If the scale factor is greater than 1, the image is larger than the preimage
What do dilations entail?Increasing the size of a figure without changing its shape is a process known as dilatation. Dilation can result in a figure growing or shrinking. Preimage is the name for the earliest figure in dilatation. A figure has been magnified Figures are warped from the center of dilatation, which is a fixed point.
What are shrinkage and growth?By enlarging or contracting a figure, the scale factor indicates how much the image will change in size.
1) If the scaling factor is between 0 and 1, the picture is smaller than the preimage. With a scale factor of between 0 and 1, reductions are known as dilations.
2) If the scale factor is more than 1, the picture will be bigger than the preimage. When a dilatation has a scale factor higher than 1, it is said to be an enlargement. Each new point in a dilated figure may be located using the prime symbol, ". The dilated version of point, which stands for "prime," would be point'.
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jorje wants to estimate the percentage of people who play sports. he surveys 330 individuals and finds that 65 play sport. find the margin of error for the confidence interval for the population proportion with a 95% confidence level.
The margin of error for the confidence interval for the population proportion with a 95% confidence level is 0.000207
How to find the margin of errorfinding the percentage of 65 of 330 individuals
65 / 330 * 100 = 19.697% = 0.19697
number of samples, n = 330
standard deviation, σ is calculated from
= √{(p(1 - p)) / n}
= √{(0.197 * (1 - 19.7)) / 330}
= √{(0.197 * (0.803)) / 330}
= 0.022
Margin of error, E
= Z(0.95) * σ/√(n)
= 0.171 * 0.022/√(330)
= 0.171 * √(0.022²/330)
= 0.000207
= 0.021%
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If 1,2 and 3 are the eigen value of A=[2 0 1; 0 2 0; a 0 2], find the value of a?
The value of a in this question is 1.
Here, we've been given the matrix A=[2 0 1; 0 2 0; a 0 2]
For eigenvalues, the characteristic polynomial of A -
= det(A- λI) = 0
= Let [(2 0 1; 0 2 0; a 0 2) - (λ 0 0; 0 λ 0; 0 0 λ)] = 0
= [2-λ 0 1; 0 2-λ 0; a 0 2-λ] = 0
= (2-λ)(2-λ)² - a[+(2-λ)] = 0
= 8+2λ² -8λ-4λ-λ³ +4λ²-2a+aλ = 0
= -λ³ +6λ² +(a-12)λ+8-2a = 0
For the given eigenvalues 1,2, and 3, the characteristic polynomial must have the roots at λ=1,2,3
= -(λ-1)(λ-2)(λ-3)
=-λ³+6λ²-11λ+6
Hence, -λ³+6λ²-11λ+6 = -λ³ +6λ² +(a-12)λ+8-2a
From equating these, we get-
a = 1
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HELP ASAP PLSPLSPSLSPLSPSLS
Rewrite the radical expression as an expression with a rational exponent.
the fourth root of seven to the fifth power
A- seven to the five fourths power
B- x20
C- x
D- seven to the four fifths power
The radical expression as an expression with a rational exponent is A- seven to the five fourths power.
What is a exponent?An exponent is the number of times that a number is multiplied by itself. It should be noted that the power is an expression which shows the multiplication for the same number.
Given, the fourth root of 7 to the fifth power, we have to write the radical as a rational exponent.
The formula to change a radical to a rational exponent is given by:
= a ^(m/n)
Now, cube root of the seventh power can be written as:
4✓7^5
Therefore, the rational exponent is A.
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What are the multiples of 3 and 10?.
Consider the following vocabulary:
Equilateral right angled triangle
Isosceles acute triangle
Scalene obtuse triangle
Which of these triangles are possible?
Which of these triangles are not possible?
Explain your reasoning.
An equilateral right angled triangle is not possible because a triangle can only consist of 180°. Since a right angle is 90°, there is no way that a triangle can be have three right angles. 180° ≠ 270°
An isosceles acute triangle is possible because two angles can be acute and have the same degree values and the last angle can have a different value of another acute angle. The two angles that are acute would have the same value for their corresponding sides.
