Answer:
D. 2.19
Step-by-step explanation:
ok so the formula for the surface area of a sphere is 4[tex]\pi[/tex][tex]r^2[/tex]
We see that 4[tex]\pi[/tex][tex]r^2[/tex]=60.
To find the radius we must isolate r on one side of the equations.
[tex]r^2[/tex]=60/4[tex]\pi[/tex]
[tex]r^2[/tex] = 4.77464829276
r = [tex]\sqrt{4.77464829276}[/tex]
That is approximately equal to 2.19
A culture of bacteria has an initial population of 9300 bacteria and doubles every 3
hours. Using the formula P = Po 25, where Pt is the population after thours, P
is the initial population, t is the time i hours and d is the doubling time, what is the
population of bacteria in the culture after 10 hours, to the nearest whole number
Answer:
The approximate population of bacteria in the culture after 10 hours is 93,738.
Step-by-step explanation:
General Concepts:Exponential Functions.Exponential Growth.Doubling Time Model.Logarithmic Form.BPEMDAS Order of Operations:
Brackets.Parenthesis.Exponents.Multiplication.Division.Addition.Subtraction.Definitions:We are given the following Exponential Growth Function (Doubling Time Model), [tex]\displaystyle\mathsf{P_{(t)}\:=\:P_0\cdot2^{(t/d)}}[/tex] where:
[tex]\displaystyle\sf{P_t\:\:\rightarrow}[/tex] The population of bacteria after “t ” number of hours. [tex]\displaystyle\sf{P_0 \:\:\rightarrow}[/tex] The initial population of bacteria. [tex]\displaystyle{t \:\:\rightarrow}[/tex] Time unit (in hours). [tex]\displaystyle{\textit d \:\:\rightarrow}[/tex] Doubling time, which represents the amount of time it takes for the population of bacteria to grow exponentially to become twice its initial quantity. Solution:Step 1: Identify the given values.
[tex]\displaystyle\sf{P_0\:=}[/tex] 9,300. t = 10 hours. d = 3.Step 2: Find value.
1. Substitute the values into the given exponential function.
[tex]\displaystyle\mathsf{P_{(t)} = P_0\cdot2^{(t/d)}}[/tex]
[tex]\displaystyle\mathsf{\longrightarrow P_{(10)} = 9300\cdot2^{(10/3)}}[/tex]
2. Evaluate using the BPEMDAS order of operations.
[tex]\displaystyle\mathsf{P_{(10)} = 9300\cdot2^{(10/3)}\quad \Longrightarrow BPEMDAS:\:(Parenthesis\:\:and\:\:Division).}[/tex]
[tex]\displaystyle\sf P_{(10)} = 9300\cdot2^{(3.333333)}\quad\Longrightarrow BPEMDAS:\:(Exponent).}[/tex]
[tex]\displaystyle\sf P_{(10)} = 9300\cdot(10.079368399)\quad \Longrightarrow BPEMDAS:(Multiplication).}[/tex]
[tex]\boxed{\displaystyle\mathsf{P_{(10)} \approx 93,738.13\:\:\:or\:\:93,738}}[/tex]
Hence, the population of bacteria in the culture after 10 hours is approximately 93,738.
Double-check:We can solve for the amount of time (t ) it takes for the population of bacteria to increase to 93,738.
1. Identify given:
[tex]\displaystyle\mathsf{P_{(t)} = 93,738 }[/tex].[tex]\displaystyle\mathsf{P_0 = 9,300}[/tex].d = 3.2. Substitute the values into the given exponential function.
