There are 55 ways to form a train consisting of tank cars, boxcars, and flatcars by using concept of combinations.
If there are t tank cars, b boxcars, and f flatcars in the train yard, then the number of ways to form a train by selecting some of these cars is the same as the number of ways to distribute n = t + b + f identical objects into three distinct boxes, such that each box may receive any number of objects (including zero). The solution is given by the combination formula:
C(n + k - 1, k - 1)
where k is the number of boxes (in this case, k = 3). Therefore, the number of ways to form a train from t tank cars, b boxcars, and f flatcars is:
C(t + b + f + 3 - 1, 3 - 1) = C(t + b + f + 2, 2) = (t + b + f + 2)! / ((t + b + f)! * 2!)
There are 4 tank cars, 3 boxcars, and 2 flatcars in the train yard, then the number of ways to form a train is:
C(4 + 3 + 2 + 2, 2) = C(11, 2) = 55
Therefore, there are 55 ways to form a train consisting of tank cars, boxcars, and flatcars
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Wendy is told ahead of time that she will need to purchase about 12 gallons of paint in order to cover the entire house. Write equivalent ratios to determine the amount of green and white paint she will need to purchase.
Based on the information, Wendy will need to purchase 48 quarts of paint
How to calculate the ratioRatio in Mathematics simply demonstrates how many times one number can be able to fit into another number. It should be noted that ratios contrast two numbers by dividing them. In this case, A/B will be the formula if one is comparing one variable (A) to another variable (B).
Wendy is told ahead of time that she will need to purchase about 12 gallons of paint in order to cover the entire house.
The amount of paint needed will be:
= 4/1 × 12
= 48 quarts
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Wendy is told ahead of time that she will need to purchase about 12 gallons of paint in order to cover the entire house. a. Write equivalent ratios to determine the amount of green and white paint she will need to purchase. b. If there are 4 quarts in 1 gallon, how many quarts of paint does she need to purchase
(d) 1, 4, 16, ____, 256, 1024, ...
The missing number in the sequence is 64
How to determine the missing numberFrom the question, we have the following parameters that can be used in our computation:
1, 4, 16, ____, 256, 1024, ...
Using the above as a guide, we have the following:
To obtain the next term, we can multiply the previous term by 4:
So, we have
Next term = 16 * 4
Next term = 64
Therefore, the next term in the sequence is 64.
The completed sequence is: 1, 4, 16, 64, 256, 1024, ...
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X is a normally distributed random variable with mean 25 and standard deviation 9.
What is the probability that X is less than 16?
The required probability that X is less than 16 is approximately 0.15866 or 15.86%.
What is the Z -a score?A Z-score is stated as the fractional model of data point to the mean using standard deviations.
Here,
We can use the standard normal distribution to find the probability that a normally distributed random variable, X, is less than a certain value. To use the standard normal distribution, we need to standardize X by subtracting the mean and dividing by the standard deviation:
Z = (X - μ) / σ
In this case, X has a mean of 25 and a standard deviation of 9,
Z = (16 - 25) / 9
z = -1
To find the probability that X is less than 16, we need to find the corresponding value of Z using the standard normal distribution table or a calculator.
P(Z < -1) ≈ 0.15866
Therefore, the probability that X is less than 16 is approximately 0.15866 or 15.86%.
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Suppose the graph of rectangle ABCD shows the plans for a safety fence that Kenny is setting up around a construction area. Each unit on the graph represents 25 feet. After studying the plans, Kenny decides to build a fence that encloses a larger area. If Kenny dilates rectangle ABCD by a scale factor of 2.5, and fencing costs $5.25 per foot, how much will he spend on fencing?
The cost of spending the fencing around will be $1312.5.
What is a perimeter?The perimeter of any two-dimensional figure is defined as the sum of all the sides of the figure. For a rectangle, the perimeter will be the sum of all the sides of the rectangle.
Given that the graph of rectangle ABCD depicts Kenny's intentions for erecting a safety fence to surround a construction site. The units on the graph each correspond to 25 ft.
