The inverse of the given statement will be- Option 3, If point B is the midpoint, then point B bisects line segment AC into two congruent segments.
Here, we are given a statement: If point B bisects line segment AC into two congruent segments, then point B is the midpoint.
According to the statement,
if B bisects AC ⇒ AB = BC
then, B is the midpoint.
The inverse of this will be-
if B is the midpoint of AB ⇒ AB = BC
then, B bisects AB
This can be written as-
If point B is the midpoint, then point B bisects line segment AC into two congruent segments.
Thus, option 3 is the correct answer.
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Your question was incomplete. Check below for full content-
Which statement is the contrapositive of the conditional statement:
Which statement is the inverse of the conditional statement: If point B bisects line segment AC into two congruent segments, then point B is the midpoint.
1. If point B is not the midpoint, then point B does not bisect line segment AC into two congruent segments.
2. Point B bisects line segment AC into two congruent segments if, and only if, point B is the midpoint.
3. If point B is the midpoint, then point B bisects line segment AC into two congruent segments.
4. If point B does not bisect line segment AC into two congruent segments, then point B is not the midpoint.
How do I express 5 gallons 5 quartz 48 ounces in standard notation?
880 oz
Step-by-step explanation:
i’m not understanding this question
(8t)^2
Answer: 64t^2
Step-by-step explanation:
everything in the parenthesis has to get the exponent so it first becomes 8^2t^2 and then you simplify
Answer:
64t^2
Step-by-step explanation:
First, you need to distribute the exponent
8^2*t^2
Then you need to simplify
64t^2
And thats the answer
Does this graph represent a function? Why or why not?
A. No, because it fails the vertical line test.
OB. No, because it is not a curve.
OC. Yes, because it passes the vertical line test.
OD. Yes, because it has two straight lines.
Answer:
the answer is D
Step-by-step explanation:
because it has two straight lines
Divide. 827 divided by 19
Enter your answer in the boxes as a mixed number in simplest form.
Answer:
43 10/19
Step-by-step explanation:
Given that one centimeter is approximately 0.01 yards, how many
inches are in 66.75 centimeters?
Provide an answer accurate to the nearest tenth.
==========================================
Work Shown:
1 cm = 0.01 yards
66.75*(1 cm) = 66.75*(0.01 yards)
66.75 cm = 0.6675 yards
1 yard = 3 feet
0.6675*(1 yard) = 0.6675*(3 feet)
0.6675 yards = 2.0025 feet
1 foot = 12 inches
2.0025*(1 foot) = 2.0025*(12 inches)
2.0025 feet = 24.03 inches
please help me with this problem
Using the Poisson and the normal distributions, the probabilities are given as follows:
a) 0.0895 = 8.95%.
b)
Without correction, P(X < 8) = 0.1251 = 12.51%.
With continuity correction, P(X < 8) = 0.0968 = 9.68%.
c)
Without correction, P(16 < X < 24) = 0.1248.
With correction, P(16 < X < 24) = 0.1558 = 15.58%.
What is the Poisson distribution?In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by:
[tex]P(X = x) = \frac{e^{-\mu}\mu^{x}}{(x)!}[/tex]
The parameters are:
x is the number of successese = 2.71828 is the Euler number[tex]\mu[/tex] is the mean in the given interval.In this problem, the mean is given by:
[tex]\mu = 12[/tex]
Hence the probability that X is less than 8 is given by:
P(X < 8) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5) + P(X = 6) + P(X = 7).
In which:
[tex]P(X = x) = \frac{e^{-\mu}\mu^{x}}{(x)!}[/tex]
[tex]P(X = 0) = \frac{e^{-12}12^{0}}{(0)!} = 0.00001[/tex]
...
[tex]P(X = 7) = \frac{e^{-12}12^{7}}{(7)!} = 0.04368[/tex]
The middle values are found applying the same formula, and adding them, the probability is given by:
P(X < 8) = 0.0895 = 8.95%.
