Answer: If they worked together, it would take 31.5 minutes
Step-by-step explanation:
There's a certain formula for equations like this:
[tex]\frac{1}{t1} +\frac{1}{t2}=\frac{1}{tb}[/tex]
t1= the time it took for the first person to complete the task.
t2= the time it took for the second person to complete the task.
tb= the time it took for both of them to complete the task.
We have the values for both t1 and t2, but not for tb.
t1= 45
t2= 105
tb= x
[tex]\frac{1}{45} +\frac{1}{105} = \frac{1}{x}[/tex]
Now it's simple algebra, and all we need to do is solve for x
The LCM for both fractions is 315, so now we multiply BOTH sides of the equation by 315.
[tex]\frac{315}{45} + \frac{315}{105} = \frac{315}{x}[/tex]
This will simplify nicely, so now we just need to get x on the other side.[tex]7 + 3 = \frac{315}{x} \\\\\ 10*x = \frac{315}{x} * x[/tex]
[tex]10x = 315 \\\\x = 31.5[/tex]
Draw out a two column proof for each problem below. Complete all problems on one page and upload ONE photo of the entire assignment Make sure your file/image is clear (not blurry) and easy to read. Problem 1. Congruent Triangle Proof (10 Points) Given: NQ is the bisector of MNP and NMQ ~ ZNPQ| Prove: A MNQA PNQ 0 Problem 2. Proof Involving CPCTC (14 Points) Given: S is the midpoint of QR QR PS and RSP and QSP are right angles. Prove: PR PQ S 0
Two or more triangles are congruent if on comparison, they have equal lengths of sides, and measure of angles.
Therefore, the required proofs for each question are shown below:
Problem 1:
Congruent triangles are triangles with equal lengths of corresponding sides and measures of internal angles.
Thus,
STATEMENT REASON
1. <NMQ ≅ <NPQ Any point on a perpendicular bisector
makes equal measure of angle with the
two ends of the line segment.
2. NQ ⊥ MP Definition of a line.
3. MQ ≅ PQ Equal segments of a bisected line.
4. MN ≅ PN Any point on a perpendicular bisector
is at the same distance to the
two ends of the line segment.
5. <MNQ ≅ <PNQ Equal measure of the bisected angle.
Problem 2:
A line segment is the shortest distance between two points.
STATEMENTS REASONS
1. m<PSR ≅ m<PSQ A perpendicular bisector is always at a right
angle to the bisected line segment.
2. m<RPS ≅ m<QPS Equal measure of the bisected angle.
3. RS ≅ QS Property of a bisected line segment.
4. PR ≅ PQ Any point on a perpendicular bisector
is at the same distance to the two ends of
the line segment.
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Solve the differential equation. (x^2 + 11)y' = xy
Separate the variables.
[tex](x^2+1) \dfrac{dy}{dx} = xy \implies \dfrac{dy}y = \dfrac x{x^2+11} \, dx[/tex]
Integrate both sides. On the right, substitute [tex]u=x^2+11[/tex] and [tex]du=2x\,dx[/tex].
[tex]\displaystyle \int \frac{dy}y = \int \frac x{x^2+11}\,dx = \frac12 \int \frac{du}u[/tex]
[tex]\ln|y| = \frac12 \ln|u| + C[/tex]
[tex]\ln|y| = \ln\left(\sqrt{x^2+11}\right) + C[/tex]
[tex]e^{\ln|y|} = e^{\ln\left(\sqrt{x^2+11}\right)+C}[/tex]
[tex]\boxed{y = C\sqrt{x^2+11}}[/tex]
Using separation of variables, the solution to the differential equation is:
y = ksqrt(x² + 11)
What is separation of variables?In separation of variables, we place all the factors of y on one side of the equation with dy, all the factors of x on the other side with dx, and integrate both sides.
