Let the random variable X be the number of days that Spongebob needs to be in STAT107's office hour to do his project 1. Suppose X has the distribution as follows; P(X) 0.16 0.2 You can find it 0.36 Find the standard deviation of days Spongebob needs to be in the office hour SD(X). You can express your answer as a fraction, or a decimal. If you asnwer in decimal, include at least 2 NON-ZERO digits after the decimal point.
Answers
The standard deviation of days Spongebob needs to be in the office hour is 3.29.
How to calculate standard deviation?First, we must find all probability distribution. Keep in mind, total probability is always equal to 1. So,
∑P(X) = 1
∑P(X) = P(X=3) + P(X=6) + P(X=7) + P(X=12)
1 = 0.16 + 0.2 + P(X=7) + 0.36
1 = 0.72 + P(X=7)
P(X=7) = 1 - 0.72
P(X=7) = 0.28
Next, to find standard deviation (σ) we can use this formula,
σ = [tex]\sqrt{\sum X^2\times P(X) - (\sum X\times P(X))^2[/tex]
= [tex]\sqrt{(3^2\times 0.16+6^2\times 0.2+7^2\times 0.28 + 12^2\times 0.36)-(3\times 0.16+6\times 0.2+7\times 0.28+12\times 0.36)}[/tex]
= [tex]\sqrt{74.2-(7.96)^2}[/tex]
= [tex]\sqrt{10.8384}[/tex]
= 3.29
So, standard deviation X or SD(X) is 3.29
Thus, standard deviation is 3.29 days for Spongebob needs to be in the office hour.
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Related Questions
identify the terms for this arithmetic sequence
Answers
The sixth term of the arithmetic sequence 11, 15, 19, 23, 27, ..... will be 31.
What is an arithmetic sequence?Let a₁ be the first term and d be a common difference.
Then the nth term of the arithmetic sequence is given as,
aₙ = a₁ + (n - 1)d
The arithmetic sequence is given below.
11, 15, 19, 23, 27, .....
The first term is 11. And the common difference between the terms is given as,
d = 15 - 11
d = 4
Then the nth term is given as,
aₙ = 11 + (n - 1) × 4
At n = 6, then the 6th term is given as,
a₆ = 11 + (6 - 1) × 4
a₆ = 11 + 5 × 4
a₆ = 11 + 20
a₆ = 31
The sixth term of the arithmetic sequence 11, 15, 19, 23, 27, ..... will be 31.
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which of the following are exponential functions? select all correct answers. select all that apply: f(x)
Answers
The functions that are exponential are f(x) = 4(1/4)ˣ , g(x) = 14(4)ˣ and k(x) = 6(5.49)ˣ , the options that are correct are (a) , (b) and (e) .
In the question ,
five function are given ,
we need to select the functions that are exponential ,
We know that , Exponential function is a function whose value is a constant raised to power of a variable ,
For Example , f(x) = cˣ, where c is any constant value and x is a variable.
Part(a) ,
f(x) = 4(1/4)ˣ
Since , x is in the exponent , hence it is an exponential function .
Part(b) ,
g(x) = 14(4)ˣ
Since , x is in the exponent , hence it is an exponential function .
Part(c) ,
h(x) = 10x⁵
Since , x is present in the base , hence , it is not an exponential function .
Part(d) ,
j(x) = −9x⁴
Since , x is present in the base , hence ,it is not an exponential function .
Part(e) ,
k(x) = 6(5.49)ˣ
Since , x is in the exponent , hence it is an exponential function .
Therefore , The exponential functions are (a) f(x) = 4(1/4)ˣ , (b) g(x) = 14(4)ˣ and (e) k(x) = 6(5.49)ˣ .
The given question is incomplete , the complete question is
which of the following are exponential functions? select all correct answers.
