From the given function, it is found that:
a. A reasonable domain for the function is of 0 ≤ d ≤ 11.
b. The y-intercept of the graph represents that the initial radius of the algae is of 7 mm.
c. The average rate of change between the 4th and the 11th day of the function means that the radius of the algae grew by an average of 0.64 mm a day.
What does the function represent?The function is modeled according to the following rule:
f(d) = 7(1.06)^d
In which:
d is the number of days.f is the radius of the algae.When the biologist concluded her study, the radius of the algae was approximately 13.29 mm, hence the upper bound of the domain is found as follows:
[tex]13.29 = 7(1.06)^d[/tex]
[tex](1.06)^d = \frac{13.29}{7}[/tex]
[tex]\log{(1.06)^d} = \log{\left(\frac{13.29}{7}\right)}[/tex]
[tex]d\log{1.06} = \log{\left(\frac{13.29}{7}\right)}[/tex]
[tex]d = \frac{\log{\left(\frac{13.29}{7}\right)}}{\log{1.06}}[/tex]
d = 11.
The smallest possible number of days is of 11, hence a reasonable domain for the function is:
0 ≤ d ≤ 11.
The y-intercept of the graph represents that the initial radius of the algae, as it is calculated when d = 0, hence it's value is given by:
[tex]f(0) = 7(1.06)^0 = 7[/tex]
The average rate of change of a function is given by the change in the output divided by change in the input, hence:
[tex]f(11) = 7(1.06)^{11} = 13.29[/tex][tex]f(4) = 7(1.06)^{4} = 8.84[/tex]r = (13.29 - 8.84)/(11 - 4) = 0.64 mm a day.
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36-(12/2)2=what i don't know the answer
The simplification of the given expression 36-(12/2)2 will be 24.
What is a simplification of an expression?Simplification involves proceeding with the pending operations in the expression. for ex; 6 + 2 is an expression whose simplified form can be obtained by doing the pending addition, that results in 8 as its simplified form. Simplification, involves making the expression simple and easy to use later.
We have been given an expression as;
36-(12/2)2
To simplify the above;
36-(12/2)2
36 - (6)2
Now multiply 6 by 2,
36 - 12
= 24
Therefore, the simplification of the given expression 36-(12/2)2 will be 24.
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Answer:
The answer is 24.
Step-by-step explanation:
(12/2)=6
36-(6)2
=36-12
=24
-4.25 ⋅ (3/10 + 1/5)
Answer: -0.85
Step-by-step explanation:
3/10 + 1/5 = 1/2
1/2 x -4.25 = -0.85
I add six to eleven, and get five. Why is this correct?
Answer:
because the six is a negative number (-6)
It takes 2 minutes to print out 3 posters at Carla's school.How long would it take to print out 14 posters
martina was interested in how students perceive the health service provided by her university. to collect data on this issue, she interviewed past and present students from her classes. martina has used a random sampling procedure that would be classified as a convenience sample.
martina has used a random sampling procedure that would be classified as a convenience sample .we can conclude that Martina's margin of error is 1.5.
Given: Average graduate student (upper limit) = 33
Random sample graduate student (lower limit) = 30
Formula to calculate margin of error is as follows.
Margin of error = upper limit - lower limit /2
Substitute the values into above formula as follows.
= 33-30/2
=1.5
Thus ,we can conclude that Martina's margin of error is 1.5.
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what is a trigonometrical complex number
A complex number z = a + bi has the trigonometric form z = r(cosθ + I sinθ ), where r = |a + bi| is z's modulus and tanθ = b.
the angle generated by the complex number on a polar graph having one real axis and one imaginary axis. This may be calculated using the right angle trigonometry for the trigonometric functions. Complex numbers are those that are represented as a+ib, where a and b are actual numbers and I is a fictitious number termed a "iota." I has the value (-1). As an illustration, the complex number 2+3i is made up of the real number 2 (Re) and the imaginary number 3i (Im).
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Complete the equation to show at 4.2 ÷ 0.35 is equivalent to 420 ÷ 35. Check Picture Above (Or Below, wherever it is!)
Answer:
[tex]4.2 / 0.35 =\frac{4.2}{0.35} *\frac{100}{100}= \frac{420}{35} = 420/35[/tex]
Step-by-step explanation:
By multiplying both the numerator and the denominator of the fraction 4.2/0.35, the resulting equivalent fraction is 420/35.
the world record for most selfies taken simultaneously is 4296. this is 51 fewer than three times the world record for the most selfies taken by one person in one hour. what is the world record for the most selfies taken by one person in one hour?
The world record for most selfies taken by a person in one hour is calculated to be 1449.
The world record for the most selfies taken by one person in one hour can be determined by using an algebraic expression.
As 4296 is 51 fewer than three times the World record for the most selfies taken by one person in one hour, we can consider x to be the world record by which we get an algebraic expression as follows;
3x - 51 = 4296
Solving for x;
3x = 4296 + 51
3x = 4347
x = 4347 / 3
x = 1449
Therefore, 1449 is calculated to be the world record for most selfies by one person in one hour.
