Each part of Nick's and Autumn's expressions mean can be explained as follows;
Nick;
the amount of substance he begins with = 20the amount of substance left after each week = 1/2Autumn:
The one outside of parentheses = the initial amount of the substance.The one inside of parentheses = 100% of the original amount of the substance.0.5 represents the 50% of the substance that is lost each time periodHow to explain each variable in an expression?ler
Number of weeks = wNick expression:
[tex] {20( \frac{1}{2} })^{w} [/tex]
Where,
the amount of substance he begins with = 20
the amount of substance left after each week = 1/2
If w = 2
[tex] {20( \frac{1}{2} })^{w} [/tex]
[tex]{20( \frac{1}{2} })^{2} [/tex]
= 20(0.25)
= 5 milligrams
Autumn's expression:
[tex] {(1 - 0.5)}^{w} [/tex]
The one outside of parentheses = the initial amount of the substance.
The one inside of parentheses = 100% of the original amount of the substance.
0.5 represents the 50% of the substance that is lost each time period
If w = 2[tex] {(1 - 0.5)}^{w} [/tex]
[tex] {(1 - 0.5)}^{2} [/tex]
= (0.5)²
= 0.25 milligrams
Complete question:
Nick starts with 20 milligrams of a radioactive substance. The amount of the substance decreases by 1/2 each week for a number of weeks, w. He writes the expression 20(12)w to find the amount of radioactive substance remaining after w weeks. Autumn starts with 1 milligrams of a radioactive substance. The amount of the substance decreases by 50% each week for a number of weeks, w. She writes the expression (1-0.5)w to find the amount of radioactive substance remaining after w weeks. Use the drop-down menus to explain what each part of Nick's and Autumn's expressions mean.
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Alfred begins collecting model cars. He buys 3 new model cars every week. Is the number of cars he owns proportional to the number of weeks that have passed since he started his collection?
Answer:yes
Step-by-step explanation:
for every week he gets 3 cars so it can only incre ment by 3. (1,3) (2,6) (3,9) and so on.
What is the value of the following numerical expression?
-23 +-15+|-17| + -35
A. -56
B.-26
C. 1-261
D. 56
The value of expression -23 +-15+|-17| + -35 is -56
In this question, we have been given a numerical expression.
-23 +-15+|-17| + -35
We need to find the value of given numerical expression.
Consider given numerical expression,
-23 +-15+|-17| + -35
= -23 + (-15) + |-17| + (-35)
= -23 - 15 + |-17| - 35
We know that for any real number a, |±a| = a
So, |-17| = 17
= -38 + 17 - 35
= -56
Therefore, the value of expression -23 +-15+|-17| + -35 is -56
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Linwood Marcus purchased a new couch for $878 and two end tables for $127 each. What is the sales taz
his purchase if he lives in Florida where the sales tax rate is 6 percent?
A. $57.89
B. $65.67
C. $60.30
D. $67.92
The sales tax of his purchase if he lives in Florida where the sales tax rate is 6 percent is $67.92
What is meant by percentage?The word "percent" comes from the Latin per centum, which means "hundred" or "by the hundredth." The symbol for "percent" emerged gradually from the Italian expression per cento, which means "for a hundred." The "per" was frequently shortened as "p." and eventually vanished. The "cento" symbol was simplified to two circles divided by a horizontal line, from which the contemporary "%" symbol was formed.
The abbreviation "pct.", "pct," and sometimes "pc" are also used. A % is a dimensionless (pure) number with no unit of measurement.
Given,
Total purchase=$878
For two tables,
2×127=254
Total=878+254
=1132
6% of 1132 is,
(6/100)×1132
=$67.92
The sales tax of his purchase if he lives in Florida where the sales tax rate is 6 percent is $67.92
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g(x) = x-2
What is the Parent function and transformation
The parent function is y = x ; shift 2 units downwards.
Given,
In the question:
The function is :
g(x) = x - 2
Now, According to the question ;
Let's know
What is the Parent function and transformation?
The transformation of the parent function is shown in blue. It is a shift down (or vertical translation down) of 1 unit. Reflection. A reflection on the x-axis is made on a function by multiplying the parent function by a negative. Multiplying by a negative “flips” the graph of the function over the x-axis.
