There are 9,999 positive integers less than 100,000 that contain at least one "1" in their decimal representation.
There are 9,999 positive integers less than 100,000 that contain at least one "1" in their decimal representation. This can be determined by counting the number of possible combinations of digits that can be formed with the numbers 0-9. Since there are five digits in a number less than 100,000, the total number of combinations is 10^5 (10 to the power of 5). Of these combinations, 1/10th will contain at least one "1" as there are 10 possible ways to include a "1" in the five-digit number. Thus, 10^5/10 = 9,999. This means that there are 9,999 positive integers less than 100,000 that contain at least one "1" in their decimal representation.
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We all know that fruit is good for us. Many of us do not eat enough. The figure provided is a histogram of the number of servings of fruit per day claimed by 74 seventeen-year-old girls from a study in Pennsylvania.
Select the best description for the variability of this distribution. O from zero to fifteen servings O from zero to eight servings O from zero to fifteen girls O from zero to eight girls
The answers are as follows:
1. Skewed to the right.
2. The center is about 2 or 3 servings of fruit.
3. From zero o eight servings.
4. No outliers
5. About 12%.
6. 26 girls
About Pennsylvania.
Although the original European immigrants were Swedes and Dutch, William Penn, a Quaker, gave the state of Pennsylvania its name in honor of his father by combining the name Penn with the Latin word Sylvania, which means "woodlands," to create "Penn's woodlands." Pennsylvania, also known as the "Keystone State," is one of the original 13 colonies (it entered the Union in 1787). The state is now dominated by two large cities: Pittsburgh, a bustling inland river port, and Philadelphia, the city of the Liberty Bell, Constitution Hall, and a vibrant metropolitan area. The Amish are a group of people who don't utilize technology and live in the Pennsylvania countryside. The ruffed grouse is the state bird and Harrisburg is home to it.
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The following question be maybe like:
We all know that fruit is good for us. Many of us do not eat enough. The figure provided is a histogram of the number of servings of fruit per day claimed by 74 seventeen-year-old girls from a study in Pennsylvania.
Image given below:
1. Choose the term that best describes the shape of this distribution.
skewed to the right skewed to the left symmetric but not bell-shaped bell-shaped2. Provide the center of this distribution (Enter your answer as a whole number.)
3. Select the best description for the variability of this distribution.
from zero to eight servings from zero to fifteen servings from zero to eight girls from zero to fifteen girls4. Are there any outliers?
Yes, there is one outlierYes, there are multiple outliers. It is impossible to say using the given information. No.5. What percent of these girls ate six or more servings of fruit per day?
About 92%. About 9%. About 4%. About 12%.6. How many of these girls ate fewer than two servings of fruit per day?
26 41 35 158. Which division problem does the model
Tess made represent?
As a result, the model's representation of the division problem is 7/4 * 1/2 = 3 1/2 as the Circled portion .
what is circle ?In the plane, a circle is created by each point that is a specific distance from another point (center). Therefore, it is a curve made up of points that are spaced out from one another in the plane in a fixed manner. It rotates symmetrically around the center at all angles. Every pair of points in the plane of a circle, which is a closed two-dimensional object, are evenly distanced from the "center." Specular symmetry is produced by a line that traverses the circle. It rotates symmetrically around the center at all angles.
given
Circled portion of the shaded partition is 7/4 of the total.
Take 1/2's reciprocal and switch the sign to multiply. 7/4 * 1/2 = 3 1/2
As a result, the model's representation of the division problem is 7/4 * 1/2 = 3 1/2 as the Circled portion .
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suppose you are solving a regression problem. you have 1000 labeled examples and decide to use ridge regression
Ridge regression is a type of linear regression used to reduce the effects of multi-collinearity. It is used with 1000 labeled examples to minimize the sum of the squared errors of the model.
Ridge regression is a type of linear regression used to reduce the effects of multi-collinearity. It adds a penalty term to the cost function that penalizes large coefficients, thus reducing their magnitude. The penalty term is a regularization term that is added to the cost function to minimize overfitting. To use ridge regression, one must select a value for the regularization parameter. This parameter determines how much the model weights the penalty term, and is usually determined through cross-validation. With 1000 labeled examples, ridge regression can be used to minimize the sum of the squared errors of the model. The model is then trained on the data, and predictions can be made. Ridge regression is a powerful tool for reducing the effects of multi-collinearity, and can be used to accurately model relationships between variables.
