In general, there are n>3 lines in the plane. Show that at least n - 2 triangles are formed by these lines.
Let's consider the following diagram, where each line is labelled with a letter:
A-B-C-D-E
Since each line intersects with at least one other line, there are at least n-2 triangles that can be formed. For example, triangle ABC, triangle ABD, triangle ABE, triangle BCD, triangle BDE, and triangle CDE are all triangles that can be formed from our five lines.
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according to the book of odds, the probability that a randomly selected u.s. adult usually eats breakfast is 0.61.1a) explain what probability 0.61 means in this setting.
The probability of finding such people will get closer to 0.61 as the sample gets bigger.
a) This means that if you were to take a large sample of US adults and inquire them about having breakfast, about 61%(i.e. 0.61) will say that they usually have breakfast.
b) It is, for sure, expected that if we take a sample of 100, around 61% of these americans will say that they usually eat breakfast. But if the number will be 61 exactly is not a certainty and it will vary from sample to sample.
The probability of finding such people will get closer to 0.61 as the sample gets bigger.
Explanation has been provided in the answers above due to their descriptive nature.
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Write this number in word form 84,052
Answer:
eighty-four thousand fifty-two
Step-by-step explanation:
the way i think about it is writing it as the sum of the digits together.
80000+4000+50+2
eighty-four thousand fifty-two
Remember
to estimate first
by rounding and multiplying
to find where the first digit
goes in the quotient.
1. 1,593/13
Answer:
Step-by-step explanation:
1593/13
122.538
answer: 122.5
What is the length of side bc of the triangle? enter your answer in the box. Units.
The length of the side BC Iis equal to 28 units which we get by using congruency.
What is congruency?In other words, if the lengths of the sides and angles are the same for two shapes, they are congruent (the same in shape and size). When two triangles are congruent, it is frequently useful to know.
* In triangle ABC
∵ Angles B and C comes to be congruent
∴ m∠B = m∠C
* In any triangle if two angles are equal in measure, then the triangle is isosceles means the two sides which opposite to the congruent angles are equal in length
∴ AB = AC
∵ AB = 4x - 7
∵ AC = 2x + 7
∴ 4x - 7 = 2x + 7 ⇒ collect same terms
∴ 4x - 2x = 7 + 7
∴ 2x = 14 ⇒ divide both the sides by 2
∴ x = 14 ÷ 2 = 7
* Now we can find the length of side BC
∵ The length of side BC = 4x ⇒ substituting the value of x
∴ The length of side BC = 4 × 7 = 28 units
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Correct QuestionWhat is the length of side BC of the triangle? Enter your answer in the box. units Triangle A B C with horizontal side B C. Vertex A lies above side B C. Angle B and angle C are marked congruent. The length of side A C is labeled as 2 x plus 7. The length of side A B is labeled as 4 x minus 7. The length of side B C is labeled as 4 x.
i want one halve of a cupcake for myself 4 halves for my friend and 3 halves for my other friend
Answer: Split it into 8 pieces.
Step-by-step explanation: If there is 4 halves for your friend, and 3 halves for your other friend, that will be 7. If you add another one, it will be 8. Therefore, you should split the cupcake into 8 pieces.
solve (4,19) and (9,24) in y=mx+b form
Answer:
Equation of the line:
y = x + 15
slope: 1
Can I get 10 comments in 10 minutes
Answer: Welp, here it is.
Step-by-step explanation:
I clicked the keyboard :)
hhhhhhhhhhhhhhhhhhhhhhhhh
what is the ratio of 500 students and 10 classrooms
Answer:
FOR EVERY 1 CLASSROOMS THERE ARE 50 STUDENTS, SO 50 STUDENTS IN EACH CLASSROOM the ration would be 50:1
Step-by-step explanation:
Answer:
I think its 50:1
Step-by-step explanation:
Darren bought 53.11 pounds of fruit for a class party. The class ate 0.6 pounds of the fruit. How much fruit is left?
At a sale, coats were sold for $104 each. If the coats originally cost $160 each, what percentage of its original price was a coat sold for?
well, if we take 160 to be the 100%, what is 104 off of it in percentage?
[tex]\begin{array}{ccll} amount&\%\\ \cline{1-2} 160 & 100\\ 104& x \end{array} \implies \cfrac{160}{104}~~=~~\cfrac{100}{x} \\\\\\ \cfrac{ 20 }{ 13 } ~~=~~ \cfrac{100}{x}\implies 20x=1300\implies x=\cfrac{1300}{20}\implies x=\stackrel{\%}{65}[/tex]
Coats sold for 65% of its original price at a sale.