In this problem, the differential equation is:
(x² + 11)y' = xy
Applying separation of variables, we have that:
y'/y = x/(x² + 11)
[tex]\int \frac{y^{\prime}}{y} = \int \frac{x}{x^2 + 11}[/tex]
[tex]\ln{y} = \frac{\ln{x^2 + 11}}{2} + K[/tex]
[tex]\ln{y} = \ln{(x^2 + 11}^{\frac{1}{2}}) + K[/tex]
[tex]\ln{y} = \ln{\sqrt{x^2 + 11}} + K[/tex]
Hence the solution is:
y = ksqrt(x² + 11)
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What is the value of b?
The value of b as described in the task content by means of solving the two equations simultaneously is; b= -10.
What is the value of b from the given equations?The given simultaneous equations as indicated have been manipulated to determine the value of a which is; 0.5 in the task content.
Hence, by substituting a= 0.5 into the equation; 5 = 30a + b; we have;
5 = 30(0.5) + b
b = 5- 15 = -10.
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Copy the problem, mark the givens in the diagram and write a statement/reason proof
Answer:
Step-by-step explanation:
<E = <T Given
M is the midpoint of TE Given
TM = ME Definition of a midpoint
<TMI = <RME Property of Vertically Opposite Angles
ΔTMI = ΔRME ASA = ASA
MI = ME Corresponding parts of Congruent triangles are Congruent
answer: reasoning:
<E = <T given
M is the midpoint of TE given
TM = ME definition of a midpoint
<TMI = <RME property of Vertically Opposite Angles
ΔTMI = ΔRME ASA = ASA
MI = ME corresponding parts of congruent triangles are Congruent
hope this helps!
Christie has $200 in her bank account. Every month, she deposits $20 into her account.
The equation of the line that models the amount of money, y, in her account x months from now is y = x .
Answer:
y = 20x + 200
Step-by-step explanation:
The 200 is the constant. It is only added once, but the monthly deposits are added at 20 every month.
After 1 month:
y = 20x + 200
y = 20(1) + 200
y = 20 + 200
y =220 money deposited.
After 2 months:
y = 20x + 200
y = 20(2) + 200
y = 40 + 200
y =240 money deposited.
After 3 months:
y = 20x + 200
y = 20(3) + 200
y = 60 + 200
y = 260 money deposited
And so on, and so on, and so on...
The walls of a square room with side length s are being torn down and rebuilt. The area of the new room can be represented by 1.75s(2s + 3).
Which expression represents the area of the new room?
3.75s + 4.75
3.75s2 + 4.75s
3.5s2 + 5.25s
3.5s + 5.25
The expression that represents the area of the new room is (c) 3.5s^2 + 5.25s
How to determine the area of the new room?The given parameters are:
Wall =Square
Length = s
When the wall of the square room is torn down and rebuilt, the area of the new room is represented by 1.75s(2s + 3).
This means that
Area= 1.75s(2s + 3)
Expand the expression
Area= 1.75s * 2s + 1.75s * 3
Evaluate the products
Area= 3.5s^2 + 5.25s
This means that the expression that represents the area of the new room is (c) 3.5s^2 + 5.25s
Hence, the expression that represents the area of the new room is (c) 3.5s^2 + 5.25s
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Researchers wanted to study if having a long beak is related to flight and birds they surveyed a total of 34 birds the data are shown in the contingency table below what is the relative risk of flying for those birds that have long beaks
The odds ratio for birds having long beaks being able to fly against birds not having long beaks being able to fly is 3.76.
What is an odds ratio?An odds ratio is a measure of the strength of an association with the exposure and outcome.
The odds ratio can be calculated by dividing the odds of the first group (exposure) by the odds of the second group (outcome).
Flies Does not fly Total
Long beak 11 7 19
Not a long beak 3 13 15
Total 14 20 34
Probability of long beaks flying = 0.79 (1/14)
Probability of not having long beaks flying = 0.21 (3/14)
Odds ratio = 3.76 (0.79/0.21)
Thus, the odds ratio for birds having long beaks being able to fly against birds not having long beaks being able to fly is 3.76, showing greater odds of association.