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convert 47 in^2 into square centimeters?
47 square centimeters is equal to 303.225 square inches.
How is cm2 converted from cm?
Measure the length and width of an object, such as a rectangle, and multiply the results to get the number in square centimeters. In the event that the length and width are 15 cm and 10 cm, respectively, the formula is 15 cm*10 cm, which equals 150 cm2.
Any number that is multiplied by itself is transformed into a square. A different word for this is a number squared. The symbol for "squared" is 22 since 2 x 2 equals 4.
In mathematics, the squared sign (2), an arithmetic operator, stands in for multiplying an integer by itself. The "square" of an integer is the sum of that number and itself. Therefore, 10,000 square meters are represented by one square centimeter.
1 square inch = 6.4516 square centimeters.
47 in^2 = 47 × 6.4516
= 303.225 sq. cm
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two students just finished ba 215. sam slacker did not complete any of the career smart goals assignments and reports. denise diligence, on the other hand, took the assignment to heart (didn't just jump through hoops) and scored 95% on all of them. assuming that each point earned will result in a $1500 increase in salary 20 years from now, how much higher will denise's salary be than slacker's? enter your answer to the nearest whole dollar. do not include the $ symbol. hint: you will need to first know how many total points all of the smart goals assignments and reports (career preparation and development section of the syllabus) are worth in order to make the calculations.
The difference in salary will be $71,250.
What is multiplication in mathematics?
Multiplication is a mathematical operation that is used to find the product of two or more numbers. It is usually represented by the symbol "x" or "*", and is often referred to as repeated addition.
Career Preparation and Development (Career SMART Goals) worth 50 points.
Denise Diligence scored 95/100 on all of the assignments and reports, so she earned a total of 47.5 points.
Since each point earned will result in a $1500 increase in salary 20 years from now, Denise's salary will be $1500 x 47.5 = $71,250 higher than Slacker's.
Sam Slacker did not complete any of the career smart goals assignments and reports, so he earned a total of 0 points.
Hence, the difference in salary will be $71,250.
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determine whether the relation represents y as a function of x
x = y^2
determine whether the relation represents y as a function of x
x^2 + y^2 =25
show work
It is false that x is a function of y
How to determine the truth or falsity?The given equation to be used to determine the truth and falsity of the statement is given as:
The given parameters are function of x
x = y²
determine whether the relation represents y as a function of x
x^2 + y^2 =25
x = y²
Set y = 2
x = (2)²
Taking the square root of the value
x = 4
Set y = -2
x = (-2)²
x = 4
From the experiment, the different values of y give the same x value.
therefore, this means that x is not a function of y
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Mid topic checkpoint chapter 4 for questions 3,and 4
3) The equation of the linear model would be y = 7.5x+60.
4) If Adam studies for 6 hours then his score would be 88.
What is the Linear equation?
An algebraic equation with only a constant and a first-order (linear) term is said to be linear if it has the formula y = mx + b, where m is the slope and b is the y-intercept. The above is occasionally referred to as a "linear equation with two variables," where y and x are the variables.
y = mx + c
where m denotes the slope.
The y-intercept is represented by the constant c. (Where x is zero)
In our instance, y-intercept equals 60.
The line's equation will therefore be:
y = mx + 60
y = mx + 60
There are given the line's coordinates (4, 90). These considerations will thus satisfy the equation.
90 = 4*m + 60
4.m = 30 m = 7.5 m = 7.5 y = 7.5x + 60 y = 7.5 * 6 + 60 y = 45 + 60 y = 105 is
y = 7.5x + 60.
If Adam's study for 6 hours then his score would be
y = 7.5x + 60.
y = 7.5(6) + 60
y = 105
Hence,
3) The equation of the linear model would be y = 7.5x+60.
4) If Adam studies for 6 hours then his score would be 88.
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Here are the top 10 season hitting percentages for members of two baseball teams, and you must determine which is the best-hitting team, defined as the average. You have to decide which type of average you use and why. Do this by hand or use SPSS.Team 1 Team 20.345 0.2430.254 0.3780.278 0.3120.331 0.2980.267 0.2870.465 0.3870.189 0.3010.312 0.4120.365 0.2540.287 0.342
The best-hitting team can be calculated by finding the mean of each team's hitting percentages. To do this, add the ten numbers for each team and divide by 10.
