Stephen Dubner and Steven Levitt are the authors of the essay, and as they develop their essay, they use a great deal of quantification.
The following are three specific examples that they used: They write, "If a martini is made with 4 ounces of gin, that’s 2.8 standard drinks. "They also said, "Let's consider the five most unsafe hours for driving, which are Saturday and Sunday mornings from 1 am to 6 am. In the middle of this time period, 3 am on Saturday morning, the likelihood of an accident is three times higher than at noon on a weekday. "In another instance, they note that "The average person who has been murdered has approximately 300 friends and relatives, which means that a homicide victim’s personal network is quite extensive. "The authors use these specific numbers to make their argument more convincing. Using quantification provides an air of authority to the author's claims. By providing specifics, the author can communicate more information than would otherwise be possible.
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a pair of headphones originally costs 95$ and is on sale for 70$ what is the percent change in the price of the headphones? be sure to show whether it is a percent increase or decrease.
The percent decrease in the price of the headphones is 26.32%.
Explanation:
To find the percent change in price, we can use the following formula:
percent change = (new value - old value) / old value * 100%
In this case, the old value is the original price of the headphones, which is $95.
The new value is the sale price, which is $70. Plugging these values into the formula, we get:percent change = (70 - 95) / 95 * 100%
percent change = -25 / 95 * 100%
percent change = -0.2632 * 100%
percent change = -26.32%
The negative sign indicates that the price has decreased, and the magnitude of the percent change is 26.32%, which means that the sale price is 26.32% lower than the original price.
the yearly rainfall of a town, recorded since records began, is normally distributed with a mean of 95 centimeters and a standard deviation of 28 centimeters. in what percentage of years will the rainfall be between 50 and 70 centimeters in that town?
In approximately 11.41% of years, the rainfall will be between 50 and 70 centimeters in that town.
To solve this problem, we need to find the percentage of years where the rainfall is between 50 and 70 centimeters. We can do this by standardizing the rainfall values and using a standard normal distribution table.
First, we need to standardize the rainfall values of 50 and 70 centimeters using the formula
z = (x - μ) / σ
where
z is the standardized value
x is the rainfall value
μ is the mean
σ is the standard deviation
For x = 50
z = (50 - 95) / 28
z = -1.607
For x = 70
z = (70 - 95) / 28
z = -0.893
Next, we use a standard normal distribution table or calculator to find the area under the curve between these two standardized values. This represents the percentage of years where the rainfall is between 50 and 70 centimeters.
Using a standard normal distribution table, we can find that the area under the curve between z = -1.607 and z = -0.893 is 0.1141. This means that approximately 11.41% of years will have rainfall between 50 and 70 centimeters in this town.
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Evaluate
8
�
−
1
+
0. 5
�
8a−1+0. 5b8, a, minus, 1, plus, 0, point, 5, b when
�
=
1
4
a=
4
1
a, equals, start fraction, 1, divided by, 4, end fraction and
�
=
10
b=10b, equals, 10
The evaluation of the algebraic expression 8a-1+0.5b when a=1/4 and b=10 is 6.
We are given an expression 8a−1+0.5b8, and we are asked to evaluate it when a = 1/4 and b = 10. Substituting these values, we get:
8(1/4) - 1 + 0.5(10) = 2 - 1 + 5
Simplifying the expression on the right-hand side, we get:
8a−1+0.5b8 = 6
Therefore, when a = 1/4 and b = 10, the value of the expression 8a−1+0.5b8 is 6.
This means that if we substitute the given values for a and b, the resulting expression will have a value of 6. It is important to correctly substitute the values before evaluating the expression to obtain the correct answer.
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____The given question is incomplete, the complete question is given below:
Evaluate 8 a − 1 + 0.5 b 8a−1+0.5b8, a, minus, 1, plus, 0, point, 5, b when a = 1 4 a= 4 1 a, equals, start fraction, 1, divided by, 4, end fraction and b = 10 b=10b, equals, 10.
g a group of people were asked if they had run a red light in the last year. responded yes, and responded no. find the probability that if a person is chosen at random, they have run a red light in the last year.
The probability that a person chosen at random has run a red light in the last year can be calculated by taking the number of people who said “yes” to running a red light and dividing it by the total number of people in the group.
For example, if 10 people said “yes” and 20 said “no”, the probability of a person chosen at random running a red light in the last year is 10/30, or 1/3.