(a) f(x) = 4(1/4)ˣ
(b) g(x) = 14(4)ˣ
(c) h(x) = 10x⁵
(d) j(x) = −9x⁴
(e) k(x) = 6(5.49)ˣ
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determine the point estimate of the population mean and the margin of error for the given confidence interval. lower bound: 12 upper bound: 20
Answers
The required point estimate of the population mean and the margin of error are 16 and 4.
How to solve the point estimate of the population mean and the margin of error?The point estimate is the value of a statistic that estimate the value of the parameter.
According to given data in the question:
Given, lower point =12, upper point = 20
we know that
Population mean(x) = 12+20/2 = 16
And formula for margin o error,
x + E = upper point , x - E = lower point
Then, 16 + E = 20
E = 4
Similarly, 16 - E = 12
E = 4
Hence, population mean and margin of error are 16 and 4 respectively.
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what is the probability that the wheel stops on a white slice, given that the wheel stops on a number less than 9?
Answers
The probability that the wheel stops on a white slice, given that the wheel stops on a number less than 9 is 1/2.
We have given that
A spinner with 8 equally size slices numbered 1 to 8 and some slices are white and other gray in colour .
Total possible outcomes = 8 = {1,2,3,4,5,6,7,8}
we have to calculate probability that the wheel stops on a white slice, given that the wheel stops on a number less than 9?
let consider two events
A : wheel stops at white
B: wheel stops on white slice and number less than 9
favourable cases for event A = 4
= { 8,4,2,1}
P( wheel stops at white colour)
= favourable cases/total possible outcomes
= 4/8 = 1/2
favourable cases for event B = 4
= {1,2,4,8}
Probability ( wheel stops white slice with numbered less than 9)= white slice with number less than 9/ total slices numbered less than 9
= 4/8 = 1/2
Hence, the required probability is 1/2.
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Complete question:
spinner has 8 equally sized slices numbered from to 1&8 Some are white and some are grey, as shown below. 1 2 3 4 5 6 7 8 . Answer the following questions Write each answer a fraction. The wheel will be spun and will stop on a slice at random (a) What Is the probabllity that the wheel stops on grey slice, glven that the (b) wheel stops on &n even-numbered slice?
unoccupied seats on flights cause airlines to lose revenue. suppose a large airline wants to estimate its average number of unoccupied seats per flight over the past year. to accomplish this, the records of 225 flights are randomly selected and the number of unoccupied seats is noted for each of the sampled flights. the sample mean is 11.2 seats and the sample standard deviation is 4.3 seats. note: if you are using a student's t-distribution, you may assume that the underlying population is normally distributed. (in general, you must first prove that assumption, though.)
Answers
The confidence interval for the mean is (10.7485, 11.6515)
Given Data:
n = 225
×= 11.2
s = 4.1
Note that, Population standard deviation([tex]\alpha[/tex]) is unknown. So we use t distribution.
Our aim is to construct a 90% confidence interval.
c = 0.90
[tex]\alpha[/tex] = 1- c = 1- 0.90 = 0.10
[tex]\alpha[/tex]/2 = 0.10/2 = 0.05
Also, d.f = n - 1 = 225 - 1 = 224
t[tex]\alpha[/tex]/2.d.f- = t[tex]\alpha[/tex]/2.n-1 = t0.05,224 = 1.652
( use t table or t calculator to find this value..)
The margin of error is given by
E = t[tex]\alpha[/tex]/2,d.f. * (s / [tex]\sqrt{n}[/tex])
= 1.652 * (4.1/ √225)
= 0.4515
Now , confidence interval for mean(\mu) is given by:
(× - E ) < μ< x + E)
(11.2 - 0.4515) < μ < (11.2 + 0.4515)
10.7485 < μ< 11.6515
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Tranlate the entence into an equation. Eight time the um of a number and 2 equal 4
Ue the variable x for the unknown number
Answers
The sentence translated to an equation is given by 8(x+2) = 4.
Let the variable be x which is the unknown number.
Sum of the variable and 2 is represented by (x+2) .