Team 1: (0.345 + 0.254 + 0.278 + 0.331 + 0.267 + 0.465 + 0.189 + 0.312 + 0.365 + 0.287) / 10 = 0.3125
Team 2: (0.243 + 0.378 + 0.312 + 0.298 + 0.287 + 0.387 + 0.301 + 0.412 + 0.254 + 0.342) / 10 = 0.3267
Team 2 has the highest mean, so it is the best-hitting team.
In this example, it was determined that Team 2 was the best-hitting team by finding the mean of each team's hitting percentages. The mean of Team 1's hitting percentages was 0.3125, and the mean of Team 2's hitting percentages was 0.3267. Since Team 2 had the highest mean, it was determined to be the best-hitting team.
The best-hitting team can be calculated by finding the mean of each team's hitting percentages. To do this, add the ten numbers for each team and divide by 10.
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Help asap please l don’t understand
Please help!!!! Thank you!
The probability that the first item is not the first to be delivered is 0.6667
How to determine the probabilityLet's call the events that the first, second, and third items arrive on the first day of February A, B, and C, respectively.
The probability that the first item arrives on the first day of February is 1/3. The probability that the second item arrives on the first day of February is 1/3, The probability that the third item arrives on the first day of February is 0.Therefore, the probability that one of the other two items arrives first is
1/3 + 1/3 = 2/3.
The probability that the first item is not the first to be delivered is
1 - 2/3 = 1/3
Evaluate
1 - 2/3 = 0.6667
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The diameter of each tire on a vehicle is 32 inches. If the tires are moving at a rate of 800 revolutions per minute find the linear speed of the vehicle in miles per hour
The linear speed of the vehicle In miles per hour is 19.04 miles per hour
What is the angular speed?Angular speed is the time rate at which an object rotates, or revolves, about an axis, or at which the angular displacement between two bodies changes. In the figure, this displacement is represented by the angle θ between a line on one body and a line on the other.
The relationship between angular and linear speed is v = wr
where w= angular speed
v = linear speed
and r is the radius
1 inch = 1.578×10^-5
r = 32/2 = 16 inches = 16×1.578×10^-5
= 25.25×10^-5 = 2.5×10^-4miles
1 revolution = 2π = 6.28
800 revolution = 6.28× 800 = 5024
1 minutes = 1/60
800rev/minutes = 5024×60= 301440 rad/hour
v = wr
v = 301440 × 1.578 × 10^-5 = 4.76 miles per hour
therefore the linear speed of the car is 4.76miles/ hour × 4 = 19.04 miles per hour
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latanya takes a trip to an amusement park and rides a ferris wheel. the height, in feet above the ground, of her car over time , measured in , is given by
The height, in feet above the ground, is 26 feet
(Achieved Peak Value - Attained Lowest Value)/2
The lowest number = is 5 if the ride starts at the bottom of the Ferris wheel, which keeps you 5 feet above the ground.
Charlie will be 47 feet off the ground at the apex, or 5 feet off the ground plus the diameter of the wheel.
Amount = a = (47-5)/2 = 21.
(2/period) = b. You can just plug in the period from the question since you will already have located it.
(Peak value + Lowest value)/2 = for d = midline.
(47+5)/2 = 52/2 = 26
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Over the past few months, Brody has eaten 3 glazed donuts and 6 other donuts. Considering this data, how many of the next 3 donuts Brody eats would you expect to be glazed donuts?
glazed donuts
Over the past few months, Brody has eaten 3 glazed donuts and 6 other donuts. we expect 1 to be glaized
What is Brody's donut preference?Generally, Based on the data provided, it seems that Brody has eaten 3 glazed donuts out of a total of
3 + 6 = 9 donuts.
This means that 3/9, or approximately 1/3, of the donuts Brody has eaten are glazed.
So, if Brody eats 3 more donuts, we would expect 1/3 of them to be glazed,
or 3*(1/3)=1.
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The walkway shows the dimensions of one paver stone used in the design.
What is the area of one paver stone?
6.5 in.
5.5 in.
