Answer:
180
Step-by-step explanation:
6 different letters.
we need to pick groups of 4.
no repetitions, but the sequence matters (code words), as e.g. RAGE is different to GEAR, although they contain the same letters.
so, we need basic permutations (instead of combinations) :
P(6, 4) = 6! / (6 - 4)! = 6! / 2! = 6×5×4×3 = 360
that is simply because regularly we would have 6 choices for the first letter, then 5 for the second, 4 for the third, and 2 for the fourth letter.
the second to the last letter is the second letter from the left in a 4-letter word.
so, we have 3 vowels for that second position.
normally, such a restriction would mean
6×3×4×3 = 216 possibilities.
but we have to distinguish the 2 cases that we pick a vowel for the first position - or not.
if not, we have 3 consonants for the first, 3 vowels for the second position as options.
if yes, we have 3 vowels for the first and 2 vowels for the second position.
that means we get
3×3×4×3 + 3×2×4×3 = 108 + 72 = 180
possibilities.
this makes also sense, when we simply say that this restriction eliminates half of our possible permutations (all with a consonant in the second position) : 360/2 = 180.
can someone please help me with this? It’s due today I need help asap.
50 points!! I will mark brainliest if it’s all correct. Do part A, B, and C
The experimental probabilities have their values to be P(3) = 1/12, P(6) = 1/4 and P(Less than 4) = 1/2
Evaluating the experimental probabilitiesExperimental probability of 3
From the table of values, we have
n(3) = 1
Total = 12
So, we have
P(3) = 1/12
Experimental probability of 6
From the table of values, we have
n(6) = 3
Total = 12
So, we have
P(6) = 3/12
P(6) = 1/4
Experimental probability of less than 4
From the table of values, we have
n(Less than 4) = 6
Total = 12
So, we have
P(Less than 4) = 6/12
P(Less than 4) = 1/2
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do you take the free samples offered in supermarkets? about 58% of all customers will take free samples. furthermore, of those who take the free samples, about 37% will buy what they have sampled. suppose you set up a counter in a supermarket offering free samples of a new product. the day you were offering free samples, 327 customers passed by your counter. (round your answers to four decimal places.)
a) The probability that more than 180 customers will take your free sample is approximately 0.9999.
b) The probability that fewer than 200 customers will take your free sample is approximately 0.0119.
c) Therefore, the probability that a customer will take a free sample and buy the product is 0.21.
d) The probability that between 60 and 80 customers will take the free sample and buy the product is approximately 0.043
a) Let X be the number of customers who take the free sample.
We know that X follows a binomial distribution with n = 327 and p = 0.58. To find the probability that more than 180 will take free sample, we need to find P(X > 180).
Using a binomial calculator or software, we get:
P(X > 180) = 1 - P(X ≤ 180) = 1 - binomial distribution (180, 327, 0.58, TRUE) ≈ 0.9999
Therefore, the probability that more than 180 customers will take your free sample is approximately 0.9999.
b) To find the probability that fewer than 200 will take your free sample, we need to find P(X < 200).
Using a binomial calculator or software, we get:.
P(X < 200) = binomial distribution (199, 327, 0.58, TRUE) ≈ 0.0119
Therefore, the probability that fewer than 200 customers will take your free sample is approximately 0.0119.
c) Let A be the event that a customer takes a free sample, and B be the event that the customer buys the product.
We are given P(B|A) = 0.35 and P(A) = 0.60.
Using the multiplication rule for dependent events, we get:
P(A ∩ B) = P(B|A) × P(A) = 0.35 × 0.60 = 0.21
Therefore, the probability that a customer will take a free sample and buy the product is 0.21.
d) Let Y be the number of customers who take the free sample and buy the product. We know that Y follows a binomial distribution with n = 327 and p = 0.21 (from part c). .
To find the probability that between 60 and 80 customers will take the free sample and buy the product, we need to find P(60 ≤ Y ≤ 80).
Using a binomial calculator or software, we get:
P(60 ≤ Y ≤ 80) = binomial distribution (80, 327, 0.21, TRUE) - binomial distribution (59, 327, 0.21, TRUE) ≈ 0.0434
Therefore, the probability that between 60 and 80 customers will take the free sample and buy the product is approximately 0.0434.
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Question: Do You Take The Free Samples Offered In Supermarkets? About 58 % Of All Customers Will Take Free Samples.