The probability of an event happening is calculated using the formula:
Probability = Number of Favorable Outcomes / Total Number of Outcomes
In this case, the favorable outcome is running a red light in the last year, and the total number of outcomes is the total number of people asked.
To calculate the probability, we take the number of people who said “yes” to running a red light in the last year and divide it by the total number of people in the group. In our example, 10/30 = 1/3, so the probability that a person chosen at random has run a red light in the last year is 1/3.
In conclusion, the probability of a person chosen at random having run a red light in the last year is calculated by taking the number of people who responded “yes” and dividing it by the total number of people in the group.
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In 2010, a total of 2187 of the employees at
Leo's company owned a petrol car.
In 2013, there were 1536 employees with
petrol cars.
Assuming this number decreases
exponentially, work out how many employees
owned a petrol car in 2019.
Give your answer to the nearest integer.
we can expect that approximately 815 employees owned a petrol car in 2019 (rounded to the nearest integer).
How to solve exponential function?We can model the number of employees owning petrol cars in the years 2010 and 2013 using the exponential decay formula:
[tex]$$N(t) = N_0 e^{-kt}$$[/tex]
where N(t) is the number of employees owning petrol cars at time t, [tex]$N_0$[/tex] is the initial number of employees owning petrol cars (in 2010), k is the decay constant, and t is the time elapsed since 2010 (in years).
We can use the given information to find the value of k:
In 2013 (3 years after 2010), the number of employees owning petrol cars decreased from 2187 to 1536:
[tex]$$1536 = 2187 e^{-3k}$$[/tex]
Dividing both sides by 2187 gives:
[tex]$$e^{-3k} = \frac{1536}{2187}$$[/tex]
Taking the natural logarithm of both sides gives:
[tex]$$-3k = \ln\left(\frac{1536}{2187}\right)$$[/tex]
Solving for k gives:
[tex]$k = -\frac{1}{3} \ln\left(\frac{1536}{2187}\right) \approx 0.1565$$[/tex]
Now we can use the exponential decay formula to find the number of employees owning petrol cars in 2019 (9 years after 2010):
[tex]$$N(9) = 2187 e^{-0.1565 \cdot 9} \approx 815$$[/tex]
Therefore, we can expect that approximately 815 employees owned a petrol car in 2019 (rounded to the nearest integer).
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Dan had 50% fewer stickers than Jeff. After Jeff gave 20 of his stickers to Dan, Dan had 40% fewer stickers than Jeff (had after he gave away 20 of his stickers). How many stickers did Dan have at first?
Dan had 50% fewer stickers than Jeff. After Jeff gave 20 of his stickers to Dan, Dan had 40% fewer stickers than Jeff. Dan had 320 stickers first.
Dan had 50% fewer stickers than Jeff.
After Jeff gave 20 of his stickers to Dan, Dan had 40% fewer stickers than Jeff (had after he gave away 20 of his stickers).
How many stickers did Dan have at first?
The total number of stickers that Jeff had is denoted by J, and the total number of stickers that Dan had is denoted by D.
In order to solve the question, let us first represent the given data mathematically:
J = 1.5D; D+20 = 0.6(J-20)
We have 2 equations and 2 unknowns, J and D.
We can solve these equations using simultaneous linear equations.
Substitute the first equation in the second equation:
D+20=0.6(J-20)
⇒ D+20=0.6J-12
⇒ D=0.6J-32
Now substitute the value of D in the first equation:
J=1.5D
⇒ J=1.5(0.6J-32)
⇒ J=0.9J-48.
Therefore, J=480
The total number of stickers that Jeff had initially was 480.
Now, to calculate the total number of stickers that Dan had, we can use the equation
J=1.5D:J=1.5D
⇒ 480=1.5D
⇒ D=320
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To find the distance across a small lake, a surveyor has taken the measurements shown. Find the distance across the lake using this information. (Assume points A and B are exactly along the shoreline, and that a = 2.62 miles and b = 3.51 miles. Round your answer to two decimal places.) mi
we will use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.
In this case, the distance across the lake is the hypotenuse, and the given measurements a and b are the other two sides.
Solution:
1. Write the Pythagorean theorem:
c² = a² + b²,
where c is the distance across the lake.