What is percentage?Percentage is defined as a given part or amount in every hundred. It is a fraction with 100 as the denominator and is represented by the symbol "%".
Given that, at a sale, coats were sold for $104 each and the coats originally cost $160 each.
Let x% of $160 be $104.
Now, x% of 160=104
x/100 ×160=104
x=104/160 ×100
x=0.65×100
x=65%
Therefore, 65% of coats original price was a coat sold for.
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chegg how many cards must be selected from a standard deck of 52 cards to guarantee that at least four hearts, four diamonds and five clubs are selected?
26 cards must be selected from a standard deck of 52 cards to guarantee that at least four hearts, four diamonds and five clubs are selected.
We have given that standard deck of 52 cards.
And we have to find the number of cards must be selected from a deck to get at least four hearts, four diamonds and five clubs.
So four hearts + four diamonds + five clubs = 13 cards
The worst case, we may select all the spade i.e 13 cards before any heart, diamond and club.
So the guarantee that at least four hearts, four diamonds and five clubs are selected, 13 + 13 = 26
Therefore 26 cards must be selected from standard deck of 52 cards to guarantee that at least four hearts, four diamonds and five clubs are selected.
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HELP PLEASE!!!! URGENT!!
573x2883 long divison
Answer:
The answer is 165,1959 if you don't need to show work.
Kiara has 80 lollipops and 32 snicker bars. She is feeling individual bags for Halloween in with like each bag contains the same combination of lollipops and snicker bars. How many bags can she feel if she wishes to have no candy left over? How many lollipops is snicker bars are in each bag?
Answer:
16 bags: 2 snicker bars and 5 lollipops in each
Step-by-step explanation:
The greatest common factor of 80 and 3 is 16.
80÷5=16
32÷2=16
And 5 represents the lollipops and 2 represents the snickers.
your parents gave you $50 to take your brother and sister to the movies. your ticket cost $8.25 and your siblings cost $4.25. if you spent an additional $20 on soda and popcorn, how much money did you bring home with you?
The money left is $13.25.
Given data,
Your parents handed you $50 to spend on movie tickets for your sister and brother. You paid $8.25 for your ticket, while your siblings paid $4.25.
To know how much money you bring home after spending an extra $20 on soda and popcorn,
Your entry cost is $8.25
$4.25 for the brother's ticket
Sister's entry fee is $4.25.
$20 for soda and popcorn.
Total = 8.25 + 4.25 + 4.25 + 20.00 = $36.75
You received $50 from your parents.
You have spent $36.75.
Balance: 50.00 - 36.75 = $13.25
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If the equation of f(x) goes through (1, 4) and (4, 6), what points does f-1(x) go through?.
The positions through which the equation of f^-1(x) travels are: (4, 1), (6, 4)
What are equations?A mathematical statement called an equation is comprised of two expressions joined together with the equal sign.
A formula would just be 3x - 5 = 16, for instance.
When this equation is solved, we observe that the value of the variable x is 7.
So, (1, 4) and (4, 6) are points through which the equation of f(x) goes.
If the f (x) equation contains (x, y).
Therefore, the f^-1(x) equation is as follows: (y, x).
Here, the f (x) equation passes through the following points: (1, 4) and (4, 6).
So, (4, 1) and (6, 4) are the points through which the equation of f^-1(x) goes through.
Therefore, the positions through which the equation of f^-1(x) travels are:
(4, 1), (6, 4)
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Correct question:
If the equation of f(x) goes through (1,4) and (4,6), what points does f^-1(x) go through?
special industrial battery must have a life of at least 400 hours. a hypothesis test is to be conducted with a 0.02 level of significance. if the batteries from a particular production run have an actual mean use life of 391 hours, the production manager wants a sampling procedure that only 10% of the time would show erroneously that the batch is acceptable. what sample size is recommended for the hypothesis test? use 45 hours as an estimate of the population standard deviation. (round your answer up to the nearest integer.)
488601 is the sample size recommended for the hypothesis test.
Given,
The life of the battery = 400 hours
Significance level = 0.02
Mean = 391 hours
The production manager needs a sampling technique that would incorrectly indicate that the batch is acceptable only 10% of the time.
We have to find the sample size recommended for the hypothesis test;
Here,
Margin of error E = Z(α/2) × (σ/n²)
From this equation we get n as
n = (z × σ /E)^2
α = 0.02
From the standard normal table value we get
z(α/2) = 2.33
σ = 30
E= 0.1
Therefore,
n =(2.33*30/0.1)^2
n =488601
That is,
The sample size recommended for the hypothesis test is 488601.
