first off let's recall that 4³ = 64, and that i⁴ = 1, so
[tex]i^{64}\implies i^{4^3}\implies i^{4\cdot 4\cdot 4}\implies i^{4\cdot 16}\implies (i^4)^{16}\implies (1)^{16}\implies \text{\LARGE 1}[/tex]
Brady jogs laps around a circular park with a fountain at the center. Which table could represent Brady’s distance from the fountain after jogging around the path for a number of minutes?
The function that represents the distance from the fountain is:
Number of minutes Distance
0 50
2 60
4 70
6 60
8 50
What is the function that represents the distance around the fountain?A circle is a bounded figure which points from its center to its circumference is equidistant.
If Brady jogs around the circular park with a fountain at its center, it means that at a point as he runs he would be further away from the fountain. And with time, he would be approaching the fountain since the park is circular. Thus, the function that represents the distance Brady runs from the fountain would be increasing at a point and then start to decrease.
If the park were a straight line, the function would be increasing with time.
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Answer:
Step-by-step explanation:
C on edge
What is each expression written as a single natural logarithm?
(a) ln 7+2 ln 5
According to the question, the given expression is a single natural logarithm and the expression is as follows:
Expression: [tex]ln7+2ln5[/tex]
Using logarithmic formulas, the above expression can be written as:
Expression: [tex]ln7+2ln5 = ln7+ln5^{2} =ln7+ln25[/tex]
Using multiplication logarithmic formula that is [tex]log(ab)=log(a)+log(b)[/tex]
Now the above expression can be written as:
Expression: [tex]ln7+ln25 = ln(7X25) = ln(175)[/tex]
The solution for the given expression is: [tex]ln(175)[/tex].
What is logarithmic function?
In terms of mathematics, the logarithmic function can be defined as the inverse of exponential function. It is always on the positive side of the ordinate axis.
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HELP QUICKLY PLS, LIST THE VALUES FROM LEATS TO GREATEST (IN THE CORRECT ORDER PLS)
Answer:
[tex]-\frac94 \to -2\frac3{20} \to-2.05\to\frac78 \to 89(percent) \to 0.9[/tex]
Step-by-step explanation:
[tex]-2\frac3{20} = -2.15\\89(percent) = 0.89\\-\frac94 = -2.25\\\frac78 = 0.875[/tex]
Answer:
[tex]-\frac{9}{4}, -2\frac{3}{20} ,-2.05, 7/8, 89%, 0.9[/tex]
Step-by-step explanation:
We know that the number line goes from negative to positive
Convert everything to decimal
89% = 0.89
[tex]-2\frac{3}{20} =-2.15[/tex]
-9/4 = [tex]-2\frac{1}{4} = -2.25[/tex]
7/8 = 0.875
[tex]-\frac{9}{4}, -2\frac{3}{20} ,-2.05, 7/8, 89%, 0.9[/tex]
Hope this helps :)
Have a great day!
By measuring the amount of carbon- 14 in an object, a paleontologist can determine its approximate age. The amount of carbon- 14 in an object is given by y=a e⁻⁰.⁰⁰⁰¹²t , where a is the amount of carbon-14 originally in the object, and t is the age of the object in years. In 2003, a bone believed to be from a dire wolf was found at the La Brea Tar Pits. The bone contains 14 % of its original carbon-14. How old is the bone?
- What numbers should you substitute for y and n ?
- What properties of logarithms and exponents can you use to solve the equation?
According to basic algebra and the logarithm, the bone is roughly 16384 years old.
Y and t may have the following values: t = 16384, y = 16380. (a). (as determined using logarithm and elementary algebra).
What is logarithm?The logarithm is exponentiation's opposite function in mathematics.
The power to which a number must be increased in order to obtain another number is known as a logarithm. This shows that the logarithm of a fixed integer base b represents the exponent to which that number must be raised in order to reach a specific number x.
The logarithm with a base of 10 is the common logarithm, commonly referred to as the value of log base 10. The common logarithm of 10 has a value of 1, or 1.
Let 'a' be the original amount of the object.
Then, according to question, for y = amount of carbon in the object, y = 0.14(a) (as the bone contains 14% of its original carbon-14).
We are also given that: y = a [tex]e^{-0.00012t}[/tex]
On substituting the value of y, we get: 0.14a = a [tex]e^{-0.00012t}[/tex]
By basic algebra, we can solve it as:
=> 0.14 = [tex]e^{-0.00012t}[/tex]
=> ln (0.14) = ln ( [tex]e^{-0.00012t}[/tex]) (taking natural logarithm on both sides)
=> ln (0.14) = - 0.00012t (as [tex]log_{b} a^{m} = m log_{b} a[/tex] ; further: [tex]log_{e} e=1[/tex] )
=> ln(0.14)/-0.00012= t
=> t = 16384 years (approx.)