2. Substitute the given measurements:
c² = (2.62)² + (3.51)²
3. Calculate the squares:
c² = 6.8644 + 12.3201
4. Add the squared values:
c² = 19.1845
5. Find the square root of the sum:
c = √19.1845
6. Calculate the distance:
c ≈ 4.38 miles
The distance across the lake is approximately 4.38 miles
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a bag contains a collection of distinguishable marbles. the bag has two red marbles, four green ones, one lavender one, six yellows, and five orange marbles. hint [see example 7.] how many sets of four marbles include exactly two green marbles? (note that this means there must be two other non-green marbles as well).
Therefore, the total number of sets of four marbles, including exactly two green marbles, is 720.
The given bag contains a total of [tex](2+4+1+6+5)=18[/tex] marbles.
There are two possibilities of selecting two green marbles and the other two marbles in a set, as shown below;GG -- NN (No Green Marbles)GG -- RR (No Green Marbles)GG -- YY (No Green Marbles)GG -- OO (No Green Marbles)GG -- GL (Lavender)GG -- RG (Red)GG -- OG (Orange)
The first two options have no green marbles; thus, they are eliminated. We can select non-green marbles in C(16,2) = 120 ways, then multiply by C(4,2) = 6 to choose two green marbles out of four.So, the total number of such sets is
[tex]120 × 6 = <<120*6=720>>720.[/tex]
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WILL GIVE BRAINLY
If sin (x) =3 cos(x), then what is sin(x) times cos (x)?
Solve the equation x² = 4.
Do u know what is x ?
Answer:
x= 2
Step-by-step explanation:
² means times the number itself 2 times.
2×2=4
Jane contributes 12% of the total cost of her individual health care. This is a $95.50 deduction from each of her biweekly paychecks.
A) Find Jane's share.
b) Total value of the insurance.
b) Calculate the employer's share.
A) Jane's share is 12% of X, which is equal to 0.12X.
B) the total cost of the insurance is $20,691.67
C) the employer's share is $18,208.67.
The total expense is what?Total cost is the collective term for the cost of production as a whole, which encompasses both fixed and variable costs. The expense necessary to produce a good is referred to in economics as the total cost. There are two parts that make up the total cost: a set price The expense is what never changes.
According to the given information:Let X be the total cost of Jane's individual health care, then:
A) Jane's share is 12% of X, which is equal to 0.12X.
B) We know that Jane's deduction from each biweekly paycheck is $95.50, so she pays a total of:
$95.50 * 26 = $2,483
This amount is equal to 0.12X, so we can set up an equation:
0.12X = $2,483
Solving for X, we get:
X = $20,691.67
Therefore, the total value of the insurance is $20,691.67.
C) The employer's share is the difference between the total cost of the insurance and Jane's share:
Employer's share = Total cost - Jane's share
Employer's share = $20,691.67 - $2,483
Employer's share = $18,208.67
Therefore, the employer's share is $18,208.67.
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Jane's share of the total cost of her individual health care is $795.83, The total value of the insurance is $795.83 + 0.88x and the employer's share is 0.88x.
What is cost?
In mathematics, cost refers to the amount of resources (such as money, time, effort, or materials) that are required to produce or obtain something.
A) To find Jane's share of the total cost of her individual health care, we can use the information that she contributes 12% of the cost, and that this is a $95.50 deduction from each of her biweekly paychecks.
Let x be the total cost of Jane's individual health care. Then:
12% of x = $95.50
0.12x = $95.50
x = $95.50 / 0.12
x = $795.83
Therefore, Jane's share of the total cost of her individual health care is $795.83.
B) To find the total value of the insurance, we can add up both Jane's share and the employer's share.
If Jane is contributing 12% of the total cost, then the employer is contributing the remaining 88% of the cost. So the employer's share can be calculated as:
88% of x = 0.88x
The total value of the insurance is then:
Total value = Jane's share + Employer's share
Total value = $795.83 + 0.88x
C) To calculate the employer's share, we can use the same information as above. The employer is contributing 88% of the total cost, so:
88% of x = 0.88x
Therefore, the employer's share of the total cost of Jane's individual health care is $0.88x, or approximately $700.33 (if we use the value of x that we found in part A).
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the cpa practice advisor reports that the mean preparation fee for federal income tax returns was . use this price as the population mean and assume the population standard deviation of preparation fees is .
The CPA Practice Advisor reports that the mean preparation fee for federal income tax returns was 261. Use this price as the population mean and assume the population standard deviation of preparation fees is 120.
We need to find the probability of selecting a random sample of 20 tax returns and a standard deviation of the sample preparation fees of 50 or less.