Furthermore, Of Those Who Take The Free Samples, About 37% Will Buy What They Have Sampled. Suppose You Set Up A Counter In A Supermarket Offering Free Samples Of A New Product. The Day You Were Offering Free Samples, 327Customers Passed By Your
Do you take the free samples offered in supermarkets? About 58% of all customers will take free samples. Furthermore, of those who take the free samples, about 37% will buy what they have sampled. Suppose you set up a counter in a supermarket offering free samples of a new product. The day you were offering free samples, 312 customers passed by your counter.(round your answers to four decimal places.)
a.) What is the probability that more than 180 will take your free sample?
b.) What is the probability that fewer than 200 will take your free sample?
c.) What is the probabilty that a customer will take a free sample and buy the product? Hint: Use the multiplication rule for dependent events. Notice that we are given the conditional probability P(buy|sample)=0.35, while P(sample)=0.60
d.) What is the probability that between 60 and 80 customers will take the free sample and buy the product? HInt: Use the probability of success calculated in part(c).
What are the values of angle a c and f
Answer:
Step-by-step explanation:
f=133
a=93
c=140
For the following problems, are they similar? if so why? (AA~, SAS~, SSS~)
Answer:
yes these 2 triangles are similar
Step-by-step explanation:
triangle ABC is similar to triangle ADE. it has a scale factor of 1.5. It is a dilated. 10×1.5=15 so it has a scale factor of 1.5 which is an enlargement. any scale factor greater than 1 increases the size of the triangle. it is proportional if you multiply both sides by the scale factor (1.5) you get 15. also The angles are equal (AA similarity) these two triangles are NOT congruent but they are similar the degrees are equal. btw SSS and SAS are congruence postulates NOT similarity. so therefore they are similar because of AA
i hope this helps :)
Syed is comparing train distances between his hometown and other nearby towns with the cost of travel fares. His results are shown in the table below. He has modeled the data with the equation y=0.1x + 12
Using the sketchpad, calculate and record the missing residuals so that Syed can determine whether a linear model is appropriate for his data set.
The data set as there are some large residuals, such as 4 and -7, indicating that the actual fares are not well-predicted by the linear equation.
Define the term residuals?In statistics, residuals refer to the differences between the observed values of a variable and the values predicted by a statistical model. They are calculated by subtracting the predicted values from the observed values.
To calculate the residuals, we first need to find the predicted fares for each distance using the equation y = 0.1 x + 12;
Miles Fares $ Predicted Fares $ Residuals $
50 14 17 -3
40 16 16 0
60 16 18 -2
30 14 15 -1
60 22 18 4
70 12 19 -7
80 24 20 4
To find the residuals, we subtract the predicted fare from the actual fare. If the predicted fare is greater than the actual fare, the residual is negative, and if the predicted fare is less than the actual fare, the residual is positive. We can see that a linear model may not be appropriate for the data set as there are some large residuals, such as 4 and -7, indicating that the actual fares are not well-predicted by the linear equation.
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5. Chang says the longest ski trail is more than three times the length of the shortest ski trail.
Is Chang correct? Explain.
The statement of Chang's is not correct.
Here given Chang's equation is x = 3y, which means that the length of the longest ski trail (x) is three times the length of the shortest ski trail (y).
Therefore, if we assume that the length of the shortest ski trail is y, then the length of the longest ski trail would be 3y.
So, in Chang's statement, he says that the longest ski trail is more than three times the length of the shortest ski trail. This would mean that x > 3y. However, according to Chang's equation, x = 3y, which contradicts his statement.
Therefore, Chang is incorrect in saying that the longest ski trail is more than three times the length of the shortest ski trail. In fact, the longest ski trail is exactly three times the length of the shortest ski trail, as per Chang's equation.
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Correct question is "Chang has an equation x=3y where x is length of longest ski trail and y is length of the shortest ski trail.
Chang says the longest ski trail is more than three times the length of the shortest ski trail.
Is Chang correct? Explain."
pls help!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer: they are adding 30 each time
Step-by-step explanation:
in 320 to 350, it adds 30 because 20 plus 30 equals 50 then you can add 300 which is 350 then 350 plus 30 is 380 which is also the next number which means you are adding 30 each time and for the first box you subtract 30 from 350 which is 320 and for the last box you add 30 which is 380 + 30 which is 410 so that is your answer.
