The least positive integer $n$ such that no matter how $10^n$ is expressed as the product of two positive integers, at least one of these two integers contains the digit 0, is 7.
Latex formula for equation.
f(x) = x^2 + 2x + 1
Let's consider the factorization of $10^n$ for increasing values of $n$.
For $n = 1$, $10^1 = 10$ which contains the digit 0.
For $n = 2$, $10^2 = 100$ which contains the digit 0.
For $n = 3$, $10^3 = 1000$ which contains the digit 0.
For $n = 4$, $10^4 = 10,000$ which contains the digit 0.
For $n = 5$, $10^5 = 100,000$ which contains the digit 0.
For $n = 6$, $10^6 = 1,000,000$ which contains the digit 0.
For $n = 7$, $10^7 = 10,000,000$ which contains no digit 0.
Therefore, the least positive integer $n$ is 7.
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two cards are dealt from an ordinary deck of 52 cards. this means that two cards are sampled uniformly at random without replacement. (a) what is the probability that both cards are aces and one of them is the ace of spades? (b) what is the probability that at least one of the cards is an ace? 6.
The probability that both cards are aces is 0.45%.
Given that,
A standard 52-card deck is used to deal two cards. In other words, two cards are uniformly and randomly sampled without being replaced.
There are four aces in the deck of 52 cards. The likelihood of drawing an ace when you draw a card is 4/52=1/13.
There are only 51 cards left when the second card is drawn, and since an ace has already been drawn, just 3 of those cards are still in the deck. Therefore, there is a 3/51 chance of drawing the second ace. The likelihood that both of these events occur is 1/13 x 3/51 = 0.00452. (approx). Thus, there is a 0.45% chance of drawing two aces.
Combinations and permutations offer a different perspective on this. There are 52C2 different methods to choose two cards from a deck. The entire sample space is shown here.
Therefore, the probability that both cards are aces is 0.45%.
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researchers recruited 60 undergraduate students, in exchange for course credit, for a study on the effect of recycling on how much wrapping paper subjects used to wrap a gift. the subjects were randomly assigned to one of two rooms. in one room there was a large recycling bin and in the other a large trash bin. subjects were asked to wrap a gift. unknown to the students, the researchers were interested in how much paper the students used. the researchers found that students in the room with the recycling bin used significantly more paper than those in the room with a trash bin. in this experiment, the amount of wrapping paper used is:
In this study, 60 undergraduate students were recruited to examine the effect of recycling on the amount of wrapping paper used to wrap a gift. The students were randomly assigned to one of two rooms, one with a recycling bin and one with a trash bin.
The researchers, who were secretly interested in measuring the amount of paper used, found that the students in the room with the recycling bin used significantly more paper than those in the room with the trash bin. This experiment suggests that the presence of a recycling bin may not have a significant effect on reducing the amount of wrapping paper used.
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William earned $52,000 last year. If the first $30,000 is taxed at 11% and income above that is taxed at 16%, how much does William owe in tax?
$6,820 is the total tax owned by William.
What is Percentage?percentage, a relative value indicating hundredth parts of any quantity.
Given that William earned $52,000 last year.
he first $30,000 is taxed at 11%
Let us find the 11% of 30000
30000×11/100
$3,300.
The tax owed on 30000 amount is $3,300.
The balance amount is 52000-30000
$22000
The above amount has a tax of 16%.
Now let us find the 16% of 52000
16/100×52000
$3520
The total tax owed by William is $3,300 + $3,520 = $6,820.
Hence, $6,820 is the total tax owned by William.
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Hello can somebody help me with this problem (Funcitons). Thank you in advance.
Functions f(x) and g(x) has same vertex and axis of symmetry. Therefore, option C and D are the correct answers.
What is the function?Functions are the fundamental part of the calculus in mathematics. The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x.
The given functions are g(x)= -1/2 x² and f(x)=x².
Graph of g(x):
Graph the parabola using the direction, vertex, focus, and axis of symmetry.
Direction: Opens Down
Vertex: (0,0)
Focus: (0,-1/2)
Axis of Symmetry: x=0
Directrix: y=1/2
Graph of f(x):
Graph the parabola using the direction, vertex, focus, and axis of symmetry.
Direction: Opens Up
Vertex: (0,0)
Focus: (0,1/4)
Axis of Symmetry: x=0
Directrix: y= -1/4
Therefore, option C and D are the correct answers.
