Answers
Following are the correct pairs given for verbal mapping statements to symbolic statements.
What is mapping?In mathematics, mapping, or function, is a relation between two sets, where each element of the first set (called the domain) is associated with exactly one element of the second set (called the range).
According to given information,
The verbal mapping statements can be matched to their equivalent symbolic statements as follows:
The figure is translated 4 units right and 3 units down.
Symbolic statement: (x,y) mapsto (x + 4, y - 3)
The figure is translated 4 units left and 3 units up.
Symbolic statement: (x,y) mapsto [tex](x - 4, y + 3)[/tex]
The figure is translated 3 units right and 4 units down.
Symbolic statement: (x,y) mapsto [tex](x + 3, y - 4)[/tex]
The figure is translated 3 units left and 4 units up.
Symbolic statement: (x,y) mapsto[tex](x - 3, y + 4)[/tex]
So the correct matching of the verbal mapping statements to their equivalent symbolic statements is:
The figure is translated 4 units right and 3 units down.
Symbolic statement: (x,y) mapsto [tex](x + 4, y - 3)[/tex]
The figure is translated 4 units left and 3 units up.
Symbolic statement: (x,y) mapsto[tex](x - 4, y + 3)[/tex]
The figure is translated 3 units right and 4 units down.
Symbolic statement: (x,y) mapsto [tex](x + 3, y - 4)[/tex]
The figure is translated 3 units left and 4 units up.
Symbolic statement: (x,y) mapsto [tex](x - 3, y + 4)[/tex]
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Related Questions
Hall deposited $920 into a savings account. The account earns 8%
interest, compounded annually. What is the balance of his account
after 11 years? Answer in dollars and round to the nearest cent.
Answers
The required balance of Hall's account after 11 years is [tex]$A = 2145.1$[/tex].
How to deal with compound interest?The formula to calculate compound interest is:
[tex]$A = P(1 + \frac{r}{n})^{nt}$[/tex]
Where:
A = Final amount
P = Principal amount
r = Annual interest rate (as a decimal)
n = Number of times the interest is compounded per year
t = Time (in years)
Here, P = 920, r = 0.08, n = 1 (compounded annually), and t = 11 years.
Plugging in the values:
[tex]$A = 920(1 + \frac{0.08}{1})^{1\times 11}$[/tex]
[tex]$A = 920(1.08)^{11}$[/tex]
[tex]$A = 2145.1$[/tex]
Therefore, the balance of Hall's account after 11 years is [tex]$A = 2145.1$[/tex].
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give the exact value of the expression
arccos ( cos pi/2)
Answers
The exact value of the inverse-trigonometric expression arccos( [tex]cos\frac{\pi }{2}[/tex] ) is found to be [tex]\frac{\pi }{2}[/tex].
What are inverse trigonometric functions?These are also called as arc functions. These trigonometric functions are inverse operations of given trigonometric functions. The cosine of the angle indicates the ratio of base of right triangle and hypotenuse of the same triangle and the inverse of the cosine is the ratio of base and hypotenuse will give the respective angle. Inverse functions can be used to unknown angles, angle of elevation or depression in any right triangle.
The given expression is arccos( [tex]cos\frac{\pi }{2}[/tex] )
we know that arc cosine or inverse cosine= [tex]cos^{-1}(-x)[/tex] = [tex]\pi - cos^{-1} - (x)[/tex]
also we know that cos(-x)=cosx
arccos( [tex]cos\frac{\pi }{2}[/tex] ) = arccos( [tex]-cos\frac{\pi }{2}[/tex] )
= [tex]\pi - cos^{-1} (cos \frac{\pi }{2})[/tex]
= [tex]\pi - \frac{\pi }{2}[/tex]
= [tex]\frac{\pi }{2}[/tex]
∴ The value of arccos( [tex]cos\frac{\pi }{2}[/tex] ) is [tex]\frac{\pi }{2}[/tex].
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The graph represents a function.
Which ordered pair can be plotted together with these four points, so that the resulting graph still represents a
function?