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1 divide by root 9 + root 8
Let's expand the rational number with the conjugate of the expression in the denominator.
[tex]C=\sqrt{9} +\sqrt{8}[/tex][tex]\frac{1}{\sqrt{9}-\sqrt{8} }. \frac{\sqrt{9}+\sqrt{8} }{\sqrt{9}+\sqrt{8} }[/tex][tex]=3+2\sqrt{2}[/tex]Answer:
Step-by-step explanation:
root of 9 is 3
root of 8 is 2.8
the equation =-2.5
With indices , solve 32⅕
Answer:
Step-by-step explanation:
32=2⁵
therefore=2⁵×⅕
=2
Calculate the Standard Deviation of the following set of data.
14, 15, 16, 16, 9, 3, 16, 20, 29, 12
a. 7.66
b. 6.78
c. 23
d. 46
Answer:46656
4634234
Step-by-step explanation:5
y5
Answer:
6.78
I hope this helps.
Step-by-step explanation:
Distance between two points khan academy
Solve
2x² + 4x + 10 = 0
Simplify answers
Answer: No Solution
Step-by-step explanation: Simply use the formula. Which then you get no solution
What value of x satisfies the equation?
3(x−5)=5x−(3−x)
Responses
-4
-12
−2/3
8/3
The value of (x) that satisfy the equation → 3(x − 5) = 5x − (3 − x) is
x = - 12.
What is Equation?
An equation is a mathematical statement with an 'equal to' symbol between two expressions that have equal values.
Given is the following equation -
3(x − 5) = 5x − (3 − x)
The given equation is -
3x - 15 = 5x - 3 + x
Simplifying for (x), we get -
3x - x - 5x = - 3 + 15
- x = 12
x = -12
Therefore, the value of (x) that satisfy the equation → 3(x − 5) = 5x − (3 − x) is x = - 12.
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What is the product of (-3)(18) • (-5)? O 270 O 49 O-59 O-87
Answer: 270
Step-by-step explanation: First, you want to multiply the -3 and the 18. That makes -54. Then, you multiply that answer (-54) by -5, which is 270.
Hope this helps!
Follow the order of PEMDAS of operations:
P - ParenthesisE - ExponentsM - MultiplicationD - DivisionsA - AdditionsS - SubtractionsMultiply and divide (from left to right).
Apply the rule: (-a)*(b) = -a*b
(-3)(18) = -13 * 18 = -54
-54(-5) = 54 * 5 = 270
The answer is 270✅ .
What are the answers for both of them
1/6+5252+65+89+12-15-874-85x54-0-059=?
Answer:
719
– ___
6
Step-by-step explanation:
= 1/6 + 5252 + 65 + 89 + 12 - 15 - 874 - 85 × 54 - 0 - 059
= 1/6 + 5252 + 65 + 89 + 12 - 15 - 874 - 4590 - 0 - 059
= 1/6 + 4529 - 4590 - 059
= 1/6 + (-120)
= 719
— ___
6
Determine which integer will make the inequality 20 > 4x + 16 true.
S:{16}
S:{20}
S:{−1}
S:{1}
Answer:
-1
Step-by-step explanation:
replace x with -1
20>4(-1)+16
20>-4+16
20>12
When a number is outside parentheses what operation does that indicate?
Answer:
When a number is outside parentheses, the operation it indicates is Multiplication
Explanation:
When a number is outside parentheses such as;
[tex]4(5+2)[/tex]The operation it indicates is Multiplication, for the example above, it means that 4 will multiply each of the numbers inside the parentheses.
[tex]4(5+2)=4\times(5+2)=4\times5+4\times2[/tex]Therefore, When a number is outside parentheses, the operation it indicates is Multiplication
The table below shows survey results for the demand related to the price of a baseball cap in a small town. As the price of the cap increases, the number of people who wish to purchase it decreases.
Price of Cap, p
(in dollars) Number of Units
in Demand, d
23 432
27 356
30 299
35 204
Which equation represents the relationship between the price of the cap and the number of units in demand?
A.
d = 850 - 19p
B.
d = 285 - 869p
C.
d = 869 - 19p
D.
d = 19 - 869p
The relationship between the price of the cap and the number of units in demand is d = 869 - 19p
What is Substitution?Substitution: A strategy for solving systems of equations that include solving for one variable and using that solution to find the other variable.
The table below shows survey results for the demand related to the price of a baseball cap in a small town. As the price of the cap increases, the number of people who wish to purchase it decreases.
Price of Cap, p(in dollars) Number of Units in Demand, d
23 432
27 356
30 299
35 204
the relationship between the price of the cap and the number of units in demand
lets substitute the values in the given options ( lets use 1st result p=23 and d=432)
A.
d = 850 - 19p
432=850-19(23)
432=850-437
432≠413
B.
d = 285 - 869p
432=285-869(23)
432=285-19,987
432≠19,702
C.
d = 869 - 19p
432=869-19(23)
432=869-437
432=432
option C is correct
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A strategy for solving systems of equations that include solving for one variable and using that solution to find the other variable.