The Equation For calculating the paver area is
Length(m) x width(m) = area(m²).
How to calculate Paver area?Concrete, natural stone, clay brick, or even porcelain can be used to make pavers. They are typically little fragments of varying sizes. Homeowners can choose from a variety of hues, patterns, and textures.
Divide your space into squares or rectangles and multiply the length by the width to find the square metres of paved surface. The total square metres should be included. There are about 38 pavers per square metre, although this varies depending on how many cuts are made and what laying pattern is used. Additionally, you must account for waste.
The area to be paved and the paver selected will determine how many pavers are required.
Determine the area that will be paved in square metres.
Equation : Length(m) x width(m) = area(m²).
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What is the vertex for the graph below ? 10 A . (- 2, 0) B . (0, - 2) . (2, 0) D . (0, 2)
The vertex for the graph is at (2, 0).
What is a parabola?A parabola is formed by cutting a right circular cone in half along a plane perpendicular to the cone's generator. It is a locus of a moving point whose separation from the focus is equal to its separation from a stationary line (directrix)
Focus is a fixed point.
Directrix is the name for fixed lines.
Given the graph is a parabola,
A parabola's vertex is the location where its symmetry line and parabola intersect. The vertices of a parabola whose equation is provided in standard form will be the lowest (lowest point) and highest (highest point) points on the graph, respectively.
The minimum point in graph is (2, 0)
Hence vertex is (2, 0).
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The complete question is in image,
Solve:
(-4)^7*(-8^)^3+12/2=?
Show your work
Answer:
−16890
Step-by-step explanation:
Simplify the expression.
A machinist must cut 12 strips of metal that are each 2 ft 6 7/8 in. long. What is the total length needed in inches?
The total length of the metal strips needed in inches is 370.5 inches
How to convert feet to inches?Number of strip metals = 12
Length of each strip metal = 2 ft 6 7/8 in.
Convert feet to inches:
1 feet = 12 inches
2 feet = 24 inches
2 ft 6 7/8 in = 30 7/8 inches
Total length of strip metals= Number of strip metals × Length of each strip metal
= 12 × 30 7/8 inches
= 12 × 247/8
= 2,964/8
= 370.5 inches
So therefore, the total length of the metal strips is 370.5 inches
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Haile Resort opened for business on June 1 with eight air conditioned units. Its trial
balance on August 31 is as follows.
Haile Resort
Trial Balance
August 31, 2022
Debit Credit
Cash Br. 39,200
Prepaid Insurance 9,000
Supplies 5,200
Land 40,000
Buildings 240,000
Equipment 32,000
Accounts Payable Br. 9,000
Unearned Rent Revenue 9,200
Mortgage Payable 100,000
Share Capital—Ordinary 200,000
Retained Earnings 0
Dividends 10,000
Rent Revenue 172,400
Salaries and Wages Expense 89,600
Utilities Expense 18,400
Maintenance and Repairs Expense 7,200
Br.490,600 Br.490,600
Other data:
1. The balance in prepaid insurance is a 1-year premium paid on June 1, 2022.
2. An inventory count on August 31 shows Br.1,300 of supplies on hand.
3. Annual depreciation rates are buildings (4%) and equipment (10%).
4. Unearned rent revenue of Br.7,600 should be recognized as revenue prior
to August 31.
5. Salaries and wages of Br.750 were unpaid at August 31.
6. Rentals of Br.1,600 were due from tenants at August 31.
7. The mortgage note is dated 1/1/2022. The mortgage interest rate is 8% per
year.
Instructions
a. Journalize the adjusting entries on August 31 for the 3-month period
June 1–August 31.
b. Prepare an adjusted trial balance on August 31.
Answer:
Step-by-step explanation:
Answer:
So the answer is
FMA Assignment 01
1. Jornal
2. Date (Mar) Accounts Title Debit ($) Credit ($)
1 Cash 60,000
Common Stock 60,000
3 Land 23,000
Buildings 9,000
Equipment 6,000
Cash 38,000
5 Advertising Expenses 1,600
Cash 1,600
6 Prepaid Insurance 1,480
Cash 1,480
10 Equipment 26,000
Accounts Payable 26,000
18 Cash 800
Golf Revenue 800
19 Cash (100 x 15) 1,500
Unearned Revenue 1,500
25 Dividends 1,000
Cash 1,000
30 Salaries Expenses 600
Cash 600
30 Accounts Payable 26,000
Cash 26,000
31 Cash 500
Golf Revenue 500
Answer these two I got them wrong
a) This equation holds true for all x values except x=0, because it would result in division by zero.
b) This equation holds true for all x values except x=0, because it would result in division by zero.