O(-5,2) O (-2,5) O (2, -1) (2,-5)
Answers
Answer:
b
Step-by-step explanation:
over the weekend,eleni ate 1/4 box of cereal,and feddie ate 3/8 of the same box.what portion of the box of cereal did they eat in all?over the weekend,eleni ate 1/4 box of cereal,and feddie ate 3/8 of the same box.what portion of the box of cereal did they eat in all?over the weekend,eleni ate 1/4 box of cereal,and feddie ate 3/8 of the same box.what portion of the box of cereal did they eat in all?over the weekend,eleni ate 1/4 box of cereal,and feddie ate 3/8 of the same box.what portion of the box of cereal did they eat in all?over the weekend,eleni ate 1/4 box of cereal,and feddie ate 3/8 of the same box.what portion of the box of cereal did they eat in all?over the weekend,eleni ate 1/4 box of cereal,and feddie ate 3/8 of the same box.what portion of the box of cereal did they eat in all?
Answers
Answer: 5/8 as a fraction 0.625 as a decimal
Step-by-step explanation:
Find the area of the shaded segment of the circle.
The area of the shaded segment is m².
(Round to the nearest tenth as needed.)
***
9m
270°
Answers
The sector has a central angle of 270° and the radius is 9m. So, the area of the sector is:
A_sector = (270/360) * π * (9m)^2 = 57.15m²
To find the area of the triangle, we need to find the height of the triangle. We can use the Pythagorean theorem to find the height:
h = √[(9m)^2 - (4.5m)^2] = √(81m^2 - 20.25m^2) = √60.75m^2 = 7.8m
The base of the triangle is 4.5m (half of the diameter), so the area of the triangle is:
A_triangle = (1/2) * 4.5m * 7.8m = 17.55m²
Therefore, the area of the shaded segment is:
A_shaded segment = A_sector - A_triangle = 57.15m² - 17.55m² = 39.6m²
Rounded to the nearest tenth, the area of the shaded segment is 39.6m².
Ahmed and Tiana buy a cake for $14 that is half chocolate and half vanilla. They cut the cake into 8 slices. If Ahmed likes chocolate four times as much as vanilla, what is the dollar value that Ahmed places on a chocolate slice?
Answers
Ahmed placed a chocolate slice is $1.75.
What is arithmetic?Arithmetic is an elementary part of mathematics that consists of the study of the properties of the traditional operations on numbers—addition, subtraction, multiplication, division, exponentiation, and extraction of roots.
Here, we have
Given: Ahmed and Tiana buy a cake for $14 that is half chocolate and half vanilla. They cut the cake into 8 slices.
Denoting the value of the slice of chocolate as C and V as the vanilla slice then
4 slices × C + 4 slices *V = $14
if Ahmed likes 4 times more the chocolate than the vanilla slice, then he finds C four times more valuable than V, thus
C = 4*V
4 slices × 4V + 4 slices ×V = $24
20 slices × P = $14
P = $0.7/slice
V = 4 × P = 4 × $0.7/slice = $2.8/slice
for a slice that is half chocolate and half vanilla
value= 1/2 slice × C + 1/2 slice × V = 1/2 slice ($0.7 /slice + $2.8/slice) = $1.75
Hence, Ahmed placed a chocolate slice is $1.75.
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Suppose 40% of recent college graduates plan on pursuing a graduate degree. Fifteen recent college graduates are randomly selected.
a. What is the probability that no more than four of the college graduates plan to pursue a graduate degree?
b. What is the probability that exactly seven of the college graduates plan to pursue a graduate degree?
c. What is the probability that at least six but no more than nine of the college graduates plan to pursue a graduate degree?
Answers
For A (15) (0.4) (0.6) (15-i) For B. Consequently, there is a 0.196 percent chance For C. As a result, there is a roughly 0.382 percent chance
Binomial distribution: what is it?The number of successes in a certain number of independent trials with the same chance of success are described by the binomial distribution, which is a probability distribution. The two parameters n and p define the binomial distribution. The parameters n and p represent the number of trials and the probability of success in each trial, respectively.