The values of y and t can be as follows: t = 16384, y = a (0.9998(16384)) = 16380(a).
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Write each logarithm as the quotient of two common logarithms. Do not simplify the quotient.
log₇2
Each logarithm as the quotient of two common logarithms is :
[tex]\frac{log\\ 2}{log \\7}[/tex]
What is logarithmic equation ?In, mathematics a logarithmic equation is inverse of exponential equation. That means, we can easily convert the logarithmic equation into exponential equation and vice versa. The basic form of the logarithm function can be written as .
[tex]log_ax=N[/tex]
where, a is the base of function or equation
x define expression
Mathematically, if [tex]a^N=x[/tex] is an exponential function then, this can be converted to logarithmic function as [tex]log_ax=N[/tex].
There are many formulas that are given to us for solving several simple and complex problems based on logarithmic functions and logarithmic equations.
Some important formulas of logarithms are :
log_c a +log_c b = log (a b)log a/b = log a - log blog a^x = x log alog a^a = 1log (√x) = 1/2 log (x)The given expression is,
[tex]log_7{2}[/tex]
as, [tex]log_bm= \frac{log_cm}{log_cb}[/tex]
therefore ,
[tex]log_7{2}[/tex] = [tex]\frac{log \ 2}{log \ 7}[/tex]
Hence, logarithm as the quotient of two common logarithms is :
[tex]\frac{log \\2}{log \\7}[/tex]
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There are 240 students in the seventh grade, and 10% are in the Environmental Club.
How many students are in the Environmental Club?
2 is subtracted from the product of 6 and a number
Answer:
6n-2
Step-by-step explanation:
Write the expression
subtracted from means it comes after
product of 6 and a number means multiply
6n
2 is subtracted from
6n-2
Answer:
It can be expressed as:
6x-2
6(coefficient)
x(variable)
2(constant)
Nautica is making a scaled copy of a square using a scale factor of 2. which of the following is NOT true?
A. each angle is multiplied by 2
B. the corresponding side lengths are multiplied by 2
C. The perimeter is multiplied by 2
D. The corresponding angles in each figure are equivalent
When Nautica is making a scaled copy of a square using a scale factor of 2, the option that isn't true is D. The corresponding angles in each figure are equivalent.
How to illustrate the information?It should be noted that based on the information given, we've to multiply the given figures by 2
Therefore, each angle is multiplied by 2, the corresponding side lengths are multiplied by 2, and the perimeter is multiplied by 2
Therefore, the correct option is D.
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What is the x equivalent to for x/5=10 ?
Answer:
50
Step-by-step explanation:
because 10 × 5 is 50
- to check 50 ÷ 4 is infact equal to 10 (make sure u always double check ur answers)
Eight friends started a business. They
will wear either a baseball cap or a shirt
imprinted with their logo while working.
They want to spend exactly $36 on the
shirts and caps. Shirts cost $6 each and Caps cost $3 each
The number of caps they can buy is 2 and the number of shirts they can buy is 6.
How many of each item should they buy?The system of equations that can be used to represent this question is:
6s + 3c = 36 equation 1
s + c = 8 equation 2
Where:
s = number of shirtsc = number of capsIn order to determine the required values, take these steps:
Multiply equation 2 by 6
6s + 6c = 42 equation 3
Subtract equation 1 from equation 3
3c = 6
c = 6/3
c = 2
Substitute for c in equation 2:
s + 2 = 8
s = 8 - 2
s = 6
Here is the complete question:
Eight friends started a business. They will wear either a baseball cap or a shirt imprinted with their logo while working. They want to spend exactly $36 on the shirts and caps. Shirts cost $6 each and Caps cost $3 each. How many of each item can they afford?
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Find the circumference and area of a circle with diameter 16 ft. Express your answer in terms of π.
Answer:
50.27 ft
Step-by-step explanation:
hope this helps :)
Evaluate the expression. 2 – 9 ÷ 3
Answer:
-1
Step-by-step explanation:
2 – (9 ÷ 3)
divide 9 and 3
2 - 3
subtract 2 from 3 and you get
-1
Answer:
-1
Step-by-step explanation:
Its just the answer.