What is inequality?
An inequality is a statement that compares two expressions and is represented by one of the following symbols: < (less than), > (greater than), ≤ (less than or equal to), ≥ (greater than or equal to), ≠ (not equal to).
a) 6x² - x³ = -x² + 2x + 3
b) 6x² - x³ ≤ -x² + 2x + 3
To solve for x in the given inequalities:
a) 6x² - x³ = -x² + 2x + 3
Start by isolating x³ on one side of the equation:
x³ = 6x² + (-x² + 2x + 3)
x³ = 6x² + 2x + 3
Now we can factor out x² from the right side of the equation:
x³ = (x²)(6 + 2/x) + 3
This equation holds true for all x values except x=0, because it would result in division by zero.
b) 6x² - x³ ≤ -x² + 2x + 3
Start by isolating x³ on one side of the inequality:
x³ ≤ 6x² + (-x² + 2x + 3)
x³ ≤ 6x² + 2x + 3
Now we can factor out x² from the right side of the inequality:
x³ ≤ (x²)(6 + 2/x) + 3
This inequality holds true for all x values except x=0, because it would result in division by zero.
Hence,
a) This equation holds true for all x values except x=0, because it would result in division by zero.
b) This equation holds true for all x values except x=0, because it would result in division by zero.
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The shipping container is a rectangular prism. Write a polynomial that represents the volume of the container. Express the answer in standard form.
The volume of the container is (x+6)(x-2)(x-1) cubic feet and it can be express as the form of polynomial.
Six faces make up the three-dimensional shape of a rectangular prism. The prism's faces are all rectangles. The shape of a rectangular prism is cuboidal.
There are two sets of parallel and congruent bases in this polyhedron. It has eight vertices, 12 sides, and six faces. Rectangular prisms are also known as a right rectangular prism, rectangular parallelepiped, and rectangular hexahedron.
Right rectangular prisms and oblique prisms are the two primary varieties of rectangular prisms. The bases of a right rectangular prism are parallel to the other faces.
The volume of a rectangular prism is simply the product of its three dimensions: in your case, the volume of the prism is, given x
[tex](x+6)(x-2)(x-1)[/tex]
A polynomial is a sum (with some coefficients) of powers of x, so, if we expand the product just written, we have.
[tex]=(x+6)(x-2)(x-1)\\\\=(x^2-2x+6x-12)(x-1)\\\\=(x^3+4x^2-12x-x^2-4x+12)\\\\=(x^3+3x^2-16x+12)[/tex]
Which is a polynomial and expresses the volume of the prism.
the complete question is,
How do you write a polynomial that represents the volume of a box that is a rectangular prism has the dimensions length x+6, width x-2, and height x-1?
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the probability of rolling an even number on an unfair die is 0.65 which of the following is closest to the probability that an even number
The probability of rolling an even number on an unfair die is 0.65, which means that if you roll the die multiple times, the proportion of times that you roll an even number will be close to 0.65.
So, the probability of rolling an even number is closest to option c) 0.65
A die is a cube with numbers on each face that are used in games or gambling. A fair die is a die that is equally likely to land on any of its faces, meaning that each face has a probability of 1/6 of being the face that lands up. An unfair die is a die that does not have an equal probability of landing on each face. It means that the probability of landing on each face is not the same.
In the given scenario, it is said that the probability of rolling an even number on an unfair die is 0.65. This means that if you roll the die multiple times, the proportion of times that you roll an even number will be close to 0.65. It means that the die is not fair, and it is more likely to roll an even number.
Therefore, the probability of rolling an even number is closest to 0.65, it is the probability of rolling an even number on an unfair die.