Kenny decides to construct a fence that encloses a wider region after carefully reviewing the drawings. Given that fencing costs $5.25 per foot and Kenny enlarges rectangle ABCD by a scale factor of 2.5
Perimeter = 4 x side x scale factor
Perimeter = 4 x 25 x 2.5
Perimeter = 250 feet.
The cost of fencing will be,
Cost = 250 x $5.25
Cost = $1312.5
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What is the range of the function?
23
4
2
4
9
16
Answer:
Step-by-step explanation:
HELP DUE TONIGHT!!!
Answer:
1. $1900
2. $9
Step-by-step explanation:
Part a:
‘If she doesn’t sell any copies of History is Fun’ means x = 0:
[tex]y = 1900 + 9(0)[/tex]
∴ y = Melissa’s total pay = $1900
Part b:
Rearranging the equation:
[tex]y = 9x + 1900[/tex]
∴m = slope of equation = positive 9
c = y-intercept = 1900
The shape of the graph would be increasing or ascending. And since the Number of copies (x) can never be negative, this means that the amount of pay CANNOT be less than $1900. The amount of $1900 is her minimum pay
The value of m for this equation indicates the change in Melissa’s total pay for every copy she sells.
∴Change in Melissa’s total pay = 9 dollars
In a group of 70 college students, 24 own only a laptop, 20 own only a desktop, 16 own both a
laptop and a desktop, and 10 own neither a laptop nor a desktop. What is the probability of
randomly selecting a student who owns at least one laptop or one desktop?
Answer:
85.71% chance of randomly selecting a student who owns at least one laptop or one desktop
Step-by-step explanation:
Out of a total of 70 students, only 10 own neither a laptop nor a desktop. This means that the probability of selecting a student with at least one of the two is [tex]\frac{60}{70}[/tex] or [tex]\frac{6}{7}[/tex].
If we convert this fraction into a percentage and round to the nearest hundredth, it equals:
85.71%
How many ways can a family of mother, father, and 3 children stand in a row if the mother and father stand at the ends of the row?
Answer:
12 ways
Step-by-step explanation:
the mother and father can either stand at the front/back or back/front respectively (2 ways)
that leaves 3 children in the middle -- there are 3 choices for the first child to go, 2 for the second, and 1 for the third = 3! = 6
6 ways for the children * 2 ways for the parents = 12 ways
a farmer measures the height of every tree in a large orchard in centimeters. the farmer wishes to present the data by grouping the results into groups of 25 cm. which graphical display would be most appropriate to display the results?
A histogram would be the most appropriate graphical display to present data by grouping the results into groups of 25 cm.
A histogram is a graphical representation of data that shows the distribution of a set of continuous data by dividing the data into bins (or intervals) and showing the frequency of observations within each bin. The histogram provides a visual representation of the distribution of data, showing the shape, central tendency, and spread of the data.
In this case, the farmer has measured the height of every tree in a large orchard in centimeters and wants to present the data in groups of 25 cm. To create a histogram for this data, the first step would be to divide the data into bins, or intervals, of 25 cm.
Once the bins are created, the next step is to count the number of observations (tree heights) that fall within each bin. This information can be represented as a bar graph, where the height of each bar represents the frequency of observations within the corresponding bin.
By presenting the data in this way, the farmer can easily see the distribution of tree heights in the orchard. The shape of the histogram can indicate whether the data is symmetrical, skewed, multimodal, or uniform.
The central tendency of the data can be determined by looking at the peak of the histogram, which represents the most frequent range of tree heights. The spread of the data can be determined by looking at the width of the histogram and the range of tree heights represented.
In conclusion, a histogram is the most appropriate graphical display to present the results of the tree heights in groups of 25 cm because it provides a visual representation of the distribution of the data and allows the farmer to see the shape, central tendency, and spread of the tree heights in the orchard.
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1.an alternative to ols is least absolute deviation (lad) regression, in which the regression line is selected to minimize the sum of the absolute vertical differences (rather than squared differences) between the line and the data. explain how this might reduce sensitivity to outliers.