If m<1 = (7x-19), and m<2 = (x + 5)°, find m2
Answer: m<2 = 18°
Step-by-step explanation:
m<1 + m<2 = 90°
7x - 19 + x + 5 = 90°
First add common variables; 7x + x = 8x || -19 + 5 = -14
8x - 14 = 90°
Second add 14 on both sides;
8x - 14 = 90°
+14 +14
8x = 104°
Third divide 8 to 104
[tex]\frac{8x}{8} = \frac{104}{8}[/tex]
x = 13
m<1 7(13) - 19 + m<2 (13) + 5 = 90°
13 * 7 = 91
91 - 19 = 72
72 + 13 = 85
85 + 5 = 90°
m<2 = 13 + 5 = 18°
Hope this helps! :]
--Blu
There are 36,102 bags filled with coins. There are 21 coins in each bag. How many coins are
there in all?
Cam you please help with math homework.
The values of the variables in the ordered pair are as follows;
18. y = 10
19. x = 6
20. y = -14
21. x = -4
22. x = -5
23. x = 40
24. y = -30
25. y = 5
What are ordered pairs?Ordered pairs are points located on the graph of a function.
In a direct variation, we have;
y = m•x
Where;
m = The slope of the line joining the points
18. (2, -4), (-5, y) the ordered pair is a direct variation
The slope = (y + 4)/((-5) - 2) = (y + 4)/(-7)
y = (y + 4)/(-7) × (-5)
7•y/5 = y + 4
7•y/5 - y = 4
2•y/5 = 4
y = 1019. (4, 16), (x, 24)
m = (24 - 16)/(x - 4) = 8/(x - 4)
y = 24
Which gives;
24 = (8/(x - 4))×x
24 × (x - 4) = 8•x
16•x = 96
x = 96/16 = 6
x = 620. (12, y), (4, 7)
m = (7 - y)/(4 - 12) = (7 - y)/(-8)
y = ((7 - y)/(-8)) × 12
12•y/(-8) = 7 - y
12•y = -56 + 8•y
4•y = -56
y = -56/4 = -14
y = -1421. (x, -16), (6, 24)
m = (24 - (-16))/(6 - x) = 40/(6 - x)
-16 = (40/(6 - x))×x
16•x - 96 = 40•x
24•x = -96
x = -96/24 = -4
x = -422. y = -18, x = 3
-18 = m×3
m = -18/3 = -6
When y = 30
x = 30/(-6) = -5
x = -523. y = 80 when x = 32
m = 80/32 = 10/4 = 2.5
When y = 100, we have;
x = 100/2.5 = 40
x = 4024. y = 10 when x = -4
m = 10/(-4) = -2.5
When x = 12, y = 12 × (-2.5) = -30
y = -3025. y = -7 when x = -28
m = -7/(-28) = 1/4 = 0.25
When x = 20, y = 0.25 × 20 = 5
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Select the correct answer from each drop-down menu.
A researcher is examining the claims made by water softener salt manufacturer. He performs an experiment using water from a variety of sources. For
each water source, he has a sample with no treatment and a sample treated with the recommended amount of the water softener salt.
He then tests each sample to measure the softness and compares the results, determining that the claims made by the manufacturer are true.
The conclusion drawn from the study is v because the sample is MEY In this instance, an
v study was
performed.
Step-by-step explanation:
Select the correct answer from each drop-down menu. A researcher is examining the claims made by a water softener salt manufacturer. He performs an experiment using water from a variety of sources. For each water source, he has a sample with no treatment and a sample treated with the recommended amount of the water softener salt. He then tests each sample to measure the softness and compares the results, determining that the claims made by the manufacturer are true. The conclusion drawn from the study is because the sample is . In this instance, an study was
Please Help me!! Use the graph at right to answer the following questions. (Hint: rate of change = slope). Calculate the average rate of change from x = 1 to x = 4
Based on the given graph, the average rate of change from x=1 to x = 4 is - ²/₃
What is the average rate of change?To find the average rate of change which is the slope, the formula is:
= (Y₂ - Y₁) / (x₂ - x₁)
The coordinates of x = 1 and x = 4 are:
(1, 5) and (4, 3)
Average rate of change is:
= (3 - 5) / (4 - 1)
= -2 / 3
= - ²/₃
In conclusion, the average rate of change is - ²/₃.
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Select which pair of lines can be proven parallel by using the given angle measures.
A. L || n
B. a || c
C. b || c
D. a || b
Answer:
C. b || c
Step-by-step explanation:
Answer:
c) b // c
Step-by-step explanation:
Two lines are said to be parallel when one of the conditions is true.
1) Corresponding angles are equal.
2) Alternate interior angles are equal.
3) Co interior angles are supplementary.