A scalene obtuse triangle is possible because one angle can be obtuse and the other ones can be acute. All the sides can be different.
I hope this helps you! Have an amazing rest of your day!
suppose a jar contains 15 red marbles and 37 blue marbles. if you reach in the jar and pull out 2 marbles at random, find the probability that both are red. write your answer in decimal form, rounded to the nearest thousandth. answer:
The probability that both are red is 0.0791.
Given,
Total marbles: 37 + 15 = 52
According to the number of red cards out of all the cards, there is a 15/52 possibility that a red card will be pulled during our initial pull.
Depending on how many red/total marbles are still in there, there is a 14/51 probability that the second marble pulled will also be red.
Our two fractions are multiplied together from here,
15/52 * 14/51
We can start by simplifying a little bit; the numbers 14 and 52 share a 2;
15/26 * 7/51
Our result is 35/442
Depending on whether you choose to maintain it in fractional, ratio, or percentage form, the result of dividing is around 0.0791, which rounds to 7.91%.
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in hypothesis testing, the tentative assumption about the population parameter is group of answer choices
The goal of a hypothesis test is to determine if the data can refuse an assumption a parameter or a population.
Statistical hypothesis test: A statistical hypothesis test is a technique for determining whether the available data are sufficient to support a specific hypothesis. We can make probabilistic claims about population parameters through hypothesis testing.
The purpose of a hypothesis test is to ascertain whether the data can refute a parameter or population assumption.
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a busy student must complete 3 problem sets before doing laundry. each problem set requires 1 day with probability 2/3 and 2 days with probability 1/3. let b be the number of days a busy student delays laundry. what is ex(b)
The value of expected time ex(b)=1 day approximately if b is the number of days a busy student delays Laundry.
What is meant by expected time?The basic anticipated value formula is (P(x) * n): the probability of an occurrence multiplied by the number of times the event occurs.
The expected value (also known as the expectation, expectancy, mathematical expectation, mean, average, or first moment) is a generalization of the weighted average in probability theory. The anticipated value is the arithmetic mean of a large number of independently chosen random variable outcomes.
Let b be the number of days a busy student puts off doing laundry.
The given information is tabulated as below:
Days(b) 1 2
Probability, p(b) 2/3 1/3
The expected time is given as,
E(b)=∑i=1ᵇp(b)
=(1×(2/3))+(2×(1/3))
=4/3
=1.3333
Therefore, the value of ex(b):
1.3333 day ≈ 1 day
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if UVWX is a parallelogram, what is the value of y?
Answer:
B. 60
Step-by-step explanation:
Side VU must be equal to side WX
15 = (1/4)y
divide both sides by 1/4
15 / (1/4) = y
60 = y
pls help 81 points pls I need help don't guys this assignment is worth 50 points
I have a D- in math right now pls don't guys pls and its almost midterms so i need this A+
so pls don't guess.
Answer:
6,942 steps left!
Step-by-step explanation:
OK so this is easy so we know that if 1 / 19 = 0.052 we minus that by - 3 because - 3 is our exponent that gives us 3.052 so now we just take 3.052 - 10,000 which gives us exactly 6942 you two steps so he needs 6942 steps left
Answer:
3,141 steps
Step-by-step explanation:
Let x be equal to the number of steps he needs to reach his goal
10,000 = [tex](\frac{1}{19} )^{-3}[/tex]+ x
10,000 = 6,859 + x
3,141 = x
How many solutions does this linear system have Y =- 6x 2 and 12x 2y =- 4 Brainly?.
The linear system of equation y =-6x+2 and 12x+ 2y =- 4 has only one solution.
The linear equation is y = -6x+2 .
Now for any value of x we find the value of y ,
at x=0 ,y = 2
at x=1 , y = -4
at x=-2 , y = 14
Hence there are infinitely many solutions on the line . All points on the straight line are solutions.
The collection of variable values in a linear equation that yields every feasible solution is referred to as the "solution of a linear equation." In order to model real-world issues, linear equations include unknown quantities as one or more variables.
The locations where the lines or planes used to illustrate the linear equations intersect or meet are known as the solutions. The set of values for each variable in a system of linear equations is known as the solution set.
Disclaimer: the complete question is :
How many solutions does this linear system have Y =- 6x + 2 and 12x + 2y =- 4?.
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Is AAS and SAA same?.
No they are not the same . AAS stands for Angle Side Angle and SAA stands for Side Angle Angle .
can someone please help me? ive been stuck on this for 5 hours
In order to keep the Bermuda Triangle on the Flat Earth from toppling over, it was balanced on the hole which leads to the interior of the hollow Earth. If the vertices of the Bermuda Triangle are given by (1,3) , (2,7) , and (6,2). In order to find the hole we will need to find the intersection of at least 2 lines. Name 2 points through which one of those lines will pass (in the form (x,y),(x,y))
The following are the two lines: y = 4x - 1. y = -1.25x + 10.5.
Their point of intersection is: (2.19, 7.76).
The two vertices through which the line y = 4x - 1 pass are as follows:
(2.19, 7.76) and (3,11).
The slope is:
m = (7 - 3)/(2 - 1) = 4.
Hence:
y = 4x + b.
When x = 1, y = 3, the intercept b is calculated as follows:
3 = 4 + b
b = -1.
The first line is then: y = 4x - 1.
The points for the second line are (2,7) and (6,2).
As a result, the slope is m = (2 - 7)/(6 - 2) = -5/4 = -1.25.
The solution is y = -1.25x + b.
When x = 2, y = 7, therefore the intercept b is as follows:
7 = -1.25(2) + b
b = 10.5.
As a result, the second line is:
y = -1.25x + 10.5.
The intersection's x-coordinate is as follows:
4x - 1 = -1.25x + 10.5
5.25x = 11.5
x = 11.5/5.25
x = 2.19.
The intersection's y-coordinate is:
y = -1.25(2.19) + 10.5 = 7.76.
Another position where the line y = 4x - 1 intersects is:
y = 4(3) - 1 = 11.
As a result, point (3,11).
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A solar panel can generate power at a maximum rate of 400 kilowatts per day. When it is cloudy, it can only generate 5 kilowatts per hour and when the sky is clear, 32 kilowatts per hour. Let X and Y represent the number of hours when the sky is cloudy and clear, respectively. What is the inequality that represents this problem?
The inequality representing the problem is 5x+32y≤400
What is an inequality?A relationship between two expressions or values that are not equal to each other is called inequality.
Given that, A solar panel can generate power at a maximum rate of 400 kilowatts per day. When it is cloudy, it can only generate 5 kilowatts per hour and when the sky is clear, 32 kilowatts per hour.
According to question,
5x+32y≤400
Hence, The inequality representing the problem is 5x+32y≤400
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Jamie buys a box of blue tiles that will cover 4ft2 . What percent of the floor can she tile using this box ? Does Jaime need to buy another box of blue tiles explain
The blue tiles on the floor is an illustration of proportions. The blue tiles will cover 25% of the floor
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three.
The relations between variables, either direct or inverse proportional, can be built to find the desired measures in the problem.
From the complete question, the dimension of the floor is 4 ft by 4 ft.
So, the area of the floor
Area = 4 x 4
Area = 16
The blue tiles cover 4 square feet.
So, the percent of floor is:
= 4/16 x 100
= 1/4 x 100
= 25%
Hence, the blue tiles will cover 25% of the floor. Also, he doesn't need to buy another set of blue tiles.
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An event manager is tracking participation in a tournament by age group. The manager created the following
histogram
Number of People
30
20
10-
0
10%
What percentage of the tournament participants are under the age of 20? Round to the nearest whole percent.
23%
30%
Tournament Participants
077%
0-19 20-39 40-59 60-79
Age Group (yr)
According to the histogram, the percentage of the tournament participants are under the age of 20 is 50%.
What is a histogram?A histogram approximately represents a distribution of grouped data with numerical values.
It uses rectangular bars to show the frequency of data items in successive numerical intervals of equal sizes.
Age Group (year) Number of People
0 to 19 30
20 to 39 20
40 to 59 10
60 to 79 0
Total 60
Percentage of ages 0-19 = 30/60 x 100 = 50%
Thus, using the histogram, we can assure the percentage of the tournament participants are under the age of 20 is 50%.
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xplain your choice. this statistic is biased, but it has a much lower standard deviation than the other two. this statistic is unbiased and has the smallest standard deviation of the three. the standard deviation of this statistic isn't the lowest, but it is the only unbiased statistic out of the three. the standard deviation of this statistic isn't the highest, but it is the only unbiased statistic out of the three. this statistic is biased, but it has a much higher standard deviation than the other two. this statistic is unbiased and has the largest standard deviation of the three.
The recommended statistic is statistic II because this statistic is unbiased and has the smallest standard deviation of three.
How to choose the recommended statistic?Unbiased statistic is more accurate than biased statistic because which on sampling distribution mean equal to population parameter.
Standard deviation is value of dispersed of observed value sampling around population parameter. Smaller standard deviation can be equated with a smaller deviation of data. Which in unbiased statistic means lots of value closer to population parameter.
If even statistic is unbiased but standard deviation high (statistic III) it not recommended because lots of value is not close enough to population parameter.
Thus, the recommended statistic is unbiased statistic and have smallest standard deviation which is statistic II.
Your question is incomplete, but most probably your full question was (image attached)
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What is the equation of the function that is graphed as line a?
y = -2 x
y = x + 1
y = x - 1
y = 2 x + 1
Answer: D. y = 2 x + 1
Step-by-step explanation:
a group of five friends go to a restaurant for dinner. the restaurant offers 20 different main dishes. (a) suppose that the group collectively orders five different dishes to share. the waiter just needs to place all five dishes in the center of the table. how many different possible orders are there for the group? (b) suppose that each individual orders a main course. the waiter must remember who ordered which dish as part of the order. it's possible for more than one person to order the same dish. how many different possible orders are there for the group? (c) suppose that each individual orders a main course. the waiter must remember who ordered which dish as part of the order. however the friends agree that no two people will order the same dish. how many different possible orders are there for the group?
The number of different possible orders that are there for the group is 15504 .
In the question ,
it is given that ,
total number of friends = 5 ,
the number of dishes that restaurant offers for dinner = 20 dishes .
It is given that, group collectively orders 5 different dishes to share and waiter just needs to place all 5 dishes in the center of the table.
So , the 5 dishes from the 20 dishes can be selected in ²⁰C₅ ways .
²⁰C₅ = 20!/(15! * 5!)
= 20*19*18*17*16*15! / (15! * 5!)
= (20*19*18*17*16)/(5*4*3*2*1)
Simplifying Further , we get
= 1860480/120
= 15504 ways
Therefore , There are 15504 possible orders for the group .
The given question is incomplete , the complete question is
A group of five friends go to a restaurant for dinner. the restaurant offers 20 different main dishes. Suppose that the group collectively orders five different dishes to share. the waiter just needs to place all five dishes in the center of the table. how many different possible orders are there for the group ?
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Samantha has two anthills in her yard. The first anthill has 982 ants. The second anthill has one and one-third the amount of ants of the first hill. Which statement correctly compares the two anthills? The first anthill is one and one-third times as many than the second anthill. The first anthill is equal in size to the second anthill. The second anthill is one and one-third times as many than the first anthill. The second anthill is one and one-third times fewer ants than the first anthill. ( ANSWER ASAP 100 POINTS!!)