The table below shows survey results for the demand related to the price of a baseball cap in a small town. As the price of the cap increases, the number of people who wish to purchase it decreases.
The relationship between the price of the cap and the number of units in demand
lets substitute the values in the given options ( lets use 1st result p=23 and d=432)
A. d = 850 - 19p
432=850-19(23)
432=850-437
432≠413
B. d = 285 - 869p
432=285-869(23)
432=285-19,987
432≠19,702
C. d = 869 - 19p
432=869-19(23)
432=869-437
432=432
I REALLY NEED HELP PLEASE THIS WORK IS FOR MONDAY.can y’all please help me:(
Answer:
B
Step-by-step explanation:
12 multiplied by 5 is 60 and 10 multiplied by 6 is 60. which is the lowest that they both will meet
Geometry I need help with finding x on triangles
Answer: ...
Step-by-step explanation: Find the hypotenuse x. Suppose angle A = 50°, angle B = 60°, and angle C = x are the angles of a triangle. ABC. By using the angle sum property we can find the value of x. angle A + angle B + angle C = 180 degrees. Solve for x in fractions, we simply do the cross multiplication and simplify the equation to find x.
Given p(x) = -4(x-15)+2, what is the value of p(7) ?
Step-by-step explanation:
Work out the total amount of money tom earned on monday
The money earned by Tom in accordance with his rate is $
In mathematics, comparing two related quantities stated in different units is known as a rate.
If the denominator of the ratio is stated as a single unit of one of these quantities and it is assumed that this number may be changed systematically, the numerator of the ratio expresses the comparable rate of change in the other (dependent) variable (i.e., is an independent variable).Speed, heart rate, and flux are a few examples of rates that are frequently expressed as "per unit of time." Electric field ratios, exchange rates, and literacy rates are a few instances of ratios with a non-time denominator (in volts per meter).The rate at which he earns is $15 per hour.
He earns over time at 1 1/3 times his wage
Overtime rate = 4 / 3 × 15 = $20
He worked for 11 hours.
Total money earned = 7 hours at rate $15 per hour and 4 hours at rate $20 per hour.
Money earned = 7 × 15 + 20 × 4 = $185
Hence the money earned at that rate is $185.
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y=3(x-4)^2 +7 in standard form
27≤−2x+7or13 > −13>−2x+7
The solution for 27≤−2x+7 is x ≤−10 and −13>−2x+7 is x≥10.
What is the solution?
An allocation of values toward the variables involved that establishes the equality there in the equation is referred to as a solution. To put it another way, a solution is just a value or collection of values (for every unknown) that, when used to replace the unknowns, cause the equation to equal itself.Given equations: 27≤−2x+7, −13>−2x+7
Solving each equation,
27≤−2x+7
−2x≥27−7
−2x≥20
x≤ (20/−2)
x≤−10
−13>−2x+7
−2x≤−13−7
−2x≤−20
x≥ (-20/-2)
x≥10
The solution for 27≤−2x+7 is x ≤−10 and −13>−2x+7 is x≥10.
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two students in mrs.johnson's preschool class are stacking blocks,are 4 cm height, and maddy's blocks are 9 cm high. how tall will their stacks be when they are the same height for the first time.
36 cm tall will their stacks be when they are the same height for the first time.
Given,
Two students in Mrs. Johnson's preschool class are stacking blocks:
The height of Reece's block = 4 cm
The height of Maddy's block = 9 cm
We have to find the height of the stacks when they are same height for the first time.
Here,
We have to find the least common multiple.
Least Common Multiple (LCM):
The smallest number that is a multiple of both of two numbers is called the least common multiple.
So here,
We have to find the least common multiple of 4 and 9.
Here, the least common multiple of 4 and 9 = 36
Then,
36 cm tall will their stacks be when they are the same height for the first time.
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James is taking out a personal loan from his local bank. if the total loan amount is $2500 at a simple interest rate of 14.99% and in the 1st 4 months he makes only interest payments, how much will he pay in those months total?
James has to pay an annual interest of 14.99% on $2500 loan.
In decimal:
14.99% = 14.99/100 = 0.1499
The interest of 1st year would be:
0.1499 * 2500 = 374.75 dollars
Monthly interest would be:
374.75/12 = $31.23
If he pays this amount each month for first 4 months, he would pay a total of:
$31.23 * 4 =
$124.92What is the image of (0,6) after a reflection over the y-axis?
Answer:
(0, 6)
Step-by-step explanation:
The point (0, 6) is on the y-axis, so after a reflection over the y-axis, it is still (0, 6).
I can buy 4 basketballs for $44. At that same rate, how much would 8 basketballs cost?
Answer:
$88.
Step-by-step explanation:
$44 dollar for 4 balls.
That means for one ball it is $11.
44 ÷ 4 = 11.
Therefore:
8 x 11 = 88.
The answer is $88.
Hope this helps!