Normal Probability DistributionThe z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score measures how many standard deviations the measure is above or below the mean. Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.The Poisson distribution can be approximated to the normal with [tex]\sigma = \sqrt{\mu}[/tex]Without continuity correction, the probability that X is less than 8 is the p-value of Z when X = 8, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{8 - 12}{\sqrt{12}}[/tex]
Z = -1.15
Z = -1.15 has a p-value of 0.1251.
Hence:
Without correction, P(X < 8) = 0.1251 = 12.51%.
With continuity correction, as the Poisson distribution is discrete and the normal is continuous, the probability is P(X < 7.5), which is the p-value of Z when X = 7.5, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{7.5 - 12}{\sqrt{12}}[/tex]
Z = -1.3
Z = -1.3 has a p-value of 0.0968.
Hence:
With continuity correction, P(X < 8) = 0.0968 = 9.68%.
For item c, without correction, the probability is the p-value of Z when X = 24 subtracted by the p-value of Z when X = 16, hence:
X = 24:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{24 - 12}{\sqrt{12}}[/tex]
Z = 3.46
Z = 3.46 has a p-value of 0.9997.
X = 16:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{16 - 12}{\sqrt{12}}[/tex]
Z = 1.15
Z = 1.15 has a p-value of 0.8749.
0.9997 - 0.8749 = 0.1248.
Hence:
Without correction, P(16 < X < 24) = 0.1248.
With correction, the probability is the p-value of Z when X = 23.5 subtracted by the p-value of Z when X = 15.5, hence:
X = 23.5:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{23.5 - 12}{\sqrt{12}}[/tex]
Z = 3.32
Z = 3.32 has a p-value of 0.9996.
X = 15.5:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{15.5 - 12}{\sqrt{12}}[/tex]
Z = 1.01
Z = 1.01 has a p-value of 0.8438.
0.9996 - 0.8438 = 0.1558.
Hence:
With correction, P(16 < X < 24) = 0.1558 = 15.58%.
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Find the mean, median, and mode of the following data. If necessary, round to one more decimal place than the largest number of decimal places given in the data. Rate of Fatal Alcohol Impaired Car Crashes per 100 Million Vehicle Miles of Travel 0.79 0.51 0.52 0.51 0.68 0.65 0.79 0.37 0.79 0.29 0.57 0.34 0.46 0.62 0.63 0.77 0.57 0.35 0.30 0.58
Mean = 0.5545, Median =0.57, Mode = 0.79 of the following data.
What is mean median and mode?
A data set's mean (average) is calculated by summing all of the numbers in the set, then dividing by the total number of values in the set. When a data collection is ranked from least to greatest, the median is the midpoint. The number that appears most frequently in a data set is called the mode.For the given data 0.29, 0.3, 0.34, 0.35, 0.37, 0.46, 0.51, 0.51, 0.52, 0.57, 0.57, 0.58, 0.62, 0.63, 0.65, 0.68, 0.77, 0.79, 0.79, 0.79.
The mean is calculated as:
Mean = (0.29 + 0.3 + 0.34 + 0.35 + 0.37 + 0.46 + 0.51 + 0.51 + 0.52 + 0.57 + 0.57 + 0.58 + 0.62 + 0.63 + 0.65 + 0.68 + 0.77 + 0.79 + 0.79 + 0.79)/20
= 11.09/20
Mean = 0.5545
Median is the middle value of the data set and since the sample size is even which is 20 hence the median is found between n/2 and n/2 +1 which is 10th value and 11th value when the data set is arrange in ascending order.
so, the 10th value is 0.57 and 11th value is also 0.57 so, the median is (0.57 + 0.57)/2 = 0.57
Median:
The median is the most occuring value in the dataset and as we can see that 0.79 appeared 3 times hence 0.79 is Mode.
So, finally:
Mean = 0.5545
Median =0.57
Mode = 0.79
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The speed limit in Canada is 100km/hr. What is the value of this limit in mi/hr given 1mi = 1.609km?