According to the above statement is;
g(x) = x -2
Hence, The parent function is y = x ; shift 2 units downwards.
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you are flying a kite and the angle of elevation from the horizon is 36 if your kite string is 15 feet long, how high are you flying the kite ?
By using a trigonometric relation we will see that the height of the kite is 8.82 feet above the point where you hold the line.
how high are you flying the kite?We can view this as a right triangle, where the hypotenuse has a measure of 15 feet, we know one angle that measures 36°, and the opposite cathetus to that angle is x, the height we want to find.
We want to get the value of x, which is the opposite cathetus to the given angle, then we can use the trigonometric relation:
sin(a) = (opposite cathetus)/(hypotenuse)
Replacing what we know we will get:
sin(36°) = x/15ft
Solving this for x we get:
x = sin(36°)*15ft = 8.82ft
The height of the kite is 8.82 feet.
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use the figure to complete the following statements
Step-by-step explanation:
I don't see the options and how they are written, but I can tell you the right answer in numbers :
sin(F) = 3/5 = 0.6
cos(F) = 4/5 = 0.8
sin(G) = 4/5 = 0.8
cos(G) = 3/5 = 0.6
why ?
remember the norm circle (radius 1) with ask the trigonometric functions.
the sine of an angle is the vertical height from that point in the circle arc down to x-axis.
the cosine of an angle is the length on the x-axis from the center of the circle to the point, where the sine touches the x-axis.
in any case, sine and cosine enclose the right angle (90°).
each function is now defined for the norm circle with radius = 1.
for angles in larger circles we need to divide the find lengths by the actual radius (we formality do this in the norm circle too, but a division by 1 does not change anything).
for the angles at F and G the radius is the side with the length 5.
Can you help me create a polynomial function from the diagram displayed below? My teacher never went over this in class.
Thanks!
Considering the dimensions of the rectangular prism and it's volume, it is found that:
The expression is: V(x) = 4x³ - 22x² + 30x.The degree is of 3, the number of terms is of 3, and the leading coefficient is of 4.How to obtain the volume of a rectangular prism?The volume of a rectangular prism is given by the multiplication of the dimensions of the prism, which are the width symbolized by w, the height symbolized by h and the length symbolized by l, that is:
V = l x w x h.
In the context of this problem, from the image, the dimensions are given as follows:
Length: l = 2x - 5.Width: w = x - 3.Height: h = 2x.Then the polynomial expression regarding the volume of the prism is obtained as follows:
V(x) = 2x(x - 3)(2x - 5)
V(x)= 2x(2x² - 11x + 15)
V(x) = 4x³ - 22x² + 30x.
The features of the polynomial expression V(x) = 4x³ - 22x² + 30x is obtained as follows:
Degree of 3, which is the highest exponent of the function V(x).Number of terms of 3, which are 4x³, 22x² and 30x.The leading coefficient is of 3, as it is the term that multiplies the term with the highest exponent x³.A similar problem, also about the volume of a rectangular prism, is presented at brainly.com/question/22070273
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pls help ASAP
just fill the blank
Answer:
Use the formula to find distance
8x + 24 I was solutions
Step-by-step explanation:
8x + 24 is a simplified expression.
It is not an equation, so it can't be solved.
There are two terms in 8x + 24, 8x and 24.
The two terms are unlike terms, so they cannot be combined together.
Solve the following
2( x + 3 ) = x - 4
2x + 6 = x - 4
x ≈ -0,67
or
x = -2^3
what is the answer what is the answer what is the step by step answer to learn to do it
The approximate percentage of sales tax is 1%
A gymnastics mat priced at $53.
A cost of mat after adding sales tax = $53.53
So, the tax amount would be,
53.53 - 53 = 0.53
We need to find the sales tax percentage.
Let x be the percentage of sales tax.
x = (0.53)/(53.53) * 100
x = 0.0099 * 100
x = 0.99%
x ≈ 1%
Therefore, the approximate percentage of sales tax is 1%
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Find m/ABD.
D
с
A
20°
B
The answer of this question can be given by using congruence
Answer is 20°
What is an example of congruence?