--The question is incomplete, answering to the question below--
"The probability of rolling an even number on an unfair die is 0.65 which of the following is closest to the probability that an even number
a. 0.35
b. 0.40
c. 0.65
d. 0.70"
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Given that ,On May 7,1992, the space shuttle Endeavour was launched on mission STS-49, the purpose of which was to install a new perigee kick motor in an Intelsat communications satellite. The table gives the velocity data for the shuttle between liftoff and the jettisoning of the solid rocket boosters.We need to use a graphing calculator or computer to model these data by a third-degree polynomial.
To create a third-degree polynomial model for the velocity data of the space shuttle Endeavour we need to use a graphing calculator or computer.
1. Enter the velocity data into the graphing calculator or computer.
2. Select the "Polynomial Regression" option.
3. Choose the degree of the polynomial (third degree).
4. Enter the polynomial regression equation displayed.
5. Select the "Graph" option to view the polynomial model.
A third-degree polynomial model can be used to accurately represent data points. To create a third-degree polynomial model for the velocity data of the space shuttle Endeavour, we need to use a graphing calculator or computer. First, we enter the velocity data into the graphing calculator or computer. Then we select the "Polynomial Regression" option and choose the degree of the polynomial (third degree). This will generate the polynomial regression equation which can then be entered. Finally, we select the "Graph" option to view the polynomial model. This will show us a graph of the velocity data points with the third-degree polynomial fitted to the points. This can be used to accurately predict the velocity of the shuttle Endeavour throughout its mission STS-49.
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The average lifetime of a certain new cell phone is three years. The manufacturer will replace any cell phone failing within two years of the date of purchase. The lifetime of these cell phones is known to follow an exponential distribution.Multiple Choice - Please provide how the answer is found.1)The decay rate is:a. 0.3333b. 0.5000c. 2d. 32)What is the median lifetime of these phones (in years)?a. 0.1941b. 1.3863c. 2.0794d. 5.5452
The decay rate of the cell phones is 0.3333, and the median lifetime of the phones is 2.0794 years.
The decay rate of the cell phones is 0.3333, and the median lifetime of the phones is 2.0794 years.
1)a. 0.3333
2)c. 2.0794
1)The decay rate is found by dividing 1 by the average lifetime (in this case, 3 years). Therefore, the decay rate is 1/3 = 0.3333.
2)The median lifetime of these phones is found by taking the natural logarithm of 0.5 (which is the probability of the phone failing within 2 years) and dividing it by the decay rate (0.3333). Therefore, the median lifetime is ln(0.5)/0.3333 = 2.0794.
The decay rate of the cell phones is 0.3333, and the median lifetime of the phones is 2.0794 years.
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The circle the right represents a planet. The radius of the planet is about 3900 miles. Find the distance d to the horizon that a person can see on a clear day from a 1461 feet above the planet. (Hint: Use the conversion factor 1 mile height h 5280 ft.) A person can see a distance of approximately miles on a clear day from a height of 1461 feet above the given planet. (Round to the nearest tenth as needed.)
A person can see a distance of approximately 32.9 miles on a clear day from a height of 1461 feet above the given planet.
d = 2 √(hR)
We can use the formula d = 2 √(hR) to calculate the distance d to the horizon that a person can see on a clear day from a 1461 feet above the given planet.
First, we need to convert the height of 1461 feet to miles. We can use the conversion factor of 1 mile = 5280 feet. Therefore, the height h = 1461/5280 ≈ 0.2772 miles.
Next, we need to find the radius of the planet. The radius of the planet is given as 3900 miles.
Finally, we can substitute h = 0.2772 miles and R = 3900 miles into the formula d = 2 √(hR).
d = 2 √(0.2772*3900) = 2 √(1083.08) ≈ 32.9 miles
Therefore, a person can see a distance of approximately 32.9 miles on a clear day from a height of 1461 feet above the given planet.
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Simplify the expression 5y + 3x + 9
What is the coefficient of y?
What is the constant?
Answer:
Expression: 5y+3x+9
Coefficients: (of y) 5, (of x) 3
Constant: 9
Hope this helps :)
Step-by-step explanation:
The coefficient(s) of an equation will always be the number that sits next to/attached to a variable. The constant of an equation will always be the number(s) that stands alone.
a business lady bought 100 quails and 80 rabbits for sh 25600.if she bought twice as many rabbits and half has many quails she would have paid sh7400 less.form two equations
The equations are 100x + 80y = 25600 and 50x + 160y = 18200.