Let's say that 40 percent of recent college grads want to earn a graduate degree. We choose fifteen recent college grads at random.
a. Using the binomial distribution formula, we can determine the likelihood that no more than four of the college grads intend to pursue a graduate degree:
P(X ≤ 4) = Σ(i=0 to 4) Choose (15) (0.4) (0.6) (15-i)
where X represents the proportion of recent college graduates who intend to pursue a graduate degree. We can determine that using a calculator or software that:
P(X ≤ 4) ≈ 0.0001
As a result, there is a roughly 0.0001 chance that no more than four of the college graduates will go on to get a graduate degree.
b. We can once more use the data to determine the likelihood that precisely seven of the college grads intend to pursue a graduate degree.
use the formula for the binomial distribution:
P(X = 7) = (15 choose 7) (15 choose 7) (0.4)⁷ (0.6⁸
We can determine that using a calculator or software that:
P(X = 7) ≈ 0.196
C . The cumulative binomial distribution function can be used to calculate the likelihood that at least six but no more than nine of the college graduates intend to pursue a graduate degree:
P(6 X 9) = (i=6 to 9) (15 choose I (0.4)i (0.6) (15-i)
We can determine that using a calculator or software that:
P(6 ≤ X ≤ 9) ≈ 0.382
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Sales of portable MP3 players grew approximately exponentially from $0.07 billion in 2001 to $0.91 billion in 2005. Predict the sales of MP3 players in 2008
Answers
the sales of portable MP3 players in 2008 will be approximately $3.50 billion. To predict the sales of MP3 players in 2008, we need to first understand the exponential growth pattern of sales from 2001 to 2005.
We are given that sales grew approximately exponentially from $0.07 billion in 2001 to $0.91 billion in 2005. This means that the sales data can be modeled by an exponential function of the form:
[tex]S(t) = a * b^t[/tex]
where S(t) is the sales at year t, a is the initial sales value (in 2001), and b is the growth factor per year. We can find the values of a and b by using the given sales data.
When t = 0 (in 2001), S(t) = $0.07 billion. So, we have:
[tex]0.07 = a * b^0\\a = 0.07[/tex]
When t = 4 (in 2005), S(t) = $0.91 billion. So, we have:
[tex]0.91 = 0.07 * b^4b = (0.91/0.07)^(1/4) = 1.770[/tex]
Therefore, the exponential function that models the sales data is:
[tex]S(t) = 0.07 * (1.770)^t[/tex]
To predict the sales of MP3 players in 2008, we need to find the value of S(7) (since 2008 is 7 years after 2001). We have:
[tex]S(7) = 0.07 * (1.770)^7= $3.50 billion[/tex]
Therefore, we can predict that the sales of portable MP3 players in 2008 will be approximately $3.50 billion.
It is important to note that this is a prediction based on the data we have and the model we have used. The actual sales value in 2008 could be different due to various factors such as market changes, competition, and technological advancements.
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Triangle missing measure
Answers
Answer:
angle 3 is 127 and angle 4 is 31
Step-by-step explanation:
If you see the base of the triangle looks like an angle measurer of 180 degrees. so if 2 is 53 then subtract 180-53 to get 127. Once you have 3 just subtract 180 - 22 and 127 to get 31
:D
A convenience store collected data on its customers to determine the most popular items purchased. The manager of the convenience store created a table of the data they gathered.
Convenience Store Item Number of Purchases
Candy 75
Snacks 100
Automotive Supplies 200
Beverages 125
Which of the following circle graphs correctly represents the data in the table?
circle graph titled convenience store purchases, with four sections labeled candy 15 percent, snacks 20 percent, auto supplies 40 percent, and beverages 25 percent
circle graph titled convenience store purchases, with four sections labeled candy 30 percent, snacks 40 percent, auto supplies 20 percent, and beverages 10 percent
circle graph titled convenience store purchases, with four sections labeled snacks 20 percent, candy 40 percent, beverages 25 percent, and auto supplies 15 percent
circle graph titled convenience store purchases, with four sections labeled snacks 25 percent, candy 15 percent, beverages 40 percent, and auto supplies 20 percent
Answers
Answer:
The answer is the first option
Step-by-step explanation:
The reason why it is the first option is because if we add up the total amount of things sold (candy, snacks, automotive supplies, and beverages) we would see that together the store sold 500 items. Using that we can diving the amount of candy, snacks, automotive supplies, and beverages by the total amount of things sold to get the percentages.
Ex: 75/500 = 0.15*100 = 15%
100/500 = 0.20*100 = 20%
etc.
Answer:
the correct answer is the last one i think
Step-by-step explanation:
Will put in chat if correct or not if i remember to do it.
25 ≤ 1.05D – 32.7 ≤ 30
Which compound inequality represents the range for the skull size of Welsh Corgis? Answer choices are rounded to the nearest tenth.