Congruent relates to anything that is "exactly equal" in terms of size and shape. The shapes hold true regardless of how we rotate, flip, or turn them. Draw two circles with the same radius, for instance, cut them out, and stack them on top of one another.
Given That:
∡DBC = 20°
DC = AD
DB is common on both triangle
As we have hypotenuse common in both triangle and 1 side equal then we can sa it is a congruent triangle by RHS
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A, B , C or D ???????? help
Answer:
The Answer is B
Step-by-step explanation:
Since 1.8 times 10 is bigger than 18% meaning its the only one that would be in correct descending order.
Answer:
Pretty sure it’s A
Step-by-step explanation:
18% is 18/100 which is then .18
1/8 is .125
1.8x10 is 18
And .188 is just .188
In a pack of Skittles, 20% are red. If 13 are red, how many skittles were in the entire bag?
The total number of skittles in the bag will be 65.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that In a pack of Skittles, 20% are red. If 13 are red. The total number of skittles will be calculated as,
N = ( 13 / 20 ) x 100
N = 130 / 2
N = 65
Therefore, the total number of skittles in the bag will be 65.
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the drying times for a certain type of cement are normally distributed with a standard deviation of 62 minutes. a researcher wishes to estimate the mean drying time for this type of cement. find the least sample size needed to assure with 90% confidence that the sample mean will not differ from the population mean by more than 5 minutes.
The least sample size needed to assure with 90% confidence that the sample mean will not differ from the population mean by more than 5 minutes will be 416.16.
What is normal distribution?A normal distribution is a data set design in which the majority of values cluster around the middle of the range and the remainder taper off symmetrically toward either end. Data in a normal distribution are symmetrically distributed and have no skew. The majority of values cluster around a central location, with values decreasing as one moves out from the center. In a normal distribution, the measures of central tendency (mean, mode, and median) are all the same. The normal distribution, like any other probability distribution, defines how the values of a variable are distributed. Because it properly captures the distribution of values for many natural occurrences, it is the most important probability distribution in statistics.
Here,
The z value at the 90 percent confidence interval is 1.645.
t ≥ z*s/√n
5≥1.645*62/√n
√n≥20.398
√n≥20.4
n≥416.16
The smallest sample size required to ensure that the sample mean does not deviate from the population mean by more than 5 minutes with 90% confidence is 416.16.
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let 0 < a < b < 1,
a) is a^x < b^x, for x>0
b) is a^x < b^x, for x<0
For 0 < a < b < 1, a^x < b^x, for x < 0.
What are inequalities and their types?
Inequality is a relation that compares two numbers or other mathematical expressions in an unequal way.
The symbol a < b indicates that a is smaller than b.
When a > b is used, it indicates that a is bigger than b.
a is less than or equal to b when a notation like a ≤ b.
a is bigger or equal value of an is indicated by the notation a ≥ b.
Given, 0 < a < b < 1.
Assuming a = 0.25 and b = 0.5.
∴ (0.25)^x < (0.5)^x for x > 0, again assuming x to be 2.
∴ (0.25)^2 = 0.625 and (0.5)^2 = 0.25.
Now, 0.625 > 0.25 which is not satisfying a^x < b^x, for x > 0.
Therefore, if 0 < a < b < 1, then a^x < b^x, for x < 0.
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10 plus the difference of 6 and 2
Answer: 14
Step-by-step explanation: 10 + (6-2) = 14
in how many ways can 4 different physics books, 3 different mathematics books, and 2 psychology books be arranged on a bookshelf if the physics books must be together and the mathematics books must be together?
Since the physics books must be together and the mathematics books must be together, There are 1728 ways to arrange the books.
What is fundamental counting principle?The basic counting principle is a method for keeping track of all the potential outcomes in a situation. According to this statement, there are n m n times m n ways to carry out both of these actions if there are n ways to perform one action and m ways to perform another action after that. How selection is made based on options is determined by the Fundamental Principle of Counting. The approach of selection, taking into account all of the potential options and their combinations for calculating the probability, is made simpler by the Fundamental Principle of Counting.
Here,
There are 3 book,
3!=6
3 different mathematics books,
3!=6
4 different physics books,
4!=24
2 psychology books
2!=2
by fundamental counting principle,
6*6*24*2=1728
There are 1728 different ways to arrange the books because the mathematics and physics books must be together.