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Complete question
Researchers wanted to study if having a long beak is related to flight in birds. They surveyed a total of 34 birds. The data are shown in the contingency table below. What is the odds ratio for birds having long beaks being able to fly against birds not having long beaks being able to fly? Round your answer to two decimal places.
Long beakNot a long beakTotalFlies11719Does not fly31315Total142034
2.) A shop sells oranges at 6 for N100. A trader sells the same kind of oranges at 8 for N120.
Which price is cheaper, by how much per orange?
The cheaper price among this set of orange sales is the one done by trader B, who sells 8 for N120.
How is the cheaper price determined?The cheaper price can be computed by finding out the price per unit.
Data and Calculations:Price of Set Unit Price
Sale of 6 oranges N100 N16.67 (N100/6)
Sale of 8 oranges N120 N15.00 (N120/8)
Thus, selling 8 oranges for N120 is cheaper than selling 6 oranges for N100, and N1.67.
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A scientist is tagging fish in the Allentown Lake. She catches a fish, tags it,and releases it back into the water. The scientist knows the exact number of fish in the lake: 32 bass,14 fluke,10 carp, and 3 bull sharks.
Calculate the probabilities that the scientist will catch:
A. a bass and then a carp
B. two consecutive bull sharks
C. a fluke and then any different type of fish
d. a bass, another bass, and a bull shark
Probability has to do with the possibility that an event may or may not happen.
What is the probability?The term probability has to do with the possibility that an event may or may not happen. The value of probability always ranges from zero to one.
Now;
Total number of fishes = 32 + 14 + 10 + 3 = 59
a) probability of catching a bass and then a carp = 32/59 * 10/59 = 320/3481
b) probability of catching two consecutive bull sharks= 3/59 * 3/59 = 9/3481
c) probability of catching a fluke and then any different type of fish 14/59 * (32/59 + 10/59 + 3/59) = 14/59 * 45/59 = 630/3481
d) probability of catching a bass, another bass, and a bull shark = 32/59 * 32/59 * 3/59 = 3072/205379
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Last month McKinneys Apothecary dispense the following liquid medication 1 gallon 3 quarts 7 pints and 3 dozens 6ounces of bottles in total how many millimeters what is dispensed
Answer: 10204 millimeters
Step-by-step explanation: A gallon = 3875 mm. A quart is 946. 946x 3 = 2838. A pint is around 473 mm which, when multiplied by 7, is 3311. Finally, there are 6 ounces which are approximately 30 mm. 6x30 = 180. We add all of this up : 3875 + 2838+ 3311 + 180 = 10204.
Mr. Black bought a television set for $450.00. He later sold the television set at a loss of 30%. (a) Calculate the amount of the loss.
The amount of the loss exists 1350.
What is the amount of loss?
Amount of Loss means an amount equivalent to the outstanding balance of the principal amount, less any amounts recognized by perfecting rights under a security agreement, together with such interest as the executive director shall permit, to a maximum of such interest as may be permitted by rule.
Given: Mr. Black purchased a television set for $450.00. He subsequently sold the television set at a defeat of 30%.
From the given information, we get
[tex]$4500\cdot \frac{30}{100}[/tex]
simplifying, we get
[tex]$4500\cdot \frac{30}{100}[/tex]
= 1350
Therefore, the amount of the loss exists 1350.
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Lets find the digit in blank space of thr following numbers so hat the number formed is divisible by 11.
a.27.......3
Thirty-two percent of workers in Troberca City are college graduates. You randomly select 50 workers and ask them is he or she is a
college graduate. Find the probability that less than 18 workers are college graduate. (Approximating a Binomial Distribution)
(A) 32.6%
B 67.4%
64.0%
36.0%
The correct option is B) 67.4%
What is the z- score table?A standard normal table (also called the unit normal table or z-score table) is a mathematical table for the values of ϕ, indicating the values of the cumulative distribution function of the normal distribution. Z-Score, also known as the standard score, indicates how many standard deviations an entity is, from the mean.