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the toasters produced by a company have a normally distributed life span with a mean of 5.8 years and a standard deviation of 0.9 years, the company is willing to have a warranty that replaces at most 10% of their toasters sold. what is the longest a blender can last and still be in the lowest 10% of life spans? homework help: 4vd. calculating probabilities to compare to set probabilities such as warranties and production guidelines (links to an external site.) (2:23) group of answer choices 4.3 years 4.5 years 5.9 years 4.6 years
The correct response is d. 4.6 years. The company is replacing at most 10% of their toasters sold 4.6 years.
To handle problems using samples that have a normal distribution, utilize the z-score formula.
The z-score of a measure X in a collection with mean and standard deviation is given by:
Z= x−μ/σ
The measure's standard deviations from the mean are determined by the [tex]Z-[/tex]score. We examine the p-value linked with the [tex]Z-[/tex]score in the [tex]Z-[/tex]score table after computing the [tex]Z-[/tex]score. This p-value is the probability that the measure's value is smaller than [tex]X[/tex], or the percentile of [tex]X[/tex]. The likelihood that the value of the measure exceeds [tex]X[/tex] is calculated by deducting [tex]1[/tex] from the pvalue.
This issue involves that:
Mean, μ[tex]=5.8[/tex]
Standard deviation,σ[tex]=0.9[/tex]
Only those who rank in the bottom 10% will be replaced.
So, if Z has a p value of 0.10, the warranty is equal to the value of X.
So it is X when
[tex]Z=-1.28[/tex]
Z= x−μ/σ
x=Z∗σ+μ
[tex]x=-1.28*0.9+5.8\\x=4.6[/tex]
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1. There are 360 stickers in a box, divided equally among a group of children. If there are six fewer children in the group, each of the remaining children would receive two additional stickers. How many children are there initially?
Using Algebra, we concluded, there are 36 children.
The study of variables and the procedures for modifying variables in formulas is known as algebra, and it is the subject that underlies almost all of mathematics. All applications of mathematics require knowledge of elementary algebra since it deals with manipulating variables as though they were numbers.
What are the Algebra Basics?In algebra, the fundamental concepts are numbers, variables, constants, expressions, equations, linear equations, and quadratic equations. Additionally, it requires adding, subtracting, multiplying, and dividing basic arithmetic operations within the algebraic formulas.
How to solve?If there are X children at first
[tex]\frac{360}{x}+2=\frac{360}{x-6}[/tex]
360(x-6)+2x(x-6)=360x
360x-2160-12x=0
(X+30)(x-36)=0
So,x+30=0 x-36=0
X=-30, x=-36
Because X Great than or equal to 0
X=36
So there are 36 children at first.
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Pls help me really fast
[tex]\huge\text{Hey there!}[/tex]
[tex]\huge\text{Square inches formula is: }\\\\\large\boxed{\mathsf{l}\rm{ength}\times\mathsf{h}\rm{eight} = \mathsf{s}\rm{quare \ inches}}}}}}}[/tex]
[tex]\huge\text{So, your equation should look like:}[/tex]
[tex]\large\boxed{\mathsf{3\ inches \times 8\ inches \times 14\ inches = square\ inches^2}}}[/tex]
[tex]\huge\text{Now let us solve for your answer to this problem:}[/tex]
[tex]\large\boxed{\mathsf{3\ inches \times 8\ inches \times 14\ inches = square\ inches^2}}}[/tex]
[tex]\large\boxed{\mathsf{24\ inches\times 14\ inches = square\ inches^2}}[/tex]
[tex]\large\boxed{\mathsf{336 = square\ inches^2}}[/tex]
[tex]\huge\text{Therefore, your answer SHOULD be:}[/tex]
[tex]\huge\boxed{\mathsf{Option\ D. \ 336}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
Simplify (24)−1. please help me find out
Step-by-step explanation:
24×-1=
-24ans
and that's the answer
If you roll a 6-sided die 42 times, what is the best prediction possible for the number of times
you will roll a six?
i am a mutiply of 5 greater than 18 less than 30
in the construction of a pie chart, how many degrees would be in the section of the pie showing the yes answers?
The section of the pie showing the "yes" answers would have 162 degrees in a pie chart.
In a pie chart, the size of each section is proportional to the proportion of the data it represents. To calculate the size of the section showing the "yes" answers, we first need to find the proportion of "yes" answers in the total sample.