If the speed limit in Canada is 100km/hr than it's limit in mi/hr will be 62.15 mi/hr.
It is given in the question that 1.609 km = 1 mi
So , 1km= 1/1.609 mi
1km = 0.6215 mi
So if a car travels 1 km in 1 hr then it will travel 0.6215 miles in hr.
that means 1km/hr = 0.6215mi/hr
Now ,
to convert 100km/hr to mi/hr
we have ,
100km/hr = 100*0.6215 mi/hr
=62.15 mi/hr
Therefore , If the speed limit in Canada is 100km/hr than it's limit in mi/hr will be 62.15 mi/hr.
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what is 83.1 divided by 5
Answer: The answer is 16.62
30 POINTS!!! PLEASE HELP ME! ASAP
Answer:
I think is higher
Step-by-step explanation:
Imani spent a third of her savings on airfare for a vacation. She then spent another $300 on hotels. If she has $250 left for meals and souvenirs, with how much did she have in savings before the trip?
The amount the she had in her savings before the trip was $825
Calculating amountFrom the question, we are to calculate how much Imani has in her savings before the trip
Let the amount she has in her savings before the trip be x
From the given information,
"Imani spent a third of her savings on airfare for a vacation"
That is,
She spent (1/3)x
The amount remaining after this time will be x - (1/3)x = (2/3)x
"She then spent another $300 on hotels"
The amount remaining after this time will be (2/3)x - $300
"If she has $250 left for meals and souvenirs"
That is,
(2/3)x - $300 = $250
Now, solve for x
(2/3)x - $300 = $250
(2/3)x = $250 + $300
(2/3)x = $550
x = $550 × 3/2
x = $825
Hence, the amount the she had in her savings before the trip was $825
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y=-3x+8 determine the y-value of each ordered pair based on the given x-value
When x = 0 in the given equation, the value of y = 8.
What are equations?An equation, in its most basic form, is a mathematical statement that shows that two mathematical expressions are equal. For example, 3x + 5 = 14 is an equation in which the expressions 3x + 5 and 14 are separated by a 'equal' sign.The value is 'x' is not given then we will consider x = 0.
Now, substitute x = 0 in the equation.
y = -3x + 8y = -3(0) + 8y = 8Therefore, the value of y = 8 when x = 0 is in the given equation.
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A 1000L tank now contains 240L of water. How long will it take to fill the tank using a pump that pumps 25L per minute
The time taken to fill the tank using a pump that pumps 25L per minute
is 30.4 minutes
Given that A 1000L tank now contains 240L of water and asked the time taken to fill the tank using a pump that pumps 25L per minute.
The amount of water that can be filled in tank=760L
Given that a pump that pumps 25L per minute ,
The time required to fill 760L {if a pump that pumps 25L per minute }=[tex]\frac{760}{25}[/tex]
The time required to fill 760L {if a pump that pumps 25L per minute }=30.4 minutes
Therefore,The time taken to fill the tank using a pump that pumps 25L per minute is 30.4 minutes
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HELP ASSAAAPPPP!!!!!!
Answer:
(-4, 0); x = -4, y = 0
Step-by-step explanation:
The solution is the point that satisfies both equations. It is the point of intersection of the two lines.
Answer: (-4, 0)
c = 1/2 ab^2
Solve for b
Answer:
b= √2ca /a
Step-by-step explanation:
it was a question on my test yesterday
pls help. ;0 This is for iready.
Answer:
10.6 ounces
Step-by-step explanation:
1. Divide the total spent by the cost per ounce to get number of ounces bought.
2.65 ÷ 0.25 = 10.6 ounces
Describe the meaning of |−36|.(1 point) the absolute value of negative 36 the absolute value of negative 36 one divided by negative 36 one divided by negative 36 the absolute value of 36 the absolute value of 36 negative 36 minus zero
The meaning of |-36| is the absolute value of negative 36.
We know that, the absolute value of any real number m is the positive value of m.
For any ±m ∈ R,
| ±m | = m
The absolute value of a number is also know as modulus of number.