Given here, P(probability that a worker is a college graduate) = 32%
= 0.32
q (probability that a worker is not a college graduate) is 1-0.32 = 0.68
now μ(mean) = n×p
= 50×0.32
= 16
Again standard deviation σ = [tex]\sqrt{npq\\}[/tex]
σ = [tex]\sqrt{50\cdot 0.32\cdot 0.68}[/tex]
σ = 3.2985
now P(x<17.5) = P((x-μ)/σ <(17.5-16)/3.2985)
= P(z<0.45)
= 0.674 [using z table]
= 67.4%
Hence option 2 is the correct answer
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What would the first step be in solving the equation 4/7x = 21
❄ Hi there,
the first step in solving this inequality is
multiplying (both sides) by 7[tex]\sf{\dfrac{4}{7}x\times7=21\times7}[/tex]. Look what happens on the left side!
[tex]\sf{4x=147}[/tex]
Multiplying both sides of an equation, or inequality, by the fraction's denominator, is a nice little trick when you need to get rid of fractions to solve in terms of a variable.
Finish solving for x by dividing both sides by 4 –
[tex]\sf{x=\dfrac{147}{4}}[/tex]
❄
Add (x^3 -2x^2+4) + (2x^3+x^2-2) express in standard form
Answer:
3x^3-x^2+0x+2Step-by-step explanation:
add both the equations then you will get
3x^3-x^2+2
but in the standard form there should be an x^1 term or x term since there is no term like that we write it as 0x
so the equation will be
3x^3-x^2+0x+2
5:
will give brainliest
The focal length of the given ellipse is given as (±6, 0)
Equation of an ellipseAn ellipse is defined as a regular oval shape, traced by a point moving in a plane so that the sum of its distances from two other points (the foci) is constant or when a cone is cut by an oblique plane which does not intersect the base.
The standard equation of an ellipse is expressed as;
x^2/a^2 + y^2/b^2 = 1
The formula for calculating the focus of the ellipse is given as:
c^2 = b^2 - a^2
Given the equation of an ellipse
(x-7)^2/64 + (y-5)^2/100 = 1
This can also be expressed as:
(x-7)^2/8^2 + (y-5)^2/10^2 = 1
Comparing with the general equation
a = 8 and b = 10
Substitute
c^2 = 10^2 - 8^2
c^2 = 100 - 64
c^2 = 36
c = 6
Hence the focal length of the given ellipse is given as (±6, 0)
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3. Jessie has 25 small
boxes to put his rock
collection in. He sorts 20
rocks into each box.
How many rocks does
he have in his collection?
Answer:
500 rocks
Step-by-step explanation:
25*20 = 500
A large high school has 3,000 students.
During a one-week period, 75 students were
selected at random various times of the day.
Each student was asked if he or she had one
or more social media accounts. The survey
found that 3 out of 75 students did not have
any social media accounts. Estimate the
number of students in the entire school who
do not have social media accounts.
Answer:
120 students don't have social media accounts
Step-by-step explanation:
Whether the sample is representative:
Estimate: [tex]\frac{3}{75} (3000)=\frac{9000}{75} =120[/tex]
Hope this helps
Someone please help me with this question thank youuu
Answer: 148 degrees
Step-by-step explanation:
The total measure of all exterior angles of a convex pentagon is 360 degrees.
If four of them equal 53 degrees then all those together is 212 degrees
53 times 4 = 212
Then you would just subtract 212 from 360 to see the measure of the last exterior angle. Which is 148 degrees!
Hope this helps :)
In a study of 250,178 cell phone users,it was found that 81 developed cancer of the brain or nervous system. Assuming that cell phones have no effect, there is 0.000412 probability of a person developing cancer of the brain or nervous system. We therefore expect about 104 cases of such cancer in a group of 250,178 people.Estimate the probability of 81 or fewer cases of such cancer in a group of 250,178. What do these results suggest about media reports that all cell phone cause cancer of the brain or nervous system?