The proportion of "yes" answers can be calculated as:
(54 YES) / (54 YES + 39 NO + 27 no-opinion) = 54 / (120) = 9/20
In a pie chart, the proportion of each section is represented as a fraction of 360 degrees. So, to find the number of degrees in the "yes" section of the pie chart, we multiply 360 by the proportion of "yes" answers:
360 * (9/20) = 162 degrees
Therefore, the section of the pie showing the "yes" answers would have 162 degrees in a pie chart.
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a carousel with a 45-foot diameter makes 3 revolutions per minute. (a) find the angular speed of the carousel in radians per minute. (round your answer to two decimal places.) radians per minute (b) find the linear speed (in feet per minute) of the platform rim of the carousel. (round your answer to two decimal places.)
A carousel with a 45-foot diameter makes 3 revolutions per minute. (a) The angular speed is 6π rad/minute. (b) The linear speed is 424 feet per minute.
Information available in the problem:
diameter of the carousel = d = 45 feet
The carousel makes 3 revolutions per minute.
a) 1 revolution = 360⁰ = 2π radians
angular speed = 3 rev/minute
angular speed = 3 x 2π radians/minute = 6π rad/minute
b) the distance travelled in a revolution is equal to the circumference of the carousel.
Circumference of carousel = πd = 45π feet
Linear speed = 3 rev/minute = 3 x 45π feet/minute
Linear speed = 424 feet per minute.
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Which is more affected by skewness, the IQR or standard deviation? IQR Neither one is affected. Standard Deviation Both are affected the same amount.
The correct answer is option 2. Neither one is affected by skewness.
The IQR (Interquartile Range) and standard deviation are both measures of variability in a data set, but they are affected by different aspects of the data. The IQR is affected by the spread of the middle 50% of the data, while the standard deviation is affected by the spread of all the data points.
Skewness, or the asymmetry of a distribution, affects the mean and median of a data set but does not directly affect either the IQR or standard deviation. However, it can indirectly affect the measures if it is severe enough to cause the data to be spread more unevenly.
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Complete Question:
Which is more affected by skewness, the IQR or standard deviation?
IQR Neither one is affected. Standard Deviation Both are affected the same amount.Help me please asap!!!!!
Answer:
435 cubic yards.
Step-by-step explanation:
Length x width x height.
Cut the shape into 2 parts.
Calculate the length for each.
13 yd - 5 yd = 8 yd
5 × 5 × 11 = 275
8 × 4 × 5 = 160
275 + 160
435 cubic yards
describe the similarity transformations and write the composition of transformations
The transformations are composed so that the sides of triangles are in the ratio of 1/2 and the angles are equal.
What is similarity transformations?Similarity transformations are a sort of mathematical transformation that preserves the length ratios of related lines in a figure. Among these transformations are:
A translation is the movement of a figure in a given direction without affecting its size or shape. The combination of two translations results in a single translation equal to the total of the distances travelled.
A rotation is a transformation that involves turning a figure around a fixed point known as the center of rotation. The combination of two revolutions results in a single rotation equal to the total of the angles of rotation.
A reflection is a transition that occurs when a figure is flipped over a line known as the line of reflection. The combination of two reflections is simply a single 180-degree rotation.
Dilation: A dilation is a transformation that enlarges or reduces a figure by a given scale factor, centered at a fixed point. The product of two dilations is a single dilation equal to the product of the scale factors.
Here,
The sides of triangles are in ratio.
4/8=6/3=1/2
The composition of transformations is the sides of triangles are in ratio of 1/2 and angles are equal.
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The side length of one triangle is 100 cm. Which pair of measurements could be the lengths of the other two sides?
One possible pair could be "80 cm and 20 cm" if the side length of one triangle is 100 cm.
What is a Triangle?Triangle is defined as a basic polygonal shape of a triangle that has three sides and three interior angles. It is one of the fundamental shapes in geometry and is represented by the symbol Δ.
As we know that a triangle is considered a valid triangle if and only if the sum of the lengths of any two sides is greater than the length of the third side.
Given one side length of a triangle is 100 cm, the possible lengths of the other two sides would be any two numbers that add up to be greater than 100 cm.
Thus, one possible pair could be "80 cm and 20 cm" for the given triangle.
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p and q are complex numbers such that |p| = 3x+2, |q|= 2x+1, and p + q = -2.