Answers
The range for the skull size of Welsh Corgis is given by the compound inequality 54.8 ≤ D ≤ 59.7.
EquationsWe can solve the given inequality 25 ≤ 1.05D – 32.7 ≤ 30 for D by adding 32.7 to all three parts of the inequality:
25 + 32.7 ≤ 1.05D – 32.7 + 32.7 ≤ 30 + 32.7
57.7 ≤ 1.05D ≤ 62.7
Then, we can divide all three parts of the inequality by 1.05:
57.7/1.05 ≤ D ≤ 62.7/1.05
54.76 ≤ D ≤ 59.71
What are inequalities?Mathematical statements that compare two quantities are known as inequality. They represent the relationship between the quantities with symbols like, >,, and. An inequality may have one or more variables, and based on the values of those variables, the inequality may be true or false. The collection of all values for the variables necessary to make an inequality true is the answer to the inequality. In real-world applications, inequalities are frequently used to indicate limitations, limits, or ranges of values.
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The table gives estimated annual salaries associated with two different careers. Career Estimated annual salary Cashier $17,380 Teacher $ 42,630 Based on the table, how much more money would a teacher earn than a cashier over a 20 year career?
O $25,250
O $347.600
505,000
852,600
Answers
Answer: $505,000
Step-by-step explanation:
The salary difference between a teacher and a cashier is:
$42,630 - $17,380 = $25,250
This means that a teacher earns $25,250 more per year than a cashier.
To find out how much more a teacher would earn over a 20-year career, we need to multiply the salary difference by the number of years:
$25,250 x 20 = $505,000
Therefore, a teacher would earn $505,000 more than a cashier over a 20-year career.
A breakfast special consists of choosing one item from each category in the following menu. Juice: Apple, Orange, Grapefruit Toast: White, Brown Eggs: Scrambled, Fried, Poached Beverage: Coffee, Tea, Milk
Answers
According to the question there are 54 different breakfast specials that can be ordered from this menu.
What is multiplication?Multiplication in mathematics is the addition of equal groups. As we proliferate, the multitude of issues in the group increases. The product as well as the two elements are part of a multiplication issue. 6 and 9 are factors in the multiplication equation 6 9 = 54, and 54 is the result.
Given,
It seems like the breakfast special menu consists of four categories, with different options for each category.
Juice: Apple, Orange, Grapefruit
Toast: White, Brown
Eggs: Scrambled, Fried, Poached
Beverage: Coffee, Tea, Milk
To order the breakfast special, a customer must choose one option from each category. For example, a customer might choose Orange juice, Brown toast, Scrambled eggs, and Coffee for their breakfast special.
The total number of different breakfast specials that can be ordered is the product of the number of options in each category. So, in this case, the total number of breakfast specials is:
3 (options for juice) x 2 (options for toast) x 3 (options for eggs) x 3 (options for beverage) = 54
Therefore, there are 54 different breakfast specials that can be ordered from this menu.
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Given the side length a=9 and the angle B=46∘ on the triangle below, find the lengths of b and c and the measure of angle A. Do not round during your calculations, but round your final answers to one decimal place.
Answers
well, since all interior angles in a triangle add up to 180°, by definition A = 44°, since B and A are complementary anyway.
[tex]\cos(46^o )=\cfrac{\stackrel{adjacent}{9}}{\underset{hypotenuse}{c}}\implies c=\cfrac{9}{\cos(46^o)}\implies c\approx 13.0 \\\\[-0.35em] ~\dotfill\\\\ \tan(46^o )=\cfrac{\stackrel{opposite}{b}}{\underset{adjacent}{9}}\implies 9\tan(46^o )=b\implies 9.3\approx b[/tex]
Make sure your calculator is in Degree mode.
Solve the equation.
7x +(4x - 5) = 3 + 2(x − 3)
-
X =
[?
Answers
Answer:
x = [tex]-\frac{2}{7}[/tex]
Step-by-step explanation:
Answer:
x = 2/9 ( or 0.2repeating)x = -2/7 ( or 0.285714 repeating)Step-by-step explanation:
there is an equation written in the question and one in the figure, to be sure I'll solve them both
Solve the equation.