∠1 =115° {Vertically opposite angles}
∠1 = ∠2 = 115°
If corresponding angles are equal, then the lines are parallel. So, b // c
Tonya is paid a salary of $650 a month at her sales job. She also earns a commission on her sales in this way: 3% on all sales up to $32,000 in a month
and 8% on all higher sales. What were Tonya's total earnings for a month where her total sales were $80,000?
Tonya's total earnings are the sum of the basic pay and other commissions so Tonya's earnings for a month including all incentives will be $5450.
What is the percentage?The percentage is defined as a given amount in every hundred. It is a fraction with 100 as the denominator percentage is represented by the one symbol %.
Basic pay of Tonya = $650
3% of 32000 ⇒
3 × 32000 / 100 = $960
Now 8% on higher of $32000
Amount higher of $32000 ⇒ 80000 - 32000 = $48000
So,
8% on 48000 ⇒
8 × 48000/100 = $3840
Total earning = 650 + 960 + 3840 = $5450
Hence "Tonya's total earnings for a month including all incentives will be $5450".
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The binomial x + 7 is a factor of polynomial p.
Use this information to complete the equation.
If the binomial (x−7) is a factor of the polynomial function f(x), then the true statement is f(-7) = 0
How to determine the true statement?The given parameters are
The binomial (x + 7) is a factor of the polynomial function f(x)
The above means that
When the function f(x) is divided by x + 7, it has no remainder
So, we have
x + 7
Set to 0
x + 7 = 0
Add -7 to both sides
x = -7
Substitute x = -7 in f(x) = 0
f(-7) = 0
Hence, if the binomial (x−7) is a factor of the polynomial function f(x), then the true statement is f(-7) = 0
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Arun bought 10 chicken wings for $10.00. How much would it cost for 3 wings?
Answer:
$3.00
Step-by-step explanation:
Solve each equation.
10x=1/100
For the given equation 10x=1/100, the value of x is 0.001
What is a linear equation?A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) component are included. The variables in the preceding equation are y and x, and it is occasionally referred to as a "linear equation of two variables."
It has the formula Ax + B = 0, with A and B being any two real integers and x being an ambiguous variable with just one possible value. One such linear equation in one variable is 9x + 78 = 18.
Given,
10x = 1/100
x = 1/1000
x = 0.001
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Divide x cubed minus 3 x squared minus 10 x + 24 by x minus 2.
Step 1 - Fill in the missing number:
A vertical line and horizontal line combine to make a L shape. There is one row of entries in the shape including 1, negative 3, negative 10, 24. On the outside to the left of the L shape is k.
On the outside to the left of the L shape is K, then the synthetic division used to represent the dividend is[tex]2x^{3} +10x^{2} +x+5[/tex].
What is Synthetic division?A more straightforward method of dividing a polynomial using a degree one polynomial equation is known as synthetic division.
a simplified method for dividing a polynomial by another polynomial of the first degree by writing down only the coefficients of the several powers of the variable and changing the sign of the constant term in the divisor so as to replace the usual subtractions by additions.
Here,
An L shape is created when a vertical line and a horizontal line are combined.
Within the form, there are two rows of entries.
Entries 2, 10, 1, and 5 are in row 1.
Row 2 has the entries -10, 0 and blank.
On the outside, to the left of the form, is entry number five.
The entry stands for the divisor's zero.
This entry for the variable, let's say x, is [tex]2x^{3} +10x^{2} +x+5[/tex].
Therefore, the Synthetic division of the dividend is [tex]2x^{3} +10x^{2} +x+5[/tex].
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Answer: Step 1: K=2, Step 2: A=1, Step 3: B=2, C=-1, D=-2 LAST QUESTION is A on edge.
Step-by-step explanation:
A scientist running an experiment starts with 100 bacteria cells. These bacteria double their population every 15 hours. Find how long it takes for the bacteria cells to increase to 300. Use the formula P t = P o 2 t d , where P o is the original number of bacteria cells, P t is the number after t hours, and d is the time taken to double the number.
Answer:
Step-by-step explanation:
Explanation:
I would write the growth function as:
y
=
100
e
k
t
So that at
t
=
0
we get:
y
=
100
e
0.02
⋅
0
=
100
bacteria.
At
t
=
5
hours we will get:
y
=
100
e
5
⋅
0.02
=
110
bacteria.
To double the initial number we need to solve:
200
=
100
e
0.02
t
e
0.02
t
=
2
Apply natural logs to both sides:
ln
(
e
0.02
t
)
=
ln
(
2
)
0.02
t
=
ln
(
2
)
t
=
ln
(
2
)
0.02
=
34.65
≈
34.6
34
hours and 36 minutes approx.
find the quotient of 68.0052 and 12 round your answer to the nearest hundredth 
ILL GOVE BRAINLIEST
Answer:
5.67
Step-by-step explanation:
The quotient was 5.6671 and rounded to the nearest hundredth is 5.67. Hope it helps.