On what interval must x fall on?
0
O
[---]
O [3,00)
0 [-1,-1]
0 (-∞, -¹]
◄
1
In complex number, that x ranges from -5 to -1/2 and the correct option is (-∞, -1/2)
What is complex number?In mathematics, a complex number is an element of a number system that extends the real numbers with a specific element denoted i, called the imaginary unit and satisfying the equation [tex]{\displaystyle i^{2}=-1};[/tex]
every complex number can be expressed in the form a + bi, where a and b are real numbers. Because no real number satisfies the above equation, i was called an imaginary number by René Descartes.
Given that,
|P| = 3x + 2
|Q| = 2x + 1
P+Q = -2
We know that, from Cauchy inequalities
|P| + |Q| > |P+Q|
3x + 2 + 2x + 1 > - 2
5x + 3 > - 2
subtract both side by 3
5x > -5
Divide both side by 5
x > -1 first condition
Note that,
|P| > 0
Then,
3x + 2 > 0
3x > -2
x > -2/3
Also,
|Q| > 0
2x + 1 > 0
2x > -1
x > -1/2
So, comparing the three conditions
We see that x ranges from -5 to -1/2, this range covers all the other ranges
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What is -6x + 15y - 24
Answer:
-3(2x-5y+8)
Step-by-step explanation:
I need to find the rate of change for this! Thank you ☀️
The function represents the exponential decay. And the rate of change is 20%.
What is an exponent?Let a be the initial value and x be the power of the exponent function and b be the increasing factor.
The exponent is given as
y = a(b)ˣ
y = a (1 ± r)ˣ
The exponent function is given below.
[tex]\rm m(t) = \left ( \dfrac{4}{5} \right)^t[/tex]
Compare the equation with the standard form. Then we have
If the value of the 1 - r is less than 1, then the rate is decaying.
1 - r = 4/5
r = 1 - 4/5
r = 1/5
r = 0.20 or 20%
The function represents the exponential decay. And the rate of change is 20%.
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given that the selected individual has at least one card, what is the probability that he or she has a visa card?
The probability that he or she has a visa card is 40%.
Probability is a mathematical concept that describes the likelihood of an event happening. In this case, the event is the selected individual having a visa card.
Let's assume that the individual has a total of n cards and v of those are visa cards. The probability of the individual having a visa card is given by the formula:
P(Visa) = v/n
This formula expresses the ratio of the number of successful outcomes (having a visa card) to the total number of possible outcomes (having any type of card).
The probability is expressed as a decimal or a percentage. If the individual has 5 cards and 2 of them are visa cards, then the probability of them having a visa card is
=> 2/5 = 0.4 or 40%.
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A boat travels S 14°E for 12 km and then changes direction to S 49°E for another 16 km.
a )Find x,the distance of the boat from its starting point to two decimal places.
b )Find b to the nearest degree.
c )Hence, find the bearing that the boat should travel on to return to the starting point.
Help please!
a) The distance of the boat from its starting point is 20 km.
b. The nearest degree is 63°
c. The bearing g that the boat should travel on to return to the starting point is 360° - 63° = 297°.
How to calculate?To find the distance of the boat from its starting point, we can use the Pythagorean theorem.
x^2 + y^2 = d^2
Substituting the values for x and y, we get:
12^2 + 16^2 = d^2
d^2 = 144 + 256
d^2 = 400
d = 20
Hence, the distance of the boat from its starting point is 20 km.
b) To find the bearing that the boat should travel on to return to the starting point, we must calculate the angle between the two legs of the journey.
b = arctan (y / x) = arctan (16 / 12) = 63.43°
To the nearest degree is 63°.
c) The bearing that the boat should travel on to return to the starting point is the opposite direction of the angle formed by the two legs of the journey. Therefore, the bearing is 360° - 63° = 297°.
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A family consisting of three persons—a, b, and c—goes to a medical clinic that always has a doctor at each of stations 1, 2, and 3. during a certain week, each member of the family visits the clinic once and is assigned at random to a station. the experiment consists of recording the station number for each member. suppose that any incoming individual is equally likely to be assigned to any of the three stations irrespective of where other individuals have been assigned. what is the probability that?
The probability of any one person visiting a particular station is 1/3. Since there are three people in the family, the probability that they would all visit the same station is 1/3 x 1/3 x 1/3, which is equal to 1/27.