7x +(4x - 5) = 3 + 2(x − 3)
7x + 4x - 5 = 3 + 2x - 6
7x + 4x - 2x = 3 - 6 + 5
9x = 2
x = 2/9 ( or 0.2repeating)
----------------------------------------------------------------------
7x + 1/2(4x - 5) = 3/2 + 2(x - 3)
7x + 2x - 5/2 = 3/2 + 2x - 6
7x - 5/2 = 3/2 - 6
14x - 5 = -9/2
14x = -9 + 5
14x = -4
x = -2/7 ( or 0.285714 repeating)
Please write equation for me as in y=mx+b thank you
Answers
Answer:
y = -50x + 500
Step-by-step explanation:
The equation is y = mx + b
m = the slope
b = y-intercept
Slope = rise/run or (y2 - y1) / (x2 - x1)
Pick 2 points (5,250) (7,150)
We see the y decrease by 100, and the x increase by 2, so the slope is
m = -100/2 = -50
Y-intercept is located at (0,500)
So, the equation is y = -50x + 500
How many solutions does this equation have?
-12g + 9 = 2q - 6-15q
no solution
one solution
or
infinitely many solutions
Answers
Answer:
One solution---------------------------
Given equation:
- 12q + 9 = 2q - 6 - 15qSolve it in below steps:
- 12q + 9 = 2q - 6 - 15q-12q + 9 = - 13q - 613q - 12q = - 6 - 9q = - 15This equation has one solution.
Help me please
A car was valued at $44,000 in the year 1992. The value depreciated to $15,000 by the year 2006.
A) What was the annual rate of change between 1992 and 2006?
r=---------------Round the rate of decrease to 4 decimal places.
B) What is the correct answer to part A written in percentage form?
r=---------------%
C) Assume that the car value continues to drop by the same percentage. What will the value be in the year 2009 ?
value = $ -----------------Round to the nearest 50 dollars.
Answers
(A) the annual rate of change between 1992 and 2006 was 0.0804
(B) r = 0.0804 * 100% = 8.04%
(C) value in 2009 = $11,650
What is the rate of change?
The rate of change is a mathematical concept that measures how much one quantity changes with respect to a change in another quantity. It is the ratio of the change in the output value of a function to the change in the input value of the function. It describes how fast or slow a variable is changing over time or distance.
A) The initial value is $44,000 and the final value is $15,000. The time elapsed is 2006 - 1992 = 14 years.
Using the formula for an annual rate of change (r):
final value = initial value * [tex](1 - r)^t[/tex]
where t is the number of years and r is the annual rate of change expressed as a decimal.
Substituting the given values, we get:
$15,000 = $44,000 * (1 - r)¹⁴
Solving for r, we get:
r = 0.0804
So, the annual rate of change between 1992 and 2006 was 0.0804 or approximately 0.0804.
B) To express the rate of change in percentage form, we need to multiply by 100 and add a percent sign:
r = 0.0804 * 100% = 8.04%
C) Assuming the car value continues to drop by the same percentage, we can use the same formula as before to find the value in the year 2009. The time elapsed from 2006 to 2009 is 3 years.
Substituting the known values, we get:
value in 2009 = $15,000 * (1 - 0.0804)³
value in 2009 = $11,628.40
Rounding to the nearest $50, we get:
value in 2009 = $11,650
Hence, (A) the annual rate of change between 1992 and 2006 was 0.0804
(B) r = 0.0804 * 100% = 8.04%
(C) value in 2009 = $11,650
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What is the radius of a cone with the diameter 4
Answers
Answer:
8
Step-by-step explanation:
In Exploration 5.3.2 Question 3, you found multiple average rates of change with different intervals and discussed in Question 6, the limiting value that your average rates are approaching. In Question 7, what was the significance of the numerical sign of the limiting value you found in 6?
Answers
The numerical sign of the limiting value is significant because it indicates the general direction of the function's behavior (increasing or decreasing) within the given interval,
Hi there! In Exploration 5.3.2, Question 3 required finding multiple average rates of change for different intervals, and in Question 6, you discussed the limiting value that those average rates are approaching. The significance of the numerical sign of the limiting value found in Question 6, addressed in Question 7, is as follows:
The sign of the limiting value (positive or negative) indicates the general direction of the function's behavior during the given interval. A positive limiting value means that the function is generally increasing, while a negative limiting value suggests that the function is generally decreasing.