Jing records the amount of time he spends studying in 1 month. He spends a total of 82 hours studying math, chemistry, and history. The number of hours he spends on chemistry is twice the number that he spends on math. He spends 7 hours more than 4 times the number of hours on history as he does on math and chemistry combined. How much time does he spend studying each subject?
The number of hours that Jing spent on each subject will be;
Mathematics = 5.36 hours
Chemistry = 10.72 hours
History = 71.32 hours
How to illustrate the information?Let the number of hours spent on Mathematics = x
Chemistry = 2x
History = 4(2x + x) + 7 = 12x + 7
Total hours = 82 hours
Therefore, the time used for each will be illustrated:
x + 2x + 12x + 7 = 82
14x + 7 = 82
14x = 82 - 7
14x = 75
x = 75 / 14
x = 5.36 hours
Mathematics = x = 5.36 hours
Chemistry = 2x = 2 × 5.36 = 10.72 hours
History = 4(2x + x) + 7 = 12x + 7 = 71.32 hours
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Find the perimeter and area of the polygon with the given vertices.
W(5,−1), X(5, 6), Y(2,−1), Z(2, 6
The perimeter of a rectangle is the total length or distance of its boundary on all sides. The perimeter is 20 unit and area is 21 unit² for vertices of a polygon W(5,−1), X(5, 6), Y(2,−1), Z(2, 6).
What is perimeter of rectangle?The perimeter of a rectangle is the total length or distance of its boundary on all sides. The perimeter of a rectangle is a linear measure and is expressed in linear units of meters, feet, inches, or yards. Let us first understand the two main properties of a rectangle.
All four angles of a rectangle are 90°.
The opposite sides of a rectangle are equal in measure.
The Perimeter of a rectangle = 2(l + w).
given coordinates:
W(5,-1), X(5,6), Y(2,-1), Z(2,6).
Now, considering the coordinates we will find the width and length of rectangle :
Taking points (2,6) and (5,6):
w=5-2=3
Taking points (5,6) and (5,-1):
l=6-(-1)=7
Now, perimeter of rectangle
= 2x(3+7)
= 20 unit
Hence, area rectangle is : 3x7=21 unit²
Therefore area is 21 unit² and perimeter is 20 units of polygon with the given vertices W(5,−1), X(5, 6), Y(2,−1), Z(2, 6).
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Question 3 Solve this system of equations without graphing: Select Choice ✓ (5x + 2y = 29 5x - 2y = 41
The solution to the system of equations is x = 7 and y = -3
What are linear equations?Linear equations are equations that have constant average rates of change. Note that the constant average rates of change can also be regarded as the slope or the gradient
How to determine the solution to the system?A system of linear equations is a collection of at least two linear equations.
In this case, the system of equations is given as
5x + 2y = 29
5x - 2y = 41
Add both equations
So, we have
10x = 70
Divide the equation by 10
So, we have
x = 7
Substitute x = 7 in 5x - 2y = 41
5 x 7 - 2y = 41
This gives
35 - 2y - 41
Evaluate
2y = -6
Divide by 2
y = -3
Hence, the solution to the system of equations is x = 7 and y = -3
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explain how to use ordered pairs of points in f(x) = 3x - 5 and g(x) x+5/3 to determine if f(x) and g(x) are inverse of each other.
This is the same as g(x) which, therefore the functions are inverse of each other.
What does a math inverse mean?
Inverse operations, such as addition and subtraction, multiplication and division, are pairs of mathematical operations where one operation reverses the effect of the other. The term "inverse" refers to the reciprocal of a number, i.e., x - 1 = 1 / x. One results from multiplying a number by its reciprocal, or inverse.for any point (x, y), that appears in one function, the point (y, x) must appear in the other function. for any point (x, y), that doesn't appear in one function, the point (y, x) must not appear in the other function.
so if you find any point that doesn't meet the above rules, you can prove that the functions are not inverses of each other.
to prove that they are inverses of each other, you need to check all points in the functions, and there is an infinity of them, so instead, you can write f(x) like this:
y = 3x - 5
solve for x:
y + 5 = 3x
x = (y + 5) / 3
swap x and y:
y = (x + 5) / 3
this is the same as g(x) which, therefore the functions are inverse of each other.
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Which of the following functions is graphed below?
Answer: Im not sure but have a wonderful day god bless you.
Step-by-step explanation: