5/45 = 1/9 represents the probability of the best-case scenario. 40/45 = 8/9 represents the probability of the worst-case scenario.
When two socks from the same pair are missing, the likelihood of the best-case scenario increases. As a result, all four pairs of socks are present. Now, 10C2 = 45 gives the total number of possible methods to choose 2 socks from a total of 5 x 2 = 10 socks. The probability of choosing one pair of socks from five pairs is equal to the number of ways to choose two socks from a pool of ten socks, and this is provided by the formula 5C1 = 5. given by 5 / 45 = 1 / 9. The worst case situation is when they are not from the same pair of socks. As a result, all three pairs of socks are present. Now, 10C2 = 45 gives the total number of possible methods to choose 2 socks from a total of 5 x 2 = 10 socks. 10C2 - 5C1 = 45 - 5 = 40 is the number of ways to choose two socks from a group of ten so that they are not from the same pair. given that by 40 / 45 = 8 / 9
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a kid is flying a kite and has reeled out his entire line of 150 ft of string. If the angle of elevation of the string is 65 then which expression gives the vertical height of the kite?
The vertical height of the kite is 165.5 ft
What are trigonometric ratios?Trigonometric Ratios are defined as the values of all the trigonometric functions based on the value of the ratio of sides in a right-angled
Given that, a kid is flying a kite and has reeled out his entire line of 150 ft of string, the angle of elevation of the string is 65°
We need to find, the vertical height of the kite,
If we see the figure (refer to the attachment), we can see that, this scene will make a right triangle, where the string of the kite will be the hypotenuse and the vertical height of the kite is the perpendicular,
Since, we need the vertical height, will use trigonometric ratios,
We have, hypotenuse and the references angle and need perpendicular,
We know that, Sine of an angle is the ratio of perpendicular to hypotenuse,
Therefore,
Sin65° = 150 / AB
AB = 165.5
Hence, the vertical height of the kite is 165.5 ft
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1. What would be a good first step to graph the solution to the following system?
y≥x+3
x<−2
A. Substitute x<−2 into the first inequality and simplify the result.
B.Graph each inequality separately.
C. Change the inequalities to equalities and solve the resulting system of linear equations.
D. Solve the first inequality for x because the second inequality is already solved for x.
2. Which system of inequalities is shown in the graph?
A. y −2x
B. y≥x−3 and y≤−2x
C. y>x−3 and y<−2x
D. y≤x−3 and y≥−2x
The first step to graph the solution to the system of equations given is option D. Change the inequalities to equalities and solve the resulting system of linear equations.
What is Linear Inequalities?Linear inequalities are defined as those expressions which are connected by inequality signs like >, <, ≤, ≥ and ≠ and the value of the exponent of the variable is 1.
1. Given system of inequalities are,
y ≥ x + 3
x < −2
In order to graph the solution, first we have to change the inequality symbols to equality and solve the resulting system of linear equations.
That is, solve y = x + 3 and x = -2
2. The equations of the given line are
y = x - 3
y = -2x
Take the linear equation y = x - 3.
The solution region of both contains the point (-1, 0).
0 = -1 - 3 = -4, correct inequality is 0 ≥ 4.
So the inequality is y ≥ x - 3.
Consider y = -2x
0 = 2, correct inequality is 0 ≤ 2.
So the inequality is y ≤ -2x.
Hence the system of inequalities shown in the graph are option B. y ≥ x - 3 and y ≤ -2x.
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20% of a is 11. what is a
Answer:
20% of 11 is 2.2
Step-by-step explanation:
11 x .20 = 2.2
question 9 a client makes loud vocal statements frequently. to collect data on this, you divide the session into shorter timed intervals. if the behavior occurs at any point during the interval, you record an occurrence. what kind of discontinuous measurement procedure are you using?
The kind of discontinuous measurement procedure that is used is partial interval recording
Given that,
A client frequently shouts things out loud. You break up the session into shorter timed segments in order to get data on this. You record an event if the behavior happens at any time throughout the interval.
To find : which discontinuous measuring technique are you employing?
An interval recording technique is partial interval recording. An interval recording approach involves watching to see if a behaviour happens or not within predetermined intervals of time. After determining the duration of an observation session, the time is divided into shorter segments that are all of the same length.
So, partial interval recording is the type of discontinuous measuring technique that is applied.
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An investor deposited $7,590 in a savings account 10 years ago that earns simple annual interest. today, the account balance is $11,916.30. what is the simple interest rate?
To find the simple interest rate, you can use the following formula:
Simple interest rate = (ending balance - starting balance) / (starting balance * number of years)
In this case, the starting balance is $7,590, the ending balance is $11,916.30, and the number of years is 10. Plugging in these values, we have:
Simple interest rate = ($11,916.30 - $7,590) / ($7,590 * 10)
= ($4,326.30) / ($7,590 * 10)
= $4,326.30 / $75,900
= 0.057 or 5.7%.
Therefore, the simple interest rate is 5.7%.
Answer:
Suppose an investor invested $7,590 in a savings account with basic yearly interest 10 years ago. The account currently has a balance of $11,916.30. 5.7% is the basic interest rate.
Why do we call something "interesting"?
You must pay interest on money you borrow, and you must add interest to money you lend. The most typical approach to display interest is as a percentage of the annualized principal amount of a loan. This ratio represents the interest rate on the loan.
What is meant by an interest example?
By examining the rate, a person can figure out exactly how much interest they will accrue or pay on a loan. For example, if a $100 loan had a nominal interest rate, there would be a $6 interest fee.of 6% ($100 X 0.06). Despite an increase in loan size, the rate doesn't change. Even if the loan amount were increased to$1,000, the borrower would still be expected to pay 6% of the total.
Step-by-step explanation:
Lindsay and Lorraine are trying to match the jump rope world record. Together, they need to jump 48 times in a row. Lindsay has gotten 14 jumps in a row and Lorraine has gotten 13. Write an equation and show your work to determine how many more jumps they need to complete. Use the variable j to represent the unknown number of jumps.
Together, Lindsay and Lorraine needs to jump 21 more jumps in a row.
What is Addition?Addition is one of the basic mathematical operations where two or more numbers is added to get a bigger number.
The process of doing addition is also called as finding the sum.
Number of jumps got by Lindsay = 14
Number of jumps got by Lorraine = 13
Total number of jumps gotten by both = 27
Let j be the number of jumps they need to jump more.
j = 48 - 27
j = 21
Hence 21 more jumps would be needed.
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[tex]( {x}^{2} + x + 12) \div (x - 5)[/tex]
Divide Using synthetic division
The division of the given expressions gives quotient as x + 6 and the remainder 42.
What is Synthetic Division?Synthetic division is the method of division used to divide a polynomial expression with the binomial.
We have to divide x² + x + 12 by x - 5.
Write the coefficients of the dividend in the order of descending powers and the constant term in the binomial as :
5 | 1 1 12
Write the leading coefficient in the bottom row and then multiply the 1 written on the bottom row with 5 and write it beneath the next coefficient of the dividend.
5 | 1 1 12
5
1
Now add 1 + 5 to get 6 and write in the bottom row.
Repeat the process by multiplying 6 with 5 and adding up.
5 | 1 1 12
5 30
1 6 42
Here, 42 is the remainder and 1 and 6 are the coefficients of the quotient.
Quotient = x + 6
Remainder = 42
Hence the quotient and remainder are x+6 and 42 respectively.
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WILL MARK BRAINLIEST
On a school trip the ratio of adults to students is 1: 10.
All of the students are in year 10 or year 11.
The ratio of year 10 to year 11 is 1: 4.
What fraction of all the people on the trip are year 11 students?
(b)
In a cinema the ratio of adults to children is 2: 3.
The children are either boys or girls.
The ratio of boys to girls is 5: 2.
What fraction of all the people in the cinema are girls?
Answer:
(a) In a school trip the ratio of adults to students is 1:10 , and all of the students are in year 10 or year 11. The ratio of year 10 to year 11 is 1:4, so the fraction of all the people on the trip who are year 11 students is 1/5.
(b) In a cinema the ratio of adults to children is 2:3, and the children are either boys or girls. The ratio of boys to girls is 5:2 , so the fraction of all the people in the cinema who are girls is 2/5.
The graph on the right shows the theoretical probability of getting a given number heads in ten flips of a fair coin.
If this experiment was performed many times you would expect an average of
heads.
If this experiment was performed many times you would expect that the average number of heads is 5.
What is probability?It is the chance of an event to occur from a total number of outcomes.
The formula for probability is given as:
Probability = Number of required events / Total number of outcomes.
We have,
From the graph,
The theoretical probability of getting 5 heads in ten flips of a fair coin.
= 0.25
= 25%
And,
The theoretical probability of getting 0 and 10, 1 and 9, 2 and 8, 3 and 7, and 4 and 6 heads is equal.
The average number of heads.
= (0 + 10)/2 = 5
Similarly,
(1 + 9)/2 = 10/2 = 5
(2 + 8)/2 = 10/2 = 5
(3 + 7)/2 = 10/2 = 5
(4 + 6)/2 = 10/2 = 5
So,
If this experiment was performed many times you would expect that the average of heads is 5.
Thus,
The expected average number of heads is 5.
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Answer:
5
Step-by-step explanation:
The answer above is correct.
ross wants to conduct a survey
The method that Ross can use to make valid conclusions on the candidate in the lead is C. Put the names of all the students in a hat, and draw 100 names. Ask those students whose names are drawn.
How should Ross conduct the survey ?When conducting the survey, it is important the Ross uses a random sample from the classmates who will be the ones to select the class treasurer.
To do this, one method of random sampling Ross can use is to draw 100 names from a hat after placing all the pupils' names inside. Students whose names were drawn can be questioned.
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The full question is :
Ross wants to conduct a survey of his 400 classmates to determine which candidate for class treasurer, Warren or Willa, is in the lead in the upcoming election.
Ross will ask the question, “If the election were today, which candidate would get your vote?”
Which of the following methods of surveying his classmates will allow Ross to make valid conclusions about which candidate is in the lead?
Select all that apply.
*Ask all of Warren's friends.
*Ask the other members of Willa's cheerleading squad.
*Put the names of all the students in a hat, and draw 100 names. Ask those students whose names are drawn.
*Ask every student in the class.
mass of a banana and can of cola
The mass of a banana is about C. 150 g.
A can of cola would be around A. 300 ml.
What is the mass of a banana ?From the options, the best estimate for the mass of a banana is 150 g. This is because 1. 5 kg is much too heavy for a single banana which makes 15 kg ridiculously heavy. 15 g would be too light however as this is the mass of about 6 pennies.
What is the quantity of a can of cola ?There are several quantities for a can of cola, and they are all in 100s of milliliteters. The most likely quantity of a can of cola from the options is therefore 300 ml.
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The level of significance in hypothesis testing is the probability of?
The level of significance in hypothesis testing is the probability of obtaining a result that is at least as extreme as the observed result, assuming that the null hypothesis is true, and is usually denoted by the symbol α (alpha).
In hypothesis testing, the level of significance is the probability of obtaining a result that is at least as extreme as the observed result, assuming that the null hypothesis is true. It is also known as the p-value and is usually denoted by the symbol α (alpha). The formula for calculating the level of significance is:
α = P (Statistic ≥ Observed Statistic | H0 is true)
For example, suppose we are testing a hypothesis that the mean height of all people in a population is 160cm. We select a sample of 50 people and measure the mean height to be 162cm. Assuming the null hypothesis is true, the level of significance is calculated as follows:
α = P (Statistic ≥ 162 | H0 is true)
This p-value measures the probability of obtaining a result that is at least as extreme as the observed result (162cm), if the null hypothesis is true. If this p-value is less than the predetermined significance level (usually 0.05 or 0.01), then the null hypothesis is rejected and we accept the alternative hypothesis.
The level of significance in hypothesis testing is the probability of obtaining a result that is at least as extreme as the observed result, assuming that the null hypothesis is true, and is usually denoted by the symbol α (alpha).
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the histogram below presents the compressive strengths of a sample of concrete blocks hardened for 28 days. one rectangle from the histogram is missing. what is its height?
The missing rectangle has a relative frequency of 0.15, and this is the same as the height.
Let us define what a frequency and relative frequency are
The frequency of a datum is the number of times a given item (datum) appears in the data set.
While the relative frequency is the fraction or proportion of times taken from the whole in which an item/datum occurs.
So, from the image I uploaded, the relative frequency column represents the height of the histogram. Let the height of the missing rectangle be x.
Therefore the heights of the rectangles written from left to right are 0.05, 0.1, 0.15, x, 0.25, 0.2, and 0.1.
From the definition of relative frequency, the total sum of relative frequency is 1, if represented as decimals or fractions it can either be expressed in percentage, or decimal (fractions). In this question, it is represented in decimal, and the sum of all the relative frequency is 1.
0.05 + 0.1 + 0.15 + x + 0.25 + 0.2 + 0.1 = 1 ;
0.85+ x =1
Therefore, x = 1 - 0.85= 0.15
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(4.6x10^6)(1.1x10^7)
Answer:
[tex]5.06*10^{13}[/tex]
Step-by-step explanation:
[tex](4.6*10^6)(1.1*10^7)=(4.6*1.1)(10^6*10^7)=5.06*10^{13}[/tex]
given a standardized normal distribution, what is the value of z if only 2.5 perent of all possible z values are larger?