The LAD method minimizes the sum of the absolute vertical differences between the observed data points and the predicted values of the regression line, making it more robust to the presence of outliers in the data.
Regression analysis is a powerful statistical tool used to estimate the relationship between two or more variables. The ordinary least squares (OLS) method is the most commonly used regression method. However, the OLS method is sensitive to outliers in the data.
LAD regression is a robust alternative to OLS regression because it minimizes the sum of the absolute vertical differences between the regression line and the data points. This method is also known as L1 regression.
Let's consider an example of a simple linear regression model with n observations, where Y is the dependent variable and X is the independent variable.
The OLS method estimates the parameters of the regression line by minimizing the sum of the squared vertical differences between the observed data points and the predicted values of the regression line.
In mathematical terms, the OLS method can be represented as follows:
minimize the sum of squared vertical differences,
min(β₀, β₁) ∑ (yₐ - β₀ - β₁ xₐ)²
However, if the data contains outliers, the OLS method may produce biased estimates of the parameters of the regression line, leading to incorrect predictions. On the other hand, LAD regression minimizes the sum of the absolute vertical differences between the observed data points and the predicted values of the regression line.
In conclusion, the LAD regression is an alternative to OLS that reduces the sensitivity to outliers. The LAD method minimizes the sum of the absolute vertical differences between the observed data points and the predicted values of the regression line, making it more robust to the presence of outliers in the data.
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Please find the missing side length using trig!
The missing side is [tex]5\sqrt{3}[/tex].
What are basic Trigonometric functions?
The angles of sine, cosine, and tangent are the primary classification of functions of trigonometry. And the three functions which are cotangent, secant, and cosecant can be derived from the primary functions. Basically, the other three functions are often used as compared to the primary trigonometric functions.
In a Right-angled triangle, the tangent of an angle is equal to the opposite side/adjacent side.
from the given figure,
tan 60° = x/5
[tex]\sqrt{3}=\frac{x}{5}\\ x=5\sqrt{3}[/tex]
Therefore, The missing side is [tex]5\sqrt{3}[/tex].
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The measures of the exterior angles of a heptagon are x, 4x, 5x, 6x, 7,x 8x, and 9x. Find the measure of the smallest exterior angle.
Answer:
9°
Step-by-step explanation:
x + 4x + 5x + 6x + 7x + 8x + 9x = 360
40x = 360
x = 9
The smallest angle measures x, and x = 9, so its measure is 9°.
Answer: 9°
Adding and subtracting rational expressions, What is the difference? 2x+5/x^2-3x - 3x+5/x^3-9x - x+1/x^2-9?
After adding and subtracting the rational expressions , the simplified rational expression is 4x - 4/x² - 5/x³ + 9 .
We first simplify each expression inside the parentheses :
that means :
⇒ (2x + 5/x² -3x) = (2x - 3x + 5/x²) = (-x + 5/x²) ;
⇒ (3x + 5/x³ - 9x) = (-6x + 5/x³) ;
⇒ (x + 1/x² - 9) = (-9 + x + 1/x²) ;
Now we substitute these expressions into original equation/expression :
we get ; (-x + 5/x²) - (-6x + 5/x³) - (-9 + x + 1/x²)
Simplifying further ,
we get ;
⇒ -x + 5/x² + 6x - 5/x³ + 9 - x - 1/x² ;
On Combining the like terms, we get ;
⇒ 4x - 4/x² - 5/x³ + 9
Therefore, the simplified rational expression is 4x - 4/x² - 5/x³ + 9.
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The given question is incomplete , the complete question is
Adding and subtracting rational expressions, Simplify the rational expression (2x + 5/x² -3x) - (3x + 5/x³ - 9x) - (x + 1/x² - 9) .
Calculate the angle marked y in
the diagram below.
by=||
57°
y
Step-by-step explanation:
2y+57=180
2y=180-57
2y=123
y=123/2=61.5°
y=61.5
Answer:
61.5
Step-by-step explanation:
As the lines are parallel you can use the alternate angle rule.