Understanding the sign of the limiting value is essential as it provides insight into the overall trend of the function in the specified range. This information can be useful in various applications, including predicting future behavior and identifying potential maximum or minimum points of the function.
In summary, providing valuable information about the function's characteristics and trends.
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Find the inverse of a function
H(x)=2(x-3)^2+4
Answers
the function is symmetric about the vertical line [tex]x = 3[/tex] . This means that the inverse function should also be symmetric about this line. We choose the positive solution for y:This gives us the inverse of H(x). We can write it as[tex]H^(-1)(x) = 3 ± sqrt((x - 4) / 2)[/tex]
What is the inverse of a function?To find the inverse of a function, we need to switch the positions of x and y and solve for y.
[tex]Let y = H(x) = 2(x-3)^2+4.[/tex]
We can begin by subtracting 4 from both sides to get:
[tex]y - 4 = 2(x-3)^2[/tex]
Next, we can divide both sides by 2 to get:
[tex](y - 4) / 2 = (x-3)^2[/tex]
Taking the square root of both sides, we obtain:
[tex]±sqrt((y - 4) / 2) = x - 3[/tex]
Adding 3 to both sides gives:
[tex]x = 3 ± sqrt((y - 4) / 2)[/tex]
Therefore, This gives us the inverse of H(x). We can write it as:
[tex]H^(-1)(x) = 3 ± sqrt((x - 4) / 2)[/tex]
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If x is so small that its fourth and higher powers may be neglected show that ∜((1+x) )+∜((1-x) )=a-bx^2 and find the numbers a and b.Hence by putting x=1/16 show that the sum of the fourth roots of 17 and of 15 is 3⋅9985 approximately
Answers
Using binomial expansion, the sum of the fourth roots of 17 and 15 is approximately 3.9985.
We are given that x is so small that its fourth and higher powers may be neglected. Therefore, we can use the binomial expansion to approximate the fourth roots of (1+x) and (1-x) as follows:
∜((1+x)) ≈ 1 + (1/4)x - (1/32)x² + O(x³)
∜((1-x)) ≈ 1 - (1/4)x - (1/32)x² + O(x³)
where O(x³) represents the neglected terms of x³ and higher powers.
Adding these approximations, we get:
∜((1+x)) + ∜((1-x)) ≈ 2 + (1/16)(-2x²) + O(x³)
Simplifying:
∜((1+x)) + ∜((1-x)) ≈ 2 - (1/8)x²
Comparing this with the given equation a - bx², we see that a = 2 and b = 1/8.
Now, we can substitute x=1/16 into the approximate expression we obtained for the sum of the fourth roots:
∜((1+(1/16))) + ∜((1-(1/16))) ≈ 2 - (1/8)(1/16)²
Simplifying:
∜(17/16) + ∜(15/16) ≈ 3.9985
Therefore, the sum of the fourth roots of 17 and 15 is approximately 3.9985.
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A number cube is tossed 60 times.
Outcome Frequency
1 12
2 13
3 11
4 6
5 10
6 8
Determine the experimental probability of landing on a number greater than 5.
8 over 60
16 over 60
18 over 60
52 over 60
Answers
The experimental probability of landing on a number greater than 5 is 8/60, which simplifies to 2/15.
What is experimental probability?Experimental probability is the probability of an event based on the results of an experiment or observation.
It is calculated by dividing the number of times the event occurs by the total number of trials or observations.
It is also called empirical probability or observed probability.
Experimental probability can be used to estimate the theoretical probability of an event, which is the probability of the event based on mathematical reasoning or modeling.
As the number of trials or observations increases, experimental probabilities tend to approach theoretical probabilities.
The experimental probability of landing on a number greater than 5 is the number of times a number greater than 5 (i.e., 6) is obtained divided by the total number of tosses.
From the table, we see that 6 is obtained 8 times out of 60 tosses.
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What is the area of the figure. Solve by decomposing the figure.