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167. for the training adaptation of maximum strength, what is the recommended number of repetitions per set?
Each strength training exercise should be performed for 2 to 6 sets with no more than 6 repetitions. To encourage the greatest outcomes, the training intensity for each set should be 85% or greater.
What is percent?In essence, percentages are fractions with a 100 as the denominator. We place the percent sign (%) next to the number to indicate that the number is a percentage. For instance, you would have received a 75% grade if you answered 75 out of 100 questions correctly on a test (75/100). %, which is a relative figure used to denote hundredths of any amount. Since one percent (symbolized as 1%) is equal to one tenth of anything, 100 percent stands for everything, while 200 percent refers to double the amount specified.
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a college prep school advertises that their students are more prepared to succeed in college than other schools. to verify this, they categorize gpa's into 4 groups and look up the proportion of students at a state college in each category. they find that 7% have a 0-0.99, 21% have a 1-1.99, 37% have a 2-2.99, and 35% have a 3-4.00 in gpa. they then take a random sample of 200 of their graduates at the state college and find that 19 has a 0-0.99, 28 have a 1-1.99, 82 have a 2-2.99, and 71 have a 3-4.00. can they conclude that the grades of their graduates are distributed differently than the general population at the school? test at the 0.05 level of significance.
Answer:
Yes, they can conclude that the grades of their graduates are distributed differently than the general population at the school. This is because the test statistic, chi-squared, is greater than the critical value, which is 7.81. This means that the difference between the observed and expected frequencies is statistically significant.
Step-by-step explanation:
There is a difference between the general population and college prep students in GPA.
What is the hypothesis?An assumption or concept is given as a hypothesis for the purpose of debating it and testing if it might be true.
Given:
Numbers Observed Proportion Expected (O - E) (O - E)² (O - E)²/E
0 - 0.99 19 0.07 14 5 25 1.79
1 - 1.99 28 0.21 42 -14 196 4.67
2 - 2.99 82 0.37 74 8 64 0.865
3 - 3.99 71 0.35 70 1 1 0.0142
Now, X² = the sum of (O - E)²/E
= 8.33
The P-Value is .039662. The result is significant at p < .05.
Hence,
H₀: There is no difference between the general population and the college prep students in GPA.
H1: There is a difference between the general population and the college prep students in GPA.
Test statistic = 8.33
p - Value = 0.039662
Therefore, the alternate hypothesis is true.
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a ship is off course. if the ship is traveling at 11 miles per hour, how far off course will it be after 3 hours?
With an off-course speed of 11 miles per hour, the ship will go 33 miles in 3 hours.
What is multiplication?Multiplying in math is the same as adding equal groups. The number of items in the group grows as we multiply. Parts of a multiplication issue include the product, the two factors, and the product. The components in the multiplication problem 6 x 9 = 54 are the numbers 6 and 9, and the result is the number 54. One of the four fundamental mathematical operations, along with addition, subtraction, and division, is multiplication. Multiply in mathematics refers to the continual addition of sets of same size.
Here,
speed of ship= 11 miles/hour
time given= 3 hours
distance= speed * time
=11*3
=33 miles
The ship will cover 33 miles in 3 hours while moving at the speed of 11 miles/ hour off course.
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What two numbers multiplies to negative 480 and adds to negative 28?
Answer:
-40 ,12
Step-by-step explanation:
you will have to look for the factors of 480 that satisfy this condition and for this case , they're -40 and 12
a newborn weighing 5 lb (2250 g) needs to eat 3 oz (90 ml) of formula every 3 hours. to meet this goal, how many ounces of formula per day will the parent need to feed the newborn? record your answer using a whole number.
it would be 72.94 ounces of formula per day will the parent need to feed the newborn
In this problem, the infant is fed for every 3 hours.
Then, the frequency of feeding for a day would be: (24hours/day) / 3(hours/times)= 6 times/ day.
The volume of feeding for a day that the infant need would be: = 473.68ml/day
The number of milk for every fed would be: (473.68ml/day)/ (6 times/day)= 72.94 ml/times
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question if x, y, and z are integers and xy z is an odd integer, is x an even integer? (1) xy xz is an even integer. (2) y xz is an odd integer.
xy + xz is an even integer & x is even and y + xz is an odd integer & either (x-1) is even or (y-z) is even .