What is an Equation?An equation is the statement of two expressions located on two sides connected with an equal to sign. The two sides of an equation is usually called as left hand side and right hand side.
Let x be the cost of a quail and y be the cost of a rabbit bought by the business lady.
Given that a business lady bought 100 quails and 80 rabbits for sh 25600.
100x + 80y = 25600
If she bought twice as many rabbits, number of rabbits = 80 × 2 = 160.
If she bought half as many quails, number of quails = 100/2 = 50
The equation is then,
50x + 160y = 25600 - 7400
50x + 160y = 18200
Hence the equations formed here at two situations are 100x + 80y = 25600 and 50x + 160y = 18200.
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Brenda is placing tile on her
bathroom floor. The area of the
floor is 15x2-8x - 7 ft². The area
of one tile is x² - 2x + 1ft². To find
the number of tiles needed,
simplify the rational expression:
15x²-8x-7
x²–2x+1
(15x+7)/(x-1) is the simplified rational expression
What is an expression?
Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Polynomials are algebraic expressions made up of coefficients and variables. Occasionally, variables are referred to as indeterminates. We can execute arithmetic operations on polynomial expressions, such as addition, subtraction, multiplication, and positive integer exponents, but not division by variables.
Factors of 15x²-8x-7 are (15x+7)(x-1)
Factors of x²–2x+1 are (x-1)²
15x²-8x-7 / x²–2x+1 = (15x+7)(x-1) / (x-1)²
common factors cancel out
(15x+7)/(x-1) is the simplified rational expression
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(3,7) & (-2,-1)
find the slope!!
The slope of the line passing through (3, 7) and (-2, -1) is 1.6
What is an equation?An equation consists of numbers and variables linked together by mathematical operations to form an expression.
A linear equation is in the form:
y = mx + b
Where m is the rate of change and b is the initial value
The slope of the line passing through (3, 7) and (-2, -1) is:
Slope = (-1 - 7) / (-2 - 3)
Slope = -8/-5 = 8 / 5
Slope = 1.6
The slope is 1.6
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which of these events are mutually exclusive if you roll a pair of dice?i. a: at least one die is a 3ii. b: at least one die is a 6iii. c: the sum is 11
When rolling a pair of dice, there are 36 possible outcomes, each representing a unique combination of the numbers on the two dice.
Event A: "at least one die is a 3" is not mutually exclusive with Event B: "at least one die is a 6" or Event C: "the sum is 11"
Event A and Event B are mutually exclusive because when one of the die is a 6, the other die cannot be a 3 and vice versa.
Event A and Event C are not mutually exclusive because there are some outcomes where at least one die is a 3 and the sum is 11. For example (3,8), (4,7) and (6,5) are all outcomes where at least one die is 3 and the sum is 11.
Event B and Event C are not mutually exclusive because there are outcomes where at least one die is a 6 and the sum is 11. For example (5,6) and (6,5) are both outcomes where at least one die is a 6 and the sum is 11.
So, in conclusion, Event A and Event B are mutually exclusive, but Event A and Event C and Event B and Event C are not mutually exclusive.
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John is 6 feet tall and standing 4 feet from a tree. If Johns shadow is 12 feet long, how tall is the tree
The height of the tree is 8 feet.
What are Similar triangles:Triangles which has the same shape but are different in size are said to be similar triangles for example all equilateral triangles are similar triangle.
It is also defined as if the corresponding sides of two triangles are in proportion then the two triangles are said to be a similar triangles. The symbol ‘~’ is used to denote the similarity between two triangles.
If two triangles ΔABC and ΔXYZ are two similar triangles then the condition between corresponding sides is given by
AB: XY = BC: YZ = AC: XZHere we have
John's height is 6 feet
He standing 4 feet from a tree
Johns's shadow is 12 feet long
We can represent the whole scenario as two similar triangles
[ Picture is given below ]
As we know in Similar triangles the ratio of corresponding sides is equal
Let 'x' be the height of the tree
From given figure
=> AC: DE = BC: EB
=> x : 6 = 16 : 12
=> x/6 = 16/12
=> 12x = 16 × 6
Divided by 6
=> 2x = 16
Divided by 2
=> x = 8
Therefore,
The height of the tree is 8 feet.
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