The expression 0.6y represents the result of
decreasing the quantity y by p%. What is the value
of p?
Answer:
P=40 and y was decreased by 40%
Step-by-step explanation:
Let's set up an equation as follows. In this case, we will set y will be equivalent to 1, as the number can be any value for this equation in the other fraction as the original number. Let us then represent the new number, 0.6y, or 0.6*1 which will be equivalent to 0.6 itself, and we will set that equal to 100-p as p will be the amount of percent it was decreased by. Here is the equation as follows:
[tex]\frac{1}{0.6} =\frac{100}{100-p}\\\\[/tex]We can use a method of solving fractions that is known as the Cross-multiplication property, which demonstrated in the image attached below this answer. Using this property, we can determine and simplify the equation to as follows:
[tex]1*(100-p)=0.6(100)[/tex], which can be simplified to [tex]100-p=60[/tex], and then solving the equation gives us the answer:
[tex]p=40[/tex]
P=40
will give brainlest
|x+3|=9
you have to spilt the equation to get the absolute value
Answer:
To solve the equation |x+3|=9, we need to split it into two separate equations, one for the positive value and one for the negative value of the absolute value:
For the positive value:
x+3=9
Solving for x, we get x=6
For the negative value:
-(x+3)=9
Multiplying both sides by -1, we get:
x+3=-9
Solving for x, we get x=-12
Therefore, the solutions to the equation |x+3|=9 are x=6 and x=-12.
Hope This Helps!
Given � ( � ) = − 2 � 2 − 4 � + 13 f(x)=−2x 2 −4x+13, find � ( − 7 ) f(−7)
The function g(-7) * f(-7) is approximately equal to *-8056.5*.
What is a function?
A function is a mathematical rule that assigns a unique output value to each input value from a given set. It represents a relationship between two sets of numbers in which each input has exactly one output. A function can be expressed symbolically, graphically, or verbally and is used to model real-world phenomena, solve equations, and make predictions in various fields of study.
According to the given information
To find g(-7) and f(-7), we need to substitute -7 for y in the function g(y) = -2ᵇ - 4b + 13 and x in the function f(x) = -2x² - 4x + 13.
g(-7) = -2⁻⁷ - 4⁻⁷ + 13
Simplifying this expression gives:
g(-7) = -1/128 + 28 + 13
g(-7) = 141 - 1/128
Therefore, g(-7) is approximately equal to 140.9922 .
f(-7) = -2(-7)² - 4(-7) + 13
Simplifying this expression gives:
f(-7) = -98 + 28 + 13
f(-7) = -57
Therefore, f(-7) is equal to -57.
So, g(-7) * f(-7) is approximately equal to -8056.5.
The correct question is
g(y ) = − 2ᵇ − 4b + 13 and f(x)=−2x² −4x+13, find g( − 7 ) f(−7)
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which aggregate function can be used with grouped data? check all true statements (there will be more than one).
The aggregate functions that can be used with grouped data include:
COUNT(), SUM(), AVG(), MIN().,MAX().
1. COUNT(): This function counts the number of rows in a group.
2. SUM(): This function adds up the values of a specified column within a group.
3. AVG(): This function calculates the average of a specified column within a group.
4. MIN(): This function finds the minimum value of a specified column within a group.
5. MAX(): This function finds the maximum value of a specified column within a group.
These functions can be used in combination with the GROUP BY clause in SQL to perform calculations on grouped data.
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Which equation represents the hanger balance?
hurry!!!!
The correct equation for the hanger balance is:= w = 2
How to balance equations?
The hanger balance equation is typically used in physics experiments to determine the weight of an object by comparing it to known weights on the other side of a balance. The equation is based on the principle of equilibrium, which states that the sum of the forces acting on an object must be zero for it to remain stationary.
The correct equation for the hanger balance is:
w = 2
This equation simply states that the weight of the object being measured (represented by "w") is equal to a known weight of 2 units. This indicates that the object being measured has a weight of 2 units.
The other equations provided, such as "6 = w + 2" and "6 = w - 2", do not accurately represent the hanger balance equation because they do not take into account the known weight on the other side of the balance. In order to determine the weight of an object using a hanger balance, it is necessary to have a known weight on the other side of the balance to compare it to.
In summary, the correct equation for the hanger balance is w = 2, which represents the weight of the object being measured as 2 units.
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5x−5≥− 18 what is x ?
