by-step explanation:
The range can be found by subtracting the lowest number in the set from the highest, so one can conclude how large the gap in between the two is.
the lowest number her is 68 and the highest is 99
99-68=31
Answer:
31 is the range
Step-by-step explanation:
the range is the number between the highest data and the lowest data. You take your largest number in the data and subtract it from the highest.
Largest 99
smallest 68
99 - 68 = 31
Hope this helps :) if it does please mark brainlest :)
What’s the definition of the number i?
Answer:
B. i = √(−1)Step-by-step explanation:
When (i) is multiplied to itself it = -1
The number (i)is used for imaginary numbers.
HELP.The grades students scored on the most recent math exam are shown on the histogram below. How many students took the exam? A. 100 B. 85 C. 95 D. 90
HELP ASAP
What are the square roots of 36 /100?
sqrt(36/100) = +-6/10
You find the square root of the numerator and the denominator.
What is the domain of y = csc(x)?
The domain of y = cosec(x) includes all real numbers except for the integer multiples of [tex]\pi[/tex], where the sine function equals zero and the cosecant function is undefined.
The domain of a function is the set of all possible input values (usually x values) for which the function is defined. In the case of y = cosec(x), the cosecant function is the reciprocal of the sine function, meaning cosec(x) = 1/sin(x). Since the sine of an angle can be zero and division by zero is undefined, the domain of y = cosec(x) must exclude any x values where sin(x) = 0.
The sine function is zero at integer multiples of [tex]\pi[/tex], so the domain of cosec(x) is all real numbers except for integer multiples of [tex]\pi[/tex]
What is the other dimension of the rectangular cross section that is perpendicular to the base (the face that is shaded) and
passes through the midpoints of the 10 cm edges?
centimeters by 18 centimeters
2
8
10
18
Answer:
8
Step-by-step explanation:
Answer:
8
Step-by-step explanation:
Find the volume of a pyramid with a square base, where the side length of the base is
8.3 in and the height of the pyramid is 7.3 in. Round your answer to the nearest
tenth of a cubic inch.
The volume of the pyramid is 167.6 cube inch (approx).
Step-by-step explanation:
Given,
Each length (l) of the base of the pyramid = 8.3 in
Height(h) of the pyramid = 7.3 in
To find the volume of the pyramid.
Formula
Volume of the pyramid = [tex]\frac{1}{3}[/tex]×area of the base×height
Area of the base = l²
Now,
The volume of the pyramid = [tex]\frac{1}{3}[/tex]×l²×h
= [tex]\frac{1}{3}[/tex]×8.3²×7.3 cube inch = 167.6 cube inch (approx)
The volume of the pyramid is calculated using the formula for a pyramid's volume, V = (1/3)bh, with a base area of 68.89 in² and height of 7.3 in, which gives a volume of approximately 167.5 in³.
Explanation:To find the volume of a pyramid with a square base, we can use the formula V = (1/3)bh, where b is the area of the base and h is the height of the pyramid. First, calculate the area of the square base by squaring the side length: b = s² = 8.3 in × 8.3 in = 68.89 in². Next, use this base area in the formula to get the volume: V = (1/3) × 68.89 in² × 7.3 in.
Doing the calculation, we find that V = (1/3) × 68.89 in² × 7.3 in = 167.4757 in³. To round to the nearest tenth, the volume of the pyramid is approximately 167.5 in³.
Will give 20 points
Given the matrices:
What is the size of the product C = AB?
that is the answer for the first part what are the answers for the second part
Find the product of C = AB.
c11 =
c12 =
c21 =
c22 =
Answer:
Next frame (6) is C
Frame 7 is D then A
Frame 8 is D
Frame 9 is scalar, neither, matrix, matrix
Step-by-step explanation:
Doing the assignment rn :)
Answer:
C =AB
2 x 2
second part
c11=-1 c12=3 c21=3 c22=-3
third part
d11=0 d12=6 d21=1 d22=-4
Step-by-step explanation:
Correct on edge 2023
Madi is 5 times as old as Brecken. In 12 years, she will be twice as old as he will be then. How old are they now?
Madi is 4 and Bracken is 20.
In 12 years Madi will be 16 and bracken will be 32 which is twice the age of Madi.
Which expression is equivalent to sine StartFraction 7 pi Over 6 EndFraction?
Answer:
The answer is D: sin 11pi/6
<3
Step-by-step explanation:
The expression that is equivalent to the given expression is Sin(11π/6).
The given trigonometric expression is: [tex]Sin \frac{7\pi }{6}[/tex]
[tex]Sin\frac{7\pi }{6}[/tex] can be written as [tex]Sin(\pi +\frac{\pi }{6} )[/tex]
What is the value of Sin(π+θ)?The value of [tex]Sin(\pi +\theta)[/tex] is [tex]-Sin\theta[/tex].