1. xy + xz is an even integer - SUFFICIENT
Given:
xy + z is odd ...(i)
xy + xz is even ...(ii)
subtracting (ii) from (i)
we get xz - z, which should be odd (* since odd - even = odd)
=> z(x-1) is odd
=> both z and (x-1) is odd
=> since (x-1) is odd, x must be even.
2. y + xz is an odd integer -INSUFFICIENT
Given:
xy + z is odd ...(i)
y + xz is odd ...(ii)
subtracting (ii) from (i)
we get xy + z - y - xz
= (x-1)(y-z) , which should be even
=> either (x-1) is even or (y-z) is even ....insufficient to determine
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Given: -6x < 36. Choose the solution set. {x | x < -6} {x | x > 6} {x | x > -6} {x | x < 6}.
The correct answer is this inequality {x | x > -6}
What does a math inequality look like?
The equation-like form of the formula 5x 4 > 2x + 3 has an arrowhead in place of the equals sign. It is an illustration of inequity. This shows that the left half, 5x 4, is bigger than the right part, 2x + 3.
Given that:
-6x < 36
we multiply -1 on both the sides
6x > -36
divide 6 on both the side
x > -6
Hence the correct answer is this inequality {x | x > -6}.
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Which of the following is TRUE about the slope of a line? *
A. The slope of a vertical line is zero.
B. The slope of a vertical line is undefined.
C. The slope of a line is always positive. D. The slope of a horizontal line is negative.
Answer:
Step-by-step explanation:
The answer is B.
The slope of a verticle line is "undefined" by nature. As it is infinite
Which of the following would you round and estimate to a sum of 11?
3.65 + 7.992
3.41 + 8.051
4.25 + 8.103
4.89 + 7.431
If x = 6 and y = -4, evaluate the following expression: 20 - 5y + 2x
answer:
20-5y+2x=52
step-by-step explanation:
plug in the values of x & y into the expression and calculate using the order of operations to get the answer. hope that helps!
Answer: 52
Step-by-step explanation:
1. plug in x and y into the expression : 20 - 5(-4) +2(6)
2. multiply the numbers in the parenthesis: 20 + 20 + 12
3. add all the numbers together (simplify): 52
a test of which hypothesis is most important when deciding whether to use a simple linear regression model to predict y from x?
The most important measure used in regression diagnostics is the simple residual.
What is linear rigression?
In statistics, a scalar response and one or more explanatory factors are modeled using a linear approach called linear regression. Simple linear regression is used when there is only one explanatory variable; multiple linear regression is used when there are numerous explanatory variables.
Hypothesis testing is used to confirm if our beta coefficients are significant in a linear regression model. Every time we run the linear regression model, we test if the line is significant or not by checking if the coefficient is significant.
If there is a significant linear relationship between the independent variable X and the dependent variable Y, the slope will not equal zero.
The null hypothesis states that the slope is equal to zero, and the alternative hypothesis states that the slope is not equal to zero.
The most important measure used in regression diagnostics is the simple residual (e). This is the difference between each observed and predicted value of Y.
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(-7, 8) and (-7, 5)
Find the slope
Answer:
Slope is undefined
Step-by-step explanation:
slope = [tex]\frac{\Delta y}{\Delta x}[/tex]
[tex]\frac{5-8}{-7-(-7)}=\frac{-3}{0}[/tex]
Anything divided by zero is undefined
This should make sense visually as the points describe a vertical line at [tex]x=-7[/tex]
Given the diagram below, if Z is the incenter of WXY, WYX =86, and WXZ=33. Find each measure.
Triangle is a two-dimensional figure which has three sides and the sum of the three angles is equal to 180 degrees.
The values of each measure:
m∠WYZ = 43
m∠WXY = 33
m∠YWX = 61
m∠ZWX = 30.5
What is a triangle?It is a two-dimensional figure which has three sides and the sum of the three angles is equal to 180 degrees.
We have,
Z is the incenter of WXY.
m∠WYX = 86
This means,
m∠WYZ = m∠XYZ = x
m∠WYZ + m∠XYZ = m∠WYX
2x = 86
x = 43
m∠WXZ = 33.
m∠WXZ = m∠WXY
Now,
The triangle WXY.
m∠YWX + m∠WXY + m∠WYX = 180
m∠YWX + 33 + 86 = 180
m∠YWX = 180 - 119
m∠YWX = 61
m∠ZWX = 61/2 = 30.5
Thus,
The values of each measure:
m∠WYZ = 43
m∠WXY = 33
m∠YWX = 61
m∠ZWX = 30.5
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