Answer:
5x−5≥−185x-5≥-18Move all terms not containing xx to the right side of the inequality.Tap for more steps...5x≥−135x≥-13Divide each term in 5x≥−135x≥-13 by 55 and simplify.Tap for more steps...x≥−135x≥-135The result can be shown in multiple forms.Inequality Form:x≥−135x≥-135Interval Notation:[−135,∞)
The required answer is x represents any real number greater than or equal to -13/5 in terms of the result of solving linear inequalities,
Given that, linear inequalities 5x−5≥− 18
To solve the inequality 5x - 5 ≥ -18, we can follow these steps:
Step 1: Add 5 to both sides of the inequality to isolate the term with x:
5x - 5 + 5 ≥ -18 + 5
This simplifies to:
5x ≥ -13
Step 2: Divide both sides of the inequality by 5 to solve for x:
(5x)/5 ≥ (-13)/5
Simplifying further:
x ≥ -13/5
So, the solution to the solving linear inequality is x ≥ -13/5.
In terms of the result of solving linear inequalities, x represents any real number greater than or equal to -13/5.
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In its simplest form work out 5/14 x 7/30
Answer:
[tex]\boxed{\frac{1}{12}}[/tex]
Step-by-step explanation:
The multiplication of fractions satisfies the following rule:
[tex]\displaystyle{\frac{a}{b}\times\frac{c}{d}=\frac{a\times c}{b\times d}[/tex]
applied to our exercise, it looks like this
[tex]\displaystyle{\frac{5}{14}\times\frac{7}{30}=\frac{5\times 7}{14\times 30}[/tex]
also, we can "decompose" denominator numbers as follows:
[tex]14=7*2[/tex]
[tex]30=5*6[/tex]
Therefore:
[tex]\displaystyle\frac{\not{5}\times \not{7}}{2 \times \not{7}\times \not{5}\times 6}= \frac{1}{12}[/tex]
In this way, only one multiplication was necessary.
[tex]\text{-B$\mathfrak{randon}$VN}[/tex]
Question 7(Multiple Choice Worth 2 points)
(Scatter Plots MC)
A marine biologist was interested in seeing the relationship between a manatee's weight and food consumption. She gathered data and wanted to construct a graph to display the data in order to observe this relationship.
Is a scatter plot or a line graph more appropriate to construct for the data, given the context of the problem? Explain.
A line graph, because it would show the association or relationship between two variables
A line graph, because it would show how a variable changes over time between each data point given
A scatter plot, because it would show the association or relationship between two variables
A scatter plot, because it would show how a variable changes over time between each data point given
A scatter plot would be more appropriate to construct for the data, given the context of the problem. The reason is that the marine biologist is interested in seeing the relationship between a manatee's weight and food consumption.
A scatter plot is a type of graph that displays the relationship between two variables, where each variable is plotted along one axis, and a point is placed at the intersection of the two values. In this case, weight would be plotted along one axis and food consumption along the other axis.
A scatter plot allows the researcher to see if there is a relationship between the two variables, and if so, what type of relationship it is (positive, negative, or no correlation). Therefore, a scatter plot is the most appropriate way to display the relationship between a manatee's weight and food consumption.
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10 to the 9th power is how many times 10 to the 8th power?
10 to the 9th power is 10 times 10 to the 8th power.
Order the set of numbers from least to greatest: (4 points)
2.71 repeating 71, 2 and 3 over 4, square root 5, 5 over 2
Group of answer choices
2.71 repeating 71, 2 and 3 over 4, square root 5, 5 over 2.
square root 5, 5 over 2, 2.71 repeating 71, 2 3 over 4
5 over 2, square root 5, 2.71 repeating 71, 2 3 over 4
2 3 over 4, 2.71 repeating 71, 5 over 2, square root 5
The correct order of the set of numbers from least to greatest is 2, 3 over 4, 2.71 repeating 71, 5 over 2, square root 5 option (D) is correct.
To order the given set of numbers from least to greatest, we need to compare their values. We start by noticing that 2 and 3 over 4 are equivalent to 2.75. Next, we compare the values of the remaining numbers. Since the square root of 5 is approximately 2.236 and 5 over 2 is equivalent to 2.5, we have:
2, 3 over 4 < 2.71 repeating 71 < 2.5 < square root 5
Therefore, the set of numbers in order from least to greatest is 2, 3 over 4, 2.71 repeating 71, 5 over 2, square root 5.