8 times the sum = 8 (x+2)
The sum is equal to 4.
∴ 8 (x+2) = 4
Therefore the required equation is 8 (x+2) = 4 .
An equation is regarded as linear when its highest power continuously equals 1. It is also stated as a one-degree equation. A linear equation with one variable typically has the form Ax + B = 0.
In this case, the variables x is a variable while the variable B is a constant. A linear equation with two variables often has the form Ax + By = C. The variables x and y, their respective coefficients A and B, and the constant C are present in this scenario.
In contrast to a linear equation with two variables, x and y, the graph of a linear equation with one variable, x, forms a vertical line that is parallel to the y-axis and vice versa.
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solve for the unknown, t
3e^9t = 100
Answers
Solving for the unknown variable t in the natural exponent expression 3e^9t = 100 gave
t = 0.3896175How to solve for tThe given expression is given in natural exponent and is solved as follows
3e^9t = 100
dividing through by 3
3e^9t / 3 = 100 / 3
e^9t = 100/3
take natural logarithm of both sides
In e^9t = In (100/3)
9t = In (100/3)
divide through by 9
9t / 9 = 3.5065578 / 9
t = 0.3896175
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I went into a tore with a 70% off ign on the door. I found a pair of pant that were originally $49. 99 for $30. 00 I didn't think thi wa 70% off o I had to make ure. What were the real percentage off?
Answers
The real percentage off of pant in the store was 39.99% in the store, which was less than the stated 70% off sign present on the door of store.
The percentage off will be calculated by the formula -
Percentage off = change in cost/original cost × 100
Change in cost = original cost - new cost
Change in cost = 49.99 - 30.
Performing subtraction on Right Hand Side of the equation
Change in cost = 19.99
Keep the values in formula for calculation of percentage off -
Percentage off = 19.99/49.99 × 100
Performing division on Right Hand Side of the equation
Percentage = 0.3999 × 100
Performing multiplication on Right Hand Side of the equation
Percentage = 39.99%
Thus, there was 39.99% off.
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In a solar system, two comets pass near the sun, which is located at the origin. Comet E is modeled by quantity y plus 16 end quantity squared over 400 plus x squared over 144 equals 1 and Comet H is modeled by quantity y plus 13 end quantity squared over 144 minus x squared over 25 equals 1 comma where all measurements are in astronomical units.
Part A: What are the vertices for the path of Comet E? Show your work. (4 points)
Part B: Which comet travels closer to the sun? Give evidence to support your answer. (5 points)
Part C: What key feature does the sun represent for both comets? Give evidence to support your answer. (6 points)
Answers
The evaluation of the paths of the ellipse and hyperbola are as follows;
Part A: The vertices are; (0, 36), (0, -4)
Part B: Comet H comes closest to the sun
Part C: The location of the Sun is the location of the x-coordinate of the path of both ellipse
What is an ellipse?An ellipse is the locus of a point that moves such that the sum of the distances from two points, known as the focal points, is a constant
Part A: The standard form of the equation of a hyperbola is presented as follows;
[tex]\dfrac{(x - h)^2}{a^2} -\dfrac{(y-k)^2}{b^2} =1[/tex]
Where;
(h, ,k) = The center of the ellipse
a = Vertex to center distance
c = The distance from center to foci
The equation of an ellipse is presented as follows
[tex]\dfrac{(x - h)^2}{a^2} +\dfrac{(y-k)^2}{b^2} =1[/tex]
The vertices of the ellipse are; a + h and k + b
The specified equation is presented as follows;
Comet E = [tex]\dfrac{(y+16)^2}{400} +\dfrac{x^2}{144} =1[/tex]
The vertices for the comet E are;
(0, 20 + 16) = (0, 36) and (0, 16 - 20) = (0, -4)
Part B: Comet H = [tex]\dfrac{(y+13)^2}{144} +\dfrac{x^2}{25} =1[/tex]
The vertex of the comet H = (0, -13 + 12) = (0, -1), and (0, -13 - 12) = (0, -25)
Based on the location of the comet H close to the origin, the comet that comes closest to the Sun is comet H
Part C; The location of the Sun at the origin is the location of the x-coordinate of the center of both comets
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Which ordered pair is a solution to the system of linear equations 2x 3y equals 6?.