[tex]\displaystyle\mathsf{P_{(t)} = P_0\cdot2^{(t/d)}}[/tex]
[tex]\displaystyle\mathsf{\longrightarrow 93,378 = 9,300\cdot2^{(t/3)}}[/tex]
3. Divide both sides by 9,300:
[tex]\displaystyle\mathsf{\longrightarrow \frac{93,378}{9,300} = \frac{9,300\cdot2^{(t/3)}}{9,300}}[/tex]
[tex]\displaystyle\mathsf{\longrightarrow 10.07936840 = 2^{(t/3)}}[/tex]
4. Transform the right-hand side of the equation into logarithmic form.
[tex]\boxed{\displaystyle\mathsf{\underbrace{ x = a^y}_{Exponential\:Form} \longrightarrow \underbrace{y = log_a x}_{Logarithmic\:Form}}}[/tex]
[tex]\displaystyle\mathsf{\longrightarrow 10.07936840 = \bigg[\:\frac{t}{3}\:\bigg]log(2)}[/tex]
5. Take the log of both sides of the equation (without rounding off any digits).
[tex]\displaystyle\mathsf{log(10.07936840) = \bigg[\:\frac{t}{3}\:\bigg]log(2)}[/tex]
[tex]\displaystyle\mathsf{\longrightarrow 1.003433319 = \bigg[\:\frac{t}{3}\:\bigg]\cdot(0.301029996)}[/tex]
6. Divide both sides by (0.301029996).
[tex]\displaystyle\mathsf{\frac{1.003433319}{0.301029996} = \frac{\bigg[\:\frac{t}{3}\:\bigg]\cdot(0.301029996) }{0.301029996}}[/tex]
[tex]\displaystyle\mathsf{\longrightarrow 3.3333333 = \frac{t}{3}}[/tex]
7. Multiply both sides of the equation by 3 to isolate "t."
[tex]\displaystyle\mathsf{(3)\cdot(3.3333333) = \bigg[\:\frac{t}{3}\:\bigg]\cdot(3)}[/tex]
[tex]\boxed{\displaystyle\mathsf{t\approx10}}[/tex]
Hence, it will take about 10 hours for the population of bacteria to increase to 93,378.
__________________________________
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What are the dimensional formula of a and b in the relation F = at² + bx, whrer F is force, t is time and x is distance ?
Heya User !
Your Answer is in the attachment, do check out.
MᎥssAbhᎥ ☁
What is 10,8,12,10,14?
Answer:
they are all called numbers
Step-by-step explanation:
A rectangular prism is 25 inches wide, 5 inches long and 6 inches high.
What is the exact volume of the prism?
125
Answer:
750
Step-by-step explanation:
FORMULA FOR VOLUME
L×W×H
L:5
W:25
G:H
5x25x6=750
factoring using the distributive property
got really sick and missed a bunch of school, would really appreciate the help !
Answer:
Step-by-step explanation:
Factorizing using distributive property: Factorize the terms Find the Greatest Common factor. Take GCF from both the terms.1) 5a² - 15
5a² = 5 * a²
15 = 5 * 3
GCF = 5
5a² - 15 = 5*a² - 5*3
= 5a(a - 3)
5) 36x²y - 48xy²
36x²y = 2 * 2 * 3 * 3 * x² * y
48xy² = 2 * 2 * 2 * 2 * 3 * x * y²
GCF = 2 * 2 * 3*x*y = 12xy
36x²y - 48xy² = (12xy * 3x) - (12xy*4y)
= 12xy*(3x - 4y)
6)75b²c³ + 60bc⁶
75b²c³ = 3 * 5 * 5 * b² * c³
60bc⁶ = 2 * 2 * 3 * 5 * b * c⁶
GCF = 3*5*b*c³ = 15bc³
75b²c³ + 60bc⁶ = [15bc³* 5b] + [15bc³ * 4bc³]
= 15bc³ * (5b + 4bc³)
The diagram below shows a park
district's plans for a new water
playground.
451/2
50 ft
What is the area of the new water
playground in square feet?
PLEASE HURRY
Answer:
I think it's 2275 square feet
Answer:
it is1125
Step-by-step explanation:
first 45x50=2250
next divide 2250 by 2 equals 1125
which of the following rational functions is graphed below
Considering it's vertical asymptotes, the rational function graphed below is given by:
B. [tex]F(x) = \frac{1}{(x - 1)(x + 1)[/tex]
What are the vertical asymptotes of a function f(x)?The vertical asymptotes are the values of x which are outside the domain, which in a fraction are the zeroes of the denominator.