So within the triangle you have 57 + x + x ( y is equal to the other angle because the lines are the same length and angle highlighted by the double lines )
And so...
180 - 57 = 123
123/2 = 61.5
1. Completeby Filling >, < 0r= 9 10 19 20
The expression when completed is 0.9 [<] 0.95
How to complete the blankFrom the question, we have the following parameters that can be used in our computation:
9 10 19 20
Rewrite the expression properly
So, we have the following representation
9/10 [ ] 19/20
Next, we evaluate the expressions
This gives
0.9 [ ] 0.95
0.9 is less than 0.95
So, we have
0.9 [<] 0.95
The above represents the complete statement
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Help please Hurry
Which of the following best describes the experimental probability of getting heads? (1 point)
• a
O b
The experimental probability is the same as the theoretical probability.
The experimental probability is 4% lower than the theoretical probability.
• с
• d
The experimental probability is 4% higher than the theoretical probability.
The experimental probability cannot be concluded from the data in the table.
The correct statement regarding the probabilities is given as follows:
c. The experimental probability is 4% higher than the theoretical probability.
How to calculate a probability?A probability is calculated as the division of the desired number of outcomes by the total number of outcomes.
For the theoretical probability, we have that the coin is equally as likely to fall heads or tails, hence:
p = 1/2
p = 0.5 = 50%.
For the experimental probability, we have that on 100 trials, 54 resulted in heads, hence:
p = 54/100
p = 0.54 = 54%.
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The binomial (x+5) is a factor of x² + 8x + 15. What is the
other factor?
O (x+3)
O (x + 7)
(x+12)
O (x+13)
4X
Factor 2
Product
Factor 1
Reset
The binomial (x+5) is a factor of x² + 8x + 15 then the other factor is x+3.
What is quadratic equation?A quadratic equation is a second-order polynomial equation in a single variable x , ax²+bx+c=0. with a ≠ 0 .
Given that binomial (x+5) is a factor of x² + 8x + 15.
We need to find the other factor.
Let us solve x² + 8x + 15=0
x² + 5x +3x+ 15=0
x(x+5)+3(x+5)=0
(x+3)(x+5)
So the other binomial factor is x+3.
Hence, the binomial (x+5) is a factor of x² + 8x + 15 then the other factor is x+3.
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If s² = 80 and n = 6, what is the sum of squares?
Answer:
s^2 + n^2 = 116
Step-by-step explanation:
s^2 + n^2 = ?
s^2 = 80
n = 6
n^2 = 36
s^2 +n^2 = 80 + 36
s^2 +n^2 = 116
Please help! Thank you so much!
The non-simplified expression that represents the total number of members after the third year is 240 + 4.5x.
The simplified expression that represents the total number of members after the third year is 4.5(53 + x).
How to explain the expressionLet's call the number of members from the other club "x".
After the first year, the total number of members is 20 + x, and it doubles to 2(20 + x) = 40 + 2x.
After the second year, half of the members from the other club leave, so there are 0.5x members left from the other club. And another 40 members join, so the total number of members is (40 + 2x - 0.5x) + 40 = 80 + 1.5x.
After the third year, the total number of members triples, so we have 3(80 + 1.5x) = 240 + 4.5x.
Therefore, the non-simplified expression that represents the total number of members after the third year is 240 + 4.5x.
To simplify, we can factor out 4.5 from the expression to get 4.5(53 + x). So the simplified expression that represents the total number of members after the third year is 4.5(53 + x).
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the circumference of head sizes of newborns is approximately normal with mean 13.5 inches and standard deviation of 0.75 inches. what percent of babies have a head circumference greater than 14 inches?
A 24.8% of babies have a head circumference greater than 14 inches.
What is Circumference?The circumference of a circle is the length of the curved boundary or the perimeter of the circular shape. It is a measurement of the distance around the circle and is equal to the arc length of the circle if it were opened up and straightened out into a line segment. The circumference of a circle is related to its diameter by the formula: C = π * d
To calculate the percentage of babies with a head circumference greater than 14 inches, we need to find the area under the normal distribution curve to the right of 14 inches.
First, we need to convert 14 inches to the standard units (z-score). We can do that using the following formula:
z = (14 - 13.5) / 0.75 = 0.67
Next, we can use a standard normal distribution table to find the area to the right of z = 0.67. The value from the table is approximately 0.752.
Therefore, approximately 75.2% of babies have a head circumference less than or equal to 14 inches, and 24.8% of babies have a head circumference greater than 14 inches.
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The Vikings, who discovered Iceland, used Ravens to help find land.
True
False
Answer: TRUE Flóki reportedly released three ravens, and then sailed in the general direction that they flew, eventually discovering Iceland.
Step-by-step explanation:
Use the word bank to complete the statements below.
A reflection over the x-axis.
A vertical stretch by 11 units.
A translation left by 5 units.
A translation up 4 units.
What is reflection over graph?The reflection of a function across the x- or y-axis is another transformation that may be used. In contrast to a horizontal reflection, which reflects a graph horizontally across the y-axis, a vertical reflection reflects a graph vertically across the x-axis.
An illustration of a transformation is a reflection, which flips a shape (referred to as the pre image) over a line (referred to as the line of reflection) to produce a new shape (called the image). Imagine what would happen if you flipped the form over the line in order to graph a reflection.
Here, f(x) = 1/x²
Now, reflect the graph over the x-axis to obtain the graph of:
f(x) = -1/x²
Now, stretch the graph vertically by 11 units to get the graph of:
f(x) = -11/x²
Again, translate the graph left by 5 units to obtain the graph of:
f(x) = - 11 / (x + 5)²
Now, translate the graph up by 4 units to obtain the graph of:
f(x) = 4 - {11 / (x + 5)²}
Hence,
A reflection over the x-axis. A vertical stretch by 11 units. A translation left by 5 units. A translation up 4 units.
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1. If LM = 6, what is the perimeter of APKQ?
X-6
P
3
X
M
5
Answer:
24.67
Step-by-step explanation:
6 x 3 = 18
18 plus 6 = 24
X-M=0.60
P-3=7
24.67
The United States Postal Service has an online guide to make life easy for people using their
postal service. This is an extract.
First Class Mail
First class mail must be used for handwritten or personal correspondence.
First Class Mail Rates - single piece rates
$0.44
First ounce (oz.) Letter size mail
Each additional oz. or fraction
First ounce Flat size mail **
Each additional oz. or fraction
First ounce Parcel ***
Each additional oz. or fraction
Standard Postcard ****
$0.17 per oz. up to 3.5 oz.
$0.88
$0.17 per oz. up to 13 oz.
$1.22
$0.17 per oz. up to 13 oz.
$0.28
* Letters: (min. dimension: 5" L, 3.5" H, 0.007" W; max. dimension: 11.5 L, 6.125" H, 0.25 W,
max. weight 3.5 oz). Letter size mai over 3.5 ounces, see Flat size prices.
**Flats: (min. dimension: 11.5 L, 6.125" H, 0.25"W; max. dimension: 15 L, 12 H, 0.75 W).
*** Parcels: Anything larger.
**** Postcards: (min. dimension: 5L, 3.5" H, 0.007"W; max. dimension: 61, 4.25 H, 0.016 W).
I want to send two items through the post using first class mail.
One fts into an envelope 20 L, 10°H and 4"W and weighs 10oz.
The other fits into an envelope 8 L, 5" H and 0.20 W and weighs 2.5oz.
How much are the items going to cost me to send?
The amount of money that the items will cost you to send through United States Postal Service would be = $13.3
How to calculate the total amount of money for the Postal Services?The dimensions of the first envelope = 20 L, 10°H and 4"W
The weight of the first envelope = 10 ounce.
The first envelope is a parcel because the dimensions are larger than 11.5 L, 6.125" H, 0.25"W.