Answers
The solution to the system of linear equations is (0,2).
What is equation?
In arithmetic, an equation may be a formula that expresses the equality of 2 expressions, by connecting them with the sign =.
Main body:
2x + 3y = 6 multiplied by 3
-3x + 5y = 10 multiplied by 2
6x + 9y = 18
-6x + 10y = 20
19y = 38
y = 38 / 19
y = 2
2x + 3x2 = 6
2x + 6 = 6
2x = 0
x = 0/2
x = 0
Therefore, The correct answer is (0,2)
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based on the central limit theorem, the sample mean can be used as a good estimator of the population mean, assuming that the sample size, , is sufficiently large.
Answers
According to the central limit theorem, the given statement is true.
In the given question we have to check the given statement is true or false.
The given statement is:
"Based on the central limit theorem, the sample mean can be used as a good estimator of the population mean, assuming that the sample size, is sufficiently large."
As we know that the average of set of data is known as a sample mean.
Regardless of the distribution of the population, the central limit theorem states that the distribution of sample means approaches a normal distribution as the sample size increases. The Central Limit Theorem is frequently thought to hold for sample sizes equal to or larger than 30.
So according to the central limit theorem, the given statement is true.
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select the best choice from among those provided. a. two thousand people are expected to attend the conference, with 965 coming from outside of the united states. b. 2,000 people are expected to attend the conference, with 965 coming from outside of the united states.
Answers
The correct choice regarding the grammar illustrated is A. two thousand people are expected to attend the conference, with 965 coming from outside of the United States.
What is grammar?The grammar of a natural language is the set of structural constraints on the composition of clauses, phrases, and words by speakers or writers. The term can also refer to the study of such constraints, which includes domains such as phonology, morphology, and syntax, which are frequently supplemented by phonetics, semantics, and pragmatics.
There are currently two approaches to grammar study: traditional grammar and theoretical grammar. In this case, it should be noted that the fact that 2000 is written in words make it more logical and better.
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write the following expression in simplest form. the expression quantity negative two thirds times x minus 6 end quantity minus quantity negative 14 plus one sixth times x end quantity
Answers
The simplified form of the expression is, negative five sixths times x plus eight.
What is word problem?
A math word problem is a mathematical question that is stated as one sentence or more and asks students to use their arithmetic skills in a "real-life" situation. Therefore, in order for kids to understand the word problem, they need to be familiar with the terminology that goes along with the mathematical symbols that they are used to.
Given that: quantity negative two thirds times x minus 6 end quantity minus quantity negative 14 plus one sixth times x end quantity
It can be write in mathematical form as,
[tex](-\frac{2}{3}x-6) - (-14+\frac{1}{6}x)[/tex]
Simplifying the parenthesis,
[tex]= -\frac{2}{3}x-6+14-\frac{1}{6}x\\ = 8 - \frac{15}{18}x\\ = 8 - \frac{5}{6}x\\= -\frac{5}{6}x+8[/tex]
Hence, the simplified form of the expression is, negative five sixths times x plus eight
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cori races her friend heading south for 9 kilometers, east for 20 kilometers, then south for 6 more kilometers. how far is cori from where she started?
Answers
The required distance of Cori from where he started is 35km.
What is meant by distance?Distance is a quantitative or qualitative measurement of the distance between two objects or places. Distance can refer to a physical length or an estimation based on other criteria in physics or everyday usage. Because spatial cognition is a rich source of conceptual metaphors in human thought, the term is also used metaphorically to mean a measurement of the amount of difference between two similar objects or a degree of separation. The concept of a metric space is used to codify most such conceptions of distance, both physical and metaphorical.