Ordering the set of numbers from least to greatest, we get:
2, 3 over 4, 2.71 repeating 71, square root 5, 5 over 2.
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The complete question is:
Order the set of numbers from least to greatest: (Group of answer choices)
A. 2.71 repeating 71, 2, and 3 over 4, square root 5, 5 over 2.
B. square root 5, 5 over 2, 2.71 repeating 71, 2 3 over 4
C. 5 over 2, square root 5, 2.71 repeating 71, 2 3 over 4
D. 2, 3 over 4, 2.71 repeating 71, 5 over 2, square root 5
The following points represent a relation where x represents the independent variable and y represents the dependent variable.
three fourths comma negative 2, 1 comma 5, negative 2 comma negative 7, 1 comma negative one half, and 6 comma 6
Does the relation represent a function? Explain.
No, because for each input there is not exactly one output
No, because for each output there is not exactly one input
Yes, because for each input there is exactly one output
Yes, because for each output there is exactly one input
The correct answer is: No, because for each input there is not exactly one output.
What is function?In mathematics, a function is a relation between two sets, where each element in the first set (called the domain) is associated with exactly one element in the second set (called the codomain or range). A function assigns a unique output value (dependent variable) to each input value (independent variable) from the domain.
According to the given information:The given relation does not represent a function because for some inputs there are multiple outputs, violating the "one-to-one" or "vertical line test" rule.
The correct answer is: No, because for each input there is not exactly one output.
In this relation, we can see that x = 1 has two different outputs, y = 5 and y = -1/2. Therefore, the relation does not meet the criteria of a function as it violates the requirement of having exactly one output for each input.
Therefore, The correct answer is: No, because for each input there is not exactly one output.
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hi i need helping checking, i already know the answer !!
26 = 60 - 2x
Answer:
x= 7
Step-by-step explanation:
Bootle Corp paid Leslie a quarterly dividend payment for $1,490. Leslie
owns 119 shares of Bootle. What was the quarterly dividend for one share
of Bootle?
The quarterly dividend fοr οne share οf Bοοtle is $12.52.
What is divisiοn?A divisiοn is οne οf the fundamental mathematical οperatiοns that divides a larger number intο smaller grοups with the same number οf cοmpοnents. Hοw many tοtal grοups will be established, fοr instance, if 20 students need tο be separated intο grοups οf five fοr a spοrting event?
The divisiοn οperatiοn makes it simple tο tackle such issues. Divide 20 by 5 in this case. 20 x 5 = 4 will be the οutcοme. There will therefοre be 4 grοups with 5 students each. By multiplying 4 by 5 and receiving the result 20, yοu may cοnfirm this value.
Tο find the quarterly dividend fοr οne share οf Bοοtle, we can divide the tοtal quarterly dividend payment by the number οf shares Leslie οwns:
Quarterly dividend per share = Tοtal quarterly dividend payment / Number οf shares
Quarterly dividend per share = $1,490 / 119
Quarterly dividend per share = $12.52 (rοunded tο twο decimal places)
Therefore, the quarterly dividend for one share of Bootle is $12.52.
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Which are correct representations of the inequality –3(2x – 5) < 5(2 – x)? Select two options. x < 5 –6x – 5 < 10 – x –6x + 15 < 10 – 5x A number line from negative 3 to 3 in increments of 1. An open circle is at 5 and a bold line starts at 5 and is pointing to the right. A number line from negative 3 to 3 in increments of 1. An open circle is at negative 5 and a bold line starts at negative 5 and is pointing to the left.
For the the inequality –3(2x – 5) < 5(2 – x) the correct options are: x < 5, –6x + 15 < 10 – 5x
What is inequalities?
In mathematics, an inequality is a mathematical statement that indicates that two expressions are not equal. It is a statement that compares two values, usually using one of the following symbols: "<" (less than), ">" (greater than), "≤" (less than or equal to), or "≥" (greater than or equal to).
The correct representations of the inequality –3(2x – 5) < 5(2 – x) are:
x < 5 (obtained by simplifying the inequality and solving for x)
–6x + 15 < 10 – 5x (obtained by distributing the terms and simplifying the inequality)
Therefore, the correct options are:
x < 5
–6x + 15 < 10 – 5x
The options that describe number lines are not applicable to this inequality since they represent a single value, whereas an inequality represents a range of values that satisfy the inequality.