We use the central limit theorem that states that, regardless of the shape of the population, the sampling distribution of the sample means approaches a normal distribution with mean μ and standard deviation
σ/√n
where μ is the population mean, σ is the population standard deviation, and n is the sample size.
Therefore, we have:
[tex]\mu = 261\]\\sigma = $120\]\\n = 20\][/tex]
[tex]S.E.= \frac{\sigma}{\sqrt{n}}\\S.E =\frac{\ 120}{\sqrt{20}}\\S.E =26.83[/tex]
The probability of selecting a random sample of 20 tax returns and a standard deviation of the sample preparation fees of 50 or less is given by:
[tex]P(Z < \frac{X - \mu}{S.E})\][/tex]
where X is the sample mean, μ is the population mean, and S.E is the standard error of the mean.
To calculate the probability, we standardize the distribution of the sample means using the z-score formula, i.e.,
[tex]\[z = \frac{X - \mu}{S.E} = \frac{\50 - \261}{\26.83} = -7.91\][/tex]
Therefore, the probability of selecting a random sample of 20 tax returns and a standard deviation of the sample preparation fees of 50 or less is zero because the z-score is less than the minimum z-score (i.e., -3.89) that corresponds to the probability of selecting a random sample of 20 tax returns and a standard deviation of the sample preparation fees of 50 or less.
Thus, it is impossible to obtain such a sample.
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jason flips a coin three times. what is the probability that the coin will land on the same side in all three tosses?
The probability that the coin will land on the same side in all three tosses is 1/8.
There are two possible outcomes for each coin flip: heads or tails. Therefore, there are 2 × 2 × 2 = 8 possible outcomes for flipping a coin three times in a row.To find the probability that the coin will land on the same side in all three tosses, we need to count the number of outcomes that satisfy this condition.
There are only two such outcomes: either all three tosses are heads or all three tosses are tails. Therefore, the probability of this happening is 2/8 or 1/4.But we are asked for the probability that the coin will land on the same side in all three tosses, not just one specific side.
Therefore, we need to divide our previous result by 2 (the number of sides of the coin) to get the final answer: 1/4 ÷ 2 = 1/8. The probability that the coin will land on the same side in all three tosses is 1/8.
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PLEAaSE HELP PLSSSS!!!!!
Answer:
= 58/33
= 1 25/33
Step-by-step explanation:
12/11 - (-2/3) =
= 12/11 + 2/3
= 36/33 + 22/22
= 58/33
= 1 25/33
Determine the equation of the circle graphed below.
Answer:
Step-by-step explanation:
Circle centre: (4,7)
Radius: 3
Equation is:
[tex](x-h)^2+(y-k)^2=r^2[/tex] (where (h,k) is center, r is radius)
[tex](x-4)^2+(y-7)^2=3^2[/tex]
[tex](x-4)^2+(y-7)^2=9[/tex] (This is the general standard form )
in expanded form,
[tex](x^2-8x+16)+(y^2-14y+49)=9[/tex]
[tex]x^2+y^2-8x-14y+56=0[/tex]
Note: Unless stated either form is an acceptable answer.
The figure below is dilated by a factor of 1/3 centered at the origin. Plot the resulting image. please helllpppp
The graph at the end of the response provides the dilated figure, which has the same format as the original figure but reduced side lengths as a result of the dilation with a scale factor of less than 1.
What is dilation?To make an opening or hollow structure wider or larger than usual, such as a blood vessel or the pupil of an eye.
The process of dilation entails growing an object's size without changing its shape.
The size of the object may rise or decrease depending on the scale factor.
Using dilation maths, a square with a side of 5 units can be made wider to have a side of 15 units, yet the square retains its original shape.
So, the coordinates of each vertex of the figure are multiplied by the scale factors to create a dilatation in the image.
The vertices for the original figure that was graphed are listed as follows:
I(0,6).
H(3,6).
G(9,0).
F(-6,-9).
E(-6,-6).
The coordinates of the resulting image are presented as follows since the dilation has a scale factor of 1/3, which means that the coordinates are multiplied by 1/3:
I'(0,2).
H'(1,2).
G'(3,0).
F'(-2,-3).
E'(-2,-2).
Therefore, the graph at the end of the response provides the dilated figure, which has the same format as the original figure but reduced side lengths as a result of the dilation with a scale factor of less than 1.