Answer:
C
Step-by-step explanation:
The problem states:
"The second anthill has one and one-third the amount of ants of the first hill."
Answer: C
Sabia and arlan bougth 45 book for r 30 each old all ok them at the rote of 24 find the different the money pent and return
If Sabia and Arlan bought 45 books for rs 30, then at the rate of rs 24, they can buy 34 books.
What is an arithmetic operation?It is defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division. It has basic four operators that are +, -, ×, and ÷.
It is given that, Sabia and Arlan bought 45 books for rs 30, then at the rate of rs 24, how many books they can buy,
Rs 30 = 45 book
Rs 30 = 45
Rs 1 = 45 / 30
Rs 24 = 3/2 × 24
Rs 24 = 34 books
Thus, if Sabia and Arlan bought 45 books for rs 30, then at the rate of rs 24, they can buy 34 books.
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What type of number is expressed in the form a bi?.
Number expressed in the form a+ bi is complex number.
What is Number system?A number system is defined as a system of writing to express numbers.
The number is expressed in the form a + bi
A complex number is a number of the form a + bi, where a and b are real numbers, and i is an indeterminate satisfying i² = −1.
The number a+bi, in which a is real number and b is imaginary number.
Hence, number expressed in the form a+ bi is complex number.
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Which is a way to solve the equation 4x = 128 if you do not know a power of 4 that equals 128?.
what is the following sum? assume x greater-than-or-equal-to 0 and y greater-than-or-equal-to 0startroot x squared y cubed endroot 2 startroot x cubed y superscript 4 baseline endroot x y startroot y endrootx squared y squared startroot y endroot minus 2 x y squared startroot x endroot2 x y startroot y endroot 2 x y squared startroot x endroot4 x y startroot x superscript 5 baseline y superscript 8 baseline endroot2 x y startroot x y endroot
The simplified equation is 2x y²√y + 2x y√y when the actual equation is √x²y³ +2√x³y⁴ +x y√y. Option -B is correct.
Given that,
The equation is
√x² y³ +2√x³y⁴ +x y√y
We have to simplify the equation.
We know that,
A mathematical statement that has a "equal to" symbol between two expressions with equal values is called an equation.
Take the equation
√x²y³ +2√x³y⁴ +x y√y
x y√y +2√x³y⁴ +x y√y
2√x³y⁴ + 2x y√y
2x y²√y + 2x y√y
Therefore, The simplified equation is 2xy²√y + 2x y√y when the actual equation is √x²y³ +2√x³y⁴ +x y√y. Option -B is correct.
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Answer:
B on edge
Step-by-step explanation:
If the coefficient of determination is a positive value, then the coefficient of correlation.
If the coefficient of determination is a positive value, then the correlation coefficient can be negative or positive, which means the value of the correlation coefficient is between -1 and +1. If the variable x increases, the variable y also increases, and if the variable x decreases, then the variable y also decreases.
What is the Coefficient of Determination?The coefficient of determination is a statistical measurement which examines how differences in one variable can be explained by the difference in a second variable, when predicting the outcome of a given event. The coefficient of determination is a number between 0 and 1 that measures how well a statistical model predicts an outcome. This provides a measure of how well observed outcomes are replicated by the model, based on the proportion of total variation of outcomes explained by the model.
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what is a continuity correction? (b) why do we use a continuity correction when we approximate a binomial probability distribution with a normal distribution but not when we approximate it with a poisson distribution?
A normal distribution is continuous, but a binomial distribution is not, and this difference is taken into account by the continuity correction factor. It is necessary to add a continuity correction factor when using a normal distribution to approach a binomial distribution. Just add or subtract, and you're done.
How does continuity correction work?When a discrete probability distribution is approximated by a continuous probability distribution, the continuity correction factor is utilized. The continuum correction factor serves as a link between the discrete binomial and the continuous normal distribution.