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Construct the graph of the equation given by solving for the intercepts. Show all of the steps in finding the intercepts and then
plot the intercepts to create the graph. Label the intercepts, as well as the axis on the graph.
2x+3y=6
The slope and the intercepts of the graph are determined.
Given:
the equation is :
2x+3y=6
we first find the slope of the equation:
m = -a/b
m = -2/3
now solve the intercepts:
to find x intercept, substitute in 0 for y and solve for x.
⇒ 2x+3y=6
⇒ 2x+3(0)=6
⇒ 2x+0=6
⇒ 2x=6
⇒ x=6/2
⇒ x=3
hence we get (3,0)
now, to find y intercept, substitute in 0 for x and solve for y.
⇒ 2x+3y=6
⇒ 2(0)+3y=6
⇒ 0+3y=6
⇒ 3y=6
⇒ y=6/3
⇒ y=2
hence we get (0,2) as the intercepts.
Therefore we plot the required graph.
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asking help for a friend
Length of the line AB is 1.414 units and midpoint of AB is (3.5,5.5).
Given in the graph,
A(4,6) and B(3,5)
Distance formula = [tex]\sqrt{(x1-x2)^{2} +(y1-y2)^{2} }[/tex]
AB = [tex]\sqrt{(4-3)^{2} +(6-5)^{2} }[/tex]
= [tex]\sqrt{1^{2} +1^{2} }[/tex]
= [tex]\sqrt{2}[/tex]
= 1.414 units
Midpoint = [tex](\frac{x1+x2}{2},\frac{y1+y2}{2})[/tex]
Let midpoint of AB be C(x,y)
C = (x,y) = [tex](\frac{4+3}{2},\frac{6+5}{2})[/tex]
= [tex](\frac{7}{2},\frac{11}{2})[/tex]
= (3.5,5.5)
Hence, length is 1.414 units and midpoint is (3.5,5.5).
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Is this rat correct tell me tell me NOWWWW teehee
Answer:
No , x = -2
Step-by-step explanation:
When Dividing the Equation by a Constant , all terms in both sides must be divided by this Constant.
So here we divided both sides by 2 , but -6 is not divided , so this step is incorrect
The correct Answer is
[tex]\frac{-6}{2}+\frac{2x}{2} =\frac{-10}{2} \\-3+x=-5\\x=-5+3=-2[/tex]
Jorge has 20 fish for his dog sled team that he wants to divide into smaller pieces. How many pieces of fish would there be if Jorge divided each fish into tenths?
2,000
200
2
0.2
Answer:
200
Step-by-step explanation:
20*10=200
Feng invests money in an account paying simple interest. He invests $70 and no money is added or removed from the investment. After one year, he has $70.70. What is the simple percent interest per year?
The simple interest is given as PRT/100, thus the simple percent interest per year is 1%.
What is simple interest?Simple interest is a way to figure out how much interest will be charged on a sum of money at a specific rate and for a specific duration of time.
Unlike compound interest, which adds the interest from the principal of prior years to determine the interest of the following year.
As per the given,
Investment = $70
Investment after one year is $70.70
Interset = 70.70 - 70 = $0.70
The interest is given as = PRT/100
0.70 = PR(1)/100
R = (0.70×100)/70
R = 1%
Hence, "The simple interest is given as PRT/100, thus the simple percent interest per year is 1%".
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Triangles geometry . PLS
Step-by-step explanation:
Angle BAC = angle BCA
as sum of angles in triangle = 180
49 + 49 + ABC = 180
180 - 49 - 49 = ABC
ABC = 82°
A line passes through points
(8, - 2) and
(-5, 7). Which ratio can be used to determine the slope of the line?
7+2/
8+5
7-2/
-5-8
8+5/
-2+7
7+2/
-5-8
Answer:
7+2/8+5
Step-by-step explanation:
Is (4, 1) a solution to this system of inequalities?