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Correct question:
The figure below is dilated by a factor of centered at the origin. Plot the resulting image. -109 -11 E Click twice to plot a segment. Click a segment to delete it. 4 -5 7 F A -9 10 9 B 4 I d 3 P BI 1 9 H 3 4 6 6 M
What is the height of the parallelogram?
12 m
A = 186 m²
Answer: 15.5
Step-by-step explanation:
H = A/B
= 186/12
= 15.5
i dont know how yo do this question
Step-by-step explanation:
2x + 2y = 28 <=====given
x * y = 40 <===given ..... re-arrange to :
y = 40 / x <===substitute this 'y' into the first equation
2x + 2 ( 40/x) = 28 <=====solve for x
2x^2 -28x + 80 = 0
x^2 -14x +40 = 0
(x -10)(x-4) = 0 shows x = 10 or 4 then y = 4 or 10
dimensions 10 and 4 inches
Answer:
4 or 10 inches
Step-by-step explanation:
I added a photo of my solution
If you have 4 purple marbles and 8 yellow marbles in a bag. What is the probability of getting a purple marble
You have a 4/12 probability.
given that kw for water is 2.4×10−14 at 37 ∘c, calculate the ph of a neutral aqueous solution at 37 ∘c, which is the normal human body temperature.
6.81 is the Ph of a neutral aqueous solution.
To calculate the pH of a neutral aqueous solution at 37°C with a KW of 2.4×10⁻¹⁴, follow these steps:
1. Identify that in a neutral aqueous solution, the concentrations of hydrogen ions (H⁺) and hydroxide ions (OH⁻) are equal. Therefore, [H⁺] = [OH⁻].
2. Use the KW expression, which is the product of [H⁺] and [OH⁻] concentrations. In this case, KW = 2.4×10⁻¹⁴.
3. Since [H⁺] = [OH⁻], you can rewrite the KW expression as KW = [H⁺]². Now, solve for [H⁺] by taking the square root of KW: [H⁺] = sqrt(KW) = sqrt(2.4×10⁻¹⁴).
4. Calculate the square root: [H⁺] ≈ 1.55×10⁻⁷ M.
5. Use the pH formula: pH = -log[H⁺]. Plug in the [H⁺] value: pH = -log(1.55×10⁻⁷).
6. Calculate the pH: pH ≈ 6.81.
The pH of a neutral aqueous solution at 37°C with a KW of 2.4×10⁻¹⁴ is approximately 6.81.
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Kyle is playing a game where he rolls a number cube twice and flips a coin twice. The number cube is labeled 1 to 6. The coin can land on heads or tails.
If the number cube lands on 5 both times and the coin lands on heads both times, Kyle wins a prize. What is the probability that Kyle wins the prize?
The chance of rolling two 5s and flipping two heads can be calculated by multiplying the odds together because each cube and coin flip is independent. the probability that Kyle wins the prize is [tex]1/144[/tex]
What is the probability?The probability of rolling a 5 on a number cube is 1/6, and the probability of flipping heads on a coin is 1/2.
Since each roll of the cube and flip of the coin is independent, we can find the probability of rolling two 5's and flipping two heads by multiplying the probabilities together:
P(rolling two 5's and flipping two heads) = P(rolling a 5) * P(rolling a 5) * P(flipping heads) * P(flipping heads)
[tex]= (1/6) \times (1/6) \times (1/2) \times (1/2)[/tex]
[tex]= 1/144[/tex]
Therefore, the probability that Kyle wins the prize is ,[tex]1/144[/tex] or approximately [tex]0.0069[/tex] (rounded to four decimal places).
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Jhoney ate 3 apples and have 2 left how much did he eat?
By probability , 3 Apples are left .
What does a probability simple definition entail?
A probability is a number that expresses the possibility or likelihood that a specific event will take place. Probabilities can be stated as proportions with a range of 0 to 1, or as percentages with a range of 0% to 100%.
The probability is a metric for determining how likely an event is to occur. It gauges how likely an event is. The probability equation is stated by the following notation: P(E) = Number of Favorable Outcomes/Number of Total Outcomes.
Jhoney ate = 3 apples
= 2 left
he eat = ³C₂
= 3!/(3-2)! 2!
= 3
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64x=8
What is the value of x that makes the equation true.
Answer:
x=8
Step-by-step explanation:
8 x 8 = 64
You can find this answer by using inverse operations.
64/8 = 8
To check your work, you can multiply...