The probability that all three members of the family visit the same station at the medical clinic is 1/27 (1/3 x 1/3 x 1/3). This is because each person has an equal chance of being assigned to any of the three stations and since there are three people in the family, the probability that they would all visit the same station is 1/3 multiplied by itself three times, which is equal to 1/27. The experiment is recording the station number for each member and since the incoming individuals are assigned to any of the three stations randomly, the probability that all three members visit the same station is 1/27.
The complete question is :
A family consisting of three persons—a, b, and c—goes to a medical clinic that always has a doctor at each of stations 1, 2, and 3. during a certain week, each member of the family visits the clinic once and is assigned at random to a station. the experiment consists of recording the station number for each member. suppose that any incoming individual is equally likely to be assigned to any of the three stations irrespective of where other individuals have been assigned. What is the probability that all three members visit the same station?
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n urn contains 13 red marbles, 33 blue marbles, and 38 yellow marbles. one marble is to be chosen from the urn without looking. what is the probability of choosing a red marble?
There is a 15.47% chance of selecting a red marble from the urn without looking.
The probability of choosing a red marble from the urn is expressed by the following formula:
P(Red Marble) = Number of Red Marbles / Total Number of Marbles
In this case, we are dealing with 13 red marbles, 33 blue marbles, and 38 yellow marbles. Therefore, the probability of choosing a red marble is 13/84, or 15.47%. We can calculate this by dividing the number of red marbles (13) by the total number of marbles (84). This means that there is a 15.47% chance of selecting a red marble from the urn without looking.
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3/8 H =-9 what does H =
Answer:
Below
Step-by-step explanation:
3/8 h = - 9 multiply both sides of the equation by 8/3
h = - 9 * 8/3 = - 24
express the following as a ratio in its simple form 1000 to 10 to 100
PLEASE HELP!! looking for the number that goes into the green box, help would be appreciated!
Converting the binary (base-10) number 77₁₀ to decimal (base-2) gives 1001101₂.
What are the types of number system?In Mathematics, there are four (4) main types of number system and these include the following:
Binary number system (Base-2): it include 1000, 1111, 1011, etc.Decimal number system (Base-10): it include 1010101.11, 10.1, 101.2, etc.Octal number system (Base-8): it include 7₈, 10₈, 12₈, etc.Hexadecimal number system (Base-16): it include 28E, AC7, etc.In this exercise, you're required to convert the given number in base 10 to base 2 and this can be done as follows:
2 | 77
2 | 38 R 1
2 | 19 R 0
2 | 9 R 1
2 | 4 R 1
2 | 2 R 0
2 | 1 R 0
2 | 0 R 1
Next, you would read the decimal number (base-2) upward and this gives:
77₁₀ = 1001101₂.
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What is the answer? I can’t figure out how to do it.
What happens if the opportunity costs of production are constant?
When the potential costs of production are constant, the cost of creating one thing remains constant regardless of how much of that good is produced. This is also known as continuous returns to scale.
What is constant?The term "constant" has several meanings in mathematics. It refers to non-variance as an adjective; as a noun, it has two meanings: A constant and well-defined integer or other mathematical object that does not change. A constant is a value or number whose expression never changes; it is always the same.
Here,
In this case, increasing the production of one good will result in a proportionate rise in the overall cost of production rather than an increase or decrease in the opportunity cost of producing that good. For example, if a corporation manufactures chairs and tables and the opportunity cost of manufacturing one chair is always two tables, the cost of making two chairs is four tables, the cost of producing three chairs is six tables, and so on.
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Which statement is true about the rectangle shown?
The right answer is C, which means "number of square feet in area equals number of feet in perimeter."
What is rectangle?A rectangle is a closed two-dimensional geometry with four sides, four corners, and four right angles (90°). A rectangle's opposite sides are equal and parallel. A rectangle is a quadrilateral with equal and parallel opposite sides. It is a four-sided polygon with four angles of 90 degrees. A rectangular form is two-dimensional. A rhombus is a quadrilateral with all sides the same length and both pairs of opposing sides parallel. The term rhomb is occasionally used instead of rhombus, and a rhombus is also known as a diamond.
Here,
area=6*3
=18 units
perimeter=2*(6+3)
=18 units
area=perimeter
The correct option is C that is "number of square feet in area is equal to number of feet in perimeter."
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HELP!!!! HELP HELP HELP
Answer:
60.83 percent hope it helps