Given a standardized normal distribution, 1.96 is the value of z if only 2.5 perent of all possible z values are larger.
In a standard normal distribution, 2.5% of all possible z-values are larger than a certain value of z, which is denoted by z*. We can use this information to find the value of z* by using the cumulative distribution function (CDF) of the standard normal distribution. The CDF of the standard normal distribution is given by the equation:
Φ(z) = 1/2 * (1 + erf(z/sqrt(2))) , where erf(z) is the error function.
Since 2.5% of all possible z-values are larger than z*, we can set Φ(z*) = 1 - 0.025 = 0.975. Then, we can solve for z* by finding the inverse of the CDF using the inverse error function:
z* = sqrt(2) * erf^(-1)(2 * Φ(z*) - 1) , where erf^(-1)(z) is the inverse error function.
Using this formula, we find that z* = 1.96, which means that if a standardized normal distribution is given, a z-value of 1.96 corresponds to 2.5% of all possible z-values being larger.
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-4(x-2)=-2(x-17/2)
solve for x. show your work.
Answer: x= - 9/4
Step-by-step explanation:
1. Move the variable to the left, and change its sign.
-4x+8+2x=17
2. Collect like terms
-2x=17-8
3. Divide each side by -2
-2x=9
Answer: x= - 9/2
the points on the graph below show the total cost for different numbers of tickets to a concert. as shown, 1 ticket costs $20, 2 tickets cost $40, 3 tickets cost $60, and 4 tickets cost $80. what is the slope of the dashed line on the graph? responses 120 1 20 1 20 12 1 2 1 2 2 2 20
The slope of the dashed line on the graph is 1 (rise/run). This can be determined by dividing the difference in the cost of tickets (20) by the difference in the number of tickets (1).
The slope of the dashed line on the graph is 1. To determine the slope, you need to divide the rise (difference in the cost of tickets) by the run (difference in the number of tickets). In this case, the difference in the cost of tickets is 20 (from $20 for 1 ticket to $40 for 2 tickets). The difference in the number of tickets is 1 (from 1 ticket to 2 tickets). Therefore, the slope of the dashed line on the graph is 1 (20/1). This means that the cost of tickets increases by $20 for every additional ticket purchased. For example, if you purchase 3 tickets, the total cost will be $60 (3 tickets x $20 = $60). If you purchase 4 tickets, the total cost will be $80 (4 tickets x $20 = $80).
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5.060 x 10 3rd power /km
Answer:
Step-by-step explanation:
charge it paigon
Will the following three lengths form a triangle? If so, classify the triangle. 8, 9, 10
The three lengths 8, 9 and 10 form a triangle.
What is Triangle Inequality?In Euclidean geometry stating that any two triangle sides added together must be greater than or equal to the third side; represented by the symbols a + b ≥c. The basic tenet of the theorem is that a straight line connects any two places.
Given:
Sides: 8, 9, 10
As from Triangle Inequality the sum of two sides are greater than the third side of triangle.
So, 8 + 9 > 10
9 + 10 > 8
10+ 8> 9
Since the triangle inequality satisfied.
Thus, the triangle can form using sides 8, 9, 10.
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Calculate the distance between each pair of numbers on a number line.
1. 5 and -2
2. -8 and -17
3. 28 and -12
4. -17 and 15
5. 33 and -2
The required distance between each pair of numbers on a number line is below in the solution part.
What is Number Line?In math, a number line can be defined as a straight line with numbers arranged at equal segments or intervals throughout. A number line is typically shown horizontally and can be extended indefinitely in any direction.
1. The distance between 5 and -2 on a number line is |5-(-2)| = 7 units.
2. The distance between -8 and -17 on a number line is |-17-(-8)| = 9 units.
3. The distance between 28 and -12 on a number line is |28-(-12)| = 40 units.
4. The distance between -17 and 15 on a number line is |15-(-17)| = 32 units.
5. The distance between 33 and -2 on a number line is |33-(-2)| = 35 units.
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If m∠A=12x+3 and m∠B=5x+2, what is m∠A
Answer:
63°
Step-by-step explanation:
The sum of the interior angles of a triangle add up to 180.