8x8 = 64.
Hope this helps!
Find the tangent of a larger acute angle in a right triangle with side 10. 24 and 26 tangent of the larger acute angel
we have found that in the given right triangle with sides 10, 24, and 26, the tangent of the larger acute angle (angle B) is 2.4.
In a right triangle, the tangent of an acute angle is defined as the ratio of the length of the opposite side to the length of the adjacent side. Let us label the sides of the right triangle as follows:
The hypotenuse (the longest side) is 26
One of the acute angles (let's call it angle A) has opposite side length of 10
The other acute angle (let's call it angle B) has opposite side length of 24
To find the tangent of the larger acute angle, which is angle B, we use the formula:
tan(B) = opposite / adjacent
In this case, the opposite side of angle B is 24, and the adjacent side is 10. So we have:
tan(B) = 24 / 10 = 2.4
Therefore, the tangent of the larger acute angle (angle B) is 2.4.
This means that if we draw a line that is tangent to the circle with radius 10 centered at the vertex of angle B, the length of that line will be 24. This is a geometric interpretation of the tangent function, where the tangent of an angle is the length of a line tangent to the unit circle at that angle.
In conclusion, we have found that in the given right triangle with sides 10, 24, and 26, the tangent of the larger acute angle (angle B) is 2.4.
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I HAVE TO GET THIS RIGHT!!!
what is 2 + 2
Step-by-step explanation:
The sum of 2 and 2 can be derived using basic arithmetic operations.
Starting with 2, we can add 1 to get 3:
2 + 1 = 3
Then, we can add another 1 to get 4:
3 + 1 = 4
Therefore, the derivation of 2 + 2 is:
2 + 2 = (2 + 1) + 1 = 3 + 1 = 4
Hence, 2 + 2 is equal to 4.
Answer:
4
Step-by-step explanation:
each page number of a 488-page book is printed one time in the book. the first page is page 1 and the last page is page 488. when printing all of the page numbers, how many more 4's are printed than 8's?
the number of more 4's printed than 8's is 188 - 59 = 129.
We can approach this problem by counting the number of times the digit 4 appears and the number of times the digit 8 appears in the page numbers from 1 to 488.
First, let's count the number of times the digit 4 appears. We can break down the counting into three cases:
The digit 4 appears in the units place (page numbers 4, 14, 24, ..., 484): there are 49 such page numbers (from 4 to 484, incrementing by 10).
The digit 4 appears in the tens place (page numbers 40 to 49, 140 to 149, ..., 440 to 449): there are 50 such page numbers.
The digit 4 appears in the hundreds place (page numbers 400 to 488): there are 89 such page numbers.
Thus, the total number of times the digit 4 appears is 49 + 50 + 89 = 188.
Next, let's count the number of times the digit 8 appears. We can break down the counting into two cases:
The digit 8 appears in the tens place (page numbers 80 to 89, 180 to 189, ..., 480 to 489): there are 50 such page numbers.
The digit 8 appears in the hundreds place (page numbers 800 to 880): there are 9 such page numbers.
Thus, the total number of times the digit 8 appears is 50 + 9 = 59.
Therefore, the number of more 4's printed than 8's is 188 - 59 = 129.
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L(-1,6), M(5,8), N(0,2), P(-8,12)
Determine whether the quadrilateral is a parallelogram using the specific method. (Distance formula)
Yes, the quadrilateral is a parallelogram. To prove this using the distance formula method, we need to show that opposite sides of the quadrilateral are equal in length.
We can calculate the distance between each pair of points using the distance formula:
d = [tex]\sqrt{((x2 - x1)^2 + (y2 - y1)^2)}[/tex]
Using this formula, we get:
d(LM) = √[tex]((5 - (-1))^2 + (8 - 6)^2)[/tex] = √(36 + 4) = √(40) = 2√(10)
d(NP) = √[tex]((-8 - 0)^2 + (12 - 2)^2)[/tex] = √(64 + 100) = √(164) = 2√(41)
d(LN) = √[tex]((0 - (-1))^2 + (2 - 6)^2)[/tex] = √(1 + 16) = √(17)
d(MP) = √[tex]((-8 - 5)^2 + (12 - 8)^2[/tex]) = √(169 + 16) = √(185)
We can see that d(LM) = d(NP) and d(LN) = d(MP), which means that opposite sides of the quadrilateral are equal in length. Therefore, the quadrilateral is a parallelogram.