P(x≤81)=[tex]P(x\leq 81)\\What do these results suggest about media reports?[/tex]
Using the normal distribution, the probability is given as follows:
P(x≤81) = 0.0158.
Since this probability is very small, less than 0.05, it suggest that the media reports overstated the proportion of cellphone users that developed cancer.
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 binomial distribution is the probability of x successes on n trials, with p probability of a success on each trial. It can be approximated to the normal distribution with [tex]\mu = np, \sigma = \sqrt{np(1-p)}[/tex].For this problem, the proportion and the sample size are given by:
p = 0.000412, n = 250178
Hence the mean and the standard deviation for the approximation are given by:
[tex]\mu = np = 250178 \times 0.000412 = 103.1[/tex].[tex]\sigma = \sqrt{np(1-p)} = \sqrt{250178 \times 0.000412 \times (1 - 0.000412)} = 10.15[/tex]The probability that x is of 81 or less than the p-value of Z when X = 81.5, accounting for continuity correction, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{81.5 - 103.1}{10.15}[/tex]
Z = -2.13
Z = -2.13 has a p-value of 0.0158.
Hence:
P(x≤81) = 0.0158.
Since this probability is very small, less than 0.05, it suggest that the media reports overstated the proportion of cellphone users that developed cancer.
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A spinner is labeled with the numbers 1,2,3,4,5,6,7,8, & 9.
Calculate the:
a. odds of spinning a 3
b. odds of not spinning a 9
c. odds of spinning an even number
d. odds of spinning a number less than 6
Answer:
Step-by-step explanation:
d
A glass inform of frustrum of cone
The volume of the cone illustrated will be 117.2 unit³.
How to illustrate the information?From the information illustrated, the glass inform of a the frustrum of a cone has the dimensions: radius 4cm and a height of 7cm.
It should be noted that the volume of a cone is calculated as:
= 1/3 πr²h.
where,
π = 3.142
r = radius = 4cm
h = height = 7cm
In this case, since we know the values of the dimensions, then we can calculate the volume. This will be:
= 1/3πr²h
= 1/3 × 3.14 × 4² × 7
= 117.2 unit³
Therefore, the volume of the shape is 117.2 unit³.
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Complete question:
A glass inform of a the frustrum of a cone has the following dimensions: radius 4cm and a height of 7cm. Calculate the volume of the shape.
plesee help me do I need it under 25min and don't answer if you don't know or else u will be reported thank you (◔‿◔)
Answer:
l = 2.25 cm
Step-by-step explanation:
given l is inversely proportional to w² then the equation relating them is
l = [tex]\frac{k}{w^2}[/tex] ← k is the constant of proportion
(i)
to find k use the condition w = 1.5 , l = 16 , then
16 = [tex]\frac{k}{1.5^2}[/tex] = [tex]\frac{k}{2.25}[/tex] ( multiply both sides by 2.25 )
36 = k
l = [tex]\frac{36}{w^2}[/tex] ← equation of proportion
(ii)
when w = 4 , then
l = [tex]\frac{36}{4^2}[/tex] = [tex]\frac{36}{16}[/tex] = 2.25 cm
see attachment for question
The percentage when Potiphar woke up late is 14.4%.
How to calculate the percentage?From the information, it was stated that Potiphar takes a horse and buggy to work everyday. In order to come on time, he must wake up promptly at 6.30am and then hop on the buggy and that anytime he wakes up late or the horse was in traffic, he will be late.
It was further illustrated based on the information given in the question that he was late 24.4% of the time and the horse was in traffic for 10% of the time.
Therefore, the percentage when he woke up late will be gotten by simply subtracting the percentages that we have above. This will be illustrated below:
= 24.4% - 10%
= 14.4%
Therefore, the percentage when Potiphar woke up late is 14.4%.
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Write a linear function that passes through the points (3, -7) and (0, 15)
Answer:
The linear function for the given pts. will be
[tex]y = \frac{ - 22}{3}x + 15[/tex]
Step-by-step explanation:
Hello!