So, [tex]Sin(\pi +\frac{\pi }{6} )=-Sin\frac{\pi }{6}[/tex]
We know that
[tex]Sin(2\pi -\theta)=-Sin\theta[/tex]
Or, [tex]-Sin\theta=Sin(2\pi -\theta)[/tex]
So, [tex]-Sin\frac{\pi }{6} =Sin(2\pi -\frac{\pi }{6} )[/tex]
[tex]-Sin\frac{\pi }{6} =Sin\frac{11\pi }{6}[/tex]
So, the required expression is [tex]Sin\frac{11\pi }{6}[/tex].
Therefore, the expression that is equivalent to the given expression is Sin(11π/6).
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a farmer is constructing a regular fenced in pen. there is 120m of fencing. determine the maximum area of the pen and the dimensions that result in maximum area
Answer: 900 square meters. 30x30
Step-by-step explanation: a square is the biggest area you can have, so 120 divided by 4 is 30, and then 30 times 30 is 900.
The area of a circular window is 113.04 square inches. What is the diameter of the window? Use 3.14 for pi.
Answer: 12inches
Step-by-step explanation:
Area of a circle= 113.04square inches
Area of a circle =pir^2
Pi=3.14
R=?
So we are looking for the radius and from there we will get the diameter
Area=pir^2
113.04=3.14×r^2
R^2= 113.04/3.14
R^2=36
R=square root of 36
R= 6
Diameter =2r
Diameter = 2×6
Diameter = 12inches
Answer:
12 inches
Step-by-step explanation:
3.14 × r² = 113.04
r² = 36
r = 6
Diameter = 2r = 12
What is the first step in evaluating the expression 3 × (5 + 4) – 27 ÷ 9?
Step-by-step explanation:
According to BODMAS
the first way to evaluate the expression is starting from brackets.,
=3 * 9 -27 / 9
= 3 * 9 - 3
= 27- 3
=24
Answer:
Parenthesis.
Step-by-step explanation:
Parenthesis
Exponent
Multiply or
Divide
Add or
Subtract
PEMDAS is the order to solve expressions like so.
Convert 0.85 to a percent.
Answer:
85%
Step-by-step explanation:
Multiply both numerator and denominator by 100. We do this to find an equivalent fraction having 100 as the denominator. 0.85 × 100100.
= (0.85 × 100) × 1100 = 85100.
Write in percentage notation: 85%
Answer:
85%
Step-by-step explanation:
To convert a number to a percent, you need to multiply it by 100 and add a percent symbol to the end. 0.85*100=85%. Hope this helps!
Please help me...
What is the function that matches the description.
A sine function whose amplitude is 5 and Period is 12.
Answer:
Last one
Step-by-step explanation:
f(x) = Asin(Bx) + C
C = 0
A = 5
B = 2pi/12 = pi/6
f(x) = 5 sin[(pi/6)x]
The diameter of a circle is 7 feet. Find the radius
Answer:
3.5 feet
Step-by-step explanation:
Diameter = 7 feet
Radius = Diameter × [tex]\frac{1}{2}[/tex]
Radius = [tex]\frac{7}{2}[/tex] = 3.5 feet
Find the area of the shaded region
A. 1256
B. 425
C. 201
D. 531
E. 603
F. 249
(12m / 8m)
Answer:
A. 1256
Step-by-step explanation:
You have to find the radius of the shaded circle
So you can add 12 + 8 = 20
Or you can find the diameter of the two circles. The diameter of the first circle is 12 + 12 = 24 and the second circle is 8 + 8 = 16 + 20 + 40 is the diameter of the shaded circle. Since radius is half of diameter 40 ÷ 2 = 20
So now since you know the radius of the shaded circle you can find the area
A = πr²
A = 3.14 x 20²
A = 3.14 x 400
A = 1256
What is a common binomial factor
Help plzz ASSAP
The function f(x) = 30x + 150 represents the total cost of a gym membership at Jon's Gym for x months plus a signup fee. Bella's Gym has a signup fee of $50 and charges $45 dollars per month. Which statement is true.
Select one
The signup fee at Jon's Gym is $100 more than the signup fee at Bella's Gym
Jon's Gym charges $15 more per month Bella's Gym
The signup fee at Jon's Gym is $15 more than the signup fee at Bella's Gym
Jon's Gym charges $100 more per month than Bella's Gym.
Answer: The signup fee at Jon's Gym is $100 more than the signup fee at Bella's Gym
Step-by-step explanation:
Hi, to answer this question we have to write an equation for the cost of Bella's Gym
Jon's Gym: f(x) = 30x + 150
Bella's Gym has a signup fee of $50 and charges $45 dollars per month.
So, we have to multiply the number of months (x) by the cost per month, and add the signup fee cost (50).