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a horizontal curve is to be designed with a 2000 feet radius. the curve has a tangent length of 400 feet and its pi is located at station 103 00. determine the stationing of the pt.
A horizontal curve is to be designed with a 2000 feet radius. The curve has a tangent length of 400 feet and its pi is located at station 103+00. Determine the stationing of the PT.
A horizontal curve is a curve that is used to provide a transition between two tangent sections of a roadway. To connect two tangent road sections, horizontal curves are used. Horizontal curves are defined by a radius and a degree of curvature. The curve's radius is given as 2000 feet. The tangent length is 400 feet.
The pi is located at station 103+00.
To determine the stationing of the PT, we must first understand what the "pi" means. PC or point of curvature, PT or point of tangency, and PI or point of intersection are the three primary geometric features of a horizontal curve. The point of intersection (PI) is the point at which the back tangent and forward tangent of the curve meet. It is an important point since it signifies the location of the true beginning and end of the curve. To calculate the PT station, we must first determine the length of the curve's arc. The formula for determining the length of the arc is as follows:
L = 2πR (D/360)Where:
L = length of the arc in feet.
R = the radius of the curve in feet.
D = the degree of curvature in degrees.
PI (103+00) indicates that the beginning of the curve is located 103 chains (a chain is equal to 100 feet) away from the road's reference point. This indicates that the beginning of the curve is located 10300 feet from the road's reference point. Now we need to calculate the degree of curvature
:Degree of curvature = 5729.58 / R= 5729.58 / 2000= 2.8648 degrees. Therefore, the arc length is:
L = 2πR (D/360)= 2π2000 (2.8648/360)= 301.6 feet.
The length of the curve's chord is equal to the length of the tangent, which is 400 feet. As a result, the length of the curve's long chord is: Long chord length = 2R sin (D/2)= 2 * 2000 * sin(2.8648/2)= 152.2 feet To determine the stationing of the PT, we can use the following formula: PT stationing = PI stationing + Length of curve's long chord= 10300 + 152.2= 10452.2Therefore, the stationing of the PT is 10452+2.
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Write the compound inequality that represents the statement. The quotient of a number y and 3, less 2 is between –7 and 4.
Solve the compound inequality.
The compound inequality is -7 < y/3 - 2 < 4 and the solution is -15 < y < 18
identifying and solving the compound inequalityTo write the compound inequality that represents the statement, we can first translate the words into symbols:
The quotient of a number y and 3, less 2: y/3 - 2
Is between -7 and 4: -7 < y/3 - 2 < 4
So the compound inequality that represents the statement is:
-7 < y/3 - 2 < 4
To solve this compound inequality, we can first add 2 to all parts of the inequality:
-7 + 2 < y/3 - 2 + 2 < 4 + 2
Simplifying, we get:
-5 < y/3 < 6
To isolate y/3, we can multiply all parts of the inequality by 3:
-15 < y < 18
Therefore, the solution to the compound inequality is: -15 < y < 18
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Polygon ABCD with vertices at A(1, −1), B(3, −1), C(3, −2), and D(1, −2) is dilated to create polygon A′B′C′D′ with vertices at A′(4, −4), B′(12, −4), C′(12, −8), and D′(4, −8). Determine the scale factor used to create the image.
1/4
1/2
2
4
The scale factor used to create the dilated polygon is 4.
What is scaler factor?
Scale factor is a numerical ratio that describes how much a geometric figure has been enlarged or reduced. It is the ratio of the length of a side, diagonal, or any other linear dimension of the new (dilated) figure to the corresponding dimension of the original figure.
The distance between two points can be calculated using the distance formula: [tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$.[/tex]
To determine the scale factor, we need to compare the distances between corresponding points in the original and dilated polygons. Let's start by finding the distance between points A and B in the original polygon:
[tex]$d_{AB}=\sqrt{(3-1)^2+(-1+1)^2}=\sqrt{4}=2$[/tex]
Now let's find the distance between corresponding points A' and B' in the dilated polygon:
[tex]$d_{A'B'}=\sqrt{(12-4)^2+(-4+4)^2}=\sqrt{64}=8$[/tex]
To find the scale factor, we divide the corresponding distances:
[tex]$scale\ factor=\frac{d_{A'B'}}{d_{AB}}=\frac{8}{2}=4$[/tex]
Therefore, the scale factor used to create the dilated polygon is 4.
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