[tex]first \: find \: the \: slope \: for \: the \: two \: pts. \\ m = \frac{y2 - y1}{x2 - x1} \\ m = \frac{(15 - ( - 7))}{(0 - 3)} where \: y2 = 15 \\ y1 = - 7 \\ x2 = 0 \\ x1 = 3 \\ m = \frac{ - 22}{3} \\ thus \: y = mx + b \: \: solve \: for \: b \: using \: one \: of \: the \: two \: points \\ lets \: take \: the \: second \: point \\ y = mx + b \\ 15 = \frac{ - 22}{3} (0) + b \\ b = 15 \\ therefore \: substitute \: this \: value \: to \: get \: the \: \\ y = \frac{ - 22}{3} x + 15[/tex]
When pricing out a menu, we know it is important to use the Edible a portion Price. What would the effect on your profit margin be, if we only used the as purchased price to determine our cost and selling price?
The effect of Edible a portion Price on your profit margin , if we only use the as purchased price to determine our cost and selling price is that it will maximize the profit because it will account for every part of the production.
What is edible portion cost?
The portion cost can be calculated by multiplying the cost of a usable kg with the portion size.
This can be represented as : portion cost = (portion size x cost of usable kg)
It should be noted that Edible portion (EP) serves as the portion of food which will be given top the customer after the preparation.
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Answer:
Step-by-step explanation:
La dodecahedral die (one with 12 sides numbered from 1 to 12) is tossed once. Find the following probability. The number on the upward face is not 7
Answer:
11/12
Step-by-step explanation:
no of sample space=12
number of 7 to occur is 1/12
number of not 7:
since the total probability is 1
so 1-1/12=11/12
In a field, there are some sheep and some goats. The ratio of sheep to goats is 3:1. If there
are 3 goats, how many sheep are there.
it is that wich is klweijxmpx
The data given to the right includes data from candies, and of them are red. The company that makes the candy claims that % of its candies are red. Use the sample data to construct a % confidence interval estimate of the percentage of red candies. What do you conclude about the claim of %?
Using the z-distribution, the 95% confidence interval for the percentage of red candies is of (7.84%, 33.18%). Since 33% is part of the interval, there is not enough evidence to conclude that the claim is wrong.
What is a confidence interval of proportions?A confidence interval of proportions is given by:
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which:
[tex]\pi[/tex] is the sample proportion.z is the critical value.n is the sample size.In this problem, we have a 95% confidence level, hence[tex]\alpha = 0.95[/tex], z is the value of Z that has a p-value of [tex]\frac{1+0.95}{2} = 0.975[/tex], so the critical value is z = 1.96.
Researching this problem on the internet, 8 out of 39 candies are red, hence the sample size and the estimate are given by:
[tex]n = 39, \pi = \frac{8}{39} = 0.2051[/tex]
Hence the bounds of the interval are:
[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.2051 - 1.96\sqrt{\frac{0.2051(0.7949)}{39}} = 0.0784[/tex][tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.2051 + 1.96\sqrt{\frac{0.2051(0.7949)}{39}} = 0.3318[/tex]As a percentage, the 95% confidence interval for the percentage of red candies is of (7.84%, 33.18%). Since 33% is part of the interval, there is not enough evidence to conclude that the claim is wrong.
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The letters of "EAGLES" should be evenly spaced across a 70-inch-wide banner, with no margins. Each letter is 10 inches wide. How many inches (x) should exist between each pair of letters
Answer:
2 Inches or ~1.43 Inches
Step-by-step explanation:
2 Inches if it's not including the spacing before the first "E" and after the "S", ~1.43 Inches if it's including the spacing.
You would get 2 Inches since if each letter is 10 inches (total 6 letters), that would be 60 inches. There are 5 total spaces in between all the letters. 70 Inches(Banner size) - 60 Inches (total letter size) = 10 Inches, divided equally within the 5 spaces. That would equal 2 :)
You also get ~1.43 Inches by doing the same process as the one shown above^ (that is if you're including the spacing before and after the word)
:)