Therefore , the solution of the given problem of probability comes out to be 0.00439, or about 0.44%.
Probability : What is it?The main goal of the mathematical field known as model parameters is to determine the probability that a statement is accurate or that a particular event will occur. It is possible to symbolise chance by using any ranging between range 0 and 1, where 1 typically denotes certainty and 0 typically denotes possibility. A probability diagram illustrates the likelihood that a particular occurrence will take place.
Here,
To calculate the likelihood of receiving a hand of five clubs, three cards, and one card from each remaining deck,
Five clubs can be obtained in the following ways:
=> C(13,5) = 1,287
where C(n,r) indicates how many different ways r things were combined from a total of n options.
After selecting the five clubs, we must select three cards, one from each of the remaining three decks.
=> C(13,2) * C(3,2) = 702
As a result, there are three cards from each of the other two decks and five clubs, giving rise to the following combinations:
=> C(13,5) * [C(39,3) - C(13,2) * C(3,2)] = 328,664
Finally, there are C(52,8) = 74,837,381 potential hands with 8 cards.
The likelihood of receiving five clubs and three cards, along with one card from each of the other three decks, is as follows:
=> P = 328,664 / 74,837,381
=> P ≈ 0.00439, or about 0.44%.
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The area of a rectangular room is 750 square feet. The width of the room is 5 feet less than the length of the room. Which equations can be used to solve for y, the length of the room? Select three options. y(y + 5) = 750 y2 – 5y = 750 750 – y(y – 5) = 0 y(y – 5) + 750 = 0 (y + 25)(y – 30) = 0 Mark this and return
Answer:
Listed below.
Step-by-step explanation:
(Let y be the length of the room and x be the width of the room.)
Because the width of the room is 5 feet less than the length of the room, we have:
x = y - 5.The area of the room can be solved by multiplying its length and width, so we have x × y or xy = 750.
Substituting x for y - 5 into this equation:
y (y - 5) = 750.If we expand the left side of the equation, we get:
[tex]y^{2}[/tex] - 5y = 750Subtracting 750 from both sides, we get:
[tex]y^{2}[/tex] - 5y - 750 = 0The equation [tex]y^{2}[/tex] - 5y - 750 = 0 can be factored into:
(y + 25) (y - 30) = 0Therefore, 3 equations you can use are:
y (y - 5) = 750[tex]y^{2}[/tex] - 5y - 750 = 0(y + 25) (y - 30) = 0
Which of the following statements is MOST LIKELY TRUE?
A-The lower half of Sample A's data is closer to the value 5 than the lower half of Sample B's data.
B-Both of the data sets range from 1 to 10 on the number line.
C-The upper half of Sample A's data is closer to the value 10 than the upper half of Sample B's data.
D-The data in Sample B is clustered around the center where Sample A is more spread out
The statement that is most likely true is: "The data in Sample B is clustered around the center where Sample A is more spread out."
What is data set?A dataset is a collection of information, often represented in a tabular form, that contains one or more variables or pieces of data for a particular set of individuals or observations. Each individual or observation in the dataset is typically represented by a row in the table, while the variables are represented by columns. Datasets can be used to study a wide variety of phenomena, from social and economic trends to scientific experiments and medical studies. They can be collected through a variety of methods, including surveys, experiments, observations, and automated data collection systems, and can be analyzed using statistical methods to gain insights into the underlying patterns and relationships in the data.
Here,
This is because Sample A has a larger range than Sample B, indicating that the data points in Sample A are more spread out across the number line. Additionally, the median for both samples is the same (5), but the mean for Sample A is higher than the mean for Sample B, which could suggest that there are some larger values pulling the mean upward in Sample A. Taken together, these characteristics suggest that Sample A has more variability in its data points, while Sample B is more clustered around the center.
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Solve the equation by completing the square
X^2 -2x=-3
50 Points!!!!!!! Please help ASAP!!
Example of The Transitivity Property that follows
Premise:
Premise:
Conclusion:
Example of The Transitivity Property that follows
Premise: If x = 3 and y = x + 2, then y = 5.
Premise: If y = 5 and z = y - 1, then z = 4.
Conclusion: If x = 3, then z = 4.
The transitivity property is a logical property that states that if a=b and b=c, then a=c. This property is commonly used in mathematics to make deductions and draw conclusions.
Example:
Premise: If x = 3 and y = x + 2, then y = 5.
Premise: If y = 5 and z = y - 1, then z = 4.
Conclusion: If x = 3, then z = 4.
Explanation: By the transitivity property, we can substitute the value of y in the second premise with the value of x + 2 from the first premise to get z = (x + 2) - 1, which simplifies to z = x + 1. Then, we can substitute x = 3 to get z = 4.
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Which shows one way to determine the factors of
The correct option is (d) i.e. by grouping x²(x + 11) -3(x +11).
What are Factors?
Factors are numbers or algebraic expressions that can be multiplied together to obtain a given product.
In algebra, factors are often used to factorize polynomials or other expressions, which involves expressing them as a product of simpler expressions.
One way to determine the factors of x³ + 11x² - 3x - 33 by grouping is:
x²(x + 11) - 3(x + 11)
We can see that the two terms have a common factor of (x + 11), so we can factor it out as follows:
= x³ + 11x² - 3x - 33
=x²(x + 11) -3(x +11)
= (x² - 3) (x+11).
The quadratic factor can be factored further using the difference of squares formula:
(x + 11)(x - √3)(x + √3)
So the factors of x³ + 11x² - 3x - 33 are (x + 11)(x - √3)(x + √3).
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what radian measure is equal to 315?
The radian measure for 315° is (7/4)π radians.
What exactly is a radian measure?
Radian measure is a unit of measurement for angles, where one radian is defined as the central angle subtended by an arc of a circle with a length equal to the radius of the circle. Therefore, to convert degrees to radians, we need to multiply the degree measure by pi/180.
Now,
To convert 315 degrees to radians, we can use the formula:
radians = degrees x π/180
So, we have:
radians = 315 x π/180
Simplifying this expression, we get:
radians = (7/4) x π
Therefore,
315 degrees is equal to (7/4) π radians.
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A company’s employees are 40% male and 60% female. Of the male employees, 15% of them have advanced degrees and 20% of the female employees have advanced degrees.
Part A
Let c represent the total number of employees in the company. Which expression represents the number of employees in the company who have advanced degrees?
Responses
0.15c+0.20c 0 point 1 5 c plus 0 point 2 0 c
0.40c(0.15)+0.60c(0.20) 0 point 4 0 c 0 point 1 5 plus 0 point 6 0 c 0 point 2 0
(0.40c−0.15)+(0.60c−0.20) open paren 0 point 4 0 c minus 0 point 1 5 close paren plus open paren 0 point 6 0 c minus 0 point 2 0 close paren
(0.40+0.15)c+(0.60+0.20)c open paren 0 point 4 0 plus 0 point 1 5 close paren times c plus open paren 0 point 6 0 plus 0 point 2 0 close paren times c
Question 2
Part B
What percent of the company has advanced degrees?
The company's advanced degree holders make up 18% of the workforce.
A percentage is what?A percentage, which is denoted by the number 100, is a proportion, fraction, or piece of a whole. The Roman phrase per centum, which meaning "by the 100" or "per one hundred," is where the term "percent" originates. A numerical value and the percentage symbol (%) can be used to express percentages.
Part A:
The following expression sums up the amount of company employees with advanced degrees:
0.40c(0.15) + 0.60c(0.20)
Explanation: First, we multiply the overall amount of workers (c) by the proportions of male and female employees, which are, respectively, 40% and 60%. The number of male workers (0.40c) is then multiplied by the percentage of men who have advanced degrees (15%), and the number for female employees (0.60c) is multiplied by the percentage of women who have advanced degrees (20%). In order to calculate the overall number of workers with advanced degrees, we must add these two numbers.
If we condense this phrase, we get:
0.06c + 0.12c = 0.18c
Part B:
The number of staff members with advanced degrees must be divided by the total amount of employees, and the result must be multiplied by 100% to determine the percentage of the business that holds advanced degrees:
(0.18c/c) × 100% = 18%
Therefore, 18% of the company has advanced degrees.
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Delia hiked 7/10 mile one day and 67/100 the next she wanted to know how far she hiked in all her work is shown below
Delia hikes [tex]\tfrac{137}{100}[/tex] in all her wοrk, we get this answer by adding his first day hike and next day hike.
What is wοrk?Wοrk can be defined as tο achieve the purpοse, gοal οr result we use οur physical οr mental effοrt during the activity.
Their are mainly twο types οf wοrk οne is physical wοrk and οther is mental wοrk. Physical wοrk is sοmetime alsο refer as labοur wοrk and mental wοrk is usually denοtes as οffice wοrk.
Wοrk (W) = F * s
W = Wοrk, F = Fοrce And s = Displacement
Tοtal wοrk dοne by him = 7/10 + 67/100
[tex]\tfrac{137}{100}[/tex]
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A workman has two pieces of worse, each of length 26 m. One piece is to be bent into a square. The other piece is to be bent into a rectangle whose width is 3 m shorter than its length.
The required answers are a) 6.5 m, b) Dimensions 8 m, 5 m c) square has the greater area.
How to deal with square and rectangle?(a) Let s be the length of a side of the square. The perimeter of a square is given by 4s. Since the piece of wire used to make the square has length 26 m, we have:
[tex]$\begin{align*}4s &= 26 \s &= \frac{26}{4} = 6.5 \text{ m}\end{align*}[/tex]
Therefore, the length of a side of the square is 6.5 m.
(b) Let l be the length of the rectangle. Then the width of the rectangle is l-3. The perimeter of a rectangle is given by 2(l+w). Since the piece of wire used to make the rectangle has length 26 m, we have:
[tex]$\begin{align*}2(l + (l-3)) &= 26 \2(2l-3) &= 26 \4l - 6 &= 26 \4l &= 32 \l &= 8 \text{ m}\end{align*}[/tex]
Therefore, the length of the rectangle is 8 m and its width is 8-3=5 m.
(c) The area of the square is given by [tex]$s^2$[/tex], which in this case is [tex]$6.5^2 = 42.25$[/tex] square meters. The area of the rectangle is given by lw, which in this case is [tex]$8\times5 = 40$[/tex] square meters. Therefore, the square has the greater area.
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Complete question;
A workman has two pieces of worse, each of length 26 m. One piece is to be bent into a square. The other piece is to be bent into a rectangle whose width is 3 m shorter than its length.
(a) What is the length of a side of the square?
(b) What are the dimensions of the rectangle?
(c) Which shape has the greater area?
Write a polynomial equation with integer coefficients that has the given roots.
x =8, x = 7
The polynomial equation with the roots is P(x) = x^2 - 15x + 56
How to determine the polynomial equationFrom the question, we have the following parameters that can be used in our computation:
Roots: x = 8 and x = 7
Using the above as a guide, we have the following:
The equation can be represented as
P(x) = (x - root)
Substitute the known values in the above equation, so, we have the following representation
P(x) = (x - 8)(x - 7)
Evaluate the product
P(x) = x^2 - 8x - 7x + 56
This gives
P(x) = x^2 - 15x + 56
Hence, the equation is P(x) = x^2 - 15x + 56
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IRAs. You have $500,000 in your IRA (Individual Retirement Account) by the time you retire. You choose to invest this money in two funds: Fund A pays 5.2%/year and Fund B pays 7.7%/year. How should you divide your money between Fund A and Fund B to get an annual return of $34000?
Using the system of equations, we found that the amount to be invested in fund A is $180,000 and in fund B is $320,000.
What is meant by an equation?
A mathematical equation is a formula that uses the equals sign to represent the equality of two expressions. Two expressions are combined in an equation using an equal symbol ("="). The "left-hand side" and "right-hand side" of the equation are the two expressions on either side of the equals sign. Typically, we consider an equation's right side to be zero. As we can balance this by deducting the right-side expression from both sides' expressions, this won't reduce the generality.
The amount in the IRA account = $500,000
Let the amount invested in fund A be x and fund B be y.
x + y = 500,000
The amount received annually for fund A = 0.052x
The amount received annually for fund B = 0.077y
This amount is given as:
0.052x + 0.077y = 34,000
Now we have a system of equations.
x + y = 500,000
0.052x + 0.077y = 34,000
Multiply the first equation by 0.052.
0.052x + 0.052y = 26,000
0.052x + 0.077y = 34,000
Subtracting,
-0.025y = -8000
y = 320,000
Then, x = 500,000 - y = 500,000 - 320,000 = 180,000
Therefore using the system of equations, we found that the amount to be invested in fund A is $180,000 and in fund B is $320,000.
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Find m1 if m5 = 142 and m4 = 65
The angles measures are m∠1 is 103, m∠2 is 38, m∠3 is 77.
Describe Angles?In geometry, an angle is a measure of the amount of turn between two lines or line segments that meet at a common endpoint, called the vertex of the angle. Angles are measured in degrees or radians.
A degree is a unit of measure for angles, where one full circle contains 360 degrees. A right angle, which forms a quarter of a circle, is 90 degrees. Angles that are smaller than a right angle are called acute angles, while angles that are larger than a right angle are called obtuse angles. Angles that add up to a straight line, which forms half of a circle, are called supplementary angles, while angles that add up to a full circle are called explementary angles.
A radian is another unit of measure for angles, where one full circle contains 2π radians. A right angle, which forms a quarter of a circle, is π/2 radians.
Here, m∠5 + m∠2 = 180 [ Supplementary Angles ]
142 + m∠2 = 180
m∠2 = 180 - 142 = 38
Now, m∠2 + m∠3 + m∠4 = 180 [ Angles in a Triangle ]
38 + m∠3 + 65 = 180
m∠3 = 180 - 103
m∠3 = 77
Again, m∠3 + m∠1 = 180 [ Supplementary Angles ]
m∠1 + 77 = 180
m∠1 = 180 - 77 = 103
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The complete question is:
For what value of x is the square of the binomial x+1 one hundred and twenty greater than the square of the binomial x-3?
Answer:
x = -14
Step-by-step explanation:
(x+1)² + 120 = (x-3)²
expand each binomial:
x² + 2x + 1 + 120 = x² -6x + 9
combine 'like terms' to simplify:
8x = -112
x = -14
Members of a softball team raised $2252.25 to go to a tournament. They rented a bus for $1018.50 and budgeted $58.75 per player for meals.
Answer: 2252.25 - 1018.50 = P58.75
Step-by-step explanation:
What is the minimum value of f(x) = x^2 + 6x + 4
Answer:
-5
Step-by-step explanation:
You want the minimum value of f(x) = x² +6x +4.
Line of symmetryThe line of symmetry of a quadratic function f(x) = ax² +bx +c is given by ...
x = -b/(2a)
The line of symmetry passes through the extreme point. When a > 0, that extreme point is the minimum.
Here, we have a=1, b=6, so the line of symmetry is ...
x = -6/(2·1) = -3
ExtremeThe extreme point (minimum) is ...
f(-3) = (-3)² +6(-3) +4 = (-3 +6)(-3) +4 = -9 +4
f(-3) = -5
The minimum value of f(x) is -5.
Suppose you borrow $5000 at a 21% annual interest rate, compounded monthly (1.75% each month). At the end
of each month, you make a $325 payment.
Use this information to complete the table below. Round to the nearest cent as needed.
Month
1
2
3
4
5
Prior Balance
$
$5000
$4520.84
Question Help: Video
1.75% Interest
on Prior Balance
S
$74.81
Monthly Payment
$325
$325
$325
$325
Ending Balance
$
S
$5000
$4520.84
Answer:
Step-by-step explanation:
To fill in the table, we can use the following steps:
Calculate the interest for each month, which is the prior balance multiplied by the monthly interest rate (1.75%).
Subtract the monthly interest from the prior balance to get the new balance before the monthly payment.
Subtract the monthly payment from the new balance to get the ending balance.
Month Prior Balance 1.75% Interest on Prior Balance Monthly Payment Ending Balance
1 $5000 $87.50 $325 $4762.50
2 $4762.50 $83.39 $325 $4520.84
3 $4520.84 $79.06 $325 $4276.90
4 $4276.90 $74.50 $325 $4029.23
5 $4029.23 $69.69 $325 $3777.87
Therefore, after 5 months of making $325 payments, the remaining balance on the loan is $3777.87.
work out the help of the f/f data of company balabce sheet.inventary turnover -6,capitalturnover 9costof good sold)-2,fixed assets turnover (cost of good sold)-4,gross profit-20%,recievables collection period-2 month,account payble payement period-73 days, gross profit 60000 ,the closing stock was 5000 inexcess of the opening stock
A balance sheet is a financial statement that presents a company's financial position at a specific point in time. It shows the company's assets, liabilities, and equity.
What are the steps for the balance sheet?Here are the steps to compute a balance sheet:
List all the assets: Assets are what the company owns, and they can be classified as current assets or long-term assets. Current assets include cash, accounts receivable, inventory, and prepaid expenses. Long-term assets include property, plant, and equipment, investments, and intangible assets.
Calculate the total value of assets: Add up the value of all the assets listed in step 1.
List all the liabilities: Liabilities are what the company owes to others and can be classified as current liabilities or long-term liabilities. Current liabilities include accounts payable, short-term loans, and accrued expenses. Long-term liabilities include long-term loans and bonds.
Calculate the total value of liabilities: Add up the value of all the liabilities listed in step 3.
Calculate equity: Equity is the difference between the assets and liabilities. It can be calculated as Total Assets minus Total Liabilities.
List equity: Write down the equity value calculated in step 5.
Add up the total liabilities and equity: This should be equal to the total assets calculated in step 2.
The balance sheet formula is:
Assets = Liabilities + Equity
By following the above steps, you can compute a balance sheet for a company. It is important to note that the balance sheet is a snapshot of the company's financial position at a specific point in time and should be updated regularly.
P.S: An overview was given due to your incomplete information.
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A space shuftle orbits Earth at a rate
about 4 376 miles in 15 minutes At this rate how far does the space shattle travel around
Earth in 1 hour
I need help asap!
Answer:
17,500
Step-by-step explanation:
2. A study by the Disney World in Orlando, FL revealed that 60% of the vacationers going
to the Magic Kingdom, 50% visit the Epcot Center and 25% visit both. What is the
probability that a vacationer will visit either the Magic Kingdom or Epcot Center?
As a result, 0.85 or 85% of vacationers are likely to visit either the Magic Kingdom or Epcot Center.
what is probability ?The measurement and study of random events are the focus of the mathematic branch known as probability. It is a means to express how likely an event or series of events are to occur. Probability is stated as a number between 0 and 1, where 0 denotes the impossibility of an event and 1 denotes its certainty. An occurrence that has a probability of 0.5 (or 50%) is equally likely to occur or not. In a variety of disciplines, including statistics, economics, engineering, and science, probability is used to evaluate and forecast the possibility of specific events in light of the information and presumptions at hand.
given
The formula for the union of two events must be used to determine the likelihood that a visitor will go to either the Magic Kingdom or Epcot Center:
P(A or B) equals P(A) + P(B) - P (A and B)
P(A) represents the likelihood that event A will occur, P(B) represents the likelihood that event B will occur, and P(A and B) represents the likelihood that both events will occur at the same time.
Let's describe event A in this scenario as a trip to the Magic Kingdom, and event B as a trip to the Epcot Center. We are aware of:
P(A) = 0.60 (the Magic Kingdom is visited by 60% of tourists)
P(B) = 0.50 (50 percent of tourists go to the Epcot Center)
P(A and B) = 0.25 (25% of tourists go to both places).
The result of the formula is:
P(A or B) is equal to P(A) + P(B) - P(A and B), which is 0.60 + 0.50 - 0.25 = 0.85.
As a result, 0.85 or 85% of vacationers are likely to visit either the Magic Kingdom or Epcot Center.
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In a series of high jumps, Megan cleared 5'6" for 80% of her jumps. She wants to create a model for the probability of jumps cleared at 5'6". What is a
hypothesis Megan could make?
A. Megan will clear 5'6" for 100% of her jumps.
B. Megan will clear 5'4" for 100% of her jumps.
C. Megan will clear 56* on 80% or more of her jumps.
D. Megan will clear 5'8" on 80% or more of her jumps.
The best hypothesis based on the given information is Option C: Megan will clear 5'6" on 80% or more of her jumps.