Given,
Cori races her friend heading south for 9 kilometers, east for 20 kilometers, then south for 6 more kilometers.
The distance of Cori from starting point=9+20+6
=15+20
=35
Hence, the required distance of Cori from where he started is 35km.
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Please help me this is geometry
Answers
Answer: The last option, [tex]8\sqrt{2}[/tex]
Step-by-step explanation:
When looking at this triangle, there are two things we can note about it right away. First, it's a right triangle so we can use the Pythagorean theorem. Second, the two legs of the triangle are congruent (as shown by the dash lines) so both of them are equal to 8.
Using the Pythagorean theorem we will solve.
a² + b² = c²
(8)² + (8)² = c²
64 + 64 = c²
128 = c²
c = [tex]\sqrt{128}[/tex]
c = [tex]\sqrt{64*2}[/tex]
c = [tex]8\sqrt{2}[/tex]
Help please I’ll give brainly : )
Answers
Answer:
4x-3y=6
because it is a way to write in standard form
Answer:
Option (c)[tex] \frac{4}{5} x + 2y = 6[/tex]
is the correct answer
Step-by-step explanation:
The standard form of a equation is Ax+By=C
Third option satisfy it so option (c)is the correct Answer.
Minimize the objective function p = 45x 48y for the given constraints.
Answers
Answer:
1640y
Step-by-step explanation:
the reason is y is known as variables constant is number 48y is a monomial that is why it is 26840y
What is bigger 3/4 cup or 1/2 cup?.
Answers
Answer:
[tex]\frac{3} {4}[/tex] cup
Step-by-step explanation:
[tex]\frac{1}{2}[/tex] as a decimal = 0.5
[tex]\frac{3}{4}[/tex] as a decimal = 0.75
8. A party planner i deigning a conical canva tent for a child' birthday party. The tent ha no floor, and it ha a radiu of 3 ft, and a lant height of 5 ft. If canva ell for $23. 00/yd², how much will the material cot
Answers
The material cost will be $361.1
The tent ha no floor, and it ha a radiu of 3 ft, and a slant height of 5 ft. If canva ell for $23. 00/yd²
Then, radius of base = 3
Therefore, area of conical tent =πrl
area of conical tent = 3.14 x 3 x 5
area of conical tent = 47.1
If cost of canvas is $23. 00/yd²
1 yard = 3 feet
Then cost of canvas = (47.1/3) x 23.00
cost of canvas = 361.1
Therefore, the material cost will be $361.1
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Exercise statement: the life spans of car batteries are normally distributed, with a mean of 44 months and a standard deviation of 5 months. A car battery is selected at random. Find the probability that the life span of the battery is less than 36 months. What is the shortest life expectancy a car battery can have and still be in the top 5% of life expectancies
Answers
The shorted life expectancy to be in top 5% is 52.225
Given that.
Mean = 44
Standard Deviation = 5
a)
Z =36 – 44/5
Z =-8/5
Z =-1.6
P(z<-1.6)=normsdist(-1.6)=0.0548
b)
P(Z > 2) = 0.05
P(Z <=) = 1 -0.05 = 0.95
z=normsinv(0.95)=1.645
shorted life expentancy to be in top 5%=
= 44+1.645*5
Shorted life expentancy to be in top 5% = 52.225
For Minitab use:
Choose Calc > Probability Distributions > Normal.
Select Inverse cumulative probability.
In Mean, enter 44.
In Standard deviation, enter 5.
In Input column, enter Probability=0.95
Hence, The shorted life expectancy to be in top 5% is 52.225.
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What is unit digit in the product 784 x 618 x 917 x 463?.
Answers
2 is unit digit in the product .
What do Units digits mean?