Answers
Area of a rectangle is simply L•W, and here our length is 18 and our width is 4:
A = 18 • 4
A = 72 inches^2
Now for the triangles. The triangles are equal in measurement, so we can solve for one and multiply that area by 2 to get the total area of both triangles:
A = 1/2 b • h
We can find our base (b) by subtracting the width of the rectangle, 4, from the total side length of the shape, 7:
b = 7 - 4
b = 3 inches
Our height (h) is 8, now lets solve:
A = 1/2 (3) (8)
A = 12 inches^2
Multiply this by 2 for both triangles’ total area:
12 • 2 = 24 inches^2
Finally, add these final area up for the shape’s total area:
72 + 24 = 96 inches^2
The area of this shape is 96 in^2
Hope this helps!
Dividends Per Share Seacrest Company has 25,000 shares of cumulative preferred 2% stock, $50 par and 50,000 shares of $25 par common stock. The following amounts were distributed as dividends: 20Y1 $37,500 20Y2 20,000 20Y3 75,000 Determine the dividends per share for preferred and common stock for each year. Round all answers to two decimal places. If an answer is zero, enter '0'.
Answers
Dividends per share of preferred stock = Total dividends on preferred stock / Number of outstanding shares of preferred stock
Dividends per share of common stock = Total dividends on common stock / Number of outstanding shares of common stock
First, we need to calculate the total dividends on preferred and common stock for each year:
Year 20Y1:
Total dividends on preferred stock = 25,000 shares x $50 par x 2% = $25,000
Total dividends on common stock = $37,500
Year 20Y2:
Total dividends on preferred stock = $25,000 (cumulative preferred stock) + $20,000 x 2% = $25,400
Total dividends on common stock = $20,000
Year 20Y3:
Total dividends on preferred stock = $25,000 (cumulative preferred stock) + $20,000 (cumulative preferred stock) + $30,000 x 2% = $26,600
Total dividends on common stock = $75,000
Using the formulas above, we can calculate the dividends per share for each year:
Year 20Y1:
Dividends per share of preferred stock = $25,000 / 25,000 shares = $1.00
Dividends per share of common stock = $37,500 / 50,000 shares = $0.75
Year 20Y2:
Dividends per share of preferred stock = $25,400 / 25,000 shares = $1.02
Dividends per share of common stock = $20,000 / 50,000 shares = $0.40
Year 20Y3:
Dividends per share of preferred stock = $26,600 / 25,000 shares = $1.06
Dividends per share of common stock = $75,000 / 50,000 shares = $1.50
Therefore, the dividends per share for preferred and common stock for each year are as follows:
Year 20Y1: Preferred stock = $1.00, Common stock = $0.75
Year 20Y2: Preferred stock = $1.02, Common stock = $0.40
Year 20Y3: Preferred stock = $1.06, Common stock = $1.50
given the function below, find f(x) + g(x)
f(x)=x^2 + 6x -5
g(x)= -x^2-3x-1
Answers
Therefore , the solution of the given problem of function comes out to be 3x – 6 as a result.
What is function?The questions on the midterm exam will cover every topic, including created and actual places and also algebraic variable design. a diagram showing the relationships between different elements that cooperate to create the same result. A service is composed of numerous distinctive components that cooperate to create distinctive results for each input.
Here,
We can easily add the two functions to obtain f(x) + g(x):
=> F(x) = (x² + 6x - 5) + (-x² - 3x - 1) + G(x)
By condensing similar words, we can say:
=> x² + 6x - 5 - x² - 3x - 1 = f(x) plus g(x).
=> (x² - x²) + (6x - 3x) + f(x) + g(x) (-5 - 1)
=> f(x) + g(x) = 3x - 6
=> F(x) + G(x) = 3x – 6 as a result.
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Using everyday knowledge, which of the following statements is an if-then statement whose reverse is not correct?
Answers
If I eat too much, then I will get sick." The reverse of this statement would be "If I get sick, then I ate too much." However, this is not always true, as getting sick can have multiple causes and not just be Attributed to eating too much
An if-then statement is a type of logical statement that relates two propositions, where the second proposition is the consequence of the first. An example of an if-then statement is "If it rains, then the ground will be wet." The reverse of this statement would be "If the ground is wet, then it rained."
Using everyday knowledge, an example of an if-then statement whose reverse is not correct is "If I eat too much, then I will get sick." The reverse of this statement would be "If I get sick, then I ate too much." However, this is not always true, as getting sick can have multiple causes and not just be attributed to eating too much.