90 + (12x + 3) + (5x + 2) = 180 now solve for x
17x + 95 = 180
17x = 180 - 95 = 85
x = 85/17 = 5
m∠A = 12(5) + 3 = 63
WILL GIVE BRAINLIEST AND 100 PTS!!!!! HELP ASAPPPPP!!! SEE IMAGE BELOW!
Answer: (1, -1)
Step-by-step explanation:
you would first start out with
5x+2y=3
4x-8y=12
you would then subsitute the value of x
x=3/5-2/5 y
4x-8y=12
you then solve the equation
4(3/5-2/5 y) -8y=12
you then subsitute the vaulue of y
y=-1
then you solve the equation
x=3/5-2/5 x(-1)
A possile solution is
x=1
you should then check the solution
(x,y) = (1,-1)
Carter drove 210 miles in 7 hours. If he drove at a constant rate, how far did he travel each hour?
Answer: 30 miles
Step-by-step explanation:
We are given a constant rate of 210 miles in 7 hours. Since we are trying to find how far Carter travelled in 1 hour, we can set up a proportion.
[tex]\frac{210}{7} =\frac{x }{1}[/tex] [cross multiply]
[tex]210=7x[/tex] [divide both sides by 7]
[tex]x=30[/tex]
Therefore, Carter travelled 30 miles in one hour.
how do i solve this asap
Answer:
Step-by-step explanation:
when there is a plus before a negative, ignore it, the negative makes it irrelavant.
-4-3=-7
-4y-7
A linear function is shown on the graph. A linear function beginning with an open circle at negative 4 comma negative 1 and ending with a closed circle at 6 comma 4. What is the domain of the function? {x | −4 < x < 6} {x | −4 < x ≤ 6} {y | −1 < y < 4} {y | −1 < y ≤ 4}
Any x-value in the range of -4 to 6 (not including 6) is included in the domain of the linear function.
What is linear function?I linear function is a mathematical expression involving variable that when craft create is straight line linear function are used to model relationship between two variable such is cost and revenue price in demand in distance and time linear function can also be used to solve equation and the specialily useful for predicting future outcomes.
The domain of the linear function is {x | −4 < x < 6}, which means that the x-values of the function are all real numbers greater than -4 and less than 6. This means that any x-value in the range of -4 to 6 (not including 6) is included in the domain of the linear function.
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a toll booth has 12 cars waiting to go through. in how many different ways can the first five cars go through, if the order in which the pass distinguishes one set of five from another?
There are 95,040 different ways for the first five cars to go through the toll booth.
The first car can be chosen in 12 ways. After the first car has been chosen, the second car can be chosen in 11 ways. This process continues, so the third car can be chosen in 10 ways, the fourth car can be chosen in 9 ways, and the fifth car can be chosen in 8 ways.
So the total number of ways to choose the first five cars is as follows:
12 x 11 x 10 x 9 x 8 = 95,040
Therefore, there are 95,040 different ways for the first five cars to go through the toll booth.
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what does a correlation coefficient of 0 indicate?
Answer:
no linear relationship exists between the two variables being compared
Step-by-step explanation:
The teacher bought new crayons for her class. She bought 7 packs of 9 crayons. She already has 17 crayons in her classroom. She wants to divide the crayons evenly between her 10 students. Write an equation and show your work to determine how many crayons each student will receive. Use the variable for the number of crayons each student receives.
Please help!
Answer:
80 divded by 10 is c c=8
in 2007 in the united states there were approximately 480 cars for every 1,000 people. the total number of cars in the united states in 2007 was closest to
Nearly 150,000,000 cars were registered in the US as a whole in 2007. China, India, and the United States are the three nations with the largest populations on earth.
Average lifespan and child mortality rate are indeed the two key metrics that most accurately reflect a citizenry's standard of living.
The population of the globe is projected to reach about 10 billion people in 2050. Africa and Asia will see the most expansion in population if indeed the patterns in demographic persist.
Cultural practices, governmental regulations, and monetary support, as well as female employment prospects as well as education levels, all have an impact on the overall birthrate of a community.
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17. Crystal Porter wants to purchase a new minivan. It regularly sells for $24,987. The manufacturer is offering a
sale price of $18,994. What is the markdown?
a. $4,998
b. $5,665
c. $5,993
d.$6,007
Answer:
C. $5,993
Step-by-step explanation:
Markdown is an immediate reduction in the price of an item, performed by a merchant during a special sale. A markdown discount is most often a percentage decrease in the original price. The purpose of a markdown sale is to create a demand of a product during the time period of the sale.