In this problem, the vertical asymptotes are at [tex]x = \pm 1[/tex], hence the function is given by:
B. [tex]F(x) = \frac{1}{(x - 1)(x + 1)[/tex]
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Given sine of x equals negative 5 over 13 and cos x > 0, what is the exact solution of cos 2x?
The value of cos 2x is 119/169 after applying the trigonometric identity cos2x = 1 - 2sin²x option second is correct.
What is trigonometry?Trigonometry is a branch of mathematics that deals with the relationship between sides and angles of a right-angle triangle.
We have given:
sinx = -5/13
and cosx > 0
We know,
cos2x = 1 - 2sin²x
sinx = -5/13
Squaring on both sides:
sin²x = 25/169
Multiply by 2 on both the sides:
2sin²x = 2(25/169)
Add -1 on both sides:
-1 + 2sin²x = -1 + 2(25/169)
or
1 - 2sin²x = 1 - 2(25/169)
cos2x = 1 - 50/169
cos2x = 119/169 (as the cosx > 0)
Thus, the value of cos 2x is 119/169 after applying the trigonometric identity cos2x = 1 - 2sin²x option second is correct.
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Answer:
The guy above me is correct
Step-by-step explanation:
Look at the screen shot I got it correct
The table shows values of function f(x). The graph shows the function g(x).
What is the average rate of change of f(x) over the interval from x=2 to x=6?
Find the average rate of change of g(x) over the interval from x=0 to x=4.
What is the difference between the two functions? Which one is moving more quickly? What does it mean to have a negative answer?
The average rate of change for f(x) and g(x) are respectively 2.25 and -2 and so we can say that f(x) is moving more quickly.
How to find the average rate of Change?
Formula for the average rate of change is;
f'(x) = (f(b) - f(a))/(b - a)
Thus;
1) Average rate of change of f(x) over the interval from x = 2 to x = 6 is;
f'(x) = (f(6) - f(2))/(6 - 2)
We are given;
f(6) = 10 and f(2) = 1
Thus; f'(x) = (10 - 1)/4 = 2.25
2) Average rate of change of g(x) over the interval from x = 0 to x = 4 is;
g'(x) = (g(4) - g(0))/(4 - 0)
We are given;
g(4) = 0 and g(0) = 8
Thus; g'(x) = (0 - 8)/4 = -2
3) From the average rate of change of both functions, we see that f(x) is positive and has a higher rate of change and so we can say that f(x) is moving more quickly.
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Peter and Henry went to the movies Peter bought the two Movie tickets for 7 dollars each. How much did he spend for the movie tickets .
Answer:
Step-by-step explanation:
the cost of each ticket is 7 dollars. Peter brought 2 tickets. 7 x 2 = 14
Peter spent $14 dollars on two movie tickets.
You spin a spinner with 6 equal spaces numbered 1 through 6. What is the probability that the spinner lands on a 1 or a 6.
Answer: 1/3 The spaces are equal, and there are 2 favorable outcomes; out of 6 possible outcomes. That comes out to 2/6, and 2/6 reduced is 1/3
Write two numbers that multiply to the value on top and add to the value on bottom.
-84
17
Two numbers multiply the value on top (-84) and add to the value on the bottom (17) is 21 and -4.
What is multiplication?Multiplication is one of the four basic arithmetic operations, alongside addition, subtraction, and division. Multiplication essentially means the repeated addition.
The two given numbers are -84 and 17.
We need to write two numbers that multiply to the value on top (-84) and add to the value on the bottom (17).
If we multiply 21 and -4, we get the product as -84.
That is, 21×(-4)=-84
If we add 21 and -4, we get the sum as -17.
That is, 21+(-4)=21-4=17
Therefore, two numbers multiply the value on top (-84) and add to the value on the bottom (17) is 21 and -4.
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Find the slope of the line.
Answer:
-1
Step-by-step explanation:
Rise/Run equates it to be -1/1 wich is -1
A white tailed deer can sprint at speeds up to 30 miles per hour. American Bison can run at speeds up to 3,520 feet per minute. Which animal is faster and by how many miles per hour? There are 5.280 feet in one mile.