3x + y ≤ 14
3x + 5y < 19
(4, 1) is the solution for the given inequalities
Given,
The system of inequalities;
3x + y ≤ 14
3x + 5y < 19
We have to find that (4, 1) is a solution to the given system of inequalities;
So,
(x, y) = (4, 1)
Then,
Substitute the values of x and y in the equation;
3x + y ≤ 14
3 x 4 + 1 ≤ 14
12 + 1 ≤ 14
13 ≤ 14
Next,
3x + 5y < 19
3 x 4 + 5 x 1 < 19
12 + 5 < 19
17 < 19
Here,
(4, 1) is the solution for the given inequalities
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the chief of police in statville wanted to estimate the number of people above the age of 181818 who are using illegal substances in town. he obtained 200200200 random names of statville residents from a computer database and sent his officers to survey these people about substance abuse. once the results came in, he calculated the margin of error and got an estimate of the percentage of residents who use illegal substances. what type of statistical study did the chief of police use?
The chief of police use sample statistical study to estimate the number of people above the age of 18 who are using illegal substances in town.
In the given question,
The chief of police in statville wanted to estimate the number of people above the age of 18 who are using illegal substances in town.
He obtained 200 random names of statville residents from a computer database and sent his officers to survey these people about substance abuse.
Once the results came in, he calculated the margin of error and got an estimate of the percentage of residents who use illegal substances.
We have to explain what type of statistical study the chief of police use.
In the given question chief of police wants to check number of people who using illegal substances in town above the age of 18. So he take 200 random names from a computer database. That means he take the sample of 200 random people.
As we know that a sample is a selection from a larger population of individuals, things, or things that are used for measurement. To enable us to extrapolate the research sample's findings to the entire population, the sample must be representative of the population.
So we can say that the chief of police use sample statistical study to estimate the number of people above the age of 18 who are using illegal substances in town.
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Answer: Sample Study
No because there’s a great risk of obtaining biased answers.
What is an equation of the line that passes through the points (4, −2) and (2, 3)?
The equation of the line, in slope-intercept form, that passes through
(4, 2) and (-2, -3) is y = 5/6 x - 4/3.
What is slope-intercept form?
The meaning of slope-intercept form is the equation of a straight line in the form y = mx + b where m is the slope of the line and b is its y-intercept.
Using two points and slope-intercept form we can find the equation of the line.
According to the given question:
The formula to find the slope of two points (x₁, y₁) and (x₂, y₂) is
m = (y₂ - y₁) / (x₂ - x₁)
The points given are (4, 2) and (-2, -3)
m = (-3 - 2) / (-2 - 4)
m = -5/ -6
m = 5/6
Now using the slope and the point (4, 2) the y intercept is
y = mx + b
2 = 5/6 (4) + b
2 = 10/3 + b
By further calculation,
b = 2 - 10/3
Taking LCM
b = (6 - 10)/3 = -4/3
By writing the equation in slope intercept form
y = mx + b
y = 5/6x - 4/3
Therefore, the equation of the line in slope intercept form is
y = 5/6 x - 4/3.
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Which number should be on the bottom left stamp?
Explain what the answer is and how you got it!
The number that should be on the bottom left stamp is 1. It was gotten by dividing 2 by 2.
What will the number be?From the first picture, we have 82 and the number below it is 4. This was gotten as:
= 8 ÷ 2
= 4
The second picture has 93 and the number below it is 3. This was calculated as:
= 9 ÷ 3
= 3
The third picture has 61 and the number below it is 6. This was calculated as:
= 6 ÷ 1
= 6
The fourth picture will be:
= 2 ÷ 2
= 1
Therefore the value is 1.
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x^2-6x-3=(x-a)^2-b where a and b are constants.Find the values of a and b
Answer:
a = 3, b = 12
Step-by-step explanation:
x^2-6x-3=(x-a)^2-b
Lets expand the right side:
(x-a)^2-b = (x-a)(x-a)-b
(x-a)(x-a)-b = x^2 -2ax + a^2 - b
The left side is equal to the right, as per the original equation:
x^2-6x-3 = x^2 -2ax + (a^2 - b)
Compare each term:
1) x^2 = x^2 OK
2) -6x = -2ax; a = 3 so that -6x = -2(3)x
3) -3 = (a^2-b); a^2 = (b-3)
a = [tex]\sqrt{b-3}[/tex]
a is 3, from above
3 = [tex]\sqrt{b-3}[/tex]
9 = b-3
b = 12