In this question we have been given an absolute value |-36|
|-36| = 36
So, the meaning of |-36| would be,
- the absolute value of negative 36
Therefore, the meaning of |-36| is the absolute value of negative 36.
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Consider two neighboring island countries called Contente and Euphoria. They each have 4 million labor hours available per week that they can use to produce jeans, rye, or a combination of both. The following table shows the amount of jeans or rye that can be produced using 1 hour of labor.
Country Jeans Rye
Contente 5 10
Euphoria 4 16
Initially, suppose Contente uses 1 million hours of labor per week to produce jeans and 3 million hours per week to produce rye, while Euphoria uses 3 million hours of labor per week to produce jeans and 1 million hours per week to produce rye. Consequently, Contente produces 5 million pairs of jeans and 30 million bushels of rye, and Euphoria produces 12 million pairs of jeans and 16 million bushels of rye. Assume there are no other countries willing to trade goods, so, in the absence of trade between these two countries, each country consumes the amount of jeans and rye it produces.
Contente's opportunity cost of producing 1 pair of jeans is ___ of rye, and Euphoria's opportunity cost of producing 1 pair of jeans is ___ of rye. Therefore ___ has a comparative advantage in the production of jeans, and ___ has a comparative advantage in the production of rye.
Suppose that each country completely specializes in the production of the good in which it has a comparative advantage, producing only that good. In this case, the country that produces jeans will produce ___ million pairs per week, and the country that produces rye will produce ___ million bushels per week.
n the following table, enter each country's production decision on the third row of the table (marked “Production”).
Suppose the country that produces jeans trades 13 million pairs of jeans to the other country in exchange for 39 million bushels of rye.
In the following table, select the amount of each good that each country exports and imports in the boxes across the row marked “Trade Action,” and enter each country's final consumption of each good on the line marked “Consumption.”
When the two countries did not specialize, the total production of jeans was 17 million pairs per week, and the total production of rye was 46 million bushels per week. Because of specialization, the total production of jeans has increased by ___ million pairs per week, and the total production of rye has increased by ___ million bushels per week.
1. Euphoria's opportunity cost of producing a a bushel of rye is 4 pairs of jeans.
Contentes opportunity cost of producing a bushel of rye is 2 pairs of jeans.
2. Contente has comparative advantage in producing rye
Euphoria has comparative advantage in jeans production
How to find the opportunity Cost?For Euphoria:
The opportunity cost of producing a unit of rye in terms of jeans is;
Opportunity Cost = 20/5 = 4
For contente:
The opportunity cost of producing a unit of rye in terms of jeans is;
Opportunity Cost = 16/8 = 2
The opportunity cost of producing 1 unit of jean in terms of unit of rye:
For euphoria = 5/20 = 1/4
For contente = 8/16 = 1/2
1. Euphoria's opportunity cost of producing a a bushel of rye is 4 pairs of jeans.
Contentes opportunity cost of producing a bushel of rye is 2 pairs of jeans.
2. Contente has comparative advantage in producing rye
Euphoria has comparative advantage in jeans production
3. Contente produces 8 bushels of rye so with 4 million hours of labor = 8x4 = 32 million bushels in a week.
Euphoria 20 pairs of jean in a week, using 4 million hours of labor. 20x4 = 80 pairs of jean a week
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A fish tank at an aquarium has a volume of 648 cubic feet and a depth of 8 feet. If the base of the tank is square, what is the length of each side of the tank?
The length of each side of the tank is 9 feet.
How to calculate the value?Height = 8
Volume = 648
Let y be the cross sectional area
Therefore, 648 = 8y
y² = 648/8
y² = 81
Therefore, y = ✓81
y = 9
The length of each side of the tank is 9 feet.