The digit that goes in the place of one in a number is known as the units digit. It is the number's last digit on the right, for example. For instance, the units digit for 243 is 3 and for 39 it is 9.The Unit Place Digit refers to the digit placed in the one's position of the particular number.unit digit of (784 ×618 × 917 ×463)
unit digit of ( 4 × 8× 7 × 3 )
unit digit of ( 672)
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a local bbq restaurants offers 2 side dishes with a lunch plate. there are 7 side dishes. how many choices of side dishes does a customer have? note: there is no requirement that the customer chooses different side dishes (i.e. he or she can choose say baked beans twice as their side dish).
Answers
The number of choice out of 7 that consumer have are 42.
What is permutation?The term permutation alludes to a numerical computation of the quantity of ways a specific set can be sorted out. Set forth plainly, a change is a word that depicts the quantity of ways things can be requested or organized. With stages, the request for the course of action matters.
According to given data:Number of choices of side dishes does a customer have,
total dishes(n)=7 , r = 2
ⁿP₂
⁷P₂
7×6 = 42
Thus required number of ways are 42.
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5. Determine which property is demonstrated below:
m/HZN = m/TZY, so m/YZT = m/HZN
transitive property
O subtraction property
addition property
O distribution property
None of these are correct.
4
Answers
None of these are correct.
m/HZN = m/TZY, so m/YZT = m/HZN demonstrate commutative property
Why is it called transitive property?The term transitive refers to a transfer. If there are three quantities a, b, and c, and if an is connected to b by some rule and b is related to c by the same method, then a and c are related to each other by the same rule; this property is known as the transitive property of equality.When you multiply a value by a sum, the distributive property of multiplication over addition is used. For instance, suppose you want to multiply 5 by the sum of 10 + 3. When we have similar phrases, we normally sum the numbers and then multiply by 5. However, according to the property, you must first multiply each addend b.To learn more about commutative property refer,
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(a) find the critical numbers of (if any), (b) find the open interval(s) on which the function is increasing or decreasing, (c) apply the First Derivative Test to identify all relative extrema, and (d) use a graphing utility to confirm your results.
Answers
The critical numbers of the function x³ - 6x² + 15 is 0 and 4
The given function is x³ - 6x² + 15
To find the critical value first we need to find the derivative, then set the derivative f'(x) to zero
The derivative of x³ - 6x² + 15 is
3x³⁻¹ - 2(6)x²⁻¹ = 0
3x² - 12x = 0
3x(x - 4) = 0
3x = 0
x = 0
x - 4 = 0
x = 4
so, x = 0 or 4
Therefore, the critical numbers of the function x³ - 6x² + 15 is 0 and 4
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I will give brainlest
Answers
The constant of proportionality of the equation y = 1 / 4 x is 1 / 4.
How to solve proportional relationship?Proportional relationships are relationships between two variables where their ratios are equivalent.
A proportional relationship is one in which two quantities vary directly with each other. We say the variable y varies directly as x if:
y = k x
for some constant k , called the constant of proportionality.
Therefore, let's model the equation to the y = 1 / 4 x .
Therefore, the constant of proportionality is 1 / 4.
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You are viiting Mexico and need to convert your U. S. Dollar to the Mexican Peo. How many Mexican Peo will you have from $350?
Answers
In Mexico, 350 dollars would be equivalent to 6769.21 Mexican Pesos.
What is currency conversion?
Currency conversion is the process of exchanging one type of currency for another to facilitate transactions in which the issuer and acquirer use different currencies. Currency conversion usually incurs some additional costs for the customer.
In Mexico, 1 US dollar = 19.34 Mexican Pesos
So In Mexico, $350 = 350 * 19.34
= 6769.21 Mexican Pesos.
Hence, In Mexico, 350 dollars would be equivalent to 6769.21 Mexican Pesos.
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What is the solution set of the inequality x 2 5?.
Answers
The solution set of the inequality |x+2| ≤ 5 is x ∈ [-7,3].