Another example could be "If I study hard, then I will pass the test." The reverse of this statement would be "If I pass the test, then I studied hard." This may not always be true, as there could be other factors that contributed to passing the test. Therefore, it is important to be mindful of the validity of if-then statements and their reverses.
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Find the scale factor of trapezoid QRSTif it’s dilated
Answers
Answer:
what trapezoid? please provide the trapezoid so I can help you
A study found that the mean migration distance of the green turtle was 2200 kilometers and the standard deviation was 625 kilometers. Assuming that the distances are normally distributed, find the probability that a randomly selected green turtle migrates a distance of
(a) less than 1900 kilometers.
(b) between 2000 kilometers and 2500 kilometers.
(c) greater than 2450 kilometers.
Answers
a. the probability that a randomly selected green turtle migrates a distance of less than 1900 kilometers is approximately 0.3156 or 31.56%.
b. the probability that a randomly selected green turtle migrates a distance between 2000 kilometers and 2500 kilometers is approximately 0.3556 or 35.56%.
c. the probability that a randomly selected green turtle migrates a distance greater than 2450 kilometers is approximately 0.3446 or 34.46%.
India uses kilometres because?As the decimal system uses kilometres as the unit of measurement, distance is expressed in kilometres instead of miles. Using a unit with decimals improves accuracy and convenience. Miles are not decimal system units.
Which nation doesn't utilise kilometres?Just three nations—the United States, Liberia, and Myanmar—continue to use the imperial measurements, which relies on measurements of length, weight, height, or area that ultimately refer to human parts or commonplace objects.
We can use the standard normal distribution to solve this problem, by transforming the distances into z-scores using the formula:
z = (x - μ) / σ
Where:
x is the distance we want to find the probability forμ is the mean migration distanceσ is the standard deviation(a) To find the probability that a randomly selected green turtle migrates a distance of less than 1900 kilometers, we need to find the z-score for 1900 using the formula:
z = (1900 - 2200) / 625 = -0.48
We can then use a standard normal table or calculator to find the probability corresponding to this z-score, which is approximately 0.3156.
Therefore, the probability that a randomly selected green turtle migrates a distance of less than 1900 kilometers is approximately 0.3156 or 31.56%.
(b) To find the probability that a randomly selected green turtle migrates a distance between 2000 kilometers and 2500 kilometers, we need to find the z-scores for both distances:
z₁ = (2000 - 2200) / 625 = -0.32
z₂ = (2500 - 2200) / 625 = 0.48
We can then use a standard normal table or calculator to find the probability corresponding to each z-score and subtract them to find the probability in between, which is approximately 0.3556.
Therefore, the probability that a randomly selected green turtle migrates a distance between 2000 kilometers and 2500 kilometers is approximately 0.3556 or 35.56%.
(c) To find the probability that a randomly selected green turtle migrates a distance greater than 2450 kilometers, we need to find the z-score for 2450 using the formula:
z = (2450 - 2200) / 625 = 0.4
We can then use a standard normal table or calculator to find the probability corresponding to this z-score and subtract it from 1 to find the probability of a distance greater than 2450, which is approximately 0.3446.
Therefore, the probability that a randomly selected green turtle migrates a distance greater than 2450 kilometers is approximately 0.3446 or 34.46%.
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A group of people were asked which of three ice cream flavors they prefer. The results are shown in the table.
Ages Vanilla Strawberry Chocolate
20 years and younger 8 10 6
Over 20 years 8 6 12
What is the probability of a person being 20 years or younger and preferring strawberry ice cream?
6%
12%
18%
20%
Answers
The probability of a person being 20 years or younger and preferring strawberry ice cream is: 10 / 50 = 0.2 or 20%, So the answer is 20%.
The total number of people surveyed is?8 + 10 + 6 + 8 + 6 + 12 = 50
The number of people who are 20 years or younger and prefer strawberry ice cream is 10.
Therefore, the probability of a person being 20 years or younger and preferring strawberry ice cream is:
10 / 50 = 0.2 or 20%
So the answer is 20%.
What is the most preferred ice cream flavor among people over 20 years old?Among people over 20 years old, chocolate ice cream is the most preferred flavor with a total of 12 votes.
What is the total number of people who prefer vanilla ice cream?The total number of people who prefer vanilla ice cream is 16 (8 in the 20 years and younger group + 8 in the over 20 years group).
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