What is hypothesis?A hypothesis is an educated guess or tentative explanation for a phenomenon or observation that can be tested through further investigation and experimentation. It is a proposed explanation or prediction for an event or set of events that is based on limited evidence or observations, and which serves as the starting point for scientific inquiry.
According to question:Based on the given information, Megan cleared 5'6" for 80% of her jumps. To create a hypothesis for the probability of future jumps cleared at 5'6", we need to make an educated guess based on this data.
Option A, stating that Megan will clear 5'6" for 100% of her jumps, is too optimistic and doesn't take into account the possibility of error or difficulty in jumping.
Option B, stating that Megan will clear 5'4" for 100% of her jumps, is not relevant to the given information about Megan's performance at 5'6".
Option D, stating that Megan will clear 5'8" on 80% or more of her jumps, is also not supported by the given information and is too high of a goal for Megan to realistically achieve.
Therefore, the best hypothesis based on the given information is Option C: Megan will clear 5'6" on 80% or more of her jumps. This hypothesis is supported by the fact that Megan has already achieved this level of performance in the past, and it allows for the possibility of some variability or error in future jumps.
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21. Brian took out a 48-month (4 years) loan for $1,800 at
an annual interest rate of 12%. Andy took out a
2-year loan for $4,200 at an annual interest rate of
10%. Who paid more in interest and how much more
did he pay?
A. Andy paid $34 more in interest.
B. Brian paid $34 more in interest.
C. Andy paid $24 more in interest.
D .Brian paid $24 more in interest.
Answer:
To find the total interest paid by Brian, we can use the simple interest formula:
I = P * r * t
where I is the interest, P is the principal (the amount borrowed), r is the annual interest rate as a decimal, and t is the time period in years.
For Brian's loan, we have:
I = 1800 * 0.12 * 4 = $864
So Brian paid a total of $864 in interest over the 4-year term.
For Andy's loan, we can use the same formula:
I = 4200 * 0.10 * 2 = $840
So Andy paid a total of $840 in interest over the 2-year term.
To find the difference in interest paid, we subtract the smaller amount from the larger amount:
864 - 840 = $24
Therefore, Brian paid $24 more in interest than Andy. The answer is option D.
Answer: the answer is C. Brian paid $24 more in interest than Andy.
Step-by-step explanation: To find out how much interest each person paid, we can use the formula:
Interest = Principal x Rate x Time
where Principal is the amount borrowed, Rate is the annual interest rate (as a decimal), and Time is the length of the loan (in years).
For Brian's loan:
Principal = $1,800
Rate = 0.12
Time = 4 years
Interest = $1,800 x 0.12 x 4 = $864
For Andy's loan:
Principal = $4,200
Rate = 0.10
Time = 2 years
Interest = $4,200 x 0.10 x 2 = $840
So Andy paid $840 in interest, while Brian paid $864 in interest. To find out how much more Brian paid than Andy, we can subtract:
$864 - $840 = $24
What is 48.312 rounded to the nearest tenths?
Answer: 48.3
Step-by-step explanation:
Answer:
48.3
Step-by-step explanation:
please help i need it rn (25points for answer)
Find the volume of the region under the graph of f ( x , y ) = 3 x + y + 1 and above the region y 2 ≤ x , 0 ≤ x ≤ 9 .
A woman wants to measure the height of a nearby tower. She places a 7 ft pole in the shadow of the tower so that the shadow of the pole is exactly covered by
the shadow of the tower. The total length of the tower's shadow is 188 ft, and the pole casts a shadow that is 3.75 ft long. How tall is the tower? Round your
answer to the nearest foot. (The figure is not drawn to scale.)
Sun
Tower
Pole
Shadow of pole"
Shadow of tower
Ú
ft
X
The height of the tower obtained from the 188 ft long tower's shadow, the 3.75 ft long pole's shadow, the 7 ft height of the pole, and the equivalent ratio of the corresponding sides of similar triangles is about 351 feet
What are similar triangles?Similar triangles are triangles that have the same shape but may have different sizes.