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I need help with this
Given that
m∠1 = (x+38)° andm∠2 = 3x°To find
The angles measures.So, according to the question
We have,
m∠1 = (x+38)° andm∠2 = 3x°∵ From figure m∠1 and m∠2 divided 90° into two parts
∴ m∠1 + m∠2 = 90° ----------------------(1)
Now putting the values of m∠1 and m∠2 in equation (1)
m∠1 + m∠2 = 90° ----------------------(1)
(x+38)° + 3x° = 90°
x°+38° + 3x° = 90°
4x° = 90° - 38°
4x° = 52°
x° = (52/4)°
x° = 13°
So,
m∠1 = (x+38)°
= (13+38)°
m∠1 = 51°
And
m∠2 = 3x°
= (3 × 13)°
m∠2 = 39°
The angles are
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Susan is buying supplies for a party. If spoons only come in bags of 8 and
forks only come in bags of 6, what is the least number of spoons and the
least number of forks she can buy so that she has the same number of
each?
Answer:
24
Step-by-step explanation:
8. 6
16. 12
24. ✔️ 18
32. 24✔️
40. 30
48. 36
56. 42
64. 48
72. 54
80. 60
which one doesn't belong explain why you chose that answer.
Answer:
2 because the unit rate is not the same for all the others it is consistant
Step-by-step explanation:
I think of a number . The LCM of this number and 42 is 126. If the number lies between 60 and 70 what is the number
If the number lies between 60 and 70 then the number is 63
How to determine the number if the number lies between 60 and 70?The given parameters are
LCM = 126
Second number = 42
The initial number is said to be between 60 and 70
The only number between 60 and 70 that has the same common factor as 126 and 42 is 63
Hence, if the number lies between 60 and 70 then the number is 63
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round 72 to the neareat ten? what's the answer>
70? Is this a trick question?
Answer:
It will be 70
Step-by-step explanation:
Because poor number from 0 to 4
8
2) Which equivalent expression uses GCF and Distributive Property to find the
sum of to 16+28?
1(16+28)
O2(8+14)
2(8+28)
4(4+7)
*
4(4+7) is the equivalent expression uses GCF and Distributive Property to find the sum of to 16+28.
What is GCF?The greatest positive integer m that divides both x and y is the GCF of two or more non-zero integers, x and y. As a result, the greatest common factor is also referred to as the Highest Common Divisor (HCD), the Highest Common Factor (HCF), or the Greatest Common Divisor (GCD).
What is the Distributive Property?According to the distributive property, an expression in the form A (B + C) can be solved as A (B + C) = AB + AC. This distributive law also applies to subtraction and is denoted by A (B - C) = AB - AC. This means that the other two operands share operand A.
The given expression is 16 + 28.
The greatest common factor is 4.
So taking the greatest common factor from the both the numbers.
We get, 4 (4+7)
So the resultant expression is 4 (4+7).
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If f(x) = 3x +4, find f'(x)
Одна зі сторін прямокутника в 11 разів менша від другої. Знайдіть
сторони прямокутника, якщо його периметр дорівнює 144 см.
Answer:
for the plug-in settings to determine
Step-by-step explanation:
GG from Shahs of sunset Blvd suite is the best way to the answer to the answer to the answer to the plug-in the plug-in the whole thing is I don't have a email the e I m not sure if you have any questions or concerns please visit the plug-in settings to determine
Please help me fast. Trying to figure this out. Answer a-C. You don’t need to explain
Lindy has 64 vanilla wafers to put into bags. How many bags can she fill if she puts the same number in each bag and uses them all
How to find the least common multiple of three numbers
Answer:
The way I would best say is listing all the multiples then circle all the ones that are alike then find the lowest one they all have.
Example
Find the common multiples of 12,15,20
Multiples of 12:12, 24, 36, 48, 60, 72, 84, 96, 120……….
Multiples of 15:15, 30, 45, 60, 75, 90, 105, 120, 135, 150, 165, 180, 195, 210, 225, 240, 255, 270, 285, 300, 315, 330, 345, 360, 375, 390, 405,……..
Multiples of 20:20, 40, 60, 80, 100, 120, 140, 160, 180, and 200.
Step-by-step explanation:
They all have 60 so your lcm is 60