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The circle graph shows how a family spends its annual Income. If $25,200 is used for Food, Savings, and Insurance combined, what is the total annual income?
housing 21%
food 18%
clothing 17%
auto 14%
entertaining 12%
insurance 11%
savings 7%
Answer:41,328
Step-by-step explanation:
18+7+11=36 36%
100-36=64 64%
25,200 x 164%=41,328
What is the total area, in square inches, of the shaded sections of the trapezoid below. ?
Total area of shaded region in trapezoid is 54.4in²
Define trapezoidA trapezoid is a four-sided, quadrilateral shape with two parallel sides, which are called the bases, and two non-parallel sides, which are called the legs.
The formula for the area of a trapezoid is:
Area = (1/2) × (sum of the bases) × (height)
The Shaded region in trapezoid form right angled triangle.
Area of 1st shaded region=area of right triangle
=1/2×b×h
=1/2×6.8×7.4
=25.16in²
Area of 2nd shaded region=area of right triangle
=1/2×b×h
=1/2×6.8×8.6
=29.24in²
Hence, total area of shaded region in trapezoid is 54.4in²
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a paperback book company charges $6 for each paperback book plus $4 for shipping and handling per order. what would the total cost for 3 books.
ANSWER FAST
Answer:
$30
Step-by-step explanation:
6x3=18
+
4x3=12
=30
Mia is building a fence to form a triangle shaped garden. She has built one side 24 ft. long and another side 15 ft. long. What length could Mia build the last side of the fence? Responses 7 ft 7 ft 8 ft 8 ft 10 ft 10 ft 9 ft
To determine the length of the third side of the triangle, we can use the triangle inequality theorem, which states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
In this case, we have two sides of lengths 24 ft and 15 ft. Let x be the length of the third side. Then, according to the triangle inequality theorem, we have:
24 + 15 > x
39 > x
and
15 + x > 24
x > 9
Combining these inequalities, we have:
9 < x < 39
Therefore, the length of the third side of the fence could be any value between 9 ft and 39 ft, but it cannot be exactly 7 ft, 8 ft, or 10 ft. Out of the given options, the closest value to the range is 9 ft.
Find the cosine of angle x
X
W
90
72
V
Simplify your answer and write it as a proper fraction, improper fraction, or whole number
The cosine of angle X is 0.75 of triangle WXV.
EquationsIn a right-angled triangle, the cosine of an angle is equal to the adjacent side divided by the hypotenuse. Therefore, to find cos(X) in triangle XWV, we need to find the adjacent and hypotenuse sides that correspond to angle X.
We know that WV = 72, which is the length of the side opposite the right angle. To find the length of the hypotenuse XV, we can use the Pythagorean theorem: [tex]XV^{2}[/tex] = [tex]WV^{2}[/tex] + [tex]WX^{2}[/tex], where WX is the length of the side adjacent to angle X.
Solving for WX, we get:
[tex]WX^{2}[/tex] = [tex]XV^{2}[/tex] - [tex]WV^{2}[/tex]
[tex]WX^{2}[/tex]= [tex]90^{2}[/tex] - [tex]72^{2}[/tex]
[tex]WX^{2}[/tex] = 2916
WX = 54
Now we can find cos(X):
cos(X) = adjacent/hypotenuse
cos(X) = WX/WV
cos(X) = 54/72
cos(X) = 0.75
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Graph g(x), where f(x) = 2x − 5 and g(x) = f(x + 1). a line labeled g of x that passes through points 0, negative 4 and 2, 0 a line labeled g of x that passes through points 0, negative 3 and 4, 5 a line labeled g of x that passes through points negative 5, negative 3 and 0, 7 a line labeled g of x that passes through points 0, negative 7 and 5, 3
To graph g(x), we must replace x with x + 1 in the function f(x) = 2x - 5: g(x) = f(x + 1) = 2(x + 1) - 5 = 2x - 3 (a) To display the g of x line that passes through the coordinates 0, -4, and 2, 0, we replace x = 0 and x = 2 in the equation g(x) = 2x - 3:
g(0) = 2(0) - 3 = -3
g(2) = 2(2) - 3 = 1
Hence the line's points are (0, -3) and (2, 1):
yaml Copy code | 5 |- * (2,1) | 4 |- | 3 |- * (0,-3) | 2 |- | 1 |- | 0 |—————————— 0 1 2 3 4 5\s(b) (b) To display the g of x line that passes through points 0, -3, 4, 5, we replace x = 0 and x = 4 in the equation g(x) = 2x. - 3:
g(0) = 2(0) - 3 = -3