Bella's Gym: f(x) = 45x+ 50
Since Jon's signup fee is 150 and Bella's signup fee is 50 , the difference of both costs is 100 (150-50=100), and since Jon's gym has the more expensive fee:
The signup fee at Jon's Gym is $100 more than the signup fee at Bella's Gym
Final answer:
The statement that the signup fee at Jon's Gym is $100 more than the signup fee at Bella's Gym is true.
Jon's Gym charges $30 per month while Bella's Gym charges $45 per month; thus, Jon's Gym charges $15 less, not more.
Explanation:
Comparing the costs of gym memberships at Jon's Gym and Bella's Gym requires analysis of the initial signup fees and the monthly rates. The function for Jon's Gym, f(x) = 30x + 150, indicates a signup fee of $150 and a monthly rate of $30. Bella's Gym has a signup fee of $50 and a monthly rate of $45. To determine the true statement, we compare these numbers directly:
The signup fee at Jon's Gym is $100 more than the signup fee at Bella's Gym ($150 - $50 = $100).The other statements provided in the question can be dismissed as false:
Jon's Gym does not charge $15 more per month than Bella's Gym; it charges $15 less per month.The signup fee at Jon's Gym is not $15 more than the signup fee at Bella's Gym; it is $100 more.Jon's Gym does not charge $100 more per month than Bella's Gym.Therefore, the correct statement is that The signup fee at Jon's Gym is $100 more than the signup fee at Bella's Gym.
40x + 13 - 45x
The standard form is
A diagram of a small shed is shown below, find the volume of the composite figure. 3m 6m 5m 5m 8m
Answer:
27
Step-by-step explanation:
I need help plz only one question
Two hamburgers and three cokes cost $10.50. Four hamburgers and four cokes cost $18.00. Find the cost of a hamburger and a coke.
Answer: hamburger $3.00
Coke $1.50
Step-by-step explanation:
2hamburgers & 3cokes= $10.50
4hamburgers & 4cokes= $18.00
Let hamburger represent H
And coke represent C
2H +3C= 10.50.......equation 1
4H+4C= 18.00.......equation 2
2H =10.50 -3C...........equation 3
The 4H can be rewriting as
2(2H) right
So substitute for the 4H
So we have,
2(2H) +4C= 18
Substitute for 2H
2(10.50 -3C) +4C =18
Open the bracket
21 -6C +4C= 18
21-2C= 18
-2C = 18-21
-2C = -3
Minus cancel minus
C= 3/2 = $1.5
Substitute for c in equation 1
2H+3C =10.50
2H+3(1.5)= 10.50
2H+4.5=10.5
2H= 10.5-4.5
2H =6
H= 6/2
H=$3
So
An hamburger cost $3.00
A coke cost $1.50
What is the solution to the inequality -4(5/2+3/2x)>8?
A. x > -1/2
B. x < 1/3
C. x < -3
D. x > 3
Answer:
C
Step-by-step explanation:
Given
- 4([tex]\frac{5}{2}[/tex] + [tex]\frac{3}{2}[/tex] x) > 8 ← distribute parenthesis on left side
- 10 - 6x > 8 ( add 10 to both sides )
- 6x > 18
Divide both sides by - 6, reversing the symbol as a result of dividing by a negative quantity
x < - 3 → C
Which is not equal to 400
Answer:
399
Step-by-step explanation:
The only expression that does not equal 400 is c. 500 - 200.
How to determine the expression that is not equal to 400From the question, we have the following parameters that can be used in our computation:
a. 2 * 200
b. 800/2
c. 500 - 200
d. 300 + 100
Evaluating each of the options, we have the following
a. 2 * 200 = 400
b. 800/2 = 400
c. 500 - 200 = 300
d. 300 + 100 = 400
Hence, the only option that does not equal 400 is c. 500 - 200.
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Question
Which is not equal to 400
a. 2 * 200
b. 800/2
c. 500 - 200
d. 300 + 100
(x2 + 5x – 3) + (3x2 – 4x + 5)
(6x-3)+(7x-7)
Hope I helped :d
Answer:
[tex]4x^{2} +x+2[/tex]
how do you write 2/16 as a percent?
Answer:
[tex]\huge\boxed{\dfrac{2}{16}=12.5\%}[/tex]
Step-by-step explanation:
[tex]p\%=\dfrac{p}{100}\to p=p\cdot100\%\\\\\dfrac{2}{16}=\dfrac{2:2}{16:2}=\dfrac{1}{8}\\\\\dfrac{1}{8}=\dfrac{1}{8}\cdot100\%=\dfrac{100}{8}\%=12.5\%\\\\\text{Other method.}\\\\\dfrac{1}{8}=\dfrac{1\cdot125}{8\cdot125}=\dfrac{125}{1000}=\dfrac{125:10}{1000:10}=\dfrac{12.5}{100}=12.5\%[/tex]