In statistics, why do we utilize probability distribution?By allowing us to evaluate the variability of occurrence or provide estimates of the likelihood that a specific event will occur, probability distributions aid in the modeling of our environment. They are a typical technique to explain and maybe anticipate the likelihood of an event.
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find the equation of the line shown
The equation of the line that shown in the graph is;
y = x + 3
What is the Point-slope form?The equation of the straight line has its slope and given point.
If we have a non-vertical line that passes through any point(x1, y1) and has a gradient m. then general point (x, y) must satisfy the equation
y-y₁ = m(x-x₁)
We know that Point-Slope Form:
y - y₁ = m(x - x₁)
Where x₁ - x coordinate and y₁ - y coordinate
m - slope
Point are (3, 6) and (4,5)
Then Slope m = 1
Now Write the equation as;
y - 6 = 1(x- 3)
y = x - 3 + 6
y = x + 3
Hence, the equation of the line that shown in the graph is;
y = x + 3
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Identify the property used in each step. 12.2 18.6 â€""4.3 (â€""18.6) 12.2 â€""4.3 18.6 (â€""18.6) 12.2 â€""4.3 [18.6 (â€""18.6)] 12.2 â€""4.3 (0) 12.2 â€""4.3 7.9
Properties used in the given equation is Commutative property, Associative property, Additive inverse, Identity property.
In a commutative property multiplication and addition which posses commutative property takes place without considering the order of arrangement of data.
12.2 + 18.6 + -4.3 + (-18.6)
12.2 + -4.3 _ 18.6 + (-18.6)
The second step results into the presence of a commutative property.
12.2 + -4.3 + [18.6 + (-18.6)] is an associative property because here, regrouping of numbers which gives the same result.
[18.6 + (-18.6)] is an additive inverse since the result is zero. Additive inverse occurs when the addition of a number to another number results into zero.
12.2 + -4.3 + (0) is an identity property.
This property occurs when the addition of any number with zero eventually resulted into that number.
So here we used 4 properties which are
Commutative property,
Associative property,
Additive inverse,
Identity property.
Given question is written in wrong language.
Here is the given question 12.2 + 18.6 + -4.3 + (-18.6)12.2 + -4.3 + 18.6 + (-18.6)12.2 + -4.3 + [18.6 + (-18.6)]12.2 + (-4.3) + (0)12.2 + -4.3 7.9
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help meeeeeeeeeeee pleaseee rnnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
The amount compounded at a rate of 8% over a period of 6 years is $8,551.56
Compound InterestThe compound interest is the interest-based on the initial principal amount and the interest collected over the period of time. The formula for compound interest can be derived from the formula for simple interest. The formula for simple interest is the product of the principal, time period, and rate of interest (SI = ptr/100). Before looking into to derivation of the formula for compound interest, let us understand the basic difference between simple interest, compound interest computation. The principal remains constant over a period of time, for simple internet computation, but for compound interest computation the interest is added to the principal, for compound interest computation. The compound interest formula is given below:
A = P(1 + r/n)^nt
Compound InterestP = principalr = rate n = number of times compoundedt = timeApplying the formula of compound interest here;
A = 5300(1 + 0.08/12)^12 * 6
A = $8,551.56
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the student government at a high school wants to conduct a survey of student opinion. it wants to begin with a simple random sample of 60 students. which of the following survey methods will produce a simple random sample?
The survey methods that will produce a simple random sample of 60 students in a high school is: Number the students in the official school roster. Use a table of random numbers to choose 60 students from this roster for the survey.
What is a simple random sampling?Simple random sampling is a type of probability sampling where the researcher randomly chooses a subset of participants from a population. Each part of the population has the same chance of being selected. Then, data is collected from as large a percentage as possible of the random subset.
The American Community Survey is an example of simple random sampling. In order to gather detailed data on the population of the US, the Census Bureau officials randomly choose 3.5 million households a year and use variety of methods to make them sure to fill out the survey.
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