g(4) = 2(4) - 3 = 5
Hence the line's points are (0, -3) and (4, 5):
Copy code in yaml | 5 |- * (4,5)
|\s4 |-\s |\s3 |- * (0,-3)\s |\s2 |-\s |\s1 |-\s |\s0 |
————————-\s 0 1 2 3 4 5\s(c) (c) To display the line labeled g of x that goes through points -5, -3, and 0, 7, we use the equation g(x) = 2x - 3:
g(-5) = 2(-5) (-5) - 3 = -13\sg(0) = 2(0) - 3 = -3
Thus the line points are (-5, -13) and (0, -3):
| 5 |- | 4 |- | 3 |- | 2 |- | 1 |- | 0 |- * (0,-3) | -1 |- (-5,-13)
\ \s ——————-\s -5 -4 -3 -2 -1 0\s(d) To draw the g of x line that passes between points 0, -7, and 5, 3, In the equation g(x) = 2x - 3 we substitute x = 0 and x = 5:
g(0) = 2(0) - 3 = -3
g(5) = 2(5) (5) - 3 = 7
Hence the line's points are (0, -3) and (5, 7):
| 7 |- * yaml Copy code (5,7)
|\s6 |-\s |\s5 |- \s | * (0,-3) (0,-3)
4 |-\s |\s3 |-\s |\s2 |-\s |\s1 |-\s |\s0 |
————————-\s 0 1 2 3 4 5.
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chris l please show me how to solve this question: there are 10 questions on a discrete structures final exam. how many ways are there to assign scores to the problems if the sum of the scores is 100 and each question is worth at least 5 points?
There are 2,139,792,767,488,000 ways to assign scores to the problems if the sum of the scores is 100 and each question is worth at least 5 points.
To solve this problem, we will use the concept of combinations with repetition.
First, let's subtract 5 points from each question, since each question is worth at least 5 points. Now, we need to distribute the remaining 50 points (100 - 10*5) among the 10 questions.
Imagine that we have 50 identical balls (points) to distribute among 10 distinct boxes (questions). To do this, we can use a technique called "stars and bars". We need to place 9 dividers (bars) between the 50 balls (stars) to divide them among the 10 questions.
We will have a total of 59 positions (50 stars + 9 bars). We need to choose 9 of these positions for the bars, and the stars will fill the remaining positions.
The number of ways to do this is given by the combination formula:
C(n, k) = n! / (k! * (n - k)!)
In our case, n = 59 (total positions) and k = 9 (dividers). So, we need to calculate C(59, 9):
C(59, 9) = 59! / (9! * (59 - 9)!)
C(59, 9) = 59! / (9! * 50!)
C(59, 9) = 2,139,792,767,488,000
Therefore, there are 2,139,792,767,488,000 ways to assign scores to the problems if the sum of the scores is 100 and each question is worth at least 5 points.
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URGENT HELP NEEDED PLEASE
Step-by-step explanation:
Area of a triangle = 1/2 * base * height
For this triangle base = 9 m height = 8 m
1/2 ( 9 ) ( 8) = 36 m^2
in a binomial probability problem, if the nature of the problem is such that it is feasible to use either the binomial tables or the normal distribution to approximate the probability, which would give the more accurate answer?
If the sample size is large and the probability of success is not too close to 0 or 1, using the normal distribution to approximate the binomial probability will generally give a more accurate answer than using the binomial tables. However, if the sample size is small or the probability of success is very close to 0 or 1, using the binomial tables may be more accurate.
If the sample size is large (typically, n ≥ 30) and suppose that the probability of success (p) is not too close to 0 or 1, then we can use the normal distribution. As it gives more approximate value to the binomial probability which will generally give a more accurate answer than using the binomial tables.
This is because the normal distribution provides a more precise approximation of the binomial distribution as the sample size increases.
However, if the the probability of success is very close to 0 or 1 or sample size is small then using the binomial tables to calculate the probability directly may be more accurate. In general, it's important to check the conditions for using the normal approximation before using it and to use good judgment in deciding which method is more appropriate for a given problem.
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