The price per ounce = $1.22
10 ounce = 1.22×10 = $12.2
The dimensions of the second envelope = 8 L, 5" H and 0.20 W.
The weight of the second envelope = 2.5 ounce.
The second letter is of normal letter size because of the dimensions (min. dimension: 5" L, 3.5" H, 0.007" W; max. dimension: 11.5 L, 6.125" H, 0.25 W, max. weight 3.5 oz)
The price per ounce = $0.44
2.5 ounce = 2.5× 0.44 = $1.1
The total price = 12.2+1.1 = $13.3
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Find the formulas for the nth term of each sequences
1. 3, 5, 9, 17, ...
2. 2/5, 3/6, 4/7, 5/8, ...
Answer:
1. 2^n + 1.
2. (n +1)/(n + 4)
Step-by-step explanation:
1. 3 5 9 17....
3 = 2^1 + 1
5 = 2^2 + 1
9 = 2^3 + 1
17 = 2^4 + 1
Therefore the nth term is
2^n+ 1 .
2. Looking at the fractions we see that:
Numerators are 2, 3, 4 ,5..
and denominators are 5, 6, 7, 8
So the nth term is
(n + 1) / (n + 4)
help pls
Find the value of the following expression and round to the nearest integer:
Answer:
53
Σ900(1.04)n+1
n=1
Submit Answer
The expression is a summation formula, representing the sum of a series of values. To find the value of the expression, we need to evaluate the sum for each term.
The general formula for each term is:
900(1.04)^n
where n is the term number and 1.04 is the common ratio.
For the first term (n = 1), the formula is:
900(1.04)^1 = 900 * 1.04 = 937.6
For the second term (n = 2), the formula is:
900(1.04)^2 = 900 * 1.04^2 = 976.9792
And so on, for each term. We can continue evaluating the formula for each term until we reach the desired number of terms.
Let's evaluate the expression for n = 10 terms.
The sum of the first 10 terms is:
937.6 + 976.9792 + 1018.057312 + ... + 1412.14803883
The value of the expression is approximately 1412.15.
Rounding to the nearest integer, the answer is 1412.
PLEASE PLEASE PLEASE PLEASE PLEASE ANSWER THIS ASAP!!!!!!!!!!!!!THIS IS MATH I AM GIVING 50 POINTS!!!!!!!!!
Please Answer ASAP!
Please Give A Clear Answer Too!!
Answer:
x + y = -9
Step-by-step explanation:
let x = -8, y = -1
the equation that passes through the point (-8,-1) is x + y = -9
pls help asap geometry
Answer:
the answer is x=23.84 which is A
Step-by-step explanation:
using SOH CAH TOA
tan0 =opp/adj
where 0=40,opposite =20,adjacent =x
tan 40=20/x
0.8391=20/x
0.8391x=2
divide both sides by 0.8391
x=23.84
In a restaurant there are
8 starter dishes
15 main dishes
9 dessert dishes
Jane is going to choose one of the following combinations for her meal.
a starter dish and a main dish
or a main dish and a dessert dish
or a starter dish, a main dish and a dessert dish
How many different ways are there for her to choose the meal?
Answer:
there are 276 + 276 + 5680 = 6232 different ways for Jane to choose her meal.
Step-by-step explanation:
First, we need to find the number of different combinations of a starter dish and a main dish. This is simply the number of combinations of 2 items from 8 starters and 15 main dishes, which can be calculated using the formula for combinations:
C(8 + 15, 2) = C(23, 2) = (23 * 22) / (2 * 1) = 276
Similarly, the number of different combinations of a main dish and a dessert dish is:
C(15 + 9, 2) = C(24, 2) = (24 * 23) / (2 * 1) = 276
Finally, the number of different combinations of a starter dish, a main dish, and a dessert dish is:
C(8 + 15 + 9, 3) = C(32, 3) = (32 * 31 * 30) / (3 * 2 * 1) = 5680
In total, there are 276 + 276 + 5680 = 6232 different ways for Jane to choose her meal.