Determine the cardinality of each set.
(a) {5, 1, 4, {6, 7, 8, ...}}
(b) {ø}
(c) {{{6, 7}}}
The cardinality of a set refers to the number of elements in the set. It is found by counting the elements in the set.
What is cardinality of a set?The cardinality of a set refers to the number of elements in the set. To obtain the cardinality, we have to count the elements in the set.
a) There are 6 elements in this set hence the cardinality is 6.
b) There is only one element in the set hence its cardinality is 1.
c) There are two elements in the set hence the cardinality is 2.
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(a) If cos² (34°) - sin² (34°) = cos(A°),then
A =
degree’s
[tex]~~~~~~~\cos^2 \left(34^{\circ}\right) - \sin^2 \left( 34^{\circ} \right)=\cos A\\\\\implies \cos \left( 2 \cdot 34^{\circ} \right) = \cos A~~~~~~~~~~~~~;[\cos 2x = \cos^2 x -\sin^2 x]\\\\\implies \cos \left(68^{\circ}\right) = \cos A\\\\\implies A = 68^{\circ}[/tex]
A bicycle company is designing women's bicycle frames The frames can accommodate any woman taller than 54.5 inches. Given that the heights of adult American women are normally distributed, with a mean of 65 inches and a standard deviation of 3.5 inches, what percentage of American women CANNOT use the bicycles designed by this company?
Using the normal distribution, it is found that 0.13% of American women CANNOT use the bicycles designed by this company.
Normal Probability DistributionThe z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score measures how many standard deviations the measure is above or below the mean. Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.The mean and the standard deviation are given, respectively, by:
[tex]\mu = 65, \sigma = 3.5[/tex]
The proportion of women that cannot use the bikes(smaller than 54.5 inches) is the p-value of Z when X = 54.5, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{54.5 - 65}{3.5}[/tex]
Z = -3
Z = -3 has a p-value of 0.0013.
0.0013 = 0.13% of American women CANNOT use the bicycles designed by this company.
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I need help solving this problem system of equations
Answer:
y= -6
Step-by-step explanation:
-4x and 4x are canceled out. -2y+8y= 6y. -12-24=-36
You are left with 6y=-36 . Divide from both sides and -36/6 is -6. So, y=-6.
Hope this helped.
Collect info on minimum and maximum temperature if 7 consecutive days in creative manner
What is the slope of the line that passes through the points (1, 3) and (5, -2)?
Answer:
slope = -5/4
Step-by-step explanation:
Because you have been given two points, you can use point-slope formula to find the slope. In the equation, "m" is the slope.
1st Point: (1,3)
2nd Point: (5, -2)
y₁ - y₂ = m(x₁ - x₂) <----- Point-Slope Equation
3 - (-2) = m(1 - 5) <----- Plug "x" and "y" values into equation
5 = m(-4) <----- Combine like terms
-5/4 = m <----- Divide both sides by -4
Is this rational or irrational?
Answer:
Irrational.
Step by step explanation:
[tex]\sqrt 6 + \dfrac{2}{3}\\\\\\=\dfrac{3\sqrt 6 +2}{3}\\\\\text{The sum of the these two numbers cannot be expressed as the the ratio of two integers,}\\\\\text{So the sum is not rational.}[/tex]
What linear equation in slope intercept form does this graph represent?
Answer: Hope this helps
y = 3/5x + 100
Slope: 3/5
Y-int: 100
Step-by-step explanation:
y = mx + b
replace b with y-int
y = mx + 100
replace m with the slope which is 3/5
y = 3/5x + 100
How do you get slope?
Well I did rise/run with two points so I saw it ran 5 squares and rose only 3.
How do you get the y-int?
Well the y-int is the point where x is 0. So using the point (0,100), since x is 0, the y-int is 100.
PppppppppppppppppHELPppppppp
Step-by-step explanation:
please mark me as brainlest
THE ANSWER IS B I THINK IF ITS WRONG IM SORRY
Pleaseeee helppppp!!!!!!!!!