What is inequality?
The word inequality means a mathematical expression in which the sides are not equal to each other.
Basically, an inequality compares any two values and shows that one value is less than, greater than, or equal to the value on the other side of the equation.
What is modulus function?The modulus function, which is also called the absolute value function gives the magnitude or absolute value of a number irrespective of the number being positive or negative.
Modulus function is denoted as y = |x| or f(x) = |x|, where f: R→ (0,∞) and x ∈ R.
Here, we have an inequality |x+2| ≤ 5
Solving the modulus , we get
-5 ≤ x+2 ≤ 5
Subtracting -2 from both sides, we get
⇒ -5-2 ≤ x ≤ 5 -2
⇒ -7 ≤ x ≤ 3
⇒ x ∈ [-7,3]
Therefore, the solution set of the inequality is x ∈ [-7,3].
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NOTE : The question given here is not complete. The complete question is given below.
Question: What is the solution set of the inequality |x+2|≤ 5 ?
the cost of a small business is given by the expression 1000 15x, where x is the number of units produced. the business will be profitable whenever its profit y exceeds its cost. if the profit region is shaded in blue, which of the following graphs corresponds to the given situation?
Answers
The profit exceeds the cost as y > 1000 + 15x. So, option 1 is correct.
Gaining anything is known as profit. When the Selling price ( SP ) of the product is more than the cost price ( CP ) of the product, we gain profit. Opposite to the profit is loss i.e. losing anything is called loss. When the Selling price ( SP ) of the product is less than the cost price ( CP ) of the product, we get a loss.
Profit can be calculated by the formula,
Profit = Selling Price - Cost price
P = SP - CP
Loss can be calculated by the formula,
Loss = Cost price - Selling price
L = CP - SP
As per the question,
x = number of units producedexpression = 1000 + 15x⇒ When y > 1000 + 15x, then profit exceeds cost:
x = 50 and y = 1750x = 100 and y = 2500x = 150 and y = 3250x = 200 and y = 4000x = 0 and y = 1000Therefore, the graph in the 1st option is correct as the profit exceeds the cost.
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The complete question is
How many rearrangements of abcd are there in which no two adjacent letters are also adjacent letters in the alphabet? For example, no such rearrangements could include either ab or ba.
(A) 0
(B) 1
(C) 2
(D) 3
(E) 4
Answers
There are 2 rearrangements of abcd in which no two adjacent letters are also adjacent letters in the alphabet.
What is letter arrangements?
A sorting technique that allows the person to arrange alphabets as conditioned according to the question. Then total arrangements are calculated to know the result.
According to the given question:
Using XXXX as stencil for letters arrangement
We can't put B in either of the middle positions, as there would only be the far end at which to put both A and C and we can't put two things in one slot. That is, XBXX would require A and C to both be in the red X in order to avoid putting them next to B...can't do that, so B can't go in the middle.
Similarly, we can't put C in either of the middle positions, as there would only be the far end at which to put both B and D and we can't put two things in one slot.
So, B and C must go on the ends.
BXXC can only be filled in as BDAC.
CXXB can only be filled in as CADB.
Hence there are 2 such arrangements.
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one cubic foot will hold 7.5 gallons of water. a rectangle-shaped tank is 10 feet by 8 feet by 8 feet. how many gallons of water will this tank hold?
Answers
The rectangle-shaped tank is 10 feet by 8 feet by 8 feet is 4800 gallons of water.
Cubic foot holds 7.5 gallons of water
We need to find the amount of gallons of water can a rectangle-shaped tank is 10 feet by 8 feet by 8 feet.
Vol = L*W*H
10 x 8 x 8
640 cubic feet
1 cubic feet hold 7.5 gallons of water
640 cubic feet hold 7.5 x 640 = 4800
Therefore, the amount of gallons of water can a rectangle-shaped tank is 10 feet by 8 feet by 8 feet is 4800 gallons of water.
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