Height of the pole = 7 ft
Length of the shadow cast by the tower = 188 ft
Length of the shadow cast by the pole = 3.75 ft
The triangle formed by the length of the shadows of the tower and the pole the tower and the pole and the line of sight from the tip of the shadow to the top of the tower and the pole are similar triangles, therefore, the ratio of the corresponding sides are the same, which indicates;
[tex]\frac{3.75}{188} = \frac{7}{Height \ of \ the \ tower}[/tex]
Height of the tower × 3.75 = 7 × 188
The height of the tower = 7 × 188/3.75 ≈ 351
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GIVEN That the Matrix(2 1 )
(3 4)
the Matrix K²+k+ I where I is a 2x2 Identity matrix
Now we can add K² to k + I to get the final result: K² + k + I = (4 3) + (3 1) + (1 0) = (8 4) (8 15) (3 5).
What is matrix?A matrix is a rectangular array of numbers or other mathematical objects, such as symbols or expressions, arranged in rows and columns. Matrices are commonly used in mathematics, physics, engineering, computer science, and other fields to represent and manipulate data.
Given by the question.
To find the matrix K²+k+I, we need to first find the matrix K.
The matrix K is the given matrix:
K = (2 1)
(3 4)
To find K², we can simply multiply K by itself:
K² = K × K = (2 1) × (2 1) = (4 3)
(3 4) (8 15)
To find k + I, we need to add the identity matrix I to K:
k + I = K + I = (2 1) + (1 0) = (3 1)
(3 4) (0 1) (3 5)
To learn more about matrix:
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On a map, my house is 4.8 inches away from the school. If each inch represents two miles, how far away is my house from the school?
Trig Identities---
1. Use the pythagorean identity
Find cotθ if cosθ = 1/7 and the value exists in the first quadrant.
I have a calculus exam tomorrow and have no idea how to solve this equation, please provide a detailed explanation. I'm slow.
Answer:
Let's first recall the Pythagorean identity:
sin²θ + cos²θ = 1
We can use this identity to find the value of sinθ, given that cosθ = 1/7 and θ is in the first quadrant. Since θ is in the first quadrant, both sinθ and cosθ are positive.
cosθ = 1/7
cos²θ = (1/7)² = 1/49
sin²θ + cos²θ = 1
sin²θ + 1/49 = 1
sin²θ = 1 - 1/49 = 48/49
sinθ = √(48/49) = (4/7)√3
Now we can use the definition of cotangent to find cotθ:
cotθ = cosθ/sinθ
Substituting the values we found for cosθ and sinθ, we get:
cotθ = (1/7)/[(4/7)√3] = √3/4
Therefore, cotθ = √3/4 when cosθ = 1/7 and θ is in the first quadrant.
Challenger Deep in the Pacific Ocean is the deepest point in Earth's oceans. It is 38 797 ft. below sea level. What is this depth to the nearest fathom? Is this depth greater than or less than 7 mi.? Explain.
Answer:
Therefore, the depth of Challenger Deep to the nearest fathom is 6,466 fathoms, and it is greater than 7 miles.
Step-by-step explanation:
One fathom is equal to 6 feet. To convert 38,797 ft. to fathoms, we divide by 6:
38,797 ft. / 6 = 6,466.17 fathoms
Rounding this to the nearest fathom gives us 6,466 fathoms.
One mile is equal to 5,280 feet. Seven miles would be:
7 mi. x 5,280 ft/mi = 36,960 ft.
Since 38,797 ft. is greater than 36,960 ft., we can conclude that Challenger Deep's depth is greater than 7 miles.
Therefore, the depth of Challenger Deep to the nearest fathom is 6,466 fathoms, and it is greater than 7 miles.
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Answer:
d ≈ 4.5
Step-by-step explanation:
calculate AB using the distance formula
d = [tex]\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }[/tex]
with (x₁, y₁ ) = A (1, 0 ) and (x₂, y₂ ) = B (5, 2 )
d = [tex]\sqrt{(5-1)^2+(2-0)^2}[/tex]
= [tex]\sqrt{4^2+2^2}[/tex]
= [tex]\sqrt{16+4}[/tex]
= [tex]\sqrt{20}[/tex]
≈ 4.5 ( to the nearest tenth )