Answer:
107 degree
Step-by-step explanation:
interior angle sum of a hexagon is 720,
using S = (n - 2)*180
which is S =(4)*180
720-118-111-124-115-145=107
What’s 1938292+92268292
Step-by-step explanation:
the answer is 94206584 kk
The subtraction property of equality states that the two sides of an
equation remain unequal when you subtract the same number of each
side.
O True
O False
* 10 points
Answer:
False
Step-by-step explanation:
The answer is in its name. Its a property of equality meaning it makes sure that both sides are equal to each other
Please help I am so confused
The phone company Ringular has a monthly cellular plan where a customer pays a flat monthly fee and then a certain amount of money per minute used on the phone. If a customer uses 480 minutes, the monthly cost will be $277. If the customer uses 990 minutes, the monthly cost will be $532.
A) Find an equation in the form
y=mx+b, where x is the number of monthly minutes used and
y is the total monthly cost of the Ringular plan.
Answer:
y=
B) Use your equation to find the total monthly cost if 881 minutes are used.
Answer: If 881 minutes are used, the total cost will be
The total cost when 881 minutes is used is $477.50.
What are the equation that model the question?a + 480b = 277 equation 1
a + 990b = 532 equation 2
Where:
a = flat fee b = variable fee What is the flat fee and the variable fee?Subtract equation 1 from equation 2
510b = 255
b = 255 / 510
b = $0.50
In order to determine the flat fee, substitute for b in equation 1
a + 480(0.5) = 277
a + 240 = 277
a = 277 - 240
a = $37
What is the total cost when 881 minutes is used?
Total cost = flat fee + (variable cost x number of minutes spoken)
$37 + (881 x 0.5) = $477.50
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lanetterisbelle
6 minutes ago
Mathematics
College
Use the following information for Excercise 2-9 through Excercise 2-12 below. (Staic)
Following are the transactions of a new company called Pose-for-pics.
August 1 M. Harris, the owner, invested $6,500 cash and 33,500 of photography equipment in the company.
August 2 The company paid 2,100 cash for an insurance policy covering the next 24 months.
Aust 5 The company purchased supplies for 800 cash.
August 20 The company received 3,331 cash from taking photos for customers.
August 20 The company received 3,331 cash from taking photos for cusotmers.
August 31 The company paid $ 675 cash for August utilities.
Excercise 2-11 ( Static) Analyzing transacctions using accounting equation LO A1
Analyze each transaction above by showing its effects on the accounting equation-specifically, identify the accounts and amounts ( including + or -) Use the following partial chart of accounts: Cash; Supplies; Prepaid Insurance; Equipment; M. Harris, Capital; Services Revenue; and Utilities Expense
Date Assets = Liabilities + Equity
August 1 = +
August 1 = +
August 2 = +
August 2 = +
August 5 = +
August 5 = +
August 20 = +
August 31 Cash (+) increase 6,500 = +
Each transaction has been an analyzed in the trial balance below by showing its effects on the accounting equation-specifically, identifying the accounts and amounts.
How to prepare a Trial Balance?
The Journal Entries are:
Cash 6500
Photography equipment 33500
Capital 40000
Prepaid Insurance 2100
Cash 2100
Office Supplies 880
Cash 880
Cash 3331
Revenue 3331
Utilities Expense 675
Cash 675
Cash account = 6500 - 2100 - 880 + 3331 - 675
Cash Account = 6176
Trial Balance
Debit Credit
Cash 6176
Prepaid Insurance 2100
Supplies 880
Revenue 3331
Utilities Expense 675
Capital 40000
Photography Equipment 33500
Total 43331 43331
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help please i need to turn this in
Answer:
Q3 = $5743.49117291326
Q4 = $10955.6157151671
Step-by-step explanation:
General formula for amount in Compound Interest
Amount [A] = [tex]P(1+r)^{t}[/tex]
Here, P = principal
r = rate of interest in decimal form
t = time in years
Q3
----
Substitute current values in question with formula to give you
$5743.49117291326
Q4
----
Substitute current values in question with formula to give you
$10955.6157151671
Enter a range if values for x.